Abstract A02: Multiple spatio-temporal scale modeling with application to brain cancer
Authors: Rahman Mohammad , Feng Yusheng , Yankeelov Thomas E. , Oden J. Tinsley 
Published: March 2017

Abstract
Introduction: We aim to develop a multiple spatio-temporal scale (MSTS) framework capable of bridging tissue, cellular, and subcellular scales. Our overarching hypothesis is that an accurate and precise MSTS model, initialized with patient-specific information, can dramatically outperform current standard-of-care for diagnosis and selecting therapy for the individual cancer patient.
Methodology: We developed a MSTS framework for tumor growth and treatment outcome prediction. Our model incorporated chemotherapy so that we can predict changes in tumor volume due to various therapeutic regimens. The MSTS framework consists of a tissue scale model, a cellular activity and growth model, and a subcellular signaling pathway model. To predict tissue growth at the tissue scale, a continuum model is constructed where the biological tissue is represented as a mixture of multiple constituents with each of which represents either a volume fraction or concentration. The constituents interact with each other through mass and momentum exchange so that the governing equations are based on both mass and momentum conservation laws. The constitutive equations account for tissue heterogeneity, nonlinear behavior, and thermodynamic consistency. The system of partial differential equations is solved using finite element techniques. To bridge the tissue and cell scales, each finite element is discretized into virtual cell clusters to model cellular growth and proliferation by using an agent-based model to determine various cellular scale activities including cell division, cell death, and phenotypical alteration. The cellular scale is further discretized temporally to model the effects of selected signaling pathways (e.g., PI3K/AKT/mTOR pathway). In many cancers, mTOR pathway becomes hyperactive and promotes abnormal cell proliferation. The mechanism and effects of a mTOR inhibiting drug known as rapamycin are tested in silico. The subcellular scale is modeled using a set of ordinary differential equations. A statistical inverse algorithm is used to calibrate and validate the results using magnetic resonance imaging (MRI) data, and a Bayesian inference method is employed to account for the uncertainties in model parameters.
Results: The 3D simulation results recapitulate, at various physical and biological conditions, different tumor characteristics including morphological instability, changes in the spatio-temporal distribution of different cell phenotypes and density, and the reduction of growth rate due to drug delivery. Thus, this model has the potential to be used for patient-specific prediction of tumor growth as well as personalized treatment planning. The novelties of this modeling framework are that (1) the events at each scale are modeled using different numerical techniques suitable for that specific scale in terms of both space and time, (2) a novel numerical technique is developed to bridge the scales and solved simultaneously, (3) the tissue scale model is thermodynamically consistent with consideration of tissue heterogeneity and nonlinear behaviors, (4) various cellular events such as the phenotypical alteration, apoptosis, necrosis, mitosis, etc. are modeled at the cellular scale, and (5) the mTOR signaling pathway, an important pathway for many different cancers, is modeled at the subcellular scale.
Conclusions: Our MSTS model is capable of predicting tumor growth with considerations of various factors at different spatio-temporal scales. It can be potentially used as a patient-specific tumor growth model for in silico drug testing, treatment planning, and prognosis. A future version of this model can include cancer stem cells, angiogenesis, and metastasis.
Citation Format: Mohammad Rahman, Yusheng Feng, Thomas E. Yankeelov, J. Tinsley Oden. Multiple spatio-temporal scale modeling with application to brain cancer. [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 A02.