A finite element study of the human cranium : the impact of morphological variation on biting performance

This thesis investigated the relationship between craniofacial morphology and masticatory mechanics using finite element analysis (FEA). Chapter 1 is a literature review of the relevant background: bone mechanics, jaw-elevator muscle anatomy, imaging techniques, FEA and geometric morphometrics.The second, third and fourth chapters comprise experimental work aiming to provide a framework for FE model construction and loading. The second chapter aimed to validate the method for FE model building and assess the sensitivity of models to simplifications. Models with simplified bone anatomy and resolution predicted strains close to those measured experimentally. The third chapter assessed the predictability of muscle cross-sectional area (CSA) from bony features. It was found that muscle CSA, an estimator of muscle force, has low predictability. The fourth chapter assessed FE model sensitivity to variations in applied muscle forces. Results showed that a cranial FE model behaved reasonably robustly under variations in the muscle loading regimen.Chapter 5 uses the conclusions from the previous studies to build FE models of six human crania, including two individuals with artificial deformations of the neurocranium. Despite differences in form and the presence of deformation, all performed similarly during biting, varying mainly in the magnitudes of performance parameters. The main differences related to the form of the maxilla, irrespective of neurocranial deformation. The most orthognatic individuals with the narrowest maxilla showed the most distinctive deformation during incisor and molar bites, and achieved the greatest bite force efficiency. However, bite forces were similar among individuals irrespective of the presence of artificial deformation. This appears to relate to the preservation of normal dental occlusion, which in turn maintains similar loading and so morphogenesis of the mid face. Altogether, the results of this thesis show that FEA is reliable in comparing masticatory system functioning and point to how variations in morphology impact skeletal performance

Virtual cardiac monolayers for electrical wave propagation

The complex structure of cardiac tissue is considered to be one of the main determinants of an arrhythmogenic substrate. This study is aimed at developing the first mathematical model to describe the formation of cardiac tissue, using a joint in silico-in vitro approach. First, we performed experiments under various conditions to carefully characterise the morphology of cardiac tissue in a culture of neonatal rat ventricular cells. We considered two cell types, namely, cardiomyocytes and fibroblasts. Next, we proposed a mathematical model, based on the Glazier-Graner-Hogeweg model, which is widely used in tissue growth studies. The resultant tissue morphology was coupled to the detailed electrophysiological Korhonen-Majumder model for neonatal rat ventricular cardiomyocytes, in order to study wave propagation. The simulated waves had the same anisotropy ratio and wavefront complexity as those in the experiment. Thus, we conclude that our approach allows us to reproduce the morphological and physiological properties of cardiac tissue

Active contraction of the left ventricle with cardiac tissue modelled as a micromorphic medium

The myocardium is composed of interconnected cardiac fibres which are responsible for contraction of the heart chambers. There are several challenges related to computational modelling of cardiac muscle tissue. This is due in part to the anisotropic, non-linear and time-dependent behaviour as well as the complex hierarchical material structure of biological tissues. In general, cardiac tissue is treated as a non-linear elastic and incompressible material. Most computational studies employ the theories of classical continuum mechanics to model the passive response of the myocardium and typically assume the myocardium to be either a transversely isotropic material or an orthotropic material. In this study, instead of a classical continuum formulation, we utilise a micromorphic continuum description for cardiac tissue. The use of a micromorphic model is motivated by the complex microstructure and deformations experienced by cardiac fibres during a heartbeat. The micromorphic theory may be viewed as an extension of the classical continuum theory. Within a micromorphic continuum, continuum particles are endowed with extra degrees of freedom by attaching additional vectors, referred to as directors, to the particles. In this study the directors are chosen such that they represent the deformation experienced by the cardiac fibres. In addition to the passive stresses, the myocardium experiences active stresses as a result of the active tension generated by cardiac fibres. The active tension in the heart is taken to be a function of the sarcomere length, intracellular calcium concentration and the time after the onset of contraction. Experimental studies show that the active behaviour of the myocardium is highly dependent on the tissue arrangement in the heart wall. With a classical continuum description, the sarcomere length is usually defined as a function of the stretch in the initial fibre direction. To allow for a more realistic description of the active behaviour, we define the sarcomere orientation, and consequently also the sarcomere stretch, as a function of the director field. Furthermore, we use the director field to describe the direction in which contraction takes place. The intent of this study is to use a micromorphic continuum formulation and an active-stress model to investigate the behaviour of the left ventricular myocardium during a heartbeat. The simulated results presented here correspond well with typical ventricular mechanics observed in clinical experiments. This work demonstrates the potential of a micromorphic formulation for analysing and better understanding ventricular mechanics

A Novel Framework to Model the Short and Medium Term Mechanical Response of the Medial Gastrocnemius

Musculoskeletal disorders (MSDs) are the second largest cause of disability worldwide and cost the UK National Health Service (NHS) over £4.7 billion yearly. One holistic approach to alleviate this burden is to create in silico models that provide insight into MSDs which will improve diagnostic and therapeutic procedures. This thesis presents a modelling framework that analyses the mechanical behaviour of anatomical skeletal muscles. The anatomical geometry and fibre paths of the medial gastrocnemius muscle were acquired from the Living Human Data Library (LHDL). The medial gastrocnemius model was further sophisticated by incorporating morphological representations of the aponeurosis and myotendon transition region. Having carried out a finite element analysis on the medial gastrocnemius, it was found that the morphology and size of the transition region significantly affected the mechanical response of the muscle. Three illustrative simulations were subsequently carried out on the model, to better understand the muscle’s mechanical response in differing mechanical environments: (1) the effects of high extensions on the muscle’s mechanical response, (2) lengthening of the aponeurosis - a phenomenon often observed following aponeurosis regression - and (3) the stress-strain regime of the muscle when the tendon experiences a laceration and heals over 21 days. These models show the regions that experienced the highest strains were the muscle-tendon transition regions. As MSDs tend to be of a degenerative nature and progress over time, the temporal changes of the mechanical response of skeletal muscle tissue is of great interest. In the penultimate chapter, the medial gastrocnemius was assessed across various remodelling regimes. It was found that the muscle returned to homeostasis only when both the muscle and tendon remodelled – albeit, at different remodelling rates. Whilst this observation seems intuitive, most other growth and remodelling models of skeletal muscles have only remodelled either the muscle or tendon constituent. The model developed in this thesis therefore has the potential to inform multi-scale musculo-skeletal muscle models thus providing a significant contribution to understanding MSDs

The biomechanics of the human tongue

Includes abstract.Includes bibliographical references (p. 137-148).The human tongue is composed mainly of skeletal-muscle tissue, and has a complex architecture. Its anatomy is characterised by interweaving, yet distinct muscle groups. It is a significant contributor to the phenomenon of Obstructive Sleep Apnea (OSA). OSA is a pathological condition defined as the partial or complete closing of any part of the human upper airway (HUA) during sleep. OSA syndrome affects a significant portion of the population. Patients with OSA syndrome experience various respiratory problems, an increase in the risk of heart disease, a significant decrease in productivity, and an increase in motor-vehicle accidents [58]. The aim of this work is to report on a constitutive model for the human tongue, and to demonstrate its use in computational simulations for OSA. A realistic model of the constitution of the tongue and computational simulations are also important in areas such as linguistics and speech therapy [44]. The detailed anatomical features of the tongue have been captured using data from the Visible Human Project (VHP) [102]. The geometry of the tongue, and each muscle group of the tongue, are visually identified, and its geometry captured using Mimics [100]. Various image processing tools available in Mimics, such as image segmentation, region-growing and volume generation were used to form the three-dimensional model of the tongue geometry. Muscle fibre orientations were extracted from the same dataset, also using Mimics.The muscle model presented here is based on Hill’s three-element model for representation of the constituent parts of muscle fibres. This Hill-type muscle model also draws from recent work in muscle modelling, by Martins [88]. The model is implemented in an Abaqus user element (UEL) subroutine [24]. The transversely isotropic behaviour of the muscle tissue is accounted for, as well as the influence of muscle activation. The mechanics of the model is limited to static, small-strain, anisotropic, linear-elastic behaviour, and the governing equations are suitably linearized. The body position of the patient during an apneic episode is accounted for in the simulations, as well as the effect of gravity. The focus of this study is on tongue muscle behaviour under gravitational loading, simulating a simplified OSA event. Future models will incorporate airway pressure as well. The behaviour of the model is illustrated in a number of benchmark tests, and computational examples

Effects of ageing, a high-fat diet and physical exercise on skeletal muscle morphology

Age-related loss of skeletal muscle mass and strength can lead to reduced independence, quality of life and life expectancy, which may be exacerbated by an increased high-fat intake and a low physical exercise. This thesis investigated the effects of ageing, high-fat diet (HFD) and regular physical training on muscle morphology. Specifically, in study I, we compared intramyocellular lipid (IMCL) levels, capillarisation, fibre type and size, and oxidative capacity of fibres in locomotor (soleus and EDL) and respiratory (diaphragm) muscles in 20- (young-adult) and 79-week-old (early ageing) mice. Early ageing was characterised by an absence of muscle wasting in soleus, the EDL atrophied while the diaphragm hypertrophied without changes in the capillary numbers supplying a fibre, or their oxidative capacity. In study II, we studied the effects of a HFD on the morphology of the soleus, EDL and diaphragm in 20- and 79-week-old mice. Old mice were more susceptible to morphological alterations with a HFD compared to young mice. All fibre types showed similar adaptations in response to a HFD but they were muscle-specific with the EDL being least responsive. In study III, we assessed fibre type grouping in the vastus lateralis of athletes and nonathletes (19 - 85 years old) and evaluated to what extent any observed grouping, indicative of cycles of denervation and reinnervation following motor neuron loss, is more than expected from the fibre type composition of the muscle. Since regular physical exercise may stimulate fibre reinnervation, we hypothesised that master athletes have larger fibre groups than agematched non-athletes. An ‘enclosed fibre’ was any muscle fibre of a given type surrounded by fibres of the same type only. A ‘fibre group’ was defined as a group of fibres with at least one enclosed fibre. The prevalence of observed fibre type grouping was similar to that expected from the fibre type composition. No age-related effect on group size and group number in athletes or non-athletes was found. In conclusion, the current thesis described the morphological changes of CD-1 mouse skeletal muscles during ageing as muscle specific. Additionally, using the same mouse model, HFDinduced muscle morphological alterations depending on diet duration and age, varied between muscles. Moreover, the results of the current thesis do not show evidence for improved reinnervation of muscle fibres with regular physical training. Nevertheless, histological examination may not provide the full extent of ageing related motor unit remodelling

Modelling studies on biological tissue properties and mechanical responses under external stimuli

PhDBiological tissues maintain their homeostasis by remodelling under external mechanical stimuli. In order to understand the tissue remodelling process, it is important to characterize tissue properties before detailed mechanical responses can be investigated. This project aims to develop a computational modelling framework to characterise mechanical properties of biological tissues, and to quantify tissue responses under mechanical loading. The thesis presents, first, mechanical responses of articular cartilages under different loadings using a poroelastic model. Unique in this study, collagen fibrils are treated separately from the rest of ECM, as they only resists tension. This leads to a fibril-reinforced poroelastic model. Effects of the distribution of the collagen fibrils and their orientation on tissue mechanical responses are investigated. Most of the effort has been on the mechanical stress distribution of the human left atrium and its correlation to electrophysiology patterns in atrial fibrillation. Detailed mechanical responses of the atrial wall to a step pressure increase in the left atrium are calculated. The geometry of the left atrium is based on patient specific images using cardio CT and incorporates variations of the atrial wall thickness as well as unique fibre orientation patterns. We hypothesize that areas of high von Mises stress are correlated to foci of abnormal electrophysiology sites which sustain cardiac arrhythmia. Results from this study show a positive correlation between them. To our knowledge, this is the first study that establishes the relationship between the atrial wall stress distribution and the atrial abnormal electrophysiology sites. The project also investigates hyperelastic properties of endothelial cells and the overlying endothelial glycocalyx, based on data from AFM micro-indentation. Both endothelial cells with & without the glycocalyx layer (i.e. following enzymatic digestion) are used. This is the first time that the mechanical property of the glycocalyx is estimated using an inverse biomechanical model

A computational neuromuscular model of the human upper airway with application to the study of obstructive sleep apnoea

Includes bibliographical references.Numerous challenges are faced in investigations aimed at developing a better understanding of the pathophysiology of obstructive sleep apnoea. The anatomy of the tongue and other upper airway tissues, and the ability to model their behaviour, is central to such investigations. In this thesis, details of the construction and development of a three-dimensional finite element model of soft tissues of the human upper airway, as well as a simplified fluid model of the airway, are provided. The anatomical data was obtained from the Visible Human Project, and its underlying micro-histological data describing tongue musculature were also extracted from the same source and incorporated into the model. An overview of the mathematical models used to describe tissue behaviour, both at a macro- and microscopic level, is given. Hyperelastic constitutive models were used to describe the material behaviour, and material incompressibility was accounted for. An active Hill three-element muscle model was used to represent the muscular tissue of the tongue. The neural stimulus for each muscle group to a priori unknown external forces was determined through the use of a genetic algorithm-based neural control model. The fundamental behaviour of the tongue under gravitational and breathing-induced loading is investigated. The response of the various muscles of the tongue to the complex loading developed during breathing is determined, with a particular focus being placed to that of the genioglossus. It is demonstrated that, when a time-dependent loading is applied to the tongue, the neural model is able to control the position of the tongue and produce a physiologically realistic response for the genioglossus. A comparison is then made to the response determined under quasi-static conditions using the pressure distribution extracted from computational fluid-dynamics results. An analytical model describing the time-dependent response of the components of the tongue musculature most active during oral breathing is developed and validated. It is then modified to simulate the activity of the tongue during sleep and under conditions relating to various possible neural and physiological pathologies. The retroglossal movement of the tongue resulting from the pathologies is quantified and their role in the potential to induce airway collapse is discussed

Numerical Simulation in Biomechanics and Biomedical Engineering

In the first contribution, Morbiducci and co-workers discuss the theoretical and methodological bases supporting the Lagrangian- and Euler-based methods, highlighting their application to cardiovascular flows. The second contribution, by the Ansón and van Lenthe groups, proposes an automated virtual bench test for evaluating the stability of custom shoulder implants without the necessity of mechanical testing. Urdeitx and Doweidar, in the third paper, also adopt the finite element method for developing a computational model aim to study cardiac cell behavior under mechano-electric stimulation. In the fourth contribution, Ayensa-Jiménez et al. develop a methodology to approximate the multidimensional probability density function of the parametric analysis obtained developing a mathematical model of the cancer evolution. The fifth paper is oriented to the topological data analysis; the group of Cueto and Chinesta designs a predictive model capable of estimating the state of drivers using the data collected from motion sensors. In the sixth contribution, the Ohayon and Finet group uses wall shear stress-derived descriptors to study the role of recirculation in the arterial restenosis due to different malapposed and overlapping stent conditions. In the seventh contribution, the research group of Antón demonstrates that the simulation time can be reduced for cardiovascular numerical analysis considering an adequate geometry-reduction strategy applicable to truncated patient specific artery. In the eighth paper, Grasa and Calvo present a numerical model based on the finite element method for simulating extraocular muscle dynamics. The ninth paper, authored by Kahla et al., presents a mathematical mechano-pharmaco-biological model for bone remodeling. Martínez, Peña, and co-workers propose in the tenth paper a methodology to calibrate the dissection properties of aorta layer, with the aim of providing useful information for reliable numerical tools. In the eleventh contribution, Martínez-Bocanegra et al. present the structural behavior of a foot model using a detailed finite element model. The twelfth contribution is centered on the methodology to perform a finite, element-based, numerical model of a hydroxyapatite 3D printed bone scaffold. In the thirteenth paper, Talygin and Gorodkov present analytical expressions describing swirling jets for cardiovascular applications. In the fourteenth contribution, Schenkel and Halliday propose a novel non-Newtonian particle transport model for red blood cells. Finally, Zurita et al. propose a parametric numerical tool for analyzing a silicone customized 3D printable trachea-bronchial prosthesis