BIOENGENEERING WORK

Introduction to Bioengineering

An important topic in Bioengineering is the electrical behavior of nerves. The one-dimensional cable equation (originally derived to describe electrical signals sent over a submarine telegraph cable) is central to understanding the propagation of action potentials along a nerve axon and the electrical stimulation of nerves. Current can flow along the length of an axon (the x-direction), or can pass out of the axon through the resistance and capacitance of the membrane. The first problem below deals with the cable equation. Often when dealing with nerves and muscle, we measure the voltage V with respect to the resting potential.

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Many animals have myelinated nerves, in which the axon is wrapped in a myelin (fat) sheath to increase its membrane resistance. The myelin is interrupted every millimeter or so at the nodes of Ranvier as we have learned, so a myelinated axon consists of active regions at the nodes connected by long passive cables between nodes. The purpose of the myelin is to increase the length constant in the cable equation, and thereby speed up propagation of the action potential. The next two problems analyze myelinated axons, an analysis performed originally by Rushton.

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Neural stimulation is crucial to developing technology that can excite axons and thereby restore function. The cochlear implant, a device to stimulate the auditory nerve and restore hearing to the deaf, is an example of how neural stimulation can contribute to medicine. Deep brain stimulation to treat Parkinson’s disease is another example. Electrical stimulation of the heart is also critical in the design of cardiac pacemakers and defibrillators. The next problem considers a simple example of electrical stimulation.

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