Modeling Multiscale Necrotic and Calcified Tissue Biomechanics in Cancer Patients: Application to Ductal Carcinoma In Si

Tissue necrosis and calcification significantly affect cancer progression and clinical treatment decisions. Necrosis and calcification are inherently multiscale processes, operating at molecular to tissue scales with time scales ranging from hours to mont

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Abstract Tissue necrosis and calcification significantly affect cancer progression and clinical treatment decisions. Necrosis and calcification are inherently multiscale processes, operating at molecular to tissue scales with time scales ranging from hours to months. This chapter details key insights we have gained through mechanistic continuum and discrete multiscale models, including the first modeling of necrotic cell swelling, lysis, and calcification. Among our key findings: necrotic volume loss contributes to steady tumor sizes but can destabilize tumor morphology; steady necrotic fractions can emerge even during unstable growth; necrotic volume loss is responsible for linear ductal carcinoma in situ (DCIS) growth; fast necrotic cell swelling creates mechanical tears at the perinecrotic boundary; multiscale interactions give rise to an age-structured, stratified necrotic core; and mechanistic, patient-calibrated DCIS modeling allows us to assess our working biological assumptions and better interpret pathology and mammography. We finish by outlining our integrative computational oncology approach to developing computational tools that we hope will one day assist clinicians and patients in their treatment decisions.

P. Macklin (&)  S. Mumenthaler Keck School of Medicine, Center for Applied Molecular Medicine, University of Southern California, Los Angeles, CA, USA e-mail: [email protected] URL: http://MathCancer.org J. Lowengrub Departments of Mathematics, Chemical Engineering and Materials Science, and Biomedical Engineering, University of California, Irvine, CA, USA URL: http://math.uci.edu/*lowengrb

Stud Mechanobiol Tissue Eng Biomater (2013) 14: 349–380 DOI: 10.1007/8415_2012_150 Ó Springer-Verlag Berlin Heidelberg 2012 Published Online: 6 October 2012

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1 Introduction At its most basic level, cancer is a disease of uncontrolled cell proliferation: cancer cells, either through mutations or epigenetic alterations, overexpress oncogenes and underexpress tumor suppressor genes (TSGs). Consequently, the cells enter into and progress through the cell cycle more often than they should and disregard apoptotic signals, resulting in a net increase in proliferation and aberrant tissue growth. (See recent cancer biology tutorials for modelers and physical scientists, such as [50, 52, 53]). Accordingly, cell proliferation and apoptosis, along with genetic mutations and epigenetic alterations in genes controlling these processes, have been major foci of both basic cancer research and modeling. Most cancer therapies attempt to manipulate these processes either by cytostatic (suppressing entry to or progression through the cell cycle) or cytotoxic (inducing apoptosis: programmed cell death) mechanisms. For example, chemotherapy agents such as doxorubicin are considered to be cytotoxic [10]; therapies that target hormoneaddicted cells (e.g., tamoxifen in estrogen-driven breast cancer) are considered to be cytostatic [74]. Key biological and clinical terms Basement membrane (BM) Extracell