An experimental and finite element investigation of the biomechanics of vertebral compression fractures

Osteoporosis is a disease characterized by low bone mass and micro-architectural deterioration of bone tissue, with a consequent increase in bone fragility and susceptibility to fracture. Osteoporosis affects over 200 million people worldwide, with an estimated 1.5 million fractures annually in the United States alone, and with attendant costs exceeding $10 billion dollars per annum. Osteoporosis reduces bone density through a series of structural changes to the honeycomb-like trabecular bone structure (micro-structure). The reduced bone density, coupled with the microstructural changes, results in significant loss of bone strength and increased fracture risk. Vertebral compression fractures are the most common type of osteoporotic fracture and are associated with pain, increased thoracic curvature, reduced mobility, and difficulty with self care. Surgical interventions, such as kyphoplasty or vertebroplasty, are used to treat osteoporotic vertebral fractures by restoring vertebral stability and alleviating pain. These minimally invasive procedures involve injecting bone cement into the fractured vertebrae. The techniques are still relatively new and while initial results are promising, with the procedures relieving pain in 70-95% of cases, medium-term investigations are now indicating an increased risk of adjacent level fracture following the procedure. With the aging population, understanding and treatment of osteoporosis is an increasingly important public health issue in developed Western countries. The aim of this study was to investigate the biomechanics of spinal osteoporosis and osteoporotic vertebral compression fractures by developing multi-scale computational, Finite Element (FE) models of both healthy and osteoporotic vertebral bodies. The multi-scale approach included the overall vertebral body anatomy, as well as a detailed representation of the internal trabecular microstructure. This novel, multi-scale approach overcame limitations of previous investigations by allowing simultaneous investigation of the mechanics of the trabecular micro-structure as well as overall vertebral body mechanics. The models were used to simulate the progression of osteoporosis, the effect of different loading conditions on vertebral strength and stiffness, and the effects of vertebroplasty on vertebral and trabecular mechanics. The model development process began with the development of an individual trabecular strut model using 3D beam elements, which was used as the building block for lattice-type, structural trabecular bone models, which were in turn incorporated into the vertebral body models. At each stage of model development, model predictions were compared to analytical solutions and in-vitro data from existing literature. The incremental process provided confidence in the predictions of each model before incorporation into the overall vertebral body model. The trabecular bone model, vertebral body model and vertebroplasty models were validated against in-vitro data from a series of compression tests performed using human cadaveric vertebral bodies. Firstly, trabecular bone samples were acquired and morphological parameters for each sample were measured using high resolution micro-computed tomography (CT). Apparent mechanical properties for each sample were then determined using uni-axial compression tests. Bone tissue properties were inversely determined using voxel-based FE models based on the micro-CT data. Specimen specific trabecular bone models were developed and the predicted apparent stiffness and strength were compared to the experimentally measured apparent stiffness and strength of the corresponding specimen. Following the trabecular specimen tests, a series of 12 whole cadaveric vertebrae were then divided into treated and non-treated groups and vertebroplasty performed on the specimens of the treated group. The vertebrae in both groups underwent clinical-CT scanning and destructive uniaxial compression testing. Specimen specific FE vertebral body models were developed and the predicted mechanical response compared to the experimentally measured responses. The validation process demonstrated that the multi-scale FE models comprising a lattice network of beam elements were able to accurately capture the failure mechanics of trabecular bone; and a trabecular core represented with beam elements enclosed in a layer of shell elements to represent the cortical shell was able to adequately represent the failure mechanics of intact vertebral bodies with varying degrees of osteoporosis. Following model development and validation, the models were used to investigate the effects of progressive osteoporosis on vertebral body mechanics and trabecular bone mechanics. These simulations showed that overall failure of the osteoporotic vertebral body is initiated by failure of the trabecular core, and the failure mechanism of the trabeculae varies with the progression of osteoporosis; from tissue yield in healthy trabecular bone, to failure due to instability (buckling) in osteoporotic bone with its thinner trabecular struts. The mechanical response of the vertebral body under load is highly dependent on the ability of the endplates to deform to transmit the load to the underlying trabecular bone. The ability of the endplate to evenly transfer the load through the core diminishes with osteoporosis. Investigation into the effect of different loading conditions on the vertebral body found that, because the trabecular bone structural changes which occur in osteoporosis result in a structure that is highly aligned with the loading direction, the vertebral body is consequently less able to withstand non-uniform loading states such as occurs in forward flexion. Changes in vertebral body loading due to disc degeneration were simulated, but proved to have little effect on osteoporotic vertebra mechanics. Conversely, differences in vertebral body loading between simulated invivo (uniform endplate pressure) and in-vitro conditions (where the vertebral endplates are rigidly cemented) had a dramatic effect on the predicted vertebral mechanics. This investigation suggested that in-vitro loading using bone cement potting of both endplates has major limitations in its ability to represent vertebral body mechanics in-vivo. And lastly, FE investigation into the biomechanical effect of vertebroplasty was performed. The results of this investigation demonstrated that the effect of vertebroplasty on overall vertebra mechanics is strongly governed by the cement distribution achieved within the trabecular core. In agreement with a recent study, the models predicted that vertebroplasty cement distributions which do not form one continuous mass which contacts both endplates have little effect on vertebral body stiffness or strength. In summary, this work presents the development of a novel, multi-scale Finite Element model of the osteoporotic vertebral body, which provides a powerful new tool for investigating the mechanics of osteoporotic vertebral compression fractures at the trabecular bone micro-structural level, and at the vertebral body level.

Identification of reduced models of power system areas using phasor measurement units

In this paper an approach is presented for identification of a reduced model for coherent areas in power systems using phasor measurement units to represent the inter-area oscillations of the system. The generators which are coherent in a wide range of operating conditions form the areas in power systems and the reduced model is obtained by representing each area by an equivalent machine. The reduced nonlinear model is then identified based on the data obtained from measurement units. The simulation is performed on three test systems and the obtained results show high accuracy of identification process.

Ex vivo investigation of novel wound healing therapies and development of a 3-D human skin equivalent wound model

It has previously been found that complexes comprised of vitronectin and growth factors (VN:GF) enhance keratinocyte protein synthesis and migration. More specifically, these complexes have been shown to significantly enhance the migration of dermal keratinocytes derived from human skin. In view of this, it was thought that these complexes may hold potential as a novel therapy for healing chronic wounds. However, there was no evidence indicating that the VN:GF complexes would retain their effect on keratinocytes in the presence of chronic wound fluid. The studies in this thesis demonstrate for the first time that the VN:GF complexes not only stimulate proliferation and migration of keratinocytes, but also these effects are maintained in the presence of chronic wound fluid in a 2-dimensional (2-D) cell culture model. Whilst the 2-D culture system provided insights into how the cells might respond to the VN:GF complexes, this investigative approach is not ideal as skin is a 3-dimensional (3-D) tissue. In view of this, a 3-D human skin equivalent (HSE) model, which reflects more closely the in vivo environment, was used to test the VN:GF complexes on epidermopoiesis. These studies revealed that the VN:GF complexes enable keratinocytes to migrate, proliferate and differentiate on a de-epidermalised dermis (DED), ultimately forming a fully stratified epidermis. In addition, fibroblasts were seeded on DED and shown to migrate into the DED in the presence of the VN:GF complexes and hyaluronic acid, another important biological factor in the wound healing cascade. This HSE model was then further developed to enable studies examining the potential of the VN:GF complexes in epidermal wound healing. Specifically, a reproducible partial-thickness HSE wound model was created in fully-defined media and monitored as it healed. In this situation, the VN:GF complexes were shown to significantly enhance keratinocyte migration and proliferation, as well as differentiation. This model was also subsequently utilized to assess the wound healing potential of a synthetic fibrin-like gel that had previously been demonstrated to bind growth factors. Of note, keratinocyte re-epitheliasation was shown to be markedly improved in the presence of this 3-D matrix, highlighting its future potential for use as a delivery vehicle for the VN:GF complexes. Furthermore, this synthetic fibrin-like gel was injected into a 4 mm diameter full-thickness wound created in the HSE, both keratinocytes and fibroblasts were shown to migrate into this gel, as revealed by immunofluorescence. Interestingly, keratinocyte migration into this matrix was found to be dependent upon the presence of the fibroblasts. Taken together, these data indicate that reproducible wounds, as created in the HSEs, provide a relevant ex vivo tool to assess potential wound healing therapies. Moreover, the models will decrease our reliance on animals for scientific experimentation. Additionally, it is clear that these models will significantly assist in the development of novel treatments, such as the VN:GF complexes and the synthetic fibrin-like gel described herein, ultimately facilitating their clinical trial in the treatment of chronic wounds.

Development of a 3-dimensional human skin equivalent wound model for investigating novel wound healing therapies

Numerous difficulties are associated with the conduct of preclinical studies related to skin and wound repair. Use of small animal models such as rodents is not optimal because of their physiological differences to human skin and mode of wound healing. Although pigs have previously been used because of their human-like mode of healing, the expense and logistics related to their use also renders them suboptimal. In view of this, alternatives are urgently required to advance the field. The experiments reported herein were aimed at developing and validating a simple, reproducible, three-dimensional ex vivo de-epidermised dermis human skin equivalent wound model for the preclinical evaluation of novel wound therapies. Having established that the human skin equivalent wound model does in fact “heal," we tested the effect of two novel wound healing therapies. We also examined the utility of the model for studies exploring the mechanisms underpinning these therapies. Taken together the data demonstrate that these new models will have wide-spread application for the generation of fundamental new information on wound healing processes and also hold potential in facilitating preclinical optimization of dosage, duration of therapies, and treatment strategies prior to clinical trials.

Investigating epidermogenesis in a human skin equivalent model

Skin is the largest, and arguably, the most important organ of the body. It is a complex and multi-dimensional tissue, thus making it essentially impossible to fully model in vitro in conventional 2-dimensional culture systems. In view of this, rodents or pigs are utilised to study wound healing therapeutics or to investigate the biological effects of treatments on skin. However, there are many differences between the wound healing processes in rodents compared to humans (contraction vs. re-epithelialisation) and there are also ethical issues associated with animal testing for scientific research. Therefore, the development of skin equivalent (HSE) models from surgical discard human skin has become an important area of research. The studies in this thesis compare, for the first time, native human skin and the epidermogenesis process in a HSE model. The HSE was reported to be a comparable model for human skin in terms of expression and localisation of key epidermal cell markers. This validated HSE model was utilised to study the potential wound healing therapeutic, hyperbaric oxygen (HBO) therapy. There is a significant body of evidence suggesting that lack of cutaneous oxygen results in and potentiates the chronic, non-healing wound environment. Although the evidence is anecdotal, HBO therapy has displayed positive effects on re-oxygenation of chronic wounds and the clinical outcomes suggest that HBO treatment may be beneficial. Therefore, the HSE was subjected to a daily clinical HBO regime and assessed in terms of keratinocyte migration, proliferation, differentiation and epidermal thickening. HBO treatment was observed to increase epidermal thickness, in particular stratum corneum thickening, but it did not alter the expression or localisation of standard epidermal cell markers. In order to elucidate the mechanistic changes occurring in response to HBO treatment in the HSE model, gene microarrays were performed, followed by qRT-PCR of select genes which were differentially regulated in response to HBO treatment. The biological diversity of the HSEs created from individual skin donors, however, overrode the differences in gene expression between treatment groups. Network analysis of functional changes in the HSE model revealed general trends consistent with normal skin growth and maturation. As a more robust and longer term study of these molecular changes, protein localisation and expression was investigated in sections from the HSEs undergoing epidermogenesis in response to HBO treatment. These proteins were CDCP1, Metallothionein, Kallikrein (KLK) 1 and KLK7 and early growth response 1. While the protein expression within the HSE models exposed to HBO treatment were not consistent in all HSEs derived from all skin donors, this is the first study to detect and compare both KLK1 and CDCP1 protein expression in both a HSE model and native human skin. Furthermore, this is the first study to provide such an in depth analysis of the effect of HBO treatment on a HSE model. The data presented in this thesis, demonstrates high levels of variation between individuals and their response to HBO treatment, consistent with the clinical variation that is currently observed.

Characterisation of a human skin equivalent model to study the effects of ultraviolet B radiation on keratinocytes

The incidences of skin cancers resulting from chronic ultraviolet radiation (UVR) exposure are on the incline both in Australia and globally. Hence, the cellular and molecular pathways associated with UVR-induced photocarcinogenesis urgently need to be elucidated, in order to develop more robust preventative and treatment strategies against skin cancers. In vitro investigations into the effects of UVR (in particular the highly-mutagenic UVB wavelength) have, to date, mainly involved the use of cell culture and animal models. However, these models possess biological disparities to native skin, which to some extent have limited their relevance to the in vivo situation. To address this, we characterised a 3-dimensional, tissue-engineered human skin equivalent (HSE) model (consisting of primary human keratinocytes cultured on a dermal-derived scaffold) as a representation of a more physiologically-relevant platform to study keratinocyte responses to UVB. Significantly, we demonstrate that this model retains several important epidermal properties of native skin. Moreover, UVB-irradiation of the HSE constructs was shown to induce key markers of photodamage in the HSE keratinocytes, including the formation of cyclobutane pyrimidine dimers, the activation of apoptotic pathways, the accumulation of p53 and the secretion of inflammatory cytokines. Importantly, we also demonstrate that the UVB-exposed HSE constructs retain the capacity for epidermal repair and regeneration following photodamage. Together, our results demonstrate the potential of this skin equivalent model as a tool to study various aspects of the acute responses of human keratinocytes to UVB radiation damage.

CTCombine : rotating and combining CT data with an accurate detector model, to simulate radiotherapy portal imaging at non-zero beam angles

Established Monte Carlo user codes BEAMnrc and DOSXYZnrc permit the accurate and straightforward simulation of radiotherapy experiments and treatments delivered from multiple beam angles. However, when an electronic portal imaging detector (EPID) is included in these simulations, treatment delivery from non-zero beam angles becomes problematic. This study introduces CTCombine, a purpose-built code for rotating selected CT data volumes, converting CT numbers to mass densities, combining the results with model EPIDs and writing output in a form which can easily be read and used by the dose calculation code DOSXYZnrc. The geometric and dosimetric accuracy of CTCombine’s output has been assessed by simulating simple and complex treatments applied to a rotated planar phantom and a rotated humanoid phantom and comparing the resulting virtual EPID images with the images acquired using experimental measurements and independent simulations of equivalent phantoms. It is expected that CTCombine will be useful for Monte Carlo studies of EPID dosimetry as well as other EPID imaging applications.

An event-based traffic flow model for traffic control at railway junctions

This paper introduces an event-based traffic model for railway systems adopting fixed-block signalling schemes. In this model, the events of trains' arrival at and departure from signalling blocks constitute the states of the traffic flow. A state transition is equivalent to the progress of the trains by one signalling block and it is realised by referring to past and present states, as well as a number of pre-calculated look-up tables of run-times in the signalling block under various signalling conditions. Simulation results are compared with those from a time-based multi-train simulator to study the improvement of processing time and accuracy.

Empirical Bayes method in the study of traffic safety via heterogeneous negative multinomial model

In the study of traffic safety, expected crash frequencies across sites are generally estimated via the negative binomial model, assuming time invariant safety. Since the time invariant safety assumption may be invalid, Hauer (1997) proposed a modified empirical Bayes (EB) method. Despite the modification, no attempts have been made to examine the generalisable form of the marginal distribution resulting from the modified EB framework. Because the hyper-parameters needed to apply the modified EB method are not readily available, an assessment is lacking on how accurately the modified EB method estimates safety in the presence of the time variant safety and regression-to-the-mean (RTM) effects. This study derives the closed form marginal distribution, and reveals that the marginal distribution in the modified EB method is equivalent to the negative multinomial (NM) distribution, which is essentially the same as the likelihood function used in the random effects Poisson model. As a result, this study shows that the gamma posterior distribution from the multivariate Poisson-gamma mixture can be estimated using the NM model or the random effects Poisson model. This study also shows that the estimation errors from the modified EB method are systematically smaller than those from the comparison group method by simultaneously accounting for the RTM and time variant safety effects. Hence, the modified EB method via the NM model is a generalisable method for estimating safety in the presence of the time variant safety and the RTM effects.

Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical VC dimension, empirical VC entropy, and margin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

Designing radical business model innovation : a case study

“The process of innovation is often seen as being very linear, with research results, new technologies or user insights being channelled, often prematurely, into specific products and process” (Kyffin and Gardien 2009). It is precisely this perception of innovation-as-linear-process which this paper seeks to challenge. While there are many current theories and much contemporary literature available which discuss the management and catalysts of innovation, what is missing are examples of how innovation occurs from the application of these theories and literature (Wrigley & Bucolo 2010). This paper addresses both this gap and perceptions of the viability of linear innovation by presenting a case study for the commercialisation of a core technology (a cleantech, semi-portable mass-energy generator posited as a direct competitor to conventional energy provision systems), within an 18-month timeframe by the use of the Design-Led Innovation approach: “a process of creating a sustainable competitive advantage by radically changing the customer value proposition” (Bucolo & Matthews 2011).

Statistical eye model for normal eyes

Purpose. To create a binocular statistical eye model based on previously measured ocular biometric data. Methods. Thirty-nine parameters were determined for a group of 127 healthy subjects (37 male, 90 female; 96.8% Caucasian) with an average age of 39.9 ± 12.2 years and spherical equivalent refraction of −0.98 ± 1.77 D. These parameters described the biometry of both eyes and the subjects' age. Missing parameters were complemented by data from a previously published study. After confirmation of the Gaussian shape of their distributions, these parameters were used to calculate their mean and covariance matrices. These matrices were then used to calculate a multivariate Gaussian distribution. From this, an amount of random biometric data could be generated, which were then randomly selected to create a realistic population of random eyes. Results. All parameters had Gaussian distributions, with the exception of the parameters that describe total refraction (i.e., three parameters per eye). After these non-Gaussian parameters were omitted from the model, the generated data were found to be statistically indistinguishable from the original data for the remaining 33 parameters (TOST [two one-sided t tests]; P < 0.01). Parameters derived from the generated data were also significantly indistinguishable from those calculated with the original data (P > 0.05). The only exception to this was the lens refractive index, for which the generated data had a significantly larger SD. Conclusions. A statistical eye model can describe the biometric variations found in a population and is a useful addition to the classic eye models.

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Solving tri-diagonal linear systems using field programmable gate arrays

In this paper, we present the outcomes of a project on the exploration of the use of Field Programmable Gate Arrays(FPGAs) as co-processors for scientific computation. We designed a custom circuit for the pipelined solving of multiple tri-diagonal linear systems. The design is well suited for applications that require many independent tri diagonal system solves, such as finite difference methods for solving PDEs or applications utilising cubic spline interpolation. The selected solver algorithm was the Tri Diagonal Matrix Algorithm (TDMA or Thomas Algorithm). Our solver supports user specified precision thought the use of a custom floating point VHDL library supporting addition, subtraction, multiplication and division. The variable precision TDMA solver was tested for correctness in simulation mode. The TDMA pipeline was tested successfully in hardware using a simplified solver model. The details of implementation, the limitations, and future work are also discussed.

Dynamic equivalent state estimation for multi-area power systems with synchronized phasor measurement units

This paper proposes a new approach for state estimation of angles and frequencies of equivalent areas in large power systems with synchronized phasor measurement units. Defining coherent generators and their correspondent areas, generators are aggregated and system reduction is performed in each area of inter-connected power systems. The structure of the reduced system is obtained based on the characteristics of the reduced linear model and measurement data to form the non-linear model of the reduced system. Then a Kalman estimator is designed for the reduced system to provide an equivalent dynamic system state estimation using the synchronized phasor measurement data. The method is simulated on two test systems to evaluate the feasibility of the proposed method.