{"title": "Multi-scale Hyper-time Hardware Emulation of Human Motor Nervous System Based on Spiking Neurons using FPGA", "book": "Advances in Neural Information Processing Systems", "page_first": 37, "page_last": 45, "abstract": "Our central goal is to quantify the long-term progression of pediatric neurological diseases, such as a typical 10-15 years progression of child dystonia. To this purpose, quantitative models are convincing only if they can provide multi-scale details ranging from neuron spikes to limb biomechanics. The models also need to be evaluated in hyper-time, i.e. significantly faster than real-time, for producing useful predictions. We designed a platform with digital VLSI hardware for multi-scale hyper-time emulations of human motor nervous systems. The platform is constructed on a scalable, distributed array of Field Programmable Gate Array (FPGA) devices. All devices operate asynchronously with 1 millisecond time granularity, and the overall system is accelerated to 365x real-time. Each physiological component is implemented using models from well documented studies and can be flexibly modified. Thus the validity of emulation can be easily advised by neurophysiologists and clinicians. For maximizing the speed of emulation, all calculations are implemented in combinational logic instead of clocked iterative circuits. This paper presents the methodology of building FPGA modules in correspondence to components of a monosynaptic spinal loop. Results of emulated activities are shown. The paper also discusses the rationale of approximating neural circuitry by organizing neurons with sparse interconnections. In conclusion, our platform allows introducing various abnormalities into the neural emulation such that the emerging motor symptoms can be analyzed. It compels us to test the origins of childhood motor disorders and predict their long-term progressions.", "full_text": "Multi-scale Hyper-time Hardware Emulation of\nHuman Motor Nervous System Based on Spiking\n\nNeurons using FPGA\n\nC. Minos Niu\n\nDepartment of Biomedical Engineering\n\nUniversity of Southern California\n\nLos Angeles, CA 90089\n\nminos.niu@sangerlab.net\n\nSirish K. Nandyala\n\nDepartment of Biomedical Engineering\n\nUniversity of Southern California\n\nLos Angeles, CA 90089\nnandyala@usc.edu\n\nWon Joon Sohn\n\nDepartment of Biomedical Engineering\n\nUniversity of Southern California\n\nLos Angeles, CA 90089\nwonjsohn@gmail.com\n\nTerence D. Sanger\n\nDepartment of Biomedical Engineering\n\nDepartment of Neurology\n\nDepartment of Biokinesiology\n\nUniversity of Southern California\n\nLos Angeles, CA 90089\n\nterry@sangerlab.net\n\nAbstract\n\nOur central goal is to quantify the long-term progression of pediatric neurologi-\ncal diseases, such as a typical 10-15 years progression of child dystonia. To this\npurpose, quantitative models are convincing only if they can provide multi-scale\ndetails ranging from neuron spikes to limb biomechanics. The models also need\nto be evaluated in hyper-time, i.e. signi\ufb01cantly faster than real-time, for producing\nuseful predictions. We designed a platform with digital VLSI hardware for multi-\nscale hyper-time emulations of human motor nervous systems. The platform is\nconstructed on a scalable, distributed array of Field Programmable Gate Array\n(FPGA) devices. All devices operate asynchronously with 1 millisecond time\ngranularity, and the overall system is accelerated to 365x real-time. Each physi-\nological component is implemented using models from well documented studies\nand can be \ufb02exibly modi\ufb01ed. Thus the validity of emulation can be easily advised\nby neurophysiologists and clinicians. For maximizing the speed of emulation,\nall calculations are implemented in combinational logic instead of clocked iter-\native circuits. This paper presents the methodology of building FPGA modules\nemulating a monosynaptic spinal loop. Emulated activities are qualitatively sim-\nilar to real human data. Also discussed is the rationale of approximating neural\ncircuitry by organizing neurons with sparse interconnections. In conclusion, our\nplatform allows emulating pathological abnormalities such that motor symptoms\nwill emerge and can be analyzed. It compels us to test the origins of childhood\nmotor disorders and predict their long-term progressions.\n\n1 Challenges of studying developmental motor disorders\n\nThere is currently no quantitative model of how a neuropathological condition, which mainly affects\nthe function of neurons, ends up causing the functional abnormalities identi\ufb01ed in clinical exami-\nnations. The gap in knowledge is particularly evident for disorders in developing human nervous\nsystems, i.e. childhood neurological diseases. In these cases, the ultimate clinical effect of cellu-\n\n1\n\n\flar injury is compounded by a complex interplay among the child\u2019s injury, development, behavior,\nexperience, plasticity, etc. Qualitative insight has been provided by clinical experiences into the\nassociation between particular types of injury and particular types of outcome. Their quantitative\nlinkages, nevertheless, have yet to be created \u2013 neither in clinic nor in cellular physiological tests.\nThis discrepancy is signi\ufb01cantly more prominent for individual child patients, which makes it very\ndif\ufb01cult to estimate the ef\ufb01cacy of treatment plans. In order to understand the consequence of in-\njury and discover new treatments, it is necessary to create a modeling toolset with certain design\nguidelines, such that child neurological diseases can be quantitatively analyzed.\nPerhaps more than any other organ, the brain necessarily operates on multiple spatial and temporal\nscales. On the one hand, it is the neurons that perform fundamental computations, but neurons have\nto interact with large-scale organs (ears, eyes, skeletal muscles, etc.) to achieve global functions.\nThis multi-scale nature worths more attention in injuries, where the overall de\ufb01cits depend on both\nthe cellular effects of injuries and the propagated consequences. On the other hand, neural processes\nin developmental diseases usually operate on drastically different time scales, e.g. spinal re\ufb02ex in\nmilliseconds versus learning in years. Thus when studying motor nervous systems, mathematical\nmodeling is convincing only if it can provide multi-scale details, ranging from neuron spikes to limb\nbiomechanics; also the models should be evaluated with time granularity as small as 1 millisecond,\nmeanwhile the evaluation needs to continue trillions of cycles in order to cover years of life.\nIt is particularly challenging to describe the multi-scale nature of human nervous system when mod-\neling childhood movement disorders. Note that for a child who suffered brain injury at birth, the full\ndevelopment of all motor symptoms may easily take more than 10 years. Therefore the millisecond-\nbased model needs to be evaluated signi\ufb01cantly faster than real-time, otherwise the model will fail\nto produce any useful predictions in time. We have implemented realistic models for spiking mo-\ntoneurons, sensory neurons, neural circuitry, muscle \ufb01bers and proprioceptors using VLSI and pro-\ngrammable logic technologies. All models are computed in Field Programmable Gate Array (FPGA)\nhardware in 365 times real-time. Therefore one year of disease progression can be assessed after\none day of emulation. This paper presents the methodology of building the emulation platform. The\nresults demonstrate that our platform is capable of producing physiologically realistic multi-scale\nsignals, which are usually scarce in experiments. Successful emulations enabled by this platform\nwill be used to verify theories of neuropathology. New treatment mechanisms and drug effects can\nalso be emulated before animal experiments or clinical trials.\n\n2 Methodology of multi-scale neural emulation\n\nFigure 1: Illustration of the multi-scale nature of motor nervous system.\n\nThe motor part of human nervous system is responsible for maintaining body postures and generat-\ning voluntary movements. The multi-scale nature of motor nervous system is demonstrated in Fig.1.\nWhen the elbow (Fig.1A) is maintaining a posture or performing a movement, a force is estab-\nlished by the involved muscle based on how much spiking excitation the muscle receives from its \u03b1-\nmotoneurons (Fig.1B). The \u03b1-motoneurons are regulated by a variety of sensory input, part of which\ncomes directly from the proprioceptors in the muscle. As the primary proprioceptor found in skeletal\nmuscles, a muscle spindle is another complex system that has its own microscopic Multiple-Input-\nMultiple-Output structure (Fig.1C). Spindles continuously provide information about the length and\nlengthening speed of the muscle \ufb01ber. A muscle with its regulating motoneurons, sensory neu-\nrons and proprioceptors constitutes a monosynaptic spinal loop. This minimalist neurophysiological\n\n2\n\n\u03b1MNBag 1Bag 2ChainGamma dynamicinputGamma staticinputPrimaryoutputSecondaryoutputA. Human armB. Monosynaptic spinal loopC. Inner structure of muscle spindle\fstructure is used as an example for explaining the multi-scale hyper-time emulation in hardware.\nAdditional structures can be added to the backbone set-up using similar methodologies.\n\n2.1 Modularized architecture for multi-scale models\n\nDecades of studies on neurophysiology provided an abundance of models characterizing different\ncomponents of the human motor nervous system. The informational characteristics of physiological\ncomponents allowed us to model them as functional structures, i.e. each of which converting input\nsignals to certain outputs. In particular, within a monosynaptic spinal loop illustrated in Fig.1B,\nstretching the muscle will elicit a chain of physiological activities in: muscle stretch \u21d2 spindle \u21d2\nsensory neuron \u21d2 synapse \u21d2 motoneuron \u21d2 muscle contraction. The adjacent components must\nhave compatible interfaces, and the interfacing variables must also be physiologically realistic. In\nour design, each component is mathematically described in Table 1:\n\nTable 1: Functional de\ufb01nition of neural models\n\nCOMPONENT MATHEMATICAL DEFINITION\n\nNeuron\nSynapse\nMuscle\nSpindle\n\nS(t) = fneuron(I, t)\nI(t) = fsynapse(S, t)\nT (t) = fmuscle(S, L, \u02d9L, t)\nA(t) = fspindle(L, \u02d9L, \u0393dynamic, \u0393static, t)\n\nall components are modeled as black-box functions that map the inputs to the outputs. The meanings\nof these mathematical de\ufb01nitions are explained below. This design allows existing physiological\nmodels to be easily inserted and switched. In all models the input signals are time-varying, e.g.\nI = I(t), L = L(t) , etc. The argument of t in input signals are omitted throughout this paper.\n\n2.2 Selection of models for emulation\n\nModels were selected in consideration of their computational cost, physiological verisimilitude, and\nwhether it can be adapted to the mathematical form de\ufb01ned in Table 1.\n\nModel of Neuron\n\nThe informational process for a neuron is to take post-synaptic current I as the input, and produce\na binary spike train S in the output. The neuron model adopted in the emulation was developed by\nIzhikevich [1]:\n\nv(cid:48) = 0.04v2 + 5v + 140 \u2212 u + I\nu(cid:48) = a(bv \u2212 u)\nif v = 30 mV, then v \u2190 c, u \u2190 u + d\n\n(1)\n(2)\n\nwhere a, b, c, d are free parameters tuned to achieve certain \ufb01ring patterns. Membrane potential v\ndirectly determines a binary spike train S(t) that S(t) = 1 if v \u2265 30, otherwise S(t) = 0. Note that\nv in Izhikevich model is in millivolts and time t is in milliseconds. Therefore the coef\ufb01cients in eq.1\nneed to be adjusted in correspondence to SI units.\n\nModel of Synapse\n\nWhen a pre-synaptic neuron spikes, i.e. S(0) = 1, an excitatory synapse subsequently issues an\nExcitatory Post-Synaptic Current (EPSC) that drives the post-synaptic neuron. Neural recording of\nhair cells in rats [2] provided evidence that the time pro\ufb01le of EPSC can be well characterized using\nthe equations below:\n\nVm \u00d7(cid:16)\n(cid:40)\n\nI(t) =\n\n0\n\n(cid:17)\n\n\u2212 t\n\u03c4d Vm \u2212 e\n\ne\n\n\u2212 t\n\n\u03c4r Vm\n\nif t \u2265 0\notherwise\n\n(3)\n\nThe key parameters in a synapse model is the time constants for rising (\u03c4r) and decaying (\u03c4d). In\nour emulation \u03c4r = 0.001 s and \u03c4r = 0.003 s.\n\n3\n\n\fModel of Muscle force and electromyograph (EMG)\n\nThe primary effect of skeletal muscle is to convert \u03b1-motoneuron spikes S into force T , depending\non the muscle\u2019s instantaneous length L and lengthening speed \u02d9L. We used Hill\u2019s muscle model\nin the emulation with parameter tuning described in [3]. Another measurable output of muscle is\nelectromyograph (EMG). EMG is the small skin current polarized by motor unit action potential\n(MUAP) when it travels along muscle \ufb01bers. Models exist to describe the typical waveform picked\nby surface EMG electrodes. In this project we chose to implement the one described in [4].\n\nModel of Proprioceptor\n\nSpindle is a sensory organ that provides the main source of proprioceptive information. As can\nbe seen in Fig.1C, a spindle typically produces two afferent outputs (primary Ia and secondary II)\naccording to its gamma fusimotor drives (\u0393dynamic and \u0393static) and muscle states (L and \u02d9L). There\nis currently no closed-form models describing spindle functions due to spindle\u2019s signi\ufb01cant non-\nlinearity. On representative model that numerically approximates the spindle dynamics was devel-\noped by Mileusnic et al. [5]. The model used differential equations to characterize a typical cat\nsoleus spindle. Eqs.4-10 present a subset of this model for one type of spindle \ufb01ber (bag1):\n\n(cid:32)\n\n(cid:33)\n\n(4)\n\n(5)\n\n(6)\n\n(7)\n(8)\n(9)\n\n(10)\n\n\u02d9x0 =\n\n\u0393dynamic\n\n\u0393dynamic + \u21262\n\nbag1\n\n\u2212 x0\n\n/\u03c4\n\n\u02d9x1 = x2\n1\nM\n\n\u02d9x2 =\n\n[TSR \u2212 TB \u2212 TP R \u2212 \u03931x0]\n\nwhere\n\nTSR = KSR(L \u2212 x1 \u2212 LSR0)\nTB = (B0 + B1x0) \u00b7 (x1 \u2212 R) \u00b7 CSS \u00b7 |x2|0.3\nTP R = KP R (x1 \u2212 LP R0)\n\n(cid:19)\n\n(cid:18)\n\nCSS =\n\n2\n\n1 + e\u22121000x2\n\n\u2212 1\n\nEq.8 and 10 suggest that evaluating the spindle model requires multiplication, division as well as\nmore complex arithmetics like polynomials and exponentials. The implementation details are de-\nscribed in Section 3.\n\n2.3 Neuron connectivity with sparse interconnections\n\nAlthough the number of spinal neurons (~1 billion) is signi\ufb01cantly less compared to that of cortical\nneurons (~100 billion), a fully connected spinal network still means approximately 2 trillion synaptic\nendings [6].\nImplementing such a huge number of synapses imposes a major challenge, if not\nimpossible, given limited hardware resource.\nIn this platform we approximated the neural connectivity by sparsely connecting sensory neurons\nto motoneurons as parallel pathways. We do not attempt to introduce the full connectivity. The\nrationale is that in a neural control system, the effect of a single neuron can be considered as mapping\ncurrent state x to change in state \u02d9x through a band-limited channel. Therefore when a collection of\nneurons are \ufb01ring stochastically, the probability of \u02d9x depends on both x and the \ufb01ring behavior s\n(s = 1 when spiking, otherwise s = 0) of each neuron, as such:\n\np( \u02d9x|x, s) = p( \u02d9x|s = 1)p(s = 1|x) + p( \u02d9x|s = 0)p(s = 0|x)\n\n(11)\nEq.11 is a master equation that determines a probability \ufb02ow on the state. From the Kramers-Moyal\nexpansion we can associate this probability \ufb02ow with a partial differential equation:\n\n(cid:19)i\n\n(cid:18)\n\n\u221e(cid:88)\n\ni=1\n\n\u2212 \u2202\n\u2202x\n\n\u2202\n\u2202t\n\np(x, t) =\n\nD(i)(x)p(x, t)\n\n(12)\n\nwhere D(i)(x) is a time-invariant term that modi\ufb01es the change of probability density based on its\ni-th gradient.\n\n4\n\n\fUnder certain conditions [7, 8], D(i)(x) for i > 2 all vanish and therefore the probability \ufb02ow can\nbe described deterministically using a linear operator L:\n\n\u2202\n\u2202t\n\np(x, t) =\n\n(13)\nThis means that various Ls can be superimposed to achieve complex system dynamics (illustrated\nin Fig.2A).\n\nD(1)(x) +\n\n(cid:20)\n\n\u2212 \u2202\n\u2202x\n\n(cid:21)\n\n\u22022\n\u2202x2 D(2)(x)\n\np(x, t) = Lp(x, t)\n\nFigure 2: Functions of neuron population can be described as the combination of linear operators\n(A). Therefore the original neural function can be equivalently produced by sparsely connected\nneurons formalizing parallel pathways (B).\n\nAs a consequence, the statistical effect of two fully connected neuron populations is equivalent to\nones that are only sparsely connected, as long as the probability \ufb02ow can be described by the same L.\nFor a movement task, in particular, it is the statistical effect from the neuron ensemble onto skeletal\nmuscles that determines the global behavior. Therefore we argue that it is feasible to approximate\nthe spinal cord connectivity by sparsely interconnecting sensory and motor neurons (Fig.2B). Here\na pool of homogenous sensory neurons projects to another pool of homogeneous \u03b1-motoneurons.\nPseudorandom noise is added to the input of all homogeneous neurons within a population. It is\nworth noting that this approximation signi\ufb01cantly reduces the number of synapses that need to be\nimplemented in hardware.\n\n3 Hardware implementation on FPGA\n\nWe select FPGA as the implementation device due to its inherent parallelism that resembles the ner-\nvous system. FPGA is favored over GPU or clustered CPUs because it is relatively easy to network\nhundreds of nodes under \ufb02exible protocols. The platform is distributed on multiple nodes of Xilinx\nSpartan-6 devices. The interfacing among FPGAs and computers is created using OpalKelly devel-\nopment board XEM6010. The dynamic range of variables is tight in models of Izhikevich neuron,\nsynapse and EMG. This helps maintaining the accuracy of models even when they are evaluated in\n32-bit \ufb01xed-point arithmetics. The spindle model, in contrast, requires \ufb02oating-point arithmetics due\nto its wide dynamic range and complex calculations (see eq.4-10). Hyper-time computations with\n\ufb02oating-point numbers are resource consuming and therefore need to be implemented with special\nattentions.\n\n3.1 Floating-point arithmetics in combinational logic\n\nOur arithmetic implementations are compatible with IEEE-754 standard. Typical \ufb02oating-point\narithmetic IP cores are either pipe-lined or based on iterative algorithms such as CORDIC, all of\nwhich require clocks to schedule the calculation. In our platform, no clock is provided for model\nevaluations thus all arithmetics need to be executed in pure combinational logic. Taking advantage\nof combinational logic allows all model evaluations to be 1) fast, the evaluation time depends en-\ntirely on the propagating and settling time of signals, which is on the order of microseconds, and 2)\nparallel, each model is evaluated on its own circuit without waiting for any other results.\nOur implementations of adder and multiplier are inspired by the open source project \u201cFree Floating-\nPoint Madness\u201d, available at http://www.hmc.edu/chips/. Please contact the authors of this paper if\nthe modi\ufb01ed code is needed.\n\n5\n\n+\u03b1MN\u03b1MN\u03b1MN\u03b1MNSNSNSNSNSensoryInputMotorOutputB. Equivalent network with sparse interconnectionsA. Neuron function as superimposed linear operators\fFast combinational \ufb02oating-point division\n\nFloating-point division is even more resource demanding than multiplications. We avoided directly\nimplementing the dividing algorithm by approximating it with additions and multiplications. Our\napproach is inspired by an algorithm described in [9], which provides a good approximation of the\ninverse square root for any positive number x within one Newton-Raphson iteration:\n\nQ(x) =\n\n1\u221a\nx\n\n\u2248 x(1.5 \u2212 x\n2\n\n\u00b7 x2)\n\n(x > 0)\n\n(14)\n\nQ(x) can be implemented only using \ufb02oating-point adders and multipliers. Thereby any division\nwith a positive divisor can be achieved if two blocks of Q(x) are concatenated:\n\na\nb\n\n=\n\na\u221a\nb \u00b7 \u221a\n\nb\n\n= a \u00b7 Q(b) \u00b7 Q(b)\n\n(b > 0)\n\n(15)\n\nThis algorithm has been adjusted to also work with negative divisors (b < 0).\n\nNumerical integrators for differential equations\n\nEvaluating the instantaneous states of differential equation models require a \ufb01xed-step numerical\nintegrator. Backward Euler\u2019s Method was chosen to balance the numerical error and FPGA usage:\n(16)\n(17)\n\nxn+1 = xn + T f (xn+1, tn+1)\n\n\u02d9x = f (x, t)\n\nwhere T is the sampling interval. f (x, t) is the derivative function for state variable x.\n\n3.2 Asynchronous spike-based communication between FPGA chips\n\nFigure 3: Timing diagram of asynchronous spike-based communication\n\nFPGA nodes are networked by transferring 1-bit binary spikes to each other. Our design allowed\nthe sender and the receiver to operate on independent clocks without having to synchronize. The\ntiming diagram of the spike-based communication is shown in Fig.3. The sender issues Spike with\na pulse width of 1/(365 \u00d7 Femu) second. Each Spike then triggers a counting event on the receiver,\nmeanwhile each Clock \ufb01rst reads the accumulated spike count and subsequently cleans the counter.\nNote that the phase difference between Spike and Clock is not predictable due to asynchronicity.\n\n3.3 Serialize neuron evaluations within a homogeneous population\n\nDifferent neuron populations are instantiated as standalone circuits. Within in each population,\nhowever, homogeneous neurons mentioned in Section 2.3 are evaluated in series in order to optimize\nFPGA usage.\nWithin each FPGA node all modules operate with a central clock, which is the only source allowed\nto trigger any updating event. Therefore the maximal number of neurons that can be serialized\n(Nserial) is restrained by the following relationship:\n\nFfpga = C \u00d7 Nserial \u00d7 365 \u00d7 Femu\n\n(18)\nHere Ffpga is the fastest clock rate that a FPGA can operate on; C = 4 is the minimal clock cycles\nneeded for updating each state variable in the on-chip memory; Femu = 1 kHz is the time granular-\nity of emulation (1 millisecond), and 365 \u00d7 Femu represents 365x real-time. Consider that Xilinx\n\n6\n\n112123cleancountClockSpikeCounter\fSpartan-6 FPGA devices peaks at 200MHz central clock frequency, the theoretical maximum of\nneurons that can be serialized is\n\nNserial (cid:54) 200 MHz/(4 \u00d7 365 \u00d7 1 kHz) \u2248 137\n\n(19)\n\nIn the current design we choose Nserial = 128.\n\n4 Results: emulated activities of motor nervous system\n\nFigure 4 shows the implemented monosynaptic spinal loop in schematics and in operation. Each\nFPGA node is able to emulate monosynaptic spinal loops consisting of 1,024 sensory and 1,024 mo-\ntor neurons, i.e. 2,048 neurons in total. The spike-based asynchronous communication is successful\nbetween two FPGA nodes. Note that the emulation has to be signi\ufb01cantly slowed down for on-line\nplotting. When the emulation is at full speed (365x real-time) the software front-end is not able to\nvisualize the signals due to limited data throughput.\n\nFigure 4: The neural emulation platform in operation. Left: Neural circuits implemented for each\nFPGA node including 2,048 neurons. SN = Sensory Neuron; \u03b1MN = \u03b1-motoneuron. Center: One\nworking FPGA node. Right: Two FPGA nodes networked using asynchronous spiking protocol.\n\nThe emulation platform successfully created multi-scale information when the muscle is externally\nstretched (Fig.5A). We also tested if our emulated motor system is able to produce the recruitment\norder and size principles observed in real physiological data. It has been well known that when\na voluntary motor command is sent to the \u03b1-motoneuron pool, the motor units are recruited in an\norder that small ones get recruited \ufb01rst, followed by the big ones [10]. The comparison between\nour results and real data are shown in Fig.5B, where the top panel shows 20 motor unit activities\nemulated using our platform, and the bottom panel shows decoded motor unit activities from real\nhuman EMG [11]. No qualitative difference was found.\n\n5 Discussion and future work\n\nWe designed a hardware platform for emulating the multi-scale motor nervous activities in hyper-\ntime. We managed to use one node of single Xilinx Spartan-6 FPGA to emulate monosynaptic\nspinal loops consisting of 2,048 neurons, associated muscles and proprioceptors. The neurons are\norganized as parallel pathways with sparse interconnections. The emulation is successfully accel-\nerated to 365x real-time. The platform can be scaled by networking multiple FPGA nodes, which\nis enabled by an asynchronous spike-based communication protocol. The emulated monosynaptic\nspinal loops are capable of producing re\ufb02ex-like activities in response to muscle stretch. Our results\nof motor unit recruitment order are compatible with the physiological data collected in real human\nsubjects.\nThere is a question of whether this stochastic system turns out chaotic, especially with accumulated\nerrors from Backward Euler\u2019s integrator. Note that the \ufb01ring property of a neuron population is\nusually stable even with explicit noise [8], and spindle inputs are measured from real robots so the\nintegrator errors are corrected at every iteration. To our knowledge, the system is not critically\nsensitive to the initial conditions or integrator errors. This question, however, is both interesting and\nimportant for in-depth investigations in the future.\n\n7\n\n\u03b1MN\u03b1MNSNSN...8 parallel pathways2,048 neurons128 SNs128 \u03b1MNs128 SNs128 \u03b1MNs\fIt has been shown [12] that replicating classic types of spinal interneurons (propriospinal, Ia-\nexcitatory, Ia-inhibitory, Renshaw, etc.)\nis suf\ufb01cient to produce stabilizing responses and rapid\nreaching movement in a wrist. Our platform will introduce those interneurons to describe the known\nspinal circuitry in further details. Physiological models will also be re\ufb01ned as needed. For the\npurpose of modeling movement behavior or diseases, Izhikevich model is a good balance between\nverisimilitude and computational cost. Nevertheless when testing drug effects along disease progres-\nsion, neuron models are expected to cover suf\ufb01cient molecular details including how neurotransmit-\nters affect various ion channels. With the advancing of programmable semiconductor technology, it\nis expected to upgrade our neuron model to Hodgkin-Huxley\u2019s. For the muscle models, Hill\u2019s type\nof model does not \ufb01t the muscle properties accurately enough when the muscle is being shortened.\nAlternative models will be tested.\nOther studies showed that the functional dexterity of human limbs \u2013 especially in the hands \u2013 is\ncritically enabled by the tendon con\ufb01gurations and joint geometry [13]. As a result, if our platform\nis used to understand whether known neurophysiology and biomechanics are suf\ufb01cient to produce\nable and pathological movements, it will be necessary to use this platform to control human-like\nlimbs. Since the emulation speed can be \ufb02exibly adjusted from arbitrarily slow to 365x real-time,\nwhen speeded to exactly 1x real-time the platform will function as a digital controller with 1kHz\nrefresh rate.\nThe main purpose of the emulation is to learn how certain motor disorders progress during childhood\ndevelopment. This \ufb01rst requires the platform to reproduce motor symptoms that are compatible with\nclinical observations. For example it has been suggested that muscle spasticity in rats is associated\nwith decreased soma size of \u03b1-motoneurons [14], which presumably reduced the \ufb01ring threshold of\nneurons. Thus when lower \ufb01ring threshold is introduced to the emulated motoneuron pool, similar\nEMG patterns as in [15] should be observed. It is also necessary for the symptoms to evolve with\nneural plasticity. In the current version we presume that the structure of each component remains\ntime invariant. In the future work Spike Timing Dependent Plasticity (STDP) will be introduced\nsuch that all components are subject to temporal modi\ufb01cations.\n\nFigure 5: A) Physiological activity emulated by each model when the muscle is sinusoidally\nstretched. B) Comparing the emulated motor unit recruitment order with real experimental data.\n\nAcknowledgments\n\nThe authors thank Dr. Gerald Loeb for helping set up the emulation of spindle models. This project\nis supported by NIH NINDS grant R01NS069214-02.\n\n8\n\nStretchSpindle IaMuscle ForceEMGSensory post-synaptic currentMotoneuronsA. Multi-scale activities from emulationReal DataB. Verify motor unit recruitment pattern Emulation1s\fReferences\n\n[1] Izhikevich, E. M. Simple model of spiking neurons. IEEE transactions on neural networks / a publication\n\nof the IEEE Neural Networks Council 14, 1569\u20131572 (2003).\n\n[2] Glowatzki, E. & Fuchs, P. A. Transmitter release at the hair cell ribbon synapse. Nature neuroscience 5,\n\n147\u2013154 (2002).\n\n[3] Shadmehr, R. & Wise, S. P. A Mathematical Muscle Model. In Supplementary documents for \u201cCompu-\n\ntational Neurobiology of Reaching and Pointing\u201d, 1\u201318 (MIT Press, Cambridge, MA, 2005).\n\n[4] Fuglevand, A. J., Winter, D. A. & Patla, A. E. Models of recruitment and rate coding organization in\n\nmotor-unit pools. Journal of neurophysiology 70, 2470\u20132488 (1993).\n\n[5] Mileusnic, M. P., Brown, I. E., Lan, N. & Loeb, G. E. Mathematical models of proprioceptors. I. Control\n\nand transduction in the muscle spindle. Journal of neurophysiology 96, 1772\u20131788 (2006).\n\n[6] Gelfan, S., Kao, G. & Ruchkin, D. S. The dendritic tree of spinal neurons. The Journal of comparative\n\nneurology 139, 385\u2013411 (1970).\n\n[7] Sanger, T. D. Neuro-mechanical control using differential stochastic operators.\n\nIn Engineering in\nMedicine and Biology Society (EMBC), 2010 Annual International Conference of the IEEE, 4494\u20134497\n(2010).\n\n[8] Sanger, T. D. Distributed control of uncertain systems using superpositions of linear operators. Neural\n\ncomputation 23, 1911\u20131934 (2011).\n\n[9] Lomont, C. Fast inverse square root (2003). URL http://www.lomont.org/Math/Papers/\n\n2003/InvSqrt.pdf.\n\n[10] Henneman, E. Relation between size of neurons and their susceptibility to discharge. Science (New York,\n\nN.Y.) 126, 1345\u20131347 (1957).\n\n[11] De Luca, C. J. & Hostage, E. C. Relationship between \ufb01ring rate and recruitment threshold of motoneu-\n\nrons in voluntary isometric contractions. Journal of neurophysiology 104, 1034\u20131046 (2010).\n\n[12] Raphael, G., Tsianos, G. A. & Loeb, G. E. Spinal-like regulator facilitates control of a two-degree-of-\nfreedom wrist. The Journal of neuroscience : the of\ufb01cial journal of the Society for Neuroscience 30,\n9431\u20139444 (2010).\n\n[13] Valero-Cuevas, F. J. et al. The tendon network of the \ufb01ngers performs anatomical computation at a\n\nmacroscopic scale. IEEE transactions on bio-medical engineering 54, 1161\u20131166 (2007).\n\n[14] Brashear, A. & Elovic, E. Spasticity: Diagnosis and Management (Demos Medical, 2010), 1 edn.\n[15] Levin, M. F. & Feldman, A. G. The role of stretch re\ufb02ex threshold regulation in normal and impaired\n\nmotor control. Brain research 657, 23\u201330 (1994).\n\n9\n\n\f", "award": [], "sourceid": 28, "authors": [{"given_name": "C.", "family_name": "Niu", "institution": null}, {"given_name": "Sirish", "family_name": "Nandyala", "institution": null}, {"given_name": "Won", "family_name": "Sohn", "institution": null}, {"given_name": "Terence", "family_name": "Sanger", "institution": null}]}