Jerry Jacob, Nitish Patel, Sucheta Sehgal
The University of Auckland


Aim: The Fourier Series methodology (FSM) has shown promise in emula- tion of action potential (AP) of biological cells. We aim to establish a suitable implementation technique for hardware platforms - specifically FPGAs without floating point units. The Direct Digital Synthesis (DDS) and Resonant Model (RM) techniques are reported. Method: The accuracy of the FSM is reliant on the selection of harmonics. However, a trade-off between accuracy and usage of silicon real-estate is nec- essary. The AP waveshape is a significant factor and hence this study considers 4 different APs from various cell models. The comparative metrics are based on a Cyclone V FPGA as well as an ‘atomic’ NAND gate count. Specifically, we obtain the parameters of the FSM with 8 harmonics from MATLAB and implement the FSM on an FPGA using integer/fixed-point operations. Typical performance metrics have been obtained and tabulated. Results: The AP waveshapes of the cell models (FitzHugh Nagumo, Beeler Reuter, Luo Rudy I and Fenton Karma model) were used as reference. The re- construction of these AP wave- shapes with DDS and RM cap- tures 95% to 98% of the trend. However, the silicon usage varies. The synthesis of the DDS and RM design gives the NAND gate utilization summary for 32-bit inputs. Table 1 (in pdf abstract) shows the number of NAND gates used by various components of the DDS and RM. It has been seen that the silicon utilized by RM implementation is almost 8.5 times lesser than the DDS ap- proach. This comparison is also justified by the estimation of logic utilization using Cyclone V SoC in Quartus Prime 20.1 Lite. Conclusion: The RM offers a much lower hardware footprint when com- pared to the DDS. Hence, RM can emulate a large number of cells with fewer resources.