title: Tissue-scale, personalized modeling and simulation of prostate cancer growth.
abstract: Recently, mathematical modeling and simulation of diseases and their treatments have enabled the prediction of clinical outcomes and the design of optimal therapies on a personalized (i.e., patient-specific) basis. This new trend in medical research has been termed "predictive medicine." Prostate cancer (PCa) is a major health problem and an ideal candidate to explore tissue-scale, personalized modeling of cancer growth for two main reasons: First, it is a small organ, and, second, tumor growth can be estimated by measuring serum prostate-specific antigen (PSA, a PCa biomarker in blood), which may enable in vivo validation. In this paper, we present a simple continuous model that reproduces the growth patterns of PCa. We use the phase-field method to account for the transformation of healthy cells to cancer cells and use diffusion-reaction equations to compute nutrient consumption and PSA production. To accurately and efficiently compute tumor growth, our simulations leverage isogeometric analysis (IGA). Our model is shown to reproduce a known shape instability from a spheroidal pattern to fingered growth. Results of our computations indicate that such shift is a tumor response to escape starvation, hypoxia, and, eventually, necrosis. Thus, branching enables the tumor to minimize the distance from inner cells to external nutrients, contributing to cancer survival and further development. We have also used our model to perform tissue-scale, personalized simulation of a PCa patient, based on prostatic anatomy extracted from computed tomography images. This simulation shows tumor progression similar to that seen in clinical practice.
authors.affiliation: Departamento de Métodos Matemáticos e de Representación, Universidade da Coruña, 15071 A Coruña, Spain.
authors.forename: Guillermo
authors.initials: G
authors.lastname: Lorenzo
authors.affiliation: Department of Civil and Environmental Engineering, Brigham Young University, Provo, UT 84602.
authors.forename: Michael A
authors.initials: MA
authors.lastname: Scott
authors.affiliation: Department of Information Technology, Brigham Young University, Provo, UT 84602.
authors.forename: Kevin
authors.initials: K
authors.lastname: Tew
authors.affiliation: Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712-1229; hughes@ices.utexas.edu.
authors.forename: Thomas J R
authors.initials: TJ
authors.lastname: Hughes
authors.affiliation: Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213.
authors.forename: Yongjie Jessica
authors.initials: YJ
authors.lastname: Zhang
authors.affiliation: Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213.
authors.forename: Lei
authors.initials: L
authors.lastname: Liu
authors.affiliation: Departamento de Métodos Matemáticos e de Representación, Universidade da Coruña, 15071 A Coruña, Spain.
authors.forename: Guillermo
authors.initials: G
authors.lastname: Vilanova
authors.affiliation: Departamento de Métodos Matemáticos e de Representación, Universidade da Coruña, 15071 A Coruña, Spain.
authors.forename: Hector
authors.initials: H
authors.lastname: Gomez
mesh_terms: D049109:Cell Proliferation; D006801:Humans; D007610:Kallikreins / Q000097:blood; D008297:Male; D008954:Models, Biological; D017430:Prostate-Specific Antigen / Q000097:blood; D011471:Prostatic Neoplasms / Q000097:blood / Q000473:pathology*
chemical_list: C549870:KLK3 protein, human; D007610:Kallikreins; D017430:Prostate-Specific Antigen
keywords: isogeometric analysis; personalized; phase field; prostate cancer; tissue scale