Multiscale Modeling of Avascular Tumor Growth Jelena Pjesivac-Grbovic Theoretical Division 7, LANL Ramapo college of New Jersey University of Tennessee, Knoxville

Motivation The current understanding of mechanisms behind the early stages of tumor development is far from complete. Developing a complete model of tumor growth could provide better insight in the mechanisms behind tumor growth and will eventually help in predicting the results of therapy.

Tumor A relentlessly growing mass of abnormal cells, whose growth rate exceeds that of surrounding normal cells. Avascular tumors are benign tumors that grow in a spherical, layered structure consisting of necrotic, quiescent and proliferating cells.

Multicellular Tumor Spheroid (MTS) Exhibits many characteristics of avascular tumors: –Cell type differentiation Proliferating and Quiescent –Development of central necrosis Develops in precisely controlled microenvironment –Allows for easy assays of data Abundant experimental data

Cell “types” Proliferating cells –Exponentially growing –Possible mutations during mitosis Quiescent cells –Alive but not growing –Cell Cycle Phase Arrest (usually G1) –Quiescence may be caused by Concentration of Growth and Inhibitory Factors External stress/pressure Necrotic core (cells died via necrosis) –Necrosis may be caused by Nutrient deprivation Waste accumulation

Modeling tumor growth Important processes to consider cell growth and mitosis mutations metabolites growth and inhibitory factors cell-environment chemotactic interactions intercellular adhesion stress geometry and structure of cells

Multiscale Cellular Model Multiscale: – Cellular level cell growth, mitosis, mutations, chemical reaction diffusion of metabolites and factors, shedding, and necrosis – Subcellular level protein regulatory network Hybrid Model – Discrete Lattice Monte Carlo for cells – Continuous chemical reaction-diffusion for metabolites and growth and inhibitory factors – Boolean network for Protein Expression

Protein Regulatory Network Proteins have only two levels: On and Off Protein expression controls transition between G1 and S phase Protein expression is controlled by concentration of growth and inhibitory factors

Discrete Cellular Model Lattice Monte Carlo coupled with chemical- reaction diffusion Driving force is minimization of total energy –A random site is chosen and assigned to one of its neighbors –  H is calculated –Probability of accepting this change is

Cells An individual entity of a finite volume with the following characteristics: – Internal clock – Type (proliferating, quiescent, necrotic) – Phase (G1, S, G2+M) – Metabolic rates – Coupling energy (Adhesion energy) – Volume constraint – Protein levels

Chemical Reaction-Diffusion Metabolites –Oxygen –Nutrients –Waste Growth and Inhibitory factors

Algorithm Initialize simulation Run Monte Carlo Step Solve Chemical Reaction Diffusion equations Allow cells to react to microenvironment Divide cells Finalize simulation

Spheroid Cross Section Experimental EMT6/R0 Spheroid Simulation EMT6/R0 Spheroid

Aggregate Growth and Geometry

Growth curves – Number of cells

Growth Curves – MTS Volume

Summary Results of our model show good match with experimental data: –Numbers of proliferating, quiescent, and necrotic cells –Spheroid Volume –General tumor physiology

Further Work Systematic comparison with experimental data to validate the model parameters. Extending model to simulate new experimental conditions and predict spheroid growth under new conditions. Extending model to describe vascular tumors by introducing blood vessels and angiogenesis. Develop a comprehensive and predictive tumor growth model.

Research Group Yi Jiang (Principle investigator) Theoretical Division T7, LANL, Los Alamos NM James P. Freyer Bioscience Division B3, LANL, Los Alamos NM Jelena Pjesivac-Grbovic Theoretical Division T7, LANL, Los Alamos NM University of Tennessee, Knoxville, TN Charles Cantrell Theoretical Division T7, LANL, Los Alamos NM Massachusetts Institute of Technology