A Model of Cardiac Muscle Mechanics and Energetics
Geoffrey
Nunns
Auckland Bioengineering Institute, The University of Auckland
Model Status
This model is known to run in both OpenCell and COR. The units are consistent throughout, although it does not recreate all the published results. It contains a time delay, which was ignored in the model. This model simulates an isometric contraction.
Model Structure
Abstract: A model of cardiac muscle is proposed in which the contractile element is described by the sliding-filament theory of muscle contraction. The model is able to reproduce the time-varying patterns of tension, velocity of shortening, and muscle shortening as well as oxygen consumption of isometric or isotonic contractions. Quick releases can also be simulated in the model as well as changes in contractile state and initial muscle length. The results obtained with the model are in agreement with a wide range of experimental data concerning the mechanics and energetics of mammalian cardiac muscle.
model diagram
Schematic diagram depicting the actin-myosin crossbrige cycle.
The original paper reference is cited below:
A Model of Cardiac Muscle Mechanics and Energetics, Ronney B. Panerai, 1980, Journal of Biomechanics, 13, 929-940. PubMed ID: 7276000
$\frac{d n}{d t}=f(\mathrm{A\_c}-n)-gn$
$f=\begin{cases}0 & \text{if $x< 0$}\\ \frac{\mathrm{f\_1}x}{h} & \text{if $(x\ge 0)\land (x< h)$}\\ 0 & \text{otherwise}\end{cases}$
$g=\begin{cases}\mathrm{g\_2} & \text{if $x< 0$}\\ \frac{\mathrm{g\_1}x}{h} & \text{if $(x\ge 0)\land (x< h)$}\\ \frac{\mathrm{g\_1}x}{h} & \text{otherwise}\end{cases}$
$\mathrm{Ca\_f}=\mathrm{Ca\_0}\left|1-e^{-\mathrm{a\_1}t^{2}}\right|e^{-\mathrm{b\_1}(t-\mathrm{t\_d})^{2}}$
$\mathrm{c\_2}=\mathrm{c\_2\_0}e^{\mathrm{k\_i}\left(\frac{\mathrm{s\_h}}{1}\right)^{q}}\frac{d \mathrm{A\_c}}{d t}=\mathrm{c\_1}\left(\frac{\mathrm{Ca\_f}}{1}\right)^{2}(\mathrm{AT\_0}-\mathrm{A\_c})-\mathrm{c\_2}\mathrm{A\_c}$
$\mathrm{F\_SE}=\mathrm{alpha\_s}(e^{\frac{\mathrm{beta\_s}\mathrm{x\_s}}{1\times 1}}-1)$
$\mathrm{x\_s}=\mathrm{x\_so}+\mathrm{s\_h}+\mathrm{x\_m}-\mathrm{L\_max}$
$\mathrm{F\_PE}=\mathrm{alpha\_p}(e^{\frac{\mathrm{beta\_p}\mathrm{x\_p}}{1\times 1}}-1)$
$\mathrm{x\_p}=\mathrm{x\_po}-\mathrm{s\_h}$
$\mathrm{F\_CE}=\mathrm{F\_SE}-\mathrm{F\_PE}$
$\mathrm{s\_h}=\mathrm{x\_po}-\frac{1\times 1\lg (1+\frac{\mathrm{F\_PL}}{\mathrm{alpha\_p}})}{\mathrm{beta\_p}}$
$\mathrm{X\_S\_0}=\frac{1\times 1\lg (1+\frac{\mathrm{F\_PL}}{\mathrm{alpha\_s}})}{\mathrm{beta\_s}}\mathrm{X\_M\_0}=\mathrm{X\_S\_0}+\mathrm{L\_max}-\mathrm{s\_h}-\mathrm{x\_so}$
Geoff Nunns
Geoffrey
Nunns
Rogan
1980-02-21 00:00
This model is known to run in both PCEnv and COR. The units are consistent throughout, although it does not recreate all the published results. It contains a time delay, which was ignored in the model, and may be the reason for this. This model simulates an isometric contraction.
The University of Auckland
Auckland Bioengineering Institute
Geoff Nunns
2008-07-03T00:00:00+12:00
This model is known to run in both PCEnv and COR. The units are consistent throughout, although it does not recreate all the published results. It contains a time delay, which was ignored in the model, and may be the reason for this. This model simulates an isometric contraction.
Journal of Biomechanics
A Model of Cardiac Muscle Mechanics and Energetics
13
929
940
gnunns1@jhem.jhu.edu
Ronney
Panerai
B
keyword
myofilament mechanics
mechanical constitutive laws
cardiac
7276000