Introduction:. Patients with locally advanced triple-negative breast cancer (TNBC) typically receive neoadjuvant therapy (NAT) to downstage the tumor and to improve the outcome of the subsequent breast conservation surgery. A critical unmet need is the lack of a method to accurately predict how a patient with TNBC will respond to NAT before surgery. In this work, we applied a clinical-computational framework to predict response of TNBC early in the course of NAT, by integrating quantitative MRI with mechanism-based mathematical modeling. Methods:. Patients and Data. Multiparametric quantitative MRI was acquired in patients (n = 46) before, and after 2 and 4 cycles of Adriamycin/Cyclophosphamide (A/C) regimen as part of the MD Anderson Cancer Center TNBC Moonshot Program. Within each imaging session, dynamic contrast-enhanced (DCE-), diffusion-weighted imaging (DWI), and a pre-contrast T1-map were acquired. Image processing. The processing pipeline consisted of three components. First, the images within each visit were registered to account for patient motion, and the parametric maps from the DCE and DWI images were computed. Second, inter-visit image registration was achieved by a non-rigid registration applied on breast, with a rigid penalty applied on the tumor region to preserve its size and shape. Third, post-processing was performed for preparation of modeling, including segmentation of the breast contour and tissues, and calculation of voxel-wise cellularity within tumors. Mathematical modeling. A predictive model was developed based on a reaction-diffusion equation (Eq. 1). The mobility of tumor cells is represented by diffusion coupled to mechanical properties of the tissue (Eq. 2), and the proliferation of the tumor is described with logistic growth. The injection and decay of administered therapies, inducing tumor cell death, is also represented in the model (Eq. 3). The variables and parameters used are listed in Table 1. Eq. 1: ∂N(x,t)/∂t = ∇⋅(D(x,t) ∇N(x,t)) + k(x) (1 - N(x,t)/θ)N(x,t) - (λ1(x,t) + λ2(x,t))N(x,t). Eq. 2: D(x,t) = D0e-γσ(x,t). Eq. 3: λn(x,t) = αne-βnt C(x,t), n = 1, 2. For each patient, the domain and initial condition were generated from the pre-treatment images, and the images acquired during NAT were used for patient-specific calibration of parameters. The calibrated model was then used to predict the response to be observed at the end of NAT. We evaluated the model by comparing its predictions of tumor volume, longest axis, voxel-wise cellularity, and total tumor cellularity to the imaging measurements at the end of A/C. Results:. Our model predicted the tumor volume, total cellularity, and longest axis with a Pearson correlation coefficient (PCC) of 0.85, 0.80, and 0.60, respectively. The accuracy of voxel-wise cellularity achieved a PCC with the median (range) of 0.89 (0.77 - 0.93) between the prediction and the actual measurement. Moreover, we set criteria of 70% shrinkage of tumor volume to define response versus non-response cases, with which our model achieved a differentiation sensitivity/specificity of 0.90/0.73. Discussion:. Preliminary results of our study demonstrate the potential of the clinical-computational framework as a powerful tool for predicting response to NAT. Once validated, the method could also assist in optimizing treatment plans on a patient specific basis, or guiding patient selection in trials for novel NAT regimens.

Table 1.

Summary of the variables and parameters in the model

QuantitiesDefinitionAssignment
Domains Ω breast tissue domain Generated from pre-treatment MRI 
 T End time point of NAT procedure Determined from NAT schedule 
 x Coordinate in breast tissue Associated with spatial domain, Ω 
 t time Associated with temporal domain, [0, T
Variables N(x,tTumor cell number Initialized from pre-treatment ADC, computed via Eq. 1 
 D(x,tDiffusive mobility of tumor cells Computed via Eq. 2 
 λn(x,tDeath rate induced by nth type of drug Computed via Eq. 3, n = 1 and 2 for A/C 
 σ(x,tVon Mises stress Computed from gradient of N(x,t), based on Hormuth et al., 2018 
 C(x,tSpatiotemporal distribution of drugs Assigned based on NAT schedule and DCE images 
Parameters k(xProliferation rate of tumor cells Locally calibrated 
 θ Tumor cells carry capacity Globally calibrated 
 αn Efficacy rate of nth type of drug Globally calibrated 
 βn Decay rate of of nth type of drug Globally calibrated 
 D0 Diffusion coefficient of tumor cells in the absence of mechanical restrictions Globally calibrated 
 γ Stress-tumor cell diffusion coupling constant Assigned based on Hormuth et al., 2018 
QuantitiesDefinitionAssignment
Domains Ω breast tissue domain Generated from pre-treatment MRI 
 T End time point of NAT procedure Determined from NAT schedule 
 x Coordinate in breast tissue Associated with spatial domain, Ω 
 t time Associated with temporal domain, [0, T
Variables N(x,tTumor cell number Initialized from pre-treatment ADC, computed via Eq. 1 
 D(x,tDiffusive mobility of tumor cells Computed via Eq. 2 
 λn(x,tDeath rate induced by nth type of drug Computed via Eq. 3, n = 1 and 2 for A/C 
 σ(x,tVon Mises stress Computed from gradient of N(x,t), based on Hormuth et al., 2018 
 C(x,tSpatiotemporal distribution of drugs Assigned based on NAT schedule and DCE images 
Parameters k(xProliferation rate of tumor cells Locally calibrated 
 θ Tumor cells carry capacity Globally calibrated 
 αn Efficacy rate of nth type of drug Globally calibrated 
 βn Decay rate of of nth type of drug Globally calibrated 
 D0 Diffusion coefficient of tumor cells in the absence of mechanical restrictions Globally calibrated 
 γ Stress-tumor cell diffusion coupling constant Assigned based on Hormuth et al., 2018 

Citation Format: Chengyue Wu, Angela M. Jarrett, Zijian Zhou, Nabil Elshafeey, Beatriz E. Adrada, Rosalind P. Candelaria, Rania M. Mohamed, Medine Boge, Lei Huo, Jason White, Debu Tripathy, Vicente Valero, Jennifer Litton, Stacy Moulder, Clinton Yam, Jong Bum Son, Jingfei Ma, Gaiane M. Rauch, Thomas E. Yankeelov. Forecasting treatment response to neoadjuvant systemic therapy in triple negative breast cancer viamathematical modeling and quantitative MRI [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P1-08-08.