Hill-type Muscle Model Research Articles

A three filament mechanistic model of musculotendon force and impedance

The force developed by actively lengthened muscle depends on different structures across different scales of lengthening. For small perturbations, the active response of muscle is well captured by a linear-time-invariant (LTI) system: a stiff spring in parallel with a light damper. The force response of muscle to longer stretches is better represented by a compliant spring that can fix its end when activated. Experimental work has shown that the stiffness and damping (impedance) of muscle in response to small perturbations is of fundamental importance to motor learning and mechanical stability, while the huge forces developed during long active stretches are critical for simulating and predicting injury. Outside of motor learning and injury, muscle is actively lengthened as a part of nearly all terrestrial locomotion. Despite the functional importance of impedance and active lengthening, no single muscle model has all these mechanical properties. In this work, we present the viscoelastic-crossbridge active-titin (VEXAT) model that can replicate the response of muscle to length changes great and small. To evaluate the VEXAT model, we compare its response to biological muscle by simulating experiments that measure the impedance of muscle, and the forces developed during long active stretches. In addition, we have also compared the responses of the VEXAT model to a popular Hill-type muscle model. The VEXAT model more accurately captures the impedance of biological muscle and its responses to long active stretches than a Hill-type model and can still reproduce the force-velocity and force-length relations of muscle. While the comparison between the VEXAT model and biological muscle is favorable, there are some phenomena that can be improved: the low frequency phase response of the model, and a mechanism to support passive force enhancement.

A three filament mechanistic model of musculotendon force and impedance.

The force developed by actively lengthened muscle depends on different structures across different scales of lengthening. For small perturbations, the active response of muscle is well captured by a linear-time-invariant (LTI) system: a stiff spring in parallel with a light damper. The force response of muscle to longer stretches is better represented by a compliant spring that can fix its end when activated. Experimental work has shown that the stiffness and damping (impedance) of muscle in response to small perturbations is of fundamental importance to motor learning and mechanical stability, while the huge forces developed during long active stretches are critical for simulating and predicting injury. Outside of motor learning and injury, muscle is actively lengthened as a part of nearly all terrestrial locomotion. Despite the functional importance of impedance and active lengthening, no single muscle model has all these mechanical properties. In this work, we present the viscoelastic-crossbridge active-titin (VEXAT) model that can replicate the response of muscle to length changes great and small. To evaluate the VEXAT model, we compare its response to biological muscle by simulating experiments that measure the impedance of muscle, and the forces developed during long active stretches. In addition, we have also compared the responses of the VEXAT model to a popular Hill-type muscle model. The VEXAT model more accurately captures the impedance of biological muscle and its responses to long active stretches than a Hill-type model and can still reproduce the force-velocity and force-length relations of muscle. While the comparison between the VEXAT model and biological muscle is favorable, there are some phenomena that can be improved: the low frequency phase response of the model, and a mechanism to support passive force enhancement.

Finite Element Analysis of Cervical Spine Kinematic Response during Ejection Utilising a Hill-Type Dynamic Muscle Model.

To determine the impact of active muscle on the dynamic response of a pilot's neck during simulated emergency ejection, a detailed three-dimensional (3D) cervical spine (C0-T1) finite element (FE) model integrated with active muscles was constructed. Based on the Hill-type model characterising the muscle force activation mechanics, 13 major neck muscles were modelled. The active force generated by each muscle was simulated as functions of (i) active state (Na), (ii) velocity (Fv(v)), and (iii) length (FL(L)). An acceleration-time profile with an initial acceleration rate of 125 G·s-1 in the 0-80 ms period, reaching peak acceleration of 10 G, then kept constant for a further 70 ms, was applied. The rotational angles of each cervical segment under these ejection conditions were compared with those without muscles and with passive muscles derived from the previous study. Similar trends of segmental rotation were observed with S- and C-curvature of the cervical spine in the 150 ms span analysed. With active muscles, the flexion motion of the C0-C2 segments exhibited higher magnitudes of rotation compared to those without muscle and passive muscle models. The flexion motion increased rapidly and peaked at about 95-105 ms, then decreased rapidly to a lower magnitude. Lower C2-T1 segments exhibited less variation in flexion and extension motions. Overall, during emergency ejections, active muscle activities effectively reduce the variability in rotational angles across cervical segments, except C0-C2 segments in the 60-120 ms period. The role of the active state dynamics of the muscles was crucial to the magnitude of the muscle forces demonstrated. This indicates that it is crucial for pilots to consciously contract their muscles before ejection to prevent cervical spine injuries.

Full Hill-type muscle model of the I1/I3 retractor muscle complex in Aplysia californica.

The coordination of complex behavior requires knowledge of both neural dynamics and the mechanics of the periphery. The feeding system of Aplysia californica is an excellent model for investigating questions in soft body systems' neuromechanics because of its experimental tractability. Prior work has attempted to elucidate the mechanical properties of the periphery by using a Hill-type muscle model to characterize the force generation capabilities of the key protractor muscle responsible for moving Aplysia's grasper anteriorly, the I2 muscle. However, the I1/I3 muscle, which is the main driver of retractions of Aplysia's grasper, has not been characterized. Because of the importance of the musculature's properties in generating functional behavior, understanding the properties of muscles like the I1/I3 complex may help to create more realistic simulations of the feeding behavior of Aplysia, which can aid in greater understanding of the neuromechanics of soft-bodied systems. To bridge this gap, in this work, the I1/I3 muscle complex was characterized using force-frequency, length-tension, and force-velocity experiments and showed that a Hill-type model can accurately predict its force-generation properties. Furthermore, the muscle's peak isometric force and stiffness were found to exceed those of the I2 muscle, and these results were analyzed in the context of prior studies on the I1/I3 complex's kinematics in vivo.

Static versus dynamic muscle modelling in extinct species: a biomechanical case study of the Australopithecus afarensis pelvis and lower extremity.

The force a muscle generates is dependent on muscle structure, in which fibre length, pennation angle and tendon slack length all influence force production. Muscles are not preserved in the fossil record and these parameters must be estimated when constructing a musculoskeletal model. Here, we test the capability of digitally reconstructed muscles of the Australopithecus afarensis model (specimen AL 288-1) to maintain an upright, single-support limb posture. Our aim was to ascertain the influence that different architectural estimation methods have on muscle specialisation and on the subsequent inferences that can be extrapolated about limb function. Parameters were estimated for 36 muscles in the pelvis and lower limb and seven different musculoskeletal models of AL 288-1 were produced. These parameters represented either a 'static' Hill-type muscle model (n=4 variants) which only incorporated force, or instead a 'dynamic' Hill-type muscle model with an elastic tendon and fibres that could vary force-length-velocity properties (n=3 variants). Each muscle's fibre length, pennation angle, tendon slack length and maximal isometric force were calculated based upon different input variables. Static (inverse) simulations were computed in which the vertical and mediolateral ground reaction forces (GRF) were incrementally increased until limb collapse (simulation failure). All AL 288-1 variants produced somewhat similar simulated muscle activation patterns, but the maximum vertical GRF that could be exerted on a single limb was not consistent between models. Three of the four static-muscle models were unable to support >1.8 times body weight and produced models that under-performed. The dynamic-muscle models were stronger. Comparative results with a human model imply that similar muscle group activations between species are needed to sustain single-limb support at maximally applied GRFs in terms of the simplified static simulations (e.g., same walking pose) used here. This approach demonstrated the range of outputs that can be generated for a model of an extinct individual. Despite mostly comparable outputs, the models diverged mostly in terms of strength.

Optimal fibre length and maximum isometric force are the most influential parameters when modelling muscular adaptations to unloading using Hill-type muscle models.

Introduction: Spaceflight is associated with severe muscular adaptations with substantial inter-individual variability. A Hill-type muscle model is a common method to replicate muscle physiology in musculoskeletal simulations, but little is known about how the underlying parameters should be adjusted to model adaptations to unloading. The aim of this study was to determine how Hill-type muscle model parameters should be adjusted to model disuse muscular adaptations. Methods: Isokinetic dynamometer data were taken from a bed rest campaign and used to perform tracking simulations at two knee extension angular velocities (30°·s-1 and 180°·s-1). The activation and contraction dynamics were solved using an optimal control approach and direct collocation method. A Monte Carlo sampling technique was used to perturb muscle model parameters within physiological boundaries to create a range of theoretical and feasible parameters to model muscle adaptations. Results: Optimal fibre length could not be shortened by more than 67% and 61% for the knee flexors and non-knee muscles, respectively. Discussion: The Hill-type muscle model successfully replicated muscular adaptations due to unloading, and recreated salient features of muscle behaviour associated with spaceflight, such as altered force-length behaviour. Future researchers should carefully adjust the optimal fibre lengths of their muscle-models when trying to model adaptations to unloading, particularly muscles that primarily operate on the ascending and descending limbs of the force-length relationship.

Speed-specific optimal contractile conditions of the human soleus muscle from slow to maximum running speed.

The soleus is the main muscle for propulsion during human running but its operating behavior across the spectrum of physiological running speeds is currently unknown. This study experimentally investigated the soleus muscle activation patterns and contractile conditions for force generation, power production and efficient work production (i.e. force-length potential, force-velocity potential, power-velocity potential and enthalpy efficiency) at seven running speeds (3.0 m s-1 to individual maximum). During submaximal running (3.0-6.0 m s-1), the soleus fascicles shortened close to optimal length and at a velocity close to the efficiency maximum, two contractile conditions for economical work production. At higher running speeds (7.0 m s-1 to maximum), the soleus muscle fascicles still operated near optimum length, yet the fascicle shortening velocity increased and shifted towards the optimum for mechanical power production with a simultaneous increase in muscle activation, providing evidence for three cumulative mechanisms to enhance mechanical power production. Using the experimentally determined force-length-velocity potentials and muscle activation as inputs in a Hill-type muscle model, a reduction in maximum soleus muscle force at speeds ≥7.0 m s-1 and a continuous increase in maximum mechanical power with speed were predicted. The reduction in soleus maximum force was associated with a reduced force-velocity potential. The increase in maximum power was explained by an enhancement of muscle activation and contractile conditions until 7.0 m s-1, but mainly by increased muscle activation at high to maximal running speed.

Predictions of thumb, hand, and arm muscle parameters derived using force measurements of varying complexity and neural networks

Subject-specific musculoskeletal models are a promising avenue for personalized healthcare. However, current methods for producing personalized models require dense, biomechanical datasets that include expensive and time-consuming physiological measurements. For personalized models to be clinically useful, we must be able to rapidly generate models from simple, easy to collect data. In this context, the objective of this paper is to evaluate if and how simple data, namely height/weight and pinch force data, can be used to achieve model personalization via machine learning. Using simulated lateral pinch force measurements from a synthetic population of 40,000 randomly generated subjects, we train neural networks to estimate four Hill-type muscle model parameters and bone density. We compare parameter estimates to the true parameters of 10,000 additional synthetic subjects. We also generate new personalized models using the parameter estimates and perform new lateral pinch simulations to compare predicted forces using these personalized models to those generated using a baseline model. We demonstrate that increasing force measurement complexity reduces the root-mean-square error in the majority of parameter estimates. Additionally, musculoskeletal models using neural network-based parameter estimates provide up to an 80% reduction in absolute error in simulated forces when compared to a generic model. Thus, easily obtained force measurements may be suitable for personalizing models of the thumb, although extending the method to more tasks and models involving other joints likely requires additional measurements.

A three-dimensional musculoskeletal model of the pelvis and lower limb of Australopithecus afarensis.

Musculoskeletal modeling is a powerful approach for studying the biomechanics and energetics of locomotion. Australopithecus (A.) afarensis is among the best represented fossil hominins and provides critical information about the evolution of musculoskeletal design and locomotion in the hominin lineage. Here, we develop and evaluate a three-dimensional (3-D) musculoskeletal model of the pelvis and lower limb of A. afarensis for predicting muscle-tendon moment arms and moment-generating capacities across lower limb joint positions encompassing a range of locomotor behaviors. A 3-D musculoskeletal model of an adult A. afarensis pelvis and lower limb was developed based primarily on the A.L. 288-1 partial skeleton. The model includes geometric representations of bones, joints and 35 muscle-tendon units represented using 43 Hill-type muscle models. Two muscle parameter datasets were created from human and chimpanzee sources. 3-D muscle-tendon moment arms and isometric joint moments were predicted over a wide range of joint positions. Predicted muscle-tendon moment arms generally agreed with skeletal metrics, and corresponded with human and chimpanzee models. Human and chimpanzee-based muscle parameterizations were similar, with some differences in maximum isometric force-producing capabilities. The model is amenable to size scaling from A.L. 288-1 to the larger KSD-VP-1/1, which subsumes a wide range of size variation in A. afarensis. This model represents an important tool for studying the integrated function of the neuromusculoskeletal systems in A. afarensis. It is similar to current human and chimpanzee models in musculoskeletal detail, and will permit direct, comparative 3-D simulation studies.

Development and verification of a physiologically motivated internal controller for the open-source extended Hill-type muscle model in LS-DYNA

Nowadays, active human body models are becoming essential tools for the development of integrated occupant safety systems. However, their broad application in industry and research is limited due to the complexity of incorporated muscle controllers, the long simulation runtime, and the non-regular use of physiological motor control approaches. The purpose of this study is to address the challenges in all indicated directions by implementing a muscle controller with several physiologically inspired control strategies into an open-source extended Hill-type muscle model formulated as LS-DYNA user-defined umat41 subroutine written in the Fortran programming language. This results in increased usability, runtime performance and physiological accuracy compared to the standard muscle material existing in LS-DYNA. The proposed controller code is verified with extensive experimental data that include findings for arm muscles, the cervical spine region, and the whole body. Selected verification experiments cover three different muscle activation situations: (1) passive state, (2) open-loop and closed-loop muscle activation, and (3) reflexive behaviour. Two whole body finite element models, the 50th percentile female VIVA OpenHBM and the 50th percentile male THUMS v5, are used for simulations, complemented by the simplified arm model extracted from the 50th percentile male THUMS v3. The obtained results are evaluated additionally with the CORrelation and Analysis methodology and the mean squared error method, showing good to excellent biofidelity and sufficient agreement with the experimental data. It was shown additionally how the integrated controller allows simplified mimicking of the movements for similar musculoskeletal models using the parameters transfer method. Furthermore, the Hill-type muscle model presented in this paper shows better kinematic behaviour even in the passive case compared to the existing one in LS-DYNA due to its improved damping and elastic properties. These findings provide a solid evidence base motivating the application of the enhanced muscle material with the internal controller in future studies with Active Human Body Models under different loading conditions.

The force-length relation of the young adult human tibialis anterior.

Knowledge of the muscle's lengths at which maximum active isometric force is attained is important for predicting forces during movement. However, there is limited information about the in vivo force-length properties of a human muscle that plays crucial roles during locomotion; the tibialis anterior (TA). We therefore aimed to estimate TA's force-length relation from dorsiflexor torque-angle curves constructed from eight women and eight men. Participants performed maximal voluntary fixed-end contractions with their right ankle dorsiflexors from 0° to 30° plantar flexion. Muscle fascicle lengths were estimated from B-mode ultrasound images, and net ankle joint torques were measured using dynamometry. Fascicle forces were estimated by dividing maximal active torques by literature-derived, angle-specific tendon moment arm lengths while assuming a fixed 50% force contribution of TA to the total dorsiflexor force and accounting for fascicle angles. Maximal active torques were higher at 15° than 20° and 30° plantar flexion (2.4-6.4 Nm, p≤0.012), whereas maximal active TA fascicle forces were higher at 15° than 0°, 20° and 30° plantar flexion (25-61 N, p≤0.042), but not different between 15° and 10° plantar flexion (15 N, p=0.277). TA fascicle shortening magnitudes during fixed-end contractions were larger at 15° than 30° plantar flexion (3.9 mm, p=0.012), but less at 15° than 0° plantar flexion (-2.4 mm, p=0.001), with no significant differences (≤0.7 mm, p=0.871) between TA's superficial and deep muscle compartments. Series elastic element stiffness was lowest and highest at lengths 5% shorter and 5% longer than optimum fascicle length, respectively (-30 and 15 N/mm, p≤0.003). TA produced its maximum active force at 10-15° plantar flexion, and its normalized force-length relation had ascending and descending limbs that agreed with a simple scaled sarcomere model when active fascicle lengths from within TA's superficial or deep muscle compartment were considered. These findings can be used to inform the properties of the contractile and series elastic elements of Hill-type muscle models.

Tendon compliance and preload must be considered when determining the in vivo force–velocity relationship from the torque–angular velocity relation

In vivo, the force–velocity relation (F–v–r) is typically derived from the torque–angular velocity relation (T–ω–r), which is subject to two factors that may influence resulting measurements: tendon compliance and preload prior to contraction. The in vivo plantar flexors’ T–ω–r was determined during preloaded maximum voluntary shortening contractions at 0–200°/s. Additionally, we used a two factor block simulation study design to independently analyze the effects of preload and tendon compliance on the resulting T–ω–r. Therefore, we replicated the in vivo experiment using a Hill-type muscle model of the gastrocnemius medialis. The simulation results matched a key pattern observed in our recorded in vivo experimental data: during preloaded contractions, torque output of the muscle was increased when compared with non-preloaded contractions from literature. This effect increased with increasing contraction velocity and can be explained by a rapidly recoiling tendon, allowing the contractile element to contract more slowly, thus developing higher forces compared with non-preloaded contractions. Our simulation results also indicate that a more compliant tendon results in increased ankle joint torques. The simulation and the experimental data clearly show that the deduction of the in vivo F–v–r from the T–ω–r is compromised due to the two factors preloading and tendon compliance.

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.

Continuous Grasping Force Estimation With Surface EMG Based on Huxley-Type Musculoskeletal Model.

Continuous grasping force estimation based on electromyography (EMG) signals, is very useful in practical applications including prosthetic control and human force observation. However, implementing the practical grasping force estimation usually considers a trade-off between the computational precision and resources. Specifically, the estimation based on the Huxley-type muscle model reaches detailed approximation of physiological process at a cost of larger computational resources for solving nonlinear partial differential equations while the counterpart with a traditional Hill-type muscle model. In this article, we achieve the grasping force estimation based on a reduced Huxley-type musculoskeletal model with high accuracy yet low time delay. Leveraging on a balanced truncation method, we further reduce the dimensionality of the spectral method solution in the Huxley-type musculoskeletal model for the model simplification. In addition, we introduce the Kalman filter method to process the EMG signals obtained by an armband, yielding better real-time performances and accuracy compared to the signal treatment using the traditional EMG filter method. Moreover, we also implement an effective identification of the model parameters using a particle swarm method. Finally, we trained the model on the first day and made grasping force estimation experiments involved with three participants over the course of a month. We envision that this effective and practical method would further improve the practical applications in the field of grasping force estimation.

The effect of the 2-UPS/RR ankle rehabilitation robot with coupling biomechanical model on muscle behaviors.

With the popularization of biomechanical simulation technology, aiming at the rehabilitation of ankle joint injury, we imported simplified model of proposed 2-UPS/RR (two identical unconstraint kinematic branches with a universal-prismatic-spherical (UPS) structure and two rotating pair (R)) ankle rehabilitation robot into AnyBody Modeling System. Therefore, a human-machine model was established using the HILL-type muscle model and muscle recruitment criteria. This paper investigated the effects of rehabilitation trajectories on biomechanical response during rehabilitation. Additionally, three main lower limb muscles (soleus, peroneal brevis, and extensor digitorum longus) were examined under different rehabilitation trajectories (plantar dorsiflexion, varus or valgus, and compound movement) in the present study. Based on the biomechanical response of lower limbs, the results showed that different muscles had different sensitivities to the change of rehabilitation trajectories. The correlation coefficient between joint force and plantar dorsiflexion angle reached 0.99 (P < 0.01), indicating that the change of joint force was mainly dominated by plantar dorsiflexion/plantar flexion, but also affected by varus or valgus. Safe rehabilitation training can be achieved by controlling the designed 2-UPS/RR rehabilitation robot. The behavior of muscle force and joint force under different rehabilitation trajectories can meet the needs of rehabilitation and treatment of joint diseases, and provide more reasonable suggestions for early rehabilitation.

Differentiable Simulation of Inertial Musculotendons

We propose a simple and practical approach for incorporating the effects of muscle inertia, which has been ignored by previous musculoskeletal simulators in both graphics and biomechanics. We approximate the inertia of the muscle by assuming that muscle mass is distributed along the centerline of the muscle. We express the motion of the musculotendons in terms of the motion of the skeletal joints using a chain of Jacobians, so that at the top level, only the reduced degrees of freedom of the skeleton are used to completely drive both bones and musculotendons. Our approach can handle all commonly used musculotendon path types, including those with multiple path points and wrapping surfaces. For muscle paths involving wrapping surfaces, we use neural networks to model the Jacobians, trained using existing wrapping surface libraries, which allows us to effectively handle the Jacobian discontinuities that occur when musculotendon paths collide with wrapping surfaces. We demonstrate support for higher-order time integrators, complex joints, inverse dynamics, Hill-type muscle models, and differentiability. In the limit, as the muscle mass is reduced to zero, our approach gracefully degrades to traditional simulators without support for muscle inertia. Finally, it is possible to mix and match inertial and non-inertial musculotendons, depending on the application.

Understanding altered contractile properties in advanced age: insights from a systematic muscle modelling approach

Age-related alterations of skeletal muscle are numerous and present inconsistently, and the effect of their interaction on contractile performance can be nonintuitive. Hill-type muscle models predict muscle force according to well-characterised contractile phenomena. Coupled with simple, yet reasonably realistic activation dynamics, such models consist of parameters that are meaningfully linked to fundamental aspects of muscle excitation and contraction. We aimed to illustrate the utility of a muscle model for elucidating relevant mechanisms and predicting changes in output by simulating the individual and combined effects on isometric force of several known ageing-related adaptations. Simulating literature-informed reductions in free Ca2+ concentration and Ca2+ sensitivity generated predictions at odds qualitatively with the characteristic slowing of contraction speed. Conversely, incorporating slower Ca2+ removal or a fractional increase in type I fibre area emulated expected changes; the former was required to simulate slowing of the twitch measured experimentally. Slower Ca2+ removal more than compensated for force loss arising from a large reduction in Ca2+ sensitivity or moderate reduction in Ca2+ release, producing realistic age-related shifts in the force-frequency relationship. Consistent with empirical data, reductions in free Ca2+ concentration and Ca2+ sensitivity reduced maximum tetanic force only slightly, even when acting in concert, suggesting a modest contribution to lower specific force. Lower tendon stiffness and slower intrinsic shortening speed slowed and prolonged force development in a compliance-dependent manner without affecting force decay. This work demonstrates the advantages of muscle modelling for exploring sources of variation and identifying mechanisms underpinning the altered contractile properties of aged muscle.

Design and transmission modeling of a soft elbow exosuit using double artificial tendon system

Daily life would be affected if the upper extremity is injured, especially for people with spinal cord injury, stroke and other neuromuscular disorders. In order to assist in the rehabilitation of these movement disorders, exoskeleton robots are developed. Based on the muscular length relationship and the Hill-type muscle model, a lightweight, soft exosuit is designed for elbow flexion and extension. The exosuit is composed of an actuation box and a wearing sleeve. The power is transmitted from the actuation box to the sleeve utilizing an artificial tendon transmission system. The detailed mechanism design is introduced, and the mathematical double artificial tendon transmission model is developed. Experiments and related simulations are followed to validate the model. The prototype of the soft exosuit is tested on a male subject, and the results indicate that the soft exosuit is capable and effective in helping the elbow joint with flexion and extension.

Hill type muscle models do not capture the response to stretch in clinical tests of spasticity

Hill type muscle models do not capture the response to stretch in clinical tests of spasticity

Integration of Surrogate Huxley Muscle Model into Finite Element Solver for Simulation of the Cardiac Cycle.

Clinicians can use biomechanical simulations of cardiac functioning to evaluate various real and fictional events. Our present understanding of the molecular processes behind muscle contraction has inspired Huxley-like muscle models. Huxley-type muscle models, unlike Hill-type muscle models, are capable of modeling non-uniform and unstable contractions. Huxley's computational requirements, on the other hand, are substantially higher than those of Hill-type models, making large-scale simulations impractical to use. We created a data-driven surrogate model that acts similarly to the original Huxley muscle model but requires substantially less processing power in order to make the Huxley muscle models easier to use in computer simulations. We gathered data from multiple numerical simulations and trained a deep neural network based on gated-recurrent units. Once we accomplished satisfying precision, we integrated the surrogate model into our finite element solver and simulated a full cardiac cycle. Clinical Relevance- This enables clinicians to track the effects of changes in muscles at the microscale to the cardiac contraction (macroscale).