A diffusion-weighted imaging informed continuum model of the rabbit triceps surae complex.

The NZ white rabbit is the animal of choice for much experimental work due to its muscular frame and similar response to human diseases, and is one of the few mammals that have had their genome sequenced. However, continuum-level computational models of rabbit muscle detailing fibre architecture are limited in the literature, especially the triceps surae complex (gastrocnemius, plantaris and soleus), which has similar biomechanics and translatable findings to the human. This study presents a geometrical model of the rabbit triceps surae informed with diffusion-weighted imaging (DWI)-based fibres. Passive rabbit-specific material properties are estimated using known muscle deformation inferred from magnetic resonance imaging data and dorsiflexion force measured with a custom-built rabbit rig and transducer. Muscle shape prediction is evaluated against a second rabbit. This study revealed that the triceps surae steady-state force post-rigor is close to post-mortem for small deformations but increases by a fixed ratio as the deformation increases and can be used to evaluate the passive behaviour of muscle. DWI fibre orientation significantly influences shape and mechanics during simulated computational muscle contraction. The presented triceps surae force and material properties may be used to inform the constitutive behaviour of continuum rabbit muscle models used to investigate pathology and musculotendon treatments that may be translated to the human condition.

Mechanics of the foot Part 1: a continuum framework for evaluating soft tissue stiffening in the pathologic foot.

Soft tissue stiffening is a common mechanical observation reported in foot pathologies including diabetes mellitus and gout. These material changes influence the spatial distribution of stress and affect blood flow, which is essential to nutrient entry and waste removal. An anatomically-based subject-specific foot model was developed to explore the influence of tissue stiffening on plantar pressure and internal von Mises stress at heel-strike, midstance and toe-off. This work draws on the model database developed for the Physiome project consisting of muscles, bones, soft tissue and other structures such as sensory nerves. The anisotropic structure of soft tissue was embedded in a single continuum as an efficient model for finite soft tissue deformation, and customisation methods were used to capture the unique foot profile. The model was informed by kinetics from an instrumented treadmill and kinematics from motion capture, synchronised together. Foot sole pressure predictions were evaluated against a commercial pressure platform. Key outcomes showed that internal stress can be up to 1.6 times the surface pressure with implications for internal soft tissue damage not observed at the surface. The main nerve branch stimulated during gait was the lateral plantar nerve. This subject-specific modelling framework can play an integral part in therapeutic treatments by informing assistive strategies such as mechanical noise stimulation and orthotics.

Mechanics of the foot Part 2: A coupled solid-fluid model to investigate blood transport in the pathologic foot.

A coupled computational model of the foot consisting of a three-dimensional soft tissue continuum and a one-dimensional (1D) transient blood flow network is presented in this article. The primary aim of the model is to investigate the blood flow in major arteries of the pathologic foot where the soft tissue stiffening occurs. It has been reported in the literature that there could be up to about five-fold increase in the mechanical stiffness of the plantar soft tissues in pathologic (e.g. diabetic) feet compared with healthy ones. The increased stiffness results in higher tissue hydrostatic pressure within the plantar area of the foot when loaded. The hydrostatic pressure acts on the external surface of blood vessels and tend to reduce the flow cross-section area and hence the blood supply. The soft tissue continuum model of the foot was modelled as a tricubic Hermite finite element mesh representing all the muscles, skin and fat of the foot and treated as incompressible with transversely isotropic properties. The details of the mechanical model of soft tissue are presented in the companion paper, Part 1. The deformed state of the soft tissue continuum because of the applied ground reaction force at three foot positions (heel-strike, midstance and toe-off) was obtained by solving the Cauchy equations based on the theory of finite elasticity using the Galerkin finite element method. The geometry of the main arterial network in the foot was represented using a 1D Hermite cubic finite element mesh. The flow model consists of 1D Navier-Stokes equations and a nonlinear constitutive equation to describe vessel radius-transmural pressure relation. The latter was defined as the difference between the fluid and soft tissue hydrostatic pressure. Transient flow governing equations were numerically solved using the two-step Lax-Wendroff finite difference method. The geometry of both the soft tissue continuum and arterial network is anatomically-based and was developed using the data derived from visible human images and magnetic resonance images of a healthy male volunteer. Simulation results reveal that a two-fold increase in tissue stiffness leads to about 28% reduction in blood flow to the affected region.

Subject-specific modelling of lower limb muscles in children with cerebral palsy.

BACKGROUND: Recent studies suggest that the architecture of spastic muscles in children with cerebral palsy is considerably altered; however, only little is known about the structural changes that occur other than in the gastrocnemius muscle. In the present study, Magnetic Resonance Imaging (MRI) and subject-specific modelling techniques were used to compare the lengths and volumes of six lower limb muscles between children with cerebral palsy and typically developing children. METHODS: MRI scans of the lower limbs of two children with spastic hemiplegia cerebral palsy, four children with spastic diplegia cerebral palsy (mean age 9.6 years) and a group of typically developing children (mean age 10.2 years) were acquired. Subject-specific models of six lower limb muscles were developed from the MRI data using a technique called Face Fitting. Muscle volumes and muscle lengths were derived from the models and normalised to body mass and segmental lengths, respectively. FINDINGS: Normalised muscle volumes in the children with cerebral palsy were smaller than in the control group with the difference being 22% in the calf muscles, 26% in the hamstrings and 22% in the quadriceps, respectively. Only the differences in the hamstrings and the quadriceps were statistically significant (P=0.036, P=0.038). Normalised muscle lengths in the children with cerebral palsy were significantly shorter (P<0.05), except for soleus and biceps femoris. No significant relationship was found between normalised lengths and volumes of any muscle in either group. INTERPRETATION: The present results show that lower limb muscles in ambulatory children with cerebral palsy are significantly altered, suggesting an overall mechanical deficit due to predominant muscle atrophy. Further investigations of the underlying causes of the muscle atrophy are required to better define management and treatment strategies for children with cerebral palsy.

Error propagation from kinematic data to modeled muscle-tendon lengths during walking.

Kinematic data from 3D gait analysis together with musculoskeletal modeling techniques allow the derivation of muscle-tendon lengths during walking. However, kinematic data are subject to soft tissue artifacts (STA), referring to skin marker displacements during movement. STA are known to significantly affect the computation of joint kinematics, and would therefore also have an effect on muscle-tendon lengths which are derived from the segmental positions. The present study aimed to introduce an analytical approach to calculate the error propagation from STA to modeled muscle-tendon lengths. Skin marker coordinates were assigned uncorrelated, isotropic error functions with given standard deviations accounting for STA. Two different musculoskeletal models were specified; one with the joints moving freely in all directions, and one with the joints constrained to rotation but no translation. Using reference kinematic data from two healthy boys (mean age 9y 5m), the propagation of STA to muscle-tendon lengths was quantified for semimembranosus, gastrocnemius and soleus. The resulting average SD ranged from 6% to 50% of the normalized muscle-tendon lengths during gait depending on the muscle, the STA magnitudes and the musculoskeletal model. These results highlight the potential impact STA has on the biomechanical analysis of modeled muscle-tendon lengths during walking, and suggest the need for caution in the clinical interpretation of muscle-tendon lengths derived from joint kinematics.