Hill equation and Hatze’s muscle activation dynamics complement each other: enhanced pharmacological and physiological interpretability of modelled activity-pCa curves

Rockenfeller, Robert; Günther, Michael

doi:10.1016/j.jtbi.2017.07.023

Cited by 20 publications

(10 citation statements)

References 117 publications

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“…Given the finding that the force-length dependency of contraction dynamics shifts with calcium concentration [14] which, in turn, governs activation, the computational separation of the activation and contraction dynamics may be challenged. For example, Rockenfeller and Günther recently proposed a model where muscle activation depends on the volumetric density of calcium binding sites, which in turn is a function of muscle fibre length [15,16].…”

Section: Introductionmentioning

confidence: 99%

Evaluation of linear and non-linear activation dynamics models for insect muscle

et al. 2019

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In computational modelling of sensory-motor control, the dynamics of muscle contraction is an important determinant of movement timing and joint stiffness. This is particularly so in animals with many slow muscles, as is the case in insects—many of which are important models for sensory-motor control. A muscle model is generally used to transform motoneuronal input into muscle force. Although standard models exist for vertebrate muscle innervated by many motoneurons, there is no agreement on a parametric model for single motoneuron stimulation of invertebrate muscle. Although several different models have been proposed, they have never been evaluated using a common experimental data set. We evaluate five models for isometric force production of a well-studied model system: the locust hind leg tibial extensor muscle. The response of this muscle to motoneuron spikes is best modelled as a non-linear low-pass system. Linear first-order models can approximate isometric force time courses well at high spike rates, but they cannot account for appropriate force time courses at low spike rates. A linear third-order model performs better, but only non-linear models can account for frequency-dependent change of decay time and force potentiation at intermediate stimulus frequencies. Some of the differences among published models are due to differences among experimental data sets. We developed a comprehensive toolbox for modelling muscle activation dynamics, and optimised model parameters using one data set. The “Hatze-Zakotnik model” that emphasizes an accurate single-twitch time course and uses frequency-dependent modulation of the twitch for force potentiation performs best for the slow motoneuron. Frequency-dependent modulation of a single twitch works less well for the fast motoneuron. The non-linear “Wilson” model that optimises parameters to all data set parts simultaneously performs better here. Our open-access toolbox provides powerful tools for researchers to fit appropriate models to a range of insect muscles.

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Section: Introductionmentioning

confidence: 99%

Evaluation of linear and non-linear activation dynamics models for insect muscle

et al. 2019

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“…EET acts directly with human HJ flexor muscle group [ 21 ]. During the auxiliary period of EET, the calculation method of residual total flexion biological moment M Re provided by rectus femoris and iliopsoas muscle based on Hill muscle optimization model can be expressed as follows:

M I represents the moment of iliopsoas muscle; M R represents the moment of rectus femoris; M T represents M J less than the total flexion moment of flexor at HJ during natural walking.…”

Section: Methodsmentioning

confidence: 99%

“…EET acts directly with human HJ flexor muscle group [21]. During the auxiliary period of EET, the calculation method of residual total flexion biological moment M Re provided by rectus femoris and iliopsoas muscle based on Hill muscle optimization model can be expressed as follows:…”

Section: Establishment Of Hill Muscle Optimization Modelmentioning

confidence: 99%

Construction and Simulation of Biomechanical Model of Human Hip Joint Muscle-Tendon Assisted by Elastic External Tendon by Hill Muscle Model

Luo

Cai

et al. 2022

Computational Intelligence and Neuroscience

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Based on the Hill muscle model (HMM), a biomechanical model of human hip muscle tendon assisted by elastic external tendon (EET) was preliminarily established to investigate and analyze the biomechanical transition between the hip joint (HJ) and related muscle tendons. Using the HMM, the optimal muscle fiber length and muscle force scaling variables were introduced by means of constrained optimization problems and were optimized. The optimized HMM was constructed with human parameters of 170 cm and 70 kg. The biomechanical model simulation test of the hip muscle tendon was performed in the automatic dynamic analysis of mechanical systems (ADAMS) software to analyze and optimize the changes in the root mean square error (RMSE), biological moment, muscle moment distribution coefficient (MDC), muscle moment, muscle force, muscle power, and mechanical work of the activation curves of the hip major muscle, iliopsoas muscle, rectus femoris muscle, and hamstring muscle under analyzing the optimized HMM and under different EET auxiliary stiffnesses from the joint moment level, joint level, and muscle level, respectively. It was found that the trends of the output joint moment of the optimized HMM and the biological moment of the human HJ were basically the same, r2 = 0.883 and RMSE = 0.18 Nm/kg, and the average metabolizable energy consumption of the HJ was (243.77 ± 1.59) J. In the range of 35%∼65% of gait cycle (GC), the auxiliary moment showed a significant downward trend with the increase of EET stiffness, when the EET stiffness of the human body was less than 200 Nm/rad, the biological moment of the human HJ gradually decreased with the increase of EET stiffness, and the MDC of the iliopsoas and hamstring muscles gradually decreased; when the EET stiffness was greater than 200 Nm/rad, the increase of the total moment of the extensor muscles significantly increased, the MDC of the gluteus maximus and rectus muscles gradually increased, and the gluteus maximus and hamstring muscle moments and muscle forces gradually increased; the results show that the optimized muscle model based on Hill can reflect the law of human movement and complete the simulation test of HJ movements, which provides a new idea for the analysis of energy migration in the musculoskeletal system of the lower limb.

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“…(11) The formulation includes a minimum troponin-activityq min of the muscle at rest and a linear length dependency function ̟ describing the troponin C density with varying interfilamentary spacing (Rockenfeller and Günther, 2018), based on sarcomere volume constancy (Dragomir, 1970). The Hatze exponent ν has previously (Rockenfeller and Günther, 2017a) been equated to the exponent of the Hill equation (Hill, 1910). However, so far no mechanistic explanation has been provided on how to convert the relative amount of calcium-bound troponin (troponin-activity:q ) to the relative amount of built-up cross-bridges (actual activity: a), i.e., it is implied that myosin heads will automatically bind to available active sites and proceed with force generation.…”

Section: Conflict Of Interestmentioning

confidence: 99%

Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model

et al. 2020

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Hill equation and Hatze’s muscle activation dynamics complement each other: enhanced pharmacological and physiological interpretability of modelled activity-pCa curves

Cited by 20 publications

References 117 publications

Evaluation of linear and non-linear activation dynamics models for insect muscle

Evaluation of linear and non-linear activation dynamics models for insect muscle

Construction and Simulation of Biomechanical Model of Human Hip Joint Muscle-Tendon Assisted by Elastic External Tendon by Hill Muscle Model

Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model

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