An integrated computational/experimental model of lymphoma growth

Data-driven spatio-temporal modelling of glioblastoma

Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding glioblastoma, a malignant form of brain cancer. For each approach, we summarize the scope, drawbacks and assets. We highlight the potential clinical applications of each modelling technique and discuss the connections between the mathematical models and the molecular and imaging data used to inform them. By doing so, we aim to prime cancer researchers with current and emerging computational tools for understanding tumour progression. By providing an in-depth picture of the different modelling techniques, we also aim to assist researchers who seek to build and develop their own models and the associated inference frameworks. Our article thus strikes a unique balance. On the one hand, we provide a comprehensive overview of the available modelling techniques and their applications, including key mathematical expressions. On the other hand, the content is accessible to mathematicians and biomedical scientists alike to accommodate the interdisciplinary nature of cancer research.

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.

Determinants of renin cell differentiation: a single cell epi-transcriptomics approach

Rationale

Renin cells are essential for survival. They control the morphogenesis of the kidney arterioles, and the composition and volume of our extracellular fluid, arterial blood pressure, tissue perfusion, and oxygen delivery. It is known that renin cells and associated arteriolar cells descend from FoxD1 + progenitor cells, yet renin cells remain challenging to study due in no small part to their rarity within the kidney. As such, the molecular mechanisms underlying the differentiation and maintenance of these cells remain insufficiently understood.

Objective

We sought to comprehensively evaluate the chromatin states and transcription factors (TFs) that drive the differentiation of FoxD1 + progenitor cells into those that compose the kidney vasculature with a focus on renin cells.

Methods and Results

We isolated single nuclei of FoxD1 + progenitor cells and their descendants from FoxD1 ^cre/+ ; R26R-mTmG mice at embryonic day 12 (E12) (n _cells =1234), embryonic day 18 (E18) (n _cells =3696), postnatal day 5 (P5) (n _cells =1986), and postnatal day 30 (P30) (n _cells =1196). Using integrated scRNA-seq and scATAC-seq we established the developmental trajectory that leads to the mosaic of cells that compose the kidney arterioles, and specifically identified the factors that determine the elusive, myo-endocrine adult renin-secreting juxtaglomerular (JG) cell. We confirm the role of Nfix in JG cell development and renin expression, and identified the myocyte enhancer factor-2 (MEF2) family of TFs as putative drivers of JG cell differentiation.

Conclusions

We provide the first developmental trajectory of renin cell differentiation as they become JG cells in a single-cell atlas of kidney vascular open chromatin and highlighted novel factors important for their stage-specific differentiation. This improved understanding of the regulatory landscape of renin expressing JG cells is necessary to better learn the control and function of this rare cell population as overactivation or aberrant activity of the RAS is a key factor in cardiovascular and kidney pathologies.

Integrative lymph node-mimicking models created with biomaterials and computational tools to study the immune system

The lymph node (LN) is a vital organ of the lymphatic and immune system that enables timely detection, response, and clearance of harmful substances from the body. Each LN comprises of distinct substructures, which host a plethora of immune cell types working in tandem to coordinate complex innate and adaptive immune responses. An improved understanding of LN biology could facilitate treatment in LN-associated pathologies and immunotherapeutic interventions, yet at present, animal models, which often have poor physiological relevance, are the most popular experimental platforms. Emerging biomaterial engineering offers powerful alternatives, with the potential to circumvent limitations of animal models, for in-depth characterization and engineering of the lymphatic and adaptive immune system. In addition, mathematical and computational approaches, particularly in the current age of big data research, are reliable tools to verify and complement biomaterial works. In this review, we first discuss the importance of lymph node in immunity protection followed by recent advances using biomaterials to create in vitro/vivo LN-mimicking models to recreate the lymphoid tissue microstructure and microenvironment, as well as to describe the related immuno-functionality for biological investigation. We also explore the great potential of mathematical and computational models to serve as in silico supports. Furthermore, we suggest how both in vitro/vivo and in silico approaches can be integrated to strengthen basic patho-biological research, translational drug screening and clinical personalized therapies. We hope that this review will promote synergistic collaborations to accelerate progress of LN-mimicking systems to enhance understanding of immuno-complexity.

Multicompartment modeling of protein shedding kinetics during vascularized tumor growth

Identification of protein biomarkers for cancer diagnosis and prognosis remains a critical unmet clinical need. A major reason is that the dynamic relationship between proliferating and necrotic cell populations during vascularized tumor growth, and the associated extra- and intra-cellular protein outflux from these populations into blood circulation remains poorly understood. Complementary to experimental efforts, mathematical approaches have been employed to effectively simulate the kinetics of detectable surface proteins (e.g., CA-125) shed into the bloodstream. However, existing models can be difficult to tune and may be unable to capture the dynamics of non-extracellular proteins, such as those shed from necrotic and apoptosing cells. The models may also fail to account for intra-tumoral spatial and microenvironmental heterogeneity. We present a new multi-compartment model to simulate heterogeneously vascularized growing tumors and the corresponding protein outflux. Model parameters can be tuned from histology data, including relative vascular volume, mean vessel diameter, and distance from vasculature to necrotic tissue. The model enables evaluating the difference in shedding rates between extra- and non-extracellular proteins from viable and necrosing cells as a function of heterogeneous vascularization. Simulation results indicate that under certain conditions it is possible for non-extracellular proteins to have superior outflux relative to extracellular proteins. This work contributes towards the goal of cancer biomarker identification by enabling simulation of protein shedding kinetics based on tumor tissue-specific characteristics. Ultimately, we anticipate that models like the one introduced herein will enable examining origins and circulating dynamics of candidate biomarkers, thus facilitating marker selection for validation studies.

Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors

Tumor growth curves are classically modeled by means of ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two parameters of the model, which could be used to reduce the dimensionality and improve predictive power. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (population approach). This allowed the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 833 measurements in 94 animals. Candidate models of tumor growth included the exponential, logistic and Gompertz models. The exponential and-more notably-logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The previously reported population-level correlation between the Gompertz parameters was further confirmed in our analysis (R2 > 0.92 in all groups). Combining this structural correlation with rigorous population parameter estimation, we propose a reduced Gompertz function consisting of a single individual parameter (and one population parameter). Leveraging the population approach using Bayesian inference, we estimated times of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using Bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy (prediction error) was 12.2% versus 78% and mean precision (width of the 95% prediction interval) was 15.6 days versus 210 days, for the breast cancer cell line. These results demonstrate the superior predictive power of the reduced Gompertz model, especially when combined with Bayesian estimation. They offer possible clinical perspectives for personalized prediction of the age of a tumor from limited data at diagnosis. The code and data used in our analysis are publicly available at https://github.com/cristinavaghi/plumky.

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.

Mathematical model of T-cell lymphoblastic lymphoma: disease, treatment, cure or relapse of a virtual cohort of patients

T lymphoblastic lymphoma (T-LBL) is a rare type of lymphoma with a good prognosis with a remission rate of 85%. Patients can be completely cured or can relapse during or after a 2-year treatment. Relapses usually occur early after the remission of the acute phase. The median time of relapse is equal to 1 year, after the occurrence of complete remission (range 0.2-5.9 years) (Uyttebroeck et al., 2008). It can be assumed that patients may be treated longer than necessary with undue toxicity.The aim of our model was to investigate whether the duration of the maintenance therapy could be reduced without increasing the risk of relapses and to determine the minimum treatment duration that could be tested in a future clinical trial.We developed a mathematical model of virtual patients with T-LBL in order to obtain a proportion of virtual relapses close to the one observed in the real population of patients from the EuroLB database. Our simulations reproduced a 2-year follow-up required to study the onset of the disease, the treatment of the acute phase and the maintenance treatment phase.

Simulation of Multispecies Desmoplastic Cancer Growth via a Fully Adaptive Non-linear Full Multigrid Algorithm

A fully adaptive non-linear full multigrid (FMG) algorithm is implemented to computationally simulate a model of multispecies desmoplastic tumor growth in three spatial dimensions. The algorithm solves a thermodynamic mixture model employing a diffuse interface approach with Cahn-Hilliard-type fourth-order equations that are coupled, non-linear, and numerically stiff. The tumor model includes extracellular matrix (ECM) as a major component with elastic energy contribution in its chemical potential term. Blood and lymphatic vasculatures are simulated via continuum representations. The model employs advection-reaction-diffusion partial differential equations (PDEs) for the cell, ECM, and vascular components, and reaction-diffusion PDEs for the elements diffusing from the vessels. This study provides the details of the numerical solution obtained by applying the fully adaptive non-linear FMG algorithm with finite difference method to solve this complex system of PDEs. The results indicate that this type of computational model can simulate the extracellular matrix-rich desmoplastic tumor microenvironment typical of fibrotic tumors, such as pancreatic adenocarcinoma.

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.

Cancer Immunotherapy Getting Brainy: Visualizing the Distinctive CNS Metastatic Niche to Illuminate Therapeutic Resistance

The advent of cancer immunotherapy (CIT) and its success in treating primary and metastatic cancer may offer substantially improved outcomes for patients. Despite recent advancements, many malignancies remain resistant to CIT, among which are brain metastases, a particularly virulent disease with no apparent cure. The immunologically unique niche of the brain has prompted compelling new questions in immuno-oncology such as the effects of tissue-specific differences in immune response, heterogeneity between primary tumors and distant metastases, and the role of spatiotemporal dynamics in shaping an effective anti-tumor immune response. Current methods to examine the immunobiology of metastases in the brain are constrained by tissue processing methods that limit spatial data collection, omit dynamic information, and cannot recapitulate the heterogeneity of the tumor microenvironment. In the current review, we describe how high-resolution, live imaging tools, particularly intravital microscopy (IVM), are instrumental in answering these questions. IVM of pre-clinical cancer models enables short- and long-term observations of critical immunobiology and metastatic growth phenomena to potentially generate revolutionary insights into the spatiotemporal dynamics of brain metastasis, interactions of CIT with immune elements therein, and influence of chemo- and radiotherapy. We describe the utility of IVM to study brain metastasis in mice by tracking the migration and growth of fluorescently-labeled cells, including cancer cells and immune subsets, while monitoring the physical environment within optical windows using imaging dyes and other signal generation mechanisms to illuminate angiogenesis, hypoxia, and/or CIT drug expression within the metastatic niche. Our review summarizes the current knowledge regarding brain metastases and the immune milieu, presents the current status of CIT and its prospects in targeting brain metastases to circumvent therapeutic resistance, and proposes avenues to utilize IVM to study CIT drug delivery and therapeutic efficacy in preclinical models that will ultimately facilitate novel drug discovery and innovative combination therapies.

Model of vascular desmoplastic multispecies tumor growth

We present a three-dimensional nonlinear tumor growth model composed of heterogeneous cell types in a multicomponent-multispecies system, including viable, dead, healthy host, and extra-cellular matrix (ECM) tissue species. The model includes the capability for abnormal ECM dynamics noted in tumor development, as exemplified by pancreatic ductal adenocarcinoma, including dense desmoplasia typically characterized by a significant increase of interstitial connective tissue. An elastic energy is implemented to provide elasticity to the connective tissue. Cancer-associated fibroblasts (myofibroblasts) are modeled as key contributors to this ECM remodeling. The tumor growth is driven by growth factors released by these stromal cells as well as by oxygen and glucose provided by blood vasculature which along with lymphatics are stimulated to proliferate in and around the tumor based on pro-angiogenic factors released by hypoxic tissue regions. Cellular metabolic processes are simulated, including respiration and glycolysis with lactate fermentation. The bicarbonate buffering system is included for cellular pH regulation. This model system may be of use to simulate the complex interactions between tumor and stromal cells as well as the associated ECM and vascular remodeling that typically characterize malignant cancers notorious for poor therapeutic response.

Progress Towards Computational 3-D Multicellular Systems Biology

Tumors cannot be understood in isolation from their microenvironment. Tumor and stromal cells change phenotype based upon biochemical and biophysical inputs from their surroundings, even as they interact with and remodel the microenvironment. Cancer should be investigated as an adaptive, multicellular system in a dynamical microenvironment. Computational modeling offers the potential to detangle this complex system, but the modeling platform must ideally account for tumor heterogeneity, substrate and signaling factor biotransport, cell and tissue biophysics, tissue and vascular remodeling, microvascular and interstitial flow, and links between all these sub-systems. Such a platform should leverage high-throughput experimental data, while using open data standards for reproducibility. In this chapter, we review advances by our groups in these key areas, particularly in advanced models of tissue mechanics and interstitial flow, open source simulation software, high-throughput phenotypic screening, and multicellular data standards. In the future, we expect a transformation of computational cancer biology from individual groups modeling isolated parts of cancer, to coalitions of groups combining compatible tools to simulate the 3-D multicellular systems biology of cancer tissues.

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.

Imaging the pharmacology of nanomaterials by intravital microscopy: Toward understanding their biological behavior

Therapeutic nanoparticles (NPs) can deliver cytotoxic chemotherapeutics and other drugs more safely and efficiently to patients; furthermore, selective delivery to target tissues can theoretically be accomplished actively through coating NPs with molecular ligands, and passively through exploiting physiological "enhanced permeability and retention" features. However, clinical trial results have been mixed in showing improved efficacy with drug nanoencapsulation, largely due to heterogeneous NP accumulation at target sites across patients. Thus, a clear need exists to better understand why many NP strategies fail in vivo and not result in significantly improved tumor uptake or therapeutic response. Multicolor in vivo confocal fluorescence imaging (intravital microscopy; IVM) enables integrated pharmacokinetic and pharmacodynamic (PK/PD) measurement at the single-cell level, and has helped answer key questions regarding the biological mechanisms of in vivo NP behavior. This review summarizes progress to date and also describes useful technical strategies for successful IVM experimentation.

Inferring Growth Control Mechanisms in Growing Multi-cellular Spheroids of NSCLC Cells from Spatial-Temporal Image Data

We develop a quantitative single cell-based mathematical model for multi-cellular tumor spheroids (MCTS) of SK-MES-1 cells, a non-small cell lung cancer (NSCLC) cell line, growing under various nutrient conditions: we confront the simulations performed with this model with data on the growth kinetics and spatial labeling patterns for cell proliferation, extracellular matrix (ECM), cell distribution and cell death. We start with a simple model capturing part of the experimental observations. We then show, by performing a sensitivity analysis at each development stage of the model that its complexity needs to be stepwise increased to account for further experimental growth conditions. We thus ultimately arrive at a model that mimics the MCTS growth under multiple conditions to a great extent. Interestingly, the final model, is a minimal model capable of explaining all data simultaneously in the sense, that the number of mechanisms it contains is sufficient to explain the data and missing out any of its mechanisms did not permit fit between all data and the model within physiological parameter ranges. Nevertheless, compared to earlier models it is quite complex i.e., it includes a wide range of mechanisms discussed in biological literature. In this model, the cells lacking oxygen switch from aerobe to anaerobe glycolysis and produce lactate. Too high concentrations of lactate or too low concentrations of ATP promote cell death. Only if the extracellular matrix density overcomes a certain threshold, cells are able to enter the cell cycle. Dying cells produce a diffusive growth inhibitor. Missing out the spatial information would not permit to infer the mechanisms at work. Our findings suggest that this iterative data integration together with intermediate model sensitivity analysis at each model development stage, provide a promising strategy to infer predictive yet minimal (in the above sense) quantitative models of tumor growth, as prospectively of other tissue organization processes. Importantly, calibrating the model with two nutriment-rich growth conditions, the outcome for two nutriment-poor growth conditions could be predicted. As the final model is however quite complex, incorporating many mechanisms, space, time, and stochastic processes, parameter identification is a challenge. This calls for more efficient strategies of imaging and image analysis, as well as of parameter identification in stochastic agent-based simulations.

We here present how to parameterize a mathematical agent-based model of growing MCTS almost completely from experimental data. MCTS show a similar establishment of pathophysiological gradients and concentric arrangement of heterogeneous cell populations as found in avascular tumor nodules. We build a process chain of imaging, image processing and analysis, and mathematical modeling. In this model, each individual cell is represented by an agent populating one site of a three dimensional un-structured lattice. The spatio-temporal multi-cellular behavior, including migration, growth, division, death of each cell, is considered by a stochastic process, simulated numerically by the Gillespie algorithm. Processes on the molecular scale are described by deterministic partial differential equations for molecular concentrations, coupled to intracellular and cellular decision processes. The parameters of the multi-scale model are inferred from comparisons to the growth kinetics and from image analysis of spheroid cryosections stained for cell death, proliferation and collagen IV. Our final model assumes ATP to be the critical resource that cells try to keep constant over a wide range of oxygen and glucose medium concentrations, by switching between aerobic and anaerobic metabolism. Besides ATP, lactate is shown to be a possible explanation for the control of the necrotic core size. Direct confrontation of the model simulation results with image data on the spatial profiles of cell proliferation, ECM distribution and cell death, indicates that in addition, the effects of ECM and waste factors have to be added to explain the data. Hence the model is a tool to identify likely mechanisms at work that may subsequently be studied experimentally, proposing a model-guided experimental strategy.

Spatial Modeling of Drug Delivery Routes for Treatment of Disseminated Ovarian Cancer

In ovarian cancer, metastasis is typically confined to the peritoneum. Surgical removal of the primary tumor and macroscopic secondary tumors is a common practice, but more effective strategies are needed to target microscopic spheroids persisting in the peritoneal fluid after debulking surgery. To treat this residual disease, therapeutic agents can be administered by either intravenous or intraperitoneal infusion. Here, we describe the use of a cellular Potts model to compare tumor penetration of two classes of drugs (cisplatin and pertuzumab) when delivered by these two alternative routes. The model considers the primary route when the drug is administered either intravenously or intraperitoneally, as well as the subsequent exchange into the other delivery volume as a secondary route. By accounting for these dynamics, the model revealed that intraperitoneal infusion is the markedly superior route for delivery of both small-molecule and antibody therapies into microscopic, avascular tumors typical of patients with ascites. Small tumors attached to peritoneal organs, with vascularity ranging from 2% to 10%, also show enhanced drug delivery via the intraperitoneal route, even though tumor vessels can act as sinks during the dissemination of small molecules. Furthermore, we assessed the ability of the antibody to enter the tumor by in silico and in vivo methods and suggest that optimization of antibody delivery is an important criterion underlying the efficacy of these and other biologics. The use of both delivery routes may provide the best total coverage of tumors, depending on their size and vascularity.

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.

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.

Oxygen-Driven Tumour Growth Model: A Pathology-Relevant Mathematical Approach

Xenografts -as simplified animal models of cancer- differ substantially in vasculature and stromal architecture when compared to clinical tumours. This makes mathematical model-based predictions of clinical outcome challenging. Our objective is to further understand differences in tumour progression and physiology between animal models and the clinic.

To achieve that, we propose a mathematical model based upon tumour pathophysiology, where oxygen -as a surrogate for endocrine delivery- is our main focus. The Oxygen-Driven Model (ODM), using oxygen diffusion equations, describes tumour growth, hypoxia and necrosis. The ODM describes two key physiological parameters. Apparent oxygen uptake rate (kR′) represents the amount of oxygen cells seem to need to proliferate. The more oxygen they appear to need, the more the oxygen transport. kR′ gathers variability from the vasculature, stroma and tumour morphology. Proliferating rate (k_p) deals with cell line specific factors to promote growth. The K_H,K_N describe the switch of hypoxia and necrosis. Retrospectively, using archived data, we looked at longitudinal tumour volume datasets for 38 xenografted cell lines and 5 patient-derived xenograft-like models.

Exploration of the parameter space allows us to distinguish 2 groups of parameters. Group 1 of cell lines shows a spread in values of kR′ and lower k_p, indicating that tumours are poorly perfused and slow growing. Group 2 share the value of the oxygen uptake rate (kR′) and vary greatly in k_p, which we interpret as having similar oxygen transport, but more tumour intrinsic variability in growth.

However, the ODM has some limitations when tested in explant-like animal models, whose complex tumour-stromal morphology may not be captured in the current version of the model. Incorporation of stroma in the ODM will help explain these discrepancies. We have provided an example. The ODM is a very simple -and versatile- model suitable for the design of preclinical experiments, which can be modified and enhanced whilst maintaining confidence in its predictions.

Tumour-bearing animal models of cancer are needed to discover new drugs to treat cancer. We aim in this article to capture—through mathematics- some underlying phenomena of tumour growth in animals. We propose a set of equations that, despite being very simple, describe tumour growth, hypoxia and necrosis. Cells under low oxygen levels change into a stress state called “hypoxia”, which will ultimately lead to tissue death, also known as “necrosis” and “apoptosis”. Hypoxic cells undergo a variety of changes which impact tumour growth, development, metastasis and -most importantly- response to therapy. Hence, oxygen distribution is important. We simulate oxygen profiles to locate hypoxic and necrotic tumour regions. Finally, this mathematical model allows us to compare and classify animal models from a grounded and physiological perspective, rather than a more convenient and empirical one. This will help us understand how well (or poorly) animal tumours mimic tumours in patients. The simplicity of our mathematical model allows us to obtain more information out of the same animal sets without any further experiments, hopefully saving time, money and animal usage.

Bridging the gap between in vitro and in vivo: Dose and schedule predictions for the ATR inhibitor AZD6738

Understanding the therapeutic effect of drug dose and scheduling is critical to inform the design and implementation of clinical trials. The increasing complexity of both mono, and particularly combination therapies presents a substantial challenge in the clinical stages of drug development for oncology. Using a systems pharmacology approach, we have extended an existing PK-PD model of tumor growth with a mechanistic model of the cell cycle, enabling simulation of mono and combination treatment with the ATR inhibitor AZD6738 and ionizing radiation. Using AZD6738, we have developed multi-parametric cell based assays measuring DNA damage and cell cycle transition, providing quantitative data suitable for model calibration. Our in vitro calibrated cell cycle model is predictive of tumor growth observed in in vivo mouse xenograft studies. The model is being used for phase I clinical trial designs for AZD6738, with the aim of improving patient care through quantitative dose and scheduling prediction.

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.

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.

3D tumor models: history, advances and future perspectives

ABSTRACT: 

Evaluation of cancer therapeutics by utilizing 3D tumor models, before clinical studies, could be more advantageous than conventional 2D tumor models (monolayer cultures). The 3D systems mimic the tumor microenvironment more closely than 2D systems. The following review discusses the various 3D tumor models present today with the advantages and limitations of each. 3D tumor models replicate the elements of a tumor microenvironment such as hypoxia, necrosis, angiogenesis and cell adhesion. The review introduces application of techniques such as microfluidics, imaging and tissue engineering to improve the 3D tumor models. Despite their tremendous potential to better screen chemotherapeutics, 3D tumor models still have a long way to go before they are used commonly as in vitro tumor models in pharmaceutical industrial research.

Cancer systems biology and modeling: microscopic scale and multiscale approaches

Cancer has become known as a complex and systematic disease on macroscopic, mesoscopic and microscopic scales. Systems biology employs state-of-the-art computational theories and high-throughput experimental data to model and simulate complex biological procedures such as cancer, which involves genetic and epigenetic, in addition to intracellular and extracellular complex interaction networks. In this paper, different systems biology modeling techniques such as systems of differential equations, stochastic methods, Boolean networks, Petri nets, cellular automata methods and agent-based systems are concisely discussed. We have compared the mentioned formalisms and tried to address the span of applicability they can bear on emerging cancer modeling and simulation approaches. Different scales of cancer modeling, namely, microscopic, mesoscopic and macroscopic scales are explained followed by an illustration of angiogenesis in microscopic scale of the cancer modeling. Then, the modeling of cancer cell proliferation and survival are examined on a microscopic scale and the modeling of multiscale tumor growth is explained along with its advantages.

Cancer Systems Biology: a peek into the future of patient care?

Traditionally, scientific research has focused on studying individual events, such as single mutations, gene function, or the effect that mutating one protein has on a biological phenotype. A range of technologies is beginning to provide information that will enable a holistic view of how genomic and epigenetic aberrations in cancer cells can alter the homeostasis of signalling networks within these cells, between cancer cells and the local microenvironment, and at the organ and organism level. This process, termed Systems Biology, needs to be integrated with an iterative approach wherein hypotheses and predictions that arise from modelling are refined and constrained by experimental evaluation. Systems biology approaches will be vital for developing and implementing effective strategies to deliver personalized cancer therapy. Specifically, these approaches will be important to select those patients who are most likely to benefit from targeted therapies and for the development and implementation of rational combinatorial therapies. Systems biology can help to increase therapy efficacy or bypass the emergence of resistance, thus converting the current-often short term-effects of targeted therapies into durable responses, ultimately to improve patient quality of life and provide a cure.

Predictive modeling of in vivo response to gemcitabine in pancreatic cancer

A clear contradiction exists between cytotoxic in-vitro studies demonstrating effectiveness of Gemcitabine to curtail pancreatic cancer and in-vivo studies failing to show Gemcitabine as an effective treatment. The outcome of chemotherapy in metastatic stages, where surgery is no longer viable, shows a 5-year survival <5%. It is apparent that in-vitro experiments, no matter how well designed, may fail to adequately represent the complex in-vivo microenvironmental and phenotypic characteristics of the cancer, including cell proliferation and apoptosis. We evaluate in-vitro cytotoxic data as an indicator of in-vivo treatment success using a mathematical model of tumor growth based on a dimensionless formulation describing tumor biology. Inputs to the model are obtained under optimal drug exposure conditions in-vitro. The model incorporates heterogeneous cell proliferation and death caused by spatial diffusion gradients of oxygen/nutrients due to inefficient vascularization and abundant stroma, and thus is able to simulate the effect of the microenvironment as a barrier to effective nutrient and drug delivery. Analysis of the mathematical model indicates the pancreatic tumors to be mostly resistant to Gemcitabine treatment in-vivo. The model results are confirmed with experiments in live mice, which indicate uninhibited tumor proliferation and metastasis with Gemcitabine treatment. By extracting mathematical model parameter values for proliferation and death from monolayer in-vitro cytotoxicity experiments with pancreatic cancer cells, and simulating the effects of spatial diffusion, we use the model to predict the drug response in-vivo, beyond what would have been expected from sole consideration of the cancer intrinsic resistance. We conclude that this integrated experimental/computational approach may enhance understanding of pancreatic cancer behavior and its response to various chemotherapies, and, further, that such an approach could predict resistance based on pharmacokinetic measurements with the goal to maximize effective treatment strategies.