Mathematical Modeling in Cancer Research: Emerging Driving Force for Optimal Therapy
Abstract： Computational oncology is becoming a very powerful tool in cancer research. Mathematical modeling has shown tremendous potential in characterization of cancer development and prediction of treatment outcomes.
The recent 20 years of cancer research has witnessed rapidly growing varieties of treatment agents for cancer, in the areas of cytotoxic/cytostatic chemotherapy, targeted therapy, immunotherapy and other therapies. However, the identification of optimal treatment strategies through clinical trials is hampered by the contradiction between the limited/sparsely distributed patients and the near-infinite combination treatment strategies. Practically, it is important to prospectively predict the outcomes for each treatment strategy, and then assess the favorable options in the clinic.
Because of the stochasticity, non-linearity, and heterogeneity involved in the development of cancer, the outcomes of different treatments cannot be prospectively determined by verbal reasoning alone. Consequently, mathematical modeling has shown tremendous potential in characterization of cancer development and prediction of treatment outcomes. For example, Tang et al. studied the dynamics of leukemic load in chronic myeloid leukemia (CML) patients treated with Gleevec, and predicted that Gleevec has the potential to target CML-stem cells ; Chmielecki et al. modeled the evolution of erlotinib resistance in non-small cell lung cancer (NSCLC), and predicted alternative treatment strategies that could prolong the benefit of erlotinib ; Haeno et al. simulated metastasis of pancreatic cancer (PC), and predicted that therapies that reduce the growth rate of PC cells are superior to upfront tumor resection ; Leder et al. characterized dynamics of glioblastoma (GBM) in response to radiotherapy, and managed to predict superior dosing schedules for radiotherapy and improved GBM survival in animal model .
A recent study from Dr. Benjamin Neel’s lab at University of Toronto studied the clinical dynamics of high-grade serous ovarian cancer (HG-SOC), and investigated the optimal management strategies for this disease . We built a stochastic branching model to simulate the evolution of chemotherapy resistance, based on clinical data from nearly 300 HG-SOC patients. After estimating the conversion rate from chemo-sensitive to chemo-resistant cells, we determined that most HG-SOC patients likely harbor >103 chemo-resistant cells at diagnosis. We then compared different temporal orders of treatment, and predicted that upfront optimal surgery followed by chemotherapy should be superior to upfront chemotherapy with interval surgery, largely because it more efficiently depletes chemo-resistant cells. Furthermore, we interrogated the benefits of early diagnosis of HG-SOC. We recapitulated the clinical finding that CA125-based earlier diagnosis of relapsed cancer does not improve overall survival, and further predicted that more sensitive detection methods are also unlikely beneficial with current standard chemotherapy, because it does not help deplete the chemo-resistant cells. By contrast, our model predicts that for treatment-naïve cancer, early detection could improve survival time and increase chances of cure.
With the advent of high-throughput sequencing and precision medical care for cancer, there is increasing feasibility and demand for quantitative models of cancer evolution dynamics, in order to facilitate effective combination therapy and/or prospectively prepare for disease recurrence. For future application of mathematical modeling in cancer prevention/treatment, I speculate several trends will form and exhibit significant impacts in the field: (1) incorporation of genomic data and mathematical modeling to monitor and predict dynamic clonal evolution of cancer, which would help achieve punctual precision medical care; (2) application of mathematical modeling and machine learning techniques on clinical/experimental data to extrapolate treatment resistance patterns, which would help identify additional targets for different stages of cancer development; (3) application of mathematical modeling in immunotherapy to predict the likelihood of response and explore the combination of immunotherapy and conventional therapies, which would facilitate synergistic depletion of cancer using different therapies.
 Tang, M. et al. Dynamics of chronic myeloid leukemia response to long-term targeted therapy reveal treatment effects on leukemic stem cells. Blood 118, 1622–1631 (2011).
 Chmielecki, J. et al. Optimization of dosing for EGFR-mutant non-small cell lung cancer with evolutionary cancer modeling. Sci. Transl. Med. 3, 90ra59 (2011).
 Haeno, H. et al. Computational modeling of pancreatic cancer reveals kinetics of metastasis suggesting optimum treatment strategies. Cell 148, 362–75 (2012).
 Leder, K. et al. Mathematical modeling of pdgf-driven glioblastoma reveals optimized radiation dosing schedules. Cell 156, 603–616 (2014)..
 Computational modeling of serous ovarian carcinoma dynamics: Implications for screening and therapy. at http://www.abstractsonline.com/Plan/ViewAbstract.aspx?mID=3682&sKey=0b3c3568-eecc-4a05-b2a6-eca0a1f1b029&cKey=5b08121c-eeee-4ef7-be71-c321f3ebfd4f&mKey=19573a54-ae8f-4e00-9c23-bd6d62268424.
Shengqing Gu obtained his B.S. degree from Yuanpei program in Peking University. In 2008, he joined the lab of Dr. Benjamin Neel in Department of Medical Biophysics at University of Toronto to participate in interdisciplinary research involving signaling pathways in cancer and mathematical modeling of cancer. His current research interests include mathematical modeling of cancer evolution dynamics and machine learning of therapy resistance mechanisms.