Calibrating a Predictive Model of Tumor Growth and Angiogenesis with Quantitative MRI
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.
KeywordsDW-MRI DCE-MRI Glioma Diffusion Modeling
The authors acknowledge the Texas Advanced Computing Center (TACC) for providing computing resources. This work was supported through funding from the National Cancer Institute R01CA138599 and U01CA174706, CPRIT RR160005, and AAPM Research Seed Funding.
Grant Sponsor: NCI U01 CA174706, NCI U01 CA154602, CPRIT RR160005, AAPM Research Seed Grant.
- 1.Akaike, H. A new look at the statistical model identification. New York: Springer, 1974.Google Scholar
- 12.Hormuth II, D., S. B. Eldridge, J. Weis, M. I. Miga, and T. E. Yankeelov. Mechanically coupled reaction-diffusion model to predict glioma growth: methodological details. In: Springer Methods and Protocols: Cancer Systems Biology, edited by L. von Stechow. New York: Springer, pp. 225–241, 2018. https://doi.org/10.1007/978-1-4939-7493-1_11
- 16.Huston III, J. Magnetic resonance elastography of the brain. In: Magnetic Resonance Elastography SE - 8. New York: Springer, pp. 89–98, 2014.Google Scholar
- 18.Jarrett, A., D. Hormuth, II, S. Barnes, X. Feng, W. Huang, and T. Yankeelov. Incorporating drug delivery into an imaging-driven, mechanics-coupled reaction diffusion model for predicting the response of breast cancer to neoadjuvant chemotherapy: theory and preliminary clinical results. Phys. Med. Biol. 63:105015, 2018.CrossRefGoogle Scholar
- 19.Neal, M. L., A. D. Trister, T. Cloke, R. Sodt, S. Ahn, A. L. Baldock, C. A. Bridge, A. Lai, T. F. Cloughesy, M. M. Mrugala, J. K. Rockhill, R. C. Rockne, and K. R. Swanson. Discriminating survival outcomes in patients with glioblastoma using a simulation-based. Patient-specific response metric. PLoS ONE 8:e51951, 2013.CrossRefGoogle Scholar
- 21.Padhani, A. R., G. Liu, D. Mu-Koh, T. L. Chenevert, H. C. Thoeny, T. Takahara, A. Dzik-Jurasz, B. D. Ross, M. Van Cauteren, D. Collins, D. A. Hammoud, G. J. S. Rustin, B. Taouli, and P. L. Choyke. Diffusion-weighted magnetic resonance imaging as a cancer biomarker: consensus and recommendations. Neoplasia 11:102–125, 2009.CrossRefGoogle Scholar
- 23.Roque, T., L. Risser, V. Kersemans, S. Smart, D. Allen, P. Kinchesh, S. Gilchrist, A. L. Gomes, J. A. Schnabel, and M. A. Chappell. A DCE-MRI Driven 3-D reaction-diffusion model of solid tumour growth. IEEE Trans. Med. Imaging 1, 2017Google Scholar
- 27.Sugahara, T., Y. Korogi, M. Kochi, I. Ikushima, Y. Shigematu, T. Hirai, T. Okuda, L. Liang, Y. Ge, Y. Komohara, Y. Ushio, and M. Takahashi. Usefulness of diffusion-weighted MRI with echo-planar technique in the evaluation of cellularity in gliomas. J. Magn. Reson. Imaging 9:53–60, 1999.CrossRefGoogle Scholar
- 29.Weis, J. A., M. I. Miga, L. R. Arlinghaus, X. Li, V. Abramson, A. B. Chakravarthy, P. Pendyala, and T. E. Yankeelov. Predicting the response of breast cancer to neoadjuvant therapy using a mechanically coupled reaction-diffusion model. Cancer Res. 2015. https://doi.org/10.1158/0008-5472.can-14-2945.Google Scholar