Validation of Hill-type muscle models in relation to neuromuscular recruitment and force-velocity properties: predicting patterns of in vivo muscle force

Linking in vivo muscle dynamics to force-length and force-velocity properties reveals that guinea fowl lateral gastrocnemius operates at shorter than optimal lengths

The isometric force-length (F-L) and isotonic force-velocity (F-V) relationships characterize the contractile properties of skeletal muscle under controlled conditions, yet it remains unclear how these properties relate to in vivo muscle function. Here, we map the in situ F-L and F-V characteristics of guinea fowl (Numida meleagris) lateral gastrocnemius (LG) to the in vivo operating range during walking and running. We test the hypothesis that muscle fascicles operate on the F-L plateau, near the optimal length for force (L0) and near velocities that maximize power output (Vopt) during walking and running. We found that in vivo LG velocities are consistent with optimizing power during work production, and economy of force at higher loads. However, LG does not operate near L0 at higher loads. LG length was near L0 at the time of electromyography (EMG) onset but shortened rapidly such that force development during stance occurred on the ascending limb of the F-L curve, around 0.8L0. Shortening across L0 in late swing might optimize potential for rapid force development near the swing-stance transition, providing resistance to unexpected perturbations that require rapid force development. We also found evidence of in vivo passive force rise in late swing, without EMG activity, at lengths where in situ passive force is zero, suggesting that dynamic viscoelastic effects contribute to in vivo force development. Comparison of in vivo operating ranges with F-L and F-V properties suggests the need for new approaches to characterize muscle properties in controlled conditions that more closely resemble in vivo dynamics.

Evaluation of generic EMG-Torque models across two Upper-Limb joints

Advanced single-use dynamic EMG-torque models require burdensome subject-specific calibration contractions and have historically been assumed to produce lower error than generic models (i.e., models that are identical across subjects and muscles). To investigate this assumption, we studied generic one degree of freedom (DoF) models derived from the ensemble median of subject-specific models, evaluated across subject, DoF and joint. We used elbow (N = 64) and hand-wrist (N = 9) datasets. Subject-specific elbow models performed statistically better [5.79 ± 1.89 %MVT (maximum voluntary torque) error] than generic elbow models (6.21 ± 1.85 %MVT error). However, there were no statistical differences between subject-specific vs. generic models within each hand-wrist DoF. Next, we evaluated generic models across joints. The best hand-wrist generic model had errors of 6.29 ± 1.85 %MVT when applied to the elbow. The elbow generic model had errors of 7.04 ± 2.29 %MVT when applied to the hand-wrist. The generic elbow model was statistically better in both joints, compared to the generic hand-wrist model. Finally, we tested Butterworth filter models (a simpler generic model), finding no statistical differences between optimum Butterworth and subject-specific models. Overall, generic models simplified EMG-torque training without substantive performance degradation and provided the possibility of transfer learning between joints.

Linking in vivo muscle dynamics to in situ force-length and force-velocity reveals that guinea fowl lateral gastrocnemius operates at shorter than optimal lengths

Force-length (F-L) and force-velocity (F-V) properties characterize skeletal muscle's intrinsic properties under controlled conditions, and it is thought that these properties can inform and predict in vivo muscle function. Here, we map dynamic in vivo operating range and mechanical function during walking and running, to the measured in situ F-L and F-V characteristics of guinea fowl (Numida meleagris) lateral gastrocnemius (LG), a primary ankle extensor. We use in vivo patterns of muscle tendon force, fascicle length, and activation to test the hypothesis that muscle fascicles operate at optimal lengths and velocities to maximize force or power production during walking and running. Our findings only partly support our hypothesis: in vivo LG velocities are consistent with optimizing power during work production, and economy of force at higher loads. However, LG does not operate at lengths on the force plateau (±5% Fmax) during force production. LG length was near L0 at the time of EMG onset but shortened rapidly such that force development during stance occurred almost entirely on the ascending limb of the F-L curve, at shorter than optimal lengths. These data suggest that muscle fascicles shorten across optimal lengths in late swing, to optimize the potential for rapid force development near the swing-stance transition. This may provide resistance against unexpected perturbations that require rapid force development at foot contact. We also found evidence of passive force rise (in absence of EMG activity) in late swing, at lengths where passive force is zero in situ, suggesting that dynamic history dependent and viscoelastic effects may contribute to in vivo force development. Direct comparison of in vivo work loops and physiological operating ranges to traditional measures of F-L and F-V properties suggests the need for new approaches to characterize dynamic muscle properties in controlled conditions that more closely resemble in vivo dynamics.

Numerical instability of Hill-type muscle models

Hill-type muscle models are highly preferred as phenomenological models for musculoskeletal simulation studies despite their introduction almost a century ago. The use of simple Hill-type models in simulations, instead of more recent cross-bridge models, is well justified since computationally 'light-weight'-although less accurate-Hill-type models have great value for large-scale simulations. However, this article aims to invite discussion on numerical instability issues of Hill-type muscle models in simulation studies, which can lead to computational failures and, therefore, cannot be simply dismissed as an inevitable but acceptable consequence of simplification. We will first revisit the basic premises and assumptions on the force-length and force-velocity relationships that Hill-type models are based upon, and their often overlooked but major theoretical limitations. We will then use several simple conceptual simulation studies to discuss how these numerical instability issues can manifest as practical computational problems. Lastly, we will review how such numerical instability issues are dealt with, mostly in an ad hoc fashion, in two main areas of application: musculoskeletal biomechanics and computer animation.

Intelligent Parametric Adaptive Hybrid Active–Passive Training Control Method for Rehabilitation Robot

Rehabilitation robots facilitate patients to take part in physical and occupational training. Most of the rehabilitation robots used in clinical practice adopt pure passive training or active training, which cannot sense the active participation of patients during passive training and lack adaptive dynamic adjustment of training parameters for patients. In this paper, an intelligent hybrid active–passive training control method is proposed to enhance the active participation of patients in passive training mode. Firstly, the patients’ joint mobility and maximum muscle power are modelized and calibrated. Secondly, the robot joints are actuated to train according to joint mobility and speed for two cycles. The human–machine coupled force interaction control model can recognize the patients’ active participation in the training process. Finally, the passive training joint motion speed for the next training cycle is adaptively updated by the proposed control method. The experimental results demonstrate that the control method can sense the patients’ active participation and adjust the passive training speed according to the patients’ active force interaction. In conclusion, the hybrid active–passive training control method proposed in this paper achieves the desired goal and effectively improves the patients’ rehabilitation effect.

Biorealistic Control of Hand Prosthesis Augments Functional Performance of Individuals With Amputation

The human hand has compliant properties arising from muscle biomechanics and neural reflexes, which are absent in conventional prosthetic hands. We recently proved the feasibility to restore neuromuscular reflex control (NRC) to prosthetic hands using real-time computing neuromorphic chips. Here we show that restored NRC augments the ability of individuals with forearm amputation to complete grasping tasks, including standard Box and Blocks Test (BBT), Golf Balls Test (GBT), and Potato Chips Test (PCT). The latter two were more challenging, but novel to prosthesis tests. Performance of a biorealistic controller (BC) with restored NRC was compared to that of a proportional linear feedback (PLF) controller. Eleven individuals with forearm amputation were divided into two groups: one with experience of myocontrol of a prosthetic hand and another without any. Controller performances were evaluated by success rate, failure (drop/break) rate in each grasping task. In controller property tests, biorealistic control achieved a better compliant property with a 23.2% wider range of stiffness adjustment than that of PLF control. In functional grasping tests, participants could control prosthetic hands more rapidly and steadily with neuromuscular reflex. For participants with myocontrol experience, biorealistic control yielded 20.4, 39.4, and 195.2% improvements in BBT, GBT, and PCT, respectively, compared to PLF control. Interestingly, greater improvements were achieved by participants without any myocontrol experience for BBT, GBT, and PCT at 27.4, 48.9, and 344.3%, respectively. The functional gain of biorealistic control over conventional control was more dramatic in more difficult grasp tasks of GBT and PCT, demonstrating the advantage of NRC. Results support the hypothesis that restoring neuromuscular reflex in hand prosthesis can improve neural motor compatibility to human sensorimotor system, hence enabling individuals with amputation to perform delicate grasps that are not tested with conventional prosthetic hands.

Effect of muscle stimulation intensity on the heterogeneous function of regions within an architecturally complex muscle

Skeletal muscle has fiber architectures ranging from simple to complex, alongside variations in fiber-type and neuro-anatomical compartmentalization. However, the functional implications of muscle subdivision into discrete functional units remain poorly understood. The rat medial gastrocnemius has well-characterized regions with distinct architectures and fiber type composition. Here, force-length and force-velocity contractions were performed for two stimulation intensities (supramaximal and submaximal) and for three structural units (whole muscle belly, proximal region, and distal region) to assess the effect of muscle compartmentalization on contractile force-length-velocity relationships and optimal speed for power production. Additionally, fiber strain, fiber rotation, pennation, and architectural gearing were quantified. Our results suggest that the proximal and distal muscle regions have fundamentally different physiological function. During supramaximal activation, the proximal region has shorter (8.4 ± 0.8 mm versus 10.9 ± 0.7 mm) fibers and steeper (28.7 ± 11.0° versus 19.6 ± 6.3°) fiber angles at optimum length, and operates over a larger (17.9 ± 3.8% versus 12.6 ± 2.7%) range of its force-length curve. The proximal region also exhibits larger changes in pennation angle (5.6 ± 2.2°/mm versus 2.4 ± 1.5°/mm muscle shortening) and architectural gearing (1.82 ± 0.53 versus 1.25 ± 0.24), whereas the distal region exhibits greater peak shortening speed (96.0 mm/s versus 81.3 mm/s) and 18-27% greater optimal speed. Overall, similar patterns were observed during submaximal activation. These regional differences in physiological function with respect to the whole muscle highlight how variation in motor recruitment could fundamentally shift regional functional patterns within a single muscle, which likely has important implications for whole muscle force and work output in vivo.NEW & NOTEWORTHY We show that muscle compartmentalization can influence whole muscle contractile properties, with slower-fibered proximal rat medial gastrocnemius undergoing larger changes in pennation angle and architectural gearing, whereas the faster-fibered distal region achieves greater peak and optimal shortening velocity, and power output. Consequently, regional variation in motor recruitment can fundamentally influence functional patterns within a single muscle.

Multiscale Hill-type modeling of the mechanical muscle behavior driven by the neural drive in isometric conditions

In this study, we present a new model describing the mechanical behavior of the skeletal muscle during isometric contraction. This model is based on a former Hill-inspired model detailing the electromechanical behavior of the muscle based on the Huxley formulation. However, in this new multiscale model the muscle is represented at the Motor Unit (MU) scale. The proposed model is driven by a physiological input describing the firing moments of the activated MUs. Definition of both voluntary and evoked MU recruitment schemes are described, enabling the study of both contractions in isometric conditions. During this type of contraction, there is no movement of the joints and the tendon-muscle complex remains at the same length. Moreover, some well-established macroscopic relationships such as force-length or force-velocity properties are considered. A comparison with a twitch model using the same input definition is provided with both recruitment schemes exhibiting limitations of twitch type models. Finally, the proposed model is validated with a comparison between simulated and recorded force profiles following eight electrical stimulations pulses in isometric conditions. The simulated muscle force was generated to mimic the one recorded from the quadriceps of a patient implanted with a functional electrical stimulation neuroprosthesis. This validation demonstrates the ability of the proposed model to reproduce realistically the skeletal muscle contractions and to take into account subject-specific parameters.

Krogh's principle for musculoskeletal physiology and pathology

August Krogh was a comparative physiologist who used frogs, guinea pigs, cats, dogs, and horses in his research that led to his Nobel Prize on muscle physiology. His idea to choose the most relevant organism to study problems in physiology has become known as Krogh's principle. Indeed, many important discoveries in physiology have been made using naturally occurring animal models. However, the majority of research today utilizes laboratory mouse and rat models to study problems in physiology. This paper discusses how Krogh's principle can be invoked in musculoskeletal research as a complementary approach to using standard laboratory rodent models for solving problems in musculoskeletal physiology. This approach may increase our ability to treat musculoskeletal diseases clinically. For example, it has been noted that progress in osteogenesis imperfecta research has been limited by the absence of a naturally occurring animal model. Several examples of naturally occurring animal models are discussed including osteoarthritis and osteosarcoma in dogs, resistance to disuse induced bone and skeletal muscle loss in mammalian hibernators, and bone phenotypic plasticity in fish lacking osteocytes. Many musculoskeletal diseases (e.g., osteoarthritis) occur naturally in companion animals, which may provide clues on etiology and progression of musculoskeletal diseases and accelerate the development of pharmaceutical therapies for humans.

Improved Hill-type musculotendon models with activation-force-length coupling

BACKGROUND

Hill-type musculotendon models are most commonly used in biomechanical simulations for their computational efficacy and efficiency. But these models are generally built for maximally-activated muscles and linearly scale muscle properties when applied to submaximal conditions. However, the precondition of this scaling, which is muscle activation and properties are independent each other, has been proven unreal in many studies. Actually, the maximal activation condition is not ubiquitous for muscles in vivo, so it is necessary to adapt the linear scaling approach to improve the model practicability.

OBJECTIVE

This paper aimed at proposing two improved Hill-type musculotendon models that are better suited for submaximal conditions.

METHOD

These two models were built by including the activation-force-length coupling and their biological accuracy and computation speed were evaluated by a series of benchmark simulations.

RESULTS

Compared to experimental measurements, the percent root mean square errors of forces calculated by the two AFLC models were less than 13.98% and 13.81% respectively. However, the average running time of the second AFLC model was nearly 17 times that of the first one with only a little improvement in accuracy.

CONCLUSION

The two AFLC models were validated more accurate than the common Hill-type model in submaximally activated conditions and the first one was recommended in the construction of upper-layer musculoskeletal models.

EMG-Torque Dynamics Change With Contraction Bandwidth

An accurate model for ElectroMyoGram (EMG)-torque dynamics has many uses. One of its applications which has gained high attention among researchers is its use, in estimating the muscle contraction level for the efficient control of prosthesis. In this paper, the dynamic relationship between the surface EMG and torque during isometric contractions at the human ankle was studied using system identification techniques. Subjects voluntarily modulated their ankle torque in dorsiflexion direction, by activating their tibialis anterior muscle, while tracking a pseudo-random binary sequence in a torque matching task. The effects of contraction bandwidth, described by torque spectrum, on EMG-torque dynamics were evaluated by varying the visual command switching time. Nonparametric impulse response functions (IRF) were estimated between the processed surface EMG and torque. It was demonstrated that: 1) at low contraction bandwidths, the identified IRFs had unphysiological anticipatory (i.e., non-causal) components, whose amplitude decreased as the contraction bandwidth increased. We hypothesized that this non-causal behavior arose, because the EMG input contained a component due to feedback from the output torque, i.e., it was recorded from within a closed-loop. Vision was not the feedback source since the non-causal behavior persisted when visual feedback was removed. Repeating the identification using a nonparametric closed-loop identification algorithm yielded causal IRFs at all bandwidths, supporting this hypothesis. 2) EMG-torque dynamics became faster and the bandwidth of system increased as contraction modulation rate increased. Thus, accurate prediction of torque from EMG signals must take into account the contraction bandwidth sensitivity of this system.

Contraction speed and type influences rapid utilisation of available muscle force: neural and contractile mechanisms

This study investigated the influence of contraction speed and type on the human ability to rapidly increase torque and utilise the available maximum voluntary torque (MVT) as well as the neuromuscular mechanisms underpinning any effects. Fifteen young, healthy males completed explosive-voluntary knee-extensions in five conditions: isometric (ISO), and both concentric and eccentric at two constant accelerations of 500°.s−2 (CONSLOW and ECCSLOW) and 2000°.s−2 (CONFAST and ECCFAST). Explosive torque and quadriceps EMG were recorded every 25 ms up to 150 ms from their respective onsets and normalised to the available MVT and EMG at MVT, respectively, specific to that joint angle and velocity. Neural efficacy (explosive Voluntary:Evoked octet torque) was also measured, and torque data were entered into a Hill-type muscle model to estimate muscle performance. Explosive torques normalised to MVT (and normalised muscle forces) were greatest in the concentric, followed by isometric, and eccentric conditions; and in the fast compared with slow speeds within the same contraction type (CONFAST>CONSLOW>ISO, and ECCFAST>ECCSLOW). Normalised explosive-phase EMG and neural efficacy were greatest in concentric, followed by isometric and eccentric conditions, but were similar for fast and slow contractions of the same type. Thus, distinct neuromuscular activation appeared to explain the effect of contraction type but not speed on normalised explosive torque, suggesting the speed effect is an intrinsic contractile property. These results provide novel evidence that the ability to rapidly increase torque/force and utilise the available MVT is influenced by both contraction type and speed, due to neural and contractile mechanisms, respectively.

A Bio-mechanical Model for Elbow Isokinetic and Isotonic Flexions

A new bio-mechanical model for elbow flexions is proposed to quantify the elbow torque generated as a function of the upper-arm circumferential strain and influencing factors of elbow angle and angular velocity. The upper-arm circumferential strain is used to represent the contractile intensity of the dominant flexor, biceps brachii, whose behavior is described by Hill's theory. Experiments with thirteen healthy subjects were conducted to determine the influencing factors. The temporal distributions of torque and elbow angle were measured by Biodex ®3 simultaneously, while the upper-arm circumference was obtained by a wearable anthropometric measurement device. Within the experimental range, the change of angular velocity has been found to have no effect on the torque generated. The new model was further verified experimentally with reasonable agreements obtained. The mean relative error of the torque estimated from the model is 15% and 22%, for isokinetic and isotonic flexions, respectively. The verified model establishes the relationship between the torque generated and circumference strain of the upper arm, for the first time, thus provide a scientific foundation for the anthropometric measurement technology as an alternative to sEMG for monitoring force/torque generation during elbow flexions.

A motor unit-based model of muscle fatigue

Muscle fatigue is a temporary decline in the force and power capacity of skeletal muscle resulting from muscle activity. Because control of muscle is realized at the level of the motor unit (MU), it seems important to consider the physiological properties of motor units when attempting to understand and predict muscle fatigue. Therefore, we developed a phenomenological model of motor unit fatigue as a tractable means to predict muscle fatigue for a variety of tasks and to illustrate the individual contractile responses of MUs whose collective action determines the trajectory of changes in muscle force capacity during prolonged activity. An existing MU population model was used to simulate MU firing rates and isometric muscle forces and, to that model, we added fatigue-related changes in MU force, contraction time, and firing rate associated with sustained voluntary contractions. The model accurately estimated endurance times for sustained isometric contractions across a wide range of target levels. In addition, simulations were run for situations that have little experimental precedent to demonstrate the potential utility of the model to predict motor unit fatigue for more complicated, real-world applications. Moreover, the model provided insight into the complex orchestration of MU force contributions during fatigue, that would be unattainable with current experimental approaches.

Neuromorphic meets neuromechanics, part I: the methodology and implementation

OBJECTIVE

One goal of neuromorphic engineering is to create 'realistic' robotic systems that interact with the physical world by adopting neuromechanical principles from biology. Critical to this is the methodology to implement the spinal circuitry responsible for the behavior of afferented muscles. At its core, muscle afferentation is the closed-loop behavior arising from the interactions among populations of muscle spindle afferents, alpha and gamma motoneurons, and muscle fibers to enable useful behaviors.

APPROACH

We used programmable very- large-scale-circuit (VLSI) hardware to implement simple models of spiking neurons, skeletal muscles, muscle spindle proprioceptors, alpha-motoneuron recruitment, gamma motoneuron control of spindle sensitivity, and the monosynaptic circuitry connecting them. This multi-scale system of populations of spiking neurons emulated the physiological properties of a pair of antagonistic afferented mammalian muscles (each simulated by 1024 alpha- and gamma-motoneurones) acting on a joint via long tendons.

MAIN RESULTS

This integrated system was able to maintain a joint angle, and reproduced stretch reflex responses even when driving the nonlinear biomechanics of an actual cadaveric finger. Moreover, this system allowed us to explore numerous values and combinations of gamma-static and gamma-dynamic gains when driving a robotic finger, some of which replicated some human pathological conditions. Lastly, we explored the behavioral consequences of adopting three alternative models of isometric muscle force production. We found that the dynamic responses to rate-coded spike trains produce force ramps that can be very sensitive to tendon elasticity, especially at high force output.

SIGNIFICANCE

Our methodology produced, to our knowledge, the first example of an autonomous, multi-scale, neuromorphic, neuromechanical system capable of creating realistic reflex behavior in cadaveric fingers. This research platform allows us to explore the mechanisms behind healthy and pathological sensorimotor function in the physical world by building them from first principles, and it is a precursor to neuromorphic robotic systems.

Muscle length-dependent contribution of motoneuron Cav1.3 channels to force production in model slow motor unit

Persistent inward current (PIC)-generating Ca_v1.3 channels in spinal motoneuron dendrites are thought to be actively recruited during normal behaviors. However, whether and how the activation of PIC channels influences force output of motor unit remains elusive. Here, building a physiologically realistic model of slow motor unit I demonstrated that force production induced by the PIC activation is much smaller for short than lengthened muscles during the regular firing of the motoneuron that transitions from the quiescent state by either a brief current pulse at the soma or a brief synaptic excitation at the dendrites. By contrast, the PIC-induced force potentiation was maximal for short muscles when the motoneuron switched from a stable low-frequency firing state to a stable high-frequency firing state by the current pulse at the soma. Under the synaptic excitation at the dendrites, however, the force could not be potentiated by the transitioning of the motoneuron from a low- to a high-frequency firing state due to the simultaneous onset of PIC at the dendrites and firing at the soma. The strong dependency of the input-output relationship of the motor unit on the neuromodulation and Ia afferent inputs for the PIC channels was further shown under static variations in muscle length. Taken together, these findings suggest that the PIC activation in the motoneuron dendrites may differentially affect the force production of the motor unit, depending not only on the firing state history of the motoneuron and the variation in muscle length but also on the mode of motor activity.NEW & NOTEWORTHY Ca_v1.3 channels in motoneuron dendrites are actively involved during normal motor activities. To investigate the effects of the activation of motoneuron Ca_v1.3 channels on force production, a model motor unit was built based on best-available data. The simulation results suggest that force potentiation induced by Ca_v1.3 channel activation is strongly modulated not only by firing history of the motoneuron but also by length variation of the muscle as well as neuromodulation inputs from the brainstem.

Measurement of Dynamic Joint Stiffness from Multiple Short Data Segments

This paper presents our new method, Short Segment-Structural Decomposition SubSpace (SS-SDSS), for the estimation of dynamic joint stiffness from short data segments. The main application is for data sets that are only piecewise stationary. Our approach is to: 1) derive a data-driven, mathematical model for dynamic stiffness for short data segments; 2) bin the non-stationary data into a number of short, stationary data segments; and 3) estimate the model parameters from subsets of segments with the same properties. This method extends our previous state-spacework by recognizing that initial conditions have important effects for short data segments; consequently, initial conditions are incorporated into the stiffness model and estimated for each segment. A simulation study that faithfully replicated experimental conditions delineated the range of experimental conditions for which the method can successfully identify stiffness. An experimental study on the ankle of a healthy subject during a torque matching tasks demonstrated the successful estimation of dynamic stiffness in a slow, time-varying experiment. Together, the simulation and experimental studies demonstrate that the SS-SDSS method is a valuable tool to measure stiffness in functionally important tasks.

Comparison of the validity of Hill and Huxley muscle tendon complex models using experimental data obtained from rat m. soleus in situ

The relationship between mechanical and metabolic behaviour in the widely used Hill muscle-tendon complex (MTC) model is not straightforward, while this is an integral part of the Huxley model. In this study we assessed to what extent Huxley and Hill type MTC models yield adequate predictions of mechanical muscle behaviour during stretch-shortening cycles (SSC). In fully anaesthetized male Wistar rats (N=3), m. soleus was dissected completely free, except for the insertion. Cuff electrodes were placed over the n. ischiadicus. The distal end of the tendon was connected to a servo motor, via a force transducer. The setup allowed for full control over muscle stimulation and length, while force was measured. Quick release and isovelocity contractions (part 1), and SSC (part 2) were imposed. Simulations of part 2 were made with both a Hill and a Huxley MTC model, using parameter values determined from part 1. A modification to the classic two-state Huxley model was made to incorporate series elasticity, activation dynamics and active and passive force-length relations. Results were similar for all rats. Fitting of the free parameters to data of part 1 was near perfect (R2 > .97). During SSC, predicted peak force and force during relaxation deviated from the experimental data, for both models. Overall, both models yielded similarly adequate predictions of the experimental data. We conclude that Huxley and Hill MTC models are equally valid with respect to mechanical behaviour.

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.