Abstract P6-17-33: A multi-scale mathematical model of combination targeted and cytotoxic therapy to evaluate treatment response in HER2+ breast cancer
Authors: Jarrett AM , Shah A , Bloom MJ , Yankeelov TE , Sorace AG 
Published: May 2019

Abstract
Introduction: We have previously established a tissue scale mathematical model with 5 coupled, ordinary differential equations (ODEs) describing the longitudinal relationship of vasculature, hypoxia, necrosis, immune infiltration, and tumor growth in a preclinical model of human epidermal growth factor receptor 2 positive (HER2+) breast cancer undergoing trastuzumab treatment. The purpose of this study is to expand this model to multiple scales (tissue and cellular) and to explicitly include the effects of combination trastuzumab-paclitaxel therapy as measured by time-resolved microscopy of in vitro HER2+ breast cancer cells. This requires interlacing experimental data and additional ODEs at the cellular scale to incorporate drug dynamics within the tissue scale model for overall tumor growth. An integrated multi-scale mathematical-experimental approachbridging in vivo and in vitro experimental data has potential to elucidate the optimal strategies for combination therapy for HER2+ breast cancer.
Experimental: In vitro data was collected to longitudinally evaluate BT474 HER2+ human cancer cells growth when treated with trastuzumab (25-50 ug/ml) and/or paclitaxel (10-250 nmol/L) measured by time-resolved microscopy. Changes in confluence before and after treatment are recorded every 3 hours over the course of 7 days. Ongoing studies are quantifying the change in confluence for these cells with alternating dosing and timing of the two therapies.
Modeling: Thein vivo, tissue-scale model parameters were calibrated using mean and 95% confidence intervals of tumor volume from caliper measurements, vasculature and hypoxia from imaging data, and necrosis from histology. The in vitro scale of the model is calibrated with confluence data for controls to define intervals for growth rates and carrying capacities. Experimental results for single drug applications are used to estimate cell death, and data from combinations of both the targeted anti-HER2 therapy and cytotoxic therapies provide estimates of synergistic drug effects. After calibration of parameters, the two scales of the model are coupled via the tumor volume and vasculature components to simulate the effects of combination therapy in vivo.
Results and Discussion: The confluence data shows that trastuzumab dosing in combination with paclitaxel results in the greatest reduction in tumor cells than either drug alone (p &lt; 0.05), and there are distinct differences in alternating the order and timing of these drugs. Further, preliminary results show that the model's in vitro scale equations can be calibrated with the available longitudinal data. As dosing of combination therapy in vitro provides the opportunity to quantify the effects of combination therapy that would not be feasible to collect in an in vivo setting, our aim is to generate experimentally testable predictions for improved combination therapy in vivo with our multiscale model. This is an important step for future clinical translation to provide temporal guidance of standard-of-care, combination therapies, potentially leading to significantly improved anticancer response in HER2+ breast cancer.
We acknowledge the support of NCI U01CA174706, NCI R01CA186193, CPRIT RR160005, and ACS RSG-18-006-01-CCE.
Citation Format: Jarrett AM, Shah A, Bloom MJ, Yankeelov TE, Sorace AG. A multi-scale mathematical model of combination targeted and cytotoxic therapy to evaluate treatment response in HER2+ breast cancer [abstract]. In: Proceedings of the 2018 San Antonio Breast Cancer Symposium; 2018 Dec 4-8; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2019;79(4 Suppl):Abstract nr P6-17-33.