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 on cancer biology cancer progression and response to chemotherapy. Successful therapeutic agents must 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 distin- focus on one or more phases of cancer progression guish between various underlying mechanisms governing (i.e., avascular, angiogenesis or vascular) and can typically be tumor growth [11,12]. In parallel, a critical weakness of theoreti- categorized as either a discrete, continuum or hybrid cal models is their plasticity in uncritically recapitulating train- approach [11,13,14]. Continuum models draw upon principles ing data, without regard to the model’s actual validity and pre- from fluid and continuum mechanics and describe cancer- dictive capability. Nevertheless, modeling can provide related variables, such as cell population, nutrient concentra- investigators with tools to run computational experiments that tion, oxygen distribution and growth factor concentrations as would otherwise be very difficult or impossible to recreate in an continuous fields by means of differential equations [13]. By experimental setting (e.g., varying adhesion forces between cells contrast, cellular automaton (CA) models describe the or varying membrane permeabilities of a particular cell line); dynamics of discrete elements (e.g., tumor cells) whose states

1362 Expert Rev. Anticancer Ther. 6(10), (2006) In silico cancer progression and drug response

Nanotechnology module

Cellular scale Subcellular scale Genetic scale Parameter definitionss • Cell contact • Cell signaling • Combination of • Tumor vasculature • Cell stress pathways genetic mutations pore-size: leakiness • Cell cycle profiles • Nanoparticle size • Nutrient • RES uptake rate • Drug release rate • Active transport mechanisms Tumoral scale Surrounding tissue Experimental support • Tumor versus host affinity • Tumor morphology • ECM degradation • In vivo tumors from • Material properties • Vascularity changes mice models • Nutrient • Immune response • In vitro tumor spheroid models • Human patient MRI • Cell-culture studies Vasculature module Chemotherapy module Genotype module Experimental support Experimental support Experimental support • DC MRI data • In vivo/in vitro • Protein/gene-chip • In vivo/in vitro cytotoxicity data array of tumor biopsy experiments • Drug mechanisms of determines relevant charactarizing model transport and action gene expression levels parameters • Combination therapy

Angiogenesis Blood flow Pharmacokinetics Pharmacodynamics Genotype model • TAF distribution • Nutrient delivery • Compartment • Stochastic model • Determine set of • EC density • Drug delivery modeling describing describing drug parameters governing • Fibronectin density drug transport and effect on cells tumor growth and in ECM delivery to target • Based on drug response to therapy • Vasculature morphology mechanism of action

Expert Review of Anticancer Therapy

Figure 1. Outlook for a multiscale cancer simulation under development in the mathematical oncology community. A multiscale cancer simulation is founded on the integration of experimental data and mathematical models. It should provide valuable insights into the cancer phenomenon and establish a platform information technology for analyzing the effectiveness of chemotherapeutic drugs with the potential to extend patients’ pain-free survival and cost-effectively and efficiently screen drug candidates during the drug development process. Modules are developed and coupled via sharing of information. DC MRI: Dynamic contrast magnetic resonance imaging; EC: Endothelial cell; ECM: Extracellular matrix; RES: Reticuloendothelial system; TAF: Tumor angiogenic factor. are governed by a set of deterministic and/or probabilistic be taken to produce truly predictive tumor simulators. Proc- rules. The state evolution of these elements can be tracked esses occurring at various length and time scales must be cou- through both space and time. Hybrid cancer modeling pled appropriately in order to capture all the dynamics approaches combine continuum fields with CA descriptions. involved. Previous works have developed multiscale systems In particular, substances such as oxygen, nutrient, drug and modeling complex biological processes, such as cancer [13,16–18], growth factors can be Authordescribed as a continuum in the tumor the Proofheart and lung [19–22], and various phenomena related microenvironment, while individual CA elements dynamically to developmental biology [23,24]. In particular, Jiang and col- evolve in response to local substance concentrations. leagues [18] and Alarcon and colleagues [13,16] present frame- works for building multiscale cancer progression models capa- Multiscale simulation ble of integrating a hierarchy of processes at varying length and The literature devoted to the theoretical investigation of solid time scales. Most cancer models and multiscale tumor growth and angiogenesis using continuum and CA systems [11,13,16–18,25–30] primarily produce 1D and 2D simula- modeling approaches has been reviewed in depth by Araujo and tions that are limited in their ability to capture complex in vivo McElwain [11], Moreira and Deutsch [14], and Mantzaris and tumor morphologies and microenvironment. The aim of this colleagues [15]. While most of the models described within these perspective is to describe strategies for overcoming these limita- reviews are able to provide useful insight into cancer-related tions by developing a framework focusing on accurately pre- processes occurring at a particular length and time scale, they dicting the 2D and 3D distribution of oxygen, nutrients and do not address the fundamental problem of how phenomena at growth factors in the microenvironment, evolution of complex different scales are coupled [13]. The multiscale complexity of tumor morphology, and tumor response to various treatment cancer progression warrants a multiscale modeling approach to strategies. The underlying models of the multiscale system will

www.future-drugs.com 1363 Sanga, Sinek, Frieboes, Ferrari, Fruehauf & Cristini be founded on biological principles and controlling parameters released from the necrotic tissue of a tumor lesion into sur- will be adjusted according to experimental and clinical data, rounding tissue [34]. These proteins create a chemical gradient thus developing a tumor simulator capable of producing more that triggers endothelial cells (ECs) from parent vessels in the in vivo-relevant predictions. pre-existing vasculature to migrate towards the tumor (chemo- taxis). Eventually, through a number of complex mechanisms, Modular development of a multiscale cancer simulation: the accumulation of ECs forms finger-like capillary sprouts earlier models extending from a parent vessel. Analogous to plant growth, This section provides a brief overview of a select group of these sprouts extend and grow towards the tumor along the tumor growth, angiogenesis and pharmacology models serv- chemical gradient guided by the migration of the sprout-tip. ing as the inspiration and foundation for efforts to develop a The interaction between ECs and the extracellular matrix multiscale cancer simulator. (ECM) itself is also significant in directing the sprout-tips. Fibronectin is generated and adheres to the matrix, serving to Tumor growth guide the direction of endothelial cell progression via a process Cristini and colleagues were among the first to advance mode- called haptotaxis, similar and complementary to chemotaxis. ling of complex tumor morphologies beyond the limited capa- Once capillary sprouts from the parent vessel extend far enough bilities of mathematical linear analyses and into the realm of towards the tumor, they tend to lean towards each other and nonlinear computer simulation [31]. The multifaceted nature of form tip-to-tip and tip-to-sprout fusions called anastomoses cancer requires sophisticated, nonlinear mathematical models to (thought to be caused by haptotaxis) [35,36]. Through this proc- capture more realistic growth dynamics and morphologies. ess of anastomosis, an initial network of poorly perfused, inter- Boundary-integral simulations [31] of classic continuum-based connected immature vessels is formed. The previously described tumor models [25–30] determined that a reduced set of two non- process of angiogenesis and subsequent anastomoses occurs in a dimensional parameters (related to mitosis rate, apoptosis rate, repetitive fashion using the initial network as parent vessels, cell mobility and cell adhesion) regulate morphology and growth thereby producing an extended capillary bed concentrated in (invasiveness) of avascular and vascularized tumors. In this the tumor. However, the neovasculature is irregular and poorly model, there is no morphological representation of vasculature, perfused in comparison with normal tissue vasculature and will rather the effect of vascularity is quantified by a parameter relat- be portrayed as a biological barrier to anticancer treatment ing the concentration of nutrient in the blood, nutrient transfer efficacy in upcoming sections. rate from blood to tissue and nutrient consumption by the cells. Anderson and Chaplain developed a tumor-induced angio- Essentially, critical conditions were predicted that separate com- genesis model with the ability to follow the motion of ECs at pact, noninvasive mass growth from unstable, fingering, infiltra- the capillary tips and control important processes, such as pro- tive progression [31]. However, further analysis demonstrated that liferation, branching and anastomosis [35]. Their model uses a highly vascularized tumors tend to grow in compact, nearly hybrid approach (i.e., both continuum and discrete modeling) spherical shapes showing little or no sign of invasiveness. This and focuses on three significant variables related to angiogenesis: unexpected prediction suggests that tumors could maintain sta- EC density, and PAP and fibronectin concentrations. ble morphology under normoxic microenvironmental condi- The continuum component of the Anderson and Chaplain tions. This result is supported by experimental observations indi- model describes the evolution of EC, PAP and fibronectin cating that hypoxia stimulates invasiveness and tumor distributions using a reaction-diffusion system of three partial fragmentation [32,33]. In later sections of the present article, differential equations. The equation describing EC distribu- tumor simulators built upon this framework and their impor- tion accounts for three major components: small amounts of tance in studying cancer therapy will be discussed, together with random motion possibly dependent on PAP concentration recent experimental confirmation.Author (i.e., diffusion); Proof general EC migration owing to chemotaxis; and EC adhesion to ECM owing to an interaction with Tumor-induced angiogenesis fibronectin (i.e., haptotaxis). The equation describing the Angiogenesis is the process by which cancers recruit enhanced evolution of PAP concentration uses an uptake term repre- blood supply to provide the oxygen and nutrients that are com- senting the binding of PAP to EC as they migrate through the monly considered necessary to support growth into larger, more tissue. The equation describing the evolution of fibronectin invasive tumor masses. As is the case with tumor growth, concentration includes terms representing fibronectin synthe- tumor-induced angiogenesis is a topic receiving considerable sis by endothelial cells as they migrate through the ECM, and attention from the biological modeling community and has a presumed degradation. Fibronectin exists in the ECM in been extensively reviewed (e.g., Mantzaris and colleagues [15]). bound form and is not freely diffusible, therefore no diffusion term is included. Mathematical model for tumor-induced angiogenesis The discrete component of the angiogenesis model uses a Angiogenesis is believed to be initiated by proangiogenic pro- random-walk model, which governs the movement of individ- teins (PAP), such as vascular endothelial growth factor (VEGF), ual ECs at the capillary sprout tips. The model essentially that have been induced by a lack of oxygen and nutrients to be tracks the migration of sprout tips and presumes the shape of

1364 Expert Rev. Anticancer Ther. 6(10), (2006) In silico cancer progression and drug response the full sprouts based on the sprout tip paths. Using a discre- model to investigate how adaptive remodeling affects oxygen tized version of the continuum model, the individual motion and drug supply to tumors. Alarcon and colleagues also modeled of the EC sprout tips is governed by probabilities of the EC the vascular adaptation effects in an effort to study inhomogene- being stationary or moving left, right, up or down; these prob- ity of oxygen distribution in tumors and the consequential role abilities are functions of local fibronectin and PAP of hypoxic cells in tumor invasion [13]. More recently, McDou- concentrations [35,36]. Predetermined rules for branching, anas- gall and colleagues modified their angiogenesis model to simul- tomosis and cell proliferation produce the overall morphology taneously couple vessel growth with blood flow to dynamically of realistic tumor neovasculature. include the effects of vascular adaptation [41], rather than adapt the vasculature a posteriori like Stephanou and colleagues [36] and Extension of Anderson & Chaplain angiogenesis model: Alarcon and colleagues [13]. blood flow The abnormal nature of tumor vasculature compared with Pharmacology & drug efficacy healthy tissue vasculature has been addressed [5]. Irregular In the event that a cancer has metastasized, systemic treatment tumor vasculature leads to restricted and inhomogeneous drug is generally necessary in the form of chemotherapy delivered to and nutrient extravasation to tumor tissue, which may exacer- the primary and secondary tumors through the bloodstream. bate the situation by selecting for highly resistant clones. Drugs must overcome various resistance mechanisms and barri- Anderson and Chaplain’s angiogenesis model appears to cap- ers that affect their efficacy en route to their respective targets, ture the irregularity of tumor vasculature through appropriate thus producing the overall MDR phenomenon. Individual adjustment of the governing mathematical parameters. How- mechanisms and barriers occur at different scales. At the sub- ever, their model only describes the physical structure of the cellular and cellular scale, there exists a range of drug capillary network. Nutrient, oxygen and drug distributions in a influx/efflux pumps, changes in the expression of topoisomer- tumor can be modeled in a simplified fashion by using the ases and alterations in metabolic pathways (e.g., influencing Anderson and Chaplain vasculature as a source boundary con- drug metabolism, DNA repair and/or apoptosis). At the tumor dition in a diffusion–reaction system. In reality, nutrient, oxy- and body scale, resistance can be due to normal clearance gen and drug delivery depends on blood flow through the vas- mechanisms (e.g., urinary system, reticuloendothelial system or culature; therefore using the entire vasculature as a uniform the blood–brain barrier), abnormal tumor vasculature, tumor source with blood–tissue transfer proportional to local pressures microenvironment, and tumor 3D structure [3]. Consequently, is a rather elementary description. these biobarriers impede the delivery of chemotherapeutic McDougall and colleagues developed a direct extension of drugs at effective concentrations to all cancer cells. the Anderson and Chaplain angiogenesis model [35] by describ- ing the generated vascular networks as a series of straight, rigid Pharmacokinetics cylindrical capillaries that join adjacent nodes [36]. Blood flow is In the study of drug delivery, it is common to conceptualize modeled through the cylindrical vascular network by modeling the organism as a system of interconnected pools called com- the elemental flow rate in each segment with Poiseuille’s Law, partments. The investigation of the properties of these com- which describes flow rate as a function of capillary lumen, fluid partments and the material fluxes between them is termed viscosity, capillary length and pressure drop. Using this simple ‘compartment modeling’ [42]. Conventional pharmacokinetic flow model, McDougall and colleagues identified tumor neo- (PK) models use compartment modeling to investigate cellu- vasculature as a biobarrier to chemotherapy [36]. Results of their lar drug-uptake and intracellular drug interactions, as well as simulations indicated that the highly interconnected nature of provide insight into modeling cellular-scale mechanisms con- irregular vasculature produced by tumor-induced angiogenesis tributing to drug resistance. For example, a standard three- could cause low rates Authorof drug delivery to the tumor with the compartmentProof model was used by Dordal and colleagues to potential for the drug to actually completely bypass the entire investigate cellular drug uptake [43]. Their objective was to mass depending on the tumor shape and consequent proang- quantify increased efflux, decreased intracellular sequestra- iogenic protein distribution. Additionally, the simulation tion and decreased membrane permeability as they relate to a results suggest that drug delivered by bolus injection suffers reduction in drug effectiveness. Using flow cytometry, they from severe dilution, thereby reducing drug efficacy. assessed the cellular uptake of doxorubicin and fluorescent Stephanou and colleagues [37] extended the work of McDou- rhodamine-123 in drug-resistant and -sensitive cancer cells. gall and colleagues [36] by developing an algorithm that normal- By fitting the experimental data to the compartmental izes vasculature produced by Anderson and Chaplain’s angio- model, kinetic parameters for both inward and outward genesis model [35]. They examined how pruning vessels by transport were obtained and used to quantify the relative antiangiogenic drugs might affect blood flow distribution and importance of the previously mentioned cellular mechanisms. consequently drug delivery to tumors. Their work included Specifically, their results indicate that of the three cellular blood flow simulations in fully 3D vasculature. Stephanou and mechanisms modeled, decreased intracellular sequestration in coworkers later included vascular adaptation effects [38], due to a nonexchangeable compartment is quantitatively the most shear stress generated by flowing blood [39,40], to the angiogenesis significant contributor towards drug resistance [43]. Similarly,

www.future-drugs.com 1365 Sanga, Sinek, Frieboes, Ferrari, Fruehauf & Cristini compartment modeling can be applied to investigate addi- pharmacology. The focus will now be on strategies for the tional components affecting drug delivery, such as extracellular development of a higher order computer simulator capable of drug binding and target repair mechanisms. customizing cancer drug therapy based on cancer-specific infor- mation and built upon the fundamental framework described Pharmacodynamics in the preceding sections. Here, we present current develop- While PK describes drug penetration, pharmacodynamics ments in simulation technology, including the determination of (PD) describes drug cytotoxicity. Although the mechanisms model parameter values and validation of their performance contributing to drug effects are incompletely understood, sev- based on experimental in vitro and in vivo data. eral phenomenological models adequately yield fractional cell survival, S, as a function of concentration–time exposure his- Model descriptions tory. The Hill-type model S = (1 + Axm)-1 is often used, where Zheng and colleagues produced a first-generation multi- x is a measure of cellular damage, such as extra- or intracellular dimensional tumor simulator employing a sharp-interface area under the curve (AUC). In turn, AUC is given as the inte- (level-set) finite-element numerical method for tracking the gral of concentration with respect to time ∫Ctd . Another pos- tumor boundary [47]. This model is capable of simulating 2D sibility is the exponential kill model S = e-kx, where x again is a tumor evolution through the major phases of growth, including suitable measure of damage and k is a constant. While these avascular dormancy, neovascularization and subsequent rapid are perhaps the simplest PD models in use, other equations expansion and infiltration of host tissue. Wise and colleagues can be employed. recently produced a second-generation 3D tumor simulator A study by El-Kareh and Secomb investigated several meas- employing a more physically accurate diffuse-interface formula- ures of cellular damage in conjunction with the Hill-type model tion on a finite-difference framework, which can more realisti- given above to determine which provided the best fit to experi- cally represent tissue interfaces and clonogenic mental data [44,45]. Their investigation was prompted by the heterogeneity [48]. Both simulators not only serve to model observation that models employing extracellular AUC consist- tumor progression, but also provide test-beds for therapeutic ently overestimated cytotoxicity in cases of extended exposure to strategies and hypotheses (FIGURES 2 & 3) [49,50]. the drugs cisplatin and doxorubicin. Experimentally, toxicity These models build on the continuum-based approach used would achieve a plateau, above which continued exposure, even by Cristini and colleagues, which considers tumor mass as an to continually refreshed drug, would have no effect. To explain incompressible and viscous material that locally expands and this, they hypothesized that it was not the time of exposure contracts in correspondence to variable rates of cell mitosis and per se that correlated with cytotoxicity, but rather the peak level apoptosis [31]. Tumor cells themselves are not individually rep- of DNA-bound drug [44]. Accordingly, they used this measure resented. In Zheng and colleagues’s formulation, local lesion and showed that for short exposure times, the delay in achieving environment is modeled as three sharply demarcated noninter- DNA-bound drug equilibrium could explain increasing cyto- secting domains: viable tumor, necrotic tissue and host toxicity in time. Various experimental cell survival data were fit tissue [47]. Although Wise and colleagues’ diffuse-interface for- to determine appropriate values for the constants A and m. The mulation uses a similar partitioning of the lesion environment new model was compared with previous models describing the into tissue domains, boundaries are not as strictly defined [48]. relationship between cytotoxicity and exposure time. El-Kareh Instead, at a given location, intermixing of several cancerous and Secomb’s model consistently proved to be the best fit even clones along with necrotic and host tissue can be represented by for long exposure in in vitro datasets [46], establishing that peak specifying their relative mass fractions. This cannot be done in DNA-bound cisplatin is a stronger indicator of cytotoxicity the sharp interface model and is a critical improvement towards than extra- or intracellular concentrations. Later, they extended realistically simulating mutation-driven heterogeneity. Please the model to doxorubicin [45]Author. Experimental evidence suggests and colleagues Proof were amongst the first to apply multiphase mod- that doxorubicin has two cytotoxic mechanisms, one involving eling to tumor growth by capturing both tumor cells and extra- topoisomerase II inhibition by intracellular drug and the other cellular fluid as separate continuum phases [51,52]. Work by involving apoptosis induction via extracellular drug. El-Kareh Ward and King [53,54] and Breward and colleagues [55] followed and Secomb proposed a model that combines the effects of both suit by also modeling avascular cancer growth as a two-phase mechanisms into the cellular damage by summing peak intra- description comprised of tumor tissue and dead tissue (extracel- and extracellular drug concentrations. Similar to the cisplatin lular space). This multiphase modeling is needed to capture model, their doxorubicin PD model provides better fits to avascular tumor growth as live tumor cells proliferate into the in vitro cytotoxicity datasets than previous models [45]. dead tissue space. Breward and colleagues extended their avas- cular model [54] to describe vascular tumor growth, thus incor- Integrated tumor simulation: porating a third phase to describe the spatial and temporal dis- foundations for a multiscale simulator tribution of blood vessels [56]. Along similar lines, Wise and Thus far, this perspective has focused on providing a funda- colleagues also used a multiphase modeling approach by cap- mental overview of key cancer modeling efforts in the areas of turing the evolution and interactions between intermixing mul- tumor growth, tumor-induced angiogenesis, blood flow and tiple tumor species, necrotic tissue, host tissue and interstitial

1366 Expert Rev. Anticancer Ther. 6(10), (2006) In silico cancer progression and drug response

8 A B 5.0 6 4.5 4.0 4

3.5 R: tumor radius 2 3.0

2.5 y 0

2.0 -2 1.5

Tumor radii (R and r) Tumor -4 1.0 r: necrotic radius 0.5 -6 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 -8 Normalized time (t) -8-6 -4 -2 0 246 8 x C 30 D B C 20 A D 10 10 8 0 6 4 -10 2 Z F E 0 0 -20 2 2 4 4 XY 6 6 -30 8 8 -30 -20 -10 0 10 20 30 10

Figure 2. Examples of simulated tumor evolution. (A) Byrne and Chaplain’s necrotic tumor model with a specific apoptosis rate. This model describes the shrinkage of tumor and necrotic rim. Reprinted from [29], © 1996, with permission from Elsevier. (B) Cristini and colleagues’ nonlinear continuum-based boundary- integral model, which was among the first to capture complex tumor morphologies. Adapted from [31], © 2003 Kluwer Academic Publishers. With kind permission from Springer Science and Business Media. (C) Zheng and colleagues’ [47] sharp-interface level-set model of tumoral lesion, which captures complex tumor progression including tumor-induced angiogenesis; A: Tumor boundary; B: Neovasculature; C: Viable tumor tissue; D: Necrotic tumor tissue; E: Host tissue; and F: ‘Free’ endothelial cells migrating from parent vessel (not shown). Reprinted from [45], © 2005, with permission from Elsevier. (D) Wise and colleagues’ [48] diffuse- interface model, which captures complex tumor morphology and clonogenic heterogeneity in 3D (angiogenesis not shown). fluid [48]. Araujo and McElwainAuthor recently proposed a multiphase modelProof motion through porous substrates (i.e., a continuum of model of tumor growth that includes a solid phase representing cells flowing through the extracellular matrix). Morphology, espe- the extracellular matrix, in an effort to more accurately capture cially as it pertains to invasiveness, is affected by parameters that residual stresses [57]. model cell adhesion, for instance through the definition of an While it is the growth and regression of lesion tissue that is of equivalent surface tension at the tumor boundary [27]. Based on primary interest, other processes support and interact with this inputs from other components, the growth module produces a growth, necessitating a modular design in which simulator com- cell displacement (velocity) field and advects the tumor boundary ponents are dedicated to process management. The major compo- in the case of Zheng and colleagues’ method [47], and the species nents essential to basic lesion simulation are specific to growth mass fractions in the case of Wise and colleagues’ method [48]. and regression, nutrient delivery and angiogenesis. Beyond these, Vasculature is incorporated into these simulators as an angio- modules pertaining to genetic mutation, cell-cycle and phenotype genesis module inspired by Anderson and Chaplain’s angiogen- specifics, and therapy can be added to provide pertinent informa- esis model [33,47], linked to tumor growth through the release of tion from smaller spatial and temporal scales. The growth and tumor angiogenic regulators by necrosing tumor tissue. The regression component postulates that cell velocity is proportional transition between avascular and vascular tumor growth is to pressure gradient (Darcy’s law), which is commonly used to marked by the recruitment of microvasculature from local

www.future-drugs.com 1367 Sanga, Sinek, Frieboes, Ferrari, Fruehauf & Cristini

Tumor boundary A B

Necrosis

Tumor boundary D C

Necrosis

Figure 3. Correspondence between in silico tumor progression and in vitro tumor spheroid growth. (A) Example of a fairly compact in vitro glioma spheroid with high levels of cell adhesion. (B) An in silico representation of a compact tumor based on appropriate input parameters. (C) Example of an in vitro glioma spheroid with low levels of cell adhesion. The formation of subspheroids indicates an overall morphological instability. (D) An in silico representation of an unstable tumor with low cell adhesion. Bar: 130 mm. Adapted from [49] with permission from the American Association for Cancer Research. blood vessels (i.e., angiogenesis). The governing processes of Maintaining awareness that these properties probably change angiogenesis are still very much in debate, but one proposed in vivo, it is believed that when enough information is known mechanism followed by Anderson and Chaplain’s model grows regarding the mechanisms that give rise to a cell’s behavior, new vessels from parent vessels due to chemotaxis of endothe- whether that be in a dish or in a living organism, the appropriate lial cells along an angiogenic regulator gradient towards the interplay of these mechanisms via a computer model can predict tumor [33]. ECs also interact with the extracellular matrix in a not only individual cell behavior, but also that of cellular aggregates process known as haptotaxis. within a given set of environmental conditions. This line of reason- Underlying these componentsAuthor are sophisticated numerical ing is justifiedProof by the success of cell automaton models in predict- algorithms, including adaptive computational meshes [58,59], ing cell and tissue behavior, suggesting that gene expression infor- that enable high-resolution rendering of complex tumor morph- mation and cell-signaling mechanisms involved in determining cell ologies, including fingering, invasion and reconnection, across behavior can be reduced to a subset of governing rules [60–62]. multiple length scales at the minimum computational expense. Antiangiogenic therapies target tumor neovasculature with the intention of disabling a tumor’s source of oxygen and nutrients. Simulation as an investigative tool: However, a recently proposed concept termed ‘diffusional insta- integration of experimental data with theoretical modeling bility’ suggests that antiangiogenic therapies may actually trigger A key aspect of the successful development of an advanced simu- tumor instability and tissue invasion [49]. Based on simulations of lator of in vivo tumor growth is to both derive fundamental para- tumor growth, Cristini and colleagues hypothesized that complex meter values from, and validate simulator performance through, tumor morphologies leading to local tissue invasion are caused by in vitro and in vivo experimental (and clinical) results. Often, the oxygen and nutrient gradients [49]. These gradients result in process begins with elementary properties of cells growing in regions of hypoxia and acidosis, which directly increase tumor monolayer, such as doubling time, oxygen and glucose consump- invasiveness by increasing cell motility through the production of tion, response to confluence, and uptake and response to drugs. autocrine motility factor, expression of tumor urokinase

1368 Expert Rev. Anticancer Ther. 6(10), (2006) In silico cancer progression and drug response plasminogen activator receptor, production of cathespsin B and experimentally derived parameter estimations, thereby estab- upregulation of hepatocyte growth factor [63–65]. Frieboes and col- lishing a more rigorous platform for analyzing the effective- leagues tested the hypothesis using experimentally derived para- ness of chemotherapeutic drugs (FIGURE 4). PKPD modeling is meters as inputs to the simulator [66]. The experiments varied glu- well established, with representative examples given by cose and serum conditions for in vitro human and rat Panetta [68], Gardner [69], Lankelma [70] and Jackson [71]. The glioblastoma tumor spheroids, yielding parameters relating tumor first two researchers closely examined cellular behavior with shape and relative nutrient concentration. Subsequently, simula- regard to drug, such as the fraction and sensitivity of cycling tions were used to predict and interpret in vitro tumor spheroid versus quiescent cells, response to cycle phase-specific and morphology and invasiveness. Accordingly, simulations using the nonspecific drugs, and response to cytotoxic and cytostatic experimentally determined parameters suggested that tumors drug combinations. The latter two are more concerned with might form shapes that maximize cellular exposure to oxygen, lesion scale PK effects, such as drug exposure of inner regions nutrients and growth factors by correspondingly adjusting cell of spheroids and cancer islets, and the dynamics of tumor proliferation and adhesion. Macklin and Lowengrub further response to various dosing regimes. While the model per se supported these prediction s in their simulations [67]. developed by Cristini and coworkers is not necessarily an Results of these three studies exemplify the usefulness of extension or refinement of these previous efforts, its coupling integrating experimental and theoretical research to develop with Zheng and colleagues’ tumor growth and angiogenesis valuable insight into explaining biological phenomena. Exper- simulator represents advanced modeling technology, ena- imentally derived parameters were used to drive the realism of bling the simulation and analysis of chemotherapy applied to the tumor simulators, while also interpreting nutrient gradi- vascularized in vivo tumors [47]. ents, resulting from the presence of multiple cell species, While this PKPD model was designed explicitly for cisplatin inherent diffusion limits and therapy as a mechanism for local and doxorubicin, since their primary mechanisms of action have tumor infiltration. been well characterized and both drugs are widely used, the intention is that it may be adapted to simulate therapy using Predictive modeling of chemotherapy & antiangiogenic other drugs. During a simulated intravenous drug bolus admin- treatment: implications for drug development istration, concentration is assumed constant along the vascula- Chemotherapy simulations using a 2D tumor model ture, which acts as a source throughout the tumor. Concentra- Therapy simulations performed recently by Sinek and colleagues tion subsequently decreases as drug diffuses through using Zheng and colleagues’ tumor simulator [47] along with interstitium and is taken up by cells. The model accounts Anderson and Chaplain’s vasculature model [33] were among the explicitly for tissue- and cell-level biobarriers, tracking drug first to be performed in a true multidimensional (rather than from the point of extravasation through lesion interstitium and cylindrically or radially symmetric) and vascularized setting. cell membranes, and into intracellular organelles and target. While these simulations used an elementary one-compartment The amount and time of exposure of DNA-bound drug then model (lesion mass with no cellular resolution) with the vascula- determines its effect throughout the lesion. Each element of the ture serving as the nutrient and drug source, they were neverthe- drug pathway contributes a measure of transport resistance, the less useful in highlighting potential adverse characteristics of end result being diminished and nonuniform drug-to-target tumor response to intravenously supplied cytotoxic drug [50]. presentation and consequent compromised efficacy. By provid- Among these were some of the previously mentioned biobarriers, ing precise control over parameters corresponding to PKPD ele- including the susceptibility of lesion vasculature to collapse under ments, the chemotherapy model can deliver powerful and flexi- pressure generated by cellular proliferation and its consequent ble hypothesis-testing capability. More strategically, it is contribution to nutrient and drug heterogeneity. More impor- envisioned as part of a larger scheme intended to optimize estab- tantly, it was demonstratedAuthor that these heterogeneities may impair lishedProof clinical therapies and to serve as a screening phase towards therapeutic efficacy by precipitating invasive morphology, even in improving overall efficiency and cost effectiveness during the a best-case scenario assuming uniform drug delivery from vascula- drug development process. ture (e.g., by using constant-release ‘smart’ nanovectors uniformly Special attention is paid to intracellular compartments and extravasated along vessels), a single, drug-sensitive cell-type and associated fluxes so that resistance mechanisms can be accu- negligible host toxicity. Other simulations in this study demon- rately modeled. In the case of cisplatin, glutathione conjuga- strated how angiogenic normalization might be of benefit [5,50]. tion and removal from cytosol, as well as DNA repair, are key Although this work provided qualitatively compelling results, mechanisms. The model for doxorubicin includes an addi- more detailed PK and PD are needed for quantitative analysis. tional lysosomal compartment owing to the affinity anthracy- clines express for these organelles and their hypothesized role Incorporation of a multicompartmental pharmacokinetics & in expelling drug via exocytosis. Intercompartmental fluxes are pharmacodynamics model governed by rates (the k’s in FIGURE 4), which are themselves In more recent work by Cristini and coworkers [UNPUBLISHED derived from underlying tissue and cell parameters governing DATA], a multicompartmental tissue- and cell-level PKPD the transport of drug molecules. Some of the more important model for cisplatin and doxorubicin was incorporated based on parameters are drug diffusivity, membrane permeability,

www.future-drugs.com 1369 Sanga, Sinek, Frieboes, Ferrari, Fruehauf & Cristini

()dS ⁄ ()dt = –λsmax{}SF– ,0 –1n λ = M ⁄ ()1 + A – 1s Degradation s 3 m F = 11⁄ ()+ Bs3 κ κ 2 3 where λs is the effect rate of DNA- κ κ bound drug s , M is the maximum possi- Compartment 1 12 Compartment 2 23 Compartment 3 3 Extracellular Cytosolic Nuclear ble effect rate of the drug and A, B, n concentration concentration concentration and m are parameters fit specifically to each drug/tissue. The model has been S κ S S 1 21 2 3 compared with various experimental cytotoxicity data available in the Cisplatin pharmacokinetics Doxorubicin pharmacokinetics literature and proves to be an acceptable method for modeling cell death. This PD model, in combination with the pre- viously mentioned cisplatin and doxorubicin PK models, integrates as a chemotherapy module in a tumor simulator to describe drug delivery from the vasculature to its target, and corresponding tumor regression. Specifi- cally, the drug effect rate (λ ) links the Figure 4. Multicompartmental pharmacokinetics modeling. The top depicts the three-compartment s model used to develop the pharmacokinetics (PK) equations for cisplatin. Compartment 1: Extracellular PD model with the tumor growth (and fluid/matrix; 2: Cytoplasm; 3: Nuclear/DNA-bound drug. Doxorubicin PK is based on a four-compartment regression) module, which tracks local model similar to cisplatin PK with the addition of a lysosomal compartment. The bottom depicts the PK cell densities and resulting cell velocities, equations for cisplatin and doxorubicin. Si represents drug concentration in compartment i, where i =1, 2, and consequently determines whether a 3 and 4 represent extracellular volume, intracellular cytosolic volume, target (e.g., DNA) and organelles simulated tumor grows or regresses. (e.g., lysosomes), respectively, while SM is a DNA saturation parameter relevant to doxorubicin. The parameters kij and kij represent the rate of transfer between compartments, and ki represents a rate of permanent removal from compartment i; these parameters account for important phenomena, such as Chemotherapy simulations

efflux pumps, cell permeability and DNA repair. VC is the volume of a cell and appears in the first equation FIGURES 5 & 6 are typical chemotherapy of each system to reconcile the dimensions of S1 with the dimensions of the other compartment-specific simulations using the model in FIGURE 4, equations. DS is the diffusivity of the drug through interstitial space. demonstrating some recent findings of Cristini and coworkers (UNPUBLISHED transmembrane carrier activity (e.g., PGP and MRP), DATA) regarding heterogeneous nutrient and drug distribution, organelle sequestration and DNA repair. The PDE system of corresponding cell survival, nonuniform tumor regression and equations modeling PK (e.g., cisplatin model in FIGURE 4) is stabilization at a mass far above detectable levels [50]. In particu- capable of tracking the amount of drug both spatially and lar, PKPD input parameters for doxorubicin and cisplatin temporally through multiple compartments based on govern- determined through literature and experiments have been used ing rate parameters. Parameters can be tuned not only to drug to compare the performance of these two drugs. Doxorubicin is and cancer type, but also to cancer grade as well as cellular known to quickly penetrate cell membranes and avidly bind to subtleties of individual patienAuthorts. Initially, parameter values intracellular Proof organelles and DNA, whereas cisplatin enters cells were obtained through experimental data reported in pub- much more slowly and exhibits far less binding [72,73]. These lished literature; however, it is intended that more targeted differences reveal themselves dramatically in FIGURE 5, where histological, cellular and genetic analysis of tissue biopsies will strong gradients of doxorubicin stand in contrast to minor gra- provide information necessary to dynamically determine dients of cisplatin, a behavior governed by the ratio of cellular model parameter values, yielding a truly predictive tool. uptake to diffusive flux. Furthermore, the level of DNA-bound The PD component is a phenomenological model along the doxorubicin declines almost immediately after the 2-h bolus lines of El-Kareh and Secomb’s work [44,45], which also takes infusion, whereas cisplatin within the cytosol continues to into account the extended exposure plateau of cytotoxicity. accrue on DNA for several hours longer, only showing a However, Cristini and coworkers hypothesized that this effect marked decline 8 h after the cessation of infusion. The PD was due to a resistant fraction of cells (F), and that, for a given model furthermore predicts a survival gradient of approxi- DNA-bound level of drug, the remaining sensitive fraction, mately 10% from vessel source to distal tissue face in both S - F, would follow classical exponential kill kinetics. The cases. Taking advantage of the precise control of experimental resulting PD model for both cisplatin and doxorubicin parameters available in silico, the model suggests that this is due describing the surviving fraction of cells S is as follows: to the decrease in nutrients and oxygen, which penetrates

1370 Expert Rev. Anticancer Ther. 6(10), (2006) In silico cancer progression and drug response

A B x 10-19 x 10-17 4.0 t = 4 h 5

3.5 t = 3 h 4 t = 2 h 3.0

t = 2 h 3 t = 1 h 2.5

t = 10 h 2.0 2 t = 3 h

1.5 t = 4 h 1 DNA-binding drug (moles/cell) DNA-bound drug (moles/cell) 1.0 t = 1 h t = 10 h 0.5 0 0 50 100 150 050100 150 Depth (microns) Depth (microns) C D 1.0 1.0 0.9 0.9 0.8 0.8 0.7 0.7

0.6 0.6

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0.4 0.4 Surviving fraction 0.3 Surviving fraction 0.3

0.2 0.2

0.1 0.1

0 0 015050 100 0 50 100 150 Depth (microns) Depth (microns)

Figure 5. Drug delivery to target and tumor response. (A) Simulation of 2-h bolus infusion of doxorubicin penetration, where t corresponds to time after initiation of the bolus. The inset illustrates a slab of tissue next to a vessel releasing drug. (B) 2-h bolus infusion of cisplatin, where t corresponds to time after initiation of the bolus. (C) cell survival after doxorubicin dosing of 0.30 µM whole blood concentration. (D) cell survival after cisplatin dosing of 6.20 µM whole blood concentration. Author Proof approximately 150 µm into tissue before being fully con- simulations of tumor growth linked to angiogenesis, Cristini sumed. Hypoglycemia and hypoxia affect cells in ways that and colleagues hypothesized that complex tumor morph- may create drug resistance [74] and these substrate gradients ologies leading to local tissue invasion are caused by oxygen proportionally decrease cell cycling in the model [47,50]. Sim- and nutrient gradients [49]. Frieboes and colleagues tested this ulation can be used to investigate a tumor’s morphological hypothesis through in vitro experiments using simulations to response to chemotherapy, as well as quantify drug, nutrient predict and interpret in vitro tumor spheroid morphology and pressure distributions within a tumor (FIGURE 6). and invasiveness [66]. Results from this (simplified) model indicated that diffusion gradients of nutrients and growth Antiangiogenic therapy simulations factors could indeed influence tumor morphology and inva- As mentioned earlier, antiangiogenic therapies target tumor siveness (FIGURE 3). Simulations predicted tumor shape as a neovasculature with the intention of disabling a tumor’s source function of cell proliferation and adhesion based on cellular of oxygen and nutrients. However, these therapies may trigger access to oxygen, nutrients and growth factors: low prolifera- tumor instability and tissue invasion through a recently tion rates and high cell adhesion are sufficient to maintain proposed concept termed diffusional instability [49]. Using 2D compact tumor shapes, whereas high proliferation rates and

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30 30 30

20 20 20

10 10 10 0 0 0 -10 -10 -10

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-30 -30 -30 -30-20 -10 0 10 20 -30-20 -10 0 10 20 -30-20 -10 0 10 20 Nutrient Drug Pressure 30 30 30 20 20 20 10 10 10 0 0 0

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Figure 6. Computer simulation of response to chemotherapy. Top three frames show three stages of regression of a simulated tumor undergoing chemotherapy. The next three frames, from left to right, show nutrient, drug and tissue pressure contours corresponding to the second stage of regression. Distribution heterogeneity is significant, underpinning key phenomena that diminish drug efficacy. One such result is the stabilization of regression, as depicted by curve B in the graph. Mass of tumor without chemotherapy is shown by curve A for comparison. Mass and time are in dimensionless units. low cell adhesion promote tumor fingering and eventual for- species with varying nutrient uptake and death rates can also mation of separate tumor clusters. Additionally, there is com- lead to aggressive fingering into surrounding tissue in vivo as putational evidence that the presence of multiple tumor cell a result of therapy [67].

1372 Expert Rev. Anticancer Ther. 6(10), (2006) In silico cancer progression and drug response

Conclusion find that a set of pathways converges on a particular phenotypic Cancer is a multifaceted disease with complex governing result. Thus, it would not be necessary to model each gene and processes occurring at a wide range of temporal and spatial each protein; rather, a surrogate functional token might repre- scales. Biological barriers and MDR mechanisms, such as sent the net function of a related set of genes. For instance, with body clearance systems, tumor neovasculature, drug respect to the apoptotic program, recognizing that a cell’s final influx/efflux pumps, DNA-repair mechanisms, tumor micro- commitment to apoptosis is ultimately determined by mito- environment and 3D structure, exist at each of these scales chondrial pore disposition of Cytochrome C, the openers, and hinder the efficacy of anticancer therapies. Biosimulation including Bax and Bid, could be represented by a single token, based on mathematical modeling of cancer-related phenom- while the closers, including Bcl-2 and Bcl-xL, could be repre- ena might prove to be a valuable tool for integrating the vast sented by another [76]. In this way, numerous and similarly func- amount of data produced by experimental and clinical cancer tioning pathways could be braided into far fewer and more eas- specialists, thus providing a method to analytically investigate ily managed strands. Another device to reduce complexity while cancer progression and drug resistance. Multiscale tumor sim- maintaining accuracy in cell repertoire is to employ stochastic ulation work by Arakelyan and colleagues [75] and Alarcon modeling. For example, while it may be asking for too much to and colleagues [13,16] has examined effects of oxygen/nutrient track all the chemical reactions giving rise to a glial cell’s heterogeneity and antiangiogenic therapies on tumor growth cytoskeletal flexions, its migratory trajectory may be adequately and invasion. These works have proposed that experiments represented by a biased random walk. providing in vivo-evaluated parameters and validating model The use of a cancer simulator in clinical practice or pharma- predictions are necessary. In this regard, highly sophisticated ceutical development is a more difficult question. In the clinic, it tumor simulators are currently underway relying on various must first be decided what role such a simulator would play. mathematical models and using experimentally and clinically Cancer is not a deterministic disease; its driving force, after all, is derived parameters. Simulation studies have already provided genetic mutation. One role currently envisioned – that of indi- insight into tumor morphology and metastasis [49,66] and are vidually tailored therapy – might be a difficult one, even if very expected to help optimize treatment strategies and new drug specific information on a given patient’s cancer is extracted development [50]. through genetic or proteomic analysis. Perhaps the statistical predictions would not be substantially better than today’s empir- Expert commentary ically based prognoses. The history of using in vitro chemosensi- Challenges to the successful design, in silico implementation & tivity assays to assist in patient therapy selection reminds us to utilization of a cancer simulator be cautious [77]. Technically, the design and in silico implementation of a cancer More promising is the use of simulation to enhance pharma- simulator is a monumental task and one that has been tacitly ceutical and novel therapy development. If drug/cell character- ongoing for the past few decades. Beyond this, the question of its istics could be determined adequately through traditional wet- use in clinical practice and pharmaceutical development is open. lab techniques, such as cytotoxicity assays, uptake/efflux assays To say that cancer is a complex disease is an understatement. and blot analyses, the resulting functional parameters could be With an estimated 30,000 genes, each comprised of 3000 bases used as simulation input. The resulting simulation output on average, the human genome is a fantastically complicated would therefore carry weight, at least in terms of hypothesis enigma. Its physical description has only recently been eluci- generation, and guide the next phase of inquiry. It is important dated and, while some of the functions of genes or the proteins to note that the power of this method lies in the relative ease they encode are known, the magnitude of their innumerable with which simulation could be carried out, employing param- potential interactions is certainly overwhelming. A model that eter perturbation to thoroughly explore the response space attempts too boldly toAuthor include everything biologists know beforeProof any cells, animals or humans are ever needed. The sav- regarding the cell and tissue would be far too intractable to ings in resources and lives is certainly powerful motivation in either analyze or simulate, the lightening pace of computational pursuing this line of development. improvement notwithstanding. Of course, this has never stopped scientific inquiry from succeeding, to a very high Five-year view degree, in situations that may be somewhat analogous. After all, The pharmaceutical industry spends an average of one need not fret over the exact shape of an apple, nor the US$500–800 million over a span of 10–15 years per drug devel- positions and quantum states of each of its electrons, in order oped and released into the market [78]. The overall drug-develop- to predict its trajectory to earth. ment process is highly inefficient due to the high failure rate Thus, the challenge in designing a cancer simulator is in (>75%) of the majority of drug candidates in costly clinical choosing appropriate scales of resolution and subsuming trials [79]. These considerations are apparently having an impact unnecessary detail within the chosen level. Since cancer is on the industry, as important players, such as Novartis and Glaxo- inherently multiscalar, this must be done at each scale of SmithKline, are devoting increasingly greater resources to compu- interest. At the level of the genome and its protein products, tational modeling. While the informational aspects of modeling, for example, one could find duplication of pathways, or could such as gene sequencing, expression and the statistical inference of

www.future-drugs.com 1373 Sanga, Sinek, Frieboes, Ferrari, Fruehauf & Cristini their effects, have dominated this discipline for the last decade, the in silico, predicting response before a single subject has been importance of more mechanistic modeling, linking subcellular recruited and assisting in the efficient designs of clinical tests. signaling with cellular phenotype and gross tissue response, is Therefore, it is probable that the rational development of anti- coming to light [80]. The results described in this review exemplify cancer drugs will depend heavily on the type of computational the power of this approach in isolating and explaining determi- modeling described in this paper, and that no serious pharmaceutical nants underlying cancerous progression and therapeutic success. contender will be without some level of in silico research. Simulation can provide a powerful hypothesis test-bed, examining and clarifying recurring patterns critical to the growth of cancer, Acknowledgements shedding light on the most promising avenues towards successful The authors are very grateful to the referees for their thorough anticancer therapies. This translates into an effective tool to and helpful reviews. This work was funded by the National improve drug development by preclinically screening drugs Science Foundation and the National Cancer Institute.

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