Journal of Theoretical Biology 233 (2005) 43–54 Origins and evolution of cell phenotypes in breast tumors Aydin To¨zeren à , Charles W. Coward, Sokol P. Petushi School of Biomedical Engineering, Science, and Health Systems, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA Received 22 January 2004; received in revised form 9 August 2004; accepted 15 September 2004 Abstract This study presents a stochastic model that correlates genomic instability with tumor formation. The model describes the time- andspace-variantvolumetricconcentrationsofcancercellsofvariousphenotypesinabreasttumor.Thecellsofepithelialoriginin thecancerousbreasttissueareclassifiedintofourdifferentphenotypes,normalepithelialcellsandthegrade1,grade2andgrade3 cancer cell types with increasing potential for growth and invasion. Equations governing the time course of volumetric concentrations of cell phenotypes are derived by using the principle of conservation of mass. Cell migration into and from the stroma is taken into account. The transformations between cell phenotypes are due to genetic inheritance and chromosome aberrations. These transformations are assumed to be stochastic functions of the local cell concentration. The simulations of the model for planar geometry replicate the shapes of human breast tumors and capture the time history of tumor growth in animal models. Simulations point to transformation of tumor cell population from heterogeneous compositions to a single phenotype at advancedstagesofinvasivetumors.Systematicvariationsofmodelparametersinthecomputationsindicatetheimportantrolesthe migration capacity, proliferation rate, and phenotype transition probability play in tumor growth. The model developed provides realisticsimulationsforstandardbreastcancertherapiesandcanbeusedintheoptimizationstudiesofchemotherapy,radiotherapy, hormone therapy and emerging individualized therapies for cancer. r 2004 Elsevier Ltd. All rights reserved. Keywords: Stochastic; Model; Tumor; Growth; Heterogeneous; Breast 1. Introduction Breast tissue is a composite of breast glandular epithelial cells lining the breast ducts, other cells, and the surrounding collagen-rich matrix called stroma containing blood vessels and lymph vessels (Going et al., 1988).Theepithelialcellsliningthebreastductsare highly differentiated cells that are responsive to hormo- nalstimulation(Rubinetal.,1999).Itisfromthesecells thatcancerouscellsemergeduringcyclesofcelldivision. The cancer in breast tissue follows a well-recognized pathway from non-proliferating lesions to invasive cancers (Page and Rodgers, 1992; Querzoli et al., 1995).Asthebreastdiseaseprogresses,thewellordered architecture of the breast in the form of mammary glands is disrupted (Debnath et al., 2002). Another important structural change concerns the formation of new blood vessels induced by the tumor (Ahmed et al., 2001).Breasttumorsmustcreatetheirownbloodsupply in order to grow and as a byproduct of this imperfect vasculature, the interstitial pressure increases within the tumor (Jain, 2001). The presence of nutrients, the composition of surrounding cells, and the interstitial pressureinthetumorallaffectthegrowthofcancercells in a tumor. Cell division cycle events fundamental to all cells, including DNA repair and recombination, checkpoint control of cell cycle, and transcription, are altered in cancer cells (Tyson et al., 2002). Factors such as age, child-bearing history, genetic predisposition and envir- onmental factors including radiation effects in some cases speed up the time course of emergence of ARTICLE IN PRESS www.elsevier.com/locate/yjtbi 0022-5193/$-see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtbi.2004.09.010 à Corresponding author. Tel.: +12025498128; fax:+12158953143. E-mail address: aydin.tozeren@drexel.edu (A. To¨zeren).