High-frequency oscillations as a consequence of neglected serial damping in Hill-type muscle models

Günther, Michael; Schmitt, Syn; Wank, Veit

doi:10.1007/s00422-007-0160-6

Cited by 88 publications

(147 citation statements)

References 54 publications

Supporting

Mentioning

146

Contrasting

Order By: Relevance

“…The value A rel = 1/4 was both originally found by Hill (Hill, 1938) for a frog sartorius muscle at T = 0 o C and represents the average value of further studies (Barclay, 1994(Barclay, , 1996Barclay et al, 1993;Günther et al, 2007;Houdijk et al, 2006). The Eqs.…”

mentioning

confidence: 64%

“…Energy dissipation within the muscle can be a passive (Günther et al, 2007;Minajeva et al, 2001;Wang et al, 1993) or an active (Gasser and Hill, 1924;Hartree and Hill, 1920;Hill, 1922;Levin and Wyman, 1927;Lupton, 1922Lupton, , 1923 phenomenon. Two studies point to a dependency of the PDE on muscle force (Baker and Thomas, 2000;Pate and Cooke, 1991).…”

Section: Methodsmentioning

confidence: 99%

“…The lowest and highest c˙h 0 values (0.01, 0.3) extracted from literature (Barclay, 1994(Barclay, , 1996Barclay et al, 1993;Elzinga et al, 1987;Günther et al, 2007;Hill, 1938;Houdijk et al, 2006;Wank et al, 2006) (for R P DE = 0: Eq. (16)) with the belonging factor…”

Section: Maintenance Heat Rate Enthalpy Rate Mechanical Efficiency:mentioning

confidence: 99%

“…The parameters of our model (identical to Fig. 2) represent a median piglet muscle (Günther et al, 2007): Applying the first time derivative to this approximative force equilibrium, assuming the forces borne by all elements to depend on their respective lengths (F AE on filament overlap and additionally on the muscle activation q), and using the chain rule we get However, this will only apply if the damping force in the PDE is clearly lower than the force in the AE due to its isometric force-length characteristic and elastic force also dominates in the SE. If, in contrast, the PDE term and A c c e p t e d m a n u s c r i p t submitted to the Journal of Theoretical Biology 47 damping in the SE became dominant and we further assumed that SE damping could be linearly approximated in proportion to its current contraction velocity the simplified force equilibrium…”

Section: Acknowledgementsmentioning

confidence: 99%

“…For example, it might constitute a thermodynamical state equation or a fairly complex visco-elastic force law. In numerical neuro-musculo-skeletal model simulations Hill-type models are usually used in the force law sense (Günther and Ruder, 2003;Günther et al, 2007;Houdijk et al, 2006;Kistemaker et al, 2006;van Soest and Bobbert, 1993) interpreting it uni-directionally, with the force given and the respective velocity constituting the model response.…”

mentioning

confidence: 99%

See 4 more Smart Citations

A macroscopic ansatz to deduce the Hill relation

Günther

Schmitt

2010

Journal of Theoretical Biology

Self Cite

View full text Add to dashboard Cite

In this study, we derive the hyperbolic force-velocity relation of concentric muscular contraction, first formulated empirically by A.V. Hill in 1938, from three essential model assumptions: (1) the structural assembly of three wellknown elements -i.e. active, parallel damping, and serial -fulfilling a force equilibrium, (2) the parallel damping coefficient explicitly depending on muscle force output and three parameters, and (3) the kinematic gearing ratio between active and serial element being assigned to a parameter. The energy source within the muscle represented by the force of the active element is an additional fifth parameter. As a result we find the Hill "constants"A and B as functions of our five model parameters. Using A and B values from literature on experimental data, we predict heat power release of our model. By calculating enthalpy rate and mechanical efficiency, we compare the model heat power to predictions from another Hill-type model, to Hill's original findings, and to findings from modern muscle heat measurements. We reconsider why the biggest share of heat rate during isometric contractions (maintenance heat) and the velocity-dependent heat rate during concentric contractions in addition to maintenance heat rate (shortening heat rate) may be traced back to the same mechanism represented by the kinematic gearing ratio. Namely, we suggest that the serial element transfers attachment-detachment fluctuations of actin-myosin crossbridges within one sarcomere to others in the same sarcomere and to those in parallel and in series. Numerically, in case of negligible passive muscular damping, we find the ratio between A and isometric force (relative A) to depend exclusively on the kinematic gearing ratio, whereas the maintenance heat rate scales with the square of relative A. Moreover, this mechanical coupling internal to the muscle fibres may also be behind the macroscopic force dependency of the overall parallel damping coefficient. Keywords: Hill equation, Muscle model, Contraction dynamics, Biomechanics A c c e p t e d m a n u s c r i p t submitted to the Journal of Theoretical Biology 3 LIST OF SYMBOLS, TERMS, AND DEFINITIONS

show abstract

mentioning

confidence: 64%

Section: Methodsmentioning

confidence: 99%

Section: Maintenance Heat Rate Enthalpy Rate Mechanical Efficiency:mentioning

confidence: 99%

Section: Acknowledgementsmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

A macroscopic ansatz to deduce the Hill relation

Günther

Schmitt

2010

Journal of Theoretical Biology

Self Cite

View full text Add to dashboard Cite

show abstract

Gradient‐based optimization with B‐splines on sparse grids for solving forward‐dynamics simulations of three‐dimensional, continuum‐mechanical musculoskeletal system models

Valentin

Sprenger

Pflüger

et al. 2018

Numer Methods Biomed Eng

View full text Add to dashboard Cite

Investigating the interplay between muscular activity and motion is the basis to improve our understanding of healthy or diseased musculoskeletal systems. To be able to analyze the musculoskeletal systems, computational models are used. Albeit some severe modeling assumptions, almost all existing musculoskeletal system simulations appeal to multibody simulation frameworks. Although continuum-mechanical musculoskeletal system models can compensate for some of these limitations, they are essentially not considered because of their computational complexity and cost. The proposed framework is the first activation-driven musculoskeletal system model, in which the exerted skeletal muscle forces are computed using 3-dimensional, continuum-mechanical skeletal muscle models and in which muscle activations are determined based on a constraint optimization problem. Numerical feasibility is achieved by computing sparse grid surrogates with hierarchical B-splines, and adaptive sparse grid refinement further reduces the computational effort. The choice of B-splines allows the use of all existing gradient-based optimization techniques without further numerical approximation. This paper demonstrates that the resulting surrogates have low relative errors (less than 0.76%) and can be used within forward simulations that are subject to constraint optimization. To demonstrate this, we set up several different test scenarios in which an upper limb model consisting of the elbow joint, the biceps and triceps brachii, and an external load is subjected to different optimization criteria. Even though this novel method has only been demonstrated for a 2-muscle system, it can easily be extended to musculoskeletal systems with 3 or more muscles.

show abstract

The dynamics of the skeletal muscle: A systems biophysics perspective on muscle modeling with the focus on Hill‐type muscle models

2019

Self Cite

View full text Add to dashboard Cite

Skeletal muscle is one of the most fascinating and crucial ingredients of motion generation in nature. Since the beginning of science, people dedicate their life as researchers to enhance knowledge about this biological motor. Thus, the scientific knowledge about the skeletal muscle is overwhelmingly broad and detailed. This contribution collects knowledge about the active and passive dynamics of skeletal muscle. Furthermore, it highlights a special perspective in which not only the muscle itself, but also the role muscles play in the interaction with other structures is studied. The first section introduces this systems biophysics perspective, which clusters the investigation of the relations, interactions and dependencies between muscles and the other structures in the movement apparatus. In the second section, the muscles are considered in more detail by describing three approaches to muscle modeling. The third section deals with recent advances based on Hill‐type models, such as, for example, the integration of mass.

show abstract

High-frequency oscillations as a consequence of neglected serial damping in Hill-type muscle models

Cited by 88 publications

References 54 publications

A macroscopic ansatz to deduce the Hill relation

A macroscopic ansatz to deduce the Hill relation

Gradient‐based optimization with B‐splines on sparse grids for solving forward‐dynamics simulations of three‐dimensional, continuum‐mechanical musculoskeletal system models

The dynamics of the skeletal muscle: A systems biophysics perspective on muscle modeling with the focus on Hill‐type muscle models

Contact Info

Product

Resources

About