Simulation system of spinal cord motor nuclei and associated nerves and muscles, in a Web-based architecture

A Web-based simulation system of the spinal cord circuitry responsible for muscle control is described. The simulator employs two-compartment motoneuron models for S, FR and FF types, with synaptic inputs acting through conductance variations. Four motoneuron pools with their associated interneurons are represented in the simulator, with the possibility of inclusion of more than 2,000 neurons and 2,000,000 synapses. Each motoneuron action potential is followed, after a conduction delay, by a motor unit potential and a motor unit twitch. The sums of all motor unit potentials and twitches result in the electromyogram (EMG), and the muscle force, respectively. Inputs to the motoneuron pool come from populations of interneurons (Ia reciprocal inhibitory interneurons, Ib interneurons, and Renshaw cells) and from stochastic point processes associated with descending tracts. To simulate human electrophysiological experiments, the simulator incorporates external nerve stimulation with orthodromic and antidromic propagation. This provides the mechanisms for reflex generation and activation of spinal neuronal circuits that modulate the activity of another motoneuron pool (e.g., by reciprocal inhibition). The generation of the H-reflex by the Ia-motoneuron pool system and its modulation by spinal cord interneurons is included in the simulation system. Studies with the simulator may include the statistics of individual motoneuron or interneuron spike trains or the collective effect of a motor nucleus on the dynamics of muscle force control. Properties associated with motor-unit recruitment, motor-unit synchronization, recurrent inhibition and reciprocal inhibition may be investigated.

[1]  R. W. Banks,et al.  An allometric analysis of the number of muscle spindles in mammalian skeletal muscles , 2006, Journal of anatomy.

[2]  U. Windhorst ON THE ROLE OF RECURRENT INHIBITORY FEEDBACK IN MOTOR CONTROL , 1996, Progress in Neurobiology.

[3]  Terrence J. Sejnowski,et al.  Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism , 1994, Journal of Computational Neuroscience.

[4]  C. D. De Luca,et al.  Motor unit control properties in constant-force isometric contractions. , 1996, Journal of neurophysiology.

[5]  Michael L. Hines,et al.  Neuron splitting in compute-bound parallel network simulations enables runtime scaling with twice as many processors , 2008, Journal of Computational Neuroscience.

[6]  S J Redman,et al.  The synaptic current evoked in cat spinal motoneurones by impulses in single group 1a axons. , 1983, The Journal of physiology.

[7]  Kelvin E Jones,et al.  A modelling study of locomotion‐induced hyperpolarization of voltage threshold in cat lumbar motoneurones , 2002, The Journal of physiology.

[8]  W. Rall Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic input. , 1967, Journal of neurophysiology.

[9]  Dr. D. Kernell,et al.  Relation between isometric force and stimulus rate in cat's hindlimb motor units of different twitch contraction time , 2004, Experimental Brain Research.

[10]  Carlo J. De Luca,et al.  Some properties of motor unit action potential trains recorded during constant force isometric contractions in man , 1973, Kybernetik.

[11]  D. Levine,et al.  PHYSIOLOGICAL TYPES AND HISTOCHEMICAL PROFILES , 2005 .

[12]  W. Crill,et al.  Penicillin-induced segmental myoclonus. II. Membrane properties of cat spinal motoneurons. , 1972, Archives of neurology.

[13]  David R. Cox,et al.  The statistical analysis of series of events , 1966 .

[14]  M. Hallett,et al.  Presynaptic inhibition compared with homosynaptic depression as an explanation for soleus H-reflex depression in humans , 1997, Experimental Brain Research.

[15]  J. Munson,et al.  Membrane electrical properties and prediction of motor-unit type of medial gastrocnemius motoneurons in the cat. , 1985, Journal of neurophysiology.

[16]  H Hultborn,et al.  Input‐output relations in the pathway of recurrent inhibition to motoneurones in the cat. , 1979, The Journal of physiology.

[17]  James M. Bower,et al.  The GENESIS Simulation System , 2003 .

[18]  Ping Zhou,et al.  MUAP Number Estimates in Surface EMG: Template-Matching Methods and Their Performance Boundaries , 2004, Annals of Biomedical Engineering.

[19]  F. Awiszus,et al.  The relationship between estimates of Ia-EPSP amplitude and conduction velocity in human soleus motoneurons , 2004, Experimental Brain Research.

[20]  R. Burke Spinal Cord: Ventral Horn , 2004 .

[21]  Alan V. Oppenheim,et al.  Discrete-Time Signal Pro-cessing , 1989 .

[22]  Takanori Uchiyama,et al.  Effects of spinal recurrent inhibition on motoneuron short-term synchronization , 2007, Biological Cybernetics.

[23]  R.R.L. Cisi,et al.  H-reflex depression simulated by a biologically realistic motoneuron network , 2007, 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[24]  M. Floeter,et al.  H-reflexes of different sizes exhibit differential sensitivity to low frequency depression. , 1997, Electroencephalography and clinical neurophysiology.

[25]  C. Moritz,et al.  Discharge rate variability influences the variation in force fluctuations across the working range of a hand muscle. , 2005, Journal of neurophysiology.

[26]  John E Misiaszek,et al.  The H‐reflex as a tool in neurophysiology: Its limitations and uses in understanding nervous system function , 2003, Muscle & nerve.

[27]  A J Fuglevand,et al.  Contractile properties of single motor units in human toe extensors assessed by intraneural motor axon stimulation. , 1996, Journal of neurophysiology.

[28]  M. Binder,et al.  Multiple mechanisms of spike-frequency adaptation in motoneurones , 1999, Journal of Physiology-Paris.

[29]  William W. Lytton Optimizing Synaptic Conductance Calculation for Network Simulations , 1996, Neural Computation.

[30]  T. Bui,et al.  Computational estimation of the distribution of L-type Ca(2+) channels in motoneurons based on variable threshold of activation of persistent inward currents. , 2006, Journal of neurophysiology.

[31]  Kazem Alemzadeh,et al.  29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society - Lyon, France , 2007 .

[32]  J. Valls-Solé The circuitry of the human spinal cord: Its role in motor control and movement disorders Pierrot-Deseilligny E, Burke D, editors. Hardback. Cambridge University Press; 2005. 642 p. [ISBN: 13978052182581]. , 2008, Clinical Neurophysiology.

[33]  Håkan Johansson,et al.  A model of the feline medial gastrocnemius motoneuron-muscle system subjected to recurrent inhibition , 2003, Biological Cybernetics.

[34]  Hermanus J. Hermens,et al.  EMG Modeling and Simulation , 2004 .

[35]  R. Enoka,et al.  Motor-unit synchronization increases EMG amplitude and decreases force steadiness of simulated contractions. , 2000, Journal of neurophysiology.

[36]  Michele Giugliano,et al.  Synthesis of Generalized Algorithms for the Fast Computation of Synaptic Conductances with Markov Kinetic Models in Large Network Simulations , 2000, Neural Computation.

[37]  E. Jankowska Interneuronal relay in spinal pathways from proprioceptors , 1992, Progress in Neurobiology.

[38]  G. Loeb,et al.  Mathematical models of proprioceptors. I. Control and transduction in the muscle spindle. , 2006, Journal of neurophysiology.

[39]  Marcus Fraga Vieira,et al.  Compartmental models of mammalian motoneurons of types S, FR and FF and their computer simulation , 2007, Comput. Biol. Medicine.

[40]  F E Zajac,et al.  Catch Property in Single Mammalian Motor Units , 1970, Science.

[41]  R K Powers,et al.  A variable-threshold motoneuron model that incorporates time- and voltage-dependent potassium and calcium conductances. , 1993, Journal of neurophysiology.

[42]  Frans C. T. van der Helm,et al.  Analysis of reflex modulation with a biologically realistic neural network , 2007, Journal of Computational Neuroscience.

[43]  Andrew V. Poliakov,et al.  Discharge patterns of tonically firing human motoneurones , 1995, Biological Cybernetics.

[44]  F Buchthal,et al.  Motor unit of mammalian muscle. , 1980, Physiological reviews.

[45]  Alain Destexhe,et al.  Conductance-Based Integrate-and-Fire Models , 1997, Neural Computation.

[46]  D. Cox,et al.  The statistical analysis of series of events , 1966 .

[47]  H. Hultborn,et al.  Distribution of recurrent inhibition within a motor nucleus. II. Amount of recurrent inhibition in motoneurones to fast and slow units. , 1988, Acta physiologica Scandinavica.

[48]  Sabine Meunier,et al.  Spinal use‐dependent plasticity of synaptic transmission in humans after a single cycling session , 2007, The Journal of physiology.

[49]  G. Shepherd The Synaptic Organization of the Brain , 1979 .

[50]  R. Person,et al.  Discharge frequency and discharge pattern of human motor units during voluntary contraction of muscle. , 1972, Electroencephalography and clinical neurophysiology.

[51]  James J. Feng,et al.  Mathematical simulation of muscle cross-bridge cycle and force-velocity relationship. , 2006, Biophysical journal.

[52]  Ilya A. Rybak,et al.  Modeling the spinal cord neural circuitry controlling cat hindlimb movement during locomotion , 2003, Neurocomputing.

[53]  D. Kernell High-Frequency Repetitive Firing of Cat Lumbosacral Motoneurones Stimulated by Long-Lasting Injected Currents , 1965 .

[54]  Terrence J. Sejnowski,et al.  An Efficient Method for Computing Synaptic Conductances Based on a Kinetic Model of Receptor Binding , 1994, Neural Computation.

[55]  David P. Bashor,et al.  A large-scale model of some spinal reflex circuits , 1998, Biological Cybernetics.

[56]  R. B. Stein,et al.  A method for simulating the reflex output of a motoneuron pool , 1987, Journal of Neuroscience Methods.

[57]  R E Burke,et al.  Anatomy of medial gastrocnemius and soleus motor nuclei in cat spinal cord. , 1977, Journal of neurophysiology.

[58]  W. Crill,et al.  Specific membrane properties of cat motoneurones , 1974, The Journal of physiology.

[59]  I Segev,et al.  Electrotonic architecture of type-identified alpha-motoneurons in the cat spinal cord. , 1988, Journal of neurophysiology.

[60]  J. B. Redford,et al.  Conduction studies of the anterior and posterior tibial nerves. , 1970, Archives of physical medicine and rehabilitation.

[61]  E Jankowska,et al.  Spinal interneurones; how can studies in animals contribute to the understanding of spinal interneuronal systems in man? , 2002, Brain Research Reviews.

[62]  S. Cleveland,et al.  Static input-output relations in the spinal recurrent inhibitory pathway , 1981, Biological Cybernetics.

[63]  Nozomu Hoshimiya,et al.  A muscle activation model of variable stimulation frequency response and stimulation history, based on positive feedback in calcium dynamics , 2001, Biological Cybernetics.

[64]  W. Precht The synaptic organization of the brain G.M. Shepherd, Oxford University Press (1975). 364 pp., £3.80 (paperback) , 1976, Neuroscience.

[65]  H. Clamann Statistical analysis of motor unit firing patterns in a human skeletal muscle. , 1969, Biophysical journal.

[66]  Daniel W. Stashuk,et al.  Detection of motor unit action potentials with surface electrodes: influence of electrode size and spacing , 1992, Biological Cybernetics.

[67]  John Rinzel,et al.  A minimal, compartmental model for a dendritic origin of bistability of motoneuron firing patterns , 1995, Journal of Computational Neuroscience.

[68]  D. Winter,et al.  Models of recruitment and rate coding organization in motor-unit pools. , 1993, Journal of neurophysiology.

[69]  G. Loeb,et al.  Mathematical models of proprioceptors. II. Structure and function of the Golgi tendon organ. , 2006, Journal of neurophysiology.

[70]  R. Merletti,et al.  Hermite expansions of compact support waveforms: applications to myoelectric signals , 1994, IEEE Transactions on Biomedical Engineering.

[71]  D. Kernell,et al.  Time course and properties of late adaptation in spinal motoneurones of the cat , 2004, Experimental Brain Research.

[72]  T J Doherty,et al.  Contractile properties of human motor units in health, aging, and disease , 2001, Muscle & nerve.

[73]  R. Enoka,et al.  Quantification of the factors that influence discharge correlation in model motor neurons. , 2004, Journal of neurophysiology.

[74]  S Andreassen,et al.  Impaired regulation of force and firing pattern of single motor units in patients with spasticity. , 1980, Journal of neurology, neurosurgery, and psychiatry.

[75]  S. Farmer,et al.  Central nervous pathways underlying synchronization of human motor unit firing studied during voluntary contractions. , 1991, The Journal of physiology.

[76]  M. L. McCurdy,et al.  Topography of recurrent inhibitory postsynaptic potentials between individual motoneurons in the cat. , 1994, Journal of neurophysiology.

[77]  U. Windhorst,et al.  Activation of renshaw cells , 1990, Progress in Neurobiology.

[78]  R. Dum,et al.  Physiological and histochemical characteristics of motor units in cat tibialis anterior and extensor digitorum longus muscles. , 1980, Journal of Neurophysiology.

[79]  S. Andreassen,et al.  Muscle fibre conduction velocity in motor units of the human anterior tibial muscle: a new size principle parameter. , 1987, The Journal of physiology.

[80]  B. Feinstein,et al.  Morphologic studies of motor units in normal human muscles. , 1955, Acta anatomica.

[81]  J. Fleshman,et al.  Recurrent inhibition in type-identified motoneurons. , 1981, Journal of neurophysiology.

[82]  R. Čapek,et al.  Homosynaptic depression and transmitter turnover in spinal monosynaptic pathway. , 1977, Journal of neurophysiology.

[83]  Maarten F. Bobbert,et al.  From twitch to tetanus: performance of excitation dynamics optimized for a twitch in predicting tetanic muscle forces , 1996, Biological Cybernetics.

[84]  F. J. Alvarez,et al.  Calbindin D28k expression in immunohistochemically identified Renshaw cells. , 1998, Neuroreport.

[85]  D. Kernell,et al.  The early phase of adaptation in repetitive impulse discharges of cat spinal motoneurones. , 1972, Brain research.

[86]  G. Somjen,et al.  Excitability and inhibitability of motoneurons of different sizes. , 1965, Journal of neurophysiology.

[87]  G. Mochizuki,et al.  Synchronization of motor units in human soleus muscle during standing postural tasks. , 2005, Journal of neurophysiology.

[88]  V. Vanderhorst,et al.  Organization of lumbosacral motoneuronal cell groups innervating hindlimb, pelvic floor, and axial muscles in the cat , 1997, The Journal of comparative neurology.

[89]  Michael A. Arbib,et al.  The handbook of brain theory and neural networks , 1995, A Bradford book.

[90]  S Andreassen,et al.  Regulation of the firing pattern of single motor units. , 1980, Journal of neurology, neurosurgery, and psychiatry.

[91]  M. L. McCurdy,et al.  Spatial and temporal features of recurrent facilitation among motoneurons innervating synergistic muscles of the cat. , 1994, Journal of neurophysiology.

[92]  M. Hallett,et al.  A model-based approach for the quantification of H reflex depression in humans , 1995, Proceedings of 17th International Conference of the Engineering in Medicine and Biology Society.

[93]  R Plonsey,et al.  The active fiber in a volume conductor. , 1974, IEEE transactions on bio-medical engineering.

[94]  Reinhard Blickhan,et al.  Nonlinearities make a difference: comparison of two common Hill-type models with real muscle , 2008, Biological Cybernetics.

[95]  L. Abbott,et al.  Synaptic Depression and Cortical Gain Control , 1997, Science.

[96]  C. Heckman,et al.  The Physiological Control of Motoneuron Activity , 1996 .

[97]  D. Kernell,et al.  Organization and properties of spinal motoneurones and motor units. , 1986, Progress in brain research.

[98]  Kalpathi R. Subramanian,et al.  NVIZ : An integrated environment for simulation, visualization and analysis of spinal neuronal dynamics , 2005 .

[99]  W. Rymer,et al.  Decorrelating actions of Renshaw interneurons on the firing of spinal motoneurons within a motor nucleus: a simulation study. , 1998, Journal of neurophysiology.

[100]  B. Falck,et al.  The firing rate of motor units in neuromuscular disorders , 2004, Journal of Neurology.

[101]  C. Maganaris,et al.  In vivo measurements of the triceps surae complex architecture in man: implications for muscle function , 1998, The Journal of physiology.

[102]  R. M. Nussbaumer,et al.  Computer simulation of the motoneuron pool–muscle complex. I. Input system and motoneuron pool , 2002, Biological Cybernetics.

[103]  S J Redman,et al.  Voltage dependence of Ia reciprocal inhibitory currents in cat spinal motoneurones. , 1990, The Journal of physiology.

[104]  Harry Grundfest,et al.  Control and Innervation of Skeletal Muscle. , 1968 .

[105]  S Cushing,et al.  Comparison of the morphological and electrotonic properties of Renshaw cells, Ia inhibitory interneurons, and motoneurons in the cat. , 2003, Journal of neurophysiology.

[106]  Madeleine M. Lowery,et al.  A Simulation Study to Examine the Effect of Common Motoneuron Inputs on Correlated Patterns of Motor Unit Discharge , 2005, Journal of Computational Neuroscience.

[107]  Mb Alan J. McComas Dr.,et al.  Invited review: motor unit estimation: methods, results, and present status. , 1991 .

[108]  Ronald J. MacGregor,et al.  Neural and brain modeling , 1987 .

[109]  A. McComas,et al.  A comparison of the contractile properties of the human gastrocnemius and soleus muscles , 2004, European Journal of Applied Physiology and Occupational Physiology.

[110]  B. Walmsley,et al.  An intracellular study of Renshaw cells , 1981, Brain Research.

[111]  Nicholas T. Carnevale,et al.  The NEURON Book: Epilogue , 2006 .

[112]  A. McComas Invited review: Motor unit estimation: Methods, results, and present status , 1991, Muscle & nerve.

[113]  L. Mendell,et al.  Individual EPSPs produced by single triceps surae Ia afferent fibers in homonymous and heteronymous motoneurons. , 1976, Journal of neurophysiology.

[114]  M. Gorassini,et al.  Persistent inward currents in motoneuron dendrites: Implications for motor output , 2005, Muscle & nerve.

[115]  Alan V. Oppenheim,et al.  Discrete-time signal processing (2nd ed.) , 1999 .

[116]  W Rall,et al.  Matching dendritic neuron models to experimental data. , 1992, Physiological reviews.

[117]  F. Plum Handbook of Physiology. , 1960 .

[118]  V. Edgerton,et al.  HINDLIMB MUSCLE FIBER POPULATIONS OF FIVE MAMMALS , 1973 .

[119]  M. Johnson,et al.  Data on the distribution of fibre types in thirty-six human muscles. An autopsy study. , 1973, Journal of the neurological sciences.

[120]  André Fabio Kohn,et al.  SPINAL CORD NEURONAL NETWORK SIMULATOR , 2004 .

[121]  S. Cullheim,et al.  A morphological study of the axons and recurrent axon collaterals of cat alpha‐motoneurones supplying different functional types of muscle unit. , 1978, The Journal of physiology.

[122]  Michael J. O'Donovan,et al.  Motor unit organization of human medial gastrocnemius. , 1979, The Journal of physiology.

[123]  R. Burke Motor Units: Anatomy, Physiology, and Functional Organization , 1981 .