Multiscale modelling and nonlinear simulation of vascular tumour growth

Systematically understanding the immunity leading to CRPC progression

Prostate cancer (PCa) is the most commonly diagnosed malignancy and the second leading cause of cancer-related death in American men. Androgen deprivation therapy (ADT) has become a standard treatment strategy for advanced PCa. Although a majority of patients initially respond to ADT well, most of them will eventually develop castration-resistant PCa (CRPC). Previous studies suggest that ADT-induced changes in the immune microenvironment (mE) in PCa might be responsible for the failures of various therapies. However, the role of the immune system in CRPC development remains unclear. To systematically understand the immunity leading to CRPC progression and predict the optimal treatment strategy in silico, we developed a 3D Hybrid Multi-scale Model (HMSM), consisting of an ODE system and an agent-based model (ABM), to manipulate the tumor growth in a defined immune system. Based on our analysis, we revealed that the key factors (e.g. WNT5A, TRAIL, CSF1, etc.) mediated the activation of PC-Treg and PC-TAM interaction pathways, which induced the immunosuppression during CRPC progression. Our HMSM model also provided an optimal therapeutic strategy for improving the outcomes of PCa treatment.

Three-dimensional tumor growth in time-varying chemical fields: a modeling framework and theoretical study

Background

Contemporary biological observations have revealed a large variety of mechanisms acting during the expansion of a tumor. However, there are still many qualitative and quantitative aspects of the phenomenon that remain largely unknown. In this context, mathematical and computational modeling appears as an invaluable tool providing the means for conducting in silico experiments, which are cheaper and less tedious than real laboratory experiments.

Results

This paper aims at developing an extensible and computationally efficient framework for in silico modeling of tumor growth in a 3-dimensional, inhomogeneous and time-varying chemical environment. The resulting model consists of a set of mathematically derived and algorithmically defined operators, each one addressing the effects of a particular biological mechanism on the state of the system. These operators may be extended or re-adjusted, in case a different set of starting assumptions or a different simulation scenario needs to be considered.

Conclusion

In silico modeling provides an alternative means for testing hypotheses and simulating scenarios for which exact biological knowledge remains elusive. However, finer tuning of pertinent methods presupposes qualitative and quantitative enrichment of available biological evidence. Validation in a strict sense would further require comprehensive, case-specific simulations and detailed comparisons with biomedical observations.

Methods to label, image, and analyze the complex structural architectures of microvascular networks

Microvascular networks play key roles in oxygen transport and nutrient delivery to meet the varied and dynamic metabolic needs of different tissues throughout the body, and their spatial architectures of interconnected blood vessel segments are highly complex. Moreover, functional adaptations of the microcirculation enabled by structural adaptations in microvascular network architecture are required for development, wound healing, and often invoked in disease conditions, including the top eight causes of death in the Unites States. Effective characterization of microvascular network architectures is not only limited by the available techniques to visualize microvessels but also reliant on the available quantitative metrics that accurately delineate between spatial patterns in altered networks. In this review, we survey models used for studying the microvasculature, methods to label and image microvessels, and the metrics and software packages used to quantify microvascular networks. These programs have provided researchers with invaluable tools, yet we estimate that they have collectively attained low adoption rates, possibly due to limitations with basic validation, segmentation performance, and nonstandard sets of quantification metrics. To address these existing constraints, we discuss opportunities to improve effectiveness, rigor, and reproducibility of microvascular network quantification to better serve the current and future needs of microvascular research.

Mathematical modeling in cancer nanomedicine: a review

Cancer continues to be among the leading healthcare problems worldwide, and efforts continue not just to find better drugs, but also better drug delivery methods. The need for delivering cytotoxic agents selectively to cancerous cells, for improved safety and efficacy, has triggered the application of nanotechnology in medicine. This effort has provided drug delivery systems that can potentially revolutionize cancer treatment. Nanocarriers, due to their capacity for targeted drug delivery, can shift the balance of cytotoxicity from healthy to cancerous cells. The field of cancer nanomedicine has made significant progress, but challenges remain that impede its clinical translation. Several biophysical barriers to the transport of nanocarriers to the tumor exist, and a much deeper understanding of nano-bio interactions is necessary to change the status quo. Mathematical modeling has been instrumental in improving our understanding of the physicochemical and physiological underpinnings of nanomaterial behavior in biological systems. Here, we present a comprehensive review of literature on mathematical modeling works that have been and are being employed towards a better understanding of nano-bio interactions for improved tumor delivery efficacy.

Pharmacokinetics and Pharmacodynamics Modeling and Simulation Systems to Support the Development and Regulation of Liposomal Drugs

Liposomal formulations have been developed to improve the therapeutic index of encapsulated drugs by altering the balance of on- and off-targeted distribution. The improved therapeutic efficacy of liposomal drugs is primarily attributed to enhanced distribution at the sites of action. The targeted distribution of liposomal drugs depends not only on the physicochemical properties of the liposomes, but also on multiple components of the biological system. Pharmacokinetic⁻pharmacodynamic (PK⁻PD) modeling has recently emerged as a useful tool with which to assess the impact of formulation- and system-specific factors on the targeted disposition and therapeutic efficacy of liposomal drugs. The use of PK⁻PD modeling to facilitate the development and regulatory reviews of generic versions of liposomal drugs recently drew the attention of the U.S. Food and Drug Administration. The present review summarizes the physiological factors that affect the targeted delivery of liposomal drugs, challenges that influence the development and regulation of liposomal drugs, and the application of PK⁻PD modeling and simulation systems to address these challenges.

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.

A Review of Cell-Based Computational Modeling in Cancer Biology

Cancer biology involves complex, dynamic interactions between cancer cells and their tissue microenvironments. Single-cell effects are critical drivers of clinical progression. Chemical and mechanical communication between tumor and stromal cells can co-opt normal physiologic processes to promote growth and invasion. Cancer cell heterogeneity increases cancer's ability to test strategies to adapt to microenvironmental stresses. Hypoxia and treatment can select for cancer stem cells and drive invasion and resistance. Cell-based computational models (also known as discrete models, agent-based models, or individual-based models) simulate individual cells as they interact in virtual tissues, which allows us to explore how single-cell behaviors lead to the dynamics we observe and work to control in cancer systems. In this review, we introduce the broad range of techniques available for cell-based computational modeling. The approaches can range from highly detailed models of just a few cells and their morphologies to millions of simpler cells in three-dimensional tissues. Modeling individual cells allows us to directly translate biologic observations into simulation rules. In many cases, individual cell agents include molecular-scale models. Most models also simulate the transport of oxygen, drugs, and growth factors, which allow us to link cancer development to microenvironmental conditions. We illustrate these methods with examples drawn from cancer hypoxia, angiogenesis, invasion, stem cells, and immunosurveillance. An ecosystem of interoperable cell-based simulation tools is emerging at a time when cloud computing resources make software easier to access and supercomputing resources make large-scale simulation studies possible. As the field develops, we anticipate that high-throughput simulation studies will allow us to rapidly explore the space of biologic possibilities, prescreen new therapeutic strategies, and even re-engineer tumor and stromal cells to bring cancer systems under control.

Experimental and computational analyses reveal dynamics of tumor vessel cooption and optimal treatment strategies

Cooption of the host vasculature is a strategy that some cancers use to sustain tumor progression without-or before-angiogenesis or in response to antiangiogenic therapy. Facilitated by certain growth factors, cooption can mediate tumor infiltration and confer resistance to antiangiogenic drugs. Unfortunately, this mode of tumor progression is difficult to target because the underlying mechanisms are not fully understood. Here, we analyzed the dynamics of vessel cooption during tumor progression and in response to antiangiogenic treatment in gliomas and brain metastases. We followed tumor evolution during escape from antiangiogenic treatment as cancer cells coopted, and apparently mechanically compressed, host vessels. To gain deeper understanding, we developed a mathematical model, which incorporated compression of coopted vessels, resulting in hypoxia and formation of new vessels by angiogenesis. Even if antiangiogenic therapy can block such secondary angiogenesis, the tumor can sustain itself by coopting existing vessels. Hence, tumor progression can only be stopped by combination therapies that judiciously block both angiogenesis and cooption. Furthermore, the model suggests that sequential blockade is likely to be more beneficial than simultaneous blockade.

Design Optimization of Tumor Vasculature-Bound Nanoparticles

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

Evaluation of Drug-Loaded Gold Nanoparticle Cytotoxicity as a Function of Tumor Vasculature-Induced Tissue Heterogeneity

The inherent heterogeneity of tumor tissue presents a major challenge to nanoparticle-mediated drug delivery. This heterogeneity spans from the molecular (genomic, proteomic, metabolomic) to the cellular (cell types, adhesion, migration) and to the tissue (vasculature, extra-cellular matrix) scales. In particular, tumor vasculature forms abnormally, inducing proliferative, hypoxic, and necrotic tumor tissue regions. As the vasculature is the main conduit for nanotherapy transport into tumors, vasculature-induced tissue heterogeneity can cause local inadequate delivery and concentration, leading to subpar response. Further, hypoxic tissue, although viable, would be immune to the effects of cell-cycle specific drugs. In order to enable a more systematic evaluation of such effects, here we employ computational modeling to study the therapeutic response as a function of vasculature-induced tumor tissue heterogeneity. Using data with three-layered gold nanoparticles loaded with cisplatin, nanotherapy is simulated interacting with different levels of tissue heterogeneity, and the treatment response is measured in terms of tumor regression. The results quantify the influence that varying levels of tumor vascular density coupled with the drug strength have on nanoparticle uptake and washout, and the associated tissue response. The drug strength affects the proportion of proliferating, hypoxic, and necrotic tissue fractions, which in turn dynamically affect and are affected by the vascular density. Higher drug strengths may be able to achieve stronger tumor regression but only if the intra-tumoral vascular density is above a certain threshold that affords sufficient transport. This study establishes an initial step towards a more systematic methodology to assess the effect of vasculature-induced tumor tissue heterogeneity on the response to nanotherapy.

A monolithic multiphase porous medium framework for (a-)vascular tumor growth

We present a dynamic vascular tumor model combining a multiphase porous medium framework for avascular tumor growth in a consistent Arbitrary Lagrangian Eulerian formulation and a novel approach to incorporate angiogenesis. The multiphase model is based on Thermodynamically Constrained Averaging Theory and comprises the extracellular matrix as a porous solid phase and three fluid phases: (living and necrotic) tumor cells, host cells and the interstitial fluid. Angiogenesis is modeled by treating the neovasculature as a proper additional phase with volume fraction or blood vessel density. This allows us to define consistent inter-phase exchange terms between the neovasculature and the interstitial fluid. As a consequence, transcapillary leakage and lymphatic drainage can be modeled. By including these important processes we are able to reproduce the increased interstitial pressure in tumors which is a crucial factor in drug delivery and, thus, therapeutic outcome. Different coupling schemes to solve the resulting five-phase problem are realized and compared with respect to robustness and computational efficiency. We find that a fully monolithic approach is superior to both the standard partitioned and a hybrid monolithic-partitioned scheme for a wide range of parameters. The flexible implementation of the novel model makes further extensions (e.g., inclusion of additional phases and species) straightforward.

Eco-evolutionary causes and consequences of temporal changes in intratumoural blood flow

Temporal changes in blood flow are commonly observed in malignant tumours, but the evolutionary causes and consequences are rarely considered. We propose that stochastic temporal variations in blood flow and microenvironmental conditions arise from the eco-evolutionary dynamics of tumour angiogenesis in which cancer cells, as individual units of selection, can influence and respond only to local environmental conditions. This leads to new vessels arising from the closest available vascular structure regardless of the size or capacity of this parental vessel. These dynamics produce unstable vascular networks with unpredictable spatial and temporal variations in blood flow and microenvironmental conditions. Adaptations of evolving populations to temporally varying environments in nature include increased diversity, greater motility and invasiveness, and highly plastic phenotypes, allowing for broad metabolic adaptability and rapid shifts to high rates of proliferation and profound quiescence. These adaptive strategies, when adopted in cancer cells, promote many commonly observed phenotypic properties including those found in the stem phenotype and in epithelial-to-mesenchymal transition. Temporal variations in intratumoural blood flow, which occur through the promotion of cancer cell phenotypes that facilitate both metastatic spread and resistance to therapy, may have substantial clinical consequences.

Angiogenic Factors produced by Hypoxic Cells are a leading driver of Anastomoses in Sprouting Angiogenesis-a computational study

Angiogenesis - the growth of new blood vessels from a pre-existing vasculature - is key in both physiological processes and on several pathological scenarios such as cancer progression or diabetic retinopathy. For the new vascular networks to be functional, it is required that the growing sprouts merge either with an existing functional mature vessel or with another growing sprout. This process is called anastomosis. We present a systematic 2D and 3D computational study of vessel growth in a tissue to address the capability of angiogenic factor gradients to drive anastomosis formation. We consider that these growth factors are produced only by tissue cells in hypoxia, i.e. until nearby vessels merge and become capable of carrying blood and irrigating their vicinity. We demonstrate that this increased production of angiogenic factors by hypoxic cells is able to promote vessel anastomoses events in both 2D and 3D. The simulations also verify that the morphology of these networks has an increased resilience toward variations in the endothelial cell's proliferation and chemotactic response. The distribution of tissue cells and the concentration of the growth factors they produce are the major factors in determining the final morphology of the network.

The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity

We present here a space- and phenotype-structured model of selection dynamics between cancer cells within a solid tumour. In the framework of this model, we combine formal analyses with numerical simulations to investigate in silico the role played by the spatial distribution of abiotic components of the tumour microenvironment in mediating phenotypic selection of cancer cells. Numerical simulations are performed both on the 3D geometry of an in silico multicellular tumour spheroid and on the 3D geometry of an in vivo human hepatic tumour, which was imaged using computerised tomography. The results obtained show that inhomogeneities in the spatial distribution of oxygen, currently observed in solid tumours, can promote the creation of distinct local niches and lead to the selection of different phenotypic variants within the same tumour. This process fosters the emergence of stable phenotypic heterogeneity and supports the presence of hypoxic cells resistant to cytotoxic therapy prior to treatment. Our theoretical results demonstrate the importance of integrating spatial data with ecological principles when evaluating the therapeutic response of solid tumours to cytotoxic therapy.

The pivotal role of angiogenesis in a multi-scale modeling of tumor growth exhibiting the avascular and vascular phases

The mechanisms involved in tumor growth mainly occur at the microenvironment, where the interactions between the intracellular, intercellular and extracellular scales mediate the dynamics of tumor. In this work, we present a multi-scale model of solid tumor dynamics to simulate the avascular and vascular growth as well as tumor-induced angiogenesis. The extracellular and intercellular scales are modeled using partial differential equations and cellular Potts model, respectively. Also, few biochemical and biophysical rules control the dynamics of intracellular level. On the other hand, the growth of melanoma tumors is modeled in an animal in-vivo study to evaluate the simulation. The simulation shows that the model successfully reproduces a completed image of processes involved in tumor growth such as avascular and vascular growth as well as angiogenesis. The model incorporates the phenotypes of cancerous cells including proliferating, quiescent and necrotic cells, as well as endothelial cells during angiogenesis. The results clearly demonstrate the pivotal effect of angiogenesis on the progression of cancerous cells. Also, the model exhibits important events in tumor-induced angiogenesis like anastomosis. Moreover, the computational trend of tumor growth closely follows the observations in the experimental study.

Tumorcode : A framework to simulate vascularized tumors

During the past years our group published several articles using computer simulations to address the complex interaction of tumors and the vasculature as underlying transport network. Advances in imaging and lab techniques pushed in vitro research of tumor spheroids forward and animal models as well as clinical studies provided more insights to single processes taking part in tumor growth, however, an overall picture is still missing. Computer simulations are a non-invasive option to cumulate current knowledge and form a quasi in vivo system. In our software, several known models were assembled into a multi-scale approach which allows to study length scales relevant for clinical applications. We release our code to the public domain, together with a detailed description of the implementation and several examples, with the hope of usage and futher development by the community. A justification for the included algorithms and the biological models was obtained in previous publications, here we summarize the technical aspects following the workflow of a typical simulation procedure.

Pharmacokinetic/pharmacodynamic modeling of combination-chemotherapy for lung cancer

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

A multiscale model for heterogeneous tumor spheroid in vitro

In this paper, a novel multiscale method is proposed for the study of heterogeneous tumor spheroid growth in vitro. The entire tumor spheroid is described by an ellipsoid-based model while nutrient and other environmental factors are treated as continua. The ellipsoid-based discrete component is capable of incorporating mechanical effects and deformability, while keeping a minimum set of free variables to describe complex shape variations. Moreover, our purely cell-based description of tumor avoids the complex mutual conversion between a cell-based model and continuum model within a tumor, such as force and mass transformation. This advantage makes it highly suitable for the study of tumor spheroids in vitro whose size are normally less than 800 μm in diameter. In addition, our numerical scheme provides two computational options depending on tumor size. For a small or medium tumor spheroid, a three-dimensional (3D) numerical model can be directly applied. For a large spheroid, we suggest the use of a 3D-adapted 2D cross section configuration, which has not yet been explored in the literature, as an alternative for the theoretical investigation to bridge the gap between the 2D and 3D models. Our model and its implementations have been validated and applied to various studies given in the paper. The simulation results fit corresponding in vitro experimental observations very well.

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.

The influence of soluble fragments of extracellular matrix (ECM) on tumor growth and morphology

A major challenge in matrix-metalloproteinase (MMP) target validation and MMP-inhibitor-drug development for anti-cancer clinical trials is to better understand their complex roles (often competing with each other) in tumor progression. While there is extensive research on the growth-promoting effects of MMPs, the growth-inhibiting effects of MMPs has not been investigated thoroughly. So we develop a continuum model of tumor growth and invasion including chemotaxis and haptotaxis in order to examine the complex interaction between the tumor and its host microenvironment and to explore the inhibiting influence of the gradients of soluble fragments of extracellular matrix (ECM) density on tumor growth and morphology. Previously, it was shown both computationally (in one spatial dimension) and experimentally that the chemotactic pull due to soluble ECM gradients is anti-invasive, contrary to the traditional view of the role of chemotaxis in malignant invasion [1]. With two-dimensional numerical simulation and using a level set based tumor-host interface capturing method, we examine the effects of chemotaxis on the progression and morphology of a tumor growing in nutrient-rich and nutrient-poor microenvironments which was not investigated before. In particular we examine how the geometry of the growing tumor is affected when placed in different environments. We also investigate the effects of varying ECM degradation rate, the production rate of matrix degrading enzymes (MDE), and the conversion of ECM into soluble ECM. We find that chemotaxis due to ECM-fragment gradients strongly influences tumor growth and morphology, and that the instabilities caused by tumor cell proliferation and haptotactic movements can be prevented if chemotaxis is sufficiently strong. The influence of chemotaxis and the above factors on tumor growth and morphology are found to be more prominent in nutrient-poor environments than in nutrient-rich environments. So we extend our investigations of these antinvasive chemotactic influences by examining the effects of cell-cell and cell-ECM adhesion and low proliferation rate for tumors growing in low-nutrient environments. We find that as the extent of chemotaxis increases, the effects of adhesion on tumor growth and shape become negligible. Under conditions of low cell mitosis, chemotaxis may cause the tumor to shrink, as the extent of chemotaxis increases. Both stable and unstable tumor shrinkage are predicted by our model. Unexpectedly, in some cases chemotaxis may contribute toward developing instability where haptotaxis alone induces stable growth.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Drug delivery to solid tumors: the predictive value of the multicellular tumor spheroid model for nanomedicine screening

The increasing number of publications on the subject shows that nanomedicine is an attractive field for investigations aiming to considerably improve anticancer chemotherapy. Based on selective tumor targeting while sparing healthy tissue, carrier-mediated drug delivery has been expected to provide significant benefits to patients. However, despite reduced systemic toxicity, most nanodrugs approved for clinical use have been less effective than previously anticipated. The gap between experimental results and clinical outcomes demonstrates the necessity to perform comprehensive drug screening by using powerful preclinical models. In this context, in vitro three-dimensional models can provide key information on drug behavior inside the tumor tissue. The multicellular tumor spheroid (MCTS) model closely mimics a small avascular tumor with the presence of proliferative cells surrounding quiescent cells and a necrotic core. Oxygen, pH and nutrient gradients are similar to those of solid tumor. Furthermore, extracellular matrix (ECM) components and stromal cells can be embedded in the most sophisticated spheroid design. All these elements together with the physicochemical properties of nanoparticles (NPs) play a key role in drug transport, and therefore, the MCTS model is appropriate to assess the ability of NP to penetrate the tumor tissue. This review presents recent developments in MCTS models for a better comprehension of the interactions between NPs and tumor components that affect tumor drug delivery. MCTS is particularly suitable for the high-throughput screening of new nanodrugs.

A mathematical model of tumour angiogenesis: growth, regression and regrowth

Cancerous tumours have the ability to recruit new blood vessels through a process called angiogenesis. By stimulating vascular growth, tumours get connected to the circulatory system, receive nutrients and open a way to colonize distant organs. Tumour-induced vascular networks become unstable in the absence of tumour angiogenic factors (TAFs). They may undergo alternating stages of growth, regression and regrowth. Following a phase-field methodology, we propose a model of tumour angiogenesis that reproduces the aforementioned features and highlights the importance of vascular regression and regrowth. In contrast with previous theories which focus on vessel remodelling due to the absence of flow, we model an alternative regression mechanism based on the dependency of tumour-induced vascular networks on TAFs. The model captures capillaries at full scale, the plastic dynamics of tumour-induced vessel networks at long time scales, and shows the key role played by filopodia during angiogenesis. The predictions of our model are in agreement with in vivo experiments and may prove useful for the design of antiangiogenic therapies.

Model of vascular desmoplastic multispecies tumor growth

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

Predicting brain tumor regrowth in relation to motor areas by functional brain mapping

Background

Due to frequent recurrences, high-grade gliomas still confer a poor prognosis. Several regrowth prediction models have been developed, but most of these models are based on cellular models or dynamic mathematical calculations, thus limiting direct clinical use. The present study aims to evaluate whether navigated transcranial magnetic stimulation (nTMS) or functional magnetic resonance imaging (fMRI) may be used to predict the direction of tumor regrowth.

Methods

Sixty consecutive patients with high-grade gliomas were enrolled prospectively and analyzed in a case-control design after tumor recurrence. All patients underwent serial MRI after surgery and suffered from recurrent tumors during a mean follow-up of 13.2 ± 14.9 months. Tumor regrowth speed and direction were measured in relation to motor areas defined by nTMS, nTMS-based tractography, and fMRI. Depending on initial resection, patients were separated into three groups (group 1: without residual tumor, group 2: residual tumor away from motor areas, and group 3: residual tumor facing motor areas).

Results

Sixty-nine percent of patients in group 1, 64.3% in group 2, and 66.7% in group 3 showed tumor recurrence towards motor eloquence on contrast-enhanced T1-weighted sequences (P = .9527). Average growth towards motor areas on contrast-enhanced T1-weighted sequences was 0.6 ± 1.5 (group 1), 0.6 ± 2.4 (group 2), and 2.3 ± 5.5 (group 3) mm/month (P = .0492).

Conclusion

This study suggests a new strategy to predict tumor regrowth patterns in high-grade glioma patients. Our approach could be directly applied in the clinical setting, thus having clinical impact on both surgical treatment and radiotherapy planning.

Ethics Committee Registration Number

2793/10.

Modelling Tumor-induced Angiogenesis: Combination of Stochastic Sprout Spacing and Sprout Progression

BACKGROUND

Angiogenesis initiated by cancerous cells is the process by which new blood vessels are formed to enhance oxygenation and growth of tumor.

OBJECTIVE

In this paper, we present a new multiscale mathematical model for the formation of a vascular network in tumor angiogenesis process.

METHODS

Our model couples an improved sprout spacing model as a stochastic mathematical model of sprouting along an existing parent blood vessel, with a mathematical model of sprout progression in the extracellular matrix (ECM) in response to some tumor angiogenic factors (TAFs). We perform simulations of the siting of capillary sprouts on an existing blood vessel using finite difference approximation of the dynamic equations of some angiogenesis activators and inhibitors. Angiogenesis activators are chemicals secreted by hypoxic tumor cells for initiating angiogenesis, and inhibitors of the angiogenesis are chemicals that are produced around every new sprout during tumor angiogenesis to inhibit the formation of further sprouts as a feedback of sprouting in angiogenesis. Moreover, for modelling sprout progression in ECM, we use three equations for the motility of endothelial cells at the tip of the activated sprouts, the consumption of TAF and the production and uptake of Fibronectin by endothelial cells.

RESULTS

Coupling these two basic models not only does provide a better time estimation of angiogenesis process, but also it is more compatible with reality.

CONCLUSION

This model can be used to provide basic information for angiogenesis in the related studies. Related simulations can estimate the position and number of sprouts along parent blood vessel during the initial steps of angiogenesis and models the process of sprout progression in ECM until they vascularize a tumor.

Progress Towards Computational 3-D Multicellular Systems Biology

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

Computational Modelling of Cancer Development and Growth: Modelling at Multiple Scales and Multiscale Modelling

In this paper, we present two mathematical models related to different aspects and scales of cancer growth. The first model is a stochastic spatiotemporal model of both a synthetic gene regulatory network (the example of a three-gene repressilator is given) and an actual gene regulatory network, the NF-[Formula: see text]B pathway. The second model is a force-based individual-based model of the development of a solid avascular tumour with specific application to tumour cords, i.e. a mass of cancer cells growing around a central blood vessel. In each case, we compare our computational simulation results with experimental data. In the final discussion section, we outline how to take the work forward through the development of a multiscale model focussed at the cell level. This would incorporate key intracellular signalling pathways associated with cancer within each cell (e.g. p53-Mdm2, NF-[Formula: see text]B) and through the use of high-performance computing be capable of simulating up to [Formula: see text] cells, i.e. the tissue scale. In this way, mathematical models at multiple scales would be combined to formulate a multiscale computational model.

Macrophage Polarization Contributes to the Anti-Tumoral Efficacy of Mesoporous Nanovectors Loaded with Albumin-Bound Paclitaxel

Therapies targeted to the immune system, such as immunotherapy, are currently shaping a new, rapidly developing branch of promising cancer treatments, offering the potential to change the prognosis of previously non-responding patients. Macrophages comprise the most abundant population of immune cells in the tumor microenvironment (TME) and can undergo differentiation into functional phenotypes depending on the local tissue environment. Based on these functional phenotypes, tumor-associated macrophages (TAMs) can either aid tumor progression (M2 phenotype) or inhibit it (M1 phenotype). Presence of M2 macrophages and a high ratio of M2/M1 macrophages in the TME are clinically associated with poor prognosis in many types of cancers. Herein, we evaluate the effect of macrophage phenotype on the transport and anti-cancer efficacy of albumin-bound paclitaxel (nAb-PTX) loaded into porous silicon multistage nanovectors (MSV). Studies in a coculture of breast cancer cells (3D-spheroid) with macrophages and in vivo models were conducted to evaluate the therapeutic efficacy of MSV-nAb-PTX as a function of macrophage phenotype. Association with MSV increased drug accumulation within the macrophages and the tumor spheroids, shifting the inflammation state of the TME toward the pro-inflammatory, anti-tumorigenic milieu. Additionally, the treatment increased macrophage motility toward cancer cells, promoting the active transport of therapeutic nanovectors into the tumor lesion. Consequently, apoptosis of cancer cells was increased and proliferation decreased in the MSV-nAb-PTX-treated group as compared to controls. The results also confirmed that the tested system shifts the macrophage differentiation toward an M1 phenotype, possessing an anti-proliferative effect toward the breast cancer cells. These factors were further incorporated into a mathematical model to help analyze the synergistic effect of the macrophage polarization state on the efficacy of MSV-nAb-PTX in alleviating hypovascularized tumor lesions. In conclusion, the ability of MSV-nAb-PTX to polarize TAM to the M1 phenotype, causing (1) enhanced penetration of the drug-carrying macrophages to the center of the tumor lesion and (2) increased toxicity to tumor cells may explain the increased anti-cancer efficacy of the system in comparison to nAb-PTX and other controls.

Adaptation to Stochastic Temporal Variations in Intratumoral Blood Flow: The Warburg Effect as a Bet Hedging Strategy

While most cancers promote ingrowth of host blood vessels, the resulting vascular network usually fails to develop a mature organization, resulting in abnormal vascular dynamics with stochastic variations that include slowing, cessation, and even reversal of flow. Thus, substantial spatial and temporal variations in oxygen concentration are commonly observed in most cancers. Cancer cells, like all living systems, are subject to Darwinian dynamics such that their survival and proliferation are dependent on developing optimal phenotypic adaptations to local environmental conditions. Here, we consider the environmental stresses placed on tumors subject to profound, frequent, but stochastic variations in oxygen concentration as a result of temporal variations in blood flow. While vascular fluctuations will undoubtedly affect local concentrations of a wide range of molecules including growth factors (e.g., estrogen), substrate (oxygen, glucose, etc.), and metabolites ([Formula: see text], we focus on the selection forces that result solely from stochastic fluctuations in oxygen concentration. The glucose metabolism of cancer cells has been investigated for decades following observations that malignant cells ferment glucose regardless of oxygen concentration, a condition termed the Warburg effect. In contrast, normal cells cease fermentation under aerobic conditions and this physiological response is termed the Pasteur effect. Fermentation is markedly inefficient compared to cellular respiration in terms of adenosine triphosphate (ATP) production, generating just 2 ATP/glucose, whereas respiration generates 38 ATP/glucose. This inefficiency requires cancer cells to increase glycolytic flux, which subsequently increases acid production and can significantly acidify local tissue. Hence, it initially appears that cancer cells adopt a disadvantageous metabolic phenotype. Indeed, this metabolic "hallmark" of cancer is termed "energy dysregulation." However, if cancers arise through an evolutionary optimization process, any common observed property must confer an adaptive advantage. In the present work, we investigate the hypothesis that aerobic glycolysis represents an adaptation to stochastic variations in oxygen concentration stemming from disordered intratumoral blood flow. Using mathematical models, we demonstrate that the Warburg effect evolves as a conservative metabolic bet hedging strategy in response to stochastic fluctuations of oxygen. Specifically, the Warburg effect sacrifices fitness in physoxia by diverting resources from the more efficient process of respiration, but preemptively adapts cells to hypoxia because fermentation produces ATP anaerobically. An environment with sufficiently stochastic fluctuations of oxygen will select for the bet hedging (Warburg) phenotype since it is modestly successful irrespective of oxygen concentration.

Structured models of cell migration incorporating molecular binding processes

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with three examples arising from cancer invasion.

Dynamics of cancerous tissue correlates with invasiveness

Two of the classical hallmarks of cancer are uncontrolled cell division and tissue invasion, which turn the disease into a systemic, life-threatening condition. Although both processes are studied, a clear correlation between cell division and motility of cancer cells has not been described previously. Here, we experimentally characterize the dynamics of invasive and non-invasive breast cancer tissues using human and murine model systems. The intrinsic tissue velocities, as well as the divergence and vorticity around a dividing cell correlate strongly with the invasive potential of the tissue, thus showing a distinct correlation between tissue dynamics and aggressiveness. We formulate a model which treats the tissue as a visco-elastic continuum. This model provides a valid reproduction of the cancerous tissue dynamics, thus, biological signaling is not needed to explain the observed tissue dynamics. The model returns the characteristic force exerted by an invading cell and reveals a strong correlation between force and invasiveness of breast cancer cells, thus pinpointing the importance of mechanics for cancer invasion.

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

A computational model was developed to describe experimentally observed vascular changes induced by the introduction of a tumour on a mouse equipped with a dorsal skinfold chamber. The vascular structure of the host tissue was segmented from in vivo images and transposed into the computational framework. Simulations of tumour-induced vascular changes were performed and include the destabilizing effects of the growth factor VEGF on the integrity of the vessels walls. The integration of those effects, that include alteration of the vessel wall elasticity and wall breaching, were required to realistically reproduce the experimental observations. The model was then used to investigate the importance of the vascular changes for oxygen delivery and tumour development. To that end, we compared simulations obtained with a dynamic vasculature with those obtained with a static one. The results showed that the tumour growth was strongly impeded by the constant vascular changes. More precisely, it is the angiogenic process itself that was affected by vascular changes occurring in bigger upstream vessels and resulting in a less efficient angiogenic network for oxygen delivery. As a consequence, tumour cells are mostly kept in a non-proliferative hypoxic state. Tumour dormancy thus appears as one potential consequence of the intense vascular changes in the host tissue.

A Validated Multiscale In-Silico Model for Mechano-sensitive Tumour Angiogenesis and Growth

Vascularisation is a key feature of cancer growth, invasion and metastasis. To better understand the governing biophysical processes and their relative importance, it is instructive to develop physiologically representative mathematical models with which to compare to experimental data. Previous studies have successfully applied this approach to test the effect of various biochemical factors on tumour growth and angiogenesis. However, these models do not account for the experimentally observed dependency of angiogenic network evolution on growth-induced solid stresses. This work introduces two novel features: the effects of hapto- and mechanotaxis on vessel sprouting, and mechano-sensitive dynamic vascular remodelling. The proposed three-dimensional, multiscale, in-silico model of dynamically coupled angiogenic tumour growth is specified to in-vivo and in-vitro data, chosen, where possible, to provide a physiologically consistent description. The model is then validated against in-vivo data from murine mammary carcinomas, with particular focus placed on identifying the influence of mechanical factors. Crucially, we find that it is necessary to include hapto- and mechanotaxis to recapitulate observed time-varying spatial distributions of angiogenic vasculature.

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.

Stochastic multi-scale models of competition within heterogeneous cellular populations: Simulation methods and mean-field analysis

We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance to therapy since the rescued population is less sensitive to therapy.

The tumor as an organ: comprehensive spatial and temporal modeling of the tumor and its microenvironment

BACKGROUND

Research related to cancer is vast, and continues in earnest in many directions. Due to the complexity of cancer, a better understanding of tumor growth dynamics can be gleaned from a dynamic computational model. We present a comprehensive, fully executable, spatial and temporal 3D computational model of the development of a cancerous tumor together with its environment.

RESULTS

The model was created using Statecharts, which were then connected to an interactive animation front-end that we developed especially for this work, making it possible to visualize on the fly the on-going events of the system's execution, as well as the effect of various input parameters. We were thus able to gain a better understanding of, e.g., how different amounts or thresholds of oxygen and VEGF (vascular endothelial growth factor) affect the progression of the tumor. We found that the tumor has a critical turning point, where it either dies or recovers. If minimum conditions are met at that time, it eventually develops into a full, active, growing tumor, regardless of the actual amount; otherwise it dies.

CONCLUSIONS

This brings us to the conclusion that the tumor is in fact a very robust system: changing initial values of VEGF and oxygen can increase the time it takes to become fully developed, but will not necessarily completely eliminate it.

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.

A Computational/Experimental Assessment of Antitumor Activity of Polymer Nanoassemblies for pH-Controlled Drug Delivery to Primary and Metastatic Tumors

PURPOSE

Polymer nanoassemblies (PNAs) with drug release fine-tuned to occur in acidic tumor regions (pH < 7) while sparing normal tissues (pH = 7.4) were previously shown to hold promise as nanoparticle drug carriers to effectively suppress tumor growth with reduced systemic toxicity. However, therapeutic benefits of pH-controlled drug delivery remain elusive due to complex interactions between the drug carriers, tumor cells with varying drug sensitivity, and the tumor microenvironment.

METHODS

We implement a combined computational and experimental approach to evaluate the in vivo antitumor activity of acid-sensitive PNAs controlling drug release in pH 5 ~ 7.4 at different rates [PNA1 (fastest) > PNA2 > PNA3 (slowest)].

RESULTS

Computational simulations projecting the transport, drug release, and antitumor activity of PNAs in primary and metastatic tumor models of colorectal cancer correspond well with experimental observations in vivo. The simulations also reveal that all PNAs could reach peak drug concentrations in tumors at 11 h post injection, while PNAs with slower drug release (PNA2 and PNA3) reduced tumor size more effectively than fast drug releasing PNA1 (24.5 and 20.3 vs 7.5%, respectively, as fraction of untreated control).

CONCLUSION

A combined computational/experimental approach may help to evaluate pH-controlled drug delivery targeting aggressive tumors that have substantial acidity.

Simulation of tumor induced angiogenesis using an analytical adaptive modeling including dynamic sprouting and blood flow modeling

In this paper, an adaptive model for tumor induced angiogenesis is developed that integrates generation and diffusion of a growth factor originated from hypoxic cells, adaptive sprouting from a parent vessel, blood flow and structural adaptation. The proposed adaptive sprout spacing model (ASS) determines position, time and number of sprouts which are activated from a parent vessel and also the developed vascular network is modified by a novel sprout branching prediction algorithm. This algorithm couples local vascular endothelial growth factor (VEGF) concentrations, stresses due to the blood flow and stochastic branching to the structural reactions of each vessel segment in response to mechanical and biochemical stimuli. The results provide predictions for the time-dependent development of the network structure, including the position and diameters of each segment and the resulting distributions of blood flow and VEGF. Considering time delays between sprout progressions and number of sprouts activated at different time durations provides information about micro-vessel density in the network. Resulting insights could be useful for motivating experimental investigations of vascular pattern in tumor induced angiogenesis and development of therapies targeting angiogenesis.

"Active" drops as phantom models for living cells: a mesoscopic particle-based approach

Drops and biological cells share some morphological features and visco-elastic properties. The modelling of drops by mesoscopic non-atomistic models has been carried out to a high degree of success in recent years. We extend such treatment and discuss a simple, drop-like model to describe the interactions of the outer layer of cells with the surfaces of materials. Cells are treated as active mechanical objects that are able to generate adhesion forces. They appear with their true size and are made of "parcels of fluids" or beads. The beads are described by (very) few quantities/parameters related to fundamental chemical forces such as hydrophilicity and lipophilicity that represent an average of the properties of a patch of material or an area of the cell(s) surface. The investigation of adhesion dynamics, motion of individual cells, and the collective behavior of clusters of cells on materials is possible. In the simulations, the drops become active soft matter objects and different from regular droplets they do not fuse when in contact, their trajectories are not Brownian, and they can be forced "to secrete" molecules, to name some of the properties targeted by the modeling. The behavior that emerges from the simulations allows ascribing some cell properties to their mechanics, which are related to their biological features.

The effect of nanoparticle size on in vivo pharmacokinetics and cellular interaction

Nanoparticle-based technologies offer exciting new approaches to disease diagnostics and therapeutics. To take advantage of unique properties of nanoscale materials and structures, the size, shape and/or surface chemistry of nanoparticles need to be optimized, allowing their functionalities to be tailored for different biomedical applications. Here we review the effects of nanoparticle size on cellular interaction and in vivo pharmacokinetics, including cellular uptake, biodistribution and circulation half-life of nanoparticles. Important features of nanoparticle probes for molecular imaging and modeling of nanoparticle size effects are also discussed.

A Mathematical Model Coupling Tumor Growth and Angiogenesis

We present a mathematical model for vascular tumor growth. We use phase fields to model cellular growth and reaction-diffusion equations for the dynamics of angiogenic factors and nutrients. The model naturally predicts the shift from avascular to vascular growth at realistic scales. Our computations indicate that the negative regulation of the Delta-like ligand 4 signaling pathway slows down tumor growth by producing a larger density of non-functional capillaries. Our results show good quantitative agreement with experiments.