Computer Simulations of the Tumor Vasculature: Applications to Interstitial Fluid Flow, Drug Delivery, and Oxygen Supply

Development of a coupled modeling for tumor growth, angiogenesis, oxygen delivery, and phenotypic heterogeneity

Analysis of the evolution and growth dynamics of tumors is crucial for understanding cancer and the development of individually optimized therapies. During tumor growth, a hypoxic microenvironment around cancer cells caused by excessive non-vascular tumor growth induces tumor angiogenesis that plays a key role in the ensuing tumor growth and its progression into higher stages. Various mathematical simulation models have been introduced to simulate these biologically and physically complex hallmarks of cancer. Here, we developed a hybrid two-dimensional computational model that integrates spatiotemporally different components of the tumor system to investigate both angiogenesis and tumor growth/proliferation. This spatiotemporal evolution is based on partial diffusion equations, the cellular automation method, transition and probabilistic rules, and biological assumptions. The new vascular network provided by angiogenesis affects tumor microenvironmental conditions and drives individual cells to adapt themselves to spatiotemporal conditions. Furthermore, some stochastic rules are involved besides microenvironmental conditions. Overall, the conditions promote some commonly observed cellular states, i.e., proliferative, migrative, quiescent, and cell death, depending on the condition of each cell. Altogether, our results offer a theoretical basis for the biological evidence that regions of the tumor tissue near blood vessels are densely populated by proliferative phenotypic variants, while poorly oxygenated regions are sparsely populated by hypoxic phenotypic variants.

Replacement in angiogenesis research: Studying mechanisms of blood vessel development by animal-free in vitro, in vivo and in silico approaches

Angiogenesis, the development of new blood vessels from pre-existing ones, is an essential process determining numerous physiological and pathological conditions. Accordingly, there is a high demand for research approaches allowing the investigation of angiogenic mechanisms and the assessment of pro- and anti-angiogenic therapeutics. The present review provides a selective overview and critical discussion of such approaches, which, in line with the 3R principle, all share the common feature that they are not based on animal experiments. They include in vitro assays to study the viability, proliferation, migration, tube formation and sprouting activity of endothelial cells in two- and three-dimensional environments, the degradation of extracellular matrix compounds as well as the impact of hemodynamic forces on blood vessel formation. These assays can be complemented by in vivo analyses of microvascular network formation in the chorioallantoic membrane assay and early stages of zebrafish larvae. In addition, the combination of experimental data and physical laws enables the mathematical modeling of tissue-specific vascularization, blood flow patterns, interstitial fluid flow as well as oxygen, nutrient and drug distribution. All these animal-free approaches markedly contribute to an improved understanding of fundamental biological mechanisms underlying angiogenesis. Hence, they do not only represent essential tools in basic science but also in early stages of drug development. Moreover, their advancement bears the great potential to analyze angiogenesis in all its complexity and, thus, to make animal experiments superfluous in the future.

Breast cancer models: Engineering the tumor microenvironment

The mechanisms behind cancer initiation and progression are not clear. Therefore, development of clinically relevant models to study cancer biology and drug response in tumors is essential. In vivo models are very valuable tools for studying cancer biology and for testing drugs; however, they often suffer from not accurately representing the clinical scenario because they lack either human cells or a functional immune system. On the other hand, two-dimensional (2D) in vitro models lack the three-dimensional (3D) network of cells and extracellular matrix (ECM) and thus do not represent the tumor microenvironment (TME). As an alternative approach, 3D models have started to gain more attention, as such models offer a platform with the ability to study cell-cell and cell-material interactions parametrically, and possibly include all the components present in the TME. Here, we first give an overview of the breast cancer TME, and then discuss the current state of the pre-clinical breast cancer models, with a focus on the engineered 3D tissue models. We also highlight two engineering approaches that we think are promising in constructing models representative of human tumors: 3D printing and microfluidics. In addition to giving basic information about the TME in the breast tissue, this review article presents the state-of-the-art tissue engineered breast cancer models. STATEMENT OF SIGNIFICANCE: Involvement of biomaterials and tissue engineering fields in cancer research enables realistic mimicry of the cell-cell and cell-extracellular matrix (ECM) interactions in the tumor microenvironment (TME), and thus creation of better models that reflect the tumor response against drugs. Engineering the 3D in vitro models also requires a good understanding of the TME. Here, an overview of the breast cancer TME is given, and the current state of the pre-clinical breast cancer models, with a focus on the engineered 3D tissue models is discussed. This review article is useful not only for biomaterials scientists aiming to engineer 3D in vitro TME models, but also for cancer researchers willing to use these models for studying cancer biology and drug testing.

An approach for vascular tumor growth based on a hybrid embedded/homogenized treatment of the vasculature within a multiphase porous medium model

The aim of this work is to develop a novel computational approach to facilitate the modeling of angiogenesis during tumor growth. The preexisting vasculature is modeled as a 1D inclusion and embedded into the 3D tissue through a suitable coupling method, which allows for nonmatching meshes in 1D and 3D domain. The neovasculature, which is formed during angiogenesis, is represented in a homogenized way as a phase in our multiphase porous medium system. This splitting of models is motivated by the highly complex morphology, physiology, and flow patterns in the neovasculature, which are challenging and computationally expensive to resolve with a discrete, 1D angiogenesis and blood flow model. Moreover, it is questionable if a discrete representation generates any useful additional insight. By contrast, our model may be classified as a hybrid vascular multiphase tumor growth model in the sense that a discrete, 1D representation of the preexisting vasculature is coupled with a continuum model describing angiogenesis. It is based on an originally avascular model which has been derived via the thermodynamically constrained averaging theory. The new model enables us to study mass transport from the preexisting vasculature into the neovasculature and tumor tissue. We show by means of several illustrative examples that it is indeed capable of reproducing important aspects of vascular tumor growth phenomenologically.

Lattice and continuum modelling of a bioactive porous tissue scaffold

A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. We derive a model on a square grid lattice to demonstrate the importance of explicitly modelling the network structure of the porous scaffold and compare results from this model with those from a modified continuum model from the literature. We capture two-way coupling between cell growth and fluid flow by allowing cells to block pores, and by allowing the shear stress of the fluid to affect cell growth and death. We explore a range of parameters for both models and demonstrate quantitative and qualitative differences between predictions from each of these approaches, including spatial pattern formation and local oscillations in cell density present only in the lattice model. These differences suggest that for some parameter regimes, corresponding to specific cell types and scaffold geometries, the lattice model gives qualitatively different model predictions than typical continuum models. Our results inform model selection for bioactive porous tissue scaffolds, aiding in the development of successful tissue engineering experiments and eventually clinically successful technologies.

Fine-grained simulations of the microenvironment of vascularized tumours

One of many important features of the tumour microenvironment is that it is a place of active Darwinian selection where different tumour clones become adapted to the variety of ecological niches that make up the microenvironment. These evolutionary processes turn the microenvironment into a powerful source of tumour heterogeneity and contribute to the development of drug resistance in cancer. Here, we describe a computational tool to study the ecology of the microenvironment and report results about the ecology of the tumour microenvironment and its evolutionary dynamics.

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.

Study of an Oxygen Supply and Oxygen Saturation Monitoring System for Radiation Therapy Associated with the Active Breathing Coordinator

In this study, we designed an oxygen supply and oxygen saturation monitoring (OSOSM) system. This OSOSM system can provide a continuous supply of oxygen and monitor the peripheral capillary oxygen saturation (SpO2) of patients who accept radiotherapy and use an active breathing coordinator (ABC). A clinical test with 27 volunteers was conducted. The volunteers were divided into two groups based on the tendency of SpO2 decline in breath-holding without the OSOSM system: group A (12 cases) showed a decline in SpO2 of less than 2%, whereas the decline in SpO2 in group B (15 cases) was greater than 2% and reached up to 6% in some cases. The SpO2 of most volunteers declined during rest. The breath-holding time of group A without the OSOSM system was significantly longer than that of group B (p < 0.05) and was extended with the OSOSM system by 26.6% and 27.85% in groups A and B, respectively. The SpO2 recovery time was reduced by 36.1%, and the total rest time was reduced by 27.6% for all volunteers using the OSOSM system. In summary, SpO2 declines during breath-holding and rest time cannot be ignored while applying an ABC. This OSOSM system offers a simple and effective way to monitor SpO2 variation and overcome SpO2 decline, thereby lengthening breath-holding time and shortening rest time.