Mathematical Modeling of Cancer Progression and Response To

Perspective Mathematical modeling of cancer progression and response to chemotherapy Sandeep Sanga, John P Sinek, Hermann B Frieboes, Mauro Ferrari, John P Fruehauf and Vittorio Cristini† The complex, constantly evolving and multifaceted nature of cancer has made it difficult to identify unique molecular and pathophysiological signatures for each disease variant, CONTENTS consequently hindering development of effective therapies. Mathematical modeling and computer simulation are tools that can provide a robust framework to better understand Fundamental considerations cancer progression and response to chemotherapy. Successful therapeutic agents must on cancer biology overcome biological barriers occurring at multiple space and time scales and still reach Role of modeling in cancer research & targets at sufficient concentrations. A multiscale computer simulator founded on the drug development integration of experimental data and mathematical models can provide valuable insights Fundamentals of into these processes and establish a technology platform for analyzing the effectiveness of cancer modeling chemotherapeutic drugs, with the potential to cost-effectively and efficiently screen drug Integrated tumor simulation: candidates during the drug-development process. foundations for a multiscale simulator Expert Rev. Anticancer Ther. 6(10), 1361–1376 (2006) Predictive modeling of Fundamental considerations on from its newly formed vasculature, a tumor chemotherapy & cancer biology may become malignant and rapidly invade antiangiogenic treatment: implications for The physiological processes underlying cancer local tissue, usually acquiring mutations drug development are highly complex, spanning a wide range of enabling navigation through the bloodstream Conclusion interrelated temporal and spatial scales. The and lymphatics to metastasize to other loca- fundamental causes are believed to reside at tions in the body [2]. The nonlocalized nature Expert commentary the genetic level, where mutations enable cells of metastatic cancer limits the success of Five-year view to develop a selective advantage, allowing surgical and radiation treatment approaches; References them to reproduce or prolong life in defiance thus, systemically administered chemother- Affiliations of normal constraints. In time, these cells form apy continues to be the standard option in avascular masses limited to approximately a spite of varied outcomes. Authorfew millimeters in diameter owing Proof to the Tumor neovasculature plays an integral role transport limitations of oxygen and nutrients in the administration of such treatment. It is †Author for correspondence into tissue [1]. As inner layers of the nascent the first tumor-level barrier that an adminis- University of California, Deptartments of Biomedical tumor begin to necrose, tumor angiogenic reg- tered drug molecule must navigate on its Engineering and Mathematics, ulators are released by the tumor mass, which journey to its intended intracellular target, 3120 Natural Sciences II, Irvine, diffuse through the surrounding tissue and and its anatomical and functional irregulari- CA 92697–2715, USA trigger a cascade of events upon arrival at local ties are thought to significantly impair drug Tel.: +1 949 824 9132 vasculature, culminating in the recruitment of distribution to lesion tissue. For standard Fax: +1 949 824 1727 [email protected] vessels that supply blood to the burgeoning therapy, once drug molecules extravasate tumor (i.e., angiogenesis). At this point, the through vasculature, they must diffuse KEYWORDS: vascularized tumor may remain compact and through interstitial space, permeate cell mem- biobarriers, biocomputation, biosimulation, cancer, noninvasive (i.e., benign), in which case it can branes, survive a gauntlet of intracellular chemotherapy, modeling, usually be successfully removed by surgical mechanisms designed to detoxify cells and multiscale, nanotechnology, pharmacokinetics, resection or treated with radiation. Con- finally bind to subcellular targets at sufficient pharmacodynamics versely, upon receiving infusion of nutrients cytotoxic concentrations [3]. This series of www.future-drugs.com 10.1586/14737140.6.10.1361 © 2006 Future Drugs Ltd ISSN 1473-7140 1361 Sanga, Sinek, Frieboes, Ferrari, Fruehauf & Cristini barriers combines to produce an overall reduction in the effi- accordingly, modeling can provide valuable information to cacy of many unrelated anticancer drugs, a phenomenon plan effective biological experiments for testing theoretical called multidrug resistance (MDR) [4], and cannot be over- hypotheses. Data from biological experiments provide neces- come simply by administering more drug, as toxicity to host sary constraints for choosing appropriate model parameters. tissue presents a formidable challenge. Therefore, although pure theoretical or experimental investiga- For conventional chemotherapeutic treatment, strategic dos- tions alone have inherent flaws and limitations, an ideal syn- ing is used to maximize anticancer-drug effects while minimiz- ergy between the two can be approached by using a circular, ing host toxicity. However, recent antiangiogenic treatment recursive work-flow methodology. strategies center around targeting tumor neovasculature instead of the lesion itself. By destroying the vascular bed, the tumor’s Objective source of oxygen and nutrients is reduced, leading to starvation The objective of this article is to first present a brief overview of the mass. Furthermore, such therapies might reduce metasta- of current mathematical and biocomputational modeling of sis by eliminating the escape route into systemic circulation [1]. cancer progression and therapy, followed by a description of In another innovative strategy known as vascular normaliza- the integrative approach that we envision towards the develop- tion, the intent is not to destroy all the vasculature, but rather ment of higher order biocomputational technology, centered to prune it of inefficient branches, thereby normalizing the about a simulator with the capacity to predict in vivo tumor abnormal structure and function of tumor vasculature and growth and response to therapy. A virtual cancer simulator improving delivery of oxygen, nutrients and drugs [5]. Another might provide a means to efficiently and cost-effectively screen promising approach to cancer treatment is the use of nano- drug candidates with the potential of significant savings in vectored therapy, employing nanoscale devices to specifically research and development. An additional, long-term goal of target and deliver drug payloads to cancer cells [6]. These thera- this research is to customize clinical cancer therapy by using pies, along with conventional treatment, are ideal candidates cell-specific tumor information, thereby maximizing benefit to for in silico (computer) modeling, which has the power to offer both patients and providers. insight into their efficacy and potentially develop into a means The endeavor to develop software packages capable of sophisti- for predicting patient-tailored therapeutic regimens [7,8]. cated, in vivo-like tumor simulation will be based on a modular, multiscale development process where individual components are Role of modeling in cancer research & drug development built upon mathematical models simulating disease progression, Developing a detailed understanding of the underlying patho- anticancer drug pharmacology and drug resistance. These are physiology of cancer, its progression, mechanisms of drug then integrated to simulate the disease and possible therapies resistance at various scales, as well as the optimization of drug through a wide temporal and spatial range. This scalable scheme dosing protocols, is the subject of vast amounts of research allows the simulator to be enlarged by adding and appropriately directed towards the development of effective treatment and linking modules (FIGURE 1). This review is structured to familiarize prevention strategies. Owing to the complexity of this disease, readers with key modeling efforts over the past 30 years, inspiring it has proven difficult to assign quantitative weights to each the development of modules in a cancer simulator, examine the component. This may be due, in part, to the nature of experi- current status of cancer simulation, present applications of the mental investigation, where mechanisms are often studied in an simulator in the areas of drug development and optimization and isolated context. It has been suggested that a conceptual frame- indicate challenges for advancing cancer simulation towards work is necessary to fully understand the data produced in higher levels of sophistication. quantity by tumor biologists and clinical oncologists [9–11]. The challenges of better understanding the overall cancer phenome- Fundamentals of cancer modeling non and its treatment mightAuthor benefit from an evaluation of Mathematical Proof models can provide biologists and clinicians mathematical modeling and biocomputation. This approach with tools that might guide their efforts to elucidate funda- can be integrated with biological experiments and clinical trials. mental mechanisms of cancer progression and either improve Traditional clinical and biological experiments require costly current treatment strategies or stimulate the development of investments in both time and materials, and are limited by new ones [13]. Many cancer models have been proposed that equipment precision, human error and the inability to

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