Related Experiment Video
Updated: May 16, 2026
09:32
Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
Published on: April 11, 2018
Spreading out muscle mass within a Hill-type model: a computer simulation study
Michael Günther1, Oliver Röhrle, Daniel F B Haeufle
1Institut für Sport-und Bewegungswissenschaft, Universität Stuttgart, Allmandring 28, 70569 Stuttgart, Germany. s7gumi@uni-jena.de
Computational and Mathematical Methods in Medicine
|December 11, 2012
Summary
Muscle models typically ignore internal inertia. This study shows that inertia significantly impacts muscle response times, especially in larger muscles, suggesting the need for more complex models.
Area of Science:
- Biomechanics
- Muscle Physiology
- Computational Modeling
Background:
- Current muscle contraction models use the Hill relation, a first-order dynamic model.
- These models neglect muscle internal mass inertia, which may be crucial for understanding rapid muscle responses.
Purpose of the Study:
- Investigate the time scale of muscle response to force steps.
- Determine how muscle response scales with design parameters, considering internal mass inertia.
Main Methods:
- Simulated accelerated contractions using sequences of Hill-type contractile elements and point masses.
- Compared responses in a typical small muscle model versus an upscaled model for larger mammals.
Main Results:
- In small muscles, force stabilized within 0.2 ms and velocity within 0.5 ms.
- In larger muscle models, force stabilization took ~20 ms, and maximum velocity was not reached.
- Response times were found to scale with muscle design parameters.
Conclusions:
- Second-order dynamics (including inertia) are essential for accurately modeling high-frequency muscle responses, particularly in larger muscles.
- Advanced measurement techniques are needed to differentiate viscoelastic and inertial properties in rapid muscle contractions.
Related Concept Videos
01:14Multicompartment Models: Overview
Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
01:22Muscle Stimulation Frequency
The contraction strength of muscles is regulated by motor neurons, which modulate the frequency of action potentials dispatched to the motor units based on the body's requirements. This process of varying the muscle stimulation frequency allows muscles to contract with a force that is precisely tailored to the needs of the moment, whether lifting a feather or a heavy box.
Wave summation
At low firing rates, motor neurons induce individual twitch contractions in muscle fibers. These twitches...
Wave summation
At low firing rates, motor neurons induce individual twitch contractions in muscle fibers. These twitches...
01:07Conservation of Mass in Fixed, Nondeforming Control Volume
The principle of conservation of mass is fundamental in fluid dynamics and is crucial for analyzing flow within fixed control volumes, such as pipes or ducts. This principle states that the total mass within a control volume remains constant unless altered by the inflow or outflow of mass through the control surfaces. This results in a vital relationship for steady, incompressible flow where the mass entering a system equals the mass leaving it.
In the case of a sewer pipe, which can be modeled...
In the case of a sewer pipe, which can be modeled...
01:30Typical Model Studies
Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
01:14Compartment Models: Single-Compartment Model
The single-compartment model serves as a simplified representation of the human body. This model assumes that the body functions as a single, well-mixed open compartment. When a drug is administered intravenously, it enters the body and quickly distributes uniformly. The drug then undergoes biotransformation and elimination, ultimately leaving the body. The volume of this compartment is referred to as the apparent volume of distribution into which the drug can uniformly distribute. In this...
01:25Modeling with Differential Equations
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...