(693c) Multiscale Dynamic Simulations of HIV Infection and the Antiretroviral Treatment at the Latency Stage

In the last decade numerous mathematical models of varying detail have been proposed in the open literature to capture different aspects of disease progression, in an attempt to assist research efforts on the development of treatment policies that enhance the life expectancy and quality of lives of patients with established infection.

Mathematical models of chemical and biological processes traditionally take the form of deterministic differential-algebraic equation systems, however for many processes of current interest accurate descriptions need to account for phenomena at the molecular level or the intimate interplay between fast and slow evolving processes. For instance, few models take into account the pharmacokinetics and pharmacodynamics time-variability of drug effectiveness due to dosing schedules.

Previously, we developed extracellular and intracellular stochastic models of HIV infection. Populations of wild type virus as well as resistant to medication virus and host T-cells and their interactions are considered in the extracellular model. A known shortcoming of the current extracellular HIV models is that the values of the parameters that describe the infection dynamics are obtained by curve fitting of, usually sparsely available, patients' data. To increase the reliability of the predictions, developing more accurate models considering infection dynamics at both extra and intracellular levels is necessary.

The current work focuses on (a) the development of accurate HIV models for the latency stage of infection and (b) the development of an optimization problem formulation methodology and search algorithm that are tailored to the HIV infection model. Specifically, we propose the development of a multiscale model of HIV infection to incorporate both extra and intracellular dynamics. The developed intracellular model predicts the expected behavior of each infected cell as a function of the time and the amount of available medication inside the cell. The efficacy of drug is explicitly linked to plasma concentration considering half life and drug and dosing schedule. The time scale of intracellular events inside the infected host is a few orders of magnitude smaller than the time scale of cell population interactions at the extracellular level. The multiscale model simulation is actually initiated at the extracellular level. During this simulation, an extracellular event (e.g., binding of a virus particle to a T-cell) initiates the intracellular model. The intracellular model is then simulated for a period of time and all the intracellular events that take place within this time-horizon are represented as one ?coarse? event at the extracellular level. The developed model enhances the understanding of infection cycle and is useful in predicting the overall infection dynamics while considering the intracellular infection events.

The proposed intracellular/extracellular model is instrumental in correctly quantifying the effect that drug concentration has on the progression of the viral infection. This can be achieved in a stochastic setting, since drug action can be captured at the molecular level directly incorporating experimental results in the open literature. The ultimate objective of this study is formulating an optimization problem to find optimum treatment schedules to keep the population of virus particles (both wild and resistant type) under a predetermined threshold for the longest possible time.