Measurement of postural sway: posturographic instrumentation

66--components force plattformcomponents force plattform

33--components force platformscomponents force platforms

Pressure platformsPressure platforms

Measurement of postural sway: the dynamometric or force platform

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Force sensors

Distributed load on the platform⇓

Stress on the support elements ⇒ (3 or 4) force sensors⇓

Resultant stress: force (3 components) & moment (3 component)or

Resultant force vector & Center of pressure (COP)

Force platform: piezoelectric vs estensimetric (strain gauges)

Force sensors

Force sensorsPiezoelectric: strain-modulated capacitors; higher bandwidth and sensitivity,

no DC component; charge amplifiers; better for gait analysisStrain gauges: strain-modulated resistors; lower bandwidth and sensitivity; DC

component; Wheatstone bridge + operational amplifier; better for posturography

Force sensorsMono-componentMulti-component (usually 3)

Leading manufacturers: Kistler, AMTI

Force platform: 6 components

Force sensors

Multi-component force sensorslinearity between force-sensor readings and the 6 components of the resultant

stressthe proportionality matrix [M] is estimated by means of a calibration procedure

in the factory, in which stress and sensor readings are both known and is provided by the manufacturer as an integral part of the instrument

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Leading manufacturers: Kistler, AMTI, Bertec

Force platform: 3 components

Force sensors

In posturography (not in gait analysis) Fx, Fy, Mz are very small in comparison with the other components and thus can be neglected

Mono-component force sensors (strain-guage load cells)

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Local manufacturer: RGM

Measurement of postural sway: pressure mats

ElasticElasticmaterial material

FF

Matrix of force sensors that are scanned during acquisition of a force image

Reistive sensors or capacitive sensors

Problems: creep & hysteresislimited accuracy and bandwidth

Leading manufacturer: Novel

Measurement of postural sway: pressure insoles

Leading manufacturer: Tekscan

Matrix of force sensors that are scanned during acquisition of a force imageReistive sensors or capacitive sensors

Problems: creep & hysteresislimited accuracy and bandwidth

Measurement of postural sway

Relevant variables:1. Centre of mass (COM)2. Centre of Pressure (COP)3. Force of gravity (applied to the COM)4. Ground reaction (applied to the COP)5. Ankle torque

Posturographic signals: Statokinesigrams & posturograms (different visualizations of the COP)

COP vs COM

COM & COP are similar

Strongly correlated but different frequency bandwidths:

0.5 Hz vs 5 Hz

COM [mm]

COP vs COM

The COP signal is measured by the force platform.

The COM signal is evaluated indirectly in one of two methods:

1. Acquisition of full-body model by means of stereophotogrammetry + usage of an anthropometric model + application of the basic definition of COM

2. Exploiting the dynamic equation of sway and transforming it into a low-pass filter

( )COPCOMhg

dtCOMd

−=2

2( ))()()()( 2 ωωωω COPCOMCOM FF

hgFj −=

)(/

/)( 2 ωω

ω COPCOM Fhg

hgF+

=

COM [mm]

Phenomenological analysis: global parametrs

Space-time domain

Frequency domain

Phenomenological analysis: Diffusion plot

Collins and De Luca 1993

Sway is interpreted as a fractional Brownian motion

In a pure Brownian motion the variance of ∆X, ∆ Y, ∆L grows linearly with ∆t.

In a fractional Brownian motion there is a critical time

Parameters: critical time and critical variances

1. “Clusters” of samples (slow phases)2. Quick shifts from one cluster to another

Beyond the apparent randomness of theposturogram there is a regular structure,characterized by:

Definition of the Sway-Density Plot:For each time instant, the number of consecutivesamples of the COP which fall inside a circle ofgiven radius (R=2.5 mm), multiplied by thesampling time.

Baratto L, Morasso P, Re C, Spada G (2002) A new look at posturographic analysis in the clinical context: sway-density vs. other parameterizationtechniques. Motor Control, 6, 248-273

Phenomenological analysis: Sway density plot

Sway Density parameters

Sampling frequency: 100 Hz

Raw plot

Low-passfiltered plot (2.5 Hz)

MT: mean time between peaks

MP: mean value of the peaks

MD: mean distance between the peaks

Sway density plots

Most discriminant posturographic paremteres

NOR: nomaliOPR: osteoporoticiPAR: parkinsoniani

Measurement features

General characteristics of the measurement systems:Linearity/hysteresisResolution (N, Nm, mm)Frequency bandwith (Hz)

Clinically relevant features in posturography:Spatial resolution of the COP: 0.1 - 0.2 mmFrequency band: it must include 0 Hz and exceed 5 Hz

Which is the influence of the heart beat on the posturographic traces?

Method of the synchronized averaging (typically used in Evoked Potentials), using as trigger the peak P of the QRS complex in the ECG

Conforto et al 2001

Cardiac activity force

Consider the AP component of the cardiac activity force: the variance of the signal is about F=0.15 N.Supposing that the mass of the subject is m=80 kg, the height of the come is h=0.85 m, we can estimate the COP shift ∆u:τ=F⋅h=mg ⋅ ∆u ⇒ ∆u=0.16 mm

AP

The need of calibration: force platforms are precision instruments

Two approaches:static point to point loadingdynamic loading

Dynamic calibration device

Recalibration

Before calibration

After calibrationCalculating the degree of

isotropy and estimating a calibration matrix

Dynamic equations of sway

Free body diagram

( )uyhgy

e−=&&

Morasso & Sanguineti, J. Neurophysiol. 2002

Foot

0=− mgumτ

Upper body

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Instability of the system

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U(s)

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e

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/2 −−

ControllerY(s)

The COP is the control variable

The COM is the controlled variable

The plant has one pole in the right plane: eh

gs ±=

ϑττ &&Igm =+−

Instability of the system

II

mghm /τϑϑ −=&&

τm(s)

ImghsI

//1

2 −−

Controllerθ(s)

The ankle torque is the control variable

The sway angle is the controlled variable

The plant has one pole in the right plane: I

mghs ±=

ϑττ &&Igm =+−

actam K τϑτ +=– Destabilizing torque:– Control torque:

The role of intrinsic ankle stiffness

mghK c =

ϑτ mghg =

Critical value of anklestiffness

ϑττ &&Igm =+−

ϑϑτ )( aact KmghI −−=− &&

⇒<⇒>

ca

caKKKK The system is intrinsically asymptotically stable

The system is unstable and must be stabilized by active control

Estimation of ankle stiffness

Casadio et al, Gait & Posture 2005

Pattern of recovery fromunpredicted disturbances:

Backward pull due to muscle stiffness (GM+GL)

Initiation of the backward fall

Stabilization of the fall due to anticipatory activation of the TA

Direct measurement of ankle stiffness

ϑϑϑτ aaaa KBItumg ++=∆⋅= &&&)(

Direct measurement of ankle stiffness

ca KK %65≈

Stiffness control, by alone, is insufficient to stabilize upright standing

ca KK %90≈

deg05.0=∆ϑ

Direct measurement of ankle stiffness

Casadio, Morasso & Sanguineti, Gait and Posture, 2004

deg1=∆ϑ

2005

Stabilization by linear continuous closed loop control

Phase portrait

Flowlines of the inverted pendulum

Phase portrait

Phase portrait

Scalar product between the flowlines of the inverted pendulum and the swayline:

cos=1: falling

Aaverage duration of the falling phases: 0.4±0.38 s

The control is intermittent

Decomposition of the ankle torque

)()( tumgta ⋅=τ

Jacono, Casadio, Morasso, Sanguineti. Motor Control,2004

tonic component (67%)

anticipatory phasic component (13%)

stiffness component (20%)

STRATEGIES OF POSTURAL STABILIZATION: STRATEGIES OF POSTURAL STABILIZATION: COP strategyCOP strategy

Ankle Strategy or COP Strategy:direct – quick - anticipatory mechanism

Gagey et al 2002

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STRATEGIES OF POSTURAL STABILIZATION: STRATEGIES OF POSTURAL STABILIZATION: COM strategyCOM strategy

Hip Strategy or COM Strategy: Indirect – slow - feedback mechanism

Gagey et al 2002

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