Internally Constrained Mixtures of Elastic Continua

A treatment of internally constrained mixtures of elastic continua at a common temperature is developed. Internal constraints involving the deformation gradient tensors and the common mixture temperature are represented by a constraint manifold, and an internally constrained mixture of elastic continua is associated with each unique equivalence class of unconstrained mixtures. The example of intrinsic incompressibility of each constituent first proposed by Mills is discussed

Volumetric Growth of Thermoelastic Materials and Mixtures

The proteoglycan and collagen constituents of cartilage serve distinct mechanical roles. Changes to the mechanical loading conditions during cartilage growth lead to changes in the concentrations of these molecules and, consequently, the mechanical properties. The main aim of this paper is to present a theory that can describe the mechanical aspects of cartilage growth. The model for cartilage growth is based on a general thermomechanical theory for a mixture of an arbitrary number of growing elastic constituents and an inviscid fluid. Our development of a growth mixture theory is accomplished in two steps. First, the thermodynamics of growing elastic materials are considered. The resulting theory of growing thermoelastic materials is extended to continuum mixture theory. Using this general growth mixture theory, we then propose a cartilage growth model that includes two special types of internal constraints that are relevant to cartilage

A cartilage growth mixture model for infinitesimal strains: solutions of boundary-value problems related to in vitro growth experiments

A cartilage growth mixture (CGM) model is linearized for infinitesimal elastic and growth strains. Parametric studies for equilibrium and nonequilibrium boundary-value problems representing the in vitro growth of cylindrical cartilage constructs are solved. The results show that the CGM model is capable of describing the main biomechanical features of cartilage growth. The solutions to the equilibrium problems reveal that tissue composition, constituent pre-stresses, and geometry depend on collagen remodeling activity, growth symmetry, and differential growth. Also, nonhomogeneous growth leads to nonhomogeneous tissue composition and constituent pre-stresses. The solution to the nonequilibrium problem reveals that the tissue is nearly in equilibrium at all time points. The results suggest that the CGM model may be used in the design of tissue engineered cartilage constructs for the repair of cartilage defects; for example, to predict how dynamic mechanical loading affects the development of nonuniform properties during in vitro growth. Furthermore, the results lay the foundation for future analyses with nonlinear models that are needed to develop realistic models of cartilage growth

Principal component analysis of gait and cycling experiments: Crosstalk error reduction and corrected knee axes

Crosstalk is a leading source of error in motion analysis [1-2]. Due to incorrect flexion axis direction that develops from marker placement error, crosstalk results in a strong, anatomically incorrect correlation between flexion-extension (FE) and adduction-abduction (AA) motions [1-2]. Thus, crosstalk limits the ability of biomechanical models to reflect the “true” motion of the knee. Principal Component Analysis (PCA) has been proposed as a post-hoc correction for crosstalk in prior gait studies [1-2]; however, previous studies have not proposed a method to determine PCA corrected knee axes. Further, it is not clear how PCA should be implemented in motion analysis studies that involve several exercises, on the same subjects, involving a relatively high range of flexion angles. The long-term goal of this study is to determine accurate knee kinematics in a variety of exercises performed by the same subjects. This study tests two hypotheses: (1) PCA corrects for crosstalk between FE and AA angles in gait and cycling and (2) PCA corrected knee axes are similar for gait and cycling. The aims are to (1) determine PCA corrected knee angles in gait and cycling for the same subjects and their corresponding FE-AA correlations, (2) develop and implement an algorithm for determining PCA corrected knee FE and AA axes, and (3) compare the PCA corrected FE and AA axes for the same subjects to determine if they are similar in gait and cycling

EMG-Driven inverse dynamic analysis of knee contact forces during gait and cycling using OpenSim

Joint contact forces determine the loading experienced by cartilage tissue and, thus, may be used to predict risk of cartilage tissue damage and osteoarthritis (OA). Participating in low impact and/or non-weight bearing activities such as cycling may help reduce knee OA risk by limiting forces exerted during exercise [1]. Cycling is a common recommendation for rehabilitative or fitness sustainment exercise for select patients [1]. Although knee joint contact forces have been directly measured in gait and cycling using instrumented knee implants [2,3] and calculated in gait using EMG-driven analysis [4]; they have not been calculated in cycling using EMG-driven analysis. The long-term goal of this study is to identify weight control exercises for overweight (OW) and obese (OB) subjects that minimize OA risk. This current study tests the hypothesis that knee joint contact forces are significantly lower during cycling than gait. The objectives are to: (1) conduct motion analysis experiments and EMG-driven OpenSim analyses for gait and cycling, (2) compare predicted tibiofemoral (TF) contact forces to published values, and (3) test for significant differences in maximum TF compressive forces in gait and cycling

Modeling the collagen fibril network of biological tissues as a nonlinearly elastic material using a continuous volume fraction distribution function

Despite distinct mechanical functions, biological soft tissues have a common microstructure in which a ground matrix is reinforced by a collagen fibril network. The microstructural properties of the collagen network contribute to continuum mechanical tissue properties that are strongly anisotropic with tensile-compressive asymmetry. In this study, a novel approach based on a continuous distribution of collagen fibril volume fractions is developed to model fibril reinforced soft tissues as nonlinearly elastic and anisotropic material. Compared with other approaches that use a normalized number of fibrils for the definition of the distribution function, this representation is based on a distribution parameter (i.e. volume fraction) that is commonly measured experimentally while also incorporating pre-stress of the collagen fibril network in a tissue natural configuration. After motivating the form of the collagen strain energy function, examples are provided for two volume fraction distribution functions. Consequently, collagen second-Piola Kirchhoff stress and elasticity tensors are derived, first in general form and then specifically for a model that may be used for immature bovine articular cartilage. It is shown that the proposed strain energy is a convex function of the deformation gradient tensor and, thus, is suitable for the formation of a polyconvex tissue strain energy function

Knee biomechanics during cycling are similar for normal weight and obese subjects

Osteoarthritis (OA) is a degenerative disease of cartilage and bone tissue, and is linked to more than 70% of total hip and knee replacements [1]. In 1994 the direct and indirect costs of OA in the United States were $155 billion [2] and in 2006 OA resulted in approximately$10.5 billion in hospital charges [3]. Obesity is a risk factor for OA [1, 3, 4], likely due to increased knee loading [5, 6] and varus malalignment [7] in gait. Seated cycling has been recommended as a weight-loss exercise with lower knee loads than walking or jogging [8]. However, lack of biomechanical studies for obese subjects in exercises, other than gait, impedes selection of exercises that may best prevent knee OA development in the obese population. This study tests the hypothesis that cycling knee kinematics and kinetics are not different for normal weight (NW) and obese (OB) subjects. The long-term goal of our research group is to calculate knee joint loading and kinematics during select exercises to aid in selection of weight-loss exercises that minimize risk of OA development. The objectives of this study are to (1) conduct cycling experiments with a motion capture system to calculate internal knee kinematics and kinetics and (2) compare knee kinematics and kinetics for normal weight and obese subjects during cycling

Knee Joint Biomechanics in Transtibial Amputees in Gait, Cycling, and Elliptical Training

Transtibial amputees may experience decreased quality of life due to increased risk of knee joint osteoarthritis (OA). No prior studies have compared knee joint biomechanics for the same group of transtibial amputees in gait, cycling, and elliptical training. Thus, the goal of this study was to identify preferred exercises for transtibial amputees in the context of reducing risk of knee OA. The hypotheses were: 1) knee biomechanics would differ due to participant status (amputee, control), exercise, and leg type (intact, residual) and 2) gait kinematic parameters would differ due to participant status and leg type. Ten unilateral transtibial amputee and ten control participants performed exercises while kinematic and kinetic data were collected. Two-factor repeated measures analysis of variance with post-hoc Tukey tests and non-parametric equivalents were performed to determine significance. Maximum knee compressive force, extension torque, and abduction torque were lowest in cycling and highest in gait regardless of participant type. Amputee maximum knee extension torque was higher in the intact vs. residual knee in gait. Amputee maximum knee flexion angle was higher in the residual vs. intact knee in gait and elliptical. Gait midstance knee flexion angle timing was asymmetrical for amputees and knee angle was lower in the amputee residual vs. control non-dominant knees. The results suggest that cycling, and likely other non-weight bearing exercises, may be preferred exercises for amputees due to significant reductions in biomechanical asymmetries and joint loads

Elbow and shoulder joint torques are correlated with body mass index but not game pitch count in youth baseball pitchers

The number of ulnar collateral ligament (UCL) reconstructive (i.e. “Tommy John”) surgeries performed on youth baseball pitchers have more than doubled since 2000 [1]. Routinely pitching while fatigued is considered a leading factor associated with UCL injuries; adolescent pitchers who had elbow or shoulder surgery were 36 times more likely to have routinely pitched with arm fatigue [1]. MLB/USA Baseball Pitch Smart guidelines limit 9-10 yr. old pitchers to a maximum 75 pitches per game, a figure based on long-term studies related to injury prevention [2]. Several studies have shown that pitching kinematics (e.g. elbow flexion/extension and pronation/supination, scapulothoracic internal-external rotation) may change as adult pitchers reach muscular fatigue [3], and such kinematic changes could result in higher elbow and shoulder rotational torques that may increase injury risk [4]. Several biomechanical studies have been done on ~12 yr. old youth pitchers [5,6] but none have been reported at the 9-10 yr. old level. This study aims to predict elbow and shoulder joint torques throughout a simulated game of 75 pitches for 9-10 yr. old youth pitchers and investigate joint torque correlations with pitch count, pitch speed, and body mass index (BMI; kg/m2)