Mathematical modeling predicts synergistic antitumor effects of combining a macrophage-based, hypoxia-targeted gene therapy with chemotherapy

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.

Enhanced perfusion following exposure to radiotherapy: A theoretical investigation

Tumour angiogenesis leads to the formation of blood vessels that are structurally and spatially heterogeneous. Poor blood perfusion, in conjunction with increased hypoxia and oxygen heterogeneity, impairs a tumour's response to radiotherapy. The optimal strategy for enhancing tumour perfusion remains unclear, preventing its regular deployment in combination therapies. In this work, we first identify vascular architectural features that correlate with enhanced perfusion following radiotherapy, using in vivo imaging data from vascular tumours. Then, we present a novel computational model to determine the relationship between these architectural features and blood perfusion in silico. If perfusion is defined to be the proportion of vessels that support blood flow, we find that vascular networks with small mean diameters and large numbers of angiogenic sprouts show the largest increases in perfusion post-irradiation for both biological and synthetic tumours. We also identify cases where perfusion increases due to the pruning of hypoperfused vessels, rather than blood being rerouted. These results indicate the importance of considering network composition when determining the optimal irradiation strategy. In the future, we aim to use our findings to identify tumours that are good candidates for perfusion enhancement and to improve the efficacy of combination therapies.

The impact of tumor associated macrophages on tumor biology under the lens of mathematical modelling: A review

In this article, we review the role of mathematical modelling to elucidate the impact of tumor-associated macrophages (TAMs) in tumor progression and therapy design. We first outline the biology of TAMs, and its current application in tumor therapies, and their experimental methods that provide insights into tumor cell-macrophage interactions. We then focus on the mechanistic mathematical models describing the role of macrophages as drug carriers, the impact of macrophage polarized activation on tumor growth, and the role of tumor microenvironment (TME) parameters on the tumor-macrophage interactions. This review aims to identify the synergies between biological and mathematical approaches that allow us to translate knowledge on fundamental TAMs biology in addressing current clinical challenges.

Mathematical investigation into the role of macrophage heterogeneity on the temporal and spatio-temporal dynamics of non-small cell lung cancers

Non Small Cell Lung Cancer (NSCLC) is the most common type of lung cancer, and represents the leading cause of cancer-related deaths worldwide. Experimental studies have shown that these solid cancers are heavily infiltrated with macrophages: anti-tumour M1 macrophages, pro-tumour M2 macrophages, and macrophage subtypes sharing both M1 and M2 properties. In this study we aim to investigate qualitatively the role of macrophages with different functional phenotypes (especially those with mixed phenotypes) on cancer dynamics and the success of different immunotherapies for cancer. To this end, we start with two time-evolving mathematical models for cancer-immune interactions that consider: (i) the effect of the two extreme phenotypes, M1 and M2 cells; (ii) the effect of M1 and M2 cells, as well as a macrophage sub-population with a mixed phenotype (throughout this theoretical study we call these cells "M12 cells"). We compare the dynamics of the two models using computational approaches, paying particular attention to the effect of different anti-cancer immunotherapies that focus on macrophages. Since data available for NSCLC and macrophage interactions are incomplete, we perform a global sensitivity analysis to see the influence of input parameters on model outcomes. Finally, we consider extensions of the previous two models to include also the spatial movement of cells, and investigate the role of macrophages with extreme phenotypes and with mixed phenotypes, on the invasion of cancer cells into the surrounding extracellular matrix (ECM). We use numerical simulations to investigate the macrophages phenotypes at the tumour center versus the invasive margin. Again, we examine the impact of immunotherapies for cancer on the spatial dynamics of cancers and immune cells, and observe a shift in the phenotype of macrophages distributed at the tumour center and invasive margin.

Algorithmic asymptotic analysis: Extending the arsenal of cancer immunology modeling

The recent advances in cancer immunotherapy boosted the development of tumor-immune system models, with the aim to indicate more efficient treatments. Physical understanding is however difficult to be acquired, due to the complexity and the multi-scale dynamics of these models. In this work, the dynamics of a fundamental model formulating the interactions of tumor cells with natural killer cells, CD8⁺ T cells and circulating lymphocytes is examined. It is first shown that the long-term evolution of the system towards high-tumor or tumor-free equilibria is determined by the dynamics of an initial explosive stage of tumor progression. Focusing on this stage, the algorithmic Computational Singular Perturbation methodology is employed to identify the underlying mechanisms confining the system's evolution and the governing slow dynamics along them. These insights are preserved along different tumor-immune system and patient-dependent realizations. On top of these identifications, a novel reduced model is algorithmically constructed, which accurately predicts the dynamics of the system during the explosive stage and includes half of the parameters of the detailed model. The present analysis demonstrates the potential of algorithmic asymptotic analysis for acquiring physical understanding and for simplifying the complexity of cancer immunology models. Along with the current techniques on the field, this analysis can provide guidelines for more effective treatment development.

A scalable solver for a stochastic, hybrid cellular automaton model of personalized breast cancer therapy

Mathematical modeling and simulation is a promising approach to personalized cancer medicine. Yet, the complexity, heterogeneity and multi-scale nature of cancer pose significant computational challenges. Coupling discrete cell-based models with continuous models using hybrid cellular automata (CA) is a powerful approach for mimicking biological complexity and describing the dynamical exchange of information across different scales. However, when clinically relevant cancer portions are taken into account, such models become computationally very expensive. While efficient parallelization techniques for continuous models exist, their coupling with discrete models, particularly CA, necessitates more elaborate solutions. Building upon FEniCS, a popular and powerful scientific computing platform for solving partial differential equations, we developed parallel algorithms to link stochastic CA with differential equations (https://bitbucket.org/HTasken/cansim). The algorithms minimize the communication between processes that share CA neighborhood values while also allowing for reproducibility during stochastic updates. We demonstrated the potential of our solution on a complex hybrid cellular automaton model of breast cancer treated with combination chemotherapy. On a single-core processor, we obtained nearly linear scaling with an increasing problem size, whereas weak parallel scaling showed moderate growth in solving time relative to increase in problem size. Finally, we applied the algorithm to a problem that is 500 times larger than previous work, allowing us to run personalized therapy simulations based on heterogeneous cell density and tumor perfusion conditions estimated from magnetic resonance imaging data on an unprecedented scale.

Quantitative magnetic resonance imaging and tumor forecasting of breast cancer patients in the community setting

This protocol describes a complete data acquisition, analysis and computational forecasting pipeline for employing quantitative MRI data to predict the response of locally advanced breast cancer to neoadjuvant therapy in a community-based care setting. The methodology has previously been successfully applied to a heterogeneous patient population. The protocol details how to acquire the necessary images followed by registration, segmentation, quantitative perfusion and diffusion analysis, model calibration, and prediction. The data collection portion of the protocol requires ~25 min of scanning, postprocessing requires 2-3 h, and the model calibration and prediction components require ~10 h per patient depending on tumor size. The response of individual breast cancer patients to neoadjuvant therapy is forecast by application of a biophysical, reaction-diffusion mathematical model to these data. Successful application of the protocol results in coregistered MRI data from at least two scan visits that quantifies an individual tumor's size, cellularity and vascular properties. This enables a spatially resolved prediction of how a particular patient's tumor will respond to therapy. Expertise in image acquisition and analysis, as well as the numerical solution of partial differential equations, is required to carry out this protocol.

Multiscale computational modeling of cancer growth using features derived from microCT images

Advances in medical imaging technologies now allow noninvasive image acquisition from individual patients at high spatiotemporal resolutions. A relatively new effort of predictive oncology is to develop a paradigm for forecasting the future status of an individual tumor given initial conditions and an appropriate mathematical model. The objective of this study was to introduce a comprehensive multiscale computational method to predict cancer and microvascular network growth patterns. A rectangular lattice-based model was designed so different evolutionary scenarios could be simulated and for predicting the impact of diffusible factors on tumor morphology and size. Further, the model allows prediction-based simulation of cell and microvascular behavior. Like a single cell, each agent is fully realized within the model and interactions are governed in part by machine learning methods. This multiscale computational model was developed and incorporated input information from in vivo microscale computed tomography (microCT) images acquired from breast cancer-bearing mice. It was found that as the difference between expansion of the cancer cell population and microvascular network increases, cells undergo proliferation and migration with a greater probability compared to other phenotypes. Overall, multiscale computational model agreed with both theoretical expectations and experimental findings (microCT images) not used during model training.

Modeling the effects of EMT-immune dynamics on carcinoma disease progression

During progression from carcinoma in situ to an invasive tumor, the immune system is engaged in complex sets of interactions with various tumor cells. Tumor cell plasticity alters disease trajectories via epithelial-to-mesenchymal transition (EMT). Several of the same pathways that regulate EMT are involved in tumor-immune interactions, yet little is known about the mechanisms and consequences of crosstalk between these regulatory processes. Here we introduce a multiscale evolutionary model to describe tumor-immune-EMT interactions and their impact on epithelial cancer progression from in situ to invasive disease. Through simulation of patient cohorts in silico, the model predicts that a controllable region maximizes invasion-free survival. This controllable region depends on properties of the mesenchymal tumor cell phenotype: its growth rate and its immune-evasiveness. In light of the model predictions, we analyze EMT-inflammation-associated data from The Cancer Genome Atlas, and find that association with EMT worsens invasion-free survival probabilities. This result supports the predictions of the model, and leads to the identification of genes that influence outcomes in bladder and uterine cancer, including FGF pathway members. These results suggest new means to delay disease progression, and demonstrate the importance of studying cancer-immune interactions in light of EMT.

Strategies for the treatment of breast cancer: from classical drugs to mathematical models

Breast cancer is one of the most common cancers and generally affects women. It is a heterogeneous disease that presents different entities, different biological characteristics, and differentiated clinical behaviors. With this in mind, this literature review had as its main objective to analyze the path taken from the simple use of classical drugs to the application of mathematical models, which through the many ongoing studies, have been considered as one of the reliable strategies, explaining the reasons why chemotherapy is not always successful. Besides, the most commonly mentioned strategies are immunotherapy, which includes techniques and therapies such as the use of antibodies, cytokines, antitumor vaccines, oncolytic and genomic viruses, among others, and nanoparticles, including metallic, magnetic, polymeric, liposome, dendrimer, micelle, and others, as well as drug reuse, which is a process by which new therapeutic indications are found for existing and approved drugs. The most commonly used pharmacological categories are cardiac, antiparasitic, anthelmintic, antiviral, antibiotic, and others. For the efficient development of reused drugs, there must be a process of exchange of purposes, methods, and information already available, and for their better understanding, computational mathematical models are then used, of which the methods of blind search or screening, based on the target, knowledge, signature, pathway or network and the mechanism to which it is directed, stand out. To conclude it should be noted that these different strategies can be applied alone or in combination with each other always to improve breast cancer treatment.

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2-3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.

Modeling of tumor response to macrophage and T lymphocyte interactions in the liver metastatic microenvironment

The dynamic interactions between macrophages and T-lymphocytes in the tumor microenvironment exert both antagonistic and synergistic functions affecting tumor growth. Extensive experimental effort has been expended to investigate immunotherapeutic strategies targeting macrophage polarization as well as T-cell activation with the goal to promote tumor cell killing and cancer elimination. However, these interactions remain poorly understood, and cancer immunotherapeutic strategies are often disappointing. The complex system encompassing innate and adaptive immune cell activity in response to tumor growth could benefit from a systems perspective built upon mathematical modeling. This study develops a modeling system to help evaluate the effects of macrophage and T-lymphocyte interactions on tumor growth. The system enables simulating the combined cytotoxic and tumor-promoting interactions of these two immune cell populations in a vascularized organ microenvironment, such as in liver metastases. A hypothetical immunotherapeutic strategy is simulated to increase the number of tumor-suppressive (M1-phenotype) vs. tumor-promoting (M2-phenotype) macrophages to gauge their effects on CD8+ T-cells and CD4+ T-helper cells, which in turn affect the macrophage functions. The results highlight the dynamic interactions between macrophages and T-lymphocytes in the tumor microenvironment and show that with the chosen set of parameter values, the overall cytotoxic effect from macrophages and T-lymphocytes obtained by driving the M1:M2 ratio higher could saturate and fail to achieve tumor regression. Further expansion of this modeling platform to include additional tumor-immune cell interactions, coupled with parameters representing particular tumor characteristics, could enable systematic evaluation of immunotherapeutic strategies tailored to patient-tumor specific conditions, including metastatic disease.

Digitally Fabricated and Naturally Augmented In Vitro Tissues

Human in vitro tissues are extracorporeal 3D cultures of human cells embedded in biomaterials, commonly hydrogels, which recapitulate the heterogeneous, multiscale, and architectural environment of the human body. Contemporary strategies used in 3D tissue and organ engineering integrate the use of automated digital manufacturing methods, such as 3D printing, bioprinting, and biofabrication. Human tissues and organs, and their intra- and interphysiological interplay, are particularly intricate. For this reason, attentiveness is rising to intersect materials science, medicine, and biology with arts and informatics. This report presents advances in computational modeling of bioink polymerization and its compatibility with bioprinting, the use of digital design and fabrication in the development of fluidic culture devices, and the employment of generative algorithms for modeling the natural and biological augmentation of in vitro tissues. As a future direction, the use of serially linked in vitro tissues as human body-mimicking systems and their application in drug pharmacokinetics and metabolism, disease modeling, and diagnostics are discussed.

Towards integration of 64Cu-DOTA-trastuzumab PET-CT and MRI with mathematical modeling to predict response to neoadjuvant therapy in HER2 + breast cancer

While targeted therapies exist for human epidermal growth factor receptor 2 positive (HER2 +) breast cancer, HER2 + patients do not always respond to therapy. We present the results of utilizing a biophysical mathematical model to predict tumor response for two HER2 + breast cancer patients treated with the same therapeutic regimen but who achieved different treatment outcomes. Quantitative data from magnetic resonance imaging (MRI) and 64Cu-DOTA-trastuzumab positron emission tomography (PET) are used to estimate tumor density, perfusion, and distribution of HER2-targeted antibodies for each individual patient. MRI and PET data are collected prior to therapy, and follow-up MRI scans are acquired at a midpoint in therapy. Given these data types, we align the data sets to a common image space to enable model calibration. Once the model is parameterized with these data, we forecast treatment response with and without HER2-targeted therapy. By incorporating targeted therapy into the model, the resulting predictions are able to distinguish between the two different patient responses, increasing the difference in tumor volume change between the two patients by > 40%. This work provides a proof-of-concept strategy for processing and integrating PET and MRI modalities into a predictive, clinical-mathematical framework to provide patient-specific predictions of HER2 + treatment response.

Advanced nanomaterials for hypoxia tumor therapy: challenges and solutions

In recent years, nanomaterials and nanotechnology have emerged as vital factors in the medical field with a unique contribution to cancer medicine. Given the increasing number of cancer patients, it is necessarily required to develop innovative strategies and therapeutic modalities to tackle hypoxia, which forms a hallmark and great barrier in treating solid tumors. The present review details the challenges in nanotechnology-based hypoxia, targeting the strategies and solutions for better therapeutic performances. The interaction between hypoxia and tumor is firstly introduced. Then, we review the recently developed engineered nanomaterials towards multimodal hypoxia tumor therapies, including chemotherapy, radiotherapy, and sonodynamic treatment. In the next part, we summarize the nanotechnology-based strategies for overcoming hypoxia problems. Finally, current challenges and future directions are proposed for successfully overcoming the hypoxia tumor problems.

Identifying and characterising the impact of excitability in a mathematical model of tumour-immune interactions

We study a five-compartment mathematical model originally proposed by Kuznetsov et al. (1994) to investigate the effect of nonlinear interactions between tumour and immune cells in the tumour microenvironment, whereby immune cells may induce tumour cell death, and tumour cells may inactivate immune cells. Exploiting a separation of timescales in the model, we use the method of matched asymptotics to derive a new two-dimensional, long-timescale, approximation of the full model, which differs from the quasi-steady-state approximation introduced by Kuznetsov et al. (1994), but is validated against numerical solutions of the full model. Through a phase-plane analysis, we show that our reduced model is excitable, a feature not traditionally associated with tumour-immune dynamics. Through a systematic parameter sensitivity analysis, we demonstrate that excitability generates complex bifurcating dynamics in the model. These are consistent with a variety of clinically observed phenomena, and suggest that excitability may underpin tumour-immune interactions. The model exhibits the three stages of immunoediting - elimination, equilibrium, and escape, via stable steady states with different tumour cell concentrations. Such heterogeneity in tumour cell numbers can stem from variability in initial conditions and/or model parameters that control the properties of the immune system and its response to the tumour. We identify different biophysical parameter targets that could be manipulated with immunotherapy in order to control tumour size, and we find that preferred strategies may differ between patients depending on the strength of their immune systems, as determined by patient-specific values of associated model parameters.

Recent progress of hypoxia-modulated multifunctional nanomedicines to enhance photodynamic therapy: opportunities, challenges, and future development

Hypoxia, a salient feature of most solid tumors, confers invasiveness and resistance to the tumor cells. Oxygen-consumption photodynamic therapy (PDT) suffers from the undesirable impediment of local hypoxia in tumors. Moreover, PDT could further worsen hypoxia. Therefore, developing effective strategies for manipulating hypoxia and improving the effectiveness of PDT has been a focus on antitumor treatment. In this review, the mechanism and relationship of tumor hypoxia and PDT are discussed. Moreover, we highlight recent trends in the field of nanomedicines to modulate hypoxia for enhancing PDT, such as oxygen supply systems, down-regulation of oxygen consumption and hypoxia utilization. Finally, the opportunities and challenges are put forward to facilitate the development and clinical transformation of PDT.

Characterizing Chemotherapy-Induced Neutropenia and Monocytopenia Through Mathematical Modelling

In spite of the recent focus on the development of novel targeted drugs to treat cancer, cytotoxic chemotherapy remains the standard treatment for the vast majority of patients. Unfortunately, chemotherapy is associated with high hematopoietic toxicity that may limit its efficacy. We have previously established potential strategies to mitigate chemotherapy-induced neutropenia (a lack of circulating neutrophils) using a mechanistic model of granulopoiesis to predict the interactions defining the neutrophil response to chemotherapy and to define optimal strategies for concurrent chemotherapy/prophylactic granulocyte colony-stimulating factor (G-CSF). Here, we extend our analyses to include monocyte production by constructing and parameterizing a model of monocytopoiesis. Using data for neutrophil and monocyte concentrations during chemotherapy in a large cohort of childhood acute lymphoblastic leukemia patients, we leveraged our model to determine the relationship between the monocyte and neutrophil nadirs during cyclic chemotherapy. We show that monocytopenia precedes neutropenia by 3 days, and rationalize the use of G-CSF during chemotherapy by establishing that the onset of monocytopenia can be used as a clinical marker for G-CSF dosing post-chemotherapy. This work therefore has important clinical applications as a comprehensive approach to understanding the relationship between monocyte and neutrophils after cyclic chemotherapy with or without G-CSF support.

Hybrid Modelling of Transarterial Chemoembolisation Therapies (TACE) for Hepatocellular Carcinoma (HCC)

We extend an agent-based multiscale model of vascular tumour growth and angiogenesis to describe transarterial chemoembolisation (TACE) therapies. The model accounts for tumour and normal cells that are both nested in a vascular system that changes its structure according to tumour-related growth factors. Oxygen promotes nutrients to the tissue and determines cell proliferation or death rates. Within the extended model TACE is included as a two-step process: First, the purely mechanical influence of the embolisation therapy is modelled by a local occlusion of the tumour vasculature. There we distinguish between partial and complete responders, where parts of the vascular system are occluded for the first and the whole tumour vasculature is destroyed for the latter. In the second part of the model, drug eluding beads (DEBs) carrying the chemotherapeutic drug doxorubicin are located at destroyed vascular locations, releasing the drug over a certain time-window. Simulation results are parameterised to qualitatively reproduce clinical observations. Patients that undergo a TACE-treatment are categorised in partial and complete responders one day after the treatment. Another 90 days later reoccurance or complete response are detected by volume perfusion computer tomography (VPCT). Our simulations reveal that directly after a TACE- treatment an unstable tumour state can be observed, where regrowth and total tumour death have the same likeliness. It is argued that this short time-window is favorable for another therapeutical intervention with a less radical therapy. This procedure can shift the outcome to more effectiveness. Simulation results with an oxygen therapy within the unstable time-window demonstrate a potentially positive manipulated outcome. Finally, we conclude that our TACE model can motivate new therapeutical strategies and help clinicians analyse the intertwined relations and cross-links in tumours.

Modeling immune cell behavior across scales in cancer

Detailed, mechanistic models of immune cell behavior across multiple scales in the context of cancer provide clinically relevant insights needed to understand existing immunotherapies and develop more optimal treatment strategies. We highlight mechanistic models of immune cells and their ability to become activated and promote tumor cell killing. These models capture various aspects of immune cells: (a) single‐cell behavior by predicting the dynamics of intracellular signaling networks in individual immune cells, (b) multicellular interactions between tumor and immune cells, and (c) multiscale dynamics across space and different levels of biological organization. Computational modeling is shown to provide detailed quantitative insight into immune cell behavior and immunotherapeutic strategies. However, there are gaps in the literature, and we suggest areas where additional modeling efforts should be focused to more prominently impact our understanding of the complexities of the immune system in the context of cancer.

This article is categorized under:

Biological Mechanisms > Cell Signaling

Models of Systems Properties and Processes > Mechanistic Models

Models of Systems Properties and Processes > Cellular Models

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.

Towards personalized computational oncology: from spatial models of tumour spheroids, to organoids, to tissues

A main goal of mathematical and computational oncology is to develop quantitative tools to determine the most effective therapies for each individual patient. This involves predicting the right drug to be administered at the right time and at the right dose. Such an approach is known as precision medicine. Mathematical modelling can play an invaluable role in the development of such therapeutic strategies, since it allows for relatively fast, efficient and inexpensive simulations of a large number of treatment schedules in order to find the most effective. This review is a survey of mathematical models that explicitly take into account the spatial architecture of three-dimensional tumours and address tumour development, progression and response to treatments. In particular, we discuss models of epithelial acini, multicellular spheroids, normal and tumour spheroids and organoids, and multi-component tissues. Our intent is to showcase how these in silico models can be applied to patient-specific data to assess which therapeutic strategies will be the most efficient. We also present the concept of virtual clinical trials that integrate standard-of-care patient data, medical imaging, organ-on-chip experiments and computational models to determine personalized medical treatment strategies.

Multiscale modeling reveals angiogenesis-induced drug resistance in brain tumors and predicts a synergistic drug combination targeting EGFR and VEGFR pathways

BACKGROUND

Experimental studies have demonstrated that both the extracellular vasculature or microenvironment and intracellular molecular network (e.g., epidermal growth factor receptor (EGFR) signaling pathway) are important for brain tumor growth. Additionally, some drugs have been developed to inhibit EGFR signaling pathways. However, how angiogenesis affects the response of tumor cells to drug treatment has rarely been mechanistically studied. Therefore, a multiscale model is required to investigate such complex biological systems that contain interactions and feedback among multiple levels.

RESULTS

In this study, we developed a single cell-based multiscale spatiotemporal model to simulate vascular tumor growth and the drug response based on the vascular endothelial growth factor receptor (VEGFR) signaling pathway, the EGFR signaling pathway and the cell cycle as well as several microenvironmental factors that determine cell fate switches in a temporal and spatial context. By incorporating the EGFRI treatment effect, the model showed an interesting phenomenon in which the survival rate of tumor cells decreased in the early stage but rebounded in a later stage, revealing the emergence of drug resistance. Moreover, we revealed the critical role of angiogenesis in acquired drug resistance, since inhibiting blood vessel growth using a VEGFR inhibitor prevented the recovery of the survival rate of tumor cells in the later stage. We further investigated the optimal timing of combining VEGFR inhibition with EGFR inhibition and predicted that the drug combination targeting both the EGFR pathway and VEGFR pathway has a synergistic effect. The experimental data validated the prediction of drug synergy, confirming the effectiveness of our model. In addition, the combination of EGFR and VEGFR genes showed clinical relevance in glioma patients.

CONCLUSIONS

The developed multiscale model revealed angiogenesis-induced drug resistance mechanisms of brain tumors to EGFRI treatment and predicted a synergistic drug combination targeting both EGFR and VEGFR pathways with optimal combination timing. This study explored the mechanistic and functional mechanisms of the angiogenesis underlying tumor growth and drug resistance, which advances our understanding of novel mechanisms of drug resistance and provides implications for designing more effective cancer therapies.

Mathematical modeling of tumor-immune cell interactions

The anti-tumor activity of the immune system is increasingly recognized as critical for the mounting of a prolonged and effective response to cancer growth and invasion, and for preventing recurrence following resection or treatment. As the knowledge of tumor-immune cell interactions has advanced, experimental investigation has been complemented by mathematical modeling with the goal to quantify and predict these interactions. This succinct review offers an overview of recent tumor-immune continuum modeling approaches, highlighting spatial models. The focus is on work published in the past decade, incorporating one or more immune cell types and evaluating immune cell effects on tumor progression. Due to their relevance to cancer, the following immune cells and their combinations are described: macrophages, Cytotoxic T Lymphocytes, Natural Killer cells, dendritic cells, T regulatory cells, and CD4+ T helper cells. Although important insight has been gained from a mathematical modeling perspective, the development of models incorporating patient-specific data remains an important goal yet to be realized for potential clinical benefit.

Pioglitazone increases VEGFR3 expression and promotes activation of M2 macrophages via the peroxisome proliferator‑activated receptor γ

The peroxisome proliferator-activated receptor γ (PPARγ) agonist pioglitazone has been widely used in previous studies to ameliorate diabetes mellitus and regulate inflammation. However, the present study aimed to investigate the effect of pioglitazone on macrophages and determine its impact on renal fibrosis in vivo. Firstly, bone marrow-derived macrophages (BMDM) were used to detect the effects of pioglitazone on macrophages in vitro. It was demonstrated that pioglitazone promoted M2 macrophage activation and induced vascular endothelial growth factor receptor 3 (VEGFR3) upregulation in a PPARγ-dependent manner. Furthermore, pioglitazone increased macrophage proliferation and macrophage VEGFR3 expression in a murine unilateral ureteral obstruction (UUO) model; however, it had no therapeutic effect on renal fibrosis in vivo. Therefore, the results in the present study implied that presence of M2 macrophages may inhibit pioglitazone's ability to attenuate UUO-induced renal fibrosis. In addition, the results demonstrated that macrophage-associated VEGFR3 could be induced by pioglitazone, although it is still unclear what role VEGFR3⁺ M2 macrophages have in renal fibrosis.

The many faces of mathematical modelling in oncology

The application of modelling to solve problems in biology and medicine, and specifically in oncology and radiation therapy, is increasingly established and holds big promise. We provide an overview of the basic concepts of the field and its current state, along with new tools available and future directions for research. We will outline radiobiology models, examples of other anticancer therapy models, multiscale modelling, and we will discuss mechanistic and phenomenological approaches to modelling.

Mathematical models of tumor cell proliferation: A review of the literature

INTRODUCTION

A defining hallmark of cancer is aberrant cell proliferation. Efforts to understand the generative properties of cancer cells span all biological scales: from genetic deviations and alterations of metabolic pathways to physical stresses due to overcrowding, as well as the effects of therapeutics and the immune system. While these factors have long been studied in the laboratory, mathematical and computational techniques are being increasingly applied to help understand and forecast tumor growth and treatment response. Advantages of mathematical modeling of proliferation include the ability to simulate and predict the spatiotemporal development of tumors across multiple experimental scales. Central to proliferation modeling is the incorporation of available biological data and validation with experimental data. Areas covered: We present an overview of past and current mathematical strategies directed at understanding tumor cell proliferation. We identify areas for mathematical development as motivated by available experimental and clinical evidence, with a particular emphasis on emerging, non-invasive imaging technologies. Expert commentary: The data required to legitimize mathematical models are often difficult or (currently) impossible to obtain. We suggest areas for further investigation to establish mathematical models that more effectively utilize available data to make informed predictions on tumor cell proliferation.

Tumor-targeted hybrid protein oxygen carrier to simultaneously enhance hypoxia-dampened chemotherapy and photodynamic therapy at a single dose

Hypoxia is a characteristic feature of solid tumors and an important causation of resistance to chemotherapy and photodynamic therapy (PDT). It is challenging to develop efficient functional nanomaterials for tumor oxygenation and therapeutic applications.

Methods: Through disulfide reconfiguration to hybridize hemoglobin and albumin, tumor-targeted hybrid protein oxygen carriers (HPOCs) were fabricated, serving as nanomedicines for precise tumor oxygenation and simultaneous enhancement of hypoxia-dampened chemotherapy and photodynamic therapy. Based on encapsulation of doxorubicin (DOX) and chlorin e6 (Ce6) into HPOCs to form ODC-HPOCs, the mechanism and therapeutic efficacy of oxygen-enhanced chemo-PDT was investigated in vitro and in vivo.

Results: The precise oxygen preservation and release of the HPOC guaranteed sufficient tumor oxygenation, which is able to break hypoxia-induced chemoresistance by downregulating the expressions of hypoxia-inducible factor-1α (HIF-1α), multidrug resistance 1 (MDR1) and P-glycoprotein (P-gp), resulting in minimized cellular efflux of chemodrug. Moreover, the oxygen supply is fully exploited for upgrading the generation of reactive oxygen species (ROS) during the photodynamic process. As a result, only a single-dose treatment of the HPOCs-based chemo-PDT exhibited superior tumor suppression. The combination therapy was guided by in vivo fluorescence/photoacoustic imaging with nanoparticle tracking and oxygen monitoring.

Conclusion: This well-defined HPOC as a versatile nanosystem is expected to pave a new way for breaking multiple hypoxia-induced therapeutic resistances to achieve highly effective treatment of solid tumors.

Incorporating drug delivery into an imaging-driven, mechanics-coupled reaction diffusion model for predicting the response of breast cancer to neoadjuvant chemotherapy: theory and preliminary clinical results

Clinical methods for assessing tumor response to therapy are largely rudimentary, monitoring only temporal changes in tumor size. Our goal is to predict the response of breast tumors to therapy using a mathematical model that utilizes magnetic resonance imaging (MRI) data obtained non-invasively from individual patients. We extended a previously established, mechanically coupled, reaction-diffusion model for predicting tumor response initialized with patient-specific diffusion weighted MRI (DW-MRI) data by including the effects of chemotherapy drug delivery, which is estimated using dynamic contrast-enhanced (DCE-) MRI data. The extended, drug incorporated, model is initialized using patient-specific DW-MRI and DCE-MRI data. Data sets from five breast cancer patients were used-obtained before, after one cycle, and at mid-point of neoadjuvant chemotherapy. The DCE-MRI data was used to estimate spatiotemporal variations in tumor perfusion with the extended Kety-Tofts model. The physiological parameters derived from DCE-MRI were used to model changes in delivery of therapy drugs within the tumor for incorporation in the extended model. We simulated the original model and the extended model in both 2D and 3D and compare the results for this five-patient cohort. Preliminary results show reductions in the error of model predicted tumor cellularity and size compared to the experimentally-measured results for the third MRI scan when therapy was incorporated. Comparing the two models for agreement between the predicted total cellularity and the calculated total cellularity (from the DW-MRI data) reveals an increased concordance correlation coefficient from 0.81 to 0.98 for the 2D analysis and 0.85 to 0.99 for the 3D analysis (p  <  0.01 for each) when the extended model was used in place of the original model. This study demonstrates the plausibility of using DCE-MRI data as a means to estimate drug delivery on a patient-specific basis in predictive models and represents a step toward the goal of achieving individualized prediction of tumor response to therapy.

Modeling triple-negative breast cancer heterogeneity: Effects of stromal macrophages, fibroblasts and tumor vasculature

A hallmark of breast tumors is its spatial heterogeneity that includes its distribution of cancer stem cells and progenitor cells, but also heterogeneity in the tumor microenvironment. In this study we focus on the contributions of stromal cells, specifically macrophages, fibroblasts, and endothelial cells on tumor progression. We develop a computational model of triple-negative breast cancer based on our previous work and expand it to include macrophage infiltration, fibroblasts, and angiogenesis. In vitro studies have shown that the secretomes of tumor-educated macrophages and fibroblasts increase both the migration and proliferation rates of triple-negative breast cancer cells. In vivo studies also demonstrated that blocking signaling of selected secreted factors inhibits tumor growth and metastasis in mouse xenograft models. We investigate the influences of increased migration and proliferation rates on tumor growth, the effect of the presence on fibroblasts or macrophages on growth and morphology, and the contributions of macrophage infiltration on tumor growth. We find that while the presence of macrophages increases overall tumor growth, the increase in macrophage infiltration does not substantially increase tumor growth and can even stifle tumor growth at excessive rates.

Capturing the Dynamics of a Hybrid Multiscale Cancer Model with a Continuum Model

Cancer is a complex disease involving processes at spatial scales from subcellular, like cell signalling, to tissue scale, such as vascular network formation. A number of multiscale models have been developed to study the dynamics that emerge from the coupling between the intracellular, cellular and tissue scales. Here, we develop a continuum partial differential equation model to capture the dynamics of a particular multiscale model (a hybrid cellular automaton with discrete cells, diffusible factors and an explicit vascular network). The purpose is to test under which circumstances such a continuum model gives equivalent predictions to the original multiscale model, in the knowledge that the system details are known, and differences in model results can be explained in terms of model features (rather than unknown experimental confounding factors). The continuum model qualitatively replicates the dynamics from the multiscale model, with certain discrepancies observed owing to the differences in the modelling of certain processes. The continuum model admits travelling wave solutions for normal tissue growth and tumour invasion, with similar behaviour observed in the multiscale model. However, the continuum model enables us to analyse the spatially homogeneous steady states of the system, and hence to analyse these waves in more detail. We show that the tumour microenvironmental effects from the multiscale model mean that tumour invasion exhibits a so-called pushed wave when the carrying capacity for tumour cell proliferation is less than the total cell density at the tumour wave front. These pushed waves of tumour invasion propagate by triggering apoptosis of normal cells at the wave front. Otherwise, numerical evidence suggests that the wave speed can be predicted from linear analysis about the normal tissue steady state.

The importance of geometry in the corneal micropocket angiogenesis assay

The corneal micropocket angiogenesis assay is an experimental protocol for studying vessel network formation, or neovascularization, in vivo. The assay is attractive due to the ease with which the developing vessel network can be observed in the same animal over time. Measurements from the assay have been used in combination with mathematical modeling to gain insights into the mechanisms of angiogenesis. While previous modeling studies have adopted planar domains to represent the assay, the hemispherical shape of the cornea and asymmetric positioning of the angiogenic source can be seen to affect vascular patterning in experimental images. As such, we aim to better understand: i) how the geometry of the assay influences vessel network formation and ii) how to relate observations from planar domains to those in the hemispherical cornea. To do so, we develop a three-dimensional, off-lattice mathematical model of neovascularization in the cornea, using a spatially resolved representation of the assay for the first time. Relative to the detailed model, we predict that the adoption of planar geometries has a noticeable impact on vascular patterning, leading to increased vessel 'merging', or anastomosis, in particular when circular geometries are adopted. Significant differences in the dynamics of diffusible aniogenesis simulators are also predicted between different domains. In terms of comparing predictions across domains, the 'distance of the vascular front to the limbus' metric is found to have low sensitivity to domain choice, while metrics such as densities of tip cells and vessels and 'vascularized fraction' are sensitive to domain choice. Given the widespread adoption and attractive simplicity of planar tissue domains, both in silico and in vitro, the differences identified in the present study should prove useful in relating the results of previous and future theoretical studies of neovascularization to in vivo observations in the cornea.

Mathematical modeling of tumor-associated macrophage interactions with the cancer microenvironment

Background

Immuno-oncotherapy has emerged as a promising means to target cancer. In particular, therapeutic manipulation of tumor-associated macrophages holds promise due to their various and sometimes opposing roles in tumor progression. It is established that M1-type macrophages suppress tumor progression while M2-types support it. Recently, Tie2-expressing macrophages (TEM) have been identified as a distinct sub-population influencing tumor angiogenesis and vascular remodeling as well as monocyte differentiation.

Methods

This study develops a modeling framework to evaluate macrophage interactions with the tumor microenvironment, enabling assessment of how these interactions may affect tumor progression. M1, M2, and Tie2 expressing variants are integrated into a model of tumor growth representing a metastatic lesion in a highly vascularized organ, such as the liver. Behaviors simulated include M1 release of nitric oxide (NO), M2 release of growth-promoting factors, and TEM facilitation of angiogenesis via Angiopoietin-2 and promotion of monocyte differentiation into M2 via IL-10.

Results

The results show that M2 presence leads to larger tumor growth regardless of TEM effects, implying that immunotherapeutic strategies that lead to TEM ablation may fail to restrain growth when the M2 represents a sizeable population. As TEM pro-tumor effects are less pronounced and on a longer time scale than M1-driven tumor inhibition, a more nuanced approach to influence monocyte differentiation taking into account the tumor state (e.g., under chemotherapy) may be desirable.

Conclusions

The results highlight the dynamic interaction of macrophages within a growing tumor, and, further, establish the initial feasibility of a mathematical framework that could longer term help to optimize cancer immunotherapy.

Hybrid multiscale modeling and prediction of cancer cell behavior

Background

Understanding cancer development crossing several spatial-temporal scales is of great practical significance to better understand and treat cancers. It is difficult to tackle this challenge with pure biological means. Moreover, hybrid modeling techniques have been proposed that combine the advantages of the continuum and the discrete methods to model multiscale problems.

Methods

In light of these problems, we have proposed a new hybrid vascular model to facilitate the multiscale modeling and simulation of cancer development with respect to the agent-based, cellular automata and machine learning methods. The purpose of this simulation is to create a dataset that can be used for prediction of cell phenotypes. By using a proposed Q-learning based on SVR-NSGA-II method, the cells have the capability to predict their phenotypes autonomously that is, to act on its own without external direction in response to situations it encounters.

Results

Computational simulations of the model were performed in order to analyze its performance. The most striking feature of our results is that each cell can select its phenotype at each time step according to its condition. We provide evidence that the prediction of cell phenotypes is reliable.

Conclusion

Our proposed model, which we term a hybrid multiscale modeling of cancer cell behavior, has the potential to combine the best features of both continuum and discrete models. The in silico results indicate that the 3D model can represent key features of cancer growth, angiogenesis, and its related micro-environment and show that the findings are in good agreement with biological tumor behavior. To the best of our knowledge, this paper is the first hybrid vascular multiscale modeling of cancer cell behavior that has the capability to predict cell phenotypes individually by a self-generated dataset.

Microvessel Chaste: An Open Library for Spatial Modeling of Vascularized Tissues

Spatial models of vascularized tissues are widely used in computational physiology. We introduce a software library for composing multiscale, multiphysics models for applications including tumor growth, angiogenesis, osteogenesis, coronary perfusion, and oxygen delivery. Composition of such models is time consuming, with many researchers writing custom software. Recent advances in imaging have produced detailed three-dimensional (3D) datasets of vascularized tissues at the scale of individual cells. To fully exploit such data there is an increasing need for software that allows user-friendly composition of efficient, 3D models of vascularized tissues, and comparison of predictions with in vivo or in vitro experiments and alternative computational formulations. Microvessel Chaste can be used to build simulations of vessel growth and adaptation in response to mechanical and chemical stimuli; intra- and extravascular transport of nutrients, growth factors and drugs; and cell proliferation in complex 3D geometries. In addition, it can be used to develop custom software for integrating modeling with experimental data processing workflows, facilitated by a comprehensive Python interface to solvers implemented in C++. This article links to two reproducible example problems, showing how the library can be used to build simulations of tumor growth and angiogenesis with realistic vessel networks.

Exploiting the cancer niche: Tumor-associated macrophages and hypoxia as promising synergistic targets for nano-based therapy

The tumor microenvironment has been widely exploited as an active participant in tumor progression. Extensive reports have defined the dual role of tumor-associated macrophages (TAMs) in tumor development. The protumoral effect exerted by the M2 phenotype has been correlated with a negative outcome in most solid tumors. The high infiltration of immune cells in the hypoxic cores of advanced solid tumors leads to a chain reaction of stimuli that enhances the expression of protumoral genes, thrives tumor malignancy, and leads to the emergence of drug resistance. Many studies have shown therapeutic targeting systems, solely to TAMs or tumor hypoxia, however, novel therapeutics that target both features are still warranted. In the present review, we discuss the role of hypoxia in tumor development and the clinical outcome of hypoxia-targeted therapeutics, such as hypoxia-inducible factor (HIF-1) inhibitors and hypoxia-activated prodrugs. Furthermore, we review the state-of-the-art of macrophage-based cancer therapy. We thoroughly discuss the development of novel therapeutics that simultaneously target TAMs and tumor hypoxia. Nano-based systems have been highlighted as interesting strategies for dual modality treatments, with somewhat improved tissue extravasation. Such approach could be seen as a promising strategy to overcome drug resistance and enhance the efficacy of chemotherapy in advanced solid and metastatic tumors, especially when exploiting cell-based nanotherapies. Finally, we provide an in-depth opinion on the importance of exploiting the tumor microenvironment in cancer therapy, and how this could be translated to clinical practice.

Predicting the Influence of Microvascular Structure On Tumor Response to Radiotherapy

OBJECTIVE

The purpose of this study is to investigate how theoretical predictions of tumor response to radiotherapy (RT) depend on the morphology and spatial representation of the microvascular network.

METHODS

A hybrid multiscale model, which couples a cellular automaton model of tumor growth with a model for oxygen transport from blood vessels, is used to predict the viable fraction of cells following one week of simulated RT. Both artificial and biologically derived three-dimensional (3-D) vessel networks of well vascularized tumors are considered and predictions compared with 2-D descriptions.

RESULTS

For literature-derived values of the cellular oxygen consumption rate there is little difference in predicted viable fraction when 3-D network representations of biological or artificial vessel networks are employed. Different 2-D representations are shown to either over- or under-estimate viable fractions relative to the 3-D cases, with predictions based on point-wise descriptions shown to have greater sensitivity to vessel network morphology.

CONCLUSION

The predicted RT response is relatively insensitive to the morphology of the microvessel network when 3-D representations are adopted, however, sensitivity is greater in certain 2-D representations.

SIGNIFICANCE

By using realistic 3-D vessel network geometries this study shows that real and artificial network descriptions and assumptions of spatially uniform oxygen distributions lead to similar RT response predictions in relatively small tissue volumes. This suggests that either a more detailed description of oxygen transport in the microvasculature is required or that the oxygen enhancement ratio used in the well known linear-quadratic RT response model is relatively insensitive to microvascular structure.

3D hybrid modelling of vascular network formation

We develop an off-lattice, agent-based model to describe vasculogenesis, the de novo formation of blood vessels from endothelial progenitor cells during development. The endothelial cells that comprise our vessel network are viewed as linearly elastic spheres that move in response to the forces they experience. We distinguish two types of endothelial cells: vessel elements are contained within the network and tip cells are located at the ends of vessels. Tip cells move in response to mechanical forces caused by interactions with neighbouring vessel elements and the local tissue environment, chemotactic forces and a persistence force which accounts for their tendency to continue moving in the same direction. Vessel elements are subject to similar mechanical forces but are insensitive to chemotaxis. An angular persistence force representing interactions with the local tissue is introduced to stabilise buckling instabilities caused by cell proliferation. Only vessel elements proliferate, at rates which depend on their degree of stretch: elongated elements have increased rates of proliferation, and compressed elements have reduced rates. Following division, the fate of the new cell depends on the local mechanical environment: the probability of forming a new sprout is increased if the parent vessel is highly compressed and the probability of being incorporated into the parent vessel increased if the parent is stretched. Simulation results reveal that our hybrid model can reproduce the key qualitative features of vasculogenesis. Extensive parameter sensitivity analyses show that significant changes in network size and morphology are induced by varying the chemotactic sensitivity of tip cells, and the sensitivities of the proliferation rate and the sprouting probability to mechanical stretch. Varying the chemotactic sensitivity directly influences the directionality of the networks. The degree of branching, and thereby the density of the networks, is influenced by the sprouting probability. Glyphs that simultaneously depict several network properties are introduced to show how these and other network quantities change over time and also as model parameters vary. We also show how equivalent glyphs constructed from in vivo data could be used to discriminate between normal and tumour vasculature and, in the longer term, for model validation. We conclude that our biomechanical hybrid model can generate vascular networks that are qualitatively similar to those generated from in vitro and in vivo experiments.

Enhanced performance of macrophage-encapsulated nanoparticle albumin-bound-paclitaxel in hypo-perfused cancer lesions

Hypovascularization in tumors such as liver metastases originating from breast and other organs correlates with poor chemotherapeutic response and higher mortality. Poor prognosis is linked to impaired transport of both low- and high-molecular weight drugs into the lesions and to high washout rate. Nanoparticle albumin-bound-paclitaxel (nAb-PTX) has demonstrated benefits in clinical trials when compared to paclitaxel and docetaxel. However, its therapeutic efficacy for breast cancer liver metastasis is disappointing. As macrophages are the most abundant cells in the liver tumor microenvironment, we design a multistage system employing macrophages to deliver drugs into hypovascularized metastatic lesions, and perform in vitro, in vivo, and in silico evaluation. The system encapsulates nAb-PTX into nanoporous biocompatible and biodegradable multistage vectors (MSV), thus promoting nAb-PTX retention in macrophages. We develop a 3D in vitro model to simulate clinically observed hypo-perfused tumor lesions surrounded by macrophages. This model enables evaluation of nAb-PTX and MSV-nab PTX efficacy as a function of transport barriers. Addition of macrophages to this system significantly increases MSV-nAb-PTX efficacy, revealing the role of macrophages in drug transport. In the in vivo model, a significant increase in macrophage number, as compared to unaffected liver, is observed in mice, confirming the in vitro findings. Further, a mathematical model linking drug release and retention from macrophages is implemented to project MSV-nAb-PTX efficacy in a clinical setting. Based on macrophage presence detected via liver tumor imaging and biopsy, the proposed experimental/computational approach could enable prediction of MSV-nab PTX performance to treat metastatic cancer in the liver.

Mathematical Based Calculation of Drug Penetration Depth in Solid Tumors

Cancer is a class of diseases characterized by out-of-control cells' growth which affect cells and make them damaged. Many treatment options for cancer exist. Chemotherapy as an important treatment option is the use of drugs to treat cancer. The anticancer drug travels to the tumor and then diffuses in it through capillaries. The diffusion of drugs in the solid tumor is limited by penetration depth which is different in case of different drugs and cancers. The computation of this depth is important as it helps physicians to investigate about treatment of infected tissue. Although many efforts have been made on studying and measuring drug penetration depth, less works have been done on computing this length from a mathematical point of view. In this paper, first we propose phase lagging model for diffusion of drug in the tumor. Then, using this model on one side and considering the classic diffusion on the other side, we compute the drug penetration depth in the solid tumor. This computed value of drug penetration depth is corroborated by comparison with the values measured by experiments.

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.

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

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

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

Influence of vascular normalization on interstitial flow and delivery of liposomes in tumors

Elevated interstitial fluid pressure is one of the barriers of drug delivery in solid tumors. Recent studies have shown that normalization of tumor vasculature by anti-angiogenic factors may improve the delivery of conventional cytotoxic drugs, possibly by increasing blood flow, decreasing interstitial fluid pressure, and enhancing the convective transvascular transport of drug molecules. Delivery of large therapeutic agents such as nanoparticles and liposomes might also benefit from normalization therapy since their transport depends primarily on convection. In this study, a mathematical model is presented to provide supporting evidence that normalization therapy may improve the delivery of 100 nm liposomes into solid tumors, by both increasing the total drug extravasation and providing a more homogeneous drug distribution within the tumor. However these beneficial effects largely depend on tumor size and are stronger for tumors within a certain size range. It is shown that this size effect may persist under different microenvironmental conditions and for tumors with irregular margins or heterogeneous blood supply.

In Silico Organ Modelling in Predicting Efficacy and Safety of New Medicines

The development of new medicines faces important challenges due to difficulties in the assessment of their efficacy and their safety in the targeted human population. In silico approaches through the use of mathematical modelling and computer simulations are increasingly being used to overcome some of the limitations of current experimental methods used in the development of new medicines. This chapter describes state-of-the-art in silico approaches for the evaluation of the safety and efficacy of medicines targeting important causes of mortality such as cardiovascular disease. Firstly, we describe the in silico multi-scale mathematical models and simulation techniques required to describe drug-induced effects on physiological systems such as the heart from the subcellular to the whole organ level. Then we illustrate the power of in silico approaches used to augment experimental and clinical investigations, by providing the framework to unravel multi-scale mechanisms underlying variability in the response to medicines and to focus on effects in human rather than animal models. We devote the last part of the chapter to discussing the process of validation of in silico models and simulations, which is key in building up their credibility.