Tumor-Immune Interaction, Surgical Treatment, and Cancer Recurrence in a Mathematical Model of Melanoma Steffen Eikenberry 1 *, Craig Thalhauser 2 , Yang Kuang 1 1 Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona, United States of America, 2 Department of Mathematics, University of California Irvine, Irvine, California, United States of America Abstract Malignant melanoma is a cancer of the skin arising in the melanocytes. We present a mathematical model of melanoma invasion into healthy tissue with an immune response. We use this model as a framework with which to investigate primary tumor invasion and treatment by surgical excision. We observe that the presence of immune cells can destroy tumors, hold them to minimal expansion, or, through the production of angiogenic factors, induce tumorigenic expansion. We also find that the tumor–immune system dynamic is critically important in determining the likelihood and extent of tumor regrowth following resection. We find that small metastatic lesions distal to the primary tumor mass can be held to a minimal size via the immune interaction with the larger primary tumor. Numerical experiments further suggest that metastatic disease is optimally suppressed by immune activation when the primary tumor is moderately, rather than minimally, metastatic. Furthermore, satellite lesions can become aggressively tumorigenic upon removal of the primary tumor and its associated immune tissue. This can lead to recurrence where total cancer mass increases more quickly than in primary tumor invasion, representing a clinically more dangerous disease state. These results are in line with clinical case studies involving resection of a primary melanoma followed by recurrence in local metastases. Citation: Eikenberry S, Thalhauser C, Kuang Y (2009) Tumor-Immune Interaction, Surgical Treatment, and Cancer Recurrence in a Mathematical Model of Melanoma. PLoS Comput Biol 5(4): e1000362. doi:10.1371/journal.pcbi.1000362 Editor: Carl T. Bergstrom, University of Washington, United States of America Received October 24, 2008; Accepted March 16, 2009; Published April 24, 2009 Copyright: ß 2009 Eikenberry et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: The research was partially supported by the NSF grant DMS-0436341 and the grant DMS/NIGMS-0342388 jointly funded by NIH and NSF. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: seikenbe@asu.edu Introduction Melanoma, the most dangerous form of skin cancer, arises in the melanocytes and progresses through two well-defined clinical stages. Following a period of radial growth in the epidermis, melanomas may switch to malignant, vertical growth melanoma (VGM) [1]. This switch generally occurs following the onset of angiogenesis and penetration of the basement membrane (BM) separating the dermis and epidermis [2]. These processes are tightly coupled in melanomas [2,3]. Angiogenesis is induced primarily by the release of angiogenic factors by melanoma cells and associated stromal cells and through the restructuring of the extracellular matrix (ECM) that occurs in concert with invasion [4]. Angiogenesis of lymphatic vessels (lymphangiogenesis) also occurs in melanomas and plays a role in lymphatic metastasis [5]. Melanomas are known to produce a number of angiogenic cytokines, the most prominent being vascular endothelial growth factor (VEGF) and basic fibroblast growth factor (bFGF) [2]. VEGF is overexpressed both constitu- tively and in response to hypoxia [6]. Although some angiogenesis may occur before penetration of the basement membrane, intense angiogenesis requires ECM remodeling, which in turn requires the cooperation of stromal cells. Even if the tumor is releasing large amounts of VEGF, most of it is sequestered in the ECM [7]. Fibroblast recruitment is essential for the angiogenic switch. Once recruited by platelet derived growth factor (PDGF) and other cytokines, fibroblasts begin producing ECM degrading matrix metalloproteases (MMPs) [8]. Matrix degradation releases large amounts of sequestered angiogenic growth factors, including VEGF, and eases the penetration of new capillaries [7,8]. MMPs also aid in recruiting stromal cells involved in angiogenesis. MMP-9 induces prolifera- tion and motility of endothelial precursor cells (EPCs) in the bone marrow [8], and MMP-2 recruits VEGF expressing macrophages and leukocytes [9]. Endothelial cells are the predominant cell type in the formation of new vasculature. Endothelial cell migration into the tumoral region is essential for angiogenesis and is facilitated by MMP mediated matrix remodeling [9] and migration up chemotactic and haptotactic gradients [10]. The tumoral vasculature incorpo- rates epithelial cells from the existing vasculature as well as circulating EPCs. The latter are likely important in sustained, intense angiogenesis as they provide a much larger pool of endothelial cells than the native tissue alone can provide [11,12]. Chemotaxis occurs in response to a number of factors, the most important being VEGF. Growing epithelial sprouts extend filopodia, indicating that they, like epithelial cells, can respond to a VEGF gradient [10]. The immune system is able to effectively mobilize against tumor invasion. This occurs mainly through direct tumoricidal action by natural killer (NK) cells and phagocytes, such as macrophages, and PLoS Computational Biology | www.ploscompbiol.org 1 April 2009 | Volume 5 | Issue 4 | e1000362