Abstract PO-114: Mathematical modeling of tumor heterogeneity to optimize treatment scheduling and delay the evolution of resistance
Authors: Mathur Deepti , Taylor Bradford Porter , Chatila Walid , Schultz Nikolaus , Razavi Pedram , Xavier Joao 
Published: December 2020

Abstract
One of the greatest clinical challenges in cancer facing us today is resistance to therapy. In fact, initial response followed by resistance has been observed for the majority of targeted therapies. If a heterogeneous tumor contains even one resistant clone, or the probability of generating a resistance mutation is nonzero, tumor recurrence is theoretically inevitable. New therapies that surpass resistance pathways can take many years—despite extraordinary efforts—before they are available to patients, suggesting that cancers win this arms race against resistance. However, previous literature suggests that it is possible to delay recurrence by optimizing treatment strategies with current therapy options. The purpose of our work is to use computational techniques to predict time to relapse a priori, to identify treatment strategies that could delay therapeutic resistance, and to propose ways these techniques can be applied in a clinical setting. Here, we present a population dynamics model using ordinary differential equations to model tumor growth and evolution over time. Our model simulated the growth dynamics of treatment-sensitive and -resistance subpopulations, allowing the system to incorporate both pre-existing and acquired resistance. We implemented this model into a large-scale in silico experiment with thousands of tumors with different properties, and applied various treatment schedules in order to ascertain the optimal strategy for each simulated tumor. We found that giving short, sharp pulses of therapies followed by breaks in treatment delayed time to relapse in all cases compared to continuous lower-dose treatment. Aggressive tumors were more likely have the highest benefit from pulsed strategies. Furthermore, we found that alternating back-and-forth between two therapies at short, defined intervals led to a later time to relapse than either sequential treatment or combination treatment. These results were robust to stochasticity, suggesting they might apply even in noisy clinical scenarios. To test this hypothesis we applied our model to data from patients with breast cancer. From four patients treated at MSKCC we obtained 1) longitudinal tumor marker data, indicating tumor burden over time, 2) the duration that each treatment was given, and 3) mutational profiles from bulk sequencing, including the cancer cell fraction that harbored each mutation. The first 2-3 data points from each patient were sufficient to tune the model and predict their time to relapse. The model tuned for each patient predicted pulsed treatments that might have delayed the time to relapse. Our results show that non-canonical treatment regimens could be optimized to delay resistance. Models could become more accurate if we sample patients more frequently, with better data on the tumor composition (obtained for example with single-cell sequencing), and if models include the 3-D spatial structure of heterogenous tumors. These features could be important goals for the future of cancer therapy.
Citation Format: Deepti Mathur, Bradford Porter Taylor, Walid Chatila, Nikolaus Schultz, Pedram Razavi, Joao Xavier. Mathematical modeling of tumor heterogeneity to optimize treatment scheduling and delay the evolution of resistance [abstract]. In: Proceedings of the AACR Virtual Special Conference on Tumor Heterogeneity: From Single Cells to Clinical Impact; 2020 Sep 17-18. Philadelphia (PA): AACR; Cancer Res 2020;80(21 Suppl):Abstract nr PO-114.