Virtual muscle: a computational approach to understanding the effects of muscle properties on motor control
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model has been checked in both COR and OpenCell. Currently it can be opened in COR but due to the presence of 'circular arguments' the model does not run. However the model will run in OpenCell but although it does run, it does so very, very slowly, and so far we have only been able to get it to solve for 3 iterations. The units have been checked and they are consistent.
Model Structure
Abstract: This paper describes a computational approach to modeling the complex mechanical properties of muscles and tendons under physiological conditions of recruitment and kinematics. It is embodied as a software package for use with Matlab™ and Simulink that allows the creation of realistic musculotendon elements for use in motor control simulations. The software employs graphic user interfaces (GUI) and dynamic data exchange (DDE) to facilitate building custom muscle model blocks and linking them to kinetic analyses of complete musculoskeletal systems. It is scalable in complexity and accuracy. The model is based on recently published data on muscle and tendon properties measured in feline slow- and fast-twitch muscle, and incorporates a novel approach to simulating recruitment and frequency modulation of different fiber-types in mixed muscles. This software is distributed freely over the Internet at http://ami.usc.edu/mddf/virtualmuscle.
The original paper reference is cited below:
Virtual muscle: a computational approach to understanding the effects of muscle properties on motor control, Ernest J. Cheng, Ian E. Brown and Gerald E. Loeb, 2000,
Journal of Neuroscience Methods
, 101, 117-130. PubMed ID: 10996372
reaction diagram
Schematic representation of the model equations and terms. These elements were designed to have a one-to-one correspondence with the physiological substrates of muscle contraction. The behavior of each element is governed by an equation driven by one to four input variables, with one to seven user-modifiable coefficients. The coefficients can be modified in the BuildFiberTypes function. Complete descriptions of these elements can be found in Brown and Loeb, 2000 and Brown. FPE1 represents the passive visco-elastic properties of stretching a muscle. FPE2 represents the passive resistance to compression of the thick filaments at short muscle lengths. FL represents the tetanic, isometric force–length relationship. FV represents the tetanic force–velocity (FV) relationship. Af represents the isometric, activation–frequency (Af) relationship. feff represents the time lag between changes in firing frequency and internal activation (i.e. rise and fall times). Leff represents the time lag between changes in length and the effect of length on the Af relationship. S represents the effects of ‘sag’ on the activation during a constant stimulus frequency. Y represents the effects of yielding (on activation) following movement during sub-maximal activation.
F_SE
tendon elasticity
F_PE1
parallel elastic element
F_PE2
thick filament compression
FL
force-length
FV
force-velocity
Af
effective activation
L_eff
activation delay
S
Sag
Y
yield
rise_and_fall_time
rise and fall time
$\mathrm{F\_SE}=\mathrm{cT}\mathrm{F\_max}\mathrm{kT}\ln (e^{\frac{\mathrm{LT}-\mathrm{LT\_r}}{\mathrm{kT}}}+1)$
$\mathrm{F\_PE1}=\mathrm{c1}\mathrm{k1}\ln (e^{\frac{\frac{L}{\mathrm{L\_max}}-\mathrm{L\_r1}}{\mathrm{k1}}}+1)+\mathrm{eta}V$
$\mathrm{F\_PE2}=\mathrm{c2}(e^{\mathrm{k2}(L-\mathrm{L\_r2})}-1)$
$\mathrm{FL}=e^{-\left|\frac{L^{\mathrm{beta}}-1}{\mathrm{omega}}\right|^{\mathrm{rho}}}$
$\mathrm{FV}=\begin{cases}\frac{\mathrm{V\_max}-V}{\mathrm{V\_max}+(\mathrm{cv0}+\mathrm{cv1}L)V} & \text{if $V\le 0$}\\ \frac{\mathrm{bv}-(\mathrm{av0}+\mathrm{av1}L+\mathrm{av2}L^{2})V}{\mathrm{bv}+V} & \text{otherwise}\end{cases}$
$\mathrm{Af}=1-e^{-\left(\frac{YS\mathrm{f\_eff}}{\mathrm{af}\mathrm{nf}}\right)^{\mathrm{nf}}}$
$\mathrm{F0}=\mathrm{Af}(\mathrm{FL}+\mathrm{FV}+\mathrm{F\_PE2})+\mathrm{F\_PE1}$
$\mathrm{F\_CE}=\mathrm{F0}\mathrm{F\_max}$
$\mathrm{F\_total}=\mathrm{F\_SE}-\mathrm{F\_CE}$
$\frac{d \mathrm{L\_eff}}{d \mathrm{time}}=\frac{(L-\mathrm{L\_eff})^{3}}{\mathrm{T\_L}(1-\mathrm{Af})}$
$\frac{d S}{d \mathrm{time}}=\frac{\mathrm{as\_}-S}{\mathrm{T\_s}}\mathrm{as\_}=\begin{cases}\mathrm{as1} & \text{if $\mathrm{f\_eff}< 0.1$}\\ \mathrm{as2} & \text{otherwise}\end{cases}$
$\frac{d Y}{d \mathrm{time}}=\frac{1-\mathrm{c\_Y}(1-e^{\frac{-\left|V\right|}{\mathrm{V\_Y}}})+Y}{\mathrm{T\_Y}}$
$\frac{d \mathrm{f\_int}}{d \mathrm{time}}=\frac{\mathrm{f\_env}-\mathrm{f\_int}}{\mathrm{T\_f}}\frac{d \mathrm{f\_eff}}{d \mathrm{time}}=\mathrm{df\_eff\_dt}\mathrm{df\_eff\_dt}=\frac{\mathrm{f\_int}-\mathrm{f\_eff}}{\mathrm{T\_f}}\mathrm{T\_f}=\begin{cases}\mathrm{T\_f1}L^{2}+\mathrm{T\_f2}\mathrm{f\_env} & \text{if $\mathrm{df\_eff\_dt}\ge 0$}\\ \frac{\mathrm{T\_f3}+\mathrm{T\_f4}\mathrm{Af}}{L} & \text{otherwise}\end{cases}$
$\frac{d V}{d \mathrm{time}}=\frac{\mathrm{F\_total}}{1\mathrm{mass}}$
$\mathrm{V0}=\frac{V}{\mathrm{L\_max}}$
$\mathrm{L0}=\frac{L}{\mathrm{L\_max}}$
$\frac{d L}{d \mathrm{time}}=V$
The University of Auckland, Auckland Bioengineering Institute
Journal of Neuroscience Methods
2000-09-15 00:00
Catherine
Lloyd
May
Ernest
Cheng
J
The University of Auckland
Auckland Bioengineering Institute
Gerald
Loeb
E
c.lloyd@auckland.ac.nz
Fixed one of the equations such that the model no longer produces NaNs.
keyword
myofilament mechanics
muscles
tendons
biomechanics
This CellML model has been checked in both COR and PCEnv. Currently it can be opened in COR but due to the presence of 'circular arguments' the model does not run. However, the model can be opened in the latest snapshot of PCEnv (which contains a DAE solver), but although it does run, it does so very slowly. We are still working on the model to try to get it to reproduce the Matlab results.
2009-05-29T16:44:19+12:00
Geoff
Nunns
James
Lawson
Richard
Catherine Lloyd
2008-07-25T00:00:00+00:00
10996372
2008-08-14T10:09:07+12:00
Virtual muscle: a computational approach to understanding the effects of muscle properties on motor control
101
117
130
Ian
Brown
E
updated curation status, removed reference link from documentation