Pipelined FPGA implementation of numerical integration of the Hodgkin-Huxley model

The Hodgkin-Huxley model describes the initiation and propagation of action potential in neurons' axons. The model consists of a set of nonlinear differential equations that can be solved using numerical methods for a given choice of parameters. As the equations reflect physiological processes, the value of those parameters are subject to great variability. Therefore, numerical integration is often combined with differential evolution methods in order to find which set of parameters minimizes some fitness function. As modern FPGAs are large enough to implement complex functions using double-precision floating-point arithmetic, intensive scientific computations may be carried out showing competitive performance and cost. In this work, we present a pipelined architecture for performing the 4th order Runge-Kutta integration of the equations of the Hodgkin-Huxley model, introducing convenient implementations of complex mathematical functions.