An action potential-driven model of soleus muscle activation dynamics for locomotor-like movements

OBJECTIVE The goal of this study was to develop a physiologically plausible, computationally robust model for muscle activation dynamics (A(t)) under physiologically relevant excitation and movement. APPROACH The interaction of excitation and movement on A(t) was investigated comparing the force production between a cat soleus muscle and its Hill-type model. For capturing A(t) under excitation and movement variation, a modular modeling framework was proposed comprising of three compartments: (1) spikes-to-[Ca(2+)]; (2) [Ca(2+)]-to-A; and (3) A-to-force transformation. The individual signal transformations were modeled based on physiological factors so that the parameter values could be separately determined for individual modules directly based on experimental data. MAIN RESULTS The strong dependency of A(t) on excitation frequency and muscle length was found during both isometric and dynamically-moving contractions. The identified dependencies of A(t) under the static and dynamic conditions could be incorporated in the modular modeling framework by modulating the model parameters as a function of movement input. The new modeling approach was also applicable to cat soleus muscles producing waveforms independent of those used to set the model parameters. SIGNIFICANCE This study provides a modeling framework for spike-driven muscle responses during movement, that is suitable not only for insights into molecular mechanisms underlying muscle behaviors but also for large scale simulations.

[1]  G. Zahalak A distribution-moment approximation for kinetic theories of muscular contraction , 1981 .

[2]  S. Binder-Macleod,et al.  A mathematical model that predicts skeletal muscle force , 1997, IEEE Transactions on Biomedical Engineering.

[3]  G. Zahalak,et al.  Muscle activation and contraction: constitutive relations based directly on cross-bridge kinetics. , 1990, Journal of biomechanical engineering.

[4]  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.

[5]  C. Morris,et al.  Voltage oscillations in the barnacle giant muscle fiber. , 1981, Biophysical journal.

[6]  L M Jordan,et al.  Dendritic L‐type calcium currents in mouse spinal motoneurons: implications for bistability , 2000, The European journal of neuroscience.

[7]  K. Campbell,et al.  Rate constant of muscle force redevelopment reflects cooperative activation as well as cross-bridge kinetics. , 1997, Biophysical journal.

[8]  C. Heckman,et al.  Hill muscle model errors during movement are greatest within the physiologically relevant range of motor unit firing rates. , 2003, Journal of biomechanics.

[9]  Nicholas T. Carnevale,et al.  The NEURON Simulation Environment , 1997, Neural Computation.

[10]  Dario Farina,et al.  EMG-Driven Forward-Dynamic Estimation of Muscle Force and Joint Moment about Multiple Degrees of Freedom in the Human Lower Extremity , 2012, PloS one.

[11]  Erik De Schutter,et al.  A consumer guide to neuronal modeling software , 1992, Trends in Neurosciences.

[12]  A. Sargeant,et al.  Shortening‐induced force depression in human adductor pollicis muscle , 1998, The Journal of physiology.

[13]  André Fabio Kohn,et al.  Models of passive and active dendrite motoneuron pools and their differences in muscle force control , 2012, Journal of Computational Neuroscience.

[14]  Thomas L. Daniel,et al.  Filament Compliance Influences Cooperative Activation of Thin Filaments and the Dynamics of Force Production in Skeletal Muscle , 2012, PLoS Comput. Biol..

[15]  W Herzog,et al.  Length dependence of active force production in skeletal muscle. , 1999, Journal of applied physiology.

[16]  G. E. Goslow,et al.  The cat step cycle: Hind limb joint angles and muscle lengths during unrestrained locomotion , 1973, Journal of morphology.

[17]  D. Stephenson,et al.  Length dependence of changes in sarcoplasmic calcium concentration and myofibrillar calcium sensitivity in striated muscle fibres , 1984, Journal of Muscle Research & Cell Motility.

[18]  E. Henneman,et al.  PROPERTIES OF MOTOR UNITS IN A HETEROGENEOUS PALE MUSCLE (M. GASTROCNEMIUS) OF THE CAT. , 1965, Journal of neurophysiology.

[19]  F. Zajac Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. , 1989, Critical reviews in biomedical engineering.

[20]  D. Levine,et al.  Physiological types and histochemical profiles in motor units of the cat gastrocnemius , 1973, The Journal of physiology.

[21]  E. Henneman,et al.  PROPERTIES OF MOTOR UNITS IN A HOMOGENEOUS RED MUSCLE (SOLEUS) OF THE CAT. , 1965, Journal of neurophysiology.

[22]  D. Lloyd,et al.  An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo. , 2003, Journal of biomechanics.

[23]  D. Martyn,et al.  Length-dependent Ca2+ activation in cardiac muscle: some remaining questions , 2005, Journal of Muscle Research & Cell Motility.

[24]  A. Hill The heat of shortening and the dynamic constants of muscle , 1938 .

[25]  N. Curtin,et al.  Predicting force generation by lamprey muscle during applied sinusoidal movement using a simple dynamic model. , 1998, The Journal of experimental biology.

[26]  Ian E. Brown,et al.  Mechanics of feline soleus: II design and validation of a mathematical model , 1996, Journal of Muscle Research & Cell Motility.

[27]  D. Guiraud,et al.  Smooth muscle modeling and experimental identification: application to bladder isometric contraction , 2011, Journal of neural engineering.

[28]  D. Pai,et al.  Is titin a ‘winding filament’? A new twist on muscle contraction , 2012, Proceedings of the Royal Society B: Biological Sciences.

[29]  P. Crago,et al.  Muscle-tendon model with length-history dependent activation-velocity coupling , 1995, Proceedings of 17th International Conference of the Engineering in Medicine and Biology Society.

[30]  J. Stull,et al.  Myosin light chain phosphorylation in vertebrate striated muscle: regulation and function. , 1993, The American journal of physiology.

[31]  C. Heckman,et al.  Doublet potentiation during eccentric and concentric contractions of cat soleus muscle. , 1997, Journal of applied physiology.

[32]  Pierre-Brice Wieber,et al.  Multiscale modeling of skeletal muscle properties and experimental validations in isometric conditions , 2011, Biological Cybernetics.

[33]  A. Y. Wong,et al.  Mechanics of cardiac muscle, based on Huxley's model: mathematical stimulation of isometric contraction. , 1971, Journal of biomechanics.

[34]  K. Nishikawa,et al.  What Is the Role of Titin in Active Muscle? , 2012, Exercise and sport sciences reviews.

[35]  Sherif M. Elbasiouny,et al.  Simulation of Ca2+ persistent inward currents in spinal motoneurones: mode of activation and integration of synaptic inputs , 2006, The Journal of physiology.

[36]  H. Mashima,et al.  The force-load-velocity relation and the viscous-like force in the frog skeletal muscle. , 1972, The Japanese journal of physiology.

[37]  Stuart N. Baker,et al.  Circuits Generating Corticomuscular Coherence Investigated Using a Biophysically Based Computational Model. I. Descending Systems , 2008, Journal of neurophysiology.

[38]  D. Allen,et al.  The role of sarcoplasmic reticulum in relaxation of mouse muscle; effects of 2,5‐di(tert‐butyl)‐1,4‐benzohydroquinone. , 1994, The Journal of physiology.

[39]  Richard R Neptune,et al.  A phenomenological model and validation of shortening-induced force depression during muscle contractions. , 2010, Journal of biomechanics.

[40]  L. Krishtalik,et al.  Proteins as specific polar media for charge transfer processes , 2012 .

[41]  H. Hatze,et al.  A myocybernetic control model of skeletal muscle , 1977, Biological Cybernetics.

[42]  A. Schultz,et al.  Identification of dynamic myoelectric signal-to-force models during isometric lumbar muscle contractions. , 1994, Journal of biomechanics.

[43]  Kelvin E. Jones,et al.  Asymmetry in Signal Propagation between the Soma and Dendrites Plays a Key Role in Determining Dendritic Excitability in Motoneurons , 2014, PloS one.

[44]  Andrew A Biewener,et al.  Validation of Hill-type muscle models in relation to neuromuscular recruitment and force-velocity properties: predicting patterns of in vivo muscle force. , 2014, Integrative and comparative biology.

[45]  E. J. Cheng,et al.  Measured and modeled properties of mammalian skeletal muscle. II. The effectsof stimulus frequency on force-length and force-velocity relationships , 1999, Journal of Muscle Research & Cell Motility.

[46]  Matthew Millard,et al.  Flexing computational muscle: modeling and simulation of musculotendon dynamics. , 2013, Journal of biomechanical engineering.

[47]  E. Marbán,et al.  The relationship between contractile force and intracellular [Ca2+] in intact rat cardiac trabeculae , 1995, The Journal of general physiology.

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

[49]  A J van den Bogert,et al.  Computer simulation of landing movement in downhill skiing: anterior cruciate ligament injuries. , 1996, Journal of biomechanics.

[50]  F E Zajac,et al.  Relationship among recruitment order, axonal conduction velocity, and muscle-unit properties of type-identified motor units in cat plantaris muscle. , 1985, Journal of neurophysiology.

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

[52]  C. Heckman,et al.  Force from cat soleus muscle during imposed locomotor-like movements: experimental data versus Hill-type model predictions. , 1997, Journal of neurophysiology.

[53]  A Prochazka,et al.  Isometric muscle length-tension curves do not predict angle-torque curves of human wrist in continuous active movements. , 2000, Journal of biomechanics.

[54]  H. Westerblad,et al.  Doublet discharge stimulation increases sarcoplasmic reticulum Ca2+ release and improves performance during fatiguing contractions in mouse muscle fibres , 2013, The Journal of physiology.

[55]  D M Shames,et al.  Ca(2+)-force relationship of frog skeletal muscle: a dynamic model for parameter estimation. , 1996, The American journal of physiology.

[56]  Patrick E. Crago,et al.  Muscle–Tendon Model with Length History-Dependent Activation–Velocity Coupling , 1998, Annals of Biomedical Engineering.