Using MRI-based mathematical modeling to predict the response of breast cancer to neoadjuvant therapy

Introduction: Neoadjuvant therapy (NAT) is the standard-of-care for patients with locally advanced breast cancer [1-3]. The development of novel NAT regimens provides an opportunity to tailor treatment for individual patients to improve their outcomes. Accurate and early prediction of response to NAT is essential, as this would allow clinicians to make changes to (a) improve outcomes for patients predicted to have post-treatment residual disease, and (b) reduce toxicity while maintaining outcomes for patients predicted to be disease-free after treatment [4]. Existing methods designed to accomplish these tasks are population-based and intrinsically limited in capturing tumor heterogeneity and longitudinal changes for individual patients [5]. Conversely, mechanism-based mathematical models employ patient-specific imaging data to perform tumor forecasting for individual patients [6].

We recently developed a biology-based mathematical model6 that achieved concordance correlation coefficients (CCC) of 0.95 and 0.94 between the observed and predicted change in total tumor cellularity (TTC) and tumor volume (TV), respectively, in a cohort of 56 triple-negative breast cancer (TNBC) patients [7]. We now seek to apply this model to an independent and external data set from the I-SPY 2 trial that imaged and treated patients with various breast cancer subtypes at 10 different sites, using widely available magnetic resonance imaging (MRI) methods [8]. We hypothesize our model will outperform state-of-the-art approaches by predicting change in TTC and TV with an accuracy statistically equivalent to what we have observed in other data sets of breast cancer patients.

Materials and

Methods: I-SPY 2 is a clinical trial for locally advanced breast cancer that acquired dynamic contrast enhanced (DCE) and diffusion-weighted (DW) MRI scans before and during NAT [8]. Our current subset of 77 patients includes a range of subtypes determined by the presence of human epidermal growth factor receptor 2 (HER2) and estrogen and progesterone receptors (hormone receptors, HR). The MRI data was acquired before (V1), after three weeks (V2), and after completion (V3) of the first NAT regimen (Fig. 1) [8].

For each patient, we corrected for motion within and between the DCE-MRI and DW-MRI series across time using rigid and tumor-constrained non-rigid registration [6]. We fit DW-MRI scans with b-values of 0, 100, 600, and 800 s/mm2 to obtain apparent diffusion coefficient (ADC) maps. We applied fuzzy c-means and k-means clustering to segment the tumor ROI and breast tissue, respectively. The voxel-wise tumor cellularity, NTC(x̄,t), was then calculated from the ADC map (Fig. 2) [6].

Our biology-based model is a reaction-diffusion partial differential equation describing the rate of change in NTC(x̄,t) as the balance of cell diffusion (mechanically coupled to the surrounding tissue), logistic proliferation, and death due to treatment [6-7, 9]. Global efficacy and spatially-resolved proliferation rates were calibrated using the V1 and V2 NTC(x̄,t) data via the Levenberg-Marquardt algorithm. Tissue segmentation maps defined the modeling domain, and the initial drug concentration was estimated as proportional to DCE-MRI signal intensity. The calibrated model was run forward to make patient-specific predictions for tumor status at V3 (Fig. 1, 3).

Results, Conclusions, and Discussions: For 77 patients, the CCC between the observed and predicted change from V1 to V3 was 0.94 for TTC change and 0.91 for TV change (Fig. 4). Fisher’s z-tests between our CCC values and those achieved in a previous study [7] show no significant differences, indicating our model predicted TTC and TV with a statistically equivalent accuracy in the two data sets. In general, our model accurately predicted TTC at V3, but did not capture compression of the tumor tissue (Fig. 3), leading to less accurate predictions for TV and local cellularity. However, our model successfully predicted voxels with complete elimination of measurable tumor by V3; 80% of patients had a median percent difference between the observed and predicted change in NTC(x̄,t) of less than 10%, and the cohort mean was 11.3% (Fig. 4). Thus, our tumor forecasting pipeline can accurately predict change in tumor status over a single course of treatment.

These results indicate changes in tumor cellularity early in a course of NAT, informing a biology-based mathematical model, can predict tumor status after completion of the 12-week therapy. Accurate patient-specific predictions support the feasibility of personalizing treatment using only MRI data obtained in the clinical setting. For example, after a patient receives three chemotherapy cycles, we can calibrate the model with patient-specific MRI data and make predictions at V3 for standard-of-care and alternate treatment schedules. The optimal schedule(s) based on V3 predictions can be provided to a clinician as an additional tool to guide treatment planning.

Although these initial results are promising, we plan to improve the prediction accuracy of our tumor forecasting pipeline. Based on a sensitivity analysis indicating the model is more sensitive to the drug efficacy rate than the proliferation rate, we will calibrate with a spatially-resolved efficacy and global proliferation instead of the current approach that calibrates spatially-resolved proliferation and global efficacy. To capture a wider range of feasible drug and tumor dynamics, we will calibrate and make predictions for each patient with six drug decay values from 0.05 to 3 1/days. After refining the model, we will quantify predictions by breast cancer subtype.

Acknowledgements (Optional): This work was supported by funding from NCI U01CA142565, U01CA174706, and U24CA226110, as well as CPRIT RR16005 and the Joint Center for Computational Oncology (Oden Institute for Computational Engineering and Sciences, MD Anderson Cancer Center, Texas Advanced Computing Center). This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DE2137420.

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