How tumour-induced vascular changes alter angiogenesis: Insights from a computational model

Computational simulations of tumor growth and treatment response: Benefits of high-frequency, low-dose drug regimens and concurrent vascular normalization

Implementation of effective cancer treatment strategies requires consideration of how the spatiotemporal heterogeneities within the tumor microenvironment (TME) influence tumor progression and treatment response. Here, we developed a multi-scale three-dimensional mathematical model of the TME to simulate tumor growth and angiogenesis and then employed the model to evaluate an array of single and combination therapy approaches. Treatments included maximum tolerated dose or metronomic (i.e., frequent low doses) scheduling of anti-cancer drugs combined with anti-angiogenic therapy. The results show that metronomic therapy normalizes the tumor vasculature to improve drug delivery, modulates cancer metabolism, decreases interstitial fluid pressure and decreases cancer cell invasion. Further, we find that combining an anti-cancer drug with anti-angiogenic treatment enhances tumor killing and reduces drug accumulation in normal tissues. We also show that combined anti-angiogenic and anti-cancer drugs can decrease cancer invasiveness and normalize the cancer metabolic microenvironment leading to reduced hypoxia and hypoglycemia. Our model simulations suggest that vessel normalization combined with metronomic cytotoxic therapy has beneficial effects by enhancing tumor killing and limiting normal tissue toxicity.

Computational Simulation of Tumor-Induced Angiogenesis

Cancer cells require higher oxygen levels and nutrition than normal cells. Cancer cells induce angiogenesis (the development of new blood vessels) from preexisting vessels. This biological process depends on the special, chemical, and physical properties of the microenvironment surrounding tumor tissues. The complexity of these properties hinders an understanding of their mechanisms. Various mathematical models have been developed to describe quantitative relationships related to angiogenesis. We developed a three-dimensional mathematical model that incorporates angiogenesis and tumor growth. We examined angiopoietin, which regulates the spouting and branching events in angiogenesis. The simulation successfully reproduced the transient decrease in new vessels during vascular network formation. This chapter describes the protocol used to perform the simulations.

Investigation of cancer response to chemotherapy: a hybrid multi-scale mathematical and computational model of the tumor microenvironment

Tumor microenvironment (TME) is a multi-scale biological environment that can control tumor dynamics with many biomechanical and biochemical factors. Investigating the physiology of TME with a heterogeneous structure and abnormal functions not only can achieve a deeper understanding of tumor behavior but also can help develop more efficient anti-cancer strategies. In this work, we develop a hybrid multi-scale mathematical model of TME to simulate the progression of a three-dimensional tumor and elucidate its response to different chemotherapy approaches. The chemotherapy approaches include multiple low dose (MLD) of anti-cancer drug, maximum tolerated dose (MTD) of anti-cancer drug, combination therapy of MLD and anti-angiogenic drug, and combination therapy of MTD and anti-angiogenic drug. The results show that combining anti-angiogenic agent with anti-cancer drug increases the performance of cancer treatment and decreases side effects for normal tissue. Indeed, the vascular normalization caused by anti-angiogenic therapy improves anti-cancer drug delivery for both MLD and MTD approaches. The results show that anti-cancer drug administered in a lower dose than the maximum tolerated dose repetitively over a long period treats cancer with a considerable performance and fewer side effects. We also show that tumor morphology and distribution of cancer cell phenotypes can be considered as the characteristics to distinguish different chemotherapy approaches. This robust model can be applied to predict the behavior of any type of cancer and quantify cancer response to different chemotherapy approaches. The computational results of cancer response to chemotherapy are in good agreement with experimental measurements.

A multiscale cell-based model of tumor growth for chemotherapy assessment and tumor-targeted therapy through a 3D computational approach

OBJECTIVES

Computational modeling of biological systems is a powerful tool to clarify diverse processes contributing to cancer. The aim is to clarify the complex biochemical and mechanical interactions between cells, the relevance of intracellular signaling pathways in tumor progression and related events to the cancer treatments, which are largely ignored in previous studies.

MATERIALS AND METHODS

A three-dimensional multiscale cell-based model is developed, covering multiple time and spatial scales, including intracellular, cellular, and extracellular processes. The model generates a realistic representation of the processes involved from an implementation of the signaling transduction network.

RESULTS

Considering a benign tumor development, results are in good agreement with the experimental ones, which identify three different phases in tumor growth. Simulating tumor vascular growth, results predict a highly vascularized tumor morphology in a lobulated form, a consequence of cells' motile behavior. A novel systematic study of chemotherapy intervention, in combination with targeted therapy, is presented to address the capability of the model to evaluate typical clinical protocols. The model also performs a dose comparison study in order to optimize treatment efficacy and surveys the effect of chemotherapy initiation delays and different regimens.

CONCLUSIONS

Results not only provide detailed insights into tumor progression, but also support suggestions for clinical implementation. This is a major step toward the goal of predicting the effects of not only traditional chemotherapy but also tumor-targeted therapies.

Mathematical simulation and prediction of tumor volume using RBF artificial neural network at different circumstances in the tumor microenvironment

Uncontrolled proliferation of cells in a tissue caused by genetic mutations inside a cell is referred to as a tumor. A tumor which grows rapidly encounters a barrier when it grows to a certain size in presence of preexisting vasculature. This is the time when it has to find a way to go on the growth. The tumor starts to secrete tumor angiogenic factors (TAFs) and stimulate preexisting vessels to grow new sprouts. These new sprouts will find their way to the tumor in the extracellular matrix (ECM) by the gradient of TAF. As these new capillaries anastomose and reach tumor, fresh oxygen is available for the tumor and it will reinitiate the growth. Number of initial sprouts, distance of initial tumor cells from the vessel(s) and initial density of the tumor at the time of sprout formation are questions which are to be investigated. In the present study, the aim is to find the response of tumor cells and vessels to the reciprocal effects of each other in different circumstances in the tissue. Together with a mathematical formulation, a radial basis function (RBF) neural network is established to predict the number of tumor cells at different circumstances including size and distance of initial tumors from the parent vessel. A final formulation is given for the final number of tumor cells as a function of initial tumor size and distance between a parent vessel and a tumor. Results of this simulation demonstrate that, increasing the distance between a tumor and a parent vessel decreases the number of final tumor cells. Specially, this decrement becomes faster beyond a certain distance. Moreover, initial tumors in bigger domains must become much bigger before inducing angiogenesis which makes it harder for them to survive.

Chemo-mechanistic multi-scale model of a three-dimensional tumor microenvironment to quantify the chemotherapy response of cancer

Exploring efficient chemotherapy would benefit from a deeper understanding of the tumor microenvironment (TME) and its role in tumor progression. As in vivo experimental methods are unable to isolate or control individual factors of the TME, and in vitro models often cannot include all the contributing factors, some questions are best addressed with mathematical models of systems biology. In this study, we establish a multi-scale mathematical model of the TME to simulate three-dimensional tumor growth and angiogenesis and then implement the model for an array of chemotherapy approaches to elucidate the effect of TME conditions and drug scheduling on controlling tumor progression. The hyperglycemic condition as the most common disorder for cancer patients is considered to evaluate its impact on cancer response to chemotherapy. We show that combining antiangiogenic and anticancer drugs improves the outcome of treatment and can decrease accumulation of the drug in normal tissue and enhance drug delivery to the tumor. Our results demonstrate that although both concurrent and neoadjuvant combination therapies can increase intratumoral drug exposure and therapeutic accuracy, neoadjuvant therapy surpasses this, especially against hyperglycemia. Our model provides mechanistic explanations for clinical observations of tumor progression and response to treatment and establishes a computational framework for exploring better treatment strategies.

Multiscale modeling of tumor growth and angiogenesis: Evaluation of tumor-targeted therapy

The dynamics of tumor growth and associated events cover multiple time and spatial scales, generally including extracellular, cellular and intracellular modifications. The main goal of this study is to model the biological and physical behavior of tumor evolution in presence of normal healthy tissue, considering a variety of events involved in the process. These include hyper and hypoactivation of signaling pathways during tumor growth, vessels' growth, intratumoral vascularization and competition of cancer cells with healthy host tissue. The work addresses two distinctive phases in tumor development-the avascular and vascular phases-and in each stage two cases are considered-with and without normal healthy cells. The tumor growth rate increases considerably as closed vessel loops (anastomoses) form around the tumor cells resulting from tumor induced vascularization. When taking into account the host tissue around the tumor, the results show that competition between normal cells and cancer cells leads to the formation of a hypoxic tumor core within a relatively short period of time. Moreover, a dense intratumoral vascular network is formed throughout the entire lesion as a sign of a high malignancy grade, which is consistent with reported experimental data for several types of solid carcinomas. In comparison with other mathematical models of tumor development, in this work we introduce a multiscale simulation that models the cellular interactions and cell behavior as a consequence of the activation of oncogenes and deactivation of gene signaling pathways within each cell. Simulating a therapy that blocks relevant signaling pathways results in the prevention of further tumor growth and leads to an expressive decrease in its size (82% in the simulation).

Mathematical simulation of tumour angiogenesis: angiopoietin balance is a key factor in vessel growth and regression

Excessive tumour growth results in a hypoxic environment around cancer cells, thus inducing tumour angiogenesis, which refers to the generation of new blood vessels from pre-existing vessels. This mechanism is biologically and physically complex, with various mathematical simulation models proposing to reproduce its formation. However, although temporary vessel regression is clinically known, few models succeed in reproducing this phenomenon. Here, we developed a three-dimensional simulation model encompassing both angiogenesis and tumour growth, specifically including angiopoietin. Angiopoietin regulates both adhesion and migration between vascular endothelial cells and wall cells, thus inhibiting the cell-to-cell adhesion required for angiogenesis initiation. Simulation results showed a regression, i.e. transient decrease, in the overall length of new vessels during vascular network formation. Using our model, we also evaluated the efficacy of administering the drug bevacizumab. The results highlighted differences in treatment efficacy: (1) earlier administration showed higher efficacy in inhibiting tumour growth, and (2) efficacy depended on the treatment interval even with the administration of the same dose. After thorough validation in the future, these results will contribute to the design of angiogenesis treatment protocols.

A multi-scale model for determining the effects of pathophysiology and metabolic disorders on tumor growth

The search for efficient chemotherapy drugs and other anti-cancer treatments would benefit from a deeper understanding of the tumor microenvironment (TME) and its role in tumor progression. Because in vivo experimental methods are unable to isolate or control individual factors of the TME and in vitro models often do not include all the contributing factors, some questions are best addressed with systems biology mathematical models. In this work, we present a new fully-coupled, agent-based, multi-scale mathematical model of tumor growth, angiogenesis and metabolism that includes important aspects of the TME spanning subcellular-, cellular- and tissue-level scales. The mathematical model is computationally implemented for a three-dimensional TME, and a double hybrid continuous-discrete (DHCD) method is applied to solve the governing equations. The model recapitulates the distinct morphological and metabolic stages of a solid tumor, starting with an avascular tumor and progressing through angiogenesis and vascularized tumor growth. To examine the robustness of the model, we simulated normal and abnormal blood conditions, including hyperglycemia/hypoglycemia, hyperoxemia/hypoxemia, and hypercarbia/hypocarbia - conditions common in cancer patients. The results demonstrate that tumor progression is accelerated by hyperoxemia, hyperglycemia and hypercarbia but inhibited by hypoxemia and hypoglycemia; hypocarbia had no appreciable effect. Because of the importance of interstitial fluid flow in tumor physiology, we also examined the effects of hypo- or hypertension, and the impact of decreased hydraulic conductivity common in desmoplastic tumors. The simulations show that chemotherapy-increased blood pressure, or reduction of interstitial hydraulic conductivity increase tumor growth rate and contribute to tumor malignancy.

Hybrid modeling frameworks of tumor development and treatment

Tumors are complex multicellular heterogeneous systems comprised of components that interact with and modify one another. Tumor development depends on multiple factors: intrinsic, such as genetic mutations, altered signaling pathways, or variable receptor expression; and extrinsic, such as differences in nutrient supply, crosstalk with stromal or immune cells, or variable composition of the surrounding extracellular matrix. Tumors are also characterized by high cellular heterogeneity and dynamically changing tumor microenvironments. The complexity increases when this multiscale, multicomponent system is perturbed by anticancer treatments. Modeling such complex systems and predicting how tumors will respond to therapies require mathematical models that can handle various types of information and combine diverse theoretical methods on multiple temporal and spatial scales, that is, hybrid models. In this update, we discuss the progress that has been achieved during the last 10 years in the area of the hybrid modeling of tumors. The classical definition of hybrid models refers to the coupling of discrete descriptions of cells with continuous descriptions of microenvironmental factors. To reflect on the direction that the modeling field has taken, we propose extending the definition of hybrid models to include of coupling two or more different mathematical frameworks. Thus, in addition to discussing recent advances in discrete/continuous modeling, we also discuss how these two mathematical descriptions can be coupled with theoretical frameworks of optimal control, optimization, fluid dynamics, game theory, and machine learning. All these methods will be illustrated with applications to tumor development and various anticancer treatments.

This article is characterized under:

Analytical and Computational Methods > Computational Methods

Translational, Genomic, and Systems Medicine > Therapeutic Methods

Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

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.

pH as a potential therapeutic target to improve temozolomide antitumor efficacy : A mechanistic modeling study

Despite intensive treatments including temozolomide (TMZ) administration, glioblastoma patient prognosis remains dismal and innovative therapeutic strategies are urgently needed. A systems pharmacology approach was undertaken to investigate TMZ pharmacokinetics-pharmacodynamics (PK-PD) incorporating the effect of local pH, tumor spatial configuration and micro-environment. A hybrid mathematical framework was designed coupling ordinary differential equations describing the intracellular reactions, with a spatial cellular automaton to individualize the cells. A differential drug impact on tumor and healthy cells at constant extracellular pH was computationally demonstrated as TMZ-induced DNA damage was larger in tumor cells as compared to normal cells due to less acidic intracellular pH in cancer cells. Optimality of TMZ efficacy defined as maximum difference between damage in tumor and healthy cells was reached for extracellular pH between 6.8 and 7.5. Next, TMZ PK-PD in a solid tumor was demonstrated to highly depend on its spatial configuration as spread cancer cells or fragmented tumors presented higher TMZ-induced damage as compared to compact tumor spheroid. Simulations highlighted that smaller tumors were less acidic than bigger ones allowing for faster TMZ activation and their closer distance to blood capillaries allowed for better drug penetration. For model parameters corresponding to U87 glioma cells, inter-cell variability in TMZ uptake play no role regarding the mean drug-induced damage in the whole cell population whereas this quantity was increased by inter-cell variability in TMZ efflux which was thus a disadvantage in terms of drug resistance. Overall, this study revealed pH as a new potential target to significantly improve TMZ antitumor efficacy.

Transient alleviation of tumor hypoxia during first days of antiangiogenic therapy as a result of therapy-induced alterations in nutrient supply and tumor metabolism - Analysis by mathematical modeling

A number of experiments on mouse tumor models, as well as certain clinical data, have demonstrated, that antiangiogenic therapy can lead to transient improvement in tumor oxygenation, that allows to increase efficiency of following radiotherapy. In the majority of works, this phenomenon has been explained by enhanced tumor perfusion due to normalization of capillaries' structure, that results in elevated oxygen inflow in tumor. However, changes in tumor perfusion often haven't been directly measured in relevant works, moreover, antiangiogenic therapy has been proven to have ambiguous effect on tumor perfusion both in mouse tumor models and in clinics. Herein, we suggest that elevation of blood perfusion may be not the only reason for transient alleviation of tumor hypoxia, and that it may manifest itself even under unchanged tumor blood flow. We propose that it may be as well caused by the decrease in tumor oxygen consumption rate (OCR) due to the reduction of tumor proliferation level, caused by nutrient shortage in result of antiangiogenic treatment. We provide detailed explanation of this hypothesis and visualize it using a specially developed mathematical model, which takes into account basic features of tumor growth and antiangiogenic therapy. We investigate the influence of the model parameters on oxygen dynamics; demonstrate, that transient alleviation of tumor hypoxia occurs in a fairly wide range of physiologically justified values of parameters; and point out the major factors, that determine oxygen dynamics during antiangiogenic therapy.

Pharmacokinetics variability: Why nanoparticles are not just magic-bullets in oncology

Developing nanoparticles to improve the specificity of anticancer agents towards tumor tissue and to better control drug delivery is a rising strategy in oncology. An increasing number of forms (e.g., conjugated nanoparticles, liposomes, immunoliposomes…) are now available on the shelves and numerous other scaffolds (e.g., dendrimeres, nanospheres, squalenes …) are currently at various stages of development. However, as of today most nanoparticles made available remain lipidic carriers. Pharmacokinetic variability is a major, yet largely underestimated issue with liposomal nanoparticles. A wide variety of causes (e.g., tumor type and disease staging, comorbidities, patient's immune system) can explain this variability, which can in return negatively impact pharmacodynamic endpoints such as poor efficacy or severe toxicities. This review aims to cover the main causes for erratic pharmacokinetics observed with most nanoparticles, especially liposomes used in oncology. Should the main causes of such variability be identified, specific studies in non-clinical or clinical development stages could be undertaken using dedicated models (i.e., mechanistic or semi-mechanistic mathematical models such as PBPK approaches) to better describe nanoparticles pharmacokinetics and decipher PK/PD relationships. In addition, identifying relevant biomarkers or parameters likely to impact nanoparticles pharmacokinetics would allow for either the modification of their characteristics to reduce the influence of the expected variability during development phases or the development of biomarker-based adaptive dosing strategies to maintain an optimal efficacy/toxicity balance. Broadly, we call for the development of comprehensive distribution studies and state-of-the-art modeling support to better understand and anticipate nanoparticle pharmacokinetics in oncology.

Does metronomic chemotherapy induce tumor angiogenic dormancy? A review of available preclinical and clinical data

Tumor dormancy is the ability of cancer cells to survive in a non-proliferating state. This condition can depend on three main mechanisms: cell cycle arrest (quiescence or cell dormancy), immunosurveillance (immunologic dormancy), or lack of functional blood vessels (angiogenic dormancy). In particular, under angiogenic dormancy, cancer cell proliferation is counterbalanced by apoptosis owing to poor vascularization, impeding tumor mass expansion beyond a microscopic size, with an asymptomatic and non-metastatic state. Tumor vasculogenic or non-angiogenic switch is essential to promote escape from tumor dormancy, leading to tumor mass proliferation and metastasis. In avascular lesions angiogenesis process results blocked from the equilibrium between pro- and anti-angiogenic factors, such as vascular endothelial growth factor (VEGF) and thrombospondin-1 (TSP-1), respectively. The angiogenic switch mainly depends on the disruption of this balance, in favor of pro-angiogenic factors, and on the recruitment of circulating endothelial progenitors (CEPs) that promote the formation of new blood vessels. Metronomic chemotherapy, the regular intake of doses able to sustain low but active concentrations of chemotherapeutic drugs during protracted time periods, is an encouraging therapeutic approach that has shown to upregulate anti-angiogenic factors such as TSP-1 and decline pro-angiogenic factors such as VEGF, suppressing the proangiogenic cells such as CEPs. In this perspective, metronomic chemotherapy may be one of the available therapeutic approaches capable to modulate favorably the angiogenic tumor dormancy, but further research is essential to better define this particular characteristic.

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.