ANKLE JOINT BIOMECHANICS

P. PKOCTER

Laboratorium fur Biomechanik. ETH-Zentrum. CH-PW2 Zurich

and

J. P. P\t I.

Bwn$neering Unit. University of Strathclyde, Glasgow. Scotland

Abstract--A three-dimensional analysis of the human ankle joint is presented to analyse data obtained from

gait laboratory tests. The ankle was treated as consisting of two joints. the talocrural (Tc.) and the talocalcaneonavicular (Ten.). and relevant anatomical dimensions were based upon cadaveric anthropomet-

ric data, Seven adult male subjects were studied during the stance phase of normal locomotion. Data was acquired from three orthogonally placed tine cameras and a force platform.

Two models were investigated based on force equilibrium; a Mark I model which excluded the posterior tibia1 and peroneal muscle groups and a Mark II model, which included them. The Mark II model gave the

followmp resultant peak forces expressed as multiples of body weight: Tc. joint force = 3.9; Ten. joint

forces-anterior facet = 2.4, posterior facet = 2.8. The latter model was felt to have good potential in the analytical assessment of ankle pathologies and endoprostheses.

I>TRODI CTIOS

The human ankle joint has already been extensively studied from anatomical and clinical viewpoints. In biomechanics it remains the last major joint system in

the leg for which a comprehensive three-dimensional

analysis has yet to be performed. Force analysis of the ankle joint for normal locomotion has hitherto been confined either to the consideration of external force

actions (Bresler and Frankel, 1950) or to calculation of the internal forces acting in simplified two- dimensional models of the ankle (Brewster et <I/.. 1974;

Stauffer ef al.. 1977).

The present study included the two principal joint systems of the ankle. the talocrural (Tc.) or upper ankle joint and the talocalcaneonavicular (Ten.) or lower ankle joint. The Tc. joint is usually considered to act as a simple hinge allowing flexion and extension of the talus relative to the shank segment. The Ten. joint is also thought to be basically uniaxial, permitting the motions of inversion and eversion of the hindfoot segment relative to the talus. The relative orientation of the Tc. and Ten. axes is illustrated in Fig. 1, using data published in the literature (Manter, 1941 ; Isman and Inman. 1969 : Inman. 1976). This figure illustrates the three-dimensional nature of these joints.

This paper outlines the development and evaluation of a three-dimensional model of the Tc. and Ten. joint systems for normal locomotion activity.

:t.\THROPOSIETRIC STCDIES

The ankle models formulated were based upon data gained from the literature together with dissec-

tion studies ofembalmed cadaver material. Altogether

five cadavers were dissected to obtain anthropometric data in re’spect of ligament. retinaculum and tendon

lines of action, bony reference point coordinates, and joint profiles. The cadaveric Tc. and Ten. joint axes were determined using the optical methods of Hicks

(1953) and Isman and Inman (1969); briefly this

Fig. I. The Tc. and Ten. axes projected on the right foot,

annoted sources: (al Manter (1911), (b) lsman and lnman (1969). and (c) Inman (1976).

628 P. PH(K‘TI.H and J. P. PAI L

involved fixing one segment whilst rotating the adjoin- ing segment, points of least motion indicating the location of the axis (for example fixing of the tibia and rotating the talus in Rexionextension gave stationary points medially and laterally on the talar body, through which the Tc. axis was assumed to pass). In addition joint profile information was established using the contouring techniques described by Inman (1976). who used a profile gauge to investigate the curvatures in the Tc. joint (the profile gauge is a simple device used for example by glaziers in fitting glass or tiles to irregular profiles).

One important finding of the dissection exercises was that, for the range of Tc. and Ten. joint motion obtaining in stance phase of normal locomotion (ap- proximately 30” and 10’ respectively; Root et al. 1971), the achilles tendon was the only tendon that changed its line of action by more than + 2.5” relative to the hindfoot segment.

This is illustrated in Fig. 2 for the achilles tendon and the tendons of the anterior tibia1 and peroneus brevis muscles. The relatively small deviations obser- ved in the remaining tendons were mainly attributed to the constraining effects of the bony and retinacular pulleys (although the effects of embalming upon soft tissues cannot altogether be discounted).

The data collected were simply averaged to provide one set of anthropometric data relative to an orthog- onal axis system (for a standard&d orientation of the shank and foot corresponding to erect stance).

Achilles tendon

Antersor t,b,a, tendon

Reterence‘pmnts f,xed reiat,ve to the hlndfoat segment

Flex,on-extemion t.fne of a&on angle -degrees degrees ! a b c

Fig. 2. Variation in the line of action of some shank muscle tendons relative to the foot, for different Tc. joint

Rexion*xtension angles.

I\TERPRET;\TIOS OF THE ,AS-\TOMIC.~L STL DIES

Prior to the interpretation of the anatomical data the possible strategies for solution were considered, since this has a considerable influence upon the complexity of model that can be analysed. The options considered included invasive techniques, optimisation function methods and equilibrium methods. From these an equilibrium method was selected as the approach ofchoice, there being greater doubts, at least in the authors’ minds, concerning the use of the former two. Invasive techniques are clearly precluded on ethical grounds. In the case of optimisation methods, these are still being developed and have been shown in some cases to predict muscle activity that conflicts with observed behaviour (Barbenel, 1972; Yeo, 1976).

The anatomical studies were therefore assessed with a view to reducing the unknown loads in the ankle to a level at which an equilibrium solution could be obtained.

The ligamentous and retinacular constraints were not included in the first two models developed. Phy- siologically acceptable solutions were obtained for walking activity without including these components.

The nutscles

Of the twelve muscles acting across the Tc. and Ten. joints, the plantaris and the peroneus tertius were neglected, being either small or absent altogether. The remaining muscles were combined into four groups based on phasic EMG evidence (University of Califor- nia, 1953) anatomical division and innervation (War- wick and Williams, 1973). The groups were peroneal, anterior tibial, posterior tibial, and calf. In the analysis the components of each group (with the exception of the calf group, where the component muscles share a common insertion into the calcaneus) were assigned weighting factors corresponding to their average ten- don cross-section as a proportion of the whole area for the group. As an example the total force exerted by the peroneal group was calculated as :

{F,,) = .(a. fF4 + b. (FPH)) (1)

where {Fj denotes a forcevector, with s. y and z being components. subscripts p pI_ and ,,H referring to peroneal group, peroneus longus and peroneus brevis respectively, and a = cross-sectional area of the peroneus longus tendon. b = cross-sectional area of the peroneus brevis tendon.

The assumption regarding tendon cross-section as a weighting factor was made in the absence of any other factor that was known to be a reliabte predictor of load sharing between co-operating muscles. The effect of this assumption was assessed by a perturbation me- thod in which it was assumed, for each group in turn, that only one member was active [this is the equivalent ofputting a = 1 and b = Oand then n = 0 and b = 1 in

Ankle joint blomechanlcs 629

equation (I)] uith the remaining groups keeping their assigned weighting factors. Calculations showed that

these procedures had only a small influence on the

solutions obtained in respect of resultant joint forces, the lines of action and points of application being so similar within the defined groups.

The calfgroup was the only group for kvhich the line of action was considered to change relative to the foot during walking activity. The calf line of action was calculated. for each instant of locomotion stance phase analysed, as a line passing between the origin areas of

the gastrocnemius and soleus muscles and the in- sertion of both muscles via the achilles tendon into the

posterior surface of the calcaneus. The three other muscle groups were assumed to have constant orien- tation with respect to the hindfoot segment (see earlier comments under anthropometric studies). Their orien- tation with respect to the Tc. joint was estimated at any

instant from the relative orientation of the shank and hindfoot segments.

Two internal axis systems were defined for the

models. one for each joint system. Both axis systems were defined relative to external bony points (anno-

tated in Fig. 51, for the position of the foot relative to the shank corresponding to erect stance. The Tc. axis

system was defined as fixed relative to the shank

segment and the Ten. system as fixed relative to the hindfoot segment. These definitions were necessary

because the talus is inaccessible to surface markers; the definitions mean that both the Tc. and Ten. axes systems rotate relative to the talus during stance phase, about the Tc. and Ten. axes respectively. The axes illustrated in Figs 3 and 4 are an instantaneous representation of the axes, their relative orientation

changing through stance phase. The Tc. flexion-extension axis was used as the Tc.

system 2 axis (positive direction medial to lateral), with an origin situated midway between the medial

and lateral malleoli. The Tc. Z axis together with a vector passing through the origin, perpendicular to the

sole of the foot, defined the YZ Tc. plane. The X Tc. axis was then defined by a vector normal to the YZ Tc. plane and passing through the origin (positive direc- tion posterior to anterior). The Tc. axis system is illustrated in Fig. 3(a). A similar procedure established the Ten. axis system. The Ten. inversion-eversion axis was designated as the Ten. system Z axis (positive direction anterior to posterior). The origin here was defined as the point on the Ten. axis midway between the anterior and posterior talocalcaneal articulations. The Ten. system is shown in Fig. 3(b).

Profiles of the Tc. and Ten. joint systems were made

specifically oriented to the axis systems as defined above. It was found that the centre ofcurvature and the axis of rotation approximately coincided for each

system. There was hokvever some e\ idencs LO suggest

incongruence at the Ten. joint. The general form of the ankle models. using the

features discussed abobe, is illustrated in Figs. ?(a) and

3(b).

FOR\IC’L.4TIOS OF THE \IODEL\

.i\D THEIR SOLC TlO\

The ankle was treated as two ripid free body segments, namely the talus alone and the talus plus hindfoot. The joint force systems were represented as shown in Fig. 4. The Tc. joint facets are slightly

bicondylar and the .Y and 1. Tc. forces nrrc’ divided into medial and lateral components actins through

points on the Z Tc. axis + l.Ocm either side of the origin. A component of the Tc. force was assumed to

act as a single force along the Z Tc. axis as shown m Fig. 4(a) (the possibility ofsplitting the Z Tc. force into

two components. one acting medially and the other laterally, was not considered). The Ten. fleets were also treated as two compartments, posterior talocal- caneal and anterior talocalcanesl plus talonavicular. The S and Y Ten. joint force components were assumed to pass through points on the Z Ten. axis

f2.0cm either side of the origin. This pave two components of S and Y Ten. joint force [se? Fig. 4(b)]. As in the Tc. system. a single component ofloint force

was assumed to act along the Z Ten. axis.

The choice of points on each Z axis through which

the joint force components were assumed to pass was not arbitrary; the origin for each system approx-

bi Talus lree body

Fig. 3. Free body diagrams for the ankle

P. PK(KTI.K and .I. P. P.ALI 630

/’ Fy camponAs

Fig. 4. Force actions assumed in the joint models.

imately divided the respective joint facets into two

compartments and the pointseither side ofeach origin were chosen to be centrally situated in the compart-

ments. The actual dimensions used were based upon the cadaver data.

The five components of joint force acting in each system provide suflicient necessary components for the force actions transmitted by the joints. The joint forces

together with the four muscle groups comprise a total of fourteen unknowns for which there are only twelve

equilibrium equations. Two possible models were formulated.

The Mark I model

In this model either the calf group or the anterior

tibia1 group were active. the relevant group being

selected according to the sign of the external moment acting about the Z Tc. axis. The phasic EMG evidence indicates that these groups divide in their stance phase activity. In this model there are eleven unknowns and the only component for which there is no obvious balancing factor is the moment acting about the ZTcn. axis. This moment was assigned the name Ten. residual moment. It effectively adds one more unknown, bring- ing the total to twelve.

The Mnrk II model

This included an equiiibrant for the Ten. residual

moment. Modified joint loading criteria and ligamen-

tous constraint were considered. but there is both EMG and clinical evidence to suggest that muscle force from either the posterior tibia1 or peroneal groups is the factor most likely to balance the residual

moment in the Mark I model. The criterion chosen for the inclusion of one or other of these groups was the

sign of the Ten. residual moment when referred to the right hand side of equation (5): in this case positive moment indicates peronsal activity and negative mo- ment posterior tibia1 activity. Since there is a possi-

bility that these two groups act as antagonists the solutions obtained are probably a minimum in respect of muscle and joint forces. In this model there are twelve unknowns.

Body segment inertial contributions to the moment

equations were estimated to be small (typically 1.0 N m maximum acts about the Z Tc. axis of the

ankle in stance phase) and were neglected.

Mark I model solutiort

This was obtained in two stages:

(i) the equilibrium solution for the Tc. system using the talus plus hindfoot free body. This yields the Tc. joint forces acting upon the superior talar facets, and the tension generated by either the calf or anterior tibia1 group. The Tc. equilibrium equations are:

forces: (F,,,, c) + IF,,,) + {F,; = 0 (2)

moments: {M,d, ,-i + {M,,,) + {M,) = 0 (3)

where f F) and (M) denote force and moment vectors respectively (the equations are expressed in vector notation for brevity and each comprises three com- ponent equations corresponding to .Y, _r and z direc-

tions). The subscripts are : .-it/C = anterior tibia1 or calf

group; JTc = Tc. joint force; E = external force

measurement. Equation (3) hasonly twocontributions to its Z component, due to the external force and to the muscle force; the joint force being assumed to pass through the Z Tc. axis has no moment about this axis.

The sign of the external moment Z component then indicates which of the anterior tibia1 or calf group

should be selected (tensile force being assumed to act in tendon). The joint force components may now be calculated.

(ii) the equilibrium solution for the Ten. system, using the talar free body, provides the Ten. joint forces and residual moment. The Ten. equilibrium equations

are given as:

forces: {F,,: Tm + {F,,,,: = 0 (4)

moments: {&I,,) rem + (MJTcni = 0 (5)

where subscript Ten refers the JTc components to the Ten. system, and subscript JTm designates Ten. joint

force. The Z Ten. moment equation contains only one

component, that due to the Tc. joint force resultant (it was assumed that the Ten. joint force resultant passed through the Z Ten. axis thus generating no Z com-

Ankle joint bivmechanics 631

ponrnt ). This component was earlier referred to as the

Ten. residual moment.

This \ras obtained in a similar way but this time equations 17) and (31 contain an additional unknown due either to the peroneal or to the posterior tibia1 group component : these equations become :

forces: IF ,,‘.: = -(IF,: f :F,,,,i + :F,,,))(6)

moments: ~>l,,-~~ = - (lXl,zi + ;>\I ,, (-1 + :>I,, ,,:)

(7)

where subscript P Pr refers to peroneal or posterior

tibia1 group. From the Mark I solution it was already known

which of either the calf or anterior tibiai group was active (the inclusion of either of the other two muscle groups was found not to affect this. their Z Tc. moment contributions being negligible at the point where activity sivitches from anterior tibia1 to calf). It was

known from the sign of the Ten. residual moment lvhich of the peroneal or posterior tibia1 groups were

active. Thus equations (6) and (7) could be written in terms of the approprtate unknown muscle forces. The left hand sides ofequations (6) and (7) are the Tc. joint force contributions. the right hand sides can therefore

bc substituted for the Tc. joint force components of equations (4) and (5) respectively. Equation (4) can novv be vvritten, using equation (6). as:

Fis. j E.xtsrn;il ii\es systems defined for the kinematic analysis.

and equation 15 ). using equation (7). as:

- ;:\I,: + :s1 (, (: + :\1,,,;; ,<.” L :Yl,,L,: = 0.

(9)

The Z Tc. moment equation of (7) contains only two

unknown muscle forces and the Z Ten. moment equation of (9) contains the same two unknowns (there being no Z moment components due to the joint forces in either case) thus simultaneous solution of both equations gives the two muscle forces. The solution for the joint force components proceeds as for the Mark I model, with equations (6) and (8).

THE ESPERISIE5T.4L PROCEDURES

Seven normal male subjects were studied during

normal locomotion activity (ages ranged from twenty to thirty years). Force measurements of stance phase forces were made using a Kistler force platform, the output from which was sampled at 50 Hz and stored

on tape by a PDP 12 digital computer. The kinematic data for the motion of the limb segments was obtained from tine film of bony point markers. Three orthog- onally placed tine cameras (Bolex Paillard) filmed the

subjects at fifty frames per second. The coordinates of the marked points were recovered from the films using a D-Mac trace analyser. True three-dimensional space coordinates Mere subsequently calculated, after cor- recting for parallax and errors introduced by the

camera lens and shutter mechanism. Two slternal marker systems were defined from the

kinematic data, these are both shown in Fig. 5. ,4n

external shank system, based upon a lateral malleolar origin, defined the position and orientation of the Tc. axis system and associated internal structures. the

cadaver data being scaled to fit the living subjects on a basis of uniform dilatation as used by Morrison (1970). An external hindfoot system defined the position and orientation of the Ten. system.

The kinematic data was filtered at 10 Hz using a 4th

order Butterworth filter, prior to the calculation of the external reference systems. Zarrugh and Radcliffe

(1979) considered that 20 harmonics were necessary for adequate signal reconstruction in the case olankle joint rotation. however one of their reconstructions with only 7 harmonics compares very well with the original signal over the stance phase period : 10 Hz was

therefore considered acceptable. Frame by frame the orientation and position of the

Tc. and Ten. systems were calculated relative to the external laboratory system. The kinematic data were related to the force platform origin via a marker, simultaneously visible to all three cameras, whose coordinates relative to this origin were known. The origin and principle axes of the laboratory system coincided with those of the Kistler force platform. The external forces could therefore be related directly to the Tc. and Ten. systems. All the calculations involved were performed using FORTRAN programs written for an ICL 1900 series computer.

632 P. PK(X‘TI:K and J. P. P \L L

Mark I model I

8CC A

Tensile

-t ci Tc ]olnt lateral compartment veti~cal force.

-t bl Ten. residual moment - mark I model

cl Summary EMG. curves- Unwers~ ty of Callfornla

Fig. 6. (a) Comparison of the Tc. joint lateral compartment

vertical force for Mark I and II models.(b) and (c)Illustration of the similarity between the Ten. residual moment and the

EMG. reported for the peronealiposterior tibia1 muscles.

RESULTS AND IX3XSSION

Two factors observed in the results indicated that

the Mark I model was incomplete. Firstly, the lateral compartment Tc. joint force vertical component chan- ged abruptly from compressive to tensile and then

back again at 857, of stance phase, shown in Fig. 6(a). This is clearly unacceptable since the joint force can only be compressive. Secondly the Ten. residual mo- ment, which was small for the first SO’,:< ofstance (range

O-5 N m), suddenly peaked to 35540N m at 85% stance [see Fig. 6(b)]. A further piece ofevidence from the results was that for one subject a tensile peak was observed in the medial compartment Tc. joint force vertical component coinciding with a marked negative

peak in the Ten. residual moment, again at 85% stance. These observations suggest that balancing factors that influence both Tc. and Ten. joint systems, acting

medially and laterally, are absent. The only major elements missing from the Mark I

model that are able to simultaneously provide equilib- rium for the Ten. residual loads and act on the Tc. joint are the peroneal and posterior tibia1 muscle groups. The EMG results obtained by the University of

KEY TO SUBJECTS

, ----- , -.-. 5

2 ---.-._ -_-...

I..........: 6

---

ml

0 50% 100% st once

Fig. 7. Tc. joint force resultant in the Mark II model.

California study (1953) show that peaks in the activity of both groups occur in late stance. [The University of

California results are summary curves and through this an important observation may have been ob-

scured, namely that reduced activity in the posterior

bl Postertor facet

Fig. 8. Ten. joint force resultants in the Mark II model. Key to subjects as in Fig. 7.

Ankle Joint blomechanlcs 633

+t FIG 9 Muscle group forces in the Mark II model. Key to

subjects ;ls in Fig. 7.

tibia1 group may be associated with increased peroneal

group activity and vice versa ; see Fig. 6(c)]. The prevailing clinical view is that the peroneal and

posterior tibia] groups ha!e little effect upon Tc. joint tlexion-extension control. but play an important role

in stabilising the Ten. joint. The Mark II model was formulated as described above and solved.

This provided acceptable solutions at the point where the Mark I model failed. the Tc. joint vertical force components bein: compressive throughout

stance phase [see Fig. 6(a)]. The resultant forcces cd

cu]atcd for the Ts. and Ten. joints are presented for normal locomotion of seven test subjects in Figs. 7 and

8. The associated muscle group forces are presented in

Fig. 9. The Tc. and Ten. joint forces show three distinct

peaks. nnnoted A. B and C in Figs. 7 and 8. The A peak is part of the “passive” response of the foot to the heelstrike event (Nigg er (11.. 1979). The B peak is associated with the anterior tibia] group activity.

whilst the C peak is in response to the calf muscles plus the late stance phase force peak obsensd in the

peroneal group. The dip between the B and C peaks coincides with the transfer from anterior tibiai to calf

group activity. The anterior and posterior compart- ment Ten. joint forces show similar peak characterls-

tics [see Fig. S. The peroneal and posterior tibia]

muscle groups show low levels of activity (range O-O.5 times body weight. hereafter B.W.) for the first half of

stance phase. This is followed by a sudden peak in peroneal force (in one subject posterior tibia1 I. There is

a striking similarity in the overall appearance of the peroneal group tunes of Fig. 9 and the envelope curves for EMG of the Cniversity of California [these curves are reproduced in Fig. 6(c)].

The peak forces observed and their ranges are tabulated for the Tc. and Ten. joints and the muscle groups in Table 1. The phasic activity of the calf and anterior tibia] groups corresponds closely with pub- lished EMG results (compared in Fig. IO) if account is

taken of the latenq period. The results for the prroneal

and posterior tibia1 muscles do not show such close correspondence in respect of phasic activity. but this is

undoubtedly due to the assumption that no antagonis- tic activity occurs between these groups.

There was only one case where the Mark II model was found to have problems; for one subject at very late stance the Tc. joint force passed marginally outside the joint bounds as defined by the cadaver studies. It may have been that this subject had slightly

larger Tc. joint profiles than suggested by the cadaver study. Unfortunately an X-ray study of normal sub- jects was not possible.

The probable error due to anthropometric\ariation and the assumed load sharing between muscle groups

Table I. Magnltudesandphnsingofthepeak resultant forces

634 P. PaocTEa and J. P. PALL

Fig. 10. A comparison between the temporal activity of the

muscle groups in the Mark II model and that reported horn

EMG studies.

was thought to be no worse than & lO_15?/,. The variation due to natural fluctuations in gait de- terminants was estimated as + IO’ib. This gave an overall estimate ofvariation due to experimental error,

cadaver anthropometric data and individual subject variability of *20-25’x.

CONCLUDING COMMEKTS

The Mark I model was physiologically unacceptable in respect of Tc. joint force loading. The Mark II model, a more realistic representation of the ankle joint musculoskeletal system, gave acceptable so- lutions for stance phase joint and muscle forces

without the inclusion of ligamentous constraint. It might be expected that in level surface walking liga- mentous loading would be minimal.

The peak joint force for the Tc. joint, 3.9 B.W. mean (2.9-4.7 B.W. range), is somewhat less than that re- ported by Brewster et al. (1974) (4.5-5.0 B.W.); the same source reported 3.5 B.W. mean peak achilles tendon force compared with 2.5 B.W. mean in the present study. These differences may be due to different walking velocities or to assumptions necessary in the

two-dimensional analysis of Brewster and colleagues regarding Tc. axis orientation and position. The

differences may be due in part to the problem of relating the external force system to internal structures whose exact position can only be estimated ; this is a general problem that affects all such studies.

The present study indicates substantial anterior

tibia1 activity, forces of 1.OB.W. mean peak were estimated and the group was active up to 25”/, stance on average. The model of Brewster et al. did not include this group, the calf group apparently being active for the whole of stance phase. A later model used by Stauffer et al. (1977) neglected the contribution of the anterior tibia1 group on the grounds that its peak

force was less than 0.2 B.FV. and that it was only active

for the first lo”, of stance phase (a result clearly at variance with the findings of the present study).

The analysis presented in this paper is considsrably

simpler than that required for joints higher in the leg

where inertial contributions of the limb segments must be taken into account. The Mark II model shows promise as a suitable vehicle for the study of effects of ankle pathology upon gait. and may be useful in the

assessment of different types of ankle endoprostheses. This model was used to investigate the behaviour of the normal ankle joint whilst walking upon planes sloping sideways at + 10’ and the results of this study aill be

published in a later paper. A Mark III model which

includes the medial and lateral collateral ligaments of the ankle is currently under development.

Acli,lo,vle~llleatp,lrs-This work is part oi a Ph.D thesis

recently submitted to the University of Strathclyde (Procter, 1980). The authors wish to acknowledge the support of a

British Science Research Council studentship during this study.

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