Calibrating a Predictive Model of Tumor Growth and Angiogenesis with Quantitative MRI

Abstract

The spatiotemporal variations in tumor vasculature inevitably alters cell proliferation and treatment efficacy. Thus, rigorous characterization of tumor dynamics must include a description of this phenomenon. We have developed a family of biophysical models of tumor growth and angiogenesis that are calibrated with diffusion-weighted magnetic resonance imaging (DW-MRI) and dynamic contrast-enhanced (DCE-) MRI data to provide individualized tumor growth forecasts. Tumor and blood volume fractions were evolved using two, coupled partial differential equations consisting of proliferation, diffusion, and death terms. To evaluate these models, rats (n=8) with C6 gliomas were imaged seven times. The tumor volume fraction was estimated using DW-MRI, while DCE-MRI provided estimates of the blood volume fraction. The first three time points were used to calibrate model parameters, which were then used to predict growth at the remaining four time points and compared directly to the measurements. The best performing model predicted tumor growth with less than 10.3% error in tumor volume and with less than 9.4% error at the voxel-level at all prediction time points. The best performing model resulted in less than 9.3% error in blood volume at the voxel-level. This pre-clinical study demonstrates the potential for image-based, mechanistic modeling of tumor growth and angiogenesis.

Integrating multimodal data sets into a mathematical framework to describe and predict therapeutic resistance in cancer

“…The majority of these modeling endeavors utilize a single measurement source for longitudinal data acquisition and subsequent model calibration. A few studies utilizing multimodal imaging modalities have harnessed the ability to quantify different aspects of tumor composition-such as vasculature, necrosis, and cellularity, to develop an integrated model calibration of multiple tumor system components (43,44). However, this integrated, multimodal approach has not explicitly included inference of the composition of heterogeneous subpopulations taken from separate "omics" datasets for direct model calibration.…”

Forecasting tumor and vasculature response dynamics to radiation therapy via image based mathematical modeling

“…In a single species model (i.e., considering only tumor cells of one type) the reaction diffusion model describes the spatial and temporal change in tumor cell number due to proliferation (i.e., the reaction term) and due to the outward movement (i.e., the diffusion term) of tumor cells. In our previous efforts, we extended the standard reaction-diffusion model to incorporate the effect of local tissue stress on tumor cell diffusion [24] as well as characterize the spatial-temporal evolution of both tumor cells and vasculature [25]. We present the salient features of this model system here, while Table 1 summarizes the model parameters and variables and their sources.…”

“…We (and others [6, 16–22];) have developed a series of increasingly comprehensive biophysical mathematical models of tumor and vasculature growth [5, 23–25] to provide individualized forecasts of response to radiation therapy using non-invasive quantitative imaging data. Our overall hypothesis, is that biologically-relevant models, informed and calibrated from tumor-specific imaging data, may lead to the early prediction of response, significant improvements in tumor control through the pre-treatment optimization of therapy regimens, and the adaptation of treatment regimens by accounting for the spatiotemporal variations in tumor response [26].…”

“…In that study, we demonstrated that combining both immediate and long-term effects outperformed models consisting of single effects. Additionally, we have previously demonstrated that both DW-MRI and DCE-MRI data could be used to initialize and calibrate a biophysical model of tumor growth and angiogenesis in the absence of treatment that resulted in accurate volume and voxel-wise predictions of tumor and blood volume fractions [25]. At the clinical level, one approach by Rockne et al [6] leveraged anatomical MRI and hypoxia-sensitive positron emission tomography images collected in glioblastoma multiforme patients to determine patient-specific radiosensitivity parameters.…”

Impact of tumor-parenchyma biomechanics on liver metastatic progression: a multi-model approach

“…Most current tumor growth simulation models, such as [56][57][58][59][60][61][62][63] use a diffusing growth factor (e.g., oxygen or glucose) as the main negative feedback on tumor cell proliferation by scaling cell cycling with local substrate availability. As the avascular tumor grows, it consumes and depletes the substrate, thus slowing growth in a negative feedback.…”