Development of a continuum mechanics model of passive skeletal muscle

Skeletal muscle force evaluation is difficult to implement in a clinical setting. Muscle force is typically assessed through either manual muscle testing, isokinetic/isometric dynamometry, or electromyography (EMG). Manual muscle testing is a subjective evaluation of a patient’s ability to move voluntarily against gravity and to resist force applied by an examiner. Muscle testing using dynamometers adds accuracy by quantifying functional mechanical output of a limb. However, like manual muscle testing, dynamometry only provides estimates of the joint moment. EMG quantifies neuromuscular activation signals of individual muscles, and is used to infer muscle function. Despite the abundance of work performed to determine the degree to which EMG signals and muscle forces are related, the basic problem remains that EMG cannot provide a quantitative measurement of muscle force. Intramuscular pressure (IMP), the pressure applied by muscle fibers on interstitial fluid, has been considered as a correlate for muscle force. Numerous studies have shown that an approximately linear relationship exists between IMP and muscle force. A microsensor has recently been developed that is accurate, biocompatible, and appropriately sized for clinical use. While muscle force and pressure have been shown to be correlates, IMP has been shown to be non-uniform within the muscle. As it would not be practicable to experimentally evaluate how IMP is distributed, computational modeling may provide the means to fully evaluate IMP generation in muscles of various shapes and operating conditions. The work presented in this dissertation focuses on the development and validation of computational models of passive skeletal muscle and the evaluation of their performance for prediction of IMP. A transversly isotropic, hyperelastic, and nearly incompressible model will be evaluated along with a poroelastic model

A method for assessing the fit of a constitutive material model to experimental stress-strain data

Higher-order polynomial functions can be used as a constitutive model to represent the mechanical behaviour of biological materials. The goal of this study was to present a method for assessing the fit of a given constitutive three-dimensional material model. Goodness of fit was assessed using multiple parameters including the root mean square error and Hotelling\u27s T2-test. Specifically, a polynomial model was used to characterise the stress-strain data, varying the number of model terms used (45 combinations of between 3 and 11 terms) and the manner of optimisation used to establish model coefficients (i.e. determining coefficients either by parameterisation of all data simultaneously or averaging coefficients obtained by parameterising individual data trials). This framework for model fitting helps to ensure that a given constitutive formulation provides the best characterisation of biological material mechanics. © 2010 Taylor & Francis

Validation of a finite element model of passive force and pressure in skeletal muscle

Intramuscular pressure (IMP) has been put forth as a surrogate measure for muscle force. As technological advancements have lead to the creation of smaller IMP microsensors, obtaining IMP readings in the clinic has come closer to becoming a minimally-invasive reality. However, appropriate use of data from these sensors relies upon an understanding of the mechanism of pressure changes within skeletal muscle. To that end, a constitutive model, representing muscle as a transversely isotropic, hyperelastic, and isovolumetric was created [1] for implementation in a finite element simulation. The purpose of this study was to validate this constitutive muscle model with passive elongation tests of skeletal muscle tissue from New Zealand White (NZW) rabbits. Reaction forces and hydrostatic pressures resulting from applied deformations were determined with the finite element modeling (FEM) approach and were compared with previously published experimental data [2].</jats:p

A validated finite element model of force in active and passive skeletal muscle

A fully 3D, continuum mechanics based model of skeletal muscle, validated against experimental force data, can be used to computationally solve for individual muscle forces. A constitutive formulation, representing muscle as a transversely isotropic, hyperelastic, and isovolumetric material [1] has been implemented in a finite element model (FEM) of passive skeletal muscle and validated against experimental tension measurements [2]. Of further interest is an expanded formulation that will allow for the addition of muscle activation levels on the overall skeletal muscle force generation. The purpose of this study was to expand the FEA model to include muscle activation and validate it with tests of active skeletal muscle tissue at varied lengths.</jats:p

Transversely isotropic tensile material properties of skeletal muscle tissue

Of the plethora of work performed analyzing skeletal muscle tissue, relatively little has been done in the examination of its passive material properties. Previous studies of the passive properties of skeletal muscle have been primarily performed along the longitudinal material direction. In order to ensure the accuracy of the predictions of computational models of skeletal muscles, a better understanding of the tensile three-dimensional material properties of muscle tissue is necessary. To that end, the purpose of this study was to collect a comprehensive set of tensile stress-strain data from skeletal muscle tissue. Load-deformation data was collected from eighteen extensor digitorum longus muscles, dissected free of aponeuroses, from nine New Zealand White rabbits tested under longitudinal extension (LE), transverse extension (TE), or longitudinal shear (LS). The linear modulus, ultimate stress, and failure strain were calculated from stress-strain results. Results indicate that the linear modulus under LE is significantly higher than the modulus of either TE or LS. Additionally, the ultimate stress of muscle was seen to be significantly higher under LE than TE. Conversely, the failure strain was significantly higher under TE than under LE. © 2009 Elsevier Ltd. All rights reserved

Error analysis of cine phase contrast MRI velocity measurements used for strain calculation

© 2014 Elsevier Ltd. Cine Phase Contrast (CPC) MRI offers unique insight into localized skeletal muscle behavior by providing the ability to quantify muscle strain distribution during cyclic motion. Muscle strain is obtained by temporally integrating and spatially differentiating CPC-encoded velocity. The aim of this study was to quantify CPC measurement accuracy and precision and to describe error propagation into displacement and strain. Using an MRI-compatible jig to move a B-gel phantom within a 1.5T MRI bore, CPC-encoded velocities were collected. The three orthogonal encoding gradients (through plane, frequency, and phase) were evaluated independently in post-processing. Two systematic error types were corrected: eddy current-induced bias and calibration-type error. Measurement accuracy and precision were quantified before and after removal of systematic error. Through plane- and frequency-encoded data accuracy were within 0.4. mm/s after removal of systematic error - a 70% improvement over the raw data. Corrected phase-encoded data accuracy was within 1.3. mm/s. Measured random error was between 1 to 1.4. mm/s, which followed the theoretical prediction. Propagation of random measurement error into displacement and strain was found to depend on the number of tracked time segments, time segment duration, mesh size, and dimensional order. To verify this, theoretical predictions were compared to experimentally calculated displacement and strain error. For the parameters tested, experimental and theoretical results aligned well. Random strain error approximately halved with a two-fold mesh size increase, as predicted. Displacement and strain accuracy were within 2.6. mm and 3.3%, respectively. These results can be used to predict the accuracy and precision of displacement and strain in user-specific applications