A CORDIC based real-time implementation and analysis of a respiratory central pattern generator

Abstract Central pattern generators (CPGs) are dedicated neural circuits which can generate rhythmic motor patterns even in absence of sensory input with extraordinary robustness and flexibility. In this paper, a biologically realistic model of a respiratory CPG with four neurons is implemented on a reconfigurable Field-Programmable Gate Array (FPGA) system. Considering the limitations of hardware resources, we first propose a modified respiratory CPG model with Coordinate Rotation Digital Computer (CORDIC) algorithm to save limited resources and reduce complexity. And then, all the multipliers are replaced with a method which is appropriate and effective for hardware implementation to avoid the use of the area-intensive multipliers. The implementation results show that rhythmic oscillations are successfully generated by the respiratory CPG network and the resource utilization is greatly reduced, which shows the potential for building large-scale spiking neural networks. The proposed high-performance and real-time implementation of the respiratory CPG network on the FPGA system can speed up the process to gain new insights into the respiratory network and can also be developed into applications for respiratory rhythm generation and modulation.

[1]  Karim Faez,et al.  A digital implementation of neuron-astrocyte interaction for neuromorphic applications , 2015, Neural Networks.

[2]  Roberto Barrio,et al.  Numerical detection of patterns in CPGs: Gait patterns in insect movement , 2020, Commun. Nonlinear Sci. Numer. Simul..

[3]  J. C. Smith,et al.  Models of respiratory rhythm generation in the pre-Bötzinger complex. II. Populations Of coupled pacemaker neurons. , 1999, Journal of neurophysiology.

[4]  J C Smith,et al.  Spatial and functional architecture of the mammalian brain stem respiratory network: a hierarchy of three oscillatory mechanisms. , 2007, Journal of neurophysiology.

[5]  Peter W. Glynn,et al.  Discretization Error in Simulation of One-Dimensional Reflecting Brownian Motion , 1995 .

[6]  J. Lu,et al.  A Model of a Segmental Oscillator in the Leech Heartbeat Neuronal Network , 2001, Journal of Computational Neuroscience.

[7]  Bernard Girau,et al.  The role of the asymptotic dynamics in the design of FPGA-based hardware implementations of gIF-type neural networks , 2011, Journal of Physiology-Paris.

[8]  Bruce G Lindsey,et al.  Computational models and emergent properties of respiratory neural networks. , 2012, Comprehensive Physiology.

[9]  Andres Espinal,et al.  A FPGA-Based Neuromorphic Locomotion System for Multi-Legged Robots , 2017, IEEE Access.

[10]  Rashid Rashidzadeh,et al.  A CORDIC Based Digital Hardware For Adaptive Exponential Integrate and Fire Neuron , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  Daniel K. Hartline,et al.  Pattern generation in the lobster (Panulirus) stomatogastric ganglion , 1979, Biological Cybernetics.

[12]  Bin Deng,et al.  Cost-efficient FPGA implementation of basal ganglia and their Parkinsonian analysis , 2015, Neural Networks.

[13]  Bin Deng,et al.  Efficient implementation of a real-time estimation system for thalamocortical hidden Parkinsonian properties , 2017, Scientific Reports.

[14]  Shanq-Jang Ruan,et al.  Low-power and high-quality Cordic-based Loeffler DCT for signal processing , 2007, IET Circuits Devices Syst..

[15]  E. Marder,et al.  Central pattern generators and the control of rhythmic movements , 2001, Current Biology.

[16]  K. Sridharan,et al.  50 Years of CORDIC: Algorithms, Architectures, and Applications , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  Ralph Etienne-Cummings,et al.  Toward biomorphic control using custom aVLSI CPG chips , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[18]  M. I. Cohen,et al.  Neurogenesis of respiratory rhythm in the mammal. , 1979, Physiological reviews.

[19]  Kazuyuki Aihara,et al.  Qualitative-Modeling-Based Silicon Neurons and Their Networks , 2016, Front. Neurosci..

[20]  Jianwei Zhang,et al.  A Survey on CPG-Inspired Control Models and System Implementation , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[21]  Arash Ahmadi,et al.  An analog implementation of biologically plausible neurons using CCII building blocks , 2012, Neural Networks.

[22]  Ilya A Rybak,et al.  Computational modelling of 5‐HT receptor‐mediated reorganization of the brainstem respiratory network , 2011, The European journal of neuroscience.

[23]  Jiang Wang,et al.  Digital implementations of thalamocortical neuron models and its application in thalamocortical control using FPGA for Parkinson's disease , 2016, Neurocomputing.

[24]  Yannick Bornat,et al.  Bio-Inspired Controller on an FPGA Applied to Closed-Loop Diaphragmatic Stimulation , 2016, Front. Neurosci..

[25]  Ilya A. Rybak,et al.  Interacting oscillations in neural control of breathing: modeling and qualitative analysis , 2011, Journal of Computational Neuroscience.

[26]  Sergey N Markin,et al.  Spatial organization and state-dependent mechanisms for respiratory rhythm and pattern generation. , 2007, Progress in brain research.

[27]  Arash Ahmadi,et al.  Biologically Inspired Spiking Neurons: Piecewise Linear Models and Digital Implementation , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  Derek Abbott,et al.  A Digital Neuromorphic Realization of Pair-Based and Triplet-Based Spike-Timing-Dependent Synaptic Plasticity , 2018, IEEE Transactions on Circuits and Systems II: Express Briefs.

[29]  Hassan Asgharian,et al.  FPGA implementation of a biological neural network based on the Hodgkin-Huxley neuron model , 2014, Front. Neurosci..

[30]  Juan Martín Carpio Valadez,et al.  Design of Spiking Central Pattern Generators for Multiple Locomotion Gaits in Hexapod Robots by Christiansen Grammar Evolution , 2016, Front. Neurorobot..

[31]  Hassan Mostafa,et al.  A Low Power CORDIC-Based Hardware Implementation of Izhikevich Neuron Model , 2018, 2018 16th IEEE International New Circuits and Systems Conference (NEWCAS).

[32]  A. Frigon.  Central Pattern Generators of the Mammalian Spinal Cord , 2012, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[33]  J. C. Smith,et al.  Models of respiratory rhythm generation in the pre-Bötzinger complex. I. Bursting pacemaker neurons. , 1999, Journal of neurophysiology.

[34]  César Torres-Huitzil,et al.  A CPG system based on spiking neurons for hexapod robot locomotion , 2015, Neurocomputing.

[35]  Yiran Chen,et al.  A low-cost and high-speed hardware implementation of spiking neural network , 2020, Neurocomputing.

[36]  Joseph Ayers,et al.  Oscillations and oscillatory behavior in small neural circuits , 2006, Biological Cybernetics.

[37]  Majid Ahmadi,et al.  Digital Hardware Implementation of Gaussian Wilson–Cowan Neocortex Model , 2019, IEEE Transactions on Emerging Topics in Computational Intelligence.

[38]  Jiang Wang,et al.  A real-time FPGA implementation of a biologically inspired central pattern generator network , 2017, Neurocomputing.

[39]  Yong Dou,et al.  FPGA implementation of an exact dot product and its application in variable-precision floating-point arithmetic , 2012, The Journal of Supercomputing.

[40]  John Stephen Walther,et al.  The Story of Unified Cordic , 2000, J. VLSI Signal Process..

[41]  J. C. Smith,et al.  Pre-Bötzinger complex: a brainstem region that may generate respiratory rhythm in mammals. , 1991, Science.

[42]  J C Smith,et al.  Respiratory rhythm generation in neonatal and adult mammals: the hybrid pacemaker-network model. , 2000, Respiration physiology.

[43]  Dongdong Chen,et al.  Fixed-Point CORDIC-Based QR Decomposition by Givens Rotations on FPGA , 2011, 2011 International Conference on Reconfigurable Computing and FPGAs.

[44]  G. Ermentrout,et al.  Multiple rhythmic states in a model of the respiratory central pattern generator. , 2009, Journal of neurophysiology.