Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Mesenchymal stem cell therapy for the treatment of myocardial infarction

Mesenchymal stem cells (MSCs) are currently under investigation as repair agents in the preservation of cardiac function following myocardial infarction (MI). However concerns have emerged regarding the safety of acute intracoronary (IC) MSC delivery specifically related to mortality, micro-infarction and microvascular flow restriction post cell therapy in animal models. This thesis aimed to firstly identify an optimal dose of MSC that could be tolerated when delivered via the coronary artery in a porcine model of acute MI (AMI). Initial dosing studies identified 25x106 MSC to be a safe MSC cell dose, however, angiographic observations from these studies recognised that on delivery of MSC there was a significant adverse decrease in distal blood flow within the artery. This observation along with additional supportive data in the literature (published during the course of this thesis) suggested MSC may be contributing to such adverse events through the propagation of thrombosis. Therefore further studies aimed to investigate the innate prothrombotic activity of MSC. Expression of the initiator of the coagulation cascade initiator tissue factor (TF) on MSC was detected in high levels on the surface of these cells. MSC-derived TF antigen was catalytically active, capable of supporting thrombin generation in vitro and enhancing platelet-driven thrombus deposition on collagen under flow. Infusion of MSC via IC route was associated with a decreased coronary flow reserve when delivered but not when coadministered with an antithrombin agent heparin. Heparin also reduced MSC-associated in situ thrombosis incorporating platelets and VWF in the microvasculature. Heparin-assisted MSC delivery reduced acute apoptosis and significantly improved infarct size, left ventricular ejection fraction, LV volumes, wall motion and scar formation at 6 weeks post AMI. In addition, this thesis investigated the paracrine factors secreted by MSC, in particular focusing on the effect on cardiac repair of a novel MSC-paracrine factor SPARCL1. In summary this work provides new insight into the mechanism by which MSC may be deleterious when delivered by an IC route and a means of abrogating this effect. Moreover we present new data on the MSC secretome with elucidation of the challenges encountered using a single paracrine factor cardiac repair strategy.

Progesterone attenuates microglial-driven retinal degeneration and stimulates protective Fractalkine-CX3CR1 signaling

Retinitis pigmentosa (RP) is a degenerative disease leading to photoreceptor cell loss. Mouse models of RP, such as the rd10 mouse (B6.CXBl-Pde6brd10/J), have enhanced our understanding of the disease, allowing for development of potential therapeutics. In 2011, our group first demonstrated that the synthetic progesterone analogue ‘Norgestrel’ is neuroprotective in two mouse models of retinal degeneration, including the rd10 mouse. We have since elucidated several mechanisms by which Norgestrel protects stressed photoreceptors, such as upregulating growth factors. This study consequently aimed to further characterize Norgestrel’s neuroprotective effects. Specifically, we sought to investigate the role that microglia might play; for microglial-derived inflammation has been shown to potentiate neurodegeneration. Dams of post-natal day (P) 10 rd10 pups were given a Norgestrel-supplemented diet (80mg/kg). Upon weaning, pups remained on Norgestrel. Tissue was harvested from P15-P50 rd10 mice on control or Norgestrel-supplemented diet. Norgestrel-diet administration provided significant retinal protection out to P40 in rd10 mice. Alterations in microglial activity coincided with significant protection, implicating microglial changes in Norgestrel-induced neuroprotection. Utilizing primary cultures of retinal microglia and 661W photoreceptor-like cells, we show that rd10 microglia drive neuronal cell death. We reveal a novel role of Norgestrel, acting directly on microglia to reduce pro-inflammatory activation and prevent neuronal cell death. Norgestrel effectively suppresses cytokine, chemokine and danger-associated molecular pattern molecule (DAMP) expression in the rd10 retina. Remarkably, Norgestrel upregulates fractalkine-CX3CR1 signaling 1 000-fold at the RNA level, in the rd10 mouse. Fractalkine-CX3CR1 signaling has been shown to protect neurons by regulating retinal microglial activation and migration. Ultimately, these results present Norgestrel as a promising treatment for RP, with dual actions as a neuroprotective and anti-inflammatory agent in the retina.