Donahue, Tammy L. Haut

Clinical treatments of skeletal muscle weakness are hindered by a lack of an approach to evaluate individual muscle force. Intramuscular pressure (IMP) has shown a correlation to muscle force in vivo, but patient to patient and muscle to muscle variability results in difficulty of utilizing IMP to estimate muscle force. The goal of this work was to develop a finite element model of whole skeletal muscle that can predict IMP under passive and active conditions to further investigate the mechanisms of IMP variability. A previously validated hypervisco-poroelastic constitutive approach was modified to incorporate muscle activation through an inhomogeneous geometry. Model parameters were optimized to fit model stress to experimental data, and the resulting model fluid pressurization data were utilized for validation. Model fitting was excellent (root-mean-square error or RMSE <1.5 kPa for passive and active conditions), and IMP predictive capability was strong for both passive (RMSE 3.5 mmHg) and active (RMSE 10 mmHg at in vivo lengths) conditions. Additionally, model fluid pressure was affected by length under isometric conditions, as increases in stretch yielded decreases in fluid pressurization following a contraction, resulting from counteracting Poisson effects. Model pressure also varied spatially, with the highest gradients located near aponeuroses. These findings may explain variability of in vivo IMP measurements in the clinic, and thus help reduce this variability in future studies. Further development of this model to include isotonic contractions and muscle weakness would greatly benefit this work.

Since Blix noted that force varies with muscle length [1], many investigators have worked to characterize the passive length-tension properties of skeletal muscle in the tissue’s fiber direction [2]. However, few reports have examined the properties of muscle in either transverse extension or in longitudinal shear [3–4]. Material properties in these three directions are needed to fully characterize computational models, which generally describe muscle as being transversely isotropic, hyperelastic, and isovolumetric [3–6]. Further, previous studies reporting tri-planar material properties indicate that muscle tissue is stiffer in the transverse direction compared to the longitudinal direction [3–4]. This counters conventional notions of transversely isotropic materials, which are generally stiffer in the fiber direction.

Mathematical models are non-invasive tools used for analyzing biomechanical conditions. Various models of the knee using the finite element analysis technique [1–6] and rigid body spring model (RBSM) [7] have been developed to predict pressure distribution in articulating joints, although the RBSM is considered the simplest of the modeling techniques, while still effectively predicting load distribution. These models can be used to study altered joint loading, which causes a degeneration of the articular cartilage, in order to gain an understanding of the etiology of osteoarthritis (OA). The purpose of this study is to develop a subject-specific analytical knee model using the RBSM approach that incorporates subject-specific geometry, joint health, and loading patterns to predict tibiofemoral load distributions.

The main functions of the human musculoskeletal system are to sustain loads and provide mobility. Bones and joints themselves cannot produce movement; skeletal muscles provide the ability to move. Knowledge of muscle forces during given activities can provide insight into muscle mechanics, muscle physiology, musculoskeletal mechanics, neurophysiology, and motor control. However, clinical examinations or instrumented strength testing only provides information regarding muscle groups. Musculoskeletal models are typically needed to calculate individual muscle forces.

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].

Knee menisci are semi-lunar, fibrocartilaginous structures that convert applied compressive loads to circumferential hoop stresses which are attenuated at the tibial plateau via the meniscal attachments [1]. These specialized interfaces, located at the lateral anterior (LA), lateral posterior (LP), medial anterior (MA), and medial posterior (MP) horns, are crucial to maintaining mechanical functionality of menisci, thereby preventing osteoarthritis [2]. Soft-tissues subjected to compression and shear loads are known to possess proteoglycans, which aid in resisting these applied stresses by retaining interstitial fluid [1]. Interestingly, proteoglycans are also known to be present at the meniscus to bone interface [3]. Despite the presence of these biphasic attachments and their important role in joint load transfer, there have been no quantitative investigations of the mechanical environment within these attachments under physiological and pathological loads. Recent development of a novel pressure microsensor now allows direct observation of fluid pressure, which will aid in understanding the internal mechanical environment within the attachment sites. Previous work indicates that the attachment sites are geometrically, mechanically, and histologically different [4], thus it is hypothesized that the fluid pressures would likewise differ.

Many single-phase, solid mechanics computational models of skeletal muscle have been created based on the assumptions that skeletal muscle is hyperelastic, transversely isotropic,1,2 and isovolumic. However, muscle has also been observed to have non-linear time-dependent behaviors that can be modeled using viscoelasticity or poroelasticity. The inherent viscoelasticity of muscle may not fully explain the time-dependent nature that may arise from extracellular fluid filtration3 and redistribution4 within the tissue. Further, intramuscular pressure (IMP) has been shown to have a heterogeneous distribution in muscle. This may be attributable to the movement of extracellular fluid, but the mechanisms of fluid redistribution are not completely understood. While a viscoelastic model may predict time-dependent responses of skeletal muscle, viscoelastic theory does not explain underlying causative tissue behaviors.5

Meniscal attachments serve to anchor and transfer loads from menisci to the tibia. These ligamentous tissues are composed of collagen fibers, elastin, ground substance and water. Ligaments have a time- and history-dependent viscoelastic behavior due in part to the interaction of the water and the ground substance [1]. The movement of water within ligamentous tissue is limited because of charged proteoglycan molecules. It has been shown that some exudation of water is present during cyclic loading of ligamentous tissue [2]. The movement and its inhibition could lead to changes of pressure within the meniscal attachments. Therefore, the purpose of this study was to quantify the internal pressure in human meniscal attachments subjected to physiological loading. Since it is thought that the posterior attachment is subjected to both tension and compression, while the anterior attachment is primarily subjected to tension [3–5], we hypothesized that the attachments mechanical environment is dictated by the external loads, and hence, the posterior attachment would elicit higher pressures.

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.