Integrative physical oncology

Mathematical modeling of complex ductal carcinoma in situ (DCIS) microstructures: (Left) An immersed boundary model produced micropapillary‐like DCIS structures when cell polarization was assumed. (Reprinted with permission from Ref 42. Copyright 2007 Hindawi Publishing Corporation). (Right) An agent‐based model predicted that polarized DCIS cells form micropapillary structures (iterations 200 and 500) that merge into cribriform‐like structures (iterations 800 and onward). (Reprinted with permission from Ref 43. Copyright 2010 Elsevier)

Patient‐calibrated ductal carcinoma in situ (DCIS) simulation. After calibration to patient immunohistochemistry and morphometric measurements, an agent model correctly reproduced the solid‐type DCIS microstructure: an 80‐µm viable rim with most frequent proliferation (green cells) on the outermost edge and apoptosis (red cells) throughout, a mechanical separation at the perinecrotic boundary, and an ‘age‐structured’ necrotic core with increasing pyknosis (nuclear degradation) and calcification (progression indicated by the shade of red) toward the duct center. The bright red central region is a radiologically detectable casting‐type microcalcification. These features are seen in patient hematoxylin and eosin stained histopathology, including the mechanical gap (increased by tissue dehydration), increasing pyknosis toward the duct center and central calcium phosphate microcalcifications.

Three‐dimensional computer model predicts gross morphologic features of a growing glioblastoma. Viable (light gray) and necrotic (dark gray) tissue regions and vasculature (mature blood‐conducting vessels in red; new nonconducting vessels in blue) are shown. The simulations reveal that the morphology is affected by neovascularization, vasculature maturation, and vessel cooption. (Reprinted with permission from Ref 68. Copyright 2007 Elsevier)

Individual (discrete) palisading glial cells invasion into vascularized tissue. (a) Computer simulation from a hybrid‐multiscale model showing palisading cells escaping from the perinecrotic region (dark gray) by upregulating motility and downregulating adhesion and proliferation. This phenotypic change is driven by hypoxia as the selective evolutionary force (see Discussion section). Cell migration occurs via chemotaxis and haptotaxis in response to gradients of oxygen and extracellular matrix (ECM) concentration, respectively. Brown: conducting vessels; yellow: nonconducting. (b) Background shows distribution of oxygen concentration (n = 1 in vascularized tissue and n < 1 in the tumor white/yellow perinecrotic region). (Reprinted with permission from Ref 73. Copyright 2009 American Association for Cancer Research)

Validation of model predictions against pathology‐determined ductal carcinoma in situ (DCIS) tumor sizes. Surgical tumor size versus parameter A that is related to the ratio of tumor apoptotic and mitotic indices in the breast ducts. The dotted curve represents the theoretical predictions by a continuum model. Symbols are DCIS tumor size measurements from individual patient histopathology and are subclassified by their grade. The shaded region indicates the standard deviation in the measurement of A in individual duct. (Reprinted with permission from Ref 50. Copyright 2010 Cambridge University Press)