In silico cancer modeling: is it ready for prime time?

Applications of Machine Learning (ML) and Mathematical Modeling (MM) in Healthcare with Special Focus on Cancer Prognosis and Anticancer Therapy: Current Status and Challenges

The use of data-driven high-throughput analytical techniques, which has given rise to computational oncology, is undisputed. The widespread use of machine learning (ML) and mathematical modeling (MM)-based techniques is widely acknowledged. These two approaches have fueled the advancement in cancer research and eventually led to the uptake of telemedicine in cancer care. For diagnostic, prognostic, and treatment purposes concerning different types of cancer research, vast databases of varied information with manifold dimensions are required, and indeed, all this information can only be managed by an automated system developed utilizing ML and MM. In addition, MM is being used to probe the relationship between the pharmacokinetics and pharmacodynamics (PK/PD interactions) of anti-cancer substances to improve cancer treatment, and also to refine the quality of existing treatment models by being incorporated at all steps of research and development related to cancer and in routine patient care. This review will serve as a consolidation of the advancement and benefits of ML and MM techniques with a special focus on the area of cancer prognosis and anticancer therapy, leading to the identification of challenges (data quantity, ethical consideration, and data privacy) which are yet to be fully addressed in current studies.

Nanoparticle-mediated cancer cell therapy: basic science to clinical applications

Every sixth person in the world dies due to cancer, making it the second leading severe cause of death after cardiovascular diseases. According to WHO, cancer claimed nearly 10 million deaths in 2020. The most common types of cancers reported have been breast (lung, colon and rectum, prostate cases), skin (non-melanoma) and stomach. In addition to surgery, the most widely used traditional types of anti-cancer treatment are radio- and chemotherapy. However, these do not distinguish between normal and malignant cells. Additional treatment methods have evolved over time for early detection and targeted therapy of cancer. However, each method has its limitations and the associated treatment costs are quite high with adverse effects on the quality of life of patients. Use of individual atoms or a cluster of atoms (nanoparticles) can cause a paradigm shift by virtue of providing point of sight sensing and diagnosis of cancer. Nanoparticles (1-100 nm in size) are 1000 times smaller in size than the human cell and endowed with safer relocation capability to attack mechanically and chemically at a precise location which is one avenue that can be used to destroy cancer cells precisely. This review summarises the extant understanding and the work done in this area to pave the way for physicians to accelerate the use of hybrid mode of treatments by leveraging the use of various nanoparticles.

Computational reactive-diffusive modeling for stratification and prognosis determination of patients with breast cancer receiving Olaparib

Mathematical models based on partial differential equations (PDEs) can be exploited to handle clinical data with space/time dimensions, e.g. tumor growth challenged by neoadjuvant therapy. A model based on simplified assessment of tumor malignancy and pharmacodynamics efficiency was exercised to discover new metrics of patient prognosis in the OLTRE trial. We tested in a 17-patients cohort affected by early-stage triple negative breast cancer (TNBC) treated with 3 weeks of olaparib, the capability of a PDEs-based reactive-diffusive model of tumor growth to efficiently predict the response to olaparib in terms of SUV_max detected at ¹⁸FDG-PET/CT scan, by using specific terms to characterize tumor diffusion and proliferation. Computations were performed with COMSOL Multiphysics. Driving parameters governing the mathematical model were selected with Pearson's correlations. Discrepancies between actual and computed SUV_max values were assessed with Student's t test and Wilcoxon rank sum test. The correlation between post-olaparib true and computed SUV_max was assessed with Pearson's r and Spearman's rho. After defining the proper mathematical assumptions, the nominal drug efficiency (ε_PD) and tumor malignancy (r_c) were computationally evaluated. The former parameter reflected the activity of olaparib on the tumor, while the latter represented the growth rate of metabolic activity as detected by SUV_max. ε_PD was found to be directly dependent on basal tumor-infiltrating lymphocytes (TILs) and Ki67% and was detectable through proper linear regression functions according to TILs values, while r_c was represented by the baseline Ki67-to-TILs ratio. Predicted post-olaparib SUV*_max did not significantly differ from original post-olaparib SUV_max in the overall, gBRCA-mutant and gBRCA-wild-type subpopulations (p > 0.05 in all cases), showing strong positive correlation (r = 0.9 and rho = 0.9, p < 0.0001 both). A model of simplified tumor dynamics was exercised to effectively produce an upfront prediction of efficacy of 3-week neoadjuvant olaparib in terms of SUV_max. Prospective evaluation in independent cohorts and correlation of these outcomes with more recognized efficacy endpoints is now warranted for model confirmation and tailoring of escalated/de-escalated therapeutic strategies for early-TNBC patients.

Targeting chromosome 12q amplification in relapsed glioblastoma: the use of computational biological modeling to identify effective therapy-a case report

Background

Relapsed glioblastoma (GBM) is often an imminently fatal condition with limited therapeutic options. Computation biological modeling, i.e., biosimulation, of comprehensive genomic information affords the opportunity to create a disease avatar that can be interrogated in silico with various drug combinations to identify the most effective therapies.

Case Description

We report the outcome of a GBM patient with chromosome 12q amplification who achieved substantial disease remission from a novel therapy using this approach. Following next generation sequencing (NGS) was performed on the tumor specimen. Mutation and copy number changes were input into a computational biologic model to create an avatar of disease behavior and the malignant phenotype. In silico responses to various drug combinations were biosimulated in the disease network. Efficacy scores representing the computational effect of treatment for each strategy were generated and compared to each other to ascertain the differential benefit in drug response from various regimens. Biosimulation identified CDK4/6 inhibitors, nelfinavir and leflunomide to be effective agents singly and in combination. Upon receiving this treatment, the patient achieved a prompt and clinically meaningful remission lasting 6 months.

Conclusions

Biosimulation has utility to identify active treatment combinations, stratify treatment options and identify investigational agents relevant to patients' comprehensive genomic abnormalities. Additionally, the combination of abemaciclib and nelfinavir appear promising for GBM and potentially other cancers harboring chromosome 12q amplification.

Macrophage-Targeted Punicalagin Nanoengineering to Alleviate Methotrexate-Induced Neutropenia: A Molecular Docking, DFT, and MD Simulation Analysis

Punicalagin is the most bioactive pomegranate polyphenol with high antioxidant and free-radical scavenging activity and can potentially cure different ailments related to the cardiovascular system. The current research work was envisioned to predict the targeting efficiency of punicalagin (PG) nanoparticles to the macrophages, more specifically to bone marrow macrophages. For this, we selected mannose-decorated PLGA-punicalagin nanoparticles (Mn-PLGA-PG), and before formulating this nanocarrier in laboratory settings, we predicted the targeting efficiency of this nanocarrier by in silico analysis. The analysis proceeded with macrophage mannose receptors to be acquainted with the binding affinity and punicalagin-based nanocarrier interactions with this receptor. In silico docking studies of macrophage mannose receptors and punicalagin showed binding interactions on its surface. PG interacted with hydrogen bonds to the charged residue ASP668 and GLY666 and polar residue GLN760 of the Mn receptor. Mannose with a docking score of −5.811 Kcal/mol interacted with four hydrogen bonds and the mannose receptor of macrophage, and in PLGA, it showed a −4.334 Kcal/mol docking score. Further, the analysis proceeded with density functional theory analysis (DFT) and HOMO–LUMO analysis, followed by an extensive 100 ns molecular dynamics simulation to analyse the trajectories showing the slightest deviation and fluctuation. While analysing the ligand and protein interaction, a wonderful interaction was found among the atoms of the ligand and protein residues. This computational study confirms that this nanocarrier could be a promising lead molecule to regulate the incidence of drug-induced neutropenia. Furthermore, experimental validation is required before this can be stated with complete confidence or before human use.

In Vitro Brain Organoids and Computational Models to Study Cell Death in Brain Diseases

Understanding the mechanisms underlying the formation and progression of brain diseases is challenging due to the vast variety of involved genetic/epigenetic factors and the complexity of the environment of the brain. Current preclinical monolayer culture systems fail to faithfully recapitulate the in vivo complexities of the brain. Organoids are three-dimensional (3D) culture systems that mimic much of the complexities of the brain including cell-cell and cell-matrix interactions. Complemented with a theoretical framework to model the dynamic interactions between different components of the brain, organoids can be used as a potential tool for studying disease progression, transport of therapeutic agents in tissues, drug screening, and toxicity analysis. In this chapter, we first report on the fabrication and use of a novel self-filling microwell arrays (SFMWs) platform that is self-filling and enables the formation of organoids with uniform size distributions. Next, we will introduce a mathematical framework that predicts the organoid growth, cell death, and the therapeutic responses of the organoids to different therapeutic agents. Through systematic investigations, the computational model can identify shortcomings of in vitro assays and reduce the time and effort required to improve preclinical tumor models' design. Lastly, the mathematical model provides new testable hypotheses and encourages mathematically driven experiments.

A mathematical framework for modelling 3D cell motility: applications to glioblastoma cell migration

The collection of 3D cell tracking data from live images of micro-tissues is a recent innovation made possible due to advances in imaging techniques. As such there is increased interest in studying cell motility in 3D in vitro model systems but a lack of rigorous methodology for analysing the resulting data sets. One such instance of the use of these in vitro models is in the study of cancerous tumours. Growing multicellular tumour spheroids in vitro allows for modelling of the tumour microenvironment and the study of tumour cell behaviours, such as migration, which improves understanding of these cells and in turn could potentially improve cancer treatments. In this paper, we present a workflow for the rigorous analysis of 3D cell tracking data, based on the persistent random walk model, but adaptable to other biologically informed mathematical models. We use statistical measures to assess the fit of the model to the motility data and to estimate model parameters and provide confidence intervals for those parameters, to allow for parametrization of the model taking correlation in the data into account. We use in silico simulations to validate the workflow in 3D before testing our method on cell tracking data taken from in vitro experiments on glioblastoma tumour cells, a brain cancer with a very poor prognosis. The presented approach is intended to be accessible to both modellers and experimentalists alike in that it provides tools for uncovering features of the data set that may suggest amendments to future experiments or modelling attempts.

PML Differentially Regulates Growth and Invasion in Brain Cancer

Glioblastoma is the most malignant brain tumor among adults. Despite multimodality treatment, it remains incurable, mainly because of its extensive heterogeneity and infiltration in the brain parenchyma. Recent evidence indicates dysregulation of the expression of the Promyelocytic Leukemia Protein (PML) in primary Glioblastoma samples. PML is implicated in various ways in cancer biology. In the brain, PML participates in the physiological migration of the neural progenitor cells, which have been hypothesized to serve as the cell of origin of Glioblastoma. The role of PML in Glioblastoma progression has recently gained attention due to its controversial effects in overall Glioblastoma evolution. In this work, we studied the role of PML in Glioblastoma pathophysiology using the U87MG cell line. We genetically modified the cells to conditionally overexpress the PML isoform IV and we focused on its dual role in tumor growth and invasive capacity. Furthermore, we targeted a PML action mediator, the Enhancer of Zeste Homolog 2 (EZH2), via the inhibitory drug DZNeP. We present a combined in vitro–in silico approach, that utilizes both 2D and 3D cultures and cancer-predictive computational algorithms, in order to differentiate and interpret the observed biological results. Our overall findings indicate that PML regulates growth and invasion through distinct cellular mechanisms. In particular, PML overexpression suppresses cell proliferation, while it maintains the invasive capacity of the U87MG Glioblastoma cells and, upon inhibition of the PML-EZH2 pathway, the invasion is drastically eliminated. Our in silico simulations suggest that the underlying mechanism of PML-driven Glioblastoma physiology regulates invasion by differential modulation of the cell-to-cell adhesive and diffusive capacity of the cells. Elucidating further the role of PML in Glioblastoma biology could set PML as a potential molecular biomarker of the tumor progression and its mediated pathway as a therapeutic target, aiming at inhibiting cell growth and potentially clonal evolution regarding their proliferative and/or invasive phenotype within the heterogeneous tumor mass.

Combination chemotherapy versus temozolomide for patients with methylated MGMT (m-MGMT) glioblastoma: results of computational biological modeling to predict the magnitude of treatment benefit

Background

A randomized trial in glioblastoma patients with methylated-MGMT (m-MGMT) found an improvement in median survival of 16.7 months for combination therapy with temozolomide (TMZ) and lomustine, however the approach remains controversial and relatively under-utilized. Therefore, we sought to determine whether comprehensive genomic analysis can predict which patients would derive large, intermediate, or negligible benefits from the combination compared to single agent chemotherapy.

Methods

Comprehensive genomic information from 274 newly diagnosed patients with methylated-MGMT glioblastoma (GBM) was downloaded from TCGA. Mutation and copy number changes were input into a computational biologic model to create an avatar of disease behavior and the malignant phenotypes representing hallmark behavior of cancers. In silico responses to TMZ, lomustine, and combination treatment were biosimulated. Efficacy scores representing the effect of treatment for each treatment strategy were generated and compared to each other to ascertain the differential benefit in drug response.

Results

Differential benefits for each drug were identified, including strong, modest-intermediate, negligible, and deleterious (harmful) effects for subgroups of patients. Similarly, the benefits of combination therapy ranged from synergy, little or negligible benefit, and deleterious effects compared to single agent approaches.

Conclusions

The benefit of combination chemotherapy is predicted to vary widely in the population. Biosimulation appears to be a useful tool to address the disease heterogeneity, drug response, and the relevance of particular clinical trials observations to individual patients. Biosimulation has potential to spare some patients the experience of over-treatment while identifying patients uniquely situated to benefit from combination treatment. Validation of this new artificial intelligence tool is needed.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11060-021-03780-0.

In silico authentication of amygdalin as a potent anticancer compound in the bitter kernels of family Rosaceae

Amygdalin a naturally occurring compound, predominantly in the bitter kernels of apricot, almond, apple and other members of Rosaceae family. Though, amygdalin is used as an alternative therapy to treat various types of cancer but its role in cancer pathways has rarely been explored yet. Therefore, present study was intended with the aim to investigate the alleged anti-cancerous effects of amygdalin specifically on PI3K-AKT-mTOR and Ras pathways of cancer in human body. Computational modelling and simulation techniques were used to assess the effect of amygdalin on PI3K-AKT-mTOR and Ras pathways using different level of dosage. It was observed that amygdalin had direct and substantial contribution to regulate PI3K-mTOR activities on threshold levels while the other caner pathways were effected indirectly. Consequently, amygdalin is a down-regulator of a cancer within a specified amount and contribute considerably to reduce various types of cancer in human. Furthermore, in-vitro and in-vivo analyses of amygdalin could be of helpful to authenticate its pharmacological effects.

An on-lattice agent-based Monte Carlo model simulating the growth kinetics of multicellular tumor spheroids

PURPOSE

To develop an on-lattice agent-based model describing the growth of multicellular tumor spheroids using simple Monte Carlo tools.

METHODS

Cells are situated on the vertices of a cubic grid. Different cell states (proliferative, hypoxic or dead) and cell evolution rules, driven by 10 parameters, and the effects of the culture medium are included. About twenty spheroids of MCF-7 human breast cancer were cultivated and the experimental data were used for tuning the model parameters.

RESULTS

Simulated spheroids showed adequate sizes of the necrotic nuclei and of the hypoxic and proliferative cell phases as a function of the growth time, mimicking the overall characteristics of the experimental spheroids. The relation between the radii of the necrotic nucleus and the whole spheroid obtained in the simulations was similar to the experimental one and the number of cells, as a function of the spheroid volume, was well reproduced. The statistical variability of the Monte Carlo model described the whole volume range observed for the experimental spheroids. Assuming that the model parameters vary within Gaussian distributions it was obtained a sample of spheroids that reproduced much better the experimental findings.

CONCLUSIONS

The model developed allows describing the growth of in vitro multicellular spheroids and the experimental variability can be well reproduced. Its flexibility permits to vary both the agents involved and the rules that govern the spheroid growth. More general situations, such as, e. g., tumor vascularization, radiotherapy effects on solid tumors, or the validity of the tumor growth mathematical models can be studied.

Prediction of Outcomes with a Computational Biology Model in Newly Diagnosed Glioblastoma Patients Treated with Radiation Therapy and Temozolomide

PURPOSE

Precision medicine has been most successful in targeting single mutations, but personalized medicine using broader genomic tumor profiles for individual patients is less well developed. We evaluate a genomics-informed computational biology model (CBM) to predict outcomes from standard treatments and to suggest novel therapy recommendations in glioblastoma (GBM).

METHODS AND MATERIALS

In this retrospective study, 98 patients with newly diagnosed GBM undergoing surgery followed by radiation therapy and temozolomide at a single institution with available genomic data were identified. Incorporating mutational and copy number aberration data, a CBM was used to simulate the response of GBM tumor cells and generate efficacy predictions for radiation therapy (RTeff) and temozolomide (TMZeff). RTeff and TMZeff were evaluated for association with overall survival and progression-free survival in a Cox regression model. To demonstrate a CBM-based individualized therapy strategy, treatment recommendations were generated for each patient by testing a panel of 45 central nervous system-penetrant US Food and Drug Administration-approved agents.

RESULTS

High RTeff scores were associated with longer survival on univariable analysis (P < .001), which persisted after controlling for age, extent of resection, performance status, MGMT, and IDH status (P = .017). High RTeff patients had a longer overall survival compared with low RTeff patients (median, 27.7 vs 14.6 months). High TMZeff was also associated with longer survival on univariable analysis (P = .007) but did not hold on multivariable analysis, suggesting an interplay with MGMT status. Among predictions of the 3 most efficacious combination therapies for each patient, only 2.4% (7 of 294) of 2-drug recommendations produced by the CBM included TMZ.

CONCLUSIONS

CBM-based predictions of RT and TMZ effectiveness were associated with survival in patients with newly diagnosed GBM treated with those therapies, suggesting a possible predictive utility. Furthermore, the model was able to suggest novel individualized monotherapies and combinations. Prospective evaluation of such a personalized treatment strategy in clinical trials is needed.

Toward Personalized Computer Simulation of Breast Cancer Treatment: A Multiscale Pharmacokinetic and Pharmacodynamic Model Informed by Multitype Patient Data

The usefulness of mechanistic models to disentangle complex multiscale cancer processes, such as treatment response, has been widely acknowledged. However, a major barrier for multiscale models to predict treatment outcomes in individual patients lies in their initialization and parametrization, which needs to reflect individual cancer characteristics accurately. In this study, we use multitype measurements acquired routinely on a single breast tumor, including histopathology, MRI, and molecular profiling, to personalize parts of a complex multiscale model of breast cancer treated with chemotherapeutic and antiangiogenic agents. The model accounts for drug pharmacokinetics and pharmacodynamics. We developed an open-source computer program that simulates cross-sections of tumors under 12-week therapy regimens and used it to individually reproduce and elucidate treatment outcomes of 4 patients. Two of the tumors did not respond to therapy, and model simulations were used to suggest alternative regimens with improved outcomes dependent on the tumor's individual characteristics. It was determined that more frequent and lower doses of chemotherapy reduce tumor burden in a low proliferative tumor while lower doses of antiangiogenic agents improve drug penetration in a poorly perfused tumor. Furthermore, using this model, we were able to correctly predict the outcome in another patient after 12 weeks of treatment. In summary, our model bridges multitype clinical data to shed light on individual treatment outcomes. SIGNIFICANCE: Mathematical modeling is used to validate possible mechanisms of tumor growth, resistance, and treatment outcome.

Coupled Immunological and Biomechanical Model of Emphysema Progression

Chronic Obstructive Pulmonary Disease (COPD) is a disabling respiratory pathology, with a high prevalence and a significant economic and social cost. It is characterized by different clinical phenotypes with different risk profiles. Detecting the correct phenotype, especially for the emphysema subtype, and predicting the risk of major exacerbations are key elements in order to deliver more effective treatments. However, emphysema onset and progression are influenced by a complex interaction between the immune system and the mechanical properties of biological tissue. The former causes chronic inflammation and tissue remodeling. The latter influences the effective resistance or appropriate mechanical response of the lung tissue to repeated breathing cycles. In this work we present a multi-scale model of both aspects, coupling Finite Element (FE) and Agent Based (AB) techniques that we would like to use to predict the onset and progression of emphysema in patients. The AB part is based on existing biological models of inflammation and immunological response as a set of coupled non-linear differential equations. The FE part simulates the biomechanical effects of repeated strain on the biological tissue. We devise a strategy to couple the discrete biological model at the molecular /cellular level and the biomechanical finite element simulations at the tissue level. We tested our implementation on a public emphysema image database and found that it can indeed simulate the evolution of clinical image biomarkers during disease progression.

Chemoprotection Across the Tumor Border: Cancer Cell Response to Doxorubicin Depends on Stromal Fibroblast Ratios and Interstitial Therapeutic Transport

INTRODUCTION

Increasing evidence suggests that the tumor microenvironment reduces therapeutic delivery and may lead to chemotherapeutic resistance. At tumor borders, drug is convectively transported across a unique microenvironment composed of inverse gradients of stromal and tumor cells. These regions are particularly important to overall survival, as they are often missed through surgical intervention and contain many invading cells, often responsible for metastatic spread. An understanding of how cells in this tumor-border region respond to chemotherapy could begin to elucidate the role of transport and intercellular interactions in relation to chemoresistance. Here we examine the contribution of drug transport and stromal fibroblasts to breast cancer response to doxorubicin using in silico and in vitro models of the tumor-stroma interface.

METHODS

2D culture systems were utilized to determine the effects of modulated ratios of fibroblasts and cancer cells on overall cancer cell viability. A homogenous breast mimetic in vitro 3D collagen I-based hydrogel system, with drug delivered via pressure driven flow (0.5 µm/s), was developed to determine the effects of transport and fibroblasts on doxorubicin treatment efficacy. Using a novel layered tumor bulk-to-stroma transition in vitro 3D hydrogel model, ratios of MDA-MB-231s and fibroblasts were seeded in successive layers creating cellular gradients, yielding insight into region specific cancer cell viability at the tumor border. In silico models, utilizing concentration profiles developed in COMSOL Multiphysics, were optimized for time dependent viability prediction and confirmation of in vitro findings.

RESULTS

In general, the addition of fibroblasts increased viability of cancer cells exposed to doxorubicin, indicating a protective effect of co-culture. More specifically, however, modulating ratios of cancer cells (MDA-MB-231):fibroblasts in 2D co-cultures, to mimic the tumor-stroma transition, resulted in a linear decrease in cancer cell viability from 77% (4:1) to 44% (1:4). Similar trends were seen in the breast-mimetic in vitro 3D collagen I-based homogenous hydrogel system. Our in vitro and in silico tumor border models indicate that MDA-MB-231s at the top of the gel, indicative of the tumor bulk, receive the greatest concentration of drug for the longest time, yet cellular death is lowest in this region. This trend is reversed for MDA-MB-231s alone.

CONCLUSION

Together, our data indicate that fibroblasts are chemoprotective at lower density, resulting in less tumor death in regions of higher chemotherapy concentration. Additionally, chemotherapeutic agent transport properties can modulate this effect.

Untangling the model muddle: Empirical tumour growth in Tasmanian devil facial tumour disease

A pressing and unresolved topic in cancer research is how tumours grow in the absence of treatment. Despite advances in cancer biology, therapeutic and diagnostic technologies, there is limited knowledge regarding the fundamental growth and developmental patterns in solid tumours. In this ten year study, we estimated growth curves in Tasmanian devil facial tumours, a clonal transmissible cancer, in males and females with two different karyotypes (diploid, tetraploid) and facial locations (mucosal, dermal), using established differential equation models and model selection. Logistic growth was the most parsimonious model for diploid, tetraploid and mucosal tumours, with less model certainty for dermal tumours. Estimates of daily proportional tumour growth rate per day (95% Bayesian CIs) varied with ploidy and location [diploid 0.016 (0.014–0.020), tetraploid 0.026 (0.020–0.033), mucosal 0.013 (0.011–0.015), dermal 0.020 (0.016–0.024)]. Final tumour size (cm³) also varied, particularly the upper credible interval owing to host mortality as tumours approached maximum volume [diploid 364 (136–2,475), tetraploid 172 (100–305), dermal 226 (134–471)]. To our knowledge, these are the first empirical estimates of tumour growth in the absence of treatment in a wild population. Through this animal-cancer system our findings may enhance understanding of how tumour properties interact with growth dynamics in other types of cancer.

Tissue-scale, personalized modeling and simulation of prostate cancer growth

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.

A mathematical model of tumor growth and its response to single irradiation

BACKGROUND

Mathematical modeling of biological processes is widely used to enhance quantitative understanding of bio-medical phenomena. This quantitative knowledge can be applied in both clinical and experimental settings. Recently, many investigators began studying mathematical models of tumor response to radiation therapy. We developed a simple mathematical model to simulate the growth of tumor volume and its response to a single fraction of high dose irradiation. The modelling study may provide clinicians important insights on radiation therapy strategies through identification of biological factors significantly influencing the treatment effectiveness.

METHODS

We made several key assumptions of the model. Tumor volume is composed of proliferating (or dividing) cancer cells and non-dividing (or dead) cells. Tumor growth rate (or tumor volume doubling time) is proportional to the ratio of the volumes of tumor vasculature and the tumor. The vascular volume grows slower than the tumor by introducing the vascular growth retardation factor, θ. Upon irradiation, the proliferating cells gradually die over a fixed time period after irradiation. Dead cells are cleared away with cell clearance time. The model was applied to simulate pre-treatment growth and post-treatment radiation response of rat rhabdomyosarcoma tumors and metastatic brain tumors of five patients who were treated with Gamma Knife stereotactic radiosurgery (GKSRS).

RESULTS

By selecting appropriate model parameters, we showed the temporal variation of the tumors for both the rat experiment and the clinical GKSRS cases could be easily replicated by the simple model. Additionally, the application of our model to the GKSRS cases showed that the α-value, which is an indicator of radiation sensitivity in the LQ model, and the value of θ could be predictors of the post-treatment volume change.

CONCLUSIONS

The proposed model was successful in representing both the animal experimental data and the clinically observed tumor volume changes. We showed that the model can be used to find the potential biological parameters, which may be able to predict the treatment outcome. However, there is a large statistical uncertainty of the result due to the small sample size. Therefore, a future clinical study with a larger number of patients is needed to confirm the finding.

The game theory in thoracic surgery: from the intuitions of Luca Pacioli to the operating rooms management

Game theory is a formal way to analyze the interactions among groups of subjects who behave each other. It has historically been of great interest in the economic fields in which decisions are made in a competitive environment. Game theory has fascinating potential if applied in the medical science. Few papers have been written about the application of game theory in surgery. The majority of scenarios of game theory in surgery fall into two main groups: cooperative and no cooperative games.

Simulation of the Protein-Shedding Kinetics of a Fully Vascularized Tumor

Circulating biomarkers are of significant interest for cancer detection and treatment personalization. However, the biophysical processes that determine how proteins are shed from cancer cells or their microenvironment, diffuse through tissue, enter blood vasculature, and persist in circulation remain poorly understood. Since approaches primarily focused on experimental evaluation are incapable of measuring the shedding and persistence for every possible marker candidate, we propose an interdisciplinary computational/experimental approach that includes computational modeling of tumor tissue heterogeneity. The model implements protein production, transport, and shedding based on tumor vascularization, cell proliferation, hypoxia, and necrosis, thus quantitatively relating the tumor and circulating proteomes. The results highlight the dynamics of shedding as a function of protein diffusivity and production. Linking the simulated tumor parameters to clinical tumor and vascularization measurements could potentially enable this approach to reveal the tumor-specific conditions based on the protein detected in circulation and thus help to more accurately manage cancer diagnosis and treatment.

Mathematical model and its fast numerical method for the tumor growth

In this paper, we reformulate the diffuse interface model of the tumor growth (S.M. Wise et al., Three-dimensional multispecies nonlinear tumor growth-I: model and numerical method, J. Theor. Biol. 253 (2008) 524--543). In the new proposed model, we use the conservative second-order Allen--Cahn equation with a space--time dependent Lagrange multiplier instead of using the fourth-order Cahn--Hilliard equation in the original model. To numerically solve the new model, we apply a recently developed hybrid numerical method. We perform various numerical experiments. The computational results demonstrate that the new model is not only fast but also has a good feature such as distributing excess mass from the inside of tumor to its boundary regions.

Steering Evolution with Sequential Therapy to Prevent the Emergence of Bacterial Antibiotic Resistance

The increasing rate of antibiotic resistance and slowing discovery of novel antibiotic treatments presents a growing threat to public health. Here, we consider a simple model of evolution in asexually reproducing populations which considers adaptation as a biased random walk on a fitness landscape. This model associates the global properties of the fitness landscape with the algebraic properties of a Markov chain transition matrix and allows us to derive general results on the non-commutativity and irreversibility of natural selection as well as antibiotic cycling strategies. Using this formalism, we analyze 15 empirical fitness landscapes of E. coli under selection by different β-lactam antibiotics and demonstrate that the emergence of resistance to a given antibiotic can be either hindered or promoted by different sequences of drug application. Specifically, we demonstrate that the majority, approximately 70%, of sequential drug treatments with 2-4 drugs promote resistance to the final antibiotic. Further, we derive optimal drug application sequences with which we can probabilistically 'steer' the population through genotype space to avoid the emergence of resistance. This suggests a new strategy in the war against antibiotic-resistant organisms: drug sequencing to shepherd evolution through genotype space to states from which resistance cannot emerge and by which to maximize the chance of successful therapy.

Development of a sampling-based global sensitivity analysis workflow for multiscale computational cancer models

There are two challenges that researchers face when performing global sensitivity analysis (GSA) on multiscale 'in silico' cancer models. The first is increased computational intensity, since a multiscale cancer model generally takes longer to run than does a scale-specific model. The second problem is the lack of a best GSA method that fits all types of models, which implies that multiple methods and their sequence need to be taken into account. In this study, the authors therefore propose a sampling-based GSA workflow consisting of three phases - pre-analysis, analysis and post-analysis - by integrating Monte Carlo and resampling methods with the repeated use of analysis of variance; they then exemplify this workflow using a two-dimensional multiscale lung cancer model. By accounting for all parameter rankings produced by multiple GSA methods, a summarised ranking is created at the end of the workflow based on the weighted mean of the rankings for each input parameter. For the cancer model investigated here, this analysis reveals that extracellular signal-regulated kinase, a downstream molecule of the epidermal growth factor receptor signalling pathway, has the most important impact on regulating both the tumour volume and expansion rate in the algorithm used.

Spatial and functional heterogeneities shape collective behavior of tumor-immune networks

Tumor growth involves a dynamic interplay between cancer cells and host cells, which collectively form a tumor microenvironmental network that either suppresses or promotes tumor growth under different conditions. The transition from tumor suppression to tumor promotion is mediated by a tumor-induced shift in the local immune state, and despite the clinical challenge this shift poses, little is known about how such dysfunctional immune states are initiated. Clinical and experimental observations have indicated that differences in both the composition and spatial distribution of different cell types and/or signaling molecules within the tumor microenvironment can strongly impact tumor pathogenesis and ultimately patient prognosis. How such “functional” and “spatial” heterogeneities confer such effects, however, is not known. To investigate these phenomena at a level currently inaccessible by direct observation, we developed a computational model of a nascent metastatic tumor capturing salient features of known tumor-immune interactions that faithfully recapitulates key features of existing experimental observations. Surprisingly, over a wide range of model formulations, we observed that heterogeneity in both spatial organization and cell phenotype drove the emergence of immunosuppressive network states. We determined that this observation is general and robust to parameter choice by developing a systems-level sensitivity analysis technique, and we extended this analysis to generate other parameter-independent, experimentally testable hypotheses. Lastly, we leveraged this model as an in silico test bed to evaluate potential strategies for engineering cell-based therapies to overcome tumor associated immune dysfunction and thereby identified modes of immune modulation predicted to be most effective. Collectively, this work establishes a new integrated framework for investigating and modulating tumor-immune networks and provides insights into how such interactions may shape early stages of tumor formation.

Over the course of tumor growth, cancer cells interact with normal cells via processes that are difficult to understand by experiment alone. This challenge is particularly pronounced at early stages of tumor formation, when experimental observation is most limited. Elucidating such interactions could inform both understanding of cancer and clinical practice. To address this need we developed a computational model capturing the current understanding of how individual metastatic tumor cells and immune cells sense and contribute to the tumor environment, which in turn enabled us to investigate the complex, collective behavior of these systems. Surprisingly, we discovered that tumor escape from immune control was enhanced by the existence of small differences (or heterogeneities) in the responses of individual immune cells to their environment, as well as by heterogeneities in the way that cells and the molecules they secrete are arranged in space. These conclusions held true over a range of model formulations, suggesting that this is a general feature of these tumor-immune networks. Finally, we used this model as a test bed to evaluate potential strategies for enhancing immunological control of early tumors, ultimately predicting that specifically modulating tumor-associated immune dysfunction may be more effective than simply enhanced tumor killing.

Multimodal imaging of gliomas in the context of evolving cellular and molecular therapies

The vast majority of malignant gliomas relapse after surgery and standard radio-chemotherapy. Novel molecular and cellular therapies are thus being developed, targeting specific aspects of tumor growth. While histopathology remains the gold standard for tumor classification, neuroimaging has over the years taken a central role in the diagnosis and treatment follow up of brain tumors. It is used to detect and localize lesions, define the target area for biopsies, plan surgical and radiation interventions and assess tumor progression and treatment outcome. In recent years the application of novel drugs including anti-angiogenic agents that affect the tumor vasculature, has drastically modulated the outcome of brain tumor imaging. To properly evaluate the effects of emerging experimental therapies and successfully support treatment decisions, neuroimaging will have to evolve. Multi-modal imaging systems with existing and new contrast agents, molecular tracers, technological advances and advanced data analysis can all contribute to the establishment of disease relevant biomarkers that will improve disease management and patient care. In this review, we address the challenges of glioma imaging in the context of novel molecular and cellular therapies, and take a prospective look at emerging experimental and pre-clinical imaging techniques that bear the promise of meeting these challenges.

Mathematical modeling for novel cancer drug discovery and development

INTRODUCTION

Mathematical modeling enables: the in silico classification of cancers, the prediction of disease outcomes, optimization of therapy, identification of promising drug targets and prediction of resistance to anticancer drugs. In silico pre-screened drug targets can be validated by a small number of carefully selected experiments.

AREAS COVERED

This review discusses the basics of mathematical modeling in cancer drug discovery and development. The topics include in silico discovery of novel molecular drug targets, optimization of immunotherapies, personalized medicine and guiding preclinical and clinical trials. Breast cancer has been used to demonstrate the applications of mathematical modeling in cancer diagnostics, the identification of high-risk population, cancer screening strategies, prediction of tumor growth and guiding cancer treatment.

EXPERT OPINION

Mathematical models are the key components of the toolkit used in the fight against cancer. The combinatorial complexity of new drugs discovery is enormous, making systematic drug discovery, by experimentation, alone difficult if not impossible. The biggest challenges include seamless integration of growing data, information and knowledge, and making them available for a multiplicity of analyses. Mathematical models are essential for bringing cancer drug discovery into the era of Omics, Big Data and personalized medicine.

Tumor growth in complex, evolving microenvironmental geometries: a diffuse domain approach

We develop a mathematical model of tumor growth in complex, dynamic microenvironments with active, deformable membranes. Using a diffuse domain approach, the complex domain is captured implicitly using an auxiliary function and the governing equations are appropriately modified, extended and solved in a larger, regular domain. The diffuse domain method enables us to develop an efficient numerical implementation that does not depend on the space dimension or the microenvironmental geometry. We model homotypic cell-cell adhesion and heterotypic cell-basement membrane (BM) adhesion with the latter being implemented via a membrane energy that models cell-BM interactions. We incorporate simple models of elastic forces and the degradation of the BM and ECM by tumor-secreted matrix degrading enzymes. We investigate tumor progression and BM response as a function of cell-BM adhesion and the stiffness of the BM. We find tumor sizes tend to be positively correlated with cell-BM adhesion since increasing cell-BM adhesion results in thinner, more elongated tumors. Prior to invasion of the tumor into the stroma, we find a negative correlation between tumor size and BM stiffness as the elastic restoring forces tend to inhibit tumor growth. In order to model tumor invasion of the stroma, we find it necessary to downregulate cell-BM adhesiveness, which is consistent with experimental observations. A stiff BM promotes invasiveness because at early stages the opening in the BM created by MDE degradation from tumor cells tends to be narrower when the BM is stiffer. This requires invading cells to squeeze through the narrow opening and thus promotes fragmentation that then leads to enhanced growth and invasion. In three dimensions, the opening in the BM was found to increase in size even when the BM is stiff because of pressure induced by growing tumor clusters. A larger opening in the BM can increase the potential for further invasiveness by increasing the possibility that additional tumor cells could invade the stroma.

A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane

In this paper, we extend the 3D multispecies diffuse-interface model of the tumor growth, which was derived in Wise et al. (Three-dimensional multispecies nonlinear tumor growth-I: model and numerical method, J. Theor. Biol. 253 (2008) 524-543), and incorporate the effect of a stiff membrane to model tumor growth in a confined microenvironment. We then develop accurate and efficient numerical methods to solve the model. When the membrane is endowed with a surface energy, the model is variational, and the numerical scheme, which involves adaptive mesh refinement and a nonlinear multigrid finite difference method, is demonstrably shown to be energy stable. Namely, in the absence of cell proliferation and death, the discrete energy is a nonincreasing function of time for any time and space steps. When a simplified model of membrane elastic energy is used, the resulting model is derived analogously to the surface energy case. However, the elastic energy model is actually nonvariational because certain coupling terms are neglected. Nevertheless, a very stable numerical scheme is developed following the strategy used in the surface energy case. 2D and 3D simulations are performed that demonstrate the accuracy of the algorithm and illustrate the shape instabilities and nonlinear effects of membrane elastic forces that may resist or enhance growth of the tumor. Compared with the standard Crank-Nicholson method, the time step can be up to 25 times larger using the new approach.

In silico modeling predicts drug sensitivity of patient-derived cancer cells

BACKGROUND

Glioblastoma (GBM) is an aggressive disease associated with poor survival. It is essential to account for the complexity of GBM biology to improve diagnostic and therapeutic strategies. This complexity is best represented by the increasing amounts of profiling ("omics") data available due to advances in biotechnology. The challenge of integrating these vast genomic and proteomic data can be addressed by a comprehensive systems modeling approach.

METHODS

Here, we present an in silico model, where we simulate GBM tumor cells using genomic profiling data. We use this in silico tumor model to predict responses of cancer cells to targeted drugs. Initially, we probed the results from a recent hypothesis-independent, empirical study by Garnett and co-workers that analyzed the sensitivity of hundreds of profiled cancer cell lines to 130 different anticancer agents. We then used the tumor model to predict sensitivity of patient-derived GBM cell lines to different targeted therapeutic agents.

RESULTS

Among the drug-mutation associations reported in the Garnett study, our in silico model accurately predicted ~85% of the associations. While testing the model in a prospective manner using simulations of patient-derived GBM cell lines, we compared our simulation predictions with experimental data using the same cells in vitro. This analysis yielded a ~75% agreement of in silico drug sensitivity with in vitro experimental findings.

CONCLUSIONS

These results demonstrate a strong predictability of our simulation approach using the in silico tumor model presented here. Our ultimate goal is to use this model to stratify patients for clinical trials. By accurately predicting responses of cancer cells to targeted agents a priori, this in silico tumor model provides an innovative approach to personalizing therapy and promises to improve clinical management of cancer.

Revitalizing personalized medicine: respecting biomolecular complexities beyond gene expression

Despite recent advancements in "omic" technologies, personalized medicine has not realized its fullest potential due to isolated and incomplete application of gene expression tools. In many instances, pharmacogenomics is being interchangeably used for personalized medicine, when actually it is one of the many facets of personalized medicine. Herein, we highlight key issues that are hampering the advancement of personalized medicine and highlight emerging predictive tools that can serve as a decision support mechanism for physicians to personalize treatments.

Oral mucosal injury in oncology patients: perspectives on maturation of a field

In the past decade, there have been important strategic advances relative to pathobiological modeling as well as clinical management for oral mucositis caused by cancer therapies. Prior to the 1990s, research in this field was conducted by a relatively small number of basic and clinical investigators. Increasing interest among researchers and clinicians over the past twenty years has produced a synergistic outcome characterized by a number of key dynamics, including novel discovery models for pathobiology, increased experience in designing and conducting clinical trials, and creation of international collaborations among cancer care professionals who in turn have modeled clinical care paradigms based on state-of-the-science evidence. This maturation of the science and its clinical translation has positioned investigators and oncology providers to further accelerate both the foundational research and the clinical modeling for patient management in the years ahead. The stage is now set to further capitalize upon optimizing the interactions across this interface, with the goal of strategically enhancing management of patients with cancer at risk for this toxicity while reducing the cost of cancer care.

An architecture for integrating cancer model repositories

The TUMOR project aims at developing a European clinically oriented semantic-layered cancer digital model repository from existing EU projects that will be interoperable with the US grid-enabled semantic-layered digital model repository platform at CViT.org (Center for the Development of a Virtual Tumor, Massachusetts General Hospital (MGH), Boston, USA) which is NIH/NCI-caGRID compatible. In this paper we describe the modular and federated architecture of TUMOR that effectively addresses model integration, interoperability, and security related issues.

Dealing with diversity in computational cancer modeling

This paper discusses the need for interconnecting computational cancer models from different sources and scales within clinically relevant scenarios to increase the accuracy of the models and speed up their clinical adaptation, validation, and eventual translation. We briefly review current interoperability efforts drawing upon our experiences with the development of in silico models for predictive oncology within a number of European Commission Virtual Physiological Human initiative projects on cancer. A clinically relevant scenario, addressing brain tumor modeling that illustrates the need for coupling models from different sources and levels of complexity, is described. General approaches to enabling interoperability using XML-based markup languages for biological modeling are reviewed, concluding with a discussion on efforts towards developing cancer-specific XML markup to couple multiple component models for predictive in silico oncology.

An integrated computational/experimental model of lymphoma growth

Non-Hodgkin's lymphoma is a disseminated, highly malignant cancer, with resistance to drug treatment based on molecular- and tissue-scale characteristics that are intricately linked. A critical element of molecular resistance has been traced to the loss of functionality in proteins such as the tumor suppressor p53. We investigate the tissue-scale physiologic effects of this loss by integrating in vivo and immunohistological data with computational modeling to study the spatiotemporal physical dynamics of lymphoma growth. We compare between drug-sensitive Eμ-myc Arf-/- and drug-resistant Eμ-myc p53-/- lymphoma cell tumors grown in live mice. Initial values for the model parameters are obtained in part by extracting values from the cellular-scale from whole-tumor histological staining of the tumor-infiltrated inguinal lymph node in vivo. We compare model-predicted tumor growth with that observed from intravital microscopy and macroscopic imaging in vivo, finding that the model is able to accurately predict lymphoma growth. A critical physical mechanism underlying drug-resistant phenotypes may be that the Eμ-myc p53-/- cells seem to pack more closely within the tumor than the Eμ-myc Arf-/- cells, thus possibly exacerbating diffusion gradients of oxygen, leading to cell quiescence and hence resistance to cell-cycle specific drugs. Tighter cell packing could also maintain steeper gradients of drug and lead to insufficient toxicity. The transport phenomena within the lymphoma may thus contribute in nontrivial, complex ways to the difference in drug sensitivity between Eμ-myc Arf-/- and Eμ-myc p53-/- tumors, beyond what might be solely expected from loss of functionality at the molecular scale. We conclude that computational modeling tightly integrated with experimental data gives insight into the dynamics of Non-Hodgkin's lymphoma and provides a platform to generate confirmable predictions of tumor growth.

Non-Hodgkin's lymphoma is a cancer that develops from white blood cells called lymphocytes in the immune system, whose role is to fight disease throughout the body. This cancer can spread throughout the whole body and be very lethal – in the US, one third of patients will die from this disease within five years of diagnosis. Chemotherapy is a usual treatment for lymphoma, but the cancer can become highly resistant to it. One reason is that a critical gene called p53 can become mutated and help the cancer to survive. In this work we investigate how cells with this mutation affect the cancer growth by performing experiments in mice and using a computer model. By inputting the model parameters based on data from the experiments, we are able to accurately predict the growth of the tumor as compared to tumor measurements in living mice. We conclude that computational modeling integrated with experimental data gives insight into the dynamics of Non-Hodgkin's lymphoma, and provides a platform to generate confirmable predictions of tumor growth.

Systems biology for molecular life sciences and its impact in biomedicine

Modern systems biology is already contributing to a radical transformation of molecular life sciences and biomedicine, and it is expected to have a real impact in the clinical setting in the next years. In this review, the emergence of systems biology is contextualized with a historic overview, and its present state is depicted. The present and expected future contribution of systems biology to the development of molecular medicine is underscored. Concerning the present situation, this review includes a reflection on the "inflation" of biological data and the urgent need for tools and procedures to make hidden information emerge. Descriptions of the impact of networks and models and the available resources and tools for applying them in systems biology approaches to molecular medicine are provided as well. The actual current impact of systems biology in molecular medicine is illustrated, reviewing two cases, namely, those of systems pharmacology and cancer systems biology. Finally, some of the expected contributions of systems biology to the immediate future of molecular medicine are commented.

A hybrid cellular automaton model of solid tumor growth and bioreductive drug transport

Bioreductive drugs are a class of hypoxia selective drugs that are designed to eradicate the hypoxic fraction of solid tumors. Their activity depends upon a number of biological and pharmacological factors and we used a mathematical modeling approach to explore the dynamics of tumor growth, infusion, and penetration of the bioreductive drug Tirapazamine (TPZ). An in-silico model is implemented to calculate the tumor mass considering oxygen and glucose as key microenvironmental parameters. The next stage of the model integrated extra cellular matrix (ECM), cell-cell adhesion, and cell movement parameters as growth constraints. The tumor microenvironments strongly influenced tumor morphology and growth rates. Once the growth model was established, a hybrid model was developed to study drug dynamics inside the hypoxic regions of tumors. The model used 10, 50 and 100 \mu {\rm M} as TPZ initial concentrations and determined TPZ pharmacokinetic (PK) (transport) and pharmacodynamics (cytotoxicity) properties inside hypoxic regions of solid tumor. The model results showed that diminished drug transport is a reason for TPZ failure and recommend the optimization of the drug transport properties in the emerging TPZ generations. The modeling approach used in this study is novel and can be a step to explore the behavioral dynamics of TPZ.

Towards in silico oncology: adapting a four dimensional nephroblastoma treatment model to a clinical trial case based on multi-method sensitivity analysis

In the past decades a great progress in cancer research has been made although medical treatment is still widely based on empirically established protocols which have many limitations. Computational models address such limitations by providing insight into the complex biological mechanisms of tumor progression. A set of clinically-oriented, multiscale models of solid tumor dynamics has been developed by the In Silico Oncology Group (ISOG), Institute of Communication and Computer Systems (ICCS)-National Technical University of Athens (NTUA) to study cancer growth and response to treatment. Within this context using certain representative parameter values, tumor growth and response have been modeled under a cancer preoperative chemotherapy protocol in the framework of the SIOP 2001/GPOH clinical trial. A thorough cross-method sensitivity analysis of the model has been performed. Based on the sensitivity analysis results, a reasonable adaptation of the values of the model parameters to a real clinical case of bilateral nephroblastomatosis has been achieved. The analysis presented supports the potential of the model for the study and eventually the future design of personalized treatment schemes and/or schedules using the data obtained from in vitro experiments and clinical studies.

Computational modelling of anti-angiogenic therapies based on multiparametric molecular imaging data

Computational tumour models have emerged as powerful tools for the optimization of cancer therapies; ideally, these models should incorporate patient-specific imaging data indicative of therapeutic response. The purpose of this study was to develop a tumour modelling framework in order to simulate the therapeutic effects of anti-angiogenic agents based upon clinical molecular imaging data. The model was applied to positron emission tomography (PET) data of cellular proliferation and hypoxia from a phase I clinical trial of bevacizumab, an antibody that neutralizes the vascular endothelial growth factor (VEGF). When using pre-therapy PET data in combination with literature-based dose response parameters, simulated follow-up hypoxia data yielded good qualitative agreement with imaged hypoxia levels. Improving the quantitative agreement with follow-up hypoxia and proliferation PET data required tuning of the maximum vascular growth fraction (VGF(max)) and the tumour cell cycle time to patient-specific values. VGF(max) was found to be the most sensitive model parameter (CV = 22%). Assuming availability of patient-specific, intratumoural VEGF levels, we show how bevacizumab dose levels can potentially be 'tailored' to improve levels of tumour hypoxia while maintaining proliferative response, both of which are critically important in the context of combination therapy. Our results suggest that, upon further validation, the application of image-driven computational models may afford opportunities to optimize dosing regimens and combination therapies in a patient-specific manner.

From base pair to bedside: molecular simulation and the translation of genomics to personalized medicine

Despite the promises made that genomic sequencing would transform therapy by introducing a new era of personalized medicine, relatively few tangible breakthroughs have been made. This has led to the recognition that complex interactions at multiple spatial, temporal, and organizational levels may often combine to produce disease. Understanding this complexity requires that existing and future models are used and interpreted within a framework that incorporates knowledge derived from investigations at multiple levels of biological function. It also requires a computational infrastructure capable of dealing with the vast quantities of data generated by genomic approaches. In this review, we discuss the use of molecular modeling to generate quantitative and qualitative insights at the smallest scales of the systems biology hierarchy, how it can play an important role in the development of a systems understanding of disease and in the application of such knowledge to help discover new therapies and target existing ones on a personal level.

Avascular tumour growth dynamics and the constraints of protein binding for drug transportation

The potential for the use of in-silico models of disease in progression monitoring is becoming increasingly recognised, as well as its contribution to the development of complete curative processes. In this paper we report the development of a hybrid cellular automaton model to mimic the growth of avascular tumours, including the infusion of a bioreductive drug to study the effects of protein binding on drug transportation. The growth model is operated within an extracellular tumour microenvironment. An artificial Neural Network based scheme was implemented that modelled the behaviours of each cell (proliferation, quiescence, apoptosis and/or movement) based on the complex heterogeneous microenvironment; consisting of oxygen, glucose, hydrogen ions, inhibitory factors and growth factors. To validate the growth model results, we conducted experiments with multicellular tumour spheroids. These results showed good agreement with the predicted growth dynamics. The outcome of the avascular tumour growth model suggested that tumour microenvironments have a strong impact on cell behaviour. To address the problem of cellular proteins acting as resistive factors preventing efficient drug penetration, a bioreactive drug (tirapazamine) was added to the system. This allowed us to study the drug penetration through multicellular layers of tissue after its binding to cellular proteins. The results of the in vitro model suggested that the proteins reduce the toxicity of the drug, reducing its efficacy for the most severely hypoxic fractions furthest from a functional blood vessel. Finally this research provides a unique comparison of in vitro tumour growth with an intelligent in silico model to measure bioreductive drug availability inside tumour tissue through a set of experiments.

Multiscale imaging and computational modeling of blood flow in the tumor vasculature

The evolution in our understanding of tumor angiogenesis has been the result of pioneering imaging and computational modeling studies spanning the endothelial cell, microvasculature and tissue levels. Many of these primary data on the tumor vasculature are in the form of images from pre-clinical tumor models that provide a wealth of qualitative and quantitative information in many dimensions and across different spatial scales. However, until recently, the visualization of changes in the tumor vasculature across spatial scales remained a challenge due to a lack of techniques for integrating micro- and macroscopic imaging data. Furthermore, the paucity of three-dimensional (3-D) tumor vascular data in conjunction with the challenges in obtaining such data from patients presents a serious hurdle for the development and validation of predictive, multiscale computational models of tumor angiogenesis. In this review, we discuss the development of multiscale models of tumor angiogenesis, new imaging techniques capable of reproducing the 3-D tumor vascular architecture with high fidelity, and the emergence of "image-based models" of tumor blood flow and molecular transport. Collectively, these developments are helping us gain a fundamental understanding of the cellular and molecular regulation of tumor angiogenesis that will benefit the development of new cancer therapies. Eventually, we expect this exciting integration of multiscale imaging and mathematical modeling to have widespread application beyond the tumor vasculature to other diseases involving a pathological vasculature, such as stroke and spinal cord injury.

Multiscale cancer modeling

Simulating cancer behavior across multiple biological scales in space and time, i.e., multiscale cancer modeling, is increasingly being recognized as a powerful tool to refine hypotheses, focus experiments, and enable more accurate predictions. A growing number of examples illustrate the value of this approach in providing quantitative insights in the initiation, progression, and treatment of cancer. In this review, we introduce the most recent and important multiscale cancer modeling works that have successfully established a mechanistic link between different biological scales. Biophysical, biochemical, and biomechanical factors are considered in these models. We also discuss innovative, cutting-edge modeling methods that are moving predictive multiscale cancer modeling toward clinical application. Furthermore, because the development of multiscale cancer models requires a new level of collaboration among scientists from a variety of fields such as biology, medicine, physics, mathematics, engineering, and computer science, an innovative Web-based infrastructure is needed to support this growing community.

Quantitative study of cytotoxic T-lymphocyte immunotherapy for nasopharyngeal carcinoma

BACKGROUND

In clinical practice, the common strategy for immunotherapy of nasopharyngeal carcinoma (NPC) is to infuse cytotoxic T-lymphocyte (CTL) lines several times by intravenous injection, but it is difficult by laboratory research to investigate the relationship between treatment time-point, the amount of CTL added and the therapeutic effect. The objective of this study is to establish a mathematical model to study the therapeutic effect of different treatment time-points and amounts of CTL, and to predict the change in therapeutic effect when the percentage of EBV LMP2-specific CTL is increased from 10% to 20%.

RESULTS

The concentration of epidermal growth factor receptor (EGFR) in the tumor cell cytomembranes increases after CTL is added. Concurrently, there is a marked downward trend of the phosphorylated transforming growth factor-α (TGFα)-EGFR complex in the tumor cell cytomembranes, which indicates restriction of tumor growth after CTL immunotherapy. The relationships among the time of addition of CTL, the amount of CTL added, different CTL specificities for LMP2 and the increment rate k of the total number of tumor cells were evaluated.

CONCLUSIONS

The simulation results quantify the relationships among treatment time-points, amount of CTL added, and the corresponding therapeutic effect of immunotherapy for NPC.

The dynamics of drug resistance: a mathematical perspective

Resistance to chemotherapy is a key impediment to successful cancer treatment that has been intensively studied for the last three decades. Several central mechanisms have been identified as contributing to the resistance. In the case of multidrug resistance (MDR), the cell becomes resistant to a variety of structurally and mechanistically unrelated drugs in addition to the drug initially administered. Mathematical models of drug resistance have dealt with many of the known aspects of this field, such as pharmacologic sanctuary and location/diffusion resistance, intrinsic resistance, induced resistance and acquired resistance. In addition, there are mathematical models that take into account the kinetic/phase resistance, and models that investigate intracellular mechanisms based on specific biological functions (such as ABC transporters, apoptosis and repair mechanisms). This review covers aspects of MDR that have been mathematically studied, and explains how, from a methodological perspective, mathematics can be used to study drug resistance. We discuss quantitative approaches of mathematical analysis, and demonstrate how mathematics can be used in combination with other experimental and clinical tools. We emphasize the potential benefits of integrating analytical and mathematical methods into future clinical and experimental studies of drug resistance.