Mathematical modelling of muscle recruitment and function in the lumbar spine

Low back pain is an increasing problem in industrialised countries and although it is a major socio-economic problem in terms of medical costs and lost productivity, relatively little is known about the processes underlying the development of the condition. This is in part due to the complex interactions between bone, muscle, nerves and other soft tissues of the spine, and the fact that direct observation and/or measurement of the human spine is not possible using non-invasive techniques. Biomechanical models have been used extensively to estimate the forces and moments experienced by the spine. These models provide a means of estimating the internal parameters which can not be measured directly. However, application of most of the models currently available is restricted to tasks resembling those for which the model was designed due to the simplified representation of the anatomy. The aim of this research was to develop a biomechanical model to investigate the changes in forces and moments which are induced by muscle injury. In order to accurately simulate muscle injuries a detailed quasi-static three dimensional model representing the anatomy of the lumbar spine was developed. This model includes the nine major force generating muscles of the region (erector spinae, comprising the longissimus thoracis and iliocostalis lumborum; multifidus; quadratus lumborum; latissimus dorsi; transverse abdominis; internal oblique and external oblique), as well as the thoracolumbar fascia through which the transverse abdominis and parts of the internal oblique and latissimus dorsi muscles attach to the spine. The muscles included in the model have been represented using 170 muscle fascicles each having their own force generating characteristics and lines of action. Particular attention has been paid to ensuring the muscle lines of action are anatomically realistic, particularly for muscles which have broad attachments (e.g. internal and external obliques), muscles which attach to the spine via the thoracolumbar fascia (e.g. transverse abdominis), and muscles whose paths are altered by bony constraints such as the rib cage (e.g. iliocostalis lumborum pars thoracis and parts of the longissimus thoracis pars thoracis). In this endeavour, a separate sub-model which accounts for the shape of the torso by modelling it as a series of ellipses has been developed to model the lines of action of the oblique muscles. Likewise, a separate sub-model of the thoracolumbar fascia has also been developed which accounts for the middle and posterior layers of the fascia, and ensures that the line of action of the posterior layer is related to the size and shape of the erector spinae muscle. Published muscle activation data are used to enable the model to predict the maximum forces and moments that may be generated by the muscles. These predictions are validated against published experimental studies reporting maximum isometric moments for a variety of exertions. The model performs well for fiexion, extension and lateral bend exertions, but underpredicts the axial twist moments that may be developed. This discrepancy is most likely the result of differences between the experimental methodology and the modelled task. The application of the model is illustrated using examples of muscle injuries created by surgical procedures. The three examples used represent a posterior surgical approach to the spine, an anterior approach to the spine and uni-lateral total hip replacement surgery. Although the three examples simulate different muscle injuries, all demonstrate the production of significant asymmetrical moments and/or reduced joint compression following surgical intervention. This result has implications for patient rehabilitation and the potential for further injury to the spine. The development and application of the model has highlighted a number of areas where current knowledge is deficient. These include muscle activation levels for tasks in postures other than upright standing, changes in spinal kinematics following surgical procedures such as spinal fusion or fixation, and a general lack of understanding of how the body adjusts to muscle injuries with respect to muscle activation patterns and levels, rate of recovery from temporary injuries and compensatory actions by other muscles. Thus the comprehensive and innovative anatomical model which has been developed not only provides a tool to predict the forces and moments experienced by the intervertebral joints of the spine, but also highlights areas where further clinical research is required.

A connective model for the practice-led research exegesis : an analysis of content and structure

Since the formal recognition of practice-led research in the 1990s, many higher research degree candidates in art, design and media have submitted creative works along with an accompanying written document or ‘exegesis’ for examination. Various models for the exegesis have been proposed in university guidelines and academic texts during the past decade, and students and supervisors have experimented with its contents and structure. With a substantial number of exegeses submitted and archived, it has now become possible to move beyond proposition to empirical analysis. In this article we present the findings of a content analysis of a large, local sample of submitted exegeses. We identify the emergence of a persistent pattern in the types of content included as well as overall structure. Besides an introduction and conclusion, this pattern includes three main parts, which can be summarized as situating concepts (conceptual definitions and theories); precedents of practice (traditions and exemplars in the field); and researcher’s creative practice (the creative process, the artifacts produced and their value as research). We argue that this model combines earlier approaches to the exegesis, which oscillated between academic objectivity, by providing a contextual framework for the practice, and personal reflexivity, by providing commentary on the creative practice. But this model is more than simply a hybrid: it provides a dual orientation, which allows the researcher to both situate their creative practice within a trajectory of research and do justice to its personally invested poetics. By performing the important function of connecting the practice and creative work to a wider emergent field, the model helps to support claims for a research contribution to the field. We call it a connective model of exegesis.

An environmental assessment model for knowledge-based urban development

Purpose – In recent years, knowledge-based urban development (KBUD) has introduced as a new strategic development approach for the regeneration of industrial cities. It aims to create a knowledge city consists of planning strategies, IT networks and infrastructures that achieved through supporting the continuous creation, sharing, evaluation, renewal and update of knowledge. Improving urban amenities and ecosystem services by creating sustainable urban environment is one of the fundamental components for KBUD. In this context, environmental assessment plays an important role in adjusting urban environment and economic development towards a sustainable way. The purpose of this paper is to present the role of assessment tools for environmental decision making process of knowledge cities. Design/methodology/approach – The paper proposes a new assessment tool to figure a template of a decision support system which will enable to evaluate the possible environmental impacts in an existing and future urban context. The paper presents the methodology of the proposed model named ‘ASSURE’ which consists of four main phases. Originality/value –The proposed model provides a useful guidance to evaluate the urban development and its environmental impacts to achieve sustainable knowledge-based urban futures. Practical implications – The proposed model will be an innovative approach to provide the resilience and function of urban natural systems secure against the environmental changes while maintaining the economic development of cities.

Safety-restraint use rate as function of law enforcement and other factors : preliminary analysis

Persistent use of safety restraints prevents deaths and reduces the severity and number of injuries resulting from motor vehicle crashes. However, safety-restraint use rates in the United States have been below those of other nations with safety-restraint enforcement laws. With a better understanding of the relationship between safety-restraint law enforcement and safety-restraint use, programs can be implemented to decrease the number of deaths and injuries resulting from motor vehicle crashes. Does safety-restraint use increase as enforcement increases? Do motorists increase their safety-restraint use in response to the general presence of law enforcement or to targeted law enforcement efforts? Does a relationship between enforcement and restraint use exist at the countywide level? A logistic regression model was estimated by using county-level safety-restraint use data and traffic citation statistics collected in 13 counties within the state of Florida in 1997. The model results suggest that safety-restraint use is positively correlated with enforcement intensity, is negatively correlated with safety-restraint enforcement coverage (in lanemiles of enforcement coverage), and is greater in urban than rural areas. The quantification of these relationships may assist Florida and other law enforcement agencies in raising safety-restraint use rates by allocating limited funds more efficiently either by allocating additional time for enforcement activities of the existing force or by increasing enforcement staff. In addition, the research supports a commonsense notion that enforcement activities do result in behavioral response.

Validation of the MEASURE automobile emissions model : a statistical analysis

The Mobile Emissions Assessment System for Urban and Regional Evaluation (MEASURE) model provides an external validation capability for hot stabilized option; the model is one of several new modal emissions models designed to predict hot stabilized emission rates for various motor vehicle groups as a function of the conditions under which the vehicles are operating. The validation of aggregate measurements, such as speed and acceleration profile, is performed on an independent data set using three statistical criteria. The MEASURE algorithms have proved to provide significant improvements in both average emission estimates and explanatory power over some earlier models for pollutants across almost every operating cycle tested.

Mineralized human primary osteoblast matrices as a model system to analyse interactions of prostate cancer cells with the bone microenvironment

Prostate cancer metastasis is reliant on the reciprocal interactions between cancer cells and the bone niche/micro-environment. The production of suitable matrices to study metastasis, carcinogenesis and in particular prostate cancer/bone micro-environment interaction has been limited to specific protein matrices or matrix secreted by immortalised cell lines that may have undergone transformation processes altering signaling pathways and modifying gene or receptor expression. We hypothesize that matrices produced by primary human osteoblasts are a suitable means to develop an in vitro model system for bone metastasis research mimicking in vivo conditions. We have used a decellularized matrix secreted from primary human osteoblasts as a model for prostate cancer function in the bone micro-environment. We show that this collagen I rich matrix is of fibrillar appearance, highly mineralized, and contains proteins, such as osteocalcin, osteonectin and osteopontin, and growth factors characteristic of bone extracellular matrix (ECM). LNCaP and PC3 cells grown on this matrix, adhere strongly, proliferate, and express markers consistent with a loss of epithelial phenotype. Moreover, growth of these cells on the matrix is accompanied by the induction of genes associated with attachment, migration, increased invasive potential, Ca2+ signaling and osteolysis. In summary, we show that growth of prostate cancer cells on matrices produced by primary human osteoblasts mimics key features of prostate cancer bone metastases and thus is a suitable model system to study the tumor/bone micro-environment interaction in this disease.

A model for mesoscale patterns in motile populations

Experimental observations of cell migration often describe the presence of mesoscale patterns within motile cell populations. These patterns can take the form of cells moving as aggregates or in chain-like formation. Here we present a discrete model capable of producing mesoscale patterns. These patterns are formed by biasing movements to favor a particular configuration of agent–agent attachments using a binding function f(K), where K is the scaled local coordination number. This discrete model is related to a nonlinear diffusion equation, where we relate the nonlinear diffusivity D(C) to the binding function f. The nonlinear diffusion equation supports a range of solutions which can be either smooth or discontinuous. Aggregation patterns can be produced with the discrete model, and we show that there is a transition between the presence and absence of aggregation depending on the sign of D(C). A combination of simulation and analysis shows that both the existence of mesoscale patterns and the validity of the continuum model depend on the form of f. Our results suggest that there may be no formal continuum description of a motile system with strong mesoscale patterns.

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.

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.

Fast rates for estimation error and oracle inequalities for model section

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many cases, however, where complexity penalties like this give loose upper bounds on the estimation error. In particular, if we choose a function from a suitably simple convex function class with a strictly convex loss function, then the estimation error (the difference between the risk of the empirical risk minimizer and the minimal risk in the class) approaches zero at a faster rate than the maximal deviation between empirical and true risks. In this paper, we address the question of whether it is possible to design a complexity penalized model selection method for these situations. We show that, provided the sequence of models is ordered by inclusion, in these cases we can use tight upper bounds on estimation error as a complexity penalty. Surprisingly, this is the case even in situations when the difference between the empirical risk and true risk (and indeed the error of any estimate of the approximation error) decreases much more slowly than the complexity penalty. We give an oracle inequality showing that the resulting model selection method chooses a function with risk no more than the approximation error plus a constant times the complexity penalty.

Inhibition of p38 pathway leads to OA-like changes in a rat animal model

Objectives The p38 mitogen-activated protein kinase (MAPK) signal transduction pathway is involved in a variety of inflammatory responses, including cytokine generation, cell differentiation proliferation and apoptosis. Here, we examined the effects of systemic p38 MAPK inhibition on cartilage cells and osteoarthritis (OA) disease progression by both in vitro and in vivo approaches. Methods p38 kinase activity was evaluated in normal and OA cartilage cells by measuring the amount of phosphorylated protein. To examine the function of p38 signaling pathway in vitro, normal chondrocytes were isolated and differentiated in the presence or absence of p38 inhibitor; SB203580 and analysed for chondrogenic phenotype. Effect of systemic p38 MAPK inhibition in normal and OA (induced by menisectomy) rats were analysed by treating animals with vehicle alone (DMS0) or p38 inhibitor (SB203580). Damage to the femur and tibial plateau was evaluated by modified Mankin score, histology and immunohistochemistry. Results Our in vitro studies have revealed that a down-regulation of chondrogenic and increase of hypertrophic gene expression occurs in the normal chondrocytes, when p38 is neutralized by a pharmacological inhibitor. We further observed that the basal levels of p38 phosphorylation were decreased in OA chondrocytes compared with normal chondrocytes. These findings together indicate the importance of this pathway in the regulation of cartilage physiology and its relevance to OA pathogenesis. At in vivo level, systematic administration of a specific p38 MAPK inhibitor, SB203580, continuously for over a month led to a significant loss of proteoglycan; aggrecan and cartilage thickness. On the other hand, SB203580 treated normal rats showed a significant increase in TUNEL positive cells, cartilage hypertrophy markers such as Type 10 collagen, Runt-related transcription factor and Matrix metalloproteinase-13 and substantially induced OA like phenotypic changes in the normal rats. In addition, menisectomy induced OA rat models that were treated with p38 inhibitor showed aggravation of cartilage damage. Conclusions In summary, this study has provided evidence that the component of the p38 MAPK pathway is important to maintain the cartilage health and its inhibition can lead to severe cartilage degenerative changes. The observations in this study highlight the possibility of using activators of the p38 pathway as an alternative approach in the treatment of OA.

Hypothetical model of hydrophilic lubrication in synovial joints

This paper presents a new insight into the mechanism of biolubrication of articulating mammalian joints that includes the function of surface-active phospholipids (SAPLs). SAPLs can be adsorbed on surface of cartilage membranes as a hydrophobic monolayer (H-phobic-M Madel or Hills' Model) or as a newly proposed hydrophilic bilayer (H-philic-B Model). With respect to the synovial joint's frictionless work, three processes are identified namely: monolayer/bilayer phospholipids binding to cartilage with lubricin interaction; influence of induced-pressure on interaction of hyaluronan with phospholipids; and biolubrication arising from two gliding articular hydrophilic surfaces acting as reverse micelle. Lubricin is considered to play critical role as a supplier of phospholipids, which overlay the articular surface of articular cartilage. Hyaluronic acid is considered to play a critical mediating role in the interaction between the hydrophilic part of phospholipids, the articular surface and water (hydration) in facilitating the lubrication process. Tivo models of frictionless lubrication processes, namely hydrophobic (H-phobic-M Model) and our conceptual hydrophilic (H-philic-B Model), are compared. © Institution of Engineers Australia, 2008.