Mathematical modelling of trastuzumab-induced immune response in an in vivo murine model of HER2+ breast cancer

Abstract

The goal of this study is to develop an integrated, mathematical-experimental approach for understanding the interactions between the immune system and the effects of trastuzumab on breast cancer that overexpresses the human epidermal growth factor receptor 2 (HER2+). A system of coupled, ordinary differential equations was constructed to describe the temporal changes in tumour growth, along with intratumoural changes in the immune response, vascularity, necrosis and hypoxia. The mathematical model is calibrated with serially acquired experimental data of tumour volume, vascularity, necrosis and hypoxia obtained from either imaging or histology from a murine model of HER2+ breast cancer. Sensitivity analysis shows that model components are sensitive for 12 of 13 parameters, but accounting for uncertainty in the parameter values, model simulations still agree with the experimental data. Given theinitial conditions, the mathematical model predicts an increase in the immune infiltrates over time in the treated animals. Immunofluorescent staining results are presented that validate this prediction by showing an increased co-staining of CD11c and F4/80 (proteins expressed by dendritic cells and/or macrophages) in the total tissue for the treated tumours compared to the controls ($p < 0.03$). We posit that the proposed mathematical-experimental approach can be used to elucidate driving interactions between the trastuzumab-induced responses in the tumour and the immune system that drive the stabilization of vasculature while simultaneously decreasing tumour growth-conclusions revealed by the mathematical model that were not deducible from the experimental data alone.

Crosstalk between HER2 and PD-1/PD-L1 in Breast Cancer: From Clinical Applications to Mathematical Models

“…A similar theoretical analysis can be done for the use of anti-HER2 drugs for HER2 + BC. Even though there are mathematical models related to the use of trastuzumab and T-DM1 for HER2 + BC [55,[68][69][70][71], similar models related to lapatinib, pertuzumab, and neratinib are yet to be reported.…”

“…In this section, we review existing mathematical models in this area and detail a general one that can be used to devise novel models in the context of anti-HER2 therapy and/or immune checkpoint inhibition. It is apparent that mathematical models of tumor-immune interaction with respect to HER2-targeted therapy and/or immune checkpoint blockade can be used to explore tumor dynamics in detail and to answer questions that are difficult to answer by clinical analysis [54,71,145]. Since 1954, mathematical model-based analysis has contributed heavily to various areas of cancer research such as drug scheduling, estimating drug response in terms of desired effect, testing research hypothesis, and to study interdependence and sensitivity of various parameters involved in cancer dynamics [39,40,70,[154][155][156][157].…”

“…In vitro experiments used to develop mathematical models of BC are reported in [1,26,55]. Compared to in vitro models which are based on certain BC cell lines, experimental mice models (in vivo) are used more frequently to estimate parameter values of mathematical models [71,155]. Even though many experimental studies have used drosophila, zebra fish, and chicken embryo models for cancer research, mathematical models based on these animal models are scarce [169][170][171].…”

Integrating multimodal data sets into a mathematical framework to describe and predict therapeutic resistance in cancer

“…The majority of these modeling endeavors utilize a single measurement source for longitudinal data acquisition and subsequent model calibration. A few studies utilizing multimodal imaging modalities have harnessed the ability to quantify different aspects of tumor composition-such as vasculature, necrosis, and cellularity, to develop an integrated model calibration of multiple tumor system components (43,44). However, this integrated, multimodal approach has not explicitly included inference of the composition of heterogeneous subpopulations taken from separate "omics" datasets for direct model calibration.…”

“…n doses ∑ the biomedical field using multi-objective function optimizations, the number of data points from each measurement source is typically similar, as most data is acquired longitudinally (43). However, in this case we have significantly higher time and dose resolution in our N(t) data (472 data points) compared to our f(t) data (3 data points), and thus chose to include normalization terms in our objective function (Eq.…”