"Investigating the mechanical properties of peripheral nerve tissue using new biomechanical models"
It is estimated that 2.8% of trauma patients suffer damage to the peripheral nerve system leading to potentially permanent disability. The current gold standard treatment for peripheral nerve injury, the nerve autograph, is estimated to have a success rate of 40 to 50% depending on the scale of the injury. New nerve repair options are currently being developed including the use of tissue engineered implants to replace the injured nerve. However for this to be an effective treatment, the implant must match the mechanical properties of the native tissue to prevent additional damage due to the build-up of localised stress. Peripheral nerves are complex structures with mechanical properties that vary with nerve type and along the length of each nerve. Past experimental work has inferred a link between the mechanical properties of nerve and the nano-structural make-up of the nerve. Data on the mechanical properties of living tissue is difficult to obtain, however, the data on structure of the nerve can be obtained from cadavers. Our work therefore focuses on constructing new biomechanical models that predict the mechanical properties of a nerve given structural data. To do this we use asymptotic homogenisation - an analytical technique that exploits differences in spatial scales to solve PDE systems on spatially complex domains. We will discuss our work on constructing general biomechanical models and their specific application to peripheral nerves.
"Modeling blood flow regulation and tissue oxygenation in the retina"
Glaucoma is a serious ocular disease characterized by damage to retinal ganglion cells that results in irreversible vision loss. Impaired tissue perfusion has been identified as a significant contributing factor to glaucoma. Theoretical modeling provides a useful tool for predicting the effect of several hemodynamic factors on retinal oxygenation. In this study, a heterogeneous model of the retinal arteriolar vascular network is used to show the impact of flow regulation on tissue oxygenation as oxygen demand is varied. The metabolic signal (Si) is implemented as a wall-derived signal that reflects the oxygen deficit along the network, and three cases of conduction are considered: no conduction, a constant signal, and a flow-weighted signal. The model shows that the increases in average tissue PO2 due to a flow-weighted signal are often more significant than if the entire level of signal is increased. This indicates that the heterogeneity of the downstream conducted responses serves to regulate flow better than a constant conducted response. A hybrid model is also presented that combines a heterogeneous arteriolar network with a compartmental vascular network model for the capillaries and veins. This hybrid model combines a wall-derived conducted metabolic response with spatial data from the retinal arterial network to yield improved predictions of retinal tissue oxygenation.
"Action potential propagation in a myocyte-fibroblast model of cardiac tissue"
Coupling electrophysiological models of myocytes and fibroblasts is key to understanding the electrical response of fibrotic regions and associated arrhythmias. There has been extensive work on the analysis of these cell-level models which have been upscaled to organ level. However, there is a lack of understanding of the effects of fibroblast coupling has on the spatial propagation of the action potentials. We identify two properties of the degree of fibrosis. Firstly, the number of fibroblasts in relation to the number of myocytes and secondly the geometry of the fibrotic region. Using direct numerical simulations of a monodomain model of fibrous cardiac tissue, we demonstrate that action potentials (APs) slow down as the severity of fibrosis is increased until eventually excitation is fully blocked. We also identify two cases of non-uniform fibroblast distribution. Here direct numerical simulations show that successful AP propagation is dependent on the geometry of the fibrous region and the number of fibroblasts per myocyte.
Moffitt Cancer Center
"In silico tools for deconvolution of complex tumor microenvironments: Organoid3D and silicoDCIS"
Malignant tumors are highly heterogeneous in terms of their cellular composition, varying levels of oxygenation, acidity, and nutrients, as well as local changes in the extracellular matrix. Furthermore, tumor tissue and tumor microenvironment properties can dynamically evolve not only during tumor growth but also when anticancer treatments are administered. We developed a suite of computational models to recapitulate the complexity of cancers, especially their physical and chemical microenvironments. These simulation tools were used to: derive hypotheses about the development of ductal microinvasions; formulate hypotheses on relative importance of microenvironmental factors and chemotherapeutic treatments on the growth of organoids derived from a non-tumorigenic breast cell line and its mutants; examine the interactions of tumor cell and stromal cells in co-cultures. The developed in silico tools are versatile enough to be adjusted to other organoid cultures, other tumor tissues and other components of the tumor microenvironment to generate testable hypotheses about tumor progression and response to treatments.
"Effects of cell cycle variability on stochastic gene expression"
Many models of stochastic gene expression do not incorporate a cell cycle description. I will show how this can be tackled mathematically studying how mRNA fluctuations are influenced by DNA replication and cell cycle duration stochasticity. Results show that omitting cell cycle details can introduce significant errors in the predicted mean and variance of gene expression for prokaryotic and eukaryotic organisms, reaching 25% error in the variance for mouse fibroblasts. Furthermore, we derive a negative binomial approximation to the mRNA distribution, indicating that cell cycle stochasticity introduces similar fluctuations to bursty transcription. Finally, I will show how disregarding cell cycle stochasticity can introduce inference errors in transcription rates bigger than 10%.