When a signal is initiated in the nerve, it is transmitted along each nerve 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. The additive superposition of SFAPs constitutes the compound action potential (CAP) of the nerve. The fiber diameter distribution (FDD) in the nerve can be computed from the CAP data by solving an inverse problem. This is usually achieved by dividing the fibers into a finite number of diameter groups and solve a corresponding linear system to optimize FDD. However, number of fibers in a nerve can be measured sometimes in thousands and it is possible to assume a continuous distribution for the fiber diameters which leads to a gradient optimization problem. In this paper, we have evaluated this continuous approach to the solution of the inverse problem. We have utilized an analytical function for SFAP and an assumed a polynomial form for FDD. The inverse problem involves the optimization of polynomial coefficients to obtain the best estimate for the FDD. We have observed that an eighth order polynomial for FDD can capture both unimodal and bimodal fiber distributions present in vivo, even in case of noisy CAP data. The assumed FDD distribution regularizes the ill-conditioned inverse problem and produces good results.

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 SFAPs constitutes the compound action potential (CAP) of the nerve. The fiber diameter distribution (FDD) in the nerve can be computed from the CAP data through an inverse problem. The common practice is to obtain a histogram for FDD using convolution. However, number of fibers in a nerve can be measured sometimes in thousands and it is possible to assume a continuous distribution for the fiber diameters, which is the approach we have taken in this work. Utilizing an analytical function for SFAP and assumed functional form for FDD, the inverse problem is formulated as a gradient optimization problem in order to determine the FDD that will result to the considered CAP. We have observed that an 8 th order polynomial can capture almost all fiber distributions present in vivo.