Abstract PS3-04-30: Developing virtual tumors using spherical harmonics and quantitative MRI data

Abstract Introduction: It is well-recognized that response to a particular treatment can vary greatly from patient to patient. However, clinical trials are limited in the range of treatment regimens they can evaluate due to constraints on patient numbers. To address this issue in a time- and cost-effective manner, our group has developed biology-based mathematical models that quantify the spatiotemporal changes in tumor cell number in response to treatment, using patient-specific MRI data1. These models enable in silico clinical trials, allowing us to evaluate responses to many regimens in virtual patient populations. Such trials require virtual populations that are realistic but more heterogeneous than those observed in traditional trials. Current methods of generating virtual patients are limited in capturing intra- and inter-tumor heterogeneity beyond that observed in narrow, historical trial populations. This study introduces a method of generating large, realistic, and heterogeneous virtual patient populations by applying spherical harmonics-based expansion to tumor cellularity maps of triple negative breast cancer (TNBC) patients. Methods: Pretreatment diffusion weighted MRI (DW-MRI) and dynamic contrast enhanced MRI (DCE-MRI) data from 27 TNBC patients were acquired from the I-SPY 2 trial2. Tumor regions were identified from DCE-MRI scans. DW-MRI scans were used to calculate apparent diffusion coefficient maps, ADC( x ), from which tumor cell number maps, N( x ), were calculated for each patient3. We applied spherical harmonics-based expansion to each N( x ) to compute an approximation of tumor cellularity, N * ( x ), as a weighted sum of spherical harmonic functions multiplied by suitable radial functions4. We used the concordance correlation coefficient (CCC) to determine a minimum number, n, of functions needed to obtain 90% agreement between N( x ) and N * ( x ). To generate realistic, heterogeneous tumors, probabilistic distributions were fit to coefficients corresponding to pairs of consecutive basis functions. As the basis functions are ordered in decreasing importance for reconstructing N( x ), the distributions aimed to preserve statistical relationships between pairs with similar importance. Specifically, n/2 multivariate normal distributions (MVNs) were fit to describe the set of all coefficients. Sampling all MVNs, we generated n coefficients that parameterized a virtual tumor. The two-sample Kolmogorov-Smirnov (KS) test applied to tumor volume and cellularity distributions quantified agreement between virtual and historical populations. Results: Spherical harmonics-based expansion yielded 252,279 basis functions that reconstruct N( x ) with high agreement (mean ± standard deviation CCC = 0.99±.004); importantly, 500 basis functions were sufficient for accurate reconstruction (CCC = 0.92±.024). 250 MVNs were sampled 100 times to generate 100 virtual tumors. KS test results indicated that tumor volume distributions of virtual and historical populations are not significantly different (p = 0.002) and that tumor cellularity distributions are significantly different (p = 0.79). Conclusion: Using our spherical harmonics-based framework, we generated a virtual population that preserved tumor sizes of the historical population but allowed for variation in tumor cell distribution over the volume; this heterogeneous virtual population can be used to systematically quantify the efficacy of many treatment regimens and identify interventions to test experimentally. References. 1. Wu C et al., MRI-Based Models Forecast Patient-Specific Treatment Cancer Res. 20222. Barker A et al. I-SPY 2: An Adaptive Breast Cancer Trial Design. Clin Pharm Ther. 2009.3. Jarrett AM et al. Quantitative MRI and Tumor Forecasting of Breast Cancer. Nat Protoc. 2021.4. Kileel J et al. Fast expansion into harmonics. SIAM J Sci Comput. 2025. Citation Format: G. Patel, D. A. Hormuth II, R. J. Patel, C. E. Stowers, A. Chaudhuri, E. A. Lima, J. Kileel, T. E. Yankeelov. Developing virtual tumors using spherical harmonics and quantitative MRI data [abstract]. In: Proceedings of the San Antonio Breast Cancer Symposium 2025; 2025 Dec 9-12; San Antonio, TX. Philadelphia (PA): AACR; Clin Cancer Res 2026;32(4 Suppl):Abstract nr PS3-04-30.