Introduction

Neoadjuvant systemic therapy (NAT) is the standard of care for patients with locally advanced breast cancer.^1-3 Optimizing NAT on a patient-specific basis necessitates accurate and early prediction of tumor response to therapy. Patient-specific predictions are essential because population-based approaches are limited in their ability to capture changes unique to the individual. The biology-based mathematical model used by Wu et al. achieved a concordance correlation coefficient (CCC) of 0.97 between the measured and predicted change in total tumor cellularity for triple-negative breast cancer patients (N=56).⁴ The goal of this study is to extend the modeling framework⁵ to accurately predict response to NAT for breast cancer patients of several subtypes from the multi-site, multi-drug I-SPY 2 clinical trial.⁶

Methods

Patient population. 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.⁶ Our subset of 94 patients—who received treatment and imaging at 10 clinical sites—includes a range of breast cancer subtypes as 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), and pathological complete response (pCR) status was determined at the time of surgery.

MRI analyses. For each patient, we first corrected for motion within and between the DCE-MRI and DW-MRI series across time (i.e., V1 to V3) using a combination of rigid and tumor-constrained non-rigid registration (Fig. 2).⁵ Apparent diffusion coefficient (ADC) maps were generated by fitting DW-MRI scans with b-values of 0, 100, 600, and 800 s/mm². We segmented the tumor ROI by applying fuzzy c-means clustering and segmented adipose and fibroglandular tissues with k-means clustering. The voxel-wise number of tumor cells, N_TC(x,t), was calculated from the ADC map.

Biology-based mathematical model. Our biology-based model is a reaction-diffusion partial differential equation that describes the voxel-wise rate of change in N_TC(x,t) as the balance of cell diffusion, D(x,t), logistic proliferation, k(x), and death due to treatment via Eq. 1:⁷
$$ \frac{\partial N_{TC}(\textbf{x},t)}{\partial t}=\nabla \cdot \big(D(\textbf{x},t) \nabla N_{TC} (\textbf{x},t)\big)+k(\textbf{x}) \bigg(1-\frac{N_{TC}(\textbf{x},t)}{\theta}\bigg) N_{TC}(\textbf{x},t)-\sum_i\alpha_i C_i (\textbf{x},t^*) e^{-\beta_it} N_{TC}(\textbf{x},t), \; \text{[1]} $$
where θ is the carrying capacity per voxel, C_i(x,t*) is the drug concentration, and α_i and β_i are efficacy and decay rates, respectively. Diffusion is mechanically coupled to the tissue (Eq. 2) and is subject to mechanical equilibrium (Eq. 3):
$$ D(\textbf{x},t)=D_0 e^{-\gamma \sigma_{vm}(\textbf{x},t)} \; \text{[2]} $$
$$ \nabla \cdot G \nabla \vec{u}+\nabla \frac{G}{1-2 \nu}(\nabla \cdot \vec{u})-\lambda \nabla N_{TC}(\textbf{x},t)=0 \; \text{[3]} $$
The β_i were set to literature-derived values, and D₀, k(x), and α_i were calibrated using the V1 and V2 N_TC(x,t) data via the Levenberg-Marquardt algorithm. Tissue segmentation maps defined the modeling domain geometry, the model was initialized with V1 N_TC(x,t) maps, and the drug concentration was calculated from DCE-MRI signal intensity. The calibrated model was run forward in time to make patient-specific predictions of tumor status at V3 (Fig. 1).

Analyses. For each patient in our initial subset of 52 patients, we compared the total tumor cellularity (Fig. 3a) and volume (Fig. 3b) time courses predicted by the model to the measured values. To evaluate local prediction accuracy, we visualized the measured and predicted cellularity maps (Fig. 3c) and 3D volumes (Fig. 3d). We used the concordance correlation coefficient (CCC) to quantify the degree of agreement between the measured and predicted data, globally. In particular, we calculated the CCC for the change from V1 to V3 in total tumor cellularity and volume between the measured ground truth data and the predicted data from our tumor forecasting pipeline.

Results

The total cellularity and volume predictions were accurate; the CCC between the measured and predicted change from V1 to V3 was 0.91 for total tumor cellularity (Fig. 4a) and 0.88 for tumor volume (Fig. 4b). However, we observed discrepancies between the measured and predicted local results. In general, as demonstrated in Fig. 3, the predicted tumor at V3 had a larger volume (Fig. 3d) but lower voxel-wise cellularity (Fig. 3c) than the measured V3 tumor.

Discussion and Conclusion

Although preliminary, our results demonstrate the promise of our approach in predicting tumor status for patients with various breast cancer subtypes and drug regimens using standard-of-care MRI data acquired at multiple sites. Future directions include completing image processing, calibration, and prediction for the remaining 42 patients in our dataset. While the model predicted total tumor cellularity and volume changes accurately, future work is needed to improve local predictions for the study population.

Acknowledgements

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.