Predicting the Response of Breast Cancer to Neoadjuvant Therapy Using a Mechanically Coupled Reaction-Diffusion Model

Abstract

Although there are considerable data on the use of mathematical modeling to describe tumor growth and response to therapy, previous approaches are often not of the form that can be easily applied to clinical data to generate testable predictions in individual patients. Thus, there is a clear need to develop and apply clinically relevant oncologic models that are amenable to available patient data and yet retain the most salient features of response prediction. In this study we show how a biomechanical model of tumor growth can be initialized and constrained by serial patient-specific magnetic resonance imaging data, obtained at two time points early in the course of therapy (before initiation and following one cycle of therapy), to predict the response for individual patients with breast cancer undergoing neoadjuvant therapy. Using our mechanics coupled modeling approach, we are able to predict, after the first cycle of therapy, breast cancer patients that would eventually achieve a complete pathologic response and those who would not, with receiver operating characteristic area under the curve (AUC) of 0.87, sensitivity of 92%, and specificity of 84%. Our approach significantly outperformed the AUCs achieved by standard (i.e., not mechanically coupled) reaction-diffusion predictive modeling (0.75), simple analysis of the tumor cellularity estimated from imaging data (0.73), and the Response Evaluation Criteria in Solid Tumors (0.71). Thus, we show the potential for mathematical model prediction for use as a prognostic indicator of response to therapy. The work indicates the considerable promise of image-driven biophysical modeling for predictive frameworks within therapeutic applications.

Figure 1

Schema of patient-specific mathematical modeling response predication framework. ADC maps at baseline and after one cycle of neoadjuvant therapy are converted to tumor cellularity. The mathematical model is then used to reconstruct parameter estimates of cellular proliferation and diffusion between these two time points. The model is then evaluated forward in time to predict the pathological response at the time of surgery.

Figure 2

The model prediction for one representative patient achieving pCR. Anatomical THRIVE images (A – C) and baseline DCE with ADC overlays (D – F) are shown for baseline (left column), after one cycle (middle column), and at the conclusion of neoadjuvant therapy (right column). Tumor cellularity is estimated (G – I) and used in conjunction with the mechanics coupled reaction-diffusion model to estimate key model parameters of tumor cell diffusion and proliferation (J) between the baseline and early imaging time points. Parameter estimates are then used in the model to predict tumor cellularity at the time of surgery (K) and compared to observation (I). The mechanics coupled reaction-diffusion model predicts a significant, near complete, response to neoadjuvant therapy, reflected by a significant decrease in tumor burden, in agreement to pathological determination of pCR at the time of surgery.

Figure 3

The model prediction for one representative patient not achieving pCR. Anatomical THRIVE images (A – C) and baseline DCE with ADC overlays (D – F) are shown for baseline (left column), after one cycle (middle column), and at the conclusion of neoadjuvant therapy (right column). Tumor cellularity is estimated (G – I) and used in conjunction with the mechanics coupled reaction-diffusion model to estimate key model parameters of tumor cell diffusion and proliferation (J) between the baseline and early imaging time points. Parameter estimates are then used in the model to predict tumor cellularity at the time of surgery (K) and compared to observation (I). The mechanics coupled reaction-diffusion model predicts a lack of response to neoadjuvant therapy, reflected by a significant increase in tumor burden, in agreement to pathological determination of non-pCR at the time of surgery.

Figure 4

Tumors from patients either achieving pCR or not were assessed as a percent change from t₁ to t₂ by RECIST criteria (A) and observed cellularity (B) and as a percent change from t₂ to predicted t₃ by reaction diffusion model prediction (C) and mechanics coupled model prediction (D). Data are expressed as mean with 95% confidence intervals with p values indicated for statistically significant differences between groups. ROC curves for all analysis metrics are shown along with the dashed line of identity (E).