In Haughton's footsteps: mathematical insights into bioengineering and rehabilitation

Four attempts are outlined which the author has made to develop mathematical models for topics encountered in bioengineering and rehabilitation. The first is autoregulation in the kidney, for which a nonlinear oscillator model is derived, based on observations of flow noise made by Erol Basar. The second is a nonlinear observer based on the theory of automatic control, developed to study patterns of spastic torque in paralysed legs via the pendulum test. The third is a design study of a skeletal muscle reflex arc involving the muscle spindle dynamics and invoking a principle of optimum stability. The final topic is an attempt to lay the groundwork for a mathematical theory of the cross-bridge or sliding filament mechanism of muscular contraction.