Determination of diameter distribution of nerve fibers from compound action potential data

Major nerves are made of large numbers of nerve fibers. When a signal is initiated in the nerve, it is transmitted along each fiber via an action potential (called single fiber action potential (SFAP)) which travels with a velocity that is related with the diameter of the fiber and whether the fiber is covered with a myelin sheath or not. The additive superposition of SFAP?s constitutes the compound action potential (CAP) of the nerve, a quantity that is often measured in clinical neurophysiology. The shape of the CAP and its traveling pattern is closely related with velocity distribution of the SFAP?s forming the CAP. After injuries or usage of certain drugs, the CAP profile of the nerve might change. It is important to understand which fibers are damaged/deactivated by these pathologies for diagnostic and therapeutic purposes.The number of fibers in a nerve can be measured sometimes in thousands. Hence, it is possible to assume a continuous distribution for the fiber diameters and the velocities of SFAP can be represented by an analytical function. For a given CAP, we have applied a (depending on the function type, linear or nonlinear) gradient optimization technique to determine the diameter distribution that will result to this CAP. We have assumed different types of functions, in particular polynomials and Gaussian distributions, whose parameters are found through optimization to give the best fit to the actual diameter distribution function. We have observed that an 8th order polynomial can capture almost all fiber distributions present in vivo.