Souvik Roy

Ph.D.

University of Texas at Arlington

Assistant Professor

NLST (Learn more about this study)

NLST-773

Mar 22, 2021

Data-driven mathematical modeling approach for estimating lesion potency in lung cancer

The main goal of this project is to use individual lung cancer patient data to assess the development of a lesion in a patient, classify patients according to the expectancy of the lesion developing into lung cancer cell volume and, in that case, suggest personalized targeted immunotherapeutic treatment strategies. The lesion growth dynamics will be described by a novel mathematical framework that uses a new stochastic pharmacokinetic model to understand the dynamics of the lesion cells, their interaction with different types of immune cells, and possible mutations among the lesion cells. In recent years, pharmacokinetic models are increasingly utilized in pharmaceutical research and development. An accurate analysis of the parameters in a pharmacokinetic model for lesion growth can be effectively used for early screening of the potency of the lesion to develop into tumor and, subsequently, devise fast and effective treatment strategies without the need for numerous clinical trials. Existing pharmacokinetic models for cancer dynamics do not take into account associated randomness. Moreover, traditional parameter estimation methods rely on the presence of huge datasets for accurate determination of these parameters. Thus, there is an inadequate understanding of the cancer dynamics and, subsequently, failure to come up with accurate and timely treatment strategies. Since the outcomes of treatments completely depend on individual’s biological characteristics, it is essential that we estimate the values of parameters of the pharmacokinetic model for each individual, separately. Our mathematical framework comprises of developing a new stochastic pharmacokinetic model for studying the dynamics of lesions and using a novel combination of inverse problems, optimization and statistical sensitivity analysis methods to accurately estimate the parameters of the model that will determine if a lesion is capable of growing into a tumor. Our framework will also suggest early optimal treatment options in such a case. The validation of our model will be done using lung cancer patient data.

Aim 1- Developing the pharmacokinetic model: We will develop a mathematical model using a system of non-linear partial differential equations (PDEs) with the unknown parameters of the system appearing as coefficients of this PDE system. We will test the fit of the model using the lung cancer patient data at given discrete times.

Aim 2 - Optimal parameter estimation and sensitivity analysis: The main goal here is to accurately estimate the parameters by utilizing the lung cancer patient data at discrete times by solving a parameter identification inverse problem using a PDE-constrained optimization. From the obtained optimal set of parameter values, we carry out a global sensitivity analysis for the parameters of the model to determine how a small or large perturbation in the parameters affects the lesion size at a given point and at a certain time. We will run the sensitivity analysis for each patient in the study.

Aim 3- Determining the lesion potency and classification of optimal treatment strategies: Using the obtained optimal parameters, we will estimate the lesion size at future times to determine the potency of the lesion to develop into a tumor. In this case, to determine optimal treatment strategies, we model the immunotherapeutic drugs as additional parameters in our pharmacokinetic model. We then perform a global optimization to determine the optimal drug. We further use a confidence level approach to measure the efficacy of the drugs used in the model to decrease the lesion size below a threshold value and obtain alternate therapies with the induction times for each patient in case of low efficacy, thus providing personalized treatment strategies.