Mathematical models of soft tissue injury repair : towards understanding musculoskeletal disorders

The process of soft tissue injury repair at the cellular lew I can be decomposed into three phases: acute inflammation including coagulation, proliferation and remodelling. While the later phases are well understood the early phase is less so. We produce a series of new mathematical models for the early phases coagulation and inflammation. The models produced are relevant not only to soft tissue injury repair but also to the many disease states in which coagulation and inflammation play a role. The coagulation cascade and the subsequent formation of the enzyme thrombin are central to the creation of blood clots. By focusing on a subset of reactions that occur within the coagulation cascade, we develop a model that exhibits a rich asymptotic structure. Using singular perturbation theory we produce a sequence of simpler time-dependent model which enable us to elucidate the physical mechanisms that underlie the cascade and the formation of thrombin. There is considerable interest in identifying new therapeutic targets within the coagulation cascade, as current drugs for treating pathological coagulation (thrombosis) target multiple factors and cause the unwelcome side effect of excessive bleeding. Factor XI is thought to be a potential therapeutic target, as it is implicated in pathological coagulation but not in haemostasis (the stopping of bleeding), but its mechanism of activation is controversial. By extending our previous model of the coagulation cascade to include the whole cascade (albeit in a simplistic way) we use numerical methods to simulate experimental data of the coagulation cascade under normal as well as specific-factor-deficient conditions. We then provide simulations supporting the hypothesis that thrombin activates factor XI. The interest in inflammation is now increasing due to it being implicated in such diverse conditions as Alzmeimer's disease, cancer and heart disease. Inflammation can either resolve or settle into a self-perpetuating condition which in the context of soft tissue repair is termed chronic inflammation. Inflammation has traditionally been thought gradualIy to subside but new biological interest centres on the anti-inflammatory processes (relating to macrophages) that are thought to promote resolution and the pro-inflammatory role that neutrophils can provide by causing damage to healthy tissue. We develop a new ordinary differential equation model of the inflammatory process that accounts for populations of neutrophils and macrophages. We use numerical techniques and bifurcation theory to characterise and elucidate the physiological mechanisms that are dominant during the inflammatory phase and the roles they play in the healing process. There is therapeutic interest in modifying the rate of neutrophil apoptosis but we find that increased apoptosis is dependent on macrophage removal to be anti-inflammatory. We develop a simplified version of the model of inflammation reducing a system of nine ordinary equations to six while retaining the physical processes of neutrophil apoptosis and macrophage driven anti-inflammatory mechanisms. The simplified model reproduces the key outcomes that we relate to resolution or chronic inflammation. We then present preliminary work on the inclusion of the spatial effects of chemotaxis and diffusion

Mathematical models of soft tissue injury repair : towards understanding musculoskeletal disorders

The process of soft tissue injury repair at the cellular lew I can be decomposed into three phases: acute inflammation including coagulation, proliferation and remodelling. While the later phases are well understood the early phase is less so. We produce a series of new mathematical models for the early phases coagulation and inflammation. The models produced are relevant not only to soft tissue injury repair but also to the many disease states in which coagulation and inflammation play a role. The coagulation cascade and the subsequent formation of the enzyme thrombin are central to the creation of blood clots. By focusing on a subset of reactions that occur within the coagulation cascade, we develop a model that exhibits a rich asymptotic structure. Using singular perturbation theory we produce a sequence of simpler time-dependent model which enable us to elucidate the physical mechanisms that underlie the cascade and the formation of thrombin. There is considerable interest in identifying new therapeutic targets within the coagulation cascade, as current drugs for treating pathological coagulation (thrombosis) target multiple factors and cause the unwelcome side effect of excessive bleeding. Factor XI is thought to be a potential therapeutic target, as it is implicated in pathological coagulation but not in haemostasis (the stopping of bleeding), but its mechanism of activation is controversial. By extending our previous model of the coagulation cascade to include the whole cascade (albeit in a simplistic way) we use numerical methods to simulate experimental data of the coagulation cascade under normal as well as specific-factor-deficient conditions. We then provide simulations supporting the hypothesis that thrombin activates factor XI. The interest in inflammation is now increasing due to it being implicated in such diverse conditions as Alzmeimer's disease, cancer and heart disease. Inflammation can either resolve or settle into a self-perpetuating condition which in the context of soft tissue repair is termed chronic inflammation. Inflammation has traditionally been thought gradualIy to subside but new biological interest centres on the anti-inflammatory processes (relating to macrophages) that are thought to promote resolution and the pro-inflammatory role that neutrophils can provide by causing damage to healthy tissue. We develop a new ordinary differential equation model of the inflammatory process that accounts for populations of neutrophils and macrophages. We use numerical techniques and bifurcation theory to characterise and elucidate the physiological mechanisms that are dominant during the inflammatory phase and the roles they play in the healing process. There is therapeutic interest in modifying the rate of neutrophil apoptosis but we find that increased apoptosis is dependent on macrophage removal to be anti-inflammatory. We develop a simplified version of the model of inflammation reducing a system of nine ordinary equations to six while retaining the physical processes of neutrophil apoptosis and macrophage driven anti-inflammatory mechanisms. The simplified model reproduces the key outcomes that we relate to resolution or chronic inflammation. We then present preliminary work on the inclusion of the spatial effects of chemotaxis and diffusion

Predicting tyrosinaemia: a mathematical model of 4-hydroxyphenylpyruvate dioxygenase inhibition by nitisinone in rats

Nitisinone or 2-(2-nitro-4-trifluoromethylbenzoyl)cyclohexane-1,3-dione, is a reversible inhibitor of 4- hydroxyphenylpyruvate dioxygenase (HPPD), an enzyme important in tyrosine catabolism. Today, nitisinone is successfully used to treat Hereditary Tyrosinaemia type 1, although its original expected role was as a herbicide. In laboratory animals, treatment with nitisinone leads to the elevation of plasma tyrosine (tyrosinaemia). In rats and Beagle dogs, repeat low-dose exposure to nitisinone leads to corneal opacities whilst similar studies in the mouse and Rhesus monkey showed no comparable toxicities or other treatment related findings. The differences in toxicological sensitivities have been related to the upper limit of the concentration of tyrosine that accumulates in plasma, which is driven by the amount/activity of tyrosine aminotransferase. A physiologically based, pharmacodynamics ordinary differential equation model of HPPD inhibition to bolus exposure of nitisinone in vivo is presented. Going beyond traditional approaches, asymptotic analysis is used to separate the different timescales of events involved in HPPD inhibition and tyrosinaemia. This analysis elucidates, in terms of the model parameters, a critical inhibitor concentration (at which tyrosine concentration starts to rise) and highlights the contribution of in vitro measured parameters to events in an in vivo system. Furthermore, using parameter-fitting methods, a systematically derived reduced model is shown to fit well to rat data, making explicit how the parameters are informed by such data. This model in combination with in vitro descriptors has potential as a surrogate for animal experimentation to predict tyrosinaemia, and further development can extend its application to other related medical scenarios

Exploring the constituent mechanisms of hepatitis: a dynamical systems approach

Hepatitis is the term used to describe inflammation in the liver. It is associated with a high rate of mortality, but the underlying disease mechanisms are not completely understood and treatment options are limited. We present a mathematical model of hepatitis that captures the complex interactions between hepatocytes (liver cells), hepatic stellate cells (cells in the liver that produce hepatitis-associated fibrosis) and the immune components that mediate inflammation. The model is in the form of a system of ordinary differential equations. We use numerical techniques and bifurcation analysis to characterize and elucidate the physiological mechanisms that dominate liver injury and its outcome to a healthy or unhealthy, chronic state. This study reveals the complex interactions between the multiple cell types and mediators involved in this complex disease and highlights potential problems in targeting inflammation in the liver therapeutically

A high-density immunoblotting methodology for quantification of total protein levels and phosphorylation modifications

The components of many signaling pathways have been identified and there is now a need to conduct quantitative data-rich temporal experiments for systems biology and modeling approaches to better understand pathway dynamics and regulation. Here we present a modified Western blotting method that allows the rapid and reproducible quantification and analysis of hundreds of data points per day on proteins and their phosphorylation state at individual sites. The approach is of particular use where samples show a high degree of sample-to-sample variability such as primary cells from multiple donors. We present a case study on the analysis of >800 phosphorylation data points from three phosphorylation sites in three signaling proteins over multiple time points from platelets isolated from ten donors, demonstrating the technique's potential to determine kinetic and regulatory information from limited cell numbers and to investigate signaling variation within a population. We envisage the approach being of use in the analysis of many cellular processes such as signaling pathway dynamics to identify regulatory feedback loops and the investigation of potential drug/inhibitor responses, using primary cells and tissues, to generate information about how a cell's physiological state changes over time

Perturbation theory in a framework of iteration methods

In a previous paper (J. Phys. A 36, 11807 (2003)), we introduced the `asymptotic iteration method' for solving second-order homogeneous linear differential equations. In this paper, we study perturbed problems in quantum mechanics and we use the method to find the coefficients in the perturbation series for the eigenvalues and eigenfunctions directly, without first solving the unperturbed problem.Comment: 13 page

An ovine model of hyperdynamic endotoxemia and vital organ metabolism

BACKGROUND: Animal models of endotoxemia are frequently used to understand the pathophysiology of sepsis and test new therapies. However, important differences exist between commonly used experimental models of endotoxemia and clinical sepsis. Animal models of endotoxemia frequently produce hypodynamic shock in contrast to clinical hyperdynamic shock. This difference may exaggerate the importance of hypoperfusion as a causative factor in organ dysfunction. This study sought to develop an ovine model of hyperdynamic endotoxemia and assess if there is evidence of impaired oxidative metabolism in the vital organs. METHODS: Eight sheep had microdialysis catheters implanted into the brain, heart, liver, kidney and arterial circulation. Shock was induced with a 4hr escalating dose infusion of endotoxin. After 3hrs vasopressor support was initiated with noradrenaline and vasopressin. Animals were monitored for 12hrs after endotoxemia. Blood samples were recovered for haemoglobin, white blood cell count, creatinine and proinflammatory cytokines (IL-1Beta, IL-6 & IL-8). RESULTS: The endotoxin infusion was successful in producing distributive shock with the mean arterial pressure decreasing from 84.5 ± 12.8 mmHg to 49 ± 8.03 mmHg (p < 0.001). Cardiac index remained within the normal range decreasing from 3.33 ± 0.56 l/min/m to 2.89l ± 0.36 l/min/m (p = 0.0845). Lactate/pyruvate ratios were not significantly abnormal in the heart, brain, kidney or arterial circulation. Liver microdialysis samples demonstrated persistently high lactate/pyruvate ratios (mean 37.9 ± 3.3). CONCLUSIONS: An escalating dose endotoxin infusion was successful in producing hyperdynamic shock. There was evidence of impaired oxidative metabolism in the liver suggesting impaired splanchnic perfusion. This may be a modifiable factor in the progression to multiple organ dysfunction and death

A conceptual framework and practical guide for assessing fitness-to-operate in the offshore oil and gas industry

The paper outlines a systemic approach to understanding and assessing safety capability in the offshore oil and gas industry. We present a conceptual framework and assessment guide for understanding fitness-to-operate (FTO) that builds a more comprehensive picture of safety capability for regulators and operators of offshore facilities. The FTO framework defines three enabling capitals that create safety capability: organizational capital, social capital, and human capital. For each type of capital we identify more specific dimensions based on current theories of safety, management, and organizational processes. The assessment guide matches specific characteristics to each element of the framework to support assessment of safety capability. The content and scope of the FTO framework enable a more comprehensive coverage of factors that influence short-term and long-term safety outcomes

Control of platelet CLEC-2-mediated activation by receptor clustering and tyrosine kinase signalling

Platelets are blood cells responsible for vascular integrity preservation. The activation of platelet receptor CLEC-2 could partially mediate the latter function. Although this receptor is considered to be of importance for hemostasis, the rate-limiting steps of CLEC-2 induced platelet activation are not clear. Here we aimed to investigate CLEC-2-induced platelet signal transduction using computational modelling in combination with experimental approaches. We developed a stochastic multicompartmental computational model of CLEC-2 signalling. The model described platelet activation beginning with CLEC-2 receptor clustering, followed by Syk and SFK phosphorylation, determined by the cluster size. Active Syk mediated LAT protein phosphorylation and membrane signalosome formation, which resulted in the activation of Btk, PLC and PI3K, calcium and phosphoinositide signalling. The model parameters were assessed from published experimental data. Flow cytometry, TIRF and confocal microscopy and western blotting quantification of the protein phosphorylation were used for the assessment of the experimental dynamics of CLEC-2-induced platelet activation. Analysis of the model revealed that the CLEC-2 receptor clustering leading to the membrane-based signalosome formation is a critical element required for the accurate description of the experimental data. Both receptor clustering and signalosome formation are among the rate-limiting steps of CLEC-2-mediated platelet activation. In agreement with these predictions, the CLEC-2 induced platelet activation, but not activation mediated by G-protein coupled receptors, was strongly dependent on temperature conditions and cholesterol depletion. Besides, the model predicted that CLEC-2 induced platelet activation results in cytosolic calcium spiking, which was confirmed by single platelet TIRF microscopy imaging. Our results suggest a refined picture of the platelet signal transduction network associated with CLEC-2. We show that the tyrosine kinases activation is not the only rate-limiting step in CLEC-2 induced activation of platelets. Translocation of receptor-agonist complexes to the signalling region and LAT-signalosome formation in this region are limiting CLEC-2-induced activation as well