Mathematical Models for Ovarian Cancer

Abstract

Ovarian cancer is the most fatal cancer of the female reproductive system. High-grade serous ovarian cancer (HGSOC) represent the majority of ovarian cancers and accounts for the largest proportion of deaths from the disease. From a clinical perspective, the complex, heterogeneous behaviors of this women's cancer pose questions that cannot always be answered with contemporary clinical and experimental tools.

Studying the growth, progression, and dynamic response to treatment of ovarian cancers in an integrated systems biology/mathematical framework offers an innovative tool at the disposal of the oncological community to further exploit readily available clinical data and generate novel testable hypotheses. Developing novel physiologically structured mathematical models to study the heterogeneous behavior of this malignancy would help us to better understand patient therapeutic responses and devise novel combination therapies.

As a first step, we developed a mathematical model for a quantitative explanation why transvaginal ultrasound-based (TVU) screening fails to improve low-volume detectability and overall survival (OS) of HGSOC. This mathematical model can accurately estimate the efficacy of screening for this cancer subtype. The model also explains the observed heterogeneity in cancer progression and duration of the pre-diagnosis stage. Our mathematical model is consistent with recent case reports and prospective TVU screening population studies, and provides support to the empirical recommendation against frequent HGSOC screening.

At the cell population level, we have quantitatively investigated the role of cell heterogeneity emerging from variations in cell-cycle parameters and cell-death. Many commonly used chemotherapeutic agents in treating ovarian cancers target only dividing cancer cells.

We recently demonstrated in a mathematical model, calibrated against published in vitro cell culture data, that resistance to chemotherapeutic treatment may arise from a dynamic, oscillatory balance between the dividing and non-dividing cancer cells, which is conserved through time despite high long-term drug dosages.

At the single cell level, we developed a mathematical model to explain the emerging heterogeneity in individual cancer cell responses to drugs targeting the cell-cycle, which have a broad spectrum of anti-tumor activity in ovarian cancers. This emerging heterogeneity remains a poorly understood mechanism that plays a significant role in mediating drug response, and predicts the existence of an intrinsic resistance mechanism to drug therapy.

The model incorporates an intrinsic form of heterogeneity via the duration of time single cells spend in mitosis. It uses published single cell in vitro experimental data for calibration. Herein, the goal is to better understand why, within a distinct cell line, cells treated with identical drugs exhibit a considerable degree of heterogeneity in response to prolonged drug exposure. The model can serve as a basis for future studies of the heterogeneity observed in vitro of more complex responses to anti-mitotic drugs of different cell lines.

Studying the natural history, growth, and progression of ovarian cancers in an integrated systems biology/mathematical framework represents a complementary tool that can be used to provide valuable insights into the treatment of HGSOC.

My work focuses on developing and applying quantitative, integrated mathematical modeling frameworks to pre-clinical and clinical data, in order to better understand ovarian cancer dynamics and develop new therapeutics.