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Modeling

Currently I am interested in modeling human postural control using simplified representations of the musculoskeletal system.  Specifically I am investigating how humans can remain standing when the ground moves suddenly.  This behavior is like when you get on a city-bus and attempt to remain standing while the bus makes its many starts and stops.  Below are some small interactive examples of simple models of human posture.

Cart-and-Pendulum

The cart-and-pendulum model is the simplest way of describing how the body is capable of maintaining its center-of-mass above its base-of-support.




The pendulum (black bar) represents the body, while the cart represents the perturbation (ground moving).  The goal of the body is to maintain upright by controlling the various joints of the skeleton.  In this simplified model the control of the joints is lumped into the single joint between the pendulum and the cart.

I used Matlab and Processing to develop an interactive model of this system.  Clicking and dragging on the model window will allow you to change the initial angle of the pendulum.  Here is the Web Applet.

Double-pendulum with Cart

The double-pendulum model is a simplified model of the anterior-posterior motion of a standing human. This simulation mimics an experimental protocol where a subject is placed on a translational platform.  The platform movement is sudden, causing a disturbance similar to the sudden start/stop of a subway car to the standing subject.  Examining the patterns of muscle activation and motion of the body helps to reveal how the nervous system interacts with the musculoskeletal system.  In this model the cart represents the translational platform and the links the legs and trunk of the subject. A slightly more in depth modeling project is outlined here for an inverted double pendulum.

Four-bar Linkage

The four-bar linkage model is a simplified model of human standing in the coronal plane.  This is particularly interesting for analyzing configurational changes on human stability.  Merely by changing the geometry of the skeleton the physical outcomes of perturbations and muscle forces will be different.  One can think of this as changing the body from an inverted pole into a triangle.  Push one and it is certain to fall over, push the other and it may not even move.

 

The four-bar linkage already looks like the lower half of a person facing you.  The bar at the top represents the entire upper body of a person, the other two bars are the legs.  So that's only three bars, you ask?  Well, the ground is considered as the fourth bar.

Matlab and Processing were used to implement an interactive model of this system.  Clicking and dragging on the model window will allow you to change the stance width, joint stiffness and joint damping.  Here is the Web Applet.


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