MECHANICAL PROPERTIES OF DYNAMIC ENERGY RETURN PROSTHETIC FEET

by

Andrea Haberman

A thesis submitted to the Department of Mechanical and Materials Engineering

in conformity with the requirements for

the degree of Master of Science (Engineering)

Queen’s University

Kingston, Ontario, Canada

April, 2008

Copyright ©Andrea Haberman, 2008

ii

Abstract

The long-term goal of this study is to improve the ability of designers and prosthetists to match

the mechanical characteristics of prosthetic feet to patient specific parameters, including, needs,

abilities and biomechanical characteristics. While patient measures of performance are well

developed, there is a need to develop a practical method by which non-linear and time-dependent

mechanical properties of the prosthetic component can be measured. In this study, testing

methodologies were developed that separately evaluated the elastic and time-dependent

properties. Three styles of feet were tested to span the range of designs of interest: a standard

solid ankle cushioned heel (SACH) foot, two energy return feet for active users and a new

prosthetic foot designed to provide partial energy return.

The first testing regime involved mechanically characterizing prostheses under conditions similar

to gait. The heels and toes of four sample feet were loaded to peak forces based on their design

mass at a series of angles and forces that the prosthetic system would go through during the gait

cycle, based on the waveform in ISO 22675. Tangential stiffnesses of the samples were

determined using numerical differentiation. The force-displacement responses of prosthetic feet

reflect increasing stiffnesses with increasing loads and a decreasing pylon angle. Key features

reflecting foot design are: the relative stiffness of the heel and toe and the displacement gap at

midstance. Stable feet tend to exhibit lower heel stiffnesses and higher toe stiffnesses, whereas

dynamics energy return (DER) feet tend to exhibit higher heel stiffnesses and lower toe

stiffnesses. The differences in heel and toe loading at midstance suggest that DER feet can aid in

the transition from heel to toe, providing a smooth rollover whereas SACH feet provide greater

stability.

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A second testing regime examined the time-dependent properties of the heel and toe. A three-

parameter reduced relaxation response of the form BttAAtL −−−+= )exp()1()( τ was able to

capture the force-relaxation characteristics with RMS differences ranging from 0.0006 to 0.0119.

In this model, A is the initial decay, B is the decay coefficient, a linear decay term, and τ is a time

constant. While the model is practical for comparing various prostheses at a single load level, a

fully non-linear model is required to model the time-dependent response at all loading levels.

iv

Co-Authorship

This thesis is written in manuscript format. Two manuscripts are included that were written as a

collaborative effort. The first manuscript entitled “Mechanical Characterization of Dynamic

Energy Return Prosthetic Feet,” was co-authored with Tim Bryant, PEng., PhD., Mary Beshai,

PEng., MSc. and Robert Gabourie C.P.O. The second manuscript entiled “Force-Relaxation

Properties of Dynamic Energy Return Feet,” was co-authored with Tim Bryant, PEng., PhD.

v

Acknowledgements

Otto Bock®, Dupont™ and Niagara Prosthetics and Orthotics International Ltd. donated samples

used in this study, for which I am grateful.

Rob Gabourie: your vision, passion and desire to change the world resulted in the development of

the Niagara Foot™. Thank you for providing me with the opportunity to work on this project,

taking me under your wing and sharing your expertise in all things foot related.

Tim: your quest for knowledge is surpassed only by your passion for sharing it. I feel privileged

to have had the opportunity to study with you. Thank you for your guidance, encouragement,

patience and for the opportunity to work on this project. This was an experience I will never

forget.

Mary: thank you for teaching me the meaning of insanity rather than allowing me to discover it on

my own. I can not express how much I appreciate your help and support throughout my studies.

Leone: thank you for answering my endless string of technical questions and helping to fix all of

my equipment-related blunders.

To all of my friends and family, who now know more about prosthetic feet than they ever thought

they would: your support, encouragement and patience were invaluable, especially Amanda, Iris,

Carol and my parents.

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Table of Contents Abstract ............................................................................................................................................ ii Co-Authorship................................................................................................................................. iv Acknowledgements.......................................................................................................................... v Table of Contents ............................................................................................................................ vi List of Figures ............................................................................................................................... viii List of Tables .................................................................................................................................. xi Chapter 1 Introduction ..................................................................................................................... 1

1.1 Causes of Amputation............................................................................................................ 1 1.2 Anatomical Planes, Directions and Movement ...................................................................... 3 1.3 Transtibial Prosthetic System Design Principles ................................................................... 5 1.4 Objective ................................................................................................................................ 8 1.5 Thesis Format......................................................................................................................... 8

Chapter 2 Review of the Literature.................................................................................................. 9 2.1 Normal Gait ........................................................................................................................... 9 2.2 Gait in Transtibial Amputee Patients ................................................................................... 12 2.3 Prosthetic Systems ............................................................................................................... 14

2.3.1 Sockets .......................................................................................................................... 15 2.3.2 Suspension .................................................................................................................... 16 2.3.3 Prosthetic Feet............................................................................................................... 18 2.3.4 Prosthetic Feet: Principles of Design ............................................................................ 20

2.4 Alignment ............................................................................................................................ 24 2.5 Assessing Patient Performance ............................................................................................ 26

2.5.1 Physical Measurements................................................................................................. 27 2.5.2 Self-reported Measures ................................................................................................. 28

2.6 Relationship of Mechanical Characteristics to Performance ............................................... 28 2.7 Summary .............................................................................................................................. 30

Chapter 3 Mechanical Characterization of Dynamic Energy Return Prosthetic Feet .................... 31 3.1 Introduction.......................................................................................................................... 31 3.2 Critical Points....................................................................................................................... 36 3.3 Methods................................................................................................................................ 38 3.4 Data Analysis ....................................................................................................................... 42 3.5 Results and Discussion......................................................................................................... 46

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3.6 Conclusions.......................................................................................................................... 57 Chapter 4 Force Relaxation Properties of Dynamic Energy Return Feet ...................................... 58

4.1 Introduction.......................................................................................................................... 58 4.2 Theory .................................................................................................................................. 60 4.3 Methods................................................................................................................................ 64 4.4 Results and Discussion......................................................................................................... 67 4.5 Conclusions.......................................................................................................................... 73

Chapter 5 General Discussion........................................................................................................ 74 5.1 Patient-related Variables ...................................................................................................... 78 5.2 Prosthetist-related Variables ................................................................................................ 80 5.3 Component Design Variables .............................................................................................. 80

Chapter 6 Conclusions and Future Work....................................................................................... 82 6.1 Conclusions.......................................................................................................................... 82 6.2 Future Work ......................................................................................................................... 84

Appendix A Determination of Displacement Rate ....................................................................... 89 Appendix B Linear Extrapolation and Interpolation..................................................................... 94 Appendix C Mechanical Characterization of Dynamic Energy Return Prosthetic Feet: Complete

Data Set .......................................................................................................................................... 97 Appendix D Force-Relaxation Properties of Dynamic Energy Return Feet: Complete

Data Set ........................................................................................................................................ 110

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List of Figures Figure 1: Common amputation levels. ............................................................................................. 2 Figure 2: Planes used to describe the human body. ......................................................................... 3 Figure 3: Terms used to describe joint motion................................................................................. 4 Figure 4: Right lower limb progressing through the stance phase of gait...................................... 10 Figure 5: Typical ground reaction forces occurring during normal gait ........................................ 12 Figure 6: Endoskeletal and exoskeletal transtibial prosthetic systems .......................................... 15 Figure 7: Suspension systems ........................................................................................................ 17 Figure 8: Cross section schematic of a SACH foot, a single-axis foot, a Greissinger multi-axis

foot, a Multiflex multi-axis foot, and a Flex Foot™...................................................................... 19 Figure 9: Feet having features from more than one class of foot................................................... 20 Figure 10: The Ohio Willow Wood Impulse® ............................................................................. 24 Figure 11: Loading the residual limb............................................................................................. 25 Figure 12: Testing waveforms from ISO 22675 ............................................................................ 35 Figure 13: Fifteen critical points extracted from ISO 22675 ......................................................... 37 Figure 14: Photographs of the SACH foot, Axtion™ keel and the Niagara Foot™...................... 40 Figure 15: Test configuration......................................................................................................... 41 Figure 16: Typical force displacement curve................................................................................. 43 Figure 17: Overview of the data analysis process.......................................................................... 44 Figure 18: Peak displacements that occurred as a function of time. .............................................. 45 Figure 19: First difference between peak displacements as a function of time. ............................ 45 Figure 20: The contact point between the heel and the platen at displacements of 0mm, 4mm and

8mm ............................................................................................................................................... 47 Figure 21: Force-displacement curves for the heel and the toe of the Niagara Foot™.................. 48 Figure 22: Stiffness-displacement curves for the heel and toe of the Niagara Foot™................... 49 Figure 23: Predicting displacement and stiffness profiles of prostheses during gait ..................... 51 Figure 24: Predicted displacements of the Niagara Foot ™ during gait ........................................ 52 Figure 25: Predicted tangential stiffness values of the Niagara Foot™......................................... 53 Figure 26: Normalized displacements occurring at the critical forces identified........................... 55 Figure 27: Normalized tangential stiffness values occurring at the critical forces ........................ 56 Figure 28: Typical force response of the toe of a prosthetic foot .................................................. 61 Figure 29: The reduced relaxation response, L(t) .......................................................................... 62 Figure 30: Photographs of the SACH foot, Axtion™ keel and the Niagara Foot™...................... 65

ix

Figure 31: Test configuration......................................................................................................... 66 Figure 32: Force-relaxation response for the toe of the Model 2 Version 18 Niagara Foot™. ..... 69 Figure 33: Description of a typical force deflection curve of a heel using three

parametersarameters ...................................................................................................................... 90 Figure 34: Determination of the x-intercept using linear extrapolation......................................... 94 Figure 35: Adjustment of the force-displacement data to compensate for the offset origin .......... 95 Figure 36: Determination of displacement at the design load using linear interpolation............... 96 Figure 37: Force-displacement curves for the heel and toe of the Niagara Foot™. ...................... 98 Figure 38: Stiffness-displacement curves for the heel and toe of the Niagara Foot™................... 99 Figure 39: Displacements and tangential stiffness values of the Niagara Foot ™ occurring at the

critical forces identified. .............................................................................................................. 100 Figure 40: Force-displacement curves for the heel and toe of the Axtion™ foot with a maximum

recommended user weight of 106kg ............................................................................................ 101 Figure 41: Stiffness-displacement curves for the heel and toe of the Axtion™ foot with a

maximum recommended user weight of 106kg ........................................................................... 102 Figure 42: Displacements and tangential stiffness values of the Axtion™ foot with a maximum

recommended user weight of 106kg occurring at the critical forces identified. .......................... 103 Figure 43: Force-displacement curves for the heel and toe of the Axtion™ foot with a maximum

recommended user weight of 124kg ............................................................................................ 104 Figure 44: Stiffness-displacement curves for the heel and toe of the Axtion™ foot with a

maximum recommended user weight of 124kg ........................................................................... 105 Figure 45: Displacements and tangential stiffness values of the Axtion™ foot with a maximum

recommended user weight of 124kg occurring at the critical forces identified. .......................... 106 Figure 46: Force-displacement curves for the heel and toe of the SACH foot. ........................... 107 Figure 47: Stiffness-displacement curves for the heel and toe of the SACH foot ....................... 108 Figure 48: Displacements and tangential stiffness values of the SACH foot occurring at the

critical forces identified ............................................................................................................... 109 Figure 49: Reduced relaxation data for the heel of the sample feet. ............................................ 110 Figure 50: Reduced relaxation data for the toe of the sample feet............................................... 111 Figure 51: Reduced relaxation response for the heel of the Model 2 Version 18

Niagara Foot™............................................................................................................................. 112 Figure 52: Reduced relaxation response for the toe of the Model 2 Version 18

Niagara Foot™............................................................................................................................. 113

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Figure 53: Reduced relaxation response for the heel of the Axtion® foot with a maximum

recommended user weight of 106kg. ........................................................................................... 114 Figure 54: Reduced relaxation response for the toe region of the Axtion® foot with a maximum

recommended user weight of 106kg. ........................................................................................... 115 Figure 55: Reduced relaxation response for the heel region of the Axtion™ foot with a maximum

recommended user weight of 124kg. ........................................................................................... 116 Figure 56: Reduced relaxation response for the toe region of the Axtion® foot with a maximum

recommended user weight of 124kg. ........................................................................................... 117 Figure 57: Reduced relaxation response for the heel region of the SACH foot........................... 118 Figure 58: Reduced relaxation response for the toe region of the SACH foot. ........................... 119

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List of Tables Table 1: The effect of patient-, prosthetist- and device-controlled factors on the needs of an

amputee during gait.......................................................................................................................... 6 Table 2: Data extracted from the P4 test loading level curve ........................................................ 38 Table 3: Specifications of the sample feet tested in the mechanical characterization study.......... 39 Table 4. Specifications of the sample feet tested in the force-relaxation study. ............................ 64 Table 5: Parameters and degree of fit of a two-parameter model. ................................................. 69 Table 6: Parameters and degree of fit of a three-parameter model. ............................................... 70 Table 7: Results study examining linearity using a three-parameter model. ................................. 72 Table 8: Three stiffness values from mechanical testing of a Model 2 Version 18 Niagara Foot™

conducted at varying time intervals. .............................................................................................. 91 Table 9: Stiffness values for the heel and toe regions of a Model 2 Version 18 Niagara Foot™

tested at various displacement rates. .............................................................................................. 92 Table 10: Relaxation parameters of the four sample feet. ............................................................. 93

1

Chapter 1

Introduction

1.1 Causes of Amputation

Every year, hundreds of thousands of people lose a limb due to diseases such as diabetes and

cancer, as well as to the trauma associated with automobile collisions and violence. In the United

States over 130,000 people had a lower limb amputated in 1997 [1]. Of those amputations, 67%

were as a result of complications due to diabetes. In 2001, the International Committee of the Red

Cross (ICRC) fitted a total 7,418 people with their first prostheses and distributed 9,779

prostheses to land mine survivors in fourteen post-conflict countries [2].

The level of amputation is determined by which tissues need to be removed, how well the incision

will heal and the ability to create a functional residual limb [3]. Common lower limb amputation

levels are shown in Figure 1. Lower limb amputations above the knee are referred to as

transfemoral; the most common occur at the mid thigh. Lower limb amputations that leave the

knee intact are referred to as transtibial; they can occur anywhere below the knee including the

ankle and foot. [4]. For the patient, amputation requires a period of rehabilitation to address issues

associated with pain and loss of function and may involve a number of professionals, including

psychologists, physiatrists, physiotherapists and prosthetists. The provision of mobility is a

particular focus of medical treatment.

2

Figure 1: Common (a) above knee or transfemoral and (b) below knee or transtibial amputation levels [5].

(a) (b)

3

1.2 Anatomical Planes, Directions and Movement

Anatomical Planes and Directions. The body, like any other three-dimensional object, can be

described in terms of three planes: the sagittal, transverse and frontal planes, as shown in Figure

2. The sagittal plane divides the body into left and right sections, the transverse plane divides it

into upper and lower sections and the frontal plane divides it into anterior (front) and posterior

(back) sections. Motion forward in the sagittal plane is referred to as anterior, while motion

backward is posterior. Motion toward the mid-line of the body in the frontal plane is termed

medial, while motion away from the mid-line is lateral [6].

Figure 2: Planes used to describe the human body [6].

4

Anatomical Movement. When describing joint motion, commonly used terms are: flexion,

extension, plantar flexion, dorsiflexion, inversion and eversion, as shown in Figure 3. Generally,

flexion is a movement that decreases a joint angle while extension increases it. There are specific

terms used to describe motion of the toes and ankle. Dorsiflexion and plantar flexion refer to

decreasing and increasing these joint angles and take place in the sagittal plane. When the sole of

the foot is turned inward it is referred to as inversion, turned outward is eversion [6].

(a) (b)

(c)

Figure 3: Terms used to describe joint motion: (a) flexion and extension, (b) dorsiflexion and plantar flexion, (c) inversion and eversion [6].

5

1.3 Transtibial Prosthetic System Design Principles

Transfemoral prosthetic systems are more complex than transtibial ones, as they require a

mechanism to function in place of a knee joint. These range from single hinges to computerized

active controls. Other prosthetic components are common to both transfemoral and transtibial

prosthetic systems, including feet. However, typically 80% of lower limb amputations are

transtibial [4]. As such, there is a great deal more effort in the design of components used by

transtibial amputees, and these systems are the focus of the current study.

As with other products, prosthetic components must meet the general design goals of user

acceptance, ease of use, reliability and durability [7, 8]. Additional, specific, user-based

requirements include the provision of comfort and efficient locomotion. For comfort to be

achieved, the socket must fit the residual limb well; pistoning between the residual limb and the

socket or excessive loading of tissues can lead to discomfort. To achieve efficient locomotion

three criteria must be met: (1) the foot should be stable while in contact with the ground1; (2)

rollover from when the heel strikes the ground until the toe leaves it should be smooth; and (3)

when the toe leaves the ground it should be able to efficiently propel the limb forward. These user

requirements are outlined in Table 1.

A number of complex interactions take place during gait, all of which can affect comfort and

locomotion. Each of these is influenced by one of three factors: the patient, the prosthetist and the

1 This contact is referred to as stance.

6

prosthetic components. The influence of these factors on the user requirements is shown in Table

1, in which symbols are used to indicate the relative strengths of the relationships.

Influencing Factors

Patient- controlled

Prosthetist -controlled Device-controlled

User Needs Gait Adaptations

Socket Fit Alignment Socket

Interface Foot

Design Comfort ○ ● ○ ● ○

Smooth action during stance

● ○ ● ○ ●

Stability while in stance

○ ○ ○ ● Locomotion

Efficient propulsion ● ○ ● ●

Table 1: The effect of patient-, prosthetist- and device-controlled factors on the needs of an amputee during gait; ○ indicates a relationship and ● indicates a strong influence.

Patient-controlled Factors. Patients can influence the adaptations they make during gait to a

certain degree, for instance in knee flexion and loading of the prosthetic limb [3]. The manner in

which amputees walk impacts all of the user needs, but it has the greatest influence over their

ability to have a smooth rollover in stance and efficiently propel themselves.

7

Prosthetist-controlled Factors. In North America, the socket is custom made for each patient by

a prosthetist. The socket is the part that contacts the residual limb; as such, it impacts all of the

user needs. It is the most important factor associated with comfort of the user: a poor fit can result

in blistering, skin breakdown and inappropriate pressures being applied to sensitive tissues [3].

The prosthetist also aligns or sets the position of the prosthetic foot relative to the socket.

Ensuring that the alignment of the system meets the abilities of the users also affects all of their

needs. Alignment controls the location of the contact point between the foot and the floor.

Changes in alignment can change the length of the lever arms of the heel and toe thus changing

the effective stiffness of the foot [9]. The moments experienced by the limb and joints are also

influenced by the alignment [3]. Prosthetists face an added challenge when fitting their patients

with a prosthetic system, since different sockets, socket interfaces and foot designs can result in

different gait adaptations.

Device-controlled Factors. Device-controlled factors refer to the interface between the socket

and the residual limb and the prosthetic foot. The interface usually comprises a liner and

suspension system. The devices used in a prosthetic system influence all of the user needs. A

correct interface between the socket and the limb is integral: if it restricts movement it can affect a

patient’s comfort and impede their ability to have a smooth rollover during gait [3].

The design of the foot affects all of the user needs, having the strongest influence on efficient

locomotion. The design must meet the needs and abilities of the users; otherwise it can affect the

ability to have a smooth rollover, stability and efficient propulsion [3].

8

1.4 Objective

Recently there has been an increase in the number of foot designs on the market. Scientific

understanding of these components continues to develop; however, the relationship between the

mechanical characteristics of prosthetic feet and their performance is not well defined. The long-

term goal of this study is to improve the ability of designers and prosthetists to match the

mechanical characteristics of prosthetic feet to the patient-specific locomotion needs, including

stability, smooth rollover and efficient propulsion. The specific objective of this study is to

develop a practical method by which non-linear and time-dependent mechanical properties of the

prosthetic components can be measured.

1.5 Thesis Format

This document is presented in the form of two manuscripts isolating the elastic and time-

dependent properties of prosthetic feet. The first manuscript, “Mechanical Characterization of

Dynamic Energy Return Prosthetic Feet,” examines the elastic properties of prostheses,

specifically stiffness and displacement as they relate to the performance and function of these

devices. The second manuscript, “Force Relaxation Properties of Dynamic Energy Return

Prosthetic Feet,” examines the time-dependent properties of prostheses.

Although there are some redundancies in the Introduction and Discussion of the two manuscripts,

the Literature Review (Chapter 2) is intended to be comprehensive. A General Discussion

(Chapter 5) is included to address issues common to both manuscripts. Literature Citations and

Appendices are common for all sections of the document.

9

Chapter 2

Review of the Literature

2.1 Normal Gait

Gait refers to how people propel themselves using their lower limbs. One gait cycle occurs over

the time it takes for two successive events to occur involving the same limb, usually when the foot

first impacts the ground or supporting surface [10]. This process can be broken down into two

phases, stance and swing, as shown in Figure 4.2

During the stance phase, the foot is in contact with the supporting surface. This typically makes

up 60% of the cycle. Swing makes up the remaining 40% of gait; it occurs when the foot is not in

contact with the supporting surface [11]. Twice during each gait cycle, both feet are in contact

with the ground; this is referred to as double support. At a normal walking speed, each period of

double support takes up about 10% of the gait cycle; thus 80% of the time a person’s body weight

is supported by one limb [12]. Stance can be further broken down into three parts: heel strike,

midstance and push off.

At heel strike, the heel first makes contact with the ground. In a typical subject, the horizontal

velocity reduces to 0.4 m/sec and the vertical velocity reduces to 0.05 m/sec [13]. In abnormal

gait, the heel may not be the first part of the foot that contacts the ground; it could be the toes or

the whole foot [10].

2 Different sets of terminology exist to describe the various aspects of gait, the two most common being the

traditional and the Rancho Los Amigos terminologies. The traditional terminology is used here.

10

Both the midstance and push off phases can be further broken down into subsections. During the

midstance phase, foot flat and the midstance point occur. Foot flat refers to the first time that the

foot is flat on the supporting surface. It occurs after heel strike at approximately 7% of the gait

cycle. The midstance point when a person’s body weight is directly over the supporting limb,

about 30% of the way through the gait cycle.

The push off phase consists of heel off and toe off. During heel off, the heel leaves the supporting

surface, at about 40% of the gait cycle. Next, the toe leaves the supporting surface (toe off) at

about 60% of the cycle.

Figure 4: Right lower limb progressing through the stance phase of gait [10].

11

Swing can also be broken down into three phases: acceleration, midswing and deceleration. Once

the toe leaves the ground, the leg begins to increase its angular speed; this acceleration continues

until midswing. Midswing begins when the leg is directly beneath the body and continues until

deceleration. During deceleration at late swing, the leg beings to reduce its angular speed in

preparation for heel strike [10].

During stance, there are three forces acting on the foot, the vertical ground reaction force and the

anterior-posterior and medial-lateral forces, as shown in Figure 5 as functions of time [14]. In the

vertical ground reaction force curve, there is an initial spike and two peaks that are greater than

body weight. The spike is due to the impact of the foot with the supporting surface during heel

strike. The first peak occurs during weight acceptance and the second at push off [15].

12

Figure 5: Typical ground reaction forces occurring during normal gait: V vertical ground reaction force, A anterior-posterior force, M medial-lateral force. Adapted from Trew et al. [14].

2.2 Gait in Transtibial Amputee Patients

During amputee gait, compensations for the loss of bone, joints and musculature are required on

both the affected (prosthetic) and unaffected (intact) limbs. Amputees typically unload their

affected limb faster during the latter half of midstance and the push off phase compared to the

unaffected limb. In turn, less time is spent loading their affected limb and more time loading the

unaffected one. This results in stride asymmetry with a shortened stance phase and a longer swing

phase on the affected side [16]. This asymmetry results in a discrepancy between the loading of

the two limbs. Amputees experience a greater weight acceptance peak on their unaffected limb

relative to their affected limb depending on the walking velocity. Furthermore, the peak forces are

V

A

M

13

greater than in normal gait. As walking speed increases, so does the peak force due to the increase

in acceleration; however, the increase on the unaffected side is greater than on the affected side

[15]. Amputees often have a slower than average walking speed, and knee flexion during the

stance phase on the affected side is often lower [17].

The assessment of gait characteristics is used by prosthetists and therapists in order to provide

good long-term function in patients. Treatment goals include specific features at each phase of the

gait cycle. They are:

Heel Strike

− Stride lengths on the affected and unaffected sides should be equal

− Knee on the affected side should be flexed from 5° to 10°

− The prosthetic foot should contact the ground in a linear forward progression

Foot Flat

− Flexion of the knee on the affected side should have increased to between 15° to 20°

− Heel region of the prosthesis should have compressed so plantar flexion can occur

− Position of the residual limb in the prosthetic socket should remain constant

Midstance

− Should have a smooth progression forward while maintaining knee stability

− Top of the prosthesis should be level

− Upright trunk position should occur with minimal lateral bending

Push Off

− Heel off should occur smoothly

− Knee should begin to flex as soon as the heel rises to prepare for toe off

Swing Phase

− There must be enough toe clearance to allow for swing phase

− Limb should swing forward in the line of progression

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Failure to achieve these actions can lead to pain or discomfort and increased energy exertion [3].

This is particularly challenging because prosthetic systems must do more than replace lost

musculature and bone structure; they must be customized to the individual needs and abilities of

each patient [18].

2.3 Prosthetic Systems

Prosthetic systems require integration of a number of components. Many parts are available off

the shelf, while others need to be custom made for each individual. There are two general

classifications of transtibial prosthetic systems, endoskeletal and exoskeletal, as shown in Figure

6. Both systems have three main components: a socket, suspension and foot. In addition to fitting

the patient, the components must be aligned to ensure optimal performance of the overall system

[3].

In an endoskeletal system a hollow cylindrical shaft, called a pylon, connects the socket to the

foot. This configuration, shown in Figure 6a, is lightweight, adjustable and modular in design

(meaning it is possible to replace individual components). The system can be covered with a

cosmetic skin if desired [5]. Exoskeletal designs, such as the one shown in Figure 6b, have a rigid

laminate cover that connects the socket to the foot. One advantage of this system is its durability;

however, it is the heavier of the two. The socket is fixed into position making it difficult to adjust

it or the alignment of the prosthesis [3].

15

(a) (b)

Figure 6: (a) Endoskeletal and (b) Exoskeletal transtibial prosthetic systems. Three of the four components are shown: a socket, pylon and prosthetic foot. A suspension system is not depicted here [5].

2.3.1 Sockets

The socket is the component that contacts the residual limb. A sock is often worn over the

residual limb to provide some cushioning and accommodation for fluctuation in its volume [3].

There are two types of sockets, the patellar tendon bearing (PTB) and the total surface bearing

(TSB). The principle of the PTB socket is to control pressure distribution between the socket and

underlying anatomy. It is designed to load areas such as the patellar tendon, the medial flare, and

the anterior side of the tibia, which can tolerate the pressure. Other parts of the limb remain

unloaded or minimally loaded [4]. A TSB socket loads the entire surface of the residual limb

varying the force distribution according to the different types of tissue rather than the underlying

16

anatomy. In addition, a liner is usually worn over the residual limb. Liners provide an

intermediate layer between the limb and socket to improve the pressure distribution and to reduce

the tendency of the socket to move with respect to the underlying tissue [3].

2.3.2 Suspension

Suspension systems are designed to keep the socket and, in turn, the system securely attached to

the residual limb. They are one aspect of the socket-limb interface that can affect an amputee’s

ability to have a smooth rollover during stance. There is also a strong correlation between the

suspension and the overall comfort of the system. If the suspension system is not fitted correctly,

it can place the knee in a position of too much flexion or it can lead to the knee being fully

extended during heel strike. The latter can lead to skin break down [3]. A number of suspension

systems are available, as shown in Figure 7.

17

(a) (b) (c)

(d) (e) (f)

Figure 7: Suspension systems: (a) thigh corset with knee joints [4], (b) sleeve suspension [3], (c) supracondylar suspension [5] , (d) supracondylar cuff [4], (e) waist belt and anterior strap [3], (f) shuttle lock mechanism [5].

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2.3.3 Prosthetic Feet

The stiff, structural part of a prosthetic foot is termed the keel. In single unit designs, the keel is

incorporated into the rest of the foot. In other designs, the cover is a separate component into

which the keel is inserted; this allows for the cover to be replaced when needed, while continuing

to use the same keel [5]. Prosthetic feet can generally be placed into one of four categories:

conventional, single-axis, multi-axis and dynamic energy return [19].

Conventional. Conventional feet are basic designs that have no moving components. The widely

used solid ankle cushioned heel (SACH) foot, shown in Figure 8a, is one example. SACH feet

have a wooden or rigid plastic keel that extends until the toe section. Dense foam makes up the

heel and the remainder of the foot is rubberized foam. Belting is attached to the end of the keel

and extends into the toe region.

Single-Axis. As the name suggests, a single-axis foot has a hinge or other mechanism that allows

the foot to plantar flex and dorsiflex, as shown in Figure 8b. Single-axis feet were the first

prostheses to provide ankle articulations. They typically consist of a keel, with an ankle joint and

a molded foot shell. The keel has a plantar flexion bumper located in the heel behind the ankle

joint. Some feet have a second dorsiflexion bumper anterior to the ankle. Feet that do not have

this second bumper have a dorsiflexion stop. Similar to the SACH foot, belting is attached to the

end of the keel and extends into the toes.

Multi-Axis. A typical multi-axis design, the Otto Bock® Greissinger, shown in Figure 8c, has a

multi-directional hinge that allows for eversion and inversion as well as plantar and dorsiflexion.

The Endolite Multiflex, a newer style of multi-axis foot shown in Figure 8d, has a rubber ball

19

inside the stem of the ankle assembly with an O-ring sitting just below it. This system allows for

some rotation of the foot, in addition to eversion, inversion, plantar flexion and dorsiflexion.

Dynamic Energy Return. Dynamic energy return (DER) feet are able to store and return energy

during the gait cycle [19]. As such, these are not classified in terms of the structure, but rather by

their performance characteristics. One example of a DER foot is a Flex Foot™, shown in Figure

8e. It is a leaf spring design made of a carbon fibre composite that deflects extensively to provide

motion.

(a) (b) (c)

(d) (e)

Figure 8: Cross section schematic of (a) a SACH foot [4], (b) a single-axis foot [4], (c) a Greissinger multi-axis foot [3], (d) a Multiflex multi-axis foot [3], and a photograph of (e) a Flex Foot™, one type of dynamic energy return foot [4].

belting

20

The use of elastic properties in this way is also evident in prostheses with features from more than

one class of foot, including the Niagara Foot™, a single-axis DER foot, shown in Figure 9a, and

the College Park Industries TruStep™, a multi-axis DER foot, shown in Figure 9b.

(a) (b)

Figure 9: Feet having features from more than one class of foot, (a) The Niagara Foot™ is a single-axis DER foot and (b) The College Park Industries TruStep™, is a multi-axis DER foot [20].

2.3.4 Prosthetic Feet: Principles of Design

A prosthetic foot is designed to compensate for the musculature and bone structure lost due to

amputation and to facilitate the various actions that would occur during normal gait [3]. During

gait, the human foot and ankle are able to adapt to uneven terrain and to adjust the length of the

lower limb while providing shock absorption and stabilization of the knee. Ideally, a prosthetic

foot should be able to mimic these functions; however, this remains a challenge [4].

horns

top plate

C-section

21

During heel strike, a prosthetic foot is designed to absorb the impact of the heel hitting the ground

to reduce the forces transferred to the residual limb. The point of contact of the foot with the

ground is posterior to the ankle during heel strike, causing the foot to plantar flex. Prosthetic feet

control the rate of plantar flexion, which in turn controls the time it takes to reach foot flat, a

stable position. In transtibial amputees, this helps to control the rate at which the tibia advances.

The tibia next progresses from posterior to anterior of the ankle during midstance, causing the

foot to dorsiflex. In an unaffected limb, musculature controls the speed at which this occurs,

helping to maintain stability. The keel of a prosthetic foot provides this stability.

The tibia continues to advance during the heel off phase of push off. In normal gait, the point of

contact transfers to the forefoot as the foot rolls over the metatarsophalangeal joints. In a

prosthetic foot, this joint is sometimes replaced with a mechanical element, a toe break that

simulates dorsiflexion of the toes. At this point, toe off begins and the body weight is transferred

to the other leg. Ideally, a prosthesis should provide support to aid in balance, allowing for a

smooth transition. At the end of push off, rapid knee flexion occurs, allowing the foot to clear the

ground and the swing phase to begin. A spring action in the toes of a prosthesis can facilitate this

rapid knee flexion [3].

SACH Foot Design. During heel strike, the cushioned heel of a SACH foot, shown in Figure 8a,

helps to absorb the impact of the heel hitting the ground and controls the rate of plantar flexion.

SACH feet are available in a variety of heel stiffnesses that depend on the weight of the user and

the need for stability. The softer the heel, the faster the user is able to reach the stable foot flat

position. The rigid keel of the foot controls the transition of the tibia (the pylon) from posterior to

22

anterior of the ankle. The keel continues to offer resistance until the toe break is reached. In a

SACH foot, the toe break is located at the end of the keel. Belting helps to control the dorsiflexion

of the toes, allowing the tibia to progress smoothly. At this phase of loading, the toes offer very

little support. At the end of toe off, the belting provides a small spring action of the toes to aid in

knee flexion.

Single-Axis Foot Design. The rubber heel of the foot shell and the plantar flexion bumper of a

typical single-axis foot, shown in Figure 8b, absorb the initial impact occurring at heel strike and

control the rate of plantar flexion. Similar to the heel of the SACH foot, the bumper(s) are

available in a variety of stiffnesses. The stiffness of the bumper(s) depends on the user’s weight

and the need for stability. The softer the bumper, the faster foot flat is reached. If present, the

dorsiflexion bumper controls tibia advancement. Once the dorsiflexion bumper is fully

compressed, heel off begins. For feet without a second bumper, the dorsiflexion stop transfers the

forces to the foot. Once the stop is engaged, heel rise begins. At this point, the front of the keel

acts as a rocker, and toe dorsiflexion begins. The toe break is located at the end of the keel and

behaves in a manner similar to the SACH foot. Dorsiflexion of the toes is controlled by belting.

At the end of toe off this provides a small spring action of the toes to aid in knee flexion.

Multi-Axis Foot Design. Multi-axis feet, with multi-directional hinges, shown in Figure 8c,

function in a manner similar to single-axis feet. The ball and stem style of multi-axis feet, such as

the Multiflex, shown in Figure 8d are more complex. Shock absorption is provided by the

compression of the rubber ball against the walls of the ankle stem and the O-ring compressed by

the ankle stem and the foot. These components continue to compress, controlling the rate of

plantar flexion. The O-ring is available in a variety of stiffnesses so this rate of plantar flexion can

23

be customized to the needs of the patient. During midstance, the ball and O-ring compress either

medially or laterally in addition to anteriorly to allow for eversion or inversion. The foot is

capable of limited rotation; thus reducing the rotational torque transmitted to the residual limb.

The advancement of the tibia continues until the ball is fully compressed. At this point, heel off

begins. The toe break is located at the end of the keel. As the heel rises, the edge of the keel acts

as a pivot and the toes begin to dorsiflex. The toes provide a small spring action that encourages

the knee to flex as the limb enters swing phase.

Dynamic Energy Return Foot Design. There are dozens of different designs of DER feet. Some,

like the Impulse®, shown in Figure 10, are composed of one unit. In the Impulse® design the keel

is incorporated in the rest of the foot, and it has a cushioned heel that behaves very similarly to a

SACH foot on heel strike. Other feet like the Flex Foot™, shown in Figure 8e, have a keel and a

separate cover. The keel has a distinct heel region that deflects under the weight of the user,

absorbing the impact of the heel striking the ground [3, 21]. Both plantar flexion and the

progression of the tibia are controlled by the keel; as the tibia progresses the keel deflects. The toe

section of the foot begins to dorsiflex as the point of contact moves to the forefoot. Unlike a

SACH foot, the keel extends into the toes; this longer keel provides greater stability. As the body

weight is transferred to the other limb, the keel begins to unload and return to its original shape.

Note that this action is controlled by the elasticity of the elements.

The Niagara Foot™, shown in Figure 9a, is a single-axis DER foot. It does not have a hinge or the

bumpers normally associated with single-axis feet. Instead, movement of the C-section allows for

ankle articulation and aids in propulsion of the limb. During heel loading, the gap between the

horns and the top plate increases. Upon toe loading, the horns slide across the underside of the

24

plate, causing the C-section to wind. The College Park Industries TruStep™, shown in Figure

9b, is a multi-axis DER foot. The split toe allows for eversion and inversion. Bumpers on the heel

and midsection of the foot help to control dorsiflexion and plantar flexion [20]. As the keel of a

DER foot unloads, it provides a push off and helps to start the swing phase.

Figure 10: The Ohio Willow Wood Impulse® has a composite heel plate attached to a Kevlar® and nylon keel [22].

2.4 Alignment

Alignment refers to the position of the socket relative to the foot and is set by the prosthetist. It

has a strong influence on a patients’ comfort and their ability to have a smooth rollover during

stance. Patients’ natural gait, the characteristics of their prosthetic foot and the ability of the

residual limb to tolerate pressure all influence the prosthetist’s choice in three steps: bench

alignment, static alignment and dynamic alignment.

25

Bench alignment is undertaken in the prosthetist’s lab, before the patient has worn the prosthesis.

This alignment is based on the patient’s range of motion, strength, stability, and established

practice guidelines. The socket is flexed by 3°-5°, as shown in Figure 11. This helps to distribute

the load across the length of the tibia instead of the end of the limb, which is one of the more

pressure-sensitive areas.

Figure 11: Placing the socket in a vertical position, as shown on the left, loads the distal end of the residual limb. Flexing the socket slightly, as shown on the right, spreads the load over the length of the tibia [3].

26

During static alignment, the patient stands wearing the prosthesis for the first time. Fit of the

prosthesis and the patient’s ability to evenly distribute his/her weight across both limbs is

assessed. Limb length is evaluated to ensure that both limbs are equal length. A slight variation

can lead to lower back pain over time. The forces being applied to the knee are evaluated because

incorrect socket alignment can result in the patient feeling as if his/her knee is being forced into

flexion or extension. Any problems are addressed before the patient is allowed to walk for the

next phase of alignment.

The final step is dynamic alignment. The alignment of the foot relative to the socket has a

noticeable impact on the biomechanics of amputee gait. Shifting the foot in the sagittal plane

alters the point of contact of the foot with the floor. This changes the effective lever arm of the

heel and toe, altering both of their stiffnesses. The stability of the knee is also affected. Shifting

the foot anteriorly increases the time spent with the knee extended, while shifting the foot

posteriorly increases the time spent with the knee flexed. Changing the angle of the foot affects

the maximum knee extension moment occurring during the latter half of stance. Plantar flexing

the foot increases the knee extension moments, whereas dorsiflexing the foot decreases it.

Changes in the angle of the foot also increase the mean oxygen consumption rate during gait,

especially at higher walking speeds [9].

2.5 Assessing Patient Performance

The design of the components as well as the manner in which they are aligned affects patient

performance. This can be reflected in a number of measurable parameters, including oxygen

consumption, joint motion, forces and moments, as well as patient satisfaction.

27

2.5.1 Physical Measurements

An important functional outcome of an amputee being fit with a prosthesis is the degree of

mobility attained. This level of mobility is heavily dependant on the biomechanical characteristics

of the prosthetic foot [18]. Biomechanical data are often collected and studied to determine what

if any impact different types of prosthetic feet have on various characteristics of gait. The most

commonly studied areas are stride characteristics, kinematics, kinetics, and energy expenditure.

Stride characteristics, such as self-selected walking velocity (SSWV), stride length and cadence,

have been studied at length in regards to amputee gait. An increase in any of these values is

viewed as a positive outcome [23]. Gait symmetry, the variations in the time that the sound limb

and the affected limb spend at each phase of gait, is also of interest [16].

Joint angles, specifically range of motion are also of interest when comparing the effect of various

prosthetic treatment strategies [23]. Knee flexion, in particular, is of interest. It is essential during

normal gait and found to decrease significantly during amputee gait [18].

Energy expended during gait is also frequently studied. Oxygen consumption or cost, heart rate

and respiration rate are all indicators of energy expenditure. These are all measures of efficient

propulsion, which is influenced strongly by foot design. An amputee will expend more energy

during gait than an able bodied individual; therefore prostheses that allow an amputee to expend

less energy during walking would indicate an improvement [23].

28

2.5.2 Self-reported Measures

User feedback obtained using self-reported measures can identify aspects of prosthetic function

and performance that might be overlooked in biomechanical analysis. Several methods can be

used to determine an amputee’s perceived performance and preference, ranging from descriptive

dialogue to self-reported questionnaires [23].

The most detailed analyses include numerical rating scales, such as the 20-point Borg rating of

perceived exertion, and can be adapted to reflect a variety of activities [24]. Amputees are asked

to rate specific activities and parameters, such as ascending and descending stairs, comfort and

ease of use. These data can be analyzed to determine statistical significance [23].

2.6 Relationship of Mechanical Characteristics to Performance

Studies have found that amputees prefer prosthetic feet that provide energy return over those that

do not [23-25]. However, findings of the biomechanical studies have been mixed.

Lehmann et al. [27, 28] found that there were no significant differences in the SSWV or energy

efficiency between amputees who used a SACH foot, a Seattle Foot™ and a Flex Foot™. Hafner

et al. [19] observed that trends in the published literature do indicate differences in gait and

improved performance when using a DER foot; however these trends are discounted because of a

lack of statistical significance due in part to small sample sizes and variations in the subject

populations. However these trends do appear in other studies. For example, Hsu et al. [25] found

that energy expenditure was lower when walking on a Flex Foot™ compared to a SACH foot. At

certain speeds, oxygen consumption was lower when using the C-Walk foot compared to a Flex

Foot™. The study also found that the SSWV improved when subjects used a Flex Foot™ or a C-

29

Walk™ foot. Macfarlane et al. [16] found that subjects were able to spend more time in single

support during the stance phase of the gait cycle when they used a Flex Foot™ compared to a

conventional SACH foot. The keel of the Flex Foot™ provided greater support while under

dorsiflexion allowing for a longer stride length. This allowed users wearing the Flex Foot™, to

take fewer steps while maintaining their walking speed; in addition, their trunk motion was

smoother and more uniform while walking with a Flex Foot™, indicating that there were some

biomechanical advantages to walking with a Flex Foot™ [16].

Structural properties, particularly structural stiffness, strongly influence the function of prostheses

because this affects deflection during loading [29]. In addition, when subjected to equivalent

loads, a softer system stores more energy than a stiffer one [30]. However, the concept of

structural stiffness of a prosthesis is complicated by the nature of loading and motion during gait

and such factors as the angle of force application and the displacement rate must be considered.

Geil [29] tested eleven different prosthetic feet to determine material and structural properties

including stiffness, as well as energy expended and returned upon loading and unloading. The feet

were plantar flexed at 12° and loaded at a displacement rate of 1mm/sec to a load of 800N.

Stiffness was approximated from the slope of the force deformation curve. The samples

consistently fell into one of four categories: most stiff, more stiff, less stiff, least stiff. However,

only the toe regions of the samples were tested, multiple pylon angles were not considered and the

forces applied did not reflect peak loading during gait.

Van Jaarsveld et al. [30] conducted a comprehensive study of nine different prosthetic feet with

and without shoes. The feet were loaded from -30° (dorsiflexion) to 35° (plantar flexion) in

increments of 1°. At each angle, a plate representing the floor was lowered onto the foot in 1mm

30

increments until a vertical force of 1000N or 35mm of deflection was reached. A relationship

between the pylon angles (angle of the pylon relative to the vertical) and the stiffness of the

prosthesis, as well as its energy return, was determined. While this provided a comprehensive

description of mechanical behaviour, the results did not relate to specific activities of daily living.

2.7 Summary

A variety of performance measures can be used to determine the effects of alignment and

prosthetic components on amputee gait. These measures include biomechanical data, user

preference and perceived difficulties while ambulating. Even with these measures, the

relationship between mechanical characteristics of prosthetic feet and performance is not well

understood. This is, in part, due to an inability to define these mechanical characteristics.

31

Chapter 3

Mechanical Characterization of Dynamic Energy Return Prosthetic Feet

3.1 Introduction

In recent years, there have been advances in the field of prosthetic foot design and materials, most

notably with the emergence of DER feet. These feet are designed to store energy at the beginning

of the gait cycle and return it later, helping to propel the limb forward [31]. SACH feet were one

of the first commercially available prosthetic feet, and they continue to be used to this day [3]. For

this reason, SACH feet are often used as a benchmark to compare new designs.

During heel strike, the cushioned heel of a SACH foot helps to absorb the impact of the heel

hitting the ground and controls the rate of plantar flexion. SACH feet are prescribed in a variety of

heel stiffnesses, depending on the weight of the user and the need for stability. The softer the heel,

the faster the user is able to reach the stable foot-flat position. The rigid keel of the foot controls

the transition of the tibia going from posterior to anterior of the ankle. The keel continues to offer

resistance until the toe break is reached. In a SACH foot, the toe break is located at the end of the

keel. Belting that connects the keel and toe regions helps to control dorsiflexion of the toes,

allowing the tibia to progress smoothly. At this point, the toes offer little support. At the end of

toe off, the belting provides a limited spring action of the toes to aid in knee flexion.

Many single-axis and multi-axis foot designs use a variety of similar features to control motion

[3].

Dynamic energy return feet have features specifically designed to store and release energy, in

addition to controlling motion [3]. The Ohio Willow Wood Impulse® Foot is a single-unit design

32

in which the keel is incorporated into the rest of the foot. Although this design has a cushioned

heel that is similar to a SACH foot on heel strike, the keels are made of an elastic polymer. On

other feet such as the Flex Foot™, the Otto Bock® C-Walk™, and the Niagara Foot™, the keel

and cover are separate pieces. The keel has a distinct heel region that deflects under the weight of

the user, absorbing the impact of striking the ground [3, 21]. Plantar flexion and the progression

of the tibia are also controlled by the keel. As the tibia progresses, the keel deflects and the toe

begins to dorsiflex as the point of contact moves to the forefoot. As the body weight is transferred

to the other limb, the keel begins to unload and return to its original shape, providing a push off to

start the swing phase.

Studies have found that amputees prefer prosthetic feet that provide energy return over those that

do not [24-26]. However, the biomechanical studies investigating these findings have been mixed.

Lehmann et al. [26, 27] found that there were no significant differences in the self-selected

walking velocity or energy efficiency between amputees who used a SACH foot, a Seattle Foot™

or a Flex Foot™. Hafner et al. [19] observed that trends in the published literature do indicate

differences in gait and improved performance when using a DER foot; however, these trends are

discounted because of a lack of statistical significance in part due to small sample sizes and

variations in the subject populations. These trends do, however, appear in other studies. For

example, Hsu et al. [25] found that energy expenditure was lower when walking on a Flex Foot™

compared to a SACH foot. At certain speeds, oxygen consumption was lower when using a C-

Walk foot compared to a Flex Foot™. The study also found that self-selected walking velocity

improved when a subject used a Flex Foot™ or a C-Walk foot. Macfarlane et al. [16] found that

subjects were able to spend more time in single support during the stance phase of the gait cycle

when they used a Flex Foot™ compared to a conventional SACH foot. The keel of the Flex

33

Foot™ provided greater support while under dorsiflexion, allowing for a longer stride length. This

allowed users to take fewer steps while maintaining their walking speed. In addition, their trunk

motion was smoother and more uniform while walking with a Flex Foot™, indicating that there

were some biomechanical advantages to walking with a Flex Foot™ [16].

Structural properties, particularly structural stiffness, strongly influence the function of

prostheses since this affects deflection during loading [29]. In addition, when subjected to

equivalent loads, a softer system stores more energy than a stiffer one [30]. However, the concept

of structural stiffness of a prosthesis is complicated by the nature of loading and motion during

gait. Factors such as the angle of force application and the displacement rate must be considered.

Geil [29] tested eleven different prosthetic feet to determine material and structural properties

including stiffness as well as energy expended and returned upon loading and unloading. The feet

were plantar flexed at 12° and loaded at a displacement rate of 1mm/sec to a load of 800N.

Stiffness was defined as the slope of the force deformation curve. The samples consistently fell

into one of four categories: most stiff, more stiff, less stiff, least stiff. However, only the toe

regions of the samples were tested, multiple pylon angles were not considered, and the forces

applied did not reflect peak loading during gait.

Van Jaarsveld et al. [30] conducted a comprehensive study of nine different prosthetic feet with

and without shoes. The feet were loaded from -30° (dorsiflexion) to 35° (plantar flexion) in

increments of 1°. At each angle, a plate representing the floor was lowered onto the foot in 1mm

increments until a vertical force of 1000N or 35mm of deflection of was reached. A relationship

between the pylon angles (angle of the pylon relative to the vertical) and the stiffness of the

34

prosthesis as well as their energy return was determined. While this provided a comprehensive

description of mechanical behaviour, the results did not relate to specific activities of daily living.

A standardized waveform for prosthetic gait has recently been published by the International

Organization for Standardization (ISO) in their updated standards for the testing of ankle-foot

devices and prosthetic feet (ISO 22675). The document outlines a cyclic durability testing

procedure for lower limb prosthetic devices [32]. Although the waveform was not proposed as a

general description of prosthetic loading conditions, it is a practical testing regime designed to

simulate conditions during the stance phase of prosthetic gait.

The waveform is shown in Figure 12, in which test forces and tilting angle of the loading platform

are plotted as functions of time. (ISO 22675, Figure 6). Time can be related to the percentage of

gait cycle by assuming that each cycle takes one second and the stance phase of gait accounts for

600 msec or 60% of the overall cycle. The three different loading levels, P3, P4 and P5, represent

the vertical ground reaction forces during stance. The P3 and P4 loading curves are based on gait

data of amputees whose masses were less than 60 kg and 80 kg respectively; the P5 loading curve

is based on all the data including some subjects whose masses were over 100kg. Note that the

initial impact peak, evident in Figure 5, is not reflected in the waveform. This feature is generally

omitted in testing unless the high-frequency response of the device is of interest. The tilt angle is

comparable to the pylon angle relative to the vertical during gait.

The objective of this study was to use the ISO standardized waveform as a basis for determining

mechanical properties of the heel and toe regions of prosthetic feet. It is proposed that force-

displacement testing be conducted on the heel and toe at pylon angles corresponding to the tilt

angles in the ISO 22675 testing protocol. The samples were loaded to peak loads based on their

35

design masses (the maximum recommended user mass) at a series of different angles and forces

that would occur during the gait cycle.

Time (sec)

Forc

e (N

)A

ngle ((Degrees)

tilt angle

P5

P4

P3

TiltAngle

Time (msec)

Angle (D

egrees)Fo

rce

(N)

Time (sec)

Forc

e (N

)A

ngle ((Degrees)

tilt angle

P5

P4

P3

TiltAngle

Time (msec)

Angle (D

egrees)Fo

rce

(N)

Figure 12: Testing waveforms from ISO 22675 outlining the tilting angle and test profiles for the P3, P4 and P5 loading levels for cyclic fatigue testing. Adapted from ISO 22675 [32].

36

3.2 Critical Points

To approximate the loading conditions represented in Figure 12, fifteen critical data points were

extracted from the P4 loading curve. Based on the tilting angle, force and corresponding time

values were extracted in 5° increments for angles of -20° to 0° for the heel and 0° to 35° for the

toe. These data, shown in Figure 13 and Table 2, also included whether the component was being

loaded or unloaded at the identified point. If the extracted force was higher than the force value at

the previous time, loading was occurring. This distinction is important due to the energy lost

when unloading a component; at the same displacement, a lower force exists when unloading the

structure compared to loading it. To scale the data, a multiplier at each critical point was

determined by dividing the force at that point by the design mass, in this case 80kg.

One adjustment was required to facilitate a practical testing protocol. Initial contact of the heel

occurs at -20°; at this point, both time and force are equal to zero. A rapid increase in loading of

the heel occurs from this initial contact until a pylon angle of -15° is reached, as a result there are

few data points during heel loading. In order to have data for two angles during heel loading, data

were extracted from the graph at -19.5°.

37

0

200

400

600

800

1000

1200

1400

0 100 200 300 400 500 600

Time (msec)

Forc

e (N

)

-30

-20

-10

0

10

20

30

40

50

Ang

le (D

egre

es)

LoadAngle

1

2

3

4

5 6

7

8 9

1011

12

13

14

15

Figure 13: Fifteen critical points extracted from ISO 22675 as functions of time. Negative angles indicate dorsiflexion and positive ones plantar flexion.

38

Table 2: Data extracted from the P4 test loading level curve, show in Figure 12. Negative angles indicate dorsiflexion and positive ones plantar flexion.

Section Point Number

Time (msec)

Angle (°)

Loading Direction

Force (N)

Multiplier(m/s2)

1 0 -20 Loading 0 0 2 36 -19.5 Loading 354 4.4 3 150 -15 Loading 1173 14.7 4 212 -10 Unloading 983 12.3 5 260 -5 Unloading 821 10.3

Heel

6 300 0 Unloading 785 9.8 7 300 0 Loading 785 9.8 8 337 5 Loading 831 10.4 9 372 10 Loading 885 11.1

10 408 15 Loading 1100 13.8 11 450 20 Loading 1173 14.7 12 487 25 Unloading 1062 13.3 13 522 30 Unloading 769 9.6 14 560 35 Unloading 392 4.9

Toe

15 600 40 Unloading 0 0

3.3 Methods

Force-deflection testing was conducted using an Instron™ 5500 series material testing machine

with a 5kN load cell and Merlin Version 4.3 Software at a sampling rate of 4Hz. Initial testing

showed that the sample feet had minimum time constants in the order of three seconds and as

such a sampling rate of 4Hz was sufficient to capture the behaviour of the prostheses while

providing manageable quantities of data.

Three designs of feet were tested to span the range of designs of interest: a standard SACH foot,

two energy return feet for active users and a new prosthetic foot designed to provide partial

energy return. Four different components were evaluated: an Otto Bock® SACH foot, two Otto

39

Bock® Axtion™ feet and a Model 2 Version 18 Niagara Foot™ made of Hytrel®, as described in

Table 3. All tests were conducted without footwear or covers.

Table 3: Specifications of the sample feet tested

Sample Manufacturer Length (cm)

Maximum Recommended User Mass (kg)

Notes Heel

Height (mm)

Model 2 Version18 Niagara Foot™

Niagara Prosthetics and Orthotics

25 80 kg Adapter Connection 13

Axtion™ Otto Bock® 26 106 kg Standard Pylon 13

Axtion™ Otto Bock® 26 124 kg Standard Pylon 13

SACH 01763 Otto Bock® 25 100 kg Standard Pylon 20

The SACH foot, such as the one shown in Figure 14a, is composed of a wooden or rigid plastic

keel, a cushioned heel and it has a rubber shell that is integrated into the foot. This style of foot is

targeted to less active amputees who require greater stability [3]. The Axtion™ keel, as shown in

Figure 14b, is composed of two layers of a carbon fiber composite joined by an elastomeric layer;

it has distinct heel and toe regions and is designed for active amputees [33]. Two feet of different

stiffnesses were examined. The Niagara Foot™ keel, shown in Figure 14c, is a single component

3 An older SACH foot was tested. It was the same length and had the same weight limit as the Otto Bock®

1S37 SACH Foot.

40

made of Hytrel® with distinct heel and toe regions; a C-shaped region at the top of the foot

mimics ankle articulation [34].

(a) (b) (c)

Figure 14: (a) SACH foot, (b) Axtion™ keel [33] and (c) the Niagara Foot™

A pylon or comparable adapter was attached to the sample feet and aligned according to the

manufacturers’ specifications. For the feet that required the use of a pylon, the heel of the foot

was raised by the specified heel height. A pylon was then attached to the foot and a laser level

was used to ensure that the pylon was vertical. For feet that had a smooth, flat interface, an

adapter was used, consisting of a rectangular section of steel with the threaded hole in the centre

welded to a piece of square steel tubing.

Once the foot was attached to the pylon or adapter, it was placed in a machine vice and a clamp

was used to secure the pylons in the vice. A series of gauge blocks were used to set the machine

vice to the desired angle within 0.1°. The assembly was placed in the testing machine and fixed to

the base plate using step clamps as shown in Figure 15. A flat platen, 14.6 cm in diameter, was

used to load the heel and toe. To reduce the effects of contact friction, a thin layer of silicone-

top plate

horns

C-sectionelastomeric layer

41

based spray was applied to the sample feet whose soles were smooth. In those with textured soles,

a 0.8mm thick layer of Teflon® sheet provided an interposing layer between the specimen and the

platen.

Figure 15: Test configuration, (a) testing rig in the Instron™ testing machine, (b) clamps and gauge blocks.

The samples were loaded to a peak force equal to the product of their design mass and their peak

multiplier, shown in Table 2, to within 4%. A displacement rate of 2.0mm/sec was used.4

4 The displacement rate was selected based on the results of a pilot of three Model 2 Version 18 Niagara

Feet™ loaded at different displacement rates, as described in Appendix A.

(a) (b)

42

The samples were preconditioned by loading them cyclically 10 times at each critical angle. The

order of tests was randomized between pylon angles and at least five minutes elapsed between

each successive test. To determine test precision, the Model 2 Version 18 Niagara Foot™

underwent the testing protocol on three separate occasions; a maximum of one testing protocol

was conducted per day.

It should be noted that the testing on the Otto Bock® Axtion™ with a maximum recommended

user weight of 106kg at a pylon angle of 35° could not be completed due to slippage within the

system. The adhesive was not able to resist the shear forces that occurred at this angle. As a result

the Teflon® film began to peel of during loading.

3.4 Data Analysis

A typical force displacement curve is shown in Figure 16, showing ten cycles of the Model 2

Version 18 Niagara Foot™ toe loaded to 1173N at an angle of 20°. Note the peak displacement

increasing with each successive cycle.

Data were collected and analyzed according to the steps outlined in Figure 17 for each pylon

angle. The RAW data files from the force-displacement tests were first imported into Microsoft

Excel. To determine the cycle at which the preconditioning was complete, the peak displacements

reached during loading were plotted against time. A typical plot is shown in Figure 18. The

differences between the peak loads for each subsequent cycle were also plotted against time, as

shown in Figure 19. The cycle at which this difference reached a steady state determined when

the specimen was preconditioned. One preconditioned cycle was selected for each of the samples;

data collected during this cycle was parsed and analyzed.

43

Data collected during the transition from loading to unloading were removed and force values

below 0.15N were also disregarded. The origin of the force displacement curve was defined by

linear extrapolation of the first two data points to determine the x-intercept, as outlined in

Appendix B. Similarly, small overshoots in the peak force were adjusted.5

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25 30 35 40 45

Displacement (mm)

Forc

e (N

)

Figure 16: Typical force displacement curve of a toe region loaded to 1173N at a pylon angle of 20°.

5 This target force value was generally overshot by 0.04% to 0.43%. As such, the displacement that

occurred was estimated using linear interpolation, as outlined in Appendix B; all data collected after that

point were disregarded.

44

Store as a .RAW file

Import to Excel

Plot Force vs. Disp.

Data Collection

Determine Tangential Stiffness

Adjust Force Data

Determine Steady State Response

1. Peak Displacement vs. Time

2. First Difference vs. Time

Select Pre-Conditioned

Cycle

Parse Data

Offset Compensation

1. Determine Origin Offset

2. Adjust

Loading Unloading

Determine Displacement and

Tangential Stiffness at Critical Force

Plot

Figure 17: Overview of the data analysis process.

Shown in Figure 19

Shown in Figure 18

Shown in Figure 16

Shown in Figure 24

45

37.4

37.6

37.8

38

38.2

38.4

38.6

38.8

39

0 50 100 150 200 250 300 350 400

Time (sec)

Pea

k D

ispl

acem

ent (

mm

)

Figure 18: Peak displacements that occurred as a function of time.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 50 100 150 200 250 300 350 400

Time (sec)

Firs

t Diff

eren

ce

Figure 19: First difference between peak displacements as a function of time.

46

The Instron™ material testing machine was programmed to load the feet to a force equal to the

product of their design massess times the multiplier shown in Table 2. For each point of interest,

the tangential stiffness was calculated from the force-displacement data using the first central

difference method. For the first and last data points in a given set, the first forward and first

backward difference method were used respectively.

3.5 Results and Discussion

Test Precision. For the Model 2 Version 18 Niagara Foot™, the average displacement and

stiffness values for the three test runs at each of the critical points were calculated. The coefficient

of variation (COV) and the standard deviation (SD) were also determined. High precision was

found with average SD and COV of 0.72mm and 4.34% for the displacement and 13.36 kN/m and

6.39% for the stiffness. Measurement errors compounded when calculating stiffness values likely

resulted in the larger SD and COV values observed. Based on these results, it was concluded that

one testing run would be sufficient to characterize the other samples.

Typical Results. Typical force-displacement and stiffness-displacement curves for the heel and

toe are shown in Figure 21 and Figure 22, respectively. There is a non-linear relationship between

the force and displacement values in which the stiffness of the heel and toe increases as the

applied load increases. A sudden drop in displacement values occurs as the toe begins to unload at

angles of 25°, 30° and 35°. This is likely due to friction internal to the system and is consistent

with the design of the Niagara Foot™ in which sliding occurs between the horns and the top plate

noted in Figure 20. This drop in displacement results in uncharacteristically high stiffness values

during the unloading of the toe. The pylon angle at which the feet were loaded also affected their

stiffness. As the pylon angle increases, the stiffness values decrease. These observations are

consistent with the location of the point of contact between the foot and the platen. The point

47

moves anteriorly as testing progresses, as shown in Figure 20. This causes the length of the

moment arm to decrease and the measured stiffness to increase. This effect is also noted with

pylon angle: as the pylon moves away from the vertical, the contact point moves posterior on the

heel or toe, increasing the lever arm. This results in a softer response. A complete data set is

shown in Appendix C.

(a) (b) (c)

Figure 20: The contact point between the heel and the platen at displacements of (a) 0mm, (b) 4mm and (c) 8mm. Note the sliding contact between the horns and top plate.

48

0

200

400

600

800

1000

1200

1400

0 2 4 6 8 10 12 14 16

Displacement (mm)

Forc

e (N

)

0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees

(a) heel

0

200

400

600

800

1000

1200

1400

0 10 20 30 40 50

Displacement (mm)

Forc

e (N

)

0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees

(b) toe

Figure 21: Force-displacement curves for (a) the heel and (b) the toe of the Niagara Foot™. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.

49

0

100

200

300

400

500

600

700

800

0 5 10 15

Displacement (mm)

Stif

fnes

s (k

N/m

) 0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees

(a) heel

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80

Displacement (mm)

Stiff

ness

(kN/

m)

0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees

(b) toe

Figure 22: Stiffness-displacement curves for (a) the heel and (b) the toe of the Niagara Foot™. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.

50

Stiffness is derived by differentiating the displacement data, therefore small discrepancies in the

displacement can lead to anomalies in the stiffness values. The noise in the toe stiffness data at the

angle of 30° is likely due to the two slips evident in the corresponding displacement curve at 900

N and 1100 N. The sudden drop in force values during unloading of the toe corresponds to the

high stiffness values at this point. Future consideration could be given to numerical smoothing

methods for stiffness data when this mechanical behaviour is well understood.

Behaviour of the prostheses can be predicted by extracting data from the force-displacement and

stiffness-displacement curves corresponding to the critical points. For example, to determine the

predicted displacement of the heel of the Niagara Foot™ at -15°, as shown in Figure 23c, the

force the heel was expected to experience was first extracted from the load waveform in Figure

23b (1173N). Note that Figure 23b is reproduced from Figure 13. Next, the displacement

occurring at this force was extracted from the -15° force displacement curve, as shown in Figure

23a. Note that this is for heel loading in this case, because it occurs in this portion of the gait

cycle. Finally, this displacement and the corresponding time (from Figure 23b) are plotted on a

single graph, Figure 23c. The process is repeated for all fifteen critical points.

51

0

5

10

15

20

25

30

35

40

45

0 100 200 300 400 500 600

Time (msec)

Dis

plac

emen

t (m

m)

HeelToe

0

200

400

600

800

1000

1200

1400

0 2 4 6 8 10 12 14 16

Displacement (mm)

Forc

e (N

)

0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees

0

200

400

600

800

1000

1200

1400

0 100 200 300 400 500 600

Time (msec)

Forc

e (N

)

-30

-20

-10

0

10

20

30

40

50

Ang

le (D

egre

es)

LoadAngle

1

2

3

4

5 6

7

8 9

1011

12

13

14

15

0

5

10

15

20

25

30

35

40

45

0 100 200 300 400 500 600

Time (msec)

Dis

plac

emen

t (m

m)

HeelToe

0

200

400

600

800

1000

1200

1400

0 2 4 6 8 10 12 14 16

Displacement (mm)

Forc

e (N

)

0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees

0

200

400

600

800

1000

1200

1400

0 100 200 300 400 500 600

Time (msec)

Forc

e (N

)

-30

-20

-10

0

10

20

30

40

50

Ang

le (D

egre

es)

LoadAngle

1

2

3

4

5 6

7

8 9

1011

12

13

14

15

Figure 23: Predicting displacement and stiffness profiles of prostheses during gait, (a) force-displacement curves for the heel of the Model 2 Version 18 Niagara Foot™, displacement occurring at 1173 N is highlighted, (b) critical points extracted from ISO 22675 as functions of time, predicted force occurring at a pylon angle of -15° is highlighted, (c) predicted displacement profiles of the prosthesis during gait.

.

The predicted displacement and stiffness values of the Niagara Foot™ are plotted as functions of

time in Figure 24 and Figure 25 respectively. When the heel is first loaded in this sample, a

displacement of 8.5 mm occurs at 36 msec, which corresponds to an angle of -19.5° and a force of

354 N. The displacement remains approximately constant until the heel begins to unload at 150

msec, which corresponds to an angle of -15° and a force of 1173 N. At this point, the

displacement at the critical forces continues to decrease. As shown in Figure 25, the heel stiffness

at the critical forces increases steadily as the pylon angle approaches the vertical at a time of 300

(a) (b)

(c)

52

msec. This is expected due to the decrease in lever arm as the contact point between the heel and

the platen moves anteriorly.

At 300 msec, the pylon angle is 0° and the foot is supported by both the heel and toe. Assuming

that the force is instantaneously transferred to the toe, a displacement of 15.4 mm is predicted in

Figure 24. This displacement continues to increase even after the toe begins to unload at 500

msec, which corresponds to an angle of 25° and a force of 1062 N. As shown in Figure 25, the

stiffness of the toe increases sharply at this point and then steadily decreases as the pylon angle

continues to decrease.

0

5

10

15

20

25

30

35

40

45

0 100 200 300 400 500 600

Time (msec)

Disp

lace

men

t (m

m)

HeelToe

Figure 24: Predicted displacements of the Niagara Foot ™ during gait based on the waveform in Figure 12.

53

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700

Time (msec)

Stiff

ness

(kN/

m)

HeelToe

Figure 25: Predicted tangential stiffness values of the Niagara Foot™ during gait based on the waveform in Figure 12.

Comparison of Designs. In order to compare designs, displacement and stiffness values were

normalized against the maximum recommended user mass. These normalized values are plotted

as functions of time for all four designs in Figure 26 and Figure 27.

The heel region of the SACH foot experienced the highest displacements and had the lowest

stiffness values. The heel compressed quickly during loading and the level of compression was

constant. This indicated foot flat was reached early on in the gait cycle. The SACH toe was stiffer

than the three other samples. This is consistent with the SACH design in which the toe acts as a

rocker. In contrast, the DER designs flex upon toe loading.

The heel and toe of the two Axtion™ feet had very similar displacement profiles, which is

consistent with two feet having the same design. It is likely that the absolute values of

54

displacement and stiffness are simply scaled by mass in this product. Compared to the SACH, the

heels were two-and-a-half times stiffer, while the toes were 63% softer. There were notable

differences in the heel stiffness. These can likely be attributed to small differences in the heel

displacements because the errors in stiffness are compounded in differentiation.

The toe of the Niagara Foot™ had the highest peak stiffness values despite having the highest

peak displacement values. From 350 msec-450 msec the stiffness values are constant. During this

period, the horns of the foot are sliding across the top plate. If at 450 msec the sliding stops, this

would effectively stiffen the toe. The sudden drop in displacement during unloading shown in

Figure 21 could have also contributed to the high stiffness values. The high displacement values

indicate that overall the toe region of the Niagara Foot™ is soft compared to other designs, which

has been confirmed by patients in field trials [35]. The toe region of the Niagara Foot™ also

reached its peak displacement later in the gait cycle than the Axtion™. The difference in the

timing of the peak displacements is likely due to geometric differences in the feet. The Axtion™

has heel and toe levers as does the Niagara Foot™; however, the Niagara Foot™ has a C-section

that allows for ankle articulation.

The toe region of all the feet had greater displacements than the heel at a pylon angle of 0°. The

Axtion™ feet had the smallest displacement gap between the heel and toe at this angle, whereas

the SACH foot had the largest gap. During gait at a pylon angle of 0°, the foot would be in

midstance. During testing at this angle, the heel of the Niagara™ and Axtion™ Feet were found

to be much stiffer than the toe. This difference could aid in a smoother transition from heel to toe

loading. In contrast, the heel and toe stiffness values of the SACH foot were found to be similar,

suggesting greater stability for the user.

55

0

0.1

0.2

0.3

0.4

0.5

0.6

0 100 200 300 400 500 600 700

Time (msec)

Norm

aliz

ed D

ispl

acem

ent (

mm

/kg)

Niagara FootAxtion 106kgAxtion 124 kgSACH

Figure 26: Normalized displacements occurring at the critical forces identified for all the sample feet.

56

0

1

2

3

4

5

6

7

8

9

0 100 200 300 400 500 600 700

Time (msec)

Norm

aliz

ed S

tiffn

ess

(kN/

m-k

g)Niagara FootAxtion 106kgAxtion 124kgSACH

Figure 27: Normalized tangential stiffness values occurring at the critical forces identified for all the sample feet.

These trends indicate feet designed for stability, such as the SACH, have soft heels and stiffer

toes. The softer heel allows the user to reach foot flat quickly, a position of stability. Furthermore

the toe is stiffer than the DER feet; this is consistent with it acting as a rocker late in stance.

The stiffness profile of the DER Axtion™ design was the opposite of the SACH foot. The trends

indicate that DER feet have stiff heels and soft toes. It is likely that the stiffer heel allows for a

smooth rollover from heel to toe. When subjected to equivalent loads, a softer system stores more

energy than a stiffer one [30], thus the lower toe stiffness values may provide a greater spring

action than a SACH foot at the end of stance. As the keel unloads, it provides a push off and helps

to start the swing phase.

57

The performance of the Niagara Foot™ indicates that it is an intermediate foot, having traits of

both the SACH and DER feet. The heel is quite stiff, experiencing displacements lower than the

Axtion™. Initially the toe has approximately the same stiffness as the Axtion™ feet, but it

becomes increasingly stiff as gait continues.

3.6 Conclusions

A method had been presented by which the mechanical properties of prosthetic feet can be

evaluated based on the standard loading waveform of ISO 22675. The stiffness characteristics and

displacement profile of the SACH, Axtion™ and Niagara Foot™ were consistent with their

design features, indicating that the testing protocol is able to capture the mechanical

characteristics of these designs and to detect differences in function.

This methodology could be used to classify new designs of feet based on prostheses whose

mechanical properties are well understood, such as the SACH and the Flex Foot™.

58

Chapter 4

Force Relaxation Properties of Dynamic Energy Return Feet

4.1 Introduction

Many prosthetic foot designs are intended to match the mechanical characteristics of the device to

the needs and physical demands of the user [18]. Interestingly, user preference is not always

reflected in biomechanical performance or physiological measures, such as gait characteristics or

energy expenditure [23]. This suggests that the relationship between mechanical properties of

prosthetic feet and user preference is not well defined. This may be due, in part, to a need to

improve methods of characterizing the mechanical properties of these devices. It is particularly

necessary to address factors associated with the non-linear structural response and time

dependency of the materials used in fabrication.

There are a number of approaches to determining the mechanical properties of prosthetic feet

including finite element analysis (FEA) and structural testing. FEA can be used when material

properties, loading, and boundary conditions are well defined. These methods can provide a

complete prediction of the force, deformation, stress and strain responses of the system, and have

distinct advantages in design optimization [36]. However, this approach also requires the

establishment of design objectives for the structural response of the system under varying loading

conditions. In order to provide these data, structural testing is required.

The structural response of a prosthetic foot can be defined in terms of displacements resulting

from the application of loads corresponding to vertical ground reaction forces. If loading

conditions are consistent with activities of daily living, this response can provide a robust method

for describing mechanical characteristics of a prosthesis.

59

Geil [29] tested eleven different prosthetic feet to determine material and structural properties,

including stiffness and energy expended and returned upon loading and unloading. The feet were

plantar flexed at 12°, loaded at a displacement rate of 1mm/sec to a load of 800N. Stiffness was

estimated based on the slope of the force deformation curve. The samples consistently fell into

one of four categories: most stiff, more stiff, less stiff, least stiff. However, only the toe region

was tested, multiple pylon angles were not considered and the forces applied did not reflect peak

loading values during gait.

Van Jaarsveld et al. [30] conducted a comprehensive study of nine different prosthetic feet with

and without shoes. The feet were loaded from -30° (dorsiflexion) to 35° (plantar flexion) in

increments of 1°. At each angle, a plate representing the floor was lowered onto the foot in 1mm

increments until a vertical force of 1000N or 35mm of deflection was reached. A relationship

between the pylon angles (angle of the pylon relative to the vertical) and the stiffness of the

prosthesis, as well as their energy return, was determined. While this provided a comprehensive

description of mechanical behaviour, the results did not relate to specific activities of daily living.

Time dependencies of the mechanical response have been investigated in terms of impact

response and viscoelastic modeling. Klute et al. [37] studied the initial impact of the heel region

of seven prosthetic feet. Feet were modeled as non-linear springs in parallel with position-

dependent dampers and experimental data were collected using a pendulum striking the heel at a

velocity of 0.4m/s. Although the model was able to predict the energy dissipation to within 6%, it

was less applicable as a generalized model under other loading conditions. As such, it is necessary

to develop models for the structural response of prostheses in situations other than at impact.

60

Based on a previous study, Geil [38] used a three-parameter model to examine the stiffness and

dampening properties of the toe region of eleven prosthetic feet. The approach was successful

when predicting linear mechanical responses; however, it had limited success when non-

linearities were dominant.

A recognized strategy to address the presence of structural non-linearities is to separate the time

dependency from the elastic properties. Haberman et al. [39] approached this by identifying

loading regimes for prosthetic feet that isolated the elastic characteristics from the time-dependent

response. This quasi-linear method allowed for non-linearities in the force-displacement response

to be quantified and facilitated the comparison of different foot designs.

The purpose of this study was to develop an appropriate model of the time-dependant properties

for these devices. Two viscoelastic models were examined: a standard three-parameter solid

model and one with a linear decay term included.

4.2 Theory

Fung introduced the concept of a time-dependent, quasi-linear, stress-relaxation function, K(λ,t),

for biological materials,

),()(),( )( λλ eTtGtK = where ,1)0( =G (1)

where λ is the elongation and t is time. G(t) is a normalized function of time called the reduced

relaxation function, and )()( λeT is the elastic response of the material [40].

61

The structural analogy of a stress-relaxation function can be determined using force-relaxation

testing, in which a step displacement is applied and the force response measured. In practice, a

step displacement is rarely achieved, so a high displacement rate is used until a predetermined

force or displacement is measured. A typical force response is shown in Figure 28, in which the

toe region of a sample component was displaced at a rate of 3.25mm/sec until a peak load of

1173N was attained. The displacement was then held constant and the force recorded for an

additional 90 seconds.

0

250

500

750

1000

1250

0 20 40 60 80 100 120

Time (sec)

Forc

e (N

)

Figure 28: Typical force response of the toe of a prosthetic foot. A displacement rate of 3.25mm/sec was applied until a peak load of 1173N was attained and the displacement was held constant for an additional 90 seconds. Specific data are for a Model 2 Version 18 Niagara Foot™.

62

The relaxation response can be isolated and then normalized against the peak force (F0=1173N) to

produce the reduced relaxation response, L(t), as shown in Figure 29. Thus,

,)()(0FtFtL = where .1)0( =L (2)

0.7

0.75

0.8

0.85

0.9

0.95

1

0 10 20 30 40 50 60 70 80 90 100

Time (sec)

L(t)

Figure 29: The solid line is the reduced relaxation response, L(t). The dashed line is the steady state response predicted by Equation 4.

Two functions were considered for L(t). Geil [38] used a three-parameter solid viscoelastic model

for prosthetic foot components consisting of a spring in series with a damper parallel to a second

63

spring. This leads to a reduced relaxation response which is a two-parameter equation of the form:

),exp()1()( τtAAtL −−+= (3)

where τ is a time constant, A is a constant and t is time in seconds.6 The constant, A, represents

the steady state value of the function when the exponential decay no longer dominates.

A second model was proposed for L(t), based on observations in pilot studies in which the force-

relaxation response did not achieve a constant steady state value. A linear decay term, Bt, was

added to L(t), such that

,)exp()1()( BttAAtL −−−+= τ (4)

where B is a constant, termed the decay coefficient. The term A in Equation 4 can be interpreted

by examining the response when the exponential decay no longer dominates. When the

exponential decay is removed the reduced relaxation response becomes L(t)=A-Bt, and is shown

as the dashed line in Figure 29. Note that A is the y-intercept and is defined as the initial decay. In

this case, A=0.83. To determine the effect of the linear decay term, the degree of fit between the

two models and experimental results was assessed on four test specimens.

6 Note that the number of parameters is reduced due to the normalization of the data.

64

4.3 Methods

Three styles of feet were tested to span the range of designs of interest: a standard SACH foot,

two energy return feet for active users and a new prosthetic foot designed to provide partial

energy return. They are detailed in Table 4.

Table 4. Specifications of the sample feet tested.

Sample Manufacturer Length (cm)

Maximum Recommended

User Weight (kg) Notes

Heel Height (mm)

Model 2 Version18 Niagara Foot™

Niagara Prosthetics and Orthotics

25 80 kg Adapter Connection 13

Axtion™ Otto Bock® 26 106 kg Standard Pylon 13

Axtion™ Otto Bock® 26 124 kg Standard Pylon 13

SACH 01767 Otto Bock® 25 100 kg Standard Pylon 20

SACH feet, such as the one shown in Figure 30a, are composed of a wooden keel, a cushioned

heel and they have a rubber shell that is integrated into the foot. This style of foot is targeted to

less active amputees who require greater stability. The Axtion™ keel, as shown in Figure 30b, is

composed of two layers of a carbon fiber composite joined by an elastomeric layer. It has distinct

7 An older SACH foot was tested. It was the same length and had the same weight limit as the Otto Bock®

1S37 SACH Foot.

65

heel and toe regions and is designed for active amputees. The Axtion™ keel can be placed in a

separate foot shell. Two feet of different stiffnesses were chosen to examine the sensitivity of the

reduced relaxation response to this parameter.

The Niagara Foot™ keel, shown in Figure 30c, is a single component made of a polymer and has

distinct heel and toe regions. A C-shaped region at the top of the foot mimics ankle articulation. It

can be worn with a separate cosmetic foot cover.

(a) (b) (c)

Figure 30: (a) SACH foot, (b) Axtion™ keel [33] and (c) the Niagara Foot™.

Testing parameters were selected based on peak loading conditions occurring during the gait

cycle as described by Haberman et al. [39]. The heel and toe were tested at angles of 15° and 20°

respectively. The product design mass (maximum recommended user mass) was multiplied by

14.7 to determine the maximum test forces, which correspond to the peak forces expected during

gait. Force relaxation testing was conducted using an Instron™ 5500 series material-testing

machine with a 5kN load cell and Merlin Version 4.3 Software with a sampling rate of 4 Hz.

top plate horns

C-sectionelastomeric layer

66

For the feet that required the use of a pylon, the heel of the foot was raised by the specified heel

height. A pylon was then attached to the foot and a laser level was used to ensure that the pylon

was vertical. For the Niagara Foot™, an adapter was used that consisted of a rectangular section

of steel with a threaded hole in the centre welded to a piece of square steel tubing.

Once the foot was attached, it was placed in a machine vice, and gauge blocks were used to set it

to the desired angle within 0.1°. The assembly was placed in the testing machine and was fixed to

the base plate using step clamps, as shown in Figure 31. A flat platen 5.75” in diameter was used

to load the feet.

Figure 31: Test configuration of (a) testing rig in the Instron™ and (b) clamps and gauge blocks used.

(a) (b)

67

To reduce friction between the sample and platen, a thin layer of silicone-based spray was applied

to the sample feet whose soles were smooth. A 0.8 mm thick piece of Teflon® film was attached

to the soles of the sample feet whose soles were textured or to the loading platen using a double-

sided adhesive tape.

The samples were loaded to their expected peak loads at a rate of 3.25 mm/sec. Once the peak

load was reached the platen position remained constant for 90 seconds and the resulting forces

recorded.

The data were first adjusted to obtain the reduced relaxation response as shown in Figure 29. The

parameters for Equations 3 and 4 were then determined by minimizing the squared residuals

between the models and the experimental data, using the Solver function in Microsoft Excel. The

RMS differences between the models and the experimental data were also determined.

For a quasi-linear model to be applicable, it is necessary for the reduced relaxation function to be

independent of force. A test for linearity was conducted using three Model 2 Version 14 Niagara

Feet™ made of Delrin™ ST. The heel regions of the samples were each loaded at a rate of

100mm/min on three separate occasions. They were each displaced until peak loads of 300N,

700N and 1200N were reached.

4.4 Results and Discussion

In the two-parameter model (Equation 3), τ is the time constant and A represents the steady state

value. As shown in Table 5, the time constant varied from 6-13 seconds; however, these values

did not capture the rapid decay in the early phase of the response. This is evident in the interval of

0 < t < 20s in Figure 32. In the latter phase of the response, the model fails to capture the decay

68

and instead approaches the steady state value, A. This is shown in the interval 50 < t < 90 in

Figure 32. In contrast, the three-parameter model of Equation 4 was able to capture the initial and

long-term features of the response. A complete data set is shown in Appendix D.

These differences are reflected in the RMS values found in Table 5. The average RMS values for

the Niagara Foot™ using the two-parameter model values were 0.0504 and 0.0080 for the heel

and toe respectively. For the three-parameter model, the average RMS values were 0.0067 and

0.0033 for the heel and toe respectively, providing improvements of 87% and 59% in the quality

of fit when the linear decay term was included in the model.

Similar results were observed for all feet tested as summarized in Table 5 and Table 6. Overall the

three-parameter model had RMS values 57% to 93% lower than the two-parameter one. The toe

regions of the Otto Bock® Axtion™ feet were modeled with the best fit, with the 106kg and

124kg Axtion™ toes having RMS values of 0.0007 and 0.0006 respectively. The heel and toe

regions of the SACH and the Model 2 Version 18 Niagara Foot™ were modeled with comparable

degrees of fit and had the highest RMS values.

69

0.7

0.75

0.8

0.85

0.9

0.95

1

0 20 40 60 80 100

Time (sec)

Forc

e (N

) Experimental2 Parameter3 Parameter

Figure 32: Force-relaxation response for the toe of the Model 2 Version 18 Niagara Foot™. Experimental data and curve fits are shown for a two-parameter model (Equation 3) and a three-parameter model (Equation 4).

Table 5: Parameters and degree of fit of a two-parameter model.

Heel Toe Sample A τ RMS A τ RMS Niagara Foot™ 0.752 10.417 0.0880 0.791 12.658 0.0139Axtion™ 106 kg 0.907 10.417 0.0330 0.967 13.333 0.0019Axtion™ 124 kg 0.884 8.621 0.0080 0.974 13.158 0.0016SACH 0.802 11.242 0.0726 0.775 6.046 0.0147

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Table 6: Parameters and degree of fit of a three-parameter model.

Heel Toe Sample A B τ RMS A B τ RMS

Niagara Foot™ 0.815 0.0010 4.717 0.0061 0.855 0.0098 4.926 0.0060Axtion™ 106 kg 0.931 0.0004 4.505 0.0119 0.977 0.0001 5.747 0.0007Axtion™ 124 kg 0.911 0.0004 3.891 0.0030 0.982 0.0001 5.435 0.0006SACH 0.86 0.0009 4.098 0.0059 0.817 0.0007 3.030 0.0061

In the three-parameter model (Equation 4), A is the initial decay term, τ is the time constant, and

B is the decay coefficient. The decay coefficient, B, is very small. Initially, the exponential decay

dominates the equation, and as time increases B begins to dominate. It is possible that the decay

coefficient, B, could be modeled as two time constants, a rapid one that acts early in the response

and a slow one that acts later. It is recognized that fitting multiple time constants is susceptible to

inaccuracies due to noise in the data. The use of a linear approximation of the decay is sufficient

for the time scale that is being examined and likely represents the behaviour of polymers over

long-term loading. Interestingly, the absence of B in the two-parameter model resulted in an

artificially high time constant.

Prosthetic feet experience two types of friction during use, external and internal. External friction

is due to the contact between the foot and the ground, or during loading, the platen. External

friction was minimized during testing through the use of a silicone based spray and Teflon® film.

Internal friction is due to motion within the prosthesis, such has one section sliding against

another. Hysteresis or energy loss of a material during unloading is associated with internal

friction [30]. A, the initial decay, is indicative of friction internal to the system. The higher the A

value, the less friction exists. The highest initial decay, A, values are those for the two Axtion™

71

feet compared to the other two designs, and the lowest are for the Niagara Foot™ and the SACH.

The Axtion™ designs have stiff elastic elements with low friction. In contrast, the design of the

Niagara Foot™ is such that when the heel is subjected to higher loads, the horns on the foot meet

the top of the foot. The resulting friction at this contact point could result in a greater initial decay

and a lower A value. The values for the SACH likely reflect the energy lost in compression of the

soft foam heel.

The toe of the Axtion™ had the highest time constant (τ = 5.7 sec), whereas the SACH toe had

the lowest time constant (τ = 3.0sec). This is likely due to the longer time response of the

elastomer in the Axtion™ design compared to the more rigid keel in the SACH design. The

Hytrel™ used in the Niagara Foot™ design is a semi-crystalline form of polyester with a modulus

of approximately 1.2 GPa. Its intermediate time constant is consistent with its bulk properties.

The results of the test for linearity study using the three-parameter model are shown in Table 7.

As the loading levels increased, the initial decay values, A, continued to decrease. Overall, this

difference in the A values decreased as the loading levels increased. Most notably, the time

constants tended to decrease as forces increased. Because this force dependency exists, a true non-

linear approach is required to completely model the force relaxation response of the samples

tested. However, providing the load levels are standardized, the method is useful for comparing

different designs of feet.

72

Table 7: Results study examining linearity using a three-parameter model.

300N 700N 1200N Sample A B τ RMS A B τ RMS A B τ RMS

006 0.953 0.00048 8.547 0.00111 0.918 0.0006 3.731 0.004 0.897 0.00067 1.135 0.00548 012 0.947 0.00045 3.891 0.00058 0.922 0.00061 3.891 0.00345 0.898 0.00069 2.146 0.00547 015 0.962 0.00039 8.772 0.00082 0.928 0.00059 3.953 0.00325 0.912 0.00066 3.115 0.00441

73

4.5 Conclusions

A reduced relaxation function of the form BttAAtL −−−+= )exp()1()( τ is able to capture

the time-dependent characteristics of the heel and toe regions of prosthetic feet. In this model, A

is the initial decay, B is the decay coefficient, and τ is a time constant. Lower A values indicate

that prosthetic feet have higher friction internal to the system. Low time constants indicate that the

initial decay occurs over a brief period of time, whereas high time constants indicate that the

initial decay occurs over a longer period of time. This reflects bulk material properties of the

component. The three-parameter model is practical for comparing various prostheses at single

load level. To model the reduced relaxation response at all loading levels a fully non-linear model

is required.

74

Chapter 5

General Discussion

The long-term goal of this study is to improve the ability of designers and prosthetists to match

the mechanical characteristics of prosthetic feet to the patient-specific parameters, including their

needs, abilities and biomechanical characteristics. While patient measures of performance are

well developed, there is a need to develop a practical method by which non-linear and time-

dependent mechanical properties of the prosthetic component can be measured. Testing

methodologies were developed that separately evaluated the elastic and time-dependent

properties.

The first testing regime involved mechanically characterizing prostheses under conditions similar

to gait. The heel and toe of four sample feet were loaded to peak forces based on their design

mass at a series of angles that the prosthetic system would go through during the gait cycle. Using

the force-displacement data, tangential stiffnesses of the samples were determined.

The amputee gait waveform in ISO 22675 was used to identify critical vertical forces that the foot

would be expected to experience at each pylon angle. The displacements and stiffness values

occurring at each of the critical forces were identified in four sample feet and normalized against

their design mass. This allowed for the designs to be compared against one another.

75

Differences in function, style and geometric shape were noted between the different styles of feet.

The heel of the SACH foot compressed quickly and the level of compression was constant,

indicating foot flat was reached early on in the gait cycle. These observations are consistent with

the design features of the foot. The heel and toe regions of the two Axtion™ feet had very similar

displacement profiles, which is consistent with two feet having the same design. The toe region of

the Niagara Foot™ reached its peak displacement after the Axtion™. The difference in the timing

of the peak displacements is likely due to geometric differences in the feet.

Although this method was based on a gait waveform, some simplifications were required. The

combined loading of the heel and toe regions during the midstance phase of gait was not

duplicated during testing. The midstance phase begins when foot flat occurs at approximately 7%

of the gait cycle; this is the first time that the foot is flat with the ground. The loads experienced

by the heel begin to decrease while those on the toe begin to increase. At 30% of the gait cycle

midstance occurs; at this point, a person’s body weight is directly over the supporting limb. The

heel continues to unload until heel off occurs and the heel is no longer in contact with the ground

[10]. If both regions of the foot had been loading during this complex phase of gait, it would have

been difficult to separate out the individual heel and toe responses from the data. Testing the

regions separately allowed for an understanding of the properties of these sections and how they

contributed to the performance of the foot at each point in the gait cycle.

When prosthetists prescribe a device they rely primarily on their experience and input from their

patients. Observations include the rate of ambulation, activity level and weight of the patient [41].

Predicting the behaviour of prosthetic feet during gait may make it possible for a prosthetist to

76

prescribe components that better suit the needs of their patients. In addition, this information gives

designers more control over the performance of new prosthetic feet and the ability to modify

current designs to meet the needs of users. Patients requiring greater stability are often prescribed

a foot that reaches the foot flat phase of stance quickly. This type of foot tends to have a softer

heel and stiffer toe, such as the SACH foot. More active patients are often prescribed feet that

provide greater energy return allowing for easier propulsion of the limb such as a DER foot.

These feet typically have stiffer heels and softer toes.

A recognized strategy when modeling non-linear systems is to separate the time dependency from

the elastic properties. A second testing regime examined the time-dependent properties of the heel

and toe region of prostheses. Force relaxation testing was conducted on the heel and toe regions

of four sample feet. This response was predicted using two models for the reduced relaxation

response, and the RMS errors were calculated. The first was a standard model of the form of:

).exp()1()( τtAAtL −−+=

This model was unable to capture the initial rapid decay or the quasi-linear decay occurring later

on in the response.

The second model was a reduced relaxation response in the form of:

.)exp()1()( BttAAtL −−−+= τ

This model was able to capture the initial rapid decay and the longer-term linear decay that was

noted in the relaxation behaviour. Improvements of 87% and 59% in the quality of fit for the heel

and toe respectively were achieved. Based on a previous study, Geil used a three-parameter model

77

to examine the stiffness and dampening properties of the toe region of eleven prosthetic feet. The

approach was successful when predicting linear mechanical responses; however, it had limited

success when non-linearities were dominant [38]. The addition of the decay coefficient to the

three-parameter model may increase the robustness of the model in future studies.

In this model, A is the initial decay. Friction internal to the system occurs when the Niagara

Foot™ is loaded due to its design. The Niagara Foot™ exhibited initial decay values that were

consistently lower than the other samples. Lower initial decay values likely indicate that

prosthetic feet have higher friction values internal to the system; systems with higher initial decay

values have lower internal friction levels.

B is the decay coefficient. It is possible that this parameter could also be modeled as two time

constants, a rapid one that acts early on in the response and a slow one that acts later on.

However, it is recognized that fitting multiple time constants is susceptible to inaccuracies due to

noise in the data. The use of a linear approximation of the decay was sufficient for the time period

of interest. The decay coefficient is necessary to derive parameters consistent with the relaxation

response.

τ is a time constant. Low time constants indicate that the initial decay occurred over a brief period

of time, while high time constants indicate that it occurred over a longer period of time.

Comparing these constants across feet can provide insight into how different feet function and

how different features, especially bulk properties, affect performance.

78

Using the two testing regimes, mechanical properties of the sample feet tested were determined.

Linking the testing to the gait cycles provides insight into how these properties relate to their

performance. There are, however, a number of basic assumptions that must be considered in order

to interpret the measured data. This study tested all of the prosthetic feet according to the same

standard, making it possible to compare the different designs and styles against one another and

draw conclusions about their performance. However, changes in gait due to alignment of the

prosthetic system or adaptations made by an amputee are not taken into account.

This characterization method does not consider long-term behaviour of the component. In

particular, hysteresis occurring during cyclic loading of the feet associated with normal use will

lead to an increase in the temperature of the component. Long term cycling of feet may provide

different results such as greater displacements and lower stiffness values. This should be

considered when extending this work to other activities of daily living.

5.1 Patient-related Variables

The loading levels used in the mechanical characterization and force-relaxation testing were based

on a standardized waveform found in ISO 22675. The testing regime was designed to simulate the

conditions that these components will perform under during the stance phase of prosthetic gait.

However it was designed to test the durability of prostheses, not further the understanding of how

they function.

79

The majority of the subjects who participated in the study were male, and almost half were

between the ages of 41-65 years old [42]. The types of prostheses available at the time are still

worn by amputees today; however, many prosthetic devices have been introduced since the time

of the study. The type of foot worn can influence the gait patterns of the user. For example,

Macfarlane et al. [16] found that subjects were able to spend more time in single support during

the stance when they used a Flex Foot™ compared to a conventional SACH foot. This allowed

them to take fewer steps while maintaining their walking speed. In addition, their trunk motion

was smoother and more uniform while walking with a Flex Foot™ [16]. It is expected that the

gait waveform would vary if the study were reproduced with subjects using different types of

prostheses.

Gait waveforms provide an indication of how the average person walks. The speed at which

someone walks, as well as the cause of amputation, can cause variations in gait from the normal

pattern. The speed at which someone walks affects the peak vertical ground reaction forces

occurring during gait. As walking speed increases, the peak forces on both the affected and

unaffected sides do as well. Walking speed also affects the amount of time a limb spends in

stance. As walking speed increases, the time spent in stance decreases [15]. Self-selected walking

speed varies from person to person; therefore the peak forces the prosthesis is subjected to will

vary as well. Amputees who had a limb amputated due to vascular disease tend to walk at a

slower speed with a lower cadence and a shorter stride length compared to traumatic amputees

[43]. This variation is not necessarily reflected in the test protocol.

80

5.2 Prosthetist-related Variables

Proper alignment of a prosthetic system is essential for patient comfort and their ability to

efficiently transition from heel strike to toe off during the stance phase of gait. This alignment is

carried out by a prosthetist, it varies from patient to patient, and has a noticeable impact on the

biomechanics of amputee gait. Shifting the foot in the sagittal plane alters the point of contact of

the foot with the floor. This changes the effective lever arm length of the heel and toe, altering

both of their stiffnesses. The stability of the knee is also affected. Shifting the foot anteriorly

increases the amount of time someone spends with the knee extended, whereas shifting the foot

posteriorly increases the time spent with the knee flexed. Changing the angle of the foot affects

the maximum knee extension moment occurring during the later half of stance. Plantar flexing the

foot increases the knee extension moment, while dorsiflexing the foot decreases them. Changes in

the angle also increase the mean oxygen consumption during gait especially at higher walking

speeds [9]. While the results of this study do not reflect the impact that changes in alignment

would have on the performance of the system, they do provide baseline data. Adaptations in gait

and the effects of changing the alignment can be extended in future work using methods similar to

the current study.

5.3 Component Design Variables

This study examined the mechanical properties of various prosthetic feet without covers or

footwear except for the SACH foot whose cover is integrated into the keel. This allowed for the

characteristics of the keel alone to be studied. However, feet are generally worn with cosmetic

covers and various styles of shoes.

81

Van Jaasrsveld et al. [30] studied the stiffness and hysteresis properties of nine different

prosthetic feet with and without shoes. The effects of a leather shoe and a running shoe were

examined. In all but two of the samples, the leather shoe resulted in an increase in the maximum

stiffness during loading. Six of the feet experienced a 50kN/m increase in the maximum stiffness,

while the Otto Bock® uni-axial feet experienced an 180kN/m increase. The Hanger Quantum and

Otto Bock® dynamic foot experienced a decrease in stiffness of 30kN/m. The running shoe

influenced the maximum stiffness values to a lesser extent.

Klute et al. [37] examined the deformation and energy dissipation properties of the heel region of

prosthetic feet during the initial contact at heel strike. Of the seven feet tested, one, a Seattle

Lightfoot 2 was tested with three different shoes: a walking, a running and an orthopedic shoe.

The use of all three shoes resulted in greater energy dissipation at all velocities compared to the

foot alone. The running and orthopaedic shoes resulted in an increased peak at all velocities

compared to the foot alone.

Much in the same way footwear can affect the characteristics of prostheses, covers would be

expected to do so as well. Given that different covers are made of different materials, it is likely

that they would affect the characteristics of prosthetic feet in different manners. The effect of

different shoe styles and foot covers should be examined in future studies, especially with regard

to time-dependent properties.

82

Chapter 6

Conclusions and Future Work

6.1 Conclusions

1. A method has been proposed by which the mechanical properties of prosthetic feet can be

evaluated based on the standard loading waveform in ISO 22675. The mechanical properties

of prosthetic feet can be described using a quasi-linear approach.

2. The force-displacement responses of prosthetic feet reflect increasing stiffnesses with

increasing loads and a decreasing pylon angle. These changes are consistent with the position

of the contact point during loading.

3. Key features reflecting foot design are: the relative stiffness of the heel and toe and the

displacement gap at midstance.

A) Feet designed to provide greater stability tend to exhibit lower heel stiffnesses and higher

toe stiffnesses, while the DER feet tested exhibited higher heel stiffnesses and lower toe

stiffnesses.

B) The displacement gap, the differences in heel and toe displacement at a pylon angle of 0°,

suggests that DER feet can aid in the transition from heel to toe, providing a smooth

rollover, whereas SACH feet provide greater stability.

C) Based on the characteristics of well-understood prostheses, benchmark values can be

established. New designs of prosthetic feet could be compared against these values and

classified.

83

4. The reduced relaxation response of the form BttAAtL −−−+= )exp()1()( τ is able to

capture the relaxation characteristics of the heel and toe regions of prosthetic feet. In this

model, A, is the initial decay, B is the decay coefficient, and τ, is a time constant.

5. Lower A values indicate that prosthetic feet have higher friction internal to the system.

Systems with higher A values have lower internal friction levels.

6. Low time constants indicate that the initial decay occurs over a brief period of time, while

high time constants indicate that the initial decay occurs over a longer period of time. This

reflects bulk material properties of the component.

7. The decay coefficient is not well understood; it is, however, necessary to capture the initial

rapid decay and latter phase of the relaxation response.

8. The model used to predict time-dependent properties of the feet was able to capture the

relaxation properties with a better degree of fit than in previous studies using a linear model.

The three-parameter model is practical for comparing various prostheses at single load level.

To model the reduced relaxation response at all loading levels, a fully non-linear model is

required.

84

6.2 Future Work

Future work is required to improve the methods outlined in this study. Conducting the mechanical

characterization protocol twice, once loading the heel and toe separately and a second time

allowing for combined loading, would yield a more complete data set. The results of testing the

heel and toe separately could be used to help interpret the combined loading data, which would

more accurately mimic gait. This could be achieved using a larger platen during loading that is

able to capture both the heel and toe regions of the samples.

To ensure correct alignment of the samples, a prosthetist or other trained professional should

oversee this procedure. Examining the effect of alignment on the mechanical properties of

prosthetic feet could provide insight into how different patients will perceive different prostheses.

Testing should be conducted using different alignments.

It is known that shoes can influence the mechanical properties of prosthetic feet. Conducting the

protocols with foot covers and different types of footwear would examine their effect on the

elastic and viscoelastic properties of prosthetic feet. This could also provide insight into how

patients perceive their prostheses during gait.

Understanding the effects of DER prostheses on the amputee gait waveform used would be

beneficial. Comprehensive studies should be conducted to examine the effect different prostheses

have on amputee gait. The vertical ground reaction forces relative to pylon angle are of particular

interest. Testing protocols could be customized to different styles of feet, which would produce

more realistic prediction of performance.

85

Long term cycling of feet may provide different results due to an increase in the temperature of

the component. Studies should be conducted to examine the effect that increased temperatures

will have on the displacement and stiffness values of prosthetic feet.

A fully non-linear model of the reduced relaxation response should be developed so the response

can be modelled at all loading levels.

To have a more complete understanding of the effects of design on the performance of prosthetic

feet, other activities of daily living that are well understood should be examined and modelled.

86

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[42] McKenzie, D. S., and Muilenburg, A., 1978, "Standards for Lower-Limb Prostheses – Report of a Conference 1977," International Society for Prosthetics and Orthotics.

[43] Barth, D. G., and Sienko Thomas, S., 1992, "Gait Analysis and Energy Cost of Below-Knee Amputees Wearing Six Different Prosthetic Feet," Journal of Prosthetics and Orthotics, 4(2) p. 63.

[44] Haberman, A., Bryant, J. T., Beshai, L. M., 2007, "Mechanical Characterization of Prosthetic Feet," Proceedings of the 12th World Congress of the International Society of Prosthetics and Orthotics, Vancouver, BC, p.374.

89

Appendix A

Determination of Displacement Rate

During heel strike, the vertical velocity of the foot approaches 50 mm/sec. This rate of

displacement is difficult to achieve in a laboratory setting [13]. To determine if a slower more

reasonable rate of displacement could achieve similar displacement and stiffness values, a pilot

study was conducted.

The heel region of one of three Model 2 Version 18 Niagara Feet™ was loaded ten times with

varying wait times between tests. These wait time were randomized, and are shown in Table 8.

The foot was loaded at a rate of 2.0mm/sec to a peak load of 1173N. A pylon angle of 15° was

used.

A typical force-deflection curve of a heel can be described using three parameters, as shown in

Figure 33. The k1, k2 and kh values were determined for each test and the results are shown in

Table 8. The stiffness values appeared to be independent of the wait times tested. A wait time of

five minutes between tests was determined to be sufficient.

90

0

200

400

600

800

1000

1200

1400

0 2 4 6 8 10 12

Displacement (mm)

Forc

e (N

)

Region 2Region 1

k1

k2kh

Figure 33: Typical force deflection curve of a heel can be described using three parameters: k1, the slope of the curve in the first region, is defined as the initial stiffness of the foot; k2 is defined as the slope at the design load in the second region; kh is the average stiffness between 0N and the design load. For the toe region the same protocol is followed and the analogous parameters k3, k4 and kt are used [44].

91

Table 8: Three stiffness values from mechanical testing of a Model 2 Version 18 Niagara Foot™ conducted at varying time intervals.

Time Between Tests (min)

Test Number

Testing Order

k1 (kN/m)

k2 (kN/m)

kh (kN/m)

x @ 1000 (mm)

0 32.7 260.4 113.6 8.8

5 1 2 30.8 259.6 113.6 8.8

10 2 5 32.2 261.3 117.6 8.5

15 3 7 32.2 260.7 114.9 8.7

20 4 4 32.4 260.9 114.9 8.7

25 5 6 31.5 262.2 116.3 8.6

30 6 3 32.1 260.6 113.6 8.8

40 7 8 32.4 261.9 114.9 8.7

50 8 9 32.2 259.9 114.9 8.7

60 9 1 30.8 259.3 113.6 8.8

The heel and toe regions of one of three Model 2 Version 18 Niagara Feet™ were loaded at rates

of 0.25, 0.5, 1.0, 2.0 and 5.0mm/sec to a peak force of 1173N. Pylon angles of 15° and 20° were

used for the heel and toe regions respectively, and five minutes were allowed between each test.

The initial, average and tangential stiffness at 1000N was determined, as shown in Table 9. The

breakpoint for each of the three-parameters for both regions of the foot occurred at the

displacement rate of 1.0mm/sec. A displacement rate of 2.0mm/sec was selected because it was

above the breakpoint and allowed for the testing to be done in an efficient manner.

92

Table 9: Stiffness values for the heel and toe regions of a Model 2 Version 18 Niagara Foot™ tested at various displacement rates.

Heel Toe

Displacement Rate

(mm/sec)

Test Number

k1 (kN/m)

k2 (kN/m)

kh (kN/m)

Test Number

k3 (kN/m)

k4 (kN/m)

kt (kN/m)

0.25 9 26.5 229.2 105.3 10 4.7 52.2 26.4

0.5 2 28.5 230.8 109.9 5 4.9 52.8 26.9

1.0 7 28.9 235.9 107.5 6 5.1 54.9 27.9

2.0 4 29.9 239.1 112.4 8 5.2 55.3 28

5.0 3 30.5 238.5 114.9 1 5.4 55.8 28.2

To ascertain if the same displacement rate could be used to characterize the other three sample

feet, relaxation testing was conducted using the Instron™. The heel and toe of the four samples

were loaded to 1.495 times their design mass at a rate of 3.25mm/sec. Once again, pylon angles of

15° and 20° were used for the heel and toe regions respectively. Once the peak load was reached,

the platen’s position remained constant for 90 seconds and the resulting force values were

recorded. Using these data, the relaxation time and three constants were determined for the heel

and toe region of each of the feet as shown in Table 10. The values for the Model 2 Version 18

Niagara Foot™ were used as a benchmark; values for the other three feet were compared to those

of the Niagara Foot™. The relaxation times, initial decay values and decay coefficients for the

two Axtion™ Feet and the SACH foot were of the same order of magnitude as the benchmark

93

values. As a result, the heel and toe regions of these feet were also characterized at a displacement

rate of 2.0mm/sec.

Table 10: Relaxation parameters of the four sample feet.

Heel Toe Sample

A B tau A B tau

Niagara Foot 0.815 0.001 4.717 0.855 0.00982 4.9261

Axtion™ 106 kg 0.931 0.000388 4.505 0.977 0.000148 5.7471

Axtion™ 124 kg 0.911 0.000441 3.891 0.982 0.000122 5.4348

SACH 0.86 0.000919 4.098 0.817 0.000737 3.0303

94

Appendix B

Linear Extrapolation and Interpolation

The x-intercept of the force-displacement curves were determined by extrapolating back from the

first two data points, as shown in Figure 34.

0

2

4

6

8

10

12

0 1 2 3 4 5 6 7

Displacement (mm)

Forc

e (N

)

x0

Figure 34: Determination of the x-intercept using linear extrapolation.

x0

95

The x-intercept was subtracted from the displacement data to compensate for the offset origin, as

shown in Figure 35.

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25 30 35 40

1st Cycle8th Cycle

offset

Figure 35: Adjustment of the force-displacement data to compensate for the offset origin.

96

Linear interpolation of the data points above and below the design load was conducted to

determine the displacement at the design load, as shown in Figure 36.

1172.2

1172.3

1172.4

1172.5

1172.6

1172.7

1172.8

1172.9

1173

1173.1

30.542 30.544 30.546 30.548 30.55 30.552 30.554 30.556

Displacement (mm)

Forc

e (N

)

Experimental Data

Design Load

Figure 36: Determination of displacement at the design load using linear interpolation.

X1173

97

Appendix C

Mechanical Characterization of Dynamic Energy Return Prosthetic Feet: Complete Data Set

This Appendix contains the complete data set from the mechanical characterization study. Force-

displacement and stiffness-displacement curves, as well as the forces and tangential stiffnesses

occurring at the critical forces for the sample feet are shown in the following figures.

98

The data for the Niagara Foot™ are shown in Figure 37, Figure 38 and Figure 39

0

200

400

600

800

1000

1200

1400

0 2 4 6 8 10 12 14 16

Displacement (mm)

Forc

e (N

)

0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees

(a) heel

0

200

400

600

800

1000

1200

1400

0 10 20 30 40 50

Displacement (mm)

Forc

e (N

)

0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees

(b) toe

Figure 37: Force-displacement curves for (a) the heel and (b) the toe of the Niagara Foot™. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.

99

0

100

200

300

400

500

600

700

800

0 5 10 15

Displacement (mm)

Stiff

ness

(kN

/m) 0 Degrees

-5 Degrees-10 Degrees-15 Degrees-20 Degrees

(a) heel

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80

Displacement (mm)

Stif

fnes

s (k

N/m

)

0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees

(b) toe

Figure 38: Stiffness-displacement curves for (a) the heel and (b) the toe of the Niagara Foot™. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.

100

0

5

10

15

20

25

30

35

40

45

0 100 200 300 400 500 600

Time (msec)

Dis

plac

emen

t (m

m)

HeelToe

(a)

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700

Time (msec)

Stiff

ness

(kN/

m)

HeelToe

(b)

Figure 39: (a) Displacements and (b) tangential stiffness values of the Niagara Foot ™ occurring at the critical forces identified.

101

The data for the Axtion™ with a maximum recommended user weight of 106kg are shown in

Figure 40, Figure 41 and Figure 42.

0

200

400

600

800

1000

1200

1400

1600

1800

0 5 10 15 20 25

Displacement (mm)

Forc

e (N

)

0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees

(a) heel

0

200

400

600

800

1000

1200

1400

1600

1800

0 5 10 15 20 25 30

Displacement (mm)

Forc

e (N

)

0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees

(b) toe

Figure 40: Force-displacement curves for (a) the heel and (b) the toe of the Axtion™ foot with a maximum recommended user weight of 106kg. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12. .

102

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25

Displacement (mm)

Stif

fnes

s (k

N/m

) 0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees

(a) heel

0

50

100

150

200

250

0 5 10 15 20 25 30

Displacement (mm)

Stiff

ness

(kN

/m)

0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees

(b) toe

Figure 41: Stiffness-displacement curves for (a) the heel and (b) the toe of the Axtion™ foot with a maximum recommended user weight of 106kg. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.

103

0

5

10

15

20

25

30

0 100 200 300 400 500 600

Time (msec)

Disp

lace

men

t (m

m)

HeelToe

(a)

0

100

200

300

400

500

600

700

800

0 100 200 300 400 500 600

Time (msec)

Stif

fnes

s (k

N/m

)

HeelToe

(b)

Figure 42: (a) Displacements and (b) tangential stiffness values of the Axtion™ foot with a maximum recommended user weight of 106kg occurring at the critical forces identified.

104

The data for the Axtion™ with a maximum recommended user weight of 124kg are shown in

Figure 43, Figure 44 and Figure 45.

0200400600800

100012001400160018002000

0 5 10 15 20 25 30

Displacement (mm)

Forc

e (N

)

0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees

(a) heel

0200400600800

100012001400160018002000

0 5 10 15 20 25 30 35 40

Displacement (mm)

Forc

e (N

)

0 Degrees5 Degrees10 Degress15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees

(b) toe

Figure 43: Force-displacement curves for (a) the heel and (b) the toe of the Axtion™ foot with a maximum recommended user weight of 124kg. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12

105

0100200300400500600700800900

1000

0 5 10 15 20 25 30

Displacement (mm)

Stiff

ness

(kN/

m) 0 Degrees

-5 Degrees-10 Degrees-15 Degrees-20 Degrees

(a) heel

0

50

100

150

200

250

0 5 10 15 20 25 30 35 40

Displacement (mm)

Stiff

ness

(kN/

m)

0 Degrees5 Degrees10 Degree15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees

(b) toe

Figure 44: Stiffness-displacement curves for (a) the heel and (b) the toe of the Axtion™ foot with a maximum recommended user weight of 124kg. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.

106

0

5

10

15

20

25

30

35

40

0 100 200 300 400 500 600

Time (msec)

Disp

lace

men

t (m

m)

HeelToe

(a)

0

100

200

300

400

500

600

700

800

900

0 100 200 300 400 500 600 700

Time (msec)

Stiff

ness

(kN

/m)

HeelToe

(b)

Figure 45: (a) Displacements and (b) tangential stiffness values of the Axtion™ foot with a maximum recommended user weight of 124kg occurring at the critical forces identified.

107

The data for the SACH foot are shown in Figure 46, Figure 47 and Figure 48.

0

200

400

600

800

1000

1200

1400

1600

1800

0 5 10 15 20 25 30 35 40

Displacement (mm)

Forc

e (N

)

0 Degrees-5 Degrees-10 Degrees-15 Degrees-20 Degrees

(a) heel

0

200

400

600

800

1000

1200

1400

1600

1800

0 10 20 30 40 50 60

Displacement (mm)

Forc

e (N

)

0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees

(b) toe

Figure 46: Force-displacement curves for (a) the heel and (b) the toe of the SACH foot. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.

108

0

200

400

600

800

1000

1200

1400

1600

1800

0 50 100 150 200 250 300 350 400

Displacement (mm)

Stiff

ness

(kN/

m) 0 Degrees

-5 Degrees-10 Degrees-15 Degrees-20 Degrees

(a) heel

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60

Displacement (mm)

Stiff

ness

(kN

/m)

0 Degrees5 Degrees10 Degrees15 Degrees20 Degrees25 Degrees30 Degrees35 Degrees

(b) toe

Figure 47: Stiffness-displacement curves for (a) the heel and (b) the toe of the SACH foot. Loading or unloading curves are shown depending on the angle of interest based on the P4 loading curve in Figure 12.

109

0

5

10

15

20

25

30

35

40

45

0 100 200 300 400 500 600

Time (msec)

Dis

plac

emen

t (m

m)

HeelToe

(a)

0

50

100

150

200

250

300

350

0 100 200 300 400 500 600

Time (msec)

Stif

fnes

s (k

N/m

)

HeelToe

(b)

Figure 48: (a) Displacements and (b) tangential stiffness values of the SACH foot occurring at the critical forces identified.

110

Appendix D

Force-Relaxation Properties of Dynamic Energy Return Feet: Complete Data Set

This appendix contains the complete data set from the mechanical characterization study.

Reduced relaxation curves for the heel and toe sections of the sample feet are show in Figure 49

and Figure 50 respectively.

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

0 20 40 60 80 100

Time (sec)

F(t)/

F0

Niagara FootAxtion 106kgAxtion 124kgSACH

Figure 49: Reduced relaxation data for the heel of the sample feet.

111

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

0 20 40 60 80 100

Time (sec)

F(t)/

F0

Niagara FootAxtion 106kgAxtion 124kgSACH

Figure 50: Reduced relaxation data for the toe of the sample feet.

112

Experimental data, as well as the results of the two models, are shown in Figure 51 and Figure 52,

for the heel and toe of the Niagara Foot™ respectively.

0.7

0.75

0.8

0.85

0.9

0.95

1

0 20 40 60 80 100

Time (sec)

L(t)

Experimental2 Parameter3 Parameter

Figure 51: Reduced relaxation response for the heel of the Model 2 Version 18 Niagara Foot™.

113

0.7

0.75

0.8

0.85

0.9

0.95

1

0 20 40 60 80 100

Time (sec)

Forc

e (N

) Experimental2 Parameter3 Parameter

Figure 52: Reduced relaxation response for the toe of the Model 2 Version 18 Niagara Foot™.

114

Experimental data, as well as the results of the two models, are shown in Figure 53 and Figure 54,

for the heel and toe of the Axtion™ foot with a maximum recommended user weight of 106kg.

0.88

0.9

0.92

0.94

0.96

0.98

1

0 20 40 60 80 100Time (sec)

L(t) Experimental

2 Parameter3 Parameter

Figure 53: Reduced relaxation response for the heel of the Axtion® foot with a maximum recommended user weight of 106kg.

115

0.88

0.9

0.92

0.94

0.96

0.98

1

0 20 40 60 80 100Time (sec)

L(t) Experimental

2 Parameter3 Parameter

Figure 54: Reduced relaxation response for the toe region of the Axtion® foot with a maximum recommended user weight of 106kg.

116

Experimental data, as well as the results of the two models, are shown in Figure 55 and Figure 56,

for the heel and toe of the Axtion® foot rated for 124kg.

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

0 20 40 60 80 100

Time (sec)

L(t) Experimental

2 Parameter3 Parameter

Figure 55: Reduced relaxation response for the heel region of the Axtion™ foot with a maximum recommended user weight of 124kg.

117

0.965

0.97

0.975

0.98

0.985

0.99

0.995

1

0 20 40 60 80 100

Time (sec)

L(t)

Experimental2 Parameter3 Parameter

Figure 56: Reduced relaxation response for the toe region of the Axtion® foot with a maximum recommended user weight of 124kg.

118

The experimental data, as well as the results of the two models, are shown in Figure 57 and Figure

58, for the heel and toe of the SACH foot.

0.75

0.8

0.85

0.9

0.95

1

0 20 40 60 80 100

Time (sec)

L(t)

Experimental2 Parameter3 Parameter

Figure 57: Reduced relaxation response for the heel region of the SACH foot.

119

0.7

0.75

0.8

0.85

0.9

0.95

1

0 20 40 60 80 100

Time (sec)

L(t)

Experimental2 Parameter3 Parameter

Figure 58: Reduced relaxation response for the toe region of the SACH foot.