Teaching from classic papers: Hill's model of muscle contraction
Catherine
Lloyd
Auckland Bioengineering Institute, University of Auckland
Model Status
This CellML model runs in both PCEnv and COR to reproduce the published results. The units have been checked and they are consistent.
Model Structure
ABSTRACT: A. V. Hill's 1938 paper "The heat of shortening and the dynamic constants of muscle" is an enduring classic, presenting detailed methods, meticulous experiments, and the model of muscle contraction that now bears Hill's name. Pairing a simulation based on Hill's model with a reading of his paper allows students to follow his thought process to discover key principles of muscle physiology and gain insight into how to develop quantitative models of physiological processes. In this article, the experience of the author using this approach in a graduate biomedical engineering course is outlined, along with suggestions for adapting this approach to other audiences.
Teaching from classic papers: Hill's model of muscle contraction, J.W. Holmes, 2006,
Advances in Physiology Education
, 30, 67-72.
PubMed ID: 16709736
diagram
A schematic diagram of the two component muscle model. Force in the muscle = F_SE = F_CE. By specifying Lm, Fm is calculated from the force velocity properties of CE and the force-length relationship of SE.
$v=\frac{-b(\mathrm{Po}-P)}{P+a}\mathrm{L\_se}=L-\mathrm{L\_ce}L=\begin{cases}1 & \text{if $\mathrm{time}\le 1$}\\ 0.92 & \text{if $(\mathrm{time}> 1)\land (\mathrm{time}< 5)$}\\ 0.9 & \text{otherwise}\end{cases}\frac{d \mathrm{L\_ce}}{d \mathrm{time}}=vP=\mathrm{alpha}(\mathrm{L\_se}-\mathrm{L\_se\_o})$
Fraction of muscle length
Steady-state force
Time Domain
Contribution of muscle elastic elements to fraction of muscle length
Initial contribution of muscle elastic elements to fraction of muscle length
Slope of the relationship between the change in muscle length and excess heat.
Time Domain
Chris Thompson
Contraction of skeletal muscle
Skeletal muscle contraction
Shortening velocity
Maximal isometric tetanic force
Spring constant for series elastic element
Slope excess energy rate and steady-state force relationship
Contribution of muscle contractile elements to fraction of muscle length
0.1
10