Prediction of drug response in breast cancer using integrative experimental/computational modeling

A comprehensive review of computational cell cycle models in guiding cancer treatment strategies

This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.

Morphological Stability for in silico Models of Avascular Tumors

The landscape of computational modeling in cancer systems biology is diverse, offering a spectrum of models and frameworks, each with its own trade-offs and advantages. Ideally, models are meant to be useful in refining hypotheses, to sharpen experimental procedures and, in the longer run, even for applications in personalized medicine. One of the greatest challenges is to balance model realism and detail with experimental data to eventually produce useful data-driven models. We contribute to this quest by developing a transparent, highly parsimonious, first principle in silico model of a growing avascular tumor. We initially formulate the physiological considerations and the specific model within a stochastic cell-based framework. We next formulate a corresponding mean-field model using partial differential equations which is amenable to mathematical analysis. Despite a few notable differences between the two models, we are in this way able to successfully detail the impact of all parameters in the stability of the growth process and on the eventual tumor fate of the stochastic model. This facilitates the deduction of Bayesian priors for a given situation, but also provides important insights into the underlying mechanism of tumor growth and progression. Although the resulting model framework is relatively simple and transparent, it can still reproduce the full range of known emergent behavior. We identify a novel model instability arising from nutrient starvation and we also discuss additional insight concerning possible model additions and the effects of those. Thanks to the framework's flexibility, such additions can be readily included whenever the relevant data become available.

Modeling of Mouse Experiments Suggests that Optimal Anti-Hormonal Treatment for Breast Cancer is Diet-Dependent

Estrogen receptor positive breast cancer is frequently treated with anti-hormonal treatment such as aromatase inhibitors (AI). Interestingly, a high body mass index has been shown to have a negative impact on AI efficacy, most likely due to disturbances in steroid metabolism and adipokine production. Here, we propose a mathematical model based on a system of ordinary differential equations to investigate the effect of high-fat diet on tumor growth. We inform the model with data from mouse experiments, where the animals are fed with high-fat or control (normal) diet. By incorporating AI treatment with drug resistance into the model and by solving optimal control problems we found differential responses for control and high-fat diet. To the best of our knowledge, this is the first attempt to model optimal anti-hormonal treatment for breast cancer in the presence of drug resistance. Our results underline the importance of considering high-fat diet and obesity as factors influencing clinical outcomes during anti-hormonal therapies in breast cancer patients.

Evaluation of innate and adaptive immune system interactions in the tumor microenvironment via a 3D continuum model

Immune cells in the tumor microenvironment (TME) are known to affect tumor growth, vascularization, and extracellular matrix (ECM) deposition. Marked interest in system-scale analysis of immune species interactions within the TME has encouraged progress in modeling tumor-immune interactions in silico. Due to the computational cost of simulating these intricate interactions, models have typically been constrained to representing a limited number of immune species. To expand the capability for system-scale analysis, this study develops a three-dimensional continuum mixture model of tumor-immune interactions to simulate multiple immune species in the TME. Building upon a recent distributed computing implementation that enables efficient solution of such mixture models, major immune species including monocytes, macrophages, natural killer cells, dendritic cells, neutrophils, myeloid-derived suppressor cells (MDSC), cytotoxic, helper, regulatory T-cells, and effector and regulatory B-cells and their interactions are represented in this novel implementation. Immune species extravasate from blood vasculature, undergo chemotaxis toward regions of high chemokine concentration, and influence the TME in proportion to locally defined levels of stimulation. The immune species contribute to the production of angiogenic and tumor growth factors, promotion of myofibroblast deposition of ECM, upregulation of angiogenesis, and elimination of living and dead tumor species. The results show that this modeling approach offers the capability for quantitative insight into the modulation of tumor growth by diverse immune-tumor interactions and immune-driven TME effects. In particular, MDSC-mediated effects on tumor-associated immune species' activation levels, volume fraction, and influence on the TME are explored. Longer term, linking of the model parameters to particular patient tumor information could simulate cancer-specific immune responses and move toward a more comprehensive evaluation of immunotherapeutic strategies.

A PDE Model of Breast Tumor Progression in MMTV-PyMT Mice

The evolution of breast tumors greatly depends on the interaction network among different cell types, including immune cells and cancer cells in the tumor. This study takes advantage of newly collected rich spatio-temporal mouse data to develop a data-driven mathematical model of breast tumors that considers cells' location and key interactions in the tumor. The results show that cancer cells have a minor presence in the area with the most overall immune cells, and the number of activated immune cells in the tumor is depleted over time when there is no influx of immune cells. Interestingly, in the case of the influx of immune cells, the highest concentrations of both T cells and cancer cells are in the boundary of the tumor, as we use the Robin boundary condition to model the influx of immune cells. In other words, the influx of immune cells causes a dominant outward advection for cancer cells. We also investigate the effect of cells' diffusion and immune cells' influx rates in the dynamics of cells in the tumor micro-environment. Sensitivity analyses indicate that cancer cells and adipocytes' diffusion rates are the most sensitive parameters, followed by influx and diffusion rates of cytotoxic T cells, implying that targeting them is a possible treatment strategy for breast cancer.

Optimizing Dosage-Specific Treatments in a Multi-Scale Model of a Tumor Growth

The emergence of cell resistance in cancer treatment is a complex phenomenon that emerges from the interplay of processes that occur at different scales. For instance, molecular mechanisms and population-level dynamics such as competition and cell–cell variability have been described as playing a key role in the emergence and evolution of cell resistances. Multi-scale models are a useful tool for studying biology at very different times and spatial scales, as they can integrate different processes occurring at the molecular, cellular, and intercellular levels. In the present work, we use an extended hybrid multi-scale model of 3T3 fibroblast spheroid to perform a deep exploration of the parameter space of effective treatment strategies based on TNF pulses. To explore the parameter space of effective treatments in different scenarios and conditions, we have developed an HPC-optimized model exploration workflow based on EMEWS. We first studied the effect of the cells’ spatial distribution in the values of the treatment parameters by optimizing the supply strategies in 2D monolayers and 3D spheroids of different sizes. We later study the robustness of the effective treatments when heterogeneous populations of cells are considered. We found that our model exploration workflow can find effective treatments in all the studied conditions. Our results show that cells’ spatial geometry and population variability should be considered when optimizing treatment strategies in order to find robust parameter sets.

A phenotype-structured model to reproduce the avascular growth of a tumor and its interaction with the surrounding environment

We here propose a one-dimensional spatially explicit phenotype-structured model to analyze selected aspects of avascular tumor progression. In particular, our approach distinguishes viable and necrotic cell fractions. The metabolically active part of the disease is, in turn, differentiated according to a continuous trait, that identifies cell variants with different degrees of motility and proliferation potential. A parabolic partial differential equation (PDE) then governs the spatio-temporal evolution of the phenotypic distribution of active cells within the host tissue. In this respect, active tumor agents are allowed to duplicate, move upon haptotactic and pressure stimuli, and eventually undergo necrosis. The mutual influence between the emerging malignancy and its environment (in terms of molecular landscape) is implemented by coupling the evolution law of the viable tumor mass with a parabolic PDE for oxygen kinetics and a differential equation that accounts for local consumption of extracellular matrix (ECM) elements. The resulting numerical realizations reproduce tumor growth and invasion in a number scenarios that differ for cell properties (i.e., individual migratory behavior, duplication and mutation potential) and environmental conditions (i.e., level of tissue oxygenation and homogeneity in the initial matrix profile). In particular, our simulations show that, in all cases, more mobile cell variants occupy the front edge of the tumor, whereas more proliferative clones are selected at the more internal regions. A necrotic core constantly occupies the bulk of the mass due to nutrient deprivation. This work may eventually suggest some biomedical strategies to partially reduce tumor aggressiveness, i.e., to enhance necrosis of malignant tissue and to promote the presence of more proliferative cell phenotypes over more invasive ones.

Simulation of 3D centimeter-scale continuum tumor growth at sub-millimeter resolution via distributed computing

Simulation of cm-scale tumor growth has generally been constrained by the computational cost to numerically solve the associated equations, with models limited to representing mm-scale or smaller tumors. While the work has proven useful to the study of small tumors and micro-metastases, a biologically-relevant simulation of cm-scale masses as would be typically detected and treated in patients has remained an elusive goal. This study presents a distributed computing (parallelized) implementation of a mixture model of tumor growth to simulate 3D cm-scale vascularized tissue at sub-mm resolution. The numerical solving scheme utilizes a two-stage parallelization framework. The solution is written for GPU computation using the CUDA framework, which handles all Multigrid-related computations. Message Passing Interface (MPI) handles distribution of information across multiple processes, freeing the program from RAM and the processing limitations found on single systems. On each system, Nvidia's CUDA library allows for fast processing of model data using GPU-bound computing on fewer systems. The results show that a combined MPI-CUDA implementation enables the continuum modeling of cm-scale tumors at reasonable computational cost. Further work to calibrate model parameters to particular tumor conditions could enable simulation of patient-specific tumors for clinical application.

Pumpless, unidirectional microphysiological system for testing metabolism-dependent chemotherapeutic toxicity

Drug development is often hindered by the failure of preclinical models to accurately assess and predict the efficacy and safety of drug candidates. Body-on-a-chip (BOC) microfluidic devices, a subset of microphysiological systems (MPS), are being created to better predict human responses to drugs. Each BOC is designed with separate organ chambers interconnected with microfluidic channels mimicking blood recirculation. Here, we describe the design of the first pumpless, unidirectional, multiorgan system and apply this design concept for testing anticancer drug treatments. HCT-116 colon cancer spheroids, HepG2/C3A hepatocytes, and HL-60 promyeloblasts were embedded in collagen hydrogels and cultured within compartments representing "colon tumor", "liver," and "bone marrow" tissue, respectively. Operating on a pumpless platform, the microfluidic channel design provides unidirectional perfusion at physiologically realistic ratios to multiple channels simultaneously. The metabolism-dependent toxic effect of Tegafur, an oral prodrug of 5-fluorouracil, combined with uracil was examined in each cell type. Tegafur-uracil treatment induced substantial cell death in HCT-116 cells and this cytotoxic response was reduced for multicellular spheroids compared to single cells, likely due to diffusion-limited drug penetration. Additionally, off-target toxicity was detected by HL-60 cells, which demonstrate that such systems can provide useful information on dose-limiting side effects. Collectively, this microscale cell culture analog is a valuable physiologically-based pharmacokinetic drug screening platform that may be used to support cancer drug development.

Nanocarrier anticancer drug-conjugates cause higher cellular deformations: culpable for mischief

Here we report nanocarrier-anticancer drug conjugates culpable for cellular deformations, critically evidenced through image-based analysis as a measure of karyoplasmic ratio (KR) and nuclear surface area (NSA). Multiwalled carbon nanotubes (MWCNTs) were coordinated additionally with Fe3O4 nanoparticles (NPs) to evaluate the symbiotic influence, and further conjugated to Dox for evaluating the cellular kinetics and for measuring cell deformations. Cellular entry kinetics of the CNT (CNT-Dox and CNT-Cys-Fe3O4-Dox) nanocarriers and their efficiency in nuclear localization were evaluated using cervical cancer (HeLa) cells. Of note, the Dox-bound nanocarriers showed significantly enhanced cell toxicity over the free form of the drug. CNT-Dox and CNT-Cys-Fe3O4-Dox influx occurred within 4 hours, while maximum cellular retention of Dox was observed for CNT-Dox at 24 h. However, the highest KR (∼0.51) was observed for CNT-Dox within 8 hours indicating similar cellular deformations using nanocarrier anticancer drug-conjugates to that of free Dox (KR ∼0.50) at 4 hours. In addition, we observed increased NSA at 4 h in Dox treatment whereas in the case of the Dox conjugated nanocarrier, increased NSA was noted at 8 h treatment. At 8 h exposure of HeLa cells with Dox conjugates, we observed that the cells fall into distinct regions of the morphospace with respect to KR and NSA. Conclusively, nano delivery systems considered for clinical and biomedical translations must take into account the possible negative influences imparting higher cellular deformations and secondary adverse effects over the free form of the drug.

Opportunities for Quantitative Translational Modeling in Oncology

A 2-day meeting was held by members of the UK Quantitative Systems Pharmacology Network () in November 2018 on the topic of Translational Challenges in Oncology. Participants from a wide range of backgrounds were invited to discuss current and emerging modeling applications in nonclinical and clinical drug development, and to identify areas for improvement. This resulting perspective explores opportunities for impactful quantitative pharmacology approaches. Four key themes arose from the presentations and discussions that were held, leading to the following recommendations: Evaluate the predictivity and reproducibility of animal cancer models through precompetitive collaboration. Apply mechanism of action (MoA) based mechanistic models derived from nonclinical data to clinical trial data. Apply MoA reflective models across trial data sets to more robustly quantify the natural history of disease and response to differing interventions. Quantify more robustly the dose and concentration dependence of adverse events through mathematical modelling techniques and modified trial design.

Modeling of Nanotherapy Response as a Function of the Tumor Microenvironment: Focus on Liver Metastasis

The tumor microenvironment (TME) presents a challenging barrier for effective nanotherapy-mediated drug delivery to solid tumors. In particular for tumors less vascularized than the surrounding normal tissue, as in liver metastases, the structure of the organ itself conjures with cancer-specific behavior to impair drug transport and uptake by cancer cells. Cells and elements in the TME of hypovascularized tumors play a key role in the process of delivery and retention of anti-cancer therapeutics by nanocarriers. This brief review describes the drug transport challenges and how they are being addressed with advanced in vitro 3D tissue models as well as with in silico mathematical modeling. This modeling complements network-oriented techniques, which seek to interpret intra-cellular relevant pathways and signal transduction within cells and with their surrounding microenvironment. With a concerted effort integrating experimental observations with computational analyses spanning from the molecular- to the tissue-scale, the goal of effective nanotherapy customized to patient tumor-specific conditions may be finally realized.

Drug delivery: Experiments, mathematical modelling and machine learning

We address the problem of determining from laboratory experiments the data necessary for a proper modeling of drug delivery and efficacy in anticancer therapy. There is an inherent difficulty in extracting the necessary parameters, because the experiments often yield an insufficient quantity of information. To overcome this difficulty, we propose to combine real experiments, numerical simulation, and Machine Learning (ML) based on Artificial Neural Networks (ANN), aiming at a reliable identification of the physical model factors, e.g. the killing action of the drug. To this purpose, we exploit the employed mathematical-numerical model for tumor growth and drug delivery, together with the ANN - ML procedure, to integrate the results of the experimental tests and feed back the model itself, thus obtaining a reliable predictive tool. The procedure represents a hybrid data-driven, physics-informed approach to machine learning. The physical and mathematical model employed for the numerical simulations is without extracellular matrix (ECM) and healthy cells because of the experimental conditions we reproduce.

Investigating the Physical Effects in Bacterial Therapies for Avascular Tumors

Tumor-targeting bacteria elicit anticancer effects by infiltrating hypoxic regions, releasing toxic agents and inducing immune responses. Although current research has largely focused on the influence of chemical and immunological aspects on the mechanisms of bacterial therapy, the impact of physical effects is still elusive. Here, we propose a mathematical model for the anti-tumor activity of bacteria in avascular tumors that takes into account the relevant chemo-mechanical effects. We consider a time-dependent administration of bacteria and analyze the impact of bacterial chemotaxis and killing rate. We show that active bacterial migration toward tumor hypoxic regions provides optimal infiltration and that high killing rates combined with high chemotactic values provide the smallest tumor volumes at the end of the treatment. We highlight the emergence of steady states in which a small population of bacteria is able to constrain tumor growth. Finally, we show that bacteria treatment works best in the case of tumors with high cellular proliferation and low oxygen consumption.

Using mechanistic models for the clinical interpretation of complex genomic variation

The sustained generation of genomic data in the last decade has increased the knowledge on the causal mutations of a large number of diseases, especially for highly penetrant Mendelian diseases, typically caused by a unique or a few genes. However, the discovery of causal genes in complex diseases has been far less successful. Many complex diseases are actually a consequence of the failure of complex biological modules, composed by interrelated proteins, which can happen in many different ways, which conferring a multigenic nature to the condition that can hardly be attributed to one or a few genes. We present a mechanistic model, Hipathia, implemented in a web server that allows estimating the effect that mutations, or changes in the expression of genes, have over the whole system of human signaling and the corresponding functional consequences. We show several use cases where we demonstrate how different the ultimate impact of mutations with similar loss-of-function potential can be and how the potential pathological role of a damaged gene can be inferred within the context of a signaling network. The use of systems biology-based approaches, such as mechanistic models, allows estimating the potential impact of loss-of-function mutations occurring in proteins that are part of complex biological interaction networks, such as signaling pathways. This holistic approach provides an elegant alternative to gene-centric approaches that can open new avenues in the interpretation of the genomic variability in complex diseases.

Mathematical modeling and computational prediction of cancer drug resistance

Diverse forms of resistance to anticancer drugs can lead to the failure of chemotherapy. Drug resistance is one of the most intractable issues for successfully treating cancer in current clinical practice. Effective clinical approaches that could counter drug resistance by restoring the sensitivity of tumors to the targeted agents are urgently needed. As numerous experimental results on resistance mechanisms have been obtained and a mass of high-throughput data has been accumulated, mathematical modeling and computational predictions using systematic and quantitative approaches have become increasingly important, as they can potentially provide deeper insights into resistance mechanisms, generate novel hypotheses or suggest promising treatment strategies for future testing. In this review, we first briefly summarize the current progress of experimentally revealed resistance mechanisms of targeted therapy, including genetic mechanisms, epigenetic mechanisms, posttranslational mechanisms, cellular mechanisms, microenvironmental mechanisms and pharmacokinetic mechanisms. Subsequently, we list several currently available databases and Web-based tools related to drug sensitivity and resistance. Then, we focus primarily on introducing some state-of-the-art computational methods used in drug resistance studies, including mechanism-based mathematical modeling approaches (e.g. molecular dynamics simulation, kinetic model of molecular networks, ordinary differential equation model of cellular dynamics, stochastic model, partial differential equation model, agent-based model, pharmacokinetic–pharmacodynamic model, etc.) and data-driven prediction methods (e.g. omics data-based conventional screening approach for node biomarkers, static network approach for edge biomarkers and module biomarkers, dynamic network approach for dynamic network biomarkers and dynamic module network biomarkers, etc.). Finally, we discuss several further questions and future directions for the use of computational methods for studying drug resistance, including inferring drug-induced signaling networks, multiscale modeling, drug combinations and precision medicine.

Anticancer Drug Response Prediction in Cell Lines Using Weighted Graph Regularized Matrix Factorization

Precision medicine has become a novel and rising concept, which depends much on the identification of individual genomic signatures for different patients. The cancer cell lines could reflect the “omic” diversity of primary tumors, based on which many works have been carried out to study the cancer biology and drug discovery both in experimental and computational aspects. In this work, we presented a novel method to utilize weighted graph regularized matrix factorization (WGRMF) for inferring anticancer drug response in cell lines. We constructed a p-nearest neighbor graph to sparsify drug similarity matrix and cell line similarity matrix, respectively. Using the sparsified matrices in the graph regularization terms, we performed matrix factorization to generate the latent matrices for drug and cell line. The graph regularization terms including neighbor information could help to exclude the noisy ingredient and improve the prediction accuracy. The 10-fold cross-validation was implemented, and the Pearson correlation coefficient (PCC), root-mean-square error (RMSE), PCCsr, and RMSEsr averaged over all drugs were calculated to evaluate the performance of WGRMF. The results on the Genomics of Drug Sensitivity in Cancer (GDSC) dataset are 0.64 ± 0.16, 1.37 ± 0.35, 0.73 ± 0.14, and 1.71 ± 0.44 for PCC, RMSE, PCCsr, and RMSEsr in turn. And for the Cancer Cell Line Encyclopedia (CCLE) dataset, WGRMF got results of 0.72 ± 0.09, 0.56 ± 0.19, 0.79 ± 0.07, and 0.69 ± 0.19, respectively. The results showed the superiority of WGRMF compared with previous methods. Besides, based on the prediction results using the GDSC dataset, three types of case studies were carried out. The results from both cross-validation and case studies have shown the effectiveness of WGRMF on the prediction of drug response in cell lines.

Efficacy of Surface-Modified PLGA Nanoparticles as a Function of Cervical Cancer Type

PURPOSE

Hypovascularization of cervical tumors, coupled with intrinsic and acquired drug resistance, has contributed to marginal therapeutic outcomes by hindering chemotherapeutic transport and efficacy. Recently, the heterogeneous penetration and distribution of cell penetrating peptide (CPP, here MPG) and polyethylene glycol (PEG) modified poly(lactic-co-glycolic acid) (PLGA) nanoparticles (NPs) were evaluated as a function of tumor type and morphology in cervical cancer spheroids modeling hypovascularized tumor nodules. Building upon this work, this study investigates the efficacy imparted by surface-modified Doxorubicin-loaded NPs transported into hypovascularized tissue.

METHODS

NP efficacy was measured in HeLa, CaSki, and SiHa cells. NP internalization and association, and associated cell viability, were determined in monolayer and spheroid models.

RESULTS

MPG and PEG-NP co-treatment was most efficacious in HeLa cells, while PEG NPs were most efficacious in CaSki cells. NP surface-modifications were unable to improve efficacy, relative to unmodified NPs, in SiHa cells.

CONCLUSIONS

The results highlight the dependence of efficacy on tumor type and the associated microenvironment. The results further relate previous NP transport studies to efficacy, as a function of surface-modification and cell type. Longer-term, this information may help guide the design of NP-mediated strategies to maximize efficacy based on patient-specific cervical tumor origin and characteristics.

Design Optimization of Tumor Vasculature-Bound Nanoparticles

Nanotherapy may constitute a promising approach to target tumors with anticancer drugs while minimizing systemic toxicity. Computational modeling can enable rapid evaluation of nanoparticle (NP) designs and numerical optimization. Here, an optimization study was performed using an existing tumor model to find NP size and ligand density that maximize tumoral NP accumulation while minimizing tumor size. Optimal NP avidity lies at lower bound of feasible values, suggesting reduced ligand density to prolong NP circulation. For the given set of tumor parameters, optimal NP diameters were 288 nm to maximize NP accumulation and 334 nm to minimize tumor diameter, leading to uniform NP distribution and adequate drug load. Results further show higher dependence of NP biodistribution on the NP design than on tumor morphological parameters. A parametric study with respect to drug potency was performed. The lower the potency of the drug, the bigger the difference is between the maximizer of NP accumulation and the minimizer of tumor size, indicating the existence of a specific drug potency that minimizes the differential between the two optimal solutions. This study shows the feasibility of applying optimization to NP designs to achieve efficacious cancer nanotherapy, and offers a first step towards a quantitative tool to support clinical decision making.

Pharmacokinetic/pharmacodynamic modeling of combination-chemotherapy for lung cancer

Chemotherapy for non-small cell lung cancer (NSCLC) typically involves a doublet regimen for a number of cycles. For any particular patient, a course of treatment is usually chosen from a large number of combinational protocols with drugs in concomitant or sequential administration. In spite of newer drugs and protocols, half of patients with early disease will live less than five years and 95% of those with advanced disease survive for less than one year. Here, we apply mathematical modeling to simulate tumor response to multiple drug regimens, with the capability to assess maximum tolerated dose (MTD) as well as metronomic drug administration. We couple pharmacokinetic-pharmacodynamic intracellular multi-compartment models with a model of vascularized tumor growth, setting input parameters from in vitro data, and using the models to project potential response in vivo. This represents an initial step towards the development of a comprehensive virtual system to evaluate tumor response to combinatorial drug regimens, with the goal to more efficiently identify optimal course of treatment with patient tumor-specific data. We evaluate cisplatin and gemcitabine with clinically-relevant dosages, and simulate four treatment NSCLC scenarios combining MTD and metronomic therapy. This work thus establishes a framework for systematic evaluation of tumor response to combination chemotherapy. The results with the chosen parameter set indicate that although a metronomic regimen may provide advantage over MTD, the combination of these regimens may not necessarily offer improved response. Future model evaluation of chemotherapy possibilities may help to assess their potential value to obtain sustained NSCLC regression for particular patients, with the ultimate goal of optimizing multiple-drug chemotherapy regimens in clinical practice.

Translational models of tumor angiogenesis: A nexus of in silico and in vitro models

Emerging evidence shows that endothelial cells are not only the building blocks of vascular networks that enable oxygen and nutrient delivery throughout a tissue but also serve as a rich resource of angiocrine factors. Endothelial cells play key roles in determining cancer progression and response to anti-cancer drugs. Furthermore, the endothelium-specific deposition of extracellular matrix is a key modulator of the availability of angiocrine factors to both stromal and cancer cells. Considering tumor vascular network as a decisive factor in cancer pathogenesis and treatment response, these networks need to be an inseparable component of cancer models. Both computational and in vitro experimental models have been extensively developed to model tumor-endothelium interactions. While informative, they have been developed in different communities and do not yet represent a comprehensive platform. In this review, we overview the necessity of incorporating vascular networks for both in vitro and in silico cancer models and discuss recent progresses and challenges of in vitro experimental microfluidic cancer vasculature-on-chip systems and their in silico counterparts. We further highlight how these two approaches can merge together with the aim of presenting a predictive combinatorial platform for studying cancer pathogenesis and testing the efficacy of single or multi-drug therapeutics for cancer treatment.

In Vitro/In Silico Study on the Role of Doubling Time Heterogeneity among Primary Glioblastoma Cell Lines

The application of accurate cancer predictive algorithms validated with experimental data is a field concerning both basic researchers and clinicians, especially regarding a highly aggressive form of cancer, such as Glioblastoma. In an aim to enhance prediction accuracy in realistic patient-specific environments, accounting for both inter- and intratumoral heterogeneity, we use patient-derived Glioblastoma cells from different patients. We focus on cell proliferation using in vitro experiments to estimate cell doubling times and sizes for established primary Glioblastoma cell lines. A preclinically driven mathematical model parametrization is accomplished by taking into account the experimental measurements. As a control cell line we use the well-studied U87MG cells. Both in vitro and in silico results presented support that the variance between tumor staging can be attributed to the differential proliferative capacity of the different Glioblastoma cells. More specifically, the intratumoral heterogeneity together with the overall proliferation reflected in both the proliferation rate and the mechanical cell contact inhibition can predict the in vitro evolution of different Glioblastoma cell lines growing under the same conditions. Undoubtedly, additional imaging techniques capable of providing spatial information of tumor cell physiology and microenvironment will enhance our understanding regarding Glioblastoma nature and verify and further improve our predictability.

Distribution of PLGA-modified nanoparticles in 3D cell culture models of hypo-vascularized tumor tissue

BACKGROUND

Advanced stage cancer treatments are often invasive and painful-typically comprised of surgery, chemotherapy, and/or radiation treatment. Low transport efficiency during systemic chemotherapy may require high chemotherapeutic doses to effectively target cancerous tissue, resulting in systemic toxicity. Nanotherapeutic platforms have been proposed as an alternative to more safely and effectively deliver therapeutic agents directly to tumor sites. However, cellular internalization and tumor penetration are often diametrically opposed, with limited access to tumor regions distal from vasculature, due to irregular tissue morphologies. To address these transport challenges, nanoparticles (NPs) are often surface-modified with ligands to enhance transport and longevity after localized or systemic administration. Here, we evaluate stealth polyethylene-glycol (PEG), cell-penetrating (MPG), and CPP-stealth (MPG/PEG) poly(lactic-co-glycolic-acid) (PLGA) NP co-treatment strategies in 3D cell culture representing hypo-vascularized tissue.

RESULTS

Smaller, more regularly-shaped avascular tissue was generated using the hanging drop (HD) method, while more irregularly-shaped masses were formed with the liquid overlay (LO) technique. To compare NP distribution differences within the same type of tissue as a function of different cancer types, we selected HeLa, cervical epithelial adenocarcinoma cells; CaSki, cervical epidermoid carcinoma cells; and SiHa, grade II cervical squamous cell carcinoma cells. In HD tumors, enhanced distribution relative to unmodified NPs was measured for MPG and PEG NPs in HeLa, and for all modified NPs in SiHa spheroids. In LO tumors, the greatest distribution was observed for MPG and MPG/PEG NPs in HeLa, and for PEG and MPG/PEG NPs in SiHa spheroids.

CONCLUSIONS

Pre-clinical evaluation of PLGA-modified NP distribution into hypo-vascularized tumor tissue may benefit from considering tissue morphology in addition to cancer type.

A hybrid discrete-continuous model of in vitro spheroid tumor growth and drug response

Anti-cancer therapy efficacy in solid tumors mainly depends on drug transportation through the vasculature system and the extracellular matrix, on diffusion gradients and clonal heterogeneity within the tumor mass, as well as on the responses of the individual tumor cells to drugs and their interactions with each other and their local microenvironment. In this work, we develop a mathematical predictive model for tumor growth and drug response based on 3D spheroids experiments that possess several in vivo features of tumors and are considered better for drug screening. The model takes into account the diffusion gradients of both oxygen and drug through the tumor volume, describes the tumor population at cell level and assumes a simple underlying cellular dose-response curve that is translated to a cell death probability. The model shows that although the endpoint tumor regression can be well approximated, the effects of the drug on cell fate necessitate a more sophisticated model to explain the temporal evolution of tumor regression and more quantitative information regarding the number and topology of dead and living cells, which is highly important for in vivo clinical relevant predictions. The model is built in a way that can be constrained by experimentally derived set of parameters and is capable of accommodating cell heterogeneity, sub-cellular regulatory mechanisms and drug-induced signaling cascades, as well as additional mechanisms of adapted resistance.

An agent-based model of triple-negative breast cancer: the interplay between chemokine receptor CCR5 expression, cancer stem cells, and hypoxia

Background

Triple-negative breast cancer lacks estrogen, progesterone, and HER2 receptors and is thus not possible to treat with targeted therapies for these receptors. Therefore, a greater understanding of triple-negative breast cancer is necessary for the treatment of this cancer type. In previous work from our laboratory, we found that chemokine ligand-receptor CCL5-CCR5 axis is important for the metastasis of human triple-negative breast cancer cell MDA-MB-231 to the lymph nodes and lungs, in a mouse xenograft model. We collected relevant experimental data from our and other laboratories for numbers of cancer stem cells, numbers of CCR5+ cells, and cell migration rates for different breast cancer cell lines and different experimental conditions.

Results

Using these experimental data we developed an in silico agent-based model of triple-negative breast cancer that considers surface receptor CCR5-high and CCR5-low cells and breast cancer stem cells, to predict the tumor growth rate and spatio-temporal distribution of cells in primary tumors. We find that high cancer stem cell percentages greatly increase tumor growth. We find that anti-stem cell treatment decreases tumor growth but may not lead to dormancy unless all stem cells get eliminated. We further find that hypoxia increases overall tumor growth and treatment with a CCR5 inhibitor maraviroc slightly decreases overall tumor growth. We also characterize 3D shapes of solid and invasive tumors using several shape metrics.

Conclusions

Breast cancer stem cells and CCR5+ cells affect the overall growth and morphology of breast tumors. In silico drug treatments demonstrate limited efficacy of incomplete inhibition of cancer stem cells after which tumor growth recurs, and CCR5 inhibition causes only a slight reduction in tumor growth.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0445-x) contains supplementary material, which is available to authorized users.

Automated analysis of co-localized protein expression in histologic sections of prostate cancer

An automated approach based on routinely-processed, whole-slide immunohistochemistry (IHC) was implemented to study co-localized protein expression in tissue samples. Expression of two markers was chosen to represent stromal (CD31) and epithelial (Ki-67) compartments in prostate cancer. IHC was performed on whole-slide sections representing low-, intermediate-, and high-grade disease from 15 patients. The automated workflow was developed using a training set of regions-of-interest in sequential tissue sections. Protein expression was studied on digital representations of IHC images across entire slides representing formalin-fixed paraffin embedded blocks. Using the training-set, the known association between Ki-67 and Gleason grade was confirmed. CD31 expression was more heterogeneous across samples and remained invariant with grade in this cohort. Interestingly, the Ki-67/CD31 ratio was significantly increased in high (Gleason ≥ 8) versus low/intermediate (Gleason ≤7) samples when assessed in the training-set and the whole-tissue block images. Further, the feasibility of the automated approach to process Tissue Microarray (TMA) samples in high throughput was evaluated. This work establishes an initial framework for automated analysis of co-localized protein expression and distribution in high-resolution digital microscopy images based on standard IHC techniques. Applied to a larger sample population, the approach may help to elucidate the biologic basis for the Gleason grade, which is the strongest, single factor distinguishing clinically aggressive from indolent prostate cancer.

Evaluating the influence of mechanical stress on anticancer treatments through a multiphase porous media model

Drug resistance is one of the leading causes of poor therapy outcomes in cancer. As several chemotherapeutics are designed to target rapidly dividing cells, the presence of a low-proliferating cell population contributes significantly to treatment resistance. Interestingly, recent studies have shown that compressive stresses acting on tumor spheroids are able to hinder cell proliferation, through a mechanism of growth inhibition. However, studies analyzing the influence of mechanical compression on therapeutic treatment efficacy have still to be performed. In this work, we start from an existing mathematical model for avascular tumors, including the description of mechanical compression. We introduce governing equations for transport and uptake of a chemotherapeutic agent, acting on cell proliferation. Then, model equations are adapted for tumor spheroids and the combined effect of compressive stresses and drug action is investigated. Interestingly, we find that the variation in tumor spheroid volume, due to the presence of a drug targeting cell proliferation, considerably depends on the compressive stress level of the cell aggregate. Our results suggest that mechanical compression of tumors may compromise the efficacy of chemotherapeutic agents. In particular, a drug dose that is effective in reducing tumor volume for stress-free conditions may not perform equally well in a mechanically compressed environment.

Inferences of drug responses in cancer cells from cancer genomic features and compound chemical and therapeutic properties

Accurately predicting the response of a cancer patient to a therapeutic agent is a core goal of precision medicine. Existing approaches were mainly relied primarily on genomic alterations in cancer cells that have been treated with different drugs. Here we focus on predicting drug response based on integration of the heterogeneously pharmacogenomics data from both cell and drug sides. Through a systematical approach, named as PDRCC (Predict Drug Response in Cancer Cells), the cancer genomic alterations and compound chemical and therapeutic properties were incorporated to determine the chemotherapeutic response in cancer patients. Using the Cancer Cell Line Encyclopedia (CCLE) study as the benchmark dataset, all pharmacogenomics data exhibited their roles in inferring the relationships between cancer cells and drugs. When integrating both genomic resources and compound information, the prediction coverage was significantly increased. The validity of PDRCC was also supported by its effective in uncovering the unknown cell-drug associations with database and literature evidences. It set the stage for clinical testing of novel therapeutic strategies, such as the sensitive association between cancer cell ‘A549_LUNG’ and compound ‘Topotecan’. In conclusion, PDRCC offers the possibility for faster, safer, and cheaper the development of novel anti-cancer therapeutics in the early-stage clinical trails.

The Application of Ultrasound in 3D Bio-Printing

Three-dimensional (3D) bioprinting is an emerging and promising technology in tissue engineering to construct tissues and organs for implantation. Alignment of self-assembly cell spheroids that are used as bioink could be very accurate after droplet ejection from bioprinter. Complex and heterogeneous tissue structures could be built using rapid additive manufacture technology and multiple cell lines. Effective vascularization in the engineered tissue samples is critical in any clinical application. In this review paper, the current technologies and processing steps (such as printing, preparation of bioink, cross-linking, tissue fusion and maturation) in 3D bio-printing are introduced, and their specifications are compared with each other. In addition, the application of ultrasound in this novel field is also introduced. Cells experience acoustic radiation force in ultrasound standing wave field (USWF) and then accumulate at the pressure node at low acoustic pressure. Formation of cell spheroids by this method is within minutes with uniform size and homogeneous cell distribution. Neovessel formation from USWF-induced endothelial cell spheroids is significant. Low-intensity ultrasound could enhance the proliferation and differentiation of stem cells. Its use is at low cost and compatible with current bioreactor. In summary, ultrasound application in 3D bio-printing may solve some challenges and enhance the outcomes.

Mathematical Modeling of Therapy-induced Cancer Drug Resistance: Connecting Cancer Mechanisms to Population Survival Rates

Drug resistance significantly limits the long-term effectiveness of targeted therapeutics for cancer patients. Recent experimental studies have demonstrated that cancer cell heterogeneity and microenvironment adaptations to targeted therapy play important roles in promoting the rapid acquisition of drug resistance and in increasing cancer metastasis. The systematic development of effective therapeutics to overcome drug resistance mechanisms poses a major challenge. In this study, we used a modeling approach to connect cellular mechanisms underlying cancer drug resistance to population-level patient survival. To predict progression-free survival in cancer patients with metastatic melanoma, we developed a set of stochastic differential equations to describe the dynamics of heterogeneous cell populations while taking into account micro-environment adaptations. Clinical data on survival and circulating tumor cell DNA (ctDNA) concentrations were used to confirm the effectiveness of our model. Moreover, our model predicted distinct patterns of dose-dependent synergy when evaluating a combination of BRAF and MEK inhibitors versus a combination of BRAF and PI3K inhibitors. These predictions were consistent with the findings in previously reported studies. The impact of the drug metabolism rate on patient survival was also discussed. The proposed model might facilitate the quantitative evaluation and optimization of combination therapeutics and cancer clinical trial design.

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.

The mathematics of cancer: integrating quantitative models

Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.

Treatment of non-muscle invasive bladder cancer with Bacillus Calmette-Guerin (BCG): Biological markers and simulation studies

Intravesical Bacillus Calmette-Guerin (BCG) vaccine is the preferred first line treatment for non-muscle invasive bladder carcinoma (NMIBC) in order to prevent recurrence and progression of cancer. There is ongoing need for the rational selection of i) BCG dose, ii) frequency of BCG administration along with iii) synergistic adjuvant therapy and iv) a reliable set of biochemical markers relevant to tumor response. In this review we evaluate cellular and molecular markers pertinent to the immunological response triggered by the BCG instillation and respective mathematical models of the treatment. Specific examples of markers include diverse immune cells, genetic polymorphisms, miRNAs, epigenetics, immunohistochemistry and molecular biology 'beacons' as exemplified by cell surface proteins, cytokines, signaling proteins and enzymes. We identified tumor associated macrophages (TAMs), human leukocyte antigen (HLA) class I, a combination of Ki-67/CK20, IL-2, IL-8 and IL-6/IL-10 ratio as the most promising markers for both pre-BCG and post-BCG treatment suitable for the simulation studies. The intricate and patient-specific nature of these data warrants the use of powerful multi-parametral mathematical methods in combination with molecular/cellular biology insight and clinical input.

Key signaling pathways in the muscle-invasive bladder carcinoma: Clinical markers for disease modeling and optimized treatment

In this review, we evaluate key molecular pathways and markers of muscle-invasive bladder cancer (MIBC). Overexpression and activation of EGFR, p63, and EMT genes are suggestive of basal MIBC subtype generally responsive to chemotherapy. Alterations in PPARγ, ERBB2/3, and FGFR3 gene products and their signaling along with deregulated p53, cytokeratins KRT5/6/14 in combination with the cellular proliferation (Ki-67), and cell cycle markers (p16) indicate the need for more radical treatment protocols. Similarly, the "bell-shape" dynamics of Shh expression levels may suggest aggressive MIBC. A panel of diverse biological markers may be suitable for simulation studies of MIBC and development of an optimized treatment protocol. We conducted a critical evaluation of PubMed/Medline and SciFinder databases related to MIBC covering the period 2009-2015. The free-text search was extended by adding the following keywords and phrases: bladder cancer, metastatic, muscle-invasive, basal, luminal, epithelial-to-mesenchymal transition, cancer stem cell, mutations, immune response, signaling, biological markers, molecular markers, mathematical models, simulation, epigenetics, transmembrane, transcription factor, kinase, predictor, prognosis. The resulting selection of ca 500 abstracts was further analyzed in order to select the latest publications relevant to MIBC molecular markers of immediate clinical significance.

Recapitulating the Tumor Ecosystem Along the Metastatic Cascade Using 3D Culture Models

Advances in cancer research have shown that a tumor can be likened to a foreign species that disrupts delicately balanced ecological interactions, compromising the survival of normal tissue ecosystems. In efforts to mitigate tumor expansion and metastasis, experimental approaches from ecology are becoming more frequently and successfully applied by researchers from diverse disciplines to reverse engineer and re-engineer biological systems in order to normalize the tumor ecosystem. We present a review on the use of 3D biomimetic platforms to recapitulate biotic and abiotic components of the tumor ecosystem, in efforts to delineate the underlying mechanisms that drive evolution of tumor heterogeneity, tumor dissemination, and acquisition of drug resistance.

Predictive Modeling of Drug Response in Non-Hodgkin's Lymphoma

We combine mathematical modeling with experiments in living mice to quantify the relative roles of intrinsic cellular vs. tissue-scale physiological contributors to chemotherapy drug resistance, which are difficult to understand solely through experimentation. Experiments in cell culture and in mice with drug-sensitive (Eµ-myc/Arf-/-) and drug-resistant (Eµ-myc/p53-/-) lymphoma cell lines were conducted to calibrate and validate a mechanistic mathematical model. Inputs to inform the model include tumor drug transport characteristics, such as blood volume fraction, average geometric mean blood vessel radius, drug diffusion penetration distance, and drug response in cell culture. Model results show that the drug response in mice, represented by the fraction of dead tumor volume, can be reliably predicted from these inputs. Hence, a proof-of-principle for predictive quantification of lymphoma drug therapy was established based on both cellular and tissue-scale physiological contributions. We further demonstrate that, if the in vitro cytotoxic response of a specific cancer cell line under chemotherapy is known, the model is then able to predict the treatment efficacy in vivo. Lastly, tissue blood volume fraction was determined to be the most sensitive model parameter and a primary contributor to drug resistance.

The effect of intrinsic and acquired resistances on chemotherapy effectiveness

Although chemotherapy is one of the most common treatments for cancer, it can be only partially successful. Drug resistance is the main cause of the failure of chemotherapy. In this work, we present a mathematical model to study the impact of both intrinsic (preexisting) and acquired (induced by the drugs) resistances on chemotherapy effectiveness. Our simulations show that intrinsic resistance could be as dangerous as acquired resistance. In particular, our simulations suggest that tumors composed by even a small fraction of intrinsically resistant cells may lead to an unsuccessful therapy very quickly. Our results emphasize the importance of monitoring both intrinsic and acquired resistances during treatment in order to succeed and the importance of doing more experimental and genetic research in order to develop a pretreatment clinical test to avoid intrinsic resistance.

Combinative in vitro studies and computational model to predict 3D cell migration response to drug insult

The development of drugs to counter diseases related to cell migration has resulted in a multi-billion dollar endeavor. Unfortunately, few drugs have emerged from this effort highlighting the need for new methods to enhance assays to study, analyze and control cell migration. In response to this complex process, computational models have emerged as potent tools to describe migration providing a high throughput and low cost method. However, most models are unable to predict migration response to drug with direct application to in vitro experiments. In addition to this, no model to date has attempted to describe migration in response to drugs while incorporating simultaneously protein signaling, proteolytic activity, and 3D culture. In this paper, we describe an integrated computational approach, in conjunction with in vitro observations, to serve as a platform to accurately predict migration in 3D matrices incorporating the function of matrix metalloproteinases (MMPs) and their interaction with the Extracellular signal-related kinase (ERK) signaling pathway. Our results provide biological insight into how matrix density, MMP activity, integrin adhesions, and p-ERK expression all affect speed and persistence in 3D. Predictions from the model provide insight toward improving drug combinations to more effectively reduce both speed and persistence during migration and the role of integrin adhesions in motility. In this way our integrated platform provides future potential to streamline and improve throughput toward the testing and development of migration targeting drugs with tangible application to current in vitro assays.

A network flow-based method to predict anticancer drug sensitivity

Predicting anticancer drug sensitivity can enhance the ability to individualize patient treatment, thus making development of cancer therapies more effective and safe. In this paper, we present a new network flow-based method, which utilizes the topological structure of pathways, for predicting anticancer drug sensitivities. Mutations and copy number alterations of cancer-related genes are assumed to change the pathway activity, and pathway activity difference before and after drug treatment is used as a measure of drug response. In our model, Contributions from different genetic alterations are considered as free parameters, which are optimized by the drug response data from the Cancer Genome Project (CGP). 10-fold cross validation on CGP data set showed that our model achieved comparable prediction results with existing elastic net model using much less input features.

Integrated PK-PD and agent-based modeling in oncology

Mathematical modeling has become a valuable tool that strives to complement conventional biomedical research modalities in order to predict experimental outcome, generate new medical hypotheses, and optimize clinical therapies. Two specific approaches, pharmacokinetic-pharmacodynamic (PK-PD) modeling, and agent-based modeling (ABM), have been widely applied in cancer research. While they have made important contributions on their own (e.g., PK-PD in examining chemotherapy drug efficacy and resistance, and ABM in describing and predicting tumor growth and metastasis), only a few groups have started to combine both approaches together in an effort to gain more insights into the details of drug dynamics and the resulting impact on tumor growth. In this review, we focus our discussion on some of the most recent modeling studies building on a combined PK-PD and ABM approach that have generated experimentally testable hypotheses. Some future directions are also discussed.

The effect of interstitial pressure on therapeutic agent transport: coupling with the tumor blood and lymphatic vascular systems

Vascularized tumor growth is characterized by both abnormal interstitial fluid flow and the associated interstitial fluid pressure (IFP). Here, we study the effect that these conditions have on the transport of therapeutic agents during chemotherapy. We apply our recently developed vascular tumor growth model which couples a continuous growth component with a discrete angiogenesis model to show that hypertensive IFP is a physical barrier that may hinder vascular extravasation of agents through transvascular fluid flux convection, which drives the agents away from the tumor. This result is consistent with previous work using simpler models without blood flow or lymphatic drainage. We consider the vascular/interstitial/lymphatic fluid dynamics to show that tumors with larger lymphatic resistance increase the agent concentration more rapidly while also experiencing faster washout. In contrast, tumors with smaller lymphatic resistance accumulate less agents but are able to retain them for a longer time. The agent availability (area-under-the curve, or AUC) increases for less permeable agents as lymphatic resistance increases, and correspondingly decreases for more permeable agents. We also investigate the effect of vascular pathologies on agent transport. We show that elevated vascular hydraulic conductivity contributes to the highest AUC when the agent is less permeable, but to lower AUC when the agent is more permeable. We find that elevated interstitial hydraulic conductivity contributes to low AUC in general regardless of the transvascular agent transport capability. We also couple the agent transport with the tumor dynamics to simulate chemotherapy with the same vascularized tumor under different vascular pathologies. We show that tumors with an elevated interstitial hydraulic conductivity alone require the strongest dosage to shrink. We further show that tumors with elevated vascular hydraulic conductivity are more hypoxic during therapy and that the response slows down as the tumor shrinks due to the heterogeneity and low concentration of agents in the tumor interior compared with the cases where other pathological effects may combine to flatten the IFP and thus reduce the heterogeneity. We conclude that dual normalizations of the micronevironment - both the vasculature and the interstitium - are needed to maximize the effects of chemotherapy, while normalization of only one of these may be insufficient to overcome the physical resistance and may thus lead to sub-optimal outcomes.

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.

Understanding Drug Resistance in Breast Cancer with Mathematical Oncology

Chemotherapy is mainstay of treatment for the majority of patients with breast cancer, but results in only 26% of patients with distant metastasis living 5 years past treatment in the United States, largely due to drug resistance. The complexity of drug resistance calls for an integrated approach of mathematical modeling and experimental investigation to develop quantitative tools that reveal insights into drug resistance mechanisms, predict chemotherapy efficacy, and identify novel treatment approaches. This paper reviews recent modeling work for understanding cancer drug resistance through the use of computer simulations of molecular signaling networks and cancerous tissues, with a particular focus on breast cancer. These mathematical models are developed by drawing on current advances in molecular biology, physical characterization of tumors, and emerging drug delivery methods (e.g., nanotherapeutics). We focus our discussion on representative modeling works that have provided quantitative insight into chemotherapy resistance in breast cancer and how drug resistance can be overcome or minimized to optimize chemotherapy treatment. We also discuss future directions of mathematical modeling in understanding drug resistance.

Mechanistic modeling identifies drug-uptake history as predictor of tumor drug resistance and nano-carrier-mediated response

A quantitative understanding of the advantages of nanoparticle-based drug delivery vis-à-vis conventional free drug chemotherapy has yet to be established for cancer or other diseases despite numerous investigations. Here, we employ first-principles cell biophysics, drug pharmaco-kinetics, and drug pharmaco-dynamics to model the delivery of doxorubicin (DOX) to hepatocellular carcinoma (HCC) tumor cells and predict the resultant experimental cytotoxicity data. The fundamental, mechanistic hypothesis of our mathematical model is that the integrated history of drug uptake by the cells over time of exposure, which sets the cell death rate parameter, and the uptake rate are the sole determinants of the dose response relationship. A universal solution of the model equations is capable of predicting the entire, nonlinear dose response of the cells to any drug concentration based on just two separate measurements of these cellular parameters. This analysis reveals that nanocarrier-mediated delivery overcomes resistance to the free drug because of improved cellular uptake rates, and that dose response curves to nanocarrier mediated drug delivery are equivalent to those for free-drug, but "shifted to the left;" that is, lower amounts of drug achieve the same cell kill. We then demonstrate the model's general applicability to different tumor and drug types, and cell-exposure time courses by investigating HCC cells exposed to cisplatin and 5-fluorouracil, breast cancer MCF-7 cells exposed to DOX, and pancreatic adenocarcinoma PANC-1 cells exposed to gemcitabine. The model will help in the optimal design of nanocarriers for clinical applications and improve the current, largely empirical understanding of in vivo drug transport and tumor response.

Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies

BACKGROUND

The expansion of cell colonies is driven by a delicate balance of several mechanisms including cell motility, cell-to-cell adhesion and cell proliferation. New approaches that can be used to independently identify and quantify the role of each mechanism will help us understand how each mechanism contributes to the expansion process. Standard mathematical modelling approaches to describe such cell colony expansion typically neglect cell-to-cell adhesion, despite the fact that cell-to-cell adhesion is thought to play an important role.

RESULTS

We use a combined experimental and mathematical modelling approach to determine the cell diffusivity, D, cell-to-cell adhesion strength, q, and cell proliferation rate, λ, in an expanding colony of MM127 melanoma cells. Using a circular barrier assay, we extract several types of experimental data and use a mathematical model to independently estimate D, q and λ. In our first set of experiments, we suppress cell proliferation and analyse three different types of data to estimate D and q. We find that standard types of data, such as the area enclosed by the leading edge of the expanding colony and more detailed cell density profiles throughout the expanding colony, does not provide sufficient information to uniquely identify D and q. We find that additional data relating to the degree of cell-to-cell clustering is required to provide independent estimates of q, and in turn D. In our second set of experiments, where proliferation is not suppressed, we use data describing temporal changes in cell density to determine the cell proliferation rate. In summary, we find that our experiments are best described using the range D=161-243μm2 hour-1, q=0.3-0.5 (low to moderate strength) and λ=0.0305-0.0398 hour-1, and with these parameters we can accurately predict the temporal variations in the spatial extent and cell density profile throughout the expanding melanoma cell colony.

CONCLUSIONS

Our systematic approach to identify the cell diffusivity, cell-to-cell adhesion strength and cell proliferation rate highlights the importance of integrating multiple types of data to accurately quantify the factors influencing the spatial expansion of melanoma cell colonies.

Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues

Delivery of anti-cancer drugs to tumor tissues, including their interstitial transport and cellular uptake, is a complex process involving various biochemical, mechanical, and biophysical factors. Mathematical modeling provides a means through which to understand this complexity better, as well as to examine interactions between contributing components in a systematic way via computational simulations and quantitative analyses. In this review, we present the current state of mathematical modeling approaches that address phenomena related to drug delivery. We describe how various types of models were used to predict spatio-temporal distributions of drugs within the tumor tissue, to simulate different ways to overcome barriers to drug transport, or to optimize treatment schedules. Finally, we discuss how integration of mathematical modeling with experimental or clinical data can provide better tools to understand the drug delivery process, in particular to examine the specific tissue- or compound-related factors that limit drug penetration through tumors. Such tools will be important in designing new chemotherapy targets and optimal treatment strategies, as well as in developing non-invasive diagnosis to monitor treatment response and detect tumor recurrence.