(34b) Multiscale Simulation of Breast Cancer Tumorigensis Using Single Cell Models and Kinetic Monte Carlo

Breast cancer is the most frequently diagnosed cancer in women. In 2005, there were 211,240 new cases of invasive breast cancer and 40,410 deaths in the United States. Breast cancer originates in either lobules, sites of milk production, or in ducts, channels that transport milk. If diagnosed when the cancer is restricted to the epithelial layer in either the lobules or ducts, the cancer is likely curable. However, once the cancer breaks through the basement membrane and invades the surrounding fatty, connective and lymphatic tissue of the breast, it is invasive and the prognosis worsens significantly. Our long-term objective is to construct a single-cell stochastic tumorigenesis simulation framework that employs mechanistic descriptions of the cell-cycle, cell-death and other key developmental events leading to the formation of invasive breast cancer tumors. The proposed framework can be used to better understand the molecular basis of breast cancer development, to understand the efficacy of current protein-based therapeutics at a molecular scale and to computationally determine points of fragility in the networks controlling breast cancer that could serve as a basis for future therapies.

We propose that tumorigenesis can be described at the single cell level using discrete probabilistic cellular automata models and Kinetic Monte Carlo (KMC) coupled to continuum descriptions of nutrient and treatment fields. The basis of our approach is to treat individual cells as discrete entities that execute finite probabilistic moves in response to extra- or intracellular cues. Thus, a key component of our approach is a description of a how a breast cancer cell might choose between possible moves in response to nutritional or regulatory stimuli; we propose to calculate the probability of choices, for example the likelihood that a cell will divide or die, using mechanistic cell-cycle and cell-death models. An initial parallel avascular breast cancer tumorigenesis simulation framework is presented which employs rudimentary deterministic breast cancer cell-cycle and cell-death models adapted from the literature to calculate, at the level of a single cell, the probability of cell-division or death; the two moves currently possible. The probabilities are functions of both intra- and extracellular concentrations, thus, are directly coupled to the solution of the continuum mass balance equations describing the spatial-temporal dynamics of the nutrient field. The continuum nutrient phase balances are solved in parallel for a cubic tissue section being feed by a single vessel. The time-evolution of normal and cancer cell density in the cube is modeled using a KMC algorithm that enacts a series of local biophase moves followed by an update of the continuous phase variables. The entire set of model equations are solved on NERSC (IBM p575 Power5 111-nodes, 888 CPUs) at SLAC using LAM-MPI for communication and the PETSc library for the solution of the nutrient field balances; Galerkin method used for spatial discretization followed by iterative solution using a Krylov space algorithm with Jacobi preconditioning. Model simulated three-dimensional breast cancer tumor progression and morphology are compared with a transgenic mouse model carrying a somatic mutation in the tumor-suppressor protein p53 leading to both estrogen receptor positive and negative mammary tumors. Simulated avascular tumor histology and bulk tumor growth rates are compared with experiment. It will be shown the model is capable of describing bulk tumor progression before invasion and is approximately consistent with the mouse model histology for early stage tumors. Other clinically observed features such as non-uniform spreading of cancer-cell density, the presence of necrotic or hypoxic cores and growth toward the capillary wall are also predicted. Taken together, these results encourage the further development of the framework. In particular, we will explore more complicated tissue sections, more detailed models of cell-cycle, cell-death and associated developmental events such as the destruction of the tissue matrix before invasion.