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Watching quiet human stance to shake off its straitjacket

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Abstract

The single-inverted pendulum (SIP) model is still the paradigm describing dynamics and control of quiet human stance in the sagittal plane. We used two methods to verify this paradigm. First, in an experimental approach we acquired kinematic data of both legs of ten subjects at high spatial resolution while quietly standing on two force platforms. We calculated all leg joint angles, the belonging joint torques using inverse dynamics and estimates of joint stiffnesses. Some linear correlations and regressions of both local (joint) and global (COM, COP: centre of mass respectively pressure) variables predicted by the SIP model were investigated. All three verification criteria applied to mean values extracted from experimental data revealed that the SIP is not a valid model for quiet human stance. As a second method, we used computer synthesis to demonstrate that a double-inverted pendulum (DIP) model enters a stable attractor when just the “hip” joint torque is regulated, whereas no torque is applied to the “ankle” joint. Here, angle and torque fluctuations are necessary because such a DIP strategy is of inevitable dynamic character. The two predicted eigenfrequencies of this regulated DIP model approximate the upper and lower limits of the main part of measured power spectra of quiet human stance. We suggest this dynamic necessity to be representative of the biological constraints under which a mechanically unstable inverted multi-segment chain must be stabilised.

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Abbreviations

(Time) sequence:

An array of values of measured variables (positional or force components) sampled discretely versus time

Trial:

Acquisition of one (consistent and synchronised) data set containing all (time) sequences of the measured variables

N :

Number of trials (60)

f s :

Sampling frequency of the kinematic data (115.5Hz)

f h :

High-pass cutoff-frequency of the kinetic data (\({\frac{1}{8}\,{\rm Hz}}\))

SIP:

(Single)-inverted pendulum

DIP:

Double-inverted pendulum

Segment:

A fraction of whole body mass located between joints (right and left foot, shank, thigh plus HAT)

HAT:

Segment including head, arms, and trunk

COM:

Centre of mass

COP:

Centre of pressure

HAT-COM:

COM of the HAT-segment

GRF:

Ground reaction force

DOF:

Degree of freedom

s.d.:

Standard deviation

min:

Minimum

max:

Maximum

\({\mathcal{M}}\) :

Body mass

g :

Gravitational acceleration

h :

Distance between ankle joint and COM

Θcom :

Moment of inertia for the body rotating around its COM (\({\approx \frac{1}{5}\cdot \mathcal{M}\cdot h^{2}}\))

Θ:

Body moment of inertia for rotation around ankle joint (\({=\mathcal{M}\cdot h^{2} + \Theta_{\rm com}}\))

K :

Rotational “ankle stiffness” of the SIP model (i.e., unit: N m/rad)

K ankle :

Sum of real, measured right and left ankle stiffnesses

K crit :

Critical “ankle stiffness” (\({= \mathcal{M}\cdot g\cdot h}\))

K eff :

Effective stiffness for the SIP model ( = K − K crit)

ω :

Angular eigenfrequency of the SIP model \({\left(=\sqrt{\frac{K - K_{\rm crit}}{\Theta}}\, = \,\sqrt{\frac{K_{\rm eff}}{\Theta}}\right)}\)

ν :

Eigenfrequency of the SIP model \({\left(= \frac{\omega}{2 \pi}\right)}\)

\({\tau_{\rm acc}^{2}}\) :

\({= \frac{\Theta}{K_{\rm crit}}\, = \,\left(\frac{K}{K_{\rm crit}} - 1\right) \cdot \frac{1}{\omega^{2}}\, = \,\frac{K_{\rm eff}}{K_{\rm crit}}\cdot \frac{1}{\omega^{2}}}\)

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Authors and Affiliations

  1. Orthopädische Klink, Biomechaniklabor, Eberhard-Karls-Universität, Hoppe-Seyler-Straße 3, 72076, Tübingen, Germany

    Michael Günther & Otto Müller

  2. Institut für Sportwissenschaft, Lehrstuhl für Bewegungswissenschaft, Friedrich-Schiller-Universität, Seidelstraße 20, 07749, Jena, Germany

    Michael Günther & Reinhard Blickhan

  3. Institut für Sportwissenschaft, Arbeitsbereich III, Eberhard-Karls-Universität, Wilhelmstraße 124, 72074, Tübingen, Germany

    Michael Günther

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Günther, M., Müller, O. & Blickhan, R. Watching quiet human stance to shake off its straitjacket. Arch Appl Mech 81, 283–302 (2011). https://doi.org/10.1007/s00419-010-0414-y

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