Biophysical models designed to predict the growth and response of tumors to treatment have the potential to become a valuable tool for clinicians in care of cancer patients. Specifically, individualized tumor forecasts could be used to predict response or resistance early in the course of treatment, thereby providing an opportunity for treatment selection or adaption. This chapter discusses an experimental and modeling framework in which noninvasive imaging data is used to initialize and parameterize a subject-specific model of tumor growth. This modeling approach is applied to an analysis of murine models of glioma growth.

Quantitative analysis of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data provides estimates of physiological parameters that characterize tissue volume fractions, blood flow, and vascular permeability. While it provides a reasonable description of well-vascularized tissue, the standard models do not include the effects of intra-voxel diffusion, which is hypothesized to play a significant role in distributing contrast agent in poorly vascularized voxels1. This mechanism has been studied in silico using simulated tissue regions, but the results have yet to be tested with experimental data. We hypothesize that explicit incorporation of the contrast agent diffusion into the standard models is required to accurately model delivery and retention of the contrast agent within poorly vascularized regions. To investigate the effect of the diffusion of contrast agent within a tumor, nude athymic mice are subcutaneously implanted with BT474 cancer cells, and tumors develop for 4-6 weeks prior to performing DCE-MRI. Following imaging, the tumors are extracted, sectioned, and stained for vascularity (CD31) and viability/cellularity (H&E). Stained central slice sections were digitized in high resolution, segmented in MATLAB (Natick, MA), and a finite element model (FEM) was developed. A population arterial input function (AIF)2 serves as the source of contrast agent delivery into the FEM at the vascular boundaries, while the diffusion equation distributes the contrast agent through the extracellular space. The distribution of contrast agent over time within an imaging voxel is converted from concentration to MR signal intensity, and fit to the extended Tofts model3, providing estimates of vascular permeability and perfusion (Ktrans), extravascular extracellular volume fraction (ve), and vascular volume fraction (vp). These values are then compared to the true tissue volume fractions, determined by tissue segmentation, and an assigned (reasonable) set of Ktrans values. In order to verify the accuracy of the histologically segmented FEM, the simulated DCE-MRI signal is compared to in vivo experimental DCE-MRI scans of the same tumor. Comparison is completed by registering DCE-MRI voxels to simulated voxel domains, and directly measuring the difference between simulated and experimental signal intensities. Using a Ktrans of 0.4 min-1 and a diffusion constant of 3 x 10-5 mm2/s, the extended Tofts model poorly predicts tissue properties, with predicted Ktrans errors ranging from -95% to 68%, ve errors ranging -80% to 13%, and vp errors ranging 32% to 381%. Notably, necrotic regions of the tumor are subject to the highest level of error in the Tofts approximation of these parameters. Each of the maximum absolute prediction errors listed above occur in voxels with a vp value below 0.5% and ve above 80%. In contrast, the Tofts model can more accurately predict vp when the true value is above 5%, and most accurately predicts ve when its true value is below 70%. These results indicate that the lack of a diffusion term in the extended Tofts model can lead to significant errors in the estimates of physiological properties of tumor tissue in vivo. This is especially notable in regions with both a low vp and high ve, where the tissue is necrotic and poorly perfused. These results call for the inclusion of a diffusive term in the analysis of DCE-MRI in order to accurately model and understand contrast agent perfusion in a tumor. By including such a term, the diagnostic and predictive power of Ktrans ¸ vp, and ve, could be further improved. Our ongoing efforts for this research include further refining histology segmentation and model validation by comparing both simulated and measured DCE-MRI signal intensities. 1. Barnes, et al. PLoS One . 2014;9:e108726 2. Loveless, et al. Magn Reson Med . 2012; 67:226-236. 3. Tofts & Kermode. Magn Reson Med . 1991;17:357-367. Citation Format: Ryan T. Woodall, Stephanie L. Eldridge, Anna G. Sorace, Thomas E. Yankeelov. A finite element model of perfusion and diffusion within tumors based on dynamic contrast enhanced magnetic resonance imaging. [abstract]. In: Proceedings of the AACR Special Conference on Engineering and Physical Sciences in Oncology; 2016 Jun 25-28; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2017;77(2 Suppl):Abstract nr A23.