Research

The Integrative Immunology Lab at UTA found malignant CD8+ T cells cause cardiovascular impairment in mice as they age - using mathematical models, can we find an optimal amount of T cells to preserve immune and cardiovascular function?

High ratios of CD8+ to CD4+ T cells indicate advanced cardiovascular aging and dysfunction in mice.  With anti-CD3 F(ab’)2 treatment, we can deplete T cell populations, but at the cost of immune resistance to pathogens. Using mathematical models and numerical simulations, can we find optimal amounts of drug, naïve, and mature CD8+ cells?

Pseudomonas aeruginosa is resistant to antibiotic treatment, leading scientists and physicians to propose using bacteriophages as treatment. However, since this method is so new, we propose mathematical models to learn more about phage therapy.

In our recent paper, we developed a system of ODEs to describe the dynamics of phage-bacteria interaction, performed qualitative analysis on our "SIMPL model", and performed data fitting to find a set of parameter estimates unique to our experimental observations of a specific phage and P. aeruginosa strain.

Esophageal cancer is the sixth leading cause of death in the US. Chemotherapy and radiotherapy are general therapies for cancer but come with many side effects. Instead, we explore the efficacy of immunotherapy and find patient-specific dosing.

We develop ODE models describing the dynamics of interaction between cancer cells and various types of immune cells. We thoroughly analyze these models and then employ techniques in model reduction to create computationally-friendly submodels and extend them to stochastic PDEs.

Primary liver cancers are the third-leading cause of cancer related deaths worldwide. Hepatocellular carcinoma (HCC) makes up nearly 90% of liver cancer cases and is projected to be the second deadliest cancer in American men by 2030. Treatment options for localized and recurrent liver cancer include partial hepatectomy (PH), radiation, and ablation. Although the liver's ability to self-regenerate is well-studied, pressure on hepatocytes to proliferate could lead to abnormal tissue growth and tumor development. Increasingly, there has been a push for cellular and genetic therapies.

Moya et al. found hyperactivation of the YAP gene in surrounding liver cells caused tumors to shrink up to an eighth of the tumor size with average YAP activation, leading them to suggest YAP activation as a treatment strategy for liver cancer. In our work, we investigate the competitive dynamics of cancerous and healthy hepatocytes in a regenerating liver and incorporate gene therapy where the YAP gene is activated.

Nonstandard finite difference (NSFD) methods are numerical methods to solve dynamical systems which have useful properties for solving mathematical models of biological systems, namely dynamic consistency and positivity. Much work has been done on developing, analyzing, and implementing NSFD methods to solve systems of ordinary differential equations (ODEs), but not much theory has been presented for applying NSFD methods to partial differential equations (PDEs). In this work, we are investigating extending the theory behind NSFD method in the context of parabolic PDEs, which have extensively been used to model biological phenomena.

Chronic Thromboembolic Pulmonary Hypertension (CTEPH) is a fatal, underdiagnosed, yet curable disease which afflicts the pulmonary arteries. Currently, there is no systematic way to determine which lesions to treat. Therefore, we create a patient-specific model to help physicians choose the right lesions to treat for optimal prognosis.

In this project, we first created 3D volumetric surfaces of each patient's pulmonary arterial structure using 3D Slicer. Then, with the Vascular Modeling Toolkit (VMTK), we extract centerlines, connected in a labeled tree. Nodes along the centerlines provide data about radii at different points along the vessel and also have coordinates in 3D space. Vessel junctions occur when nodes intersect, and we represent a network of vessels through a connectivity matrix. We find a representative radius for each vessel by averaging radii of relevant nodes, using our novel change point algorithm. The algorithm determines vessel radii and uncertainty and corrects junctions between vessels for physiological accuracy. To standardize network size and extend our network past limits in CT scan resolution, we prune networks to the same number of vessels and then attach asymmetric binary trees at the end of each terminal vessel. We solve a 1D fluid dynamics model in this model, predicting blood pressure and flow for each vessel.

Our results predicting mean pulmonary arterial pressure and flow in five segmentations from a healthy control’s pulmonary arteries show that the size of the tree matters, and, using ANOVA analysis, we found that vessel radii and length differ significantly between segmentations; however, sampling from the radius estimates for each vessel provides reliable predictions of pressure and flow. Segmenting CTEPH patients reveals multiple lesion types per patient, including ring lesions, total occlusions, and tortuous vessels. Future work includes generating CTEPH networks and conducting fluid dynamics simulations in CTEPH geometries. These in-silico treatments and simulations mitigate the need for invasive and expensive scanning and provide insight into optimal treatment plans for physicians.