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In haughton’s footsteps: Mathematical insights into bioengineering and rehabilitation

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Four attempts are outlined which the author has made to develop mathematical models for topics encountered in bioengineering and rehabilitation. The first isautoregulation in the kidney, for which a nonlinear oscillator model is derived, based on observations of flow noise made by Erol Basar. The second is anonlinear observer based on the theory of automatic control, developed to study patterns of spastic torque in paralysed legs via thependulum test. The third is a design study of a skeletal muscle reflex arc involving the muscle spindle dynamics and invokingprinciple 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.

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The Fourth Samuel Haughton Lecture presented to the joint meeting of the Section of Bioengineering and the Ulster Biomedical Engineering Society, Dundalk, Co. Louth, 21–22 February, 1998.

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de Paor, A. In haughton’s footsteps: Mathematical insights into bioengineering and rehabilitation. Ir. J. Med. Sc. 167, 170–180 (1998).

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