Abstract
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.
Similar content being viewed by others
References
Yankeelov TE, Quaranta V, Evans KJ, Rericha EC (2015) Toward a science of tumor forecasting for clinical oncology. Cancer Res 75(6):918–923
Atuegwu NC, Gore JC, Yankeelov TE (2010) The integration of quantitative multi-modality imaging data into mathematical models of tumors. Phys Med Biol 55(9):2429–2449
Atuegwu NC, Colvin DC, Loveless ME, Xu L, Gore JC, Yankeelov TE (2012) Incorporation of diffusion-weighted magnetic resonance imaging data into a simple mathematical model of tumor growth. Phys Med Biol 57(1):225–240
Weis JA, Miga MI, Arlinghaus LR, Li X, Chakravarthy AB, Abramson V et al (2013) A mechanically coupled reaction-diffusion model for predicting the response of breast tumors to neoadjuvant chemotherapy. Phys Med Biol 58(17):5851–5866
Hormuth DA II, Weis JA, Barnes SL, Miga MI, Rericha EC, Quaranta V et al (2015) Predicting in vivo glioma growth with the reaction diffusion equation constrained by quantitative magnetic resonance imaging data. Phys Biol 12(4):46006
Weis JA, Miga MI, Arlinghaus LR, Li X, Abramson V, Chakravarthy AB et al (2015) Predicting the response of breast cancer to neoadjuvant therapy using a mechanically coupled reaction-diffusion model. Cancer Res 75(22):4697–4707
Baldock A, Rockne R, Boone A, Neal M, Bridge C, Guyman L et al (2013) From patient-specific mathematical neuro-oncology to precision medicine. Front Oncol 3:62
Corwin D, Holdsworth C, Rockne RC, Trister AD, Mrugala MM, Rockhill JK et al (2013) Toward patient-specific, biologically optimized radiation therapy plans for the treatment of glioblastoma. PLoS One 8(11):e79115
Hogea C, Davatzikos C, Biros G (2008) An image-driven parameter estimation problem for a reaction-diffusion glioma growth model with mass effects. J Math Biol 56(6):793–825
Liu Y, Sadowski SM, Weisbrod AB, Kebebew E, Summers RM, Yao J (2014) Patient specific tumor growth prediction using multimodal images. Med Image Anal 18(3):555–566
Konukoglu E, Clatz O, Menze BH, Stieltjes B, Weber M-A, Mandonnet E et al (2010) Image guided personalization of reaction-diffusion type tumor growth models using modified anisotropic eikonal equations. IEEE Trans Med Imaging 29:77–95
Garg I, Miga MI (2008) Preliminary investigation of the inhibitory effects of mechanical stress in tumor growth. Proc SPIE 29:69182L-11
Venes D (2013) Taber’s® cyclopedic medical dictionary, 22nd edn. F. A. Davis Company, Philadelphia, PA
DeAngelis LM (2001) Brain tumors. N Engl J Med 344(2):114–123
Helmlinger G, Netti PA, Lichtenbeld HC, Melder RJ, Jain RK (1997) Solid stress inhibits the growth of multicellular tumor spheroids. Nat Biotechnol 15(8):778–783
Padhani AR, Liu G, Mu-Koh D, Chenevert TL, Thoeny HC, Takahara T et al (2009) Diffusion-weighted magnetic resonance imaging as a cancer biomarker: consensus and recommendations. Neoplasia 11(2):102–125
Yankeelov TE, Gore JC (2009) Dynamic contrast enhanced magnetic resonance imaging in oncology: theory, data acquisition, analysis, and examples. Curr Med Imaging Rev 3(2):91–107
Barth R, Kaur B (2009) Rat brain tumor models in experimental neuro-oncology: the C6, 9L, T9, RG2, F98, BT4C, RT-2 and CNS-1 gliomas. J Neuro-Oncol 94(3):299–312
Hormuth DA II, Weis JA, Barnes SL, Miga MI, Rericha EC, Quaranta V, Yankeelov TE (2017). A mechanically-coupled reaction-diffusion model that incorporates intra-tumoral heterogeneity to predict in vivo glioma growth. J R Soc Interface 14:128
Barnes SL, Sorace AG, Loveless ME, Whisenant JG, Yankeelov TE (2015) Correlation of tumor characteristics derived from DCE-MRI and DW-MRI with histology in murine models of breast cancer. NMR Biomed 28(10):1345–1356
Anderson AW, Xie J, Pizzonia J, Bronen RA, Spencer DD, Gore JC (2000) Effects of cell volume fraction changes on apparent diffusion in human cells. Magn Reson Imaging 18(6):689–695
Guo Y, Cai Y-Q, Cai Z-L, Gao Y-G, An N-Y, Ma L et al (2002) Differentiation of clinically benign and malignant breast lesions using diffusion-weighted imaging. J Magn Reson Imaging 16(2):172–178
Sugahara T, Korogi Y, Kochi M, Ikushima I, Shigematu Y, Hirai T et al (1999) Usefulness of diffusion-weighted MRI with echo-planar technique in the evaluation of cellularity in gliomas. J Magn Reson Imaging 9(1):53–60
Humphries PD, Sebire NJ, Siegel MJ, Olsen ØE (2007) Tumors in pediatric patients at diffusion-weighted mr imaging: apparent diffusion coefficient and tumor cellularity. Radiology 245(3):848–854
Whisenant JG, Ayers GD, Loveless ME, Barnes SL, Colvin DC, Yankeelov TE (2014) Assessing reproducibility of diffusion-weighted magnetic resonance imaging studies in a murine model of HER2+ breast cancer. Magn Reson Imaging 32(3):245–249
Martin I, Dozin B, Quarto R, Cancedda R, Beltrame F (1997) Computer-based technique for cell aggregation analysis and cell aggregation in in vitro chondrogenesis. Cytometry 28(2):141–146
Rouzaire-Dubois B, Milandri JB, Bostel S, Dubois JM (2000) Control of cell proliferation by cell volume alterations in rat C6 glioma cells. Pflugers Arch 440(6):881–888
Elkin BS, Ilankovan AI, Morrison B III (2011) A detailed viscoelastic characterization of the P17 and adult rat brain. J Neurotrauma 28:2235
Lee SJ, King MA, Sun J, Xie HK, Subhash G, Sarntinoranont M (2014) Measurement of viscoelastic properties in multiple anatomical regions of acute rat brain tissue slices. J Mech Behav Biomed Mater 29:213–224
Lynch D (2005) Numerical partial differential equations for environmental scientsits and engineers: a first practical course. Springer, New York, NY
Miga MI, Paulsen KD, Lemery JM, Eisner SD, Hartov A, Kennedy FE et al (1999) Model-updated image guidance: initial clinical experiences with gravity-induced brain deformation. IEEE Trans Med Imaging 10:866–874
Levenberg K (1944) A method for the solution of certain non-linear problems in least squares. Q J Appl Mathmatics II(2):164–168
Marquardt DW (1963) An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math 11(2):431–441
Eisenhauer EA, Therasse P, Bogaerts J, Schwartz LH, Sargent D, Ford R et al (2009) New response evaluation criteria in solid tumours: revised RECIST guideline (version 1.1). Eur J Cancer 45(2):228–247
Yankeelov TE, Atuegwu N, Hormuth DA, Weis JA, Barnes SL, Miga MI et al (2013) Clinically relevant modeling of tumor growth and treatment response. Sci Transl Med 5(187):187ps9
Marino S, Hogue IB, Ray CJ, Kirschner DE (September 2008) A methodology for performing global uncertainty and sensitivity analysis in systems biology. J Theor Biol 254(1):178–196
Broyden CG (1965) A class of methods for solving nonlinear simultaneous equations. Math Comput 19(92):577–593
Acknowledgments
This work was supported through funding from CPRIT RR160005 and the National Cancer Institute U01CA174706, K25CA204599, and R01CA186193, from the National Institute of Neurological Disorders and Stroke R01NS049251 and the Vanderbilt-Ingram Cancer Center Support Grant (NIH P30CA68485).
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Science+Business Media LLC
About this protocol
Cite this protocol
Hormuth, D.A., Eldridge, S.L., Weis, J.A., Miga, M.I., Yankeelov, T.E. (2018). Mechanically Coupled Reaction-Diffusion Model to Predict Glioma Growth: Methodological Details. In: von Stechow, L. (eds) Cancer Systems Biology. Methods in Molecular Biology, vol 1711. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-7493-1_11
Download citation
DOI: https://doi.org/10.1007/978-1-4939-7493-1_11
Published:
Publisher Name: Humana Press, New York, NY
Print ISBN: 978-1-4939-7492-4
Online ISBN: 978-1-4939-7493-1
eBook Packages: Springer Protocols