Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

Development and synthesis of innovative approaches to the surgical assessment of articular cartilage degeneration

This research has established, through ultrasound, near infrared spectroscopy and biomechanics experiments, parameters and parametric relationships that can form the framework for quantifying the integrity of the articular cartilage-on-bone laminate, and objectively distinguish between normal/healthy and abnormal/degenerated joint tissue, with a focus on articular cartilage. This has been achieved by: 1. using traditional experimental methods to produce new parameters for cartilage assessment; 2. using novel methodologies to develop new parameters; and 3. investigating the interrelationships between mechanical, structural and molec- ular properties to identify and select those parameters and methodologies that can be used in a future arthroscopic probe based on points 1 and 2. By combining the molecular, micro- and macro-structural characteristics of the tissue with its mechanical properties, we arrive at a set of critical benchmarking parameters for viable and early-stage non-viable cartilage. The interrelationships between these characteristics, examined using a multivariate analysis based on principal components analysis, multiple linear regression and general linear modeling, could then to deter- mine those parameters and relationships which have the potential to be developed into a future clinical device. Specifically, this research has found that the ultrasound and near infrared techniques can subsume the mechanical parameters and combine to characterise the tissue at the molecular, structural and mechanical levels over the full depth of the cartilage matrix. It is the opinion in this thesis that by enabling the determination of the precise area of in uence of a focal defect or disease in the joint, demarcating the boundaries of articular cartilage with dierent levels of degeneration around a focal defect, better surgical decisions that will advance the processes of joint management and treatment will be achieved. Providing the basis for a surgical tool, this research will contribute to the enhancement and quanti�cation of arthroscopic procedures, extending to post- treatment monitoring and as a research tool, will enable a robust method for evaluating developing (particularly focalised) treatments.

The relationship between deformity correction and clinical outcomes after thoracoscopic scoliosis surgery : a prospective series of one hundred patients

Prospective clinical case series of 100 patients receiving thoracoscopic anterior scoliosis correction surgery. The objective was to evaluate the relationship between clinical outcomes of thoracoscopic anterior scoliosis surgery and deformity correction using the Scoliosis Research Society (SRS) outcomes instrument questionnaire. The surgical treatment of scoliosis is quantitatively assessed in the clinic using radiographic measures of deformity correction, as well as the rib hump, but it is important to understand the extent to which these quantitative measures correlate with self-reported improvements in patients’ quality of life following surgery. A series of 100 consecutive adolescent idiopathic scoliosis patients received a single anterior rod via a thoracoscopic approach at the Mater Children’s Hospital, Brisbane, Australia. Patients completed SRS outcomes questionnaires pre-operatively and at 24 months post-operatively. There were 94 females and 6 males with a mean age of 16.1 years. The mean Cobb angle improved from 52º pre-operatively to 25º post-operatively (52%) and the mean rib hump improved from 16º to 8º (51%). The mean total SRS score for the cohort was 99.4/120. None of the deformity related parameters in the multiple regression were significant. However, patients with the lowest post-operative major Cobb angles reported significantly higher SRS scores than those with the highest post-operative Cobb angles, but there was no difference on the basis of rib hump correction. There were no significant differences between patients with either rod fractures or screw-related complications compared to those without complications.

Paediatric spinal deformity research at the Mater Children's Hospital, Brisbane, Australia.

The Paediatric Spine Research group was formed in 2002 to perform high quality research into the prevention and management of spinal deformity, with an emphasis on scoliosis. The group has successfully built collaborative bridges between the scientific and research expertise at QUT, and the clinical skills and experience of the spinal orthopaedic surgeons at the Mater Children’s Hospital in Brisbane. Clinical and biomechanical research is now possible as a result of the development of detailed databases of patients who have innovative and unique surgical interventions for spinal deformity such as thoracoscopic scoliosis correction, thoracoscopic staple insertion for juvenile idiopathic scoliosis and minimally invasive growing rods. The Mater in Brisbane provides these unique datasets of spinal deformity surgery patients, whose procedures are not being performed anywhere else in the Southern Hemisphere. The most detailed is a database of thoracoscopic scoliosis correction surgery which now contains 180 patients with electronic collections of X-Rays, photographs and patient questionnaires. With ethics approval, a subset of these patients has had CT scans, and a further subset have had MRI scans with and without a compressive load to simulate the erect standing position. This database has to date contributed to 17 international refereed journal papers, a further 7 journal papers either under review or in final preparation, 53 national conference presentations and 35 international conference presentations. Major findings from selected journal publications will be presented. It is anticipated that as the surgical databases grow they will continue to provide invaluable clinical data which will feed into clinically relevant projects driven by both medical and engineering researchers whose findings will benefit spinal deformity patients and scientific knowledge worldwide.

A two-compartment mechanochemical model of the roles of transforming growth factor-beta and tissue tension in dermal wound healing

The repair of dermal tissue is a complex process of interconnected phenomena, where cellular, chemical and mechanical aspects all play a role, both in an autocrine and in a paracrine fashion. Recent experimental results have shown that transforming growth factor-beta (TGF-beta) and tissue mechanics play roles in regulating cell proliferation, differentiation and the production of extracellular materials. We have developed a 1D mathematical model that considers the interaction between the cellular, chemical and mechanical phenomena, allowing the combination of TGF-beta and tissue stress to inform the activation of fibroblasts to myofibroblasts. Additionally, our model incorporates the observed feature of residual stress by considering the changing zero-stress state in the formulation for effective strain. Using this model, we predict that the continued presence of TGF-beta in dermal wounds will produce contractures due to the persistence of myofibroblasts; in contrast, early elimination of TGF-beta significantly reduces the myofibroblast numbers resulting in an increase in wound size. Similar results were obtained by varying the rate at which fibroblasts differentiate to myofibroblasts and by changing the myofibroblast apoptotic rate. Taken together, the implication is that elevated levels of myofibroblasts is the key factor behind wounds healing with excessive contraction, suggesting that clinical strategies which aim to reduce the myofibroblast density may reduce the appearance of contractures.

Falls in Parkinson's disease : kinematic evidence for impaired head and trunk control

Changes in stride characteristics and gait rhythmicity characterize gait in Parkinson's disease and are widely believed to contribute to falls in this population. However, few studies have examined gait in PD patients who fall. This study reports on the complexities of walking in PD patients who reported falling during a 12-month follow-up. Forty-nine patients clinically diagnosed with idiopathic PD and 34 controls had their gait assessed using three-dimensional motion analysis. Of the PD patients, 32 (65%) reported at least one fall during the follow-up compared with 17 (50%) controls. The results showed that PD patients had increased stride timing variability, reduced arm swing and walked with a more stooped posture than controls. Additionally, PD fallers took shorter strides, walked slower, spent more time in double-support, had poorer gait stability ratios and did not project their center of mass as far forward of their base of support when compared with controls. These stride changes were accompanied by a reduced range of angular motion for the hip and knee joints. Relative to walking velocity, PD fallers had increased mediolateral head motion compared with PD nonfallers and controls. Therefore, head motion could exceed “normal” limits, if patients increased their walking speed to match healthy individuals. This could be a limiting factor for improving gait in PD and emphasizes the importance of clinically assessing gait to facilitate the early identification of PD patients with a higher risk of falling.

The effects of muscle fatigue on knee function during landing

The human knee acts as a sophisticated shock absorber during landing movements. The ability of the knee to perform this function in the real world is remarkable given that the context of the landing movement may vary widely between performances. For this reason, humans must be capable of rapidly adjusting the mechanical properties of the knee under impact load in order to satisfy many competing demands. However, the processes involved in regulating these properties in response to changing constraints remain poorly understood. In particular, the effects of muscle fatigue on knee function during step landing are yet to be fully explored. Fatigue of the knee muscles is significant for 2 reasons. First, it is thought to have detrimental effects on the ability of the knee to act as a shock absorber and is considered a risk factor for knee injury. Second, fatigue of knee muscles provides a unique opportunity to examine the mechanisms by which healthy individuals alter knee function. A review of the literature revealed that the effect of fatigue on knee function during landing has been assessed by comparing pre and postfatigue measurements, with fatigue induced by a voluntary exercise protocol. The information is limited by inconsistent results with key measures, such as knee stiffness, showing varying results following fatigue, including increased stiffness, decreased stiffness or failure to detect any change in some experiments. Further consideration of the literature questions the validity of the models used to induce and measure fatigue, as well as the pre-post study design, which may explain the lack of consensus in the results. These limitations cast doubt on the usefulness of the available information and identify a need to investigate alternative approaches. Based on the results of this review, the aims of this thesis were to: • evaluate the methodological procedures used in validation of a fatigue model • investigate the adaptation and regulation of post-impact knee mechanics during repeated step landings • use this new information to test the effects of fatigue on knee function during a step-landing task. To address the aims of the thesis, 3 related experiments were conducted that collected kinetic, kinematic and electromyographic data from 3 separate samples of healthy male participants. The methodologies involved optoelectronic motion capture (VICON), isokinetic dynamometry (System3 Pro, BIODEX) and wireless surface electromyography (Zerowire, Aurion, Italy). Fatigue indicators and knee function measures used in each experiment were derived from the data. Study 1 compared the validity and reliability of repetitive stepping and isokinetic contractions with respect to fatigue of the quadriceps and hamstrings. Fifteen participants performed 50 repetitions of each exercise twice in randomised order, over 4 sessions. Sessions were separated by a minimum of 1 week’s rest, to ensure full recovery. Validity and reliability depended on a complex interaction between the exercise protocol, the fatigue indicator, the individual and the muscle of interest. Nevertheless, differences between exercise protocols indicated that stepping was less effective in eliciting valid and reliable changes in peak power and spectral compression, compared with isokinetic exercise. A key finding was that fatigue progressed in a biphasic pattern during both exercises. The point separating the 2 phases, known as the transition point, demonstrated superior between-test reliability during the isokinetic protocol, compared with stepping. However, a correction factor should be used to accurately apply this technique to the study of fatigue during landing. Study 2 examined alterations in knee function during repeated landings, with a different sample (N =12) performing 60 consecutive step landing trials. Each landing trial was separated by 1-minute rest periods. The results provided new information in relation to the pre-post study design in the context of detecting adjustments in knee function during landing. First, participants significantly increased or decreased pre-impact muscle activity or post-impact mechanics despite environmental and task constraints remaining unchanged. This is the 1st study to demonstrate this effect in healthy individuals without external feedback on performance. Second, single-subject analysis was more effective in detecting alterations in knee function compared to group-level analysis. Finally, repeated landing trials did not reduce inter-trial variability of knee function in some participants, contrary to assumptions underpinning previous studies. The results of studies 1 and 2 were used to modify the design of Study 3 relative to previous research. These alterations included a modified isokinetic fatigue protocol, multiple pre-fatigue measurements and singlesubject analysis to detect fatigue-related changes in knee function. The study design incorporated new analytical approaches to investigate fatiguerelated alterations in knee function during landing. Participants (N = 16) were measured during multiple pre-fatigue baseline trial blocks prior to the fatigue model. A final block of landing trials was recorded once the participant met the operational fatigue definition that was identified in Study 1. The analysis revealed that the effects of fatigue in this context are heavily dependent on the compensatory response of the individual. A continuum of responses was observed within the sample for each knee function measure. Overall, preimpact preparation and post-impact mechanics of the knee were altered with highly individualised patterns. Moreover, participants used a range of active or passive pre-impact strategies to adapt post-impact mechanics in response to quadriceps fatigue. The unique patterns identified in the data represented an optimisation of knee function based on priorities of the individual. The findings of these studies explain the lack of consensus within the literature regarding the effects of fatigue on knee function during landing. First, functional fatigue protocols lack validity in inducing fatigue-related changes in mechanical output and spectral compression of surface electromyography (sEMG) signals, compared with isokinetic exercise. Second, fatigue-related changes in knee function during landing are confounded by inter-individual variation, which limits the sensitivity of group-level analysis. By addressing these limitations, the 3rd study demonstrated the efficacies of new experimental and analytical approaches to observe fatigue-related alterations in knee function during landing. Consequently, this thesis provides new perspectives into the effects of fatigue in knee function during landing. In conclusion: • The effects of fatigue on knee function during landing depend on the response of the individual, with considerable variation present between study participants, despite similar physical characteristics. • In healthy males, adaptation of pre-impact muscle activity and postimpact knee mechanics is unique to the individual and reflects their own optimisation of demands such as energy expenditure, joint stability, sensory information and loading of knee structures. • The results of these studies should guide future exploration of adaptations in knee function to fatigue. However, research in this area should continue with reduced emphasis on the directional response of the population and a greater focus on individual adaptations of knee function.

Throwing frame and performance of elite male seated shot-putters

Seated shot-putters rely on a customized assistive device called a throwing frame. Currently, the construction of each individual throwing frame is mainly driven by an empirical approach. One way to refine the conception is to improve the basic understanding of performance of seated shot-putters. The relationship between performance and throwing technique has been well described. Remarkably, the relationship between performance and throwing frame characteristics has received limited attention. The primary objective of this study was to present a cataloguing of characteristics of throwing frames used by seated shot-putters. This cataloguing consisted of defining and grouping 26 characteristics into three main categories (i.e., whole body, foot and upper limb specific characteristics) and seven sub-categories. The secondary objective of this study was to provide raw characterisations of the throwing frames for a group of athletes who participated in a world-class event. The characterisation consisted of describing the characteristics of each throwing frame. Potential relationships between characteristics, performance and classification were also identified. The cataloguing was achieved using a 6-step heuristic approach, involving expert opinions and the analysis of 215 attempts produced by 55 male athletes during the 2006 IPC Athletics World Championships. The distribution of samples across characteristics suggested a relevant level of comprehensiveness for the proposed cataloguing. The raw data, the profile of best athletes and the frequency of characteristics provided key benchmark information for construction of a throwing frame as well as coaching, classification and officiating. Analysis of data sets relating to characteristics, performance and classification were inconclusive.

Postural balance under normal and altered sensory conditions in normal-weight and overweight children

Background Little or no research has been done in the overweight child on the relative contribution of multisensory information to maintain postural stability. Therefore, the purpose of this study was to investigate postural balance control under normal and experimentally altered sensory conditions in normal-weight versus overweight children. Methods Sixty children were stratified into a younger (7–9 yr) and an older age group (10–12 yr). Participants were also classified as normal-weight (n = 22) or overweight (n = 38), according to the international BMI cut-off points for children. Postural stability was assessed during quiet bilateral stance in four sensory conditions (eyes open or closed, normal or reduced plantar sensation), using a Kistler force plate to quantify COP dynamics. Coefficients of variation were calculated as well to describe intra-individual variability. Findings Removal of vision resulted in systematically higher amounts of postural sway, but no significant BMI group differences were demonstrated across sensory conditions. However, under normal conditions lower plantar cutaneous sensation was associated with higher COP velocities and maximal excursion of the COP in the medial-lateral direction for the overweight group. Regardless of condition, higher variability was shown in the overweight children within the 7–9 yr old subgroup for postural sway velocity, and more specifically medial–lateral velocity. Interpretation In spite of these subtle differences, results did not establish any clear underlying sensory organization impairments that may affect standing balance performance in overweight children compared to normal-weight peers. Consequently, it is believed that other factors account for overweight children's functional balance deficiencies.

Plantar enthesopathy : thickening of the enthesis is correlated with energy dissipation of the plantar fat pad during walking

Background: The enthesis of the plantar fascia is thought to play an important role in stress dissipation. However, the potential link between entheseal thickening characteristic of enthesopathy and the stress-dissipating properties of the intervening plantar fat pad have not been investigated. Purpose: This study was conducted to identify whether plantar fat pad mechanics explain variance in the thickness of the fascial enthesis in individuals with and without plantar enthesopathy. Study Design: Case-control study; Level of evidence, 3. Methods: The study population consisted of 9 patients with unilateral plantar enthesopathy and 9 asymptomatic, individually matched controls. The thickness of the enthesis of the symptomatic, asymptomatic, and a matched control limb was acquired using high-resolution ultrasound. The compressive strain of the plantar fat pad during walking was estimated from dynamic lateral radiographs acquired with a multifunction fluoroscopy unit. Peak compressive stress was simultaneously acquired via a pressure platform. Principal viscoelastic parameters were estimated from subsequent stress-strain curves. Results: The symptomatic fascial enthesis (6.7 ± 2.0 mm) was significantly thicker than the asymptomatic enthesis (4.2 ± 0.4 mm), which in turn was thicker than the enthesis (3.3 ± 0.4 mm) of control limbs (P < .05). There was no significant difference in the mean thickness, peak stress, peak strain, or secant modulus of the plantar fat pad between limbs. However, the energy dissipated by the fat pad during loading and unloading was significantly lower in the symptomatic limb (0.55 ± 0.17) when compared with asymptomatic (0.69 ± 0.13) and control (0.70 ± 0.09) limbs (P < .05). The sonographic thickness of the enthesis was correlated with the energy dissipation ratio of the plantar fat pad (r = .72, P < .05), but only in the symptomatic limb. Conclusion: The energy-dissipating properties of the plantar fat pad are associated with the sonograpic appearance of the enthesis in symptomatic limbs, providing a previously unidentified link between the mechanical behavior of the plantar fat pad and enthesopathy.

The concept of 'Organismic Asymmetry' in sport science

The concept of organismic asymmetry refers to an inherent bias for seeking explanations of human performance and behaviour based on internal mechanisms and referents. A weakness in this tendency is a failure to consider the performer–environment relationship as the relevant scale of analysis. In this paper we elucidate the philosophical roots of the bias and discuss implications of organismic asymmetry for sport science and performance analysis, highlighting examples in psychology, sports medicine and biomechanics.

The ecological dynamics of 1v1 sub-phases in association football

This paper analyzes effects of different practice task constraints on heart rate (HR) variability during 4v4 smallsided football games. Participants were sixteen football players divided into two age groups (U13, Mean age: 12.4±0.5 yrs; U15: 14.6±0.5). The task consisted of a 4v4 sub-phase without goalkeepers, on a 25x15 m field, of 15 minutes duration with an active recovery period of 6 minutes between each condition. We recorded players’ heart rates using heart rate monitors (Polar Team System, Polar Electro, Kempele, Finland) as scoring mode was manipulated (line goal: scoring by dribbling past an extended line; double goal: scoring in either of two lateral goals; and central goal: scoring only in one goal). Subsequently, %HR reserve was calculated with the Karvonen formula. We performed a time-series analysis of HR for each individual in each condition. Mean data for intra-participant variability showed that autocorrelation function was associated with more short-range dependence processes in the “line goal” condition, compared to other conditions, demonstrating that the “line goal” constraint induced more randomness in HR response. Relative to inter-individual variability, line goal constraints demonstrated lower %CV and %RMSD (U13: 9% and 19%; U15: 10% and 19%) compared with double goal (U13: 12% and 21%; U15: 12% and 21%) and central goal (U13: 14% and 24%; U15: 13% and 24%) task constraints, respectively. Results suggested that line goal constraints imposed more randomness on cardiovascular stimulation of each individual and lower inter-individual variability than double goal and central goal constraints.

Mechanical conditions in the initial phase of bone healing

Background: Bone healing is sensitive to the initial mechanical conditions with tissue differentiation being determined within days of trauma. Whilst axial compression is regarded as stimulatory, the role of interfragmentary shear is controversial. The purpose of this study was to determine how the initial mechanical conditions produced by interfragmentary shear and torsion differ from those produced by axial compressive movements. ----- ----- Methods: The finite element method was used to estimate the strain, pressure and fluid flow in the early callus tissue produced by the different modes of interfragmentary movement found in vivo. Additionally, tissue formation was predicted according to three principally different mechanobiological theories. ----- ----- Findings: Large interfragmentary shear movements produced comparable strains and less fluid flow and pressure than moderate axial interfragmentary movements. Additionally, combined axial and shear movements did not result in overall increases in the strains and the strain magnitudes were similar to those produced by axial movements alone. Only when axial movements where applied did the non-distortional component of the pressure–deformation theory influence the initial tissue predictions. ----- ----- Interpretation: This study found that the mechanical stimuli generated by interfragmentary shear and torsion differed from those produced by axial interfragmentary movements. The initial tissue formation as predicted by the mechanobiological theories was dominated by the deformation stimulus.

The mechanical heterogeneity of the hard callus influences local tissue strains during bone healing : a finite element study based on sheep experiments

During secondary fracture healing, various tissue types including new bone are formed. The local mechanical strains play an important role in tissue proliferation and differentiation. To further our mechanobiological understanding of fracture healing, a precise assessment of local strains is mandatory. Until now, static analyses using Finite Elements (FE) have assumed homogenous material properties. With the recent quantification of both the spatial tissue patterns (Vetter et al., 2010) and the development of elastic modulus of newly formed bone during healing (Manjubala et al., 2009), it is now possible to incorporate this heterogeneity. Therefore, the aim of this study is to investigate the effect of this heterogeneity on the strain patterns at six successive healing stages. The input data of the present work stemmed from a comprehensive cross-sectional study of sheep with a tibial osteotomy (Epari et al., 2006). In our FE model, each element containing bone was described by a bulk elastic modulus, which depended on both the local area fraction and the local elastic modulus of the bone material. The obtained strains were compared with the results of hypothetical FE models assuming homogeneous material properties. The differences in the spatial distributions of the strains between the heterogeneous and homogeneous FE models were interpreted using a current mechanobiological theory (Isakson et al., 2006). This interpretation showed that considering the heterogeneity of the hard callus is most important at the intermediate stages of healing, when cartilage transforms to bone via endochondral ossification.