Development and validation of a 3-D model to predict knee joint loading during dynamic movement
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML runs in OpenCell (note that it cannot be run in COR due to "circular arguments" or "DAEs"). The units have been checked and they are consistent.
Model Structure
ABSTRACT: The purpose of this study was to develop a subject-specific 3-D model of the lower extremity to predict neuromuscular control effects on 3-D knee joint loading during movements that can potentially cause injury to the anterior cruciate ligament (ACL) in the knee. The simulation consisted of a forward dynamic 3-D musculoskeletal model of the lower extremity, scaled to represent a specific subject. Inputs of the model were the initial position and velocity of the skeletal elements, and the muscle stimulation patterns. Outputs of the model were movement and ground reaction forces, as well as resultant 3-D forces and moments acting across the knee joint. An optimization method was established to find muscle stimulation patterns that best reproduced the subject's movement and ground reaction forces during a sidestepping task. The optimized model produced movements and forces that were generally within one standard deviation of the measured subject data. Resultant knee joint loading variables extracted from the optimized model were comparable to those reported in the literature. The ability of the model to successfully predict the subject's response to altered initial conditions was quantified and found acceptable for use of the model to investigate the effect of altered neuromuscular control on knee joint loading during sidestepping. Monte Carlo simulations (N = 100,000) using randomly perturbed initial kinematic conditions, based on the subject's variability, resulted in peak anterior force, valgus torque and internal torque values of 378 N, 94 Nm and 71 Nm, respectively, large enough to cause ACL rupture. We conclude that the procedures described in this paper were successful in creating valid simulations of normal movement, and in simulating injuries that are caused by perturbed neuromuscular control.
The original paper reference is cited below:
Development and validation of a 3-D model to predict knee joint loading during dynamic movement, S.G. McLean, A. Su and A.J. van den Bogert, 2003,Journal of Biomechanical Engineering, 125, 6, 864-874. PubMed ID: 14986412
$\mathrm{F\_CE}=\mathrm{f\_L\_CE}\mathrm{g\_V\_CE}a$
$\mathrm{f\_L\_CE}=\frac{\mathrm{F\_max}(1(1-\mathrm{L\_CE})-\mathrm{L\_CE\_opt}^{2})}{W^{2}\mathrm{L\_CE\_opt}^{2}}$
$\mathrm{g\_V\_CE}=\begin{cases}\frac{\mathrm{lambda\_a}\mathrm{V\_max}+\mathrm{V\_CE}}{\mathrm{lambda\_a}\mathrm{V\_max}-\frac{\mathrm{V\_CE}}{A}} & \text{if $\mathrm{V\_CE}\le 0$}\\ \frac{\mathrm{g\_max}\mathrm{V\_CE}+\mathrm{d1}}{\mathrm{V\_CE}+\mathrm{d1}} & \text{if $(0< \mathrm{V\_CE})\land (\mathrm{V\_CE}\le \mathrm{gamma}\mathrm{d1})$}\\ \mathrm{d3}+\mathrm{d2}\mathrm{V\_CE} & \text{if $\mathrm{V\_CE}> \mathrm{gamma}\mathrm{d1}$}\end{cases}$
$\mathrm{d1}=\frac{\mathrm{V\_max}A(\mathrm{g\_max}-1)}{S(A+1)}$
$\mathrm{d2}=\frac{S(A+1)}{\mathrm{V\_max}A(\mathrm{gamma}+1)^{2}}$
$\mathrm{d3}=\frac{(\mathrm{g\_max}-1)\mathrm{gamma}^{2}}{(\mathrm{gamma}+1)^{2}}+1$
$\mathrm{F\_SEE}=\begin{cases}0 & \text{if $\mathrm{L\_SEE}\le \mathrm{L\_slack}$}\\ \mathrm{k\_SEE}(\mathrm{L\_SEE}-\mathrm{L\_slack})^{2} & \text{otherwise}\end{cases}$
$\mathrm{F\_PEE}=\begin{cases}0 & \text{if $\mathrm{L\_CE}\le \mathrm{L\_slack}$}\\ \mathrm{k\_PEE}(\mathrm{L\_CE}-\mathrm{L\_slack})^{2} & \text{otherwise}\end{cases}$
$\mathrm{k\_PEE}=\frac{\mathrm{F\_max}}{(W\mathrm{L\_CE\_opt})^{2}}$
$\mathrm{V\_CE}=1\frac{\frac{1}{\mathrm{g\_V\_CE}}(\mathrm{F\_SEE}(\mathrm{L\_m}-\mathrm{L\_CE})-\mathrm{F\_PEE}\mathrm{L\_CE})}{a\mathrm{f\_L\_CE}}$
$\mathrm{F\_m}=\mathrm{F\_SEE}$
$\mathrm{lambda\_a}=1(1-e^{-3.82a}+ae^{-3.82})$
$\frac{d \mathrm{L\_CE}}{d \mathrm{time}}=1\mathrm{V\_CE}$
$\mathrm{L\_SEE}=\mathrm{L\_m}-\mathrm{L\_CE}$
$\mathrm{L\_m}=\begin{cases}0.038 & \text{if $\mathrm{time}\le 1$}\\ 0.038+0.002(\mathrm{time}-1) & \text{if $(\mathrm{time}> 1)\land (\mathrm{time}< 2)$}\\ 0.04 & \text{otherwise}\end{cases}$
S.G.
McLean
This is a model for the Muscle-Tendon Dynamics for a knee joint loading problem. Each muscle-tendon unit in the model was modeled as a three-component Hill model. The contractile element was assumed to produce a force F_CE which depends on CE length, L_CE, CE lengthening velocity V_CE, and on active state a.
2003-12-00 00:00
Paul
Harrington
Paul
Corrected units and corrected a couple of equations - one to match the paper and one to correct the piecewise equation MathML.
The dimensional inconsistencies should now have been resolved
2009-03-10T00:00:00+00:00
Catherine Lloyd
14986412
Development and Validation of a 3-D Model to Predict Knee Joint Loading During Dynamic Movement
125
864
874
Transactions of the ASME
2009-04-14T12:22:16+12:00
A.J.
van den Bogert
paul.harrington@auckland.ac.nz
Catherine
Lloyd
May
Auckland Bioengineering Institute
keyword
mechanical constitutive laws
neuromuscular
muscular skeletal
A.
Su