Document Type


Date of Degree

Summer 2010

Degree Name

PhD (Doctor of Philosophy)

Degree In

Biomedical Engineering

First Advisor

Dove, Edwin L.

Second Advisor

Shields, Richard K.

First Committee Member

Frey-Law, Laura A.

Second Committee Member

Grosland, Nicole M.

Third Committee Member

Mackey, Michael A.

Fourth Committee Member

Bai, Er-Wei


Paralyzed muscle fatigues more quickly than intact muscle. The reason for this difference is currently unknown. This work will bridge this gap in knowledge by evaluating the predictive abilities of higher-resolution closed-form mathematical models of muscle force and fatigue. Knowledge garnered from this effort will suggest possible mechanisms for the differences in fatiguability of muscle in different states of health.

The hypothesis to be tested is that the concept missing from present models, and thus the present understanding of the physiology, is the dynamic behavior of divalent calcium (Ca2+) during induced muscle contraction. If the behavior of Ca2+ can be understood as a Riccati-Bass diffusion process, muscle force and low-frequency fatigue in paralyzed muscle can be more accurately predicted over the time course of response to neuromuscular electrical stimulation. The abilities of existing mathematical models to predict force and low-frequency fatigue are compared to the predictive abilities of new models that include the Riccati-Bass equation.

There are several major findings of this study. First, it was found that the structure of the Conaway models better predicts force and low-frequency fatigue than do the Ding models. Second, the cross-bridge friction is the most influential factor in generating force in fresh muscle at frequencies greater than 5 pps. Finally, the calcium leak current is most influential in low-frequency fatigue in paralyzed muscle. It is concluded that the process of muscle fatigue occurs as calcium channel remodeling and inactivation of excitation-contraction coupling from ionic crowding accelerate with every additional contraction.


calcium current, denervated muscle, mathematical models, muscle fatigue, Riccati equation, spinal cord injury


xxvii, 375 pages


Includes bibliographical references (pages 358-375).


Copyright 2010 Matthew James Conaway