Hill-type muscle model with serial damping and eccentric force–velocity relation

Haeufle, Daniel F. B.; Günther, Michael; Bayer, A.; Schmitt, Syn

doi:10.1016/j.jbiomech.2014.02.009

Cited by 151 publications

(160 citation statements)

References 28 publications

Supporting

Mentioning

157

Contrasting

Unclassified

Order By: Relevance

“…In the early nineteen hundreds Hill developed a simple but widely accepted model of muscle function suitable for defining the basic mechanics of the muscles and for modelling specific beaviours of muscles during voluntary human movements [21,23]. Since this early work, progress had been made towards the understanding of muscular structure and its function and new Hill-type muscle models have been created [24,25].…”

Section: Hill-type Muscle Modelsmentioning

confidence: 99%

“…A range of mechanical models of muscles -Crowe (1970) [27], Gottlieb and Agarwal (1971) [28], Winter (1995) [16], Haeufle (2014) [24] -exist that describe and calculate the tension of a muscle depending on different inputs. All of these use a modified Hill-type muscle model with different connections between the CE, the PEC and the SEC elements.…”

Section: Gastrocnemius Muscle-achilles Tendon Complex Analysismentioning

confidence: 99%

“…The analytical solutions were generated symbolically in Matlab 2016a and gave equation (24) as the solution of the ordinary differential equation: (24) and one real root and a complex conjugate pair of roots for the cubic equation. However, the mathematical solutions of the cubic equation for x1 that are complex numbers cannot represent a displacement of a length.…”

Section: Nonlinearitymentioning

confidence: 99%

See 2 more Smart Citations

A mathematical model characterising Achilles tendon dynamics in flexion

Chatzistefani

Chappell

Hutchinson

et al. 2017

Mathematical Biosciences

View full text Add to dashboard Cite

Abstract:The purpose of this study is to acquire mechanistic knowledge of the gastrocnemius muscleAchilles tendon complex behaviour during specific movements in humans through mathematical modelling. Analysis of this muscle-tendon complex was performed to see if already existing muscle-tendon models of other parts of the body could be applied to the leg muscles, especially the gastrocnemius muscleAchilles tendon complex, and whether they could adequately characterise its behaviour. Five healthy volunteers were asked to take part in experiments where dorsiflexion and plantar flexion of the foot were studied. A model of the Achilles tendon-gastrocnemius muscle was developed, incorporating assumptions regarding the mechanical properties of the muscle fibres and the tendinous tissue in series. Ultrasound images of the volunteers, direct measurements and additional mathematical calculations were used to parameterise the model. Ground reaction forces, forces on specific joints and moments and angles for the ankle were obtained from a Vicon 3D motion capture system. Model validation was performed from the experimental data captured for each volunteer and from reconstruction of the movements of specific trajectories of the joints, muscles and tendons involved in those movements.

show abstract

Section: Hill-type Muscle Modelsmentioning

confidence: 99%

Section: Gastrocnemius Muscle-achilles Tendon Complex Analysismentioning

confidence: 99%

Section: Nonlinearitymentioning

confidence: 99%

See 1 more Smart Citation

A mathematical model characterising Achilles tendon dynamics in flexion

Chatzistefani

Chappell

Hutchinson

et al. 2017

Mathematical Biosciences

View full text Add to dashboard Cite

show abstract

“…In this paper we use a modified Hill-model [21,22] to describe the contraction motion of muscles. This model is based on a mechanical analogy of the muscle tendon complex (MTC) and is constituted by four basic compartments.…”

Section: Model Description and Problem Formulationmentioning

confidence: 99%

“…In Section 2 we recapitulate the muscle model given in [21] using contraction modes from [22]. For simplicity, we just consider the situation for a single muscle.…”

Section: B Introductionmentioning

confidence: 99%

Optimal Control of Isometric Muscle Dynamics

Rockenfelle¹,

Götz²

2015

j.math.fund.sci.

View full text Add to dashboard Cite

Abstract. We use an indirect optimal control approach to calculate the optimal neural stimulation needed to obtain measured isometric muscle forces. The neural stimulation of the nerve system is hereby considered to be a control function (input) of the system 'muscle' that solely determines the muscle force (output). We use a well-established muscle model and experimental data of isometric contractions. The model consists of coupled activation and contraction dynamics described by ordinary differential equations. To validate our results, we perform a comparison with commercial optimal control software.Keywords: biomechanics; inverse dynamics; muscle model; optimal control, stimulation. 0 B IntroductionMathematical models for everyday phenomena often ask for a control or input such that a system reacts in an optimal or at least in a desired way. Whether finding the optimal rotation of a stick for cooking potatoes on the open fire such that the potato has a desired temperature, see [1], or computing the optimal neural stimulation of a muscle such that the force output is as close as possible to experimentally measured data. Typical examples for biomechanical optimal control problems occur in the calculation of goal directed movements, see [2][3][4] and in robotics [5]. Concerning huge musculoskeletal systems, the load sharing problem of muscle force distribution has to be solved using optimal control [6,7]. The most common application for solving the load sharing problem is the inverse dynamics of multi-body systems (MBS) as in [8,9]. The aim is to approximate observed multi-body trajectories by a forward simulation. The problem occurs to find a set of muscle activations such that the muscle forces resulting from the MBS simulation are similar to the measured ones.Considering a general optimal control problem there is a process described by a vector of state variables which has to be influenced by control variable u ∈ within a time interval [t 0 , t 1 ] such that a given objective function ℑ( , u) is minimized subject to the model equations. These model equations can be either ordinary differential equations (ODE), partial differential equations (PDE) or differential algebraic equations (DAE). Additional constraints on the control Optimal Control of Isometric Muscle Dynamics 13 variable as well as the state variable itself can be imposed. The corresponding general optimal control problem reads as follows:For solving this minimization problem we introduce an adjoint (or costate) variable λ which operates as a penalty function, if the ODE or DAE are not fulfilled. The optimized control variable u * is found at the saddle point of the Lagrangian ℒ.Almost exclusively in biomechanical literature, the problem in Eq. (1) is solved by the technique of first discretize then optimize also known as direct method. Therefore ℑ as well as the ODE/DAE constraints are discretized on a given time grid resulting in a huge non-linear program (NLP), see [1,[10][11][12]. For solving such NLPs, several efficient solvers have been desig...

show abstract

Muscle‐driven virtual human motion generation approach based on deep reinforcement learning

Qin

Tao

Sun

et al. 2022

Computer Animation & Virtual

View full text Add to dashboard Cite

We propose a muscle-driven motion generation approach to realize virtual human motion with user interaction and higher fidelity, which can address the problem that the joint-driven fails to reflect the motion process of the human body. First, a simplified virtual human musculoskeletal model is built based on human biomechanics. Then, a hierarchical policy learning framework is constructed including motion tracking layer, SPD controller and muscle control layer. The motion tracking layer is responsible for mimicking reference motion and completing control command, using proximal policy optimization to train the policy; the muscle control layer is aimed to minimize muscle energy consumption and train the policy based on supervised learning; the SPD controller acts as a link between the two layers. At the same time, we integrate the curriculum learning to improve the efficiency and success rate of policy training. Simulation experiments show that the proposed approach can use motion capture data and pose estimation data as reference motions to generate better and more adaptable motions. Furthermore, the virtual human has the ability to respond to the user control command during the motion, and can complete the target task successfully.

show abstract

Hill-type muscle model with serial damping and eccentric force–velocity relation

Cited by 151 publications

References 28 publications

A mathematical model characterising Achilles tendon dynamics in flexion

A mathematical model characterising Achilles tendon dynamics in flexion

Optimal Control of Isometric Muscle Dynamics

Muscle‐driven virtual human motion generation approach based on deep reinforcement learning

Contact Info

Product

Resources

About