Calibrating a Predictive Model of Tumor Growth and Angiogenesis with Quantitative MRI
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Annals of Biomedical Engineering ( 2019) https://doi.org/10.1007/s10439-019-02262-9
Calibrating a Predictive Model of Tumor Growth and Angiogenesis with Quantitative MRI DAVID A. HORMUTH II ,1,5 ANGELA M. JARRETT,1,5 XINZENG FENG,1 and THOMAS E. YANKEELOV1,2,3,4,5 1 Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 E. 24th Street, POB 4.102, 1 University Station (C0200), Austin, TX 78712-1229, USA; 2Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX, USA; 3Department of Diagnostic Medicine, The University of Texas at Austin, Austin, TX, USA; 4 Department of Oncology, The University of Texas at Austin, Austin, TX, USA; and 5Livestrong Cancer Institutes, The University of Texas at Austin, Austin, TX, USA
(Received 8 February 2019; accepted 30 March 2019) Associate Editor Jane Grande-Allen oversaw the review of this article.
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 voxellevel at all prediction time points. The best performing model resulted in less than 9.3% error in blood volume at the voxellevel. This pre-clinical study demonstrates the potential for image-based, mechanistic modeling of tumor growth and angiogenesis. Keywords—DW-MRI, Modeling.
DCE-MRI,
Glioma,
Diffusion,
Address correspondence to David A. Hormuth II, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 E. 24th Street, POB 4.102, 1 University Station (C0200), Austin, TX 78712-1229, USA. Electronic mail: [email protected]
INTRODUCTION Angiogenesis is a critical component of tumor growth and invasion that is required to provide the delivery of nutrients and removal of waste to support growth past 2–3 mm3 in size. The recruited vasculature, however, is often disorganized (i.e., non-hierarchical), inefficient, and leaky, resulting in heterogeneous tumor perfusion.10,17 This spatially and temporally varying tumor perfusion yields hete
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