We investigate a three-dimensional multiscale model of vascular tumour growth, which couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport, movement of, and interactions between, normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. In particular, we determine how the domain size, aspect ratio and initial vascular network influence the tumour's growth dynamics and its long-time composition. We establish whether it is possible to extrapolate simulation results obtained for small domains to larger ones, by constructing a large simulation domain from a number of identical subdomains, each subsystem initially comprising two parallel parent vessels, with associated cells and diffusible substances. We find that the subsystem is not representative of the full domain and conclude that, for this initial vessel geometry, interactions between adjacent subsystems contribute to the overall growth dynamics. We then show that extrapolation of results from a small subdomain to a larger domain can only be made if the subdomain is sufficiently large and is initialised with a sufficiently complex vascular network. Motivated by these results, we perform simulations to investigate the tumour's response to therapy and show that the probability of tumour elimination in a larger domain can be extrapolated from simulation results on a smaller domain. Finally, we demonstrate how our model may be combined with experimental data, to predict the spatio-temporal evolution of a vascular tumour.

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.

The growing number of commercially available machines for laser deposition welding show the growing acceptance and importance of this technology for industrial applications. Their increasing usage in research and production requires process stability and user-friendly handling. A commercially available DMG MORI LT 65 3D hybrid machine used in combination with a CCD-based coaxial temperature measurement system was utilized in this work to investigate what information relating to the intensity distribution of melt pool surfaces could be appropriate to draw conclusions about process conditions. In this study it is shown how the minimal required specific energy for a stable process can be determined, and it is indicated that the evolution of a plasma plume depends on thermal energy within the base material. An estimated melt pool area—calculated by the number of pixels (NOP) with intensities larger than a fixed, predefined threshold—builds the main measure in analysing images from the process camera. The melt pool area and its temporal variance can also serve as an indicator for an increased working distance.

We present a three-dimensional, multiscale model of vascular tumour growth, which couples nutrient/growth factor transport, blood flow, angiogenesis, vascular remodelling, movement of and interactions between normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. We present computational simulations which show how a vascular network may evolve and

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

We develop here a novel modelling approach with the aim of closing the conceptual gap between tumour-level metabolic processes and the metabolic processes occurring in individual cancer cells. In particular, the metabolism in hepatocellular carcinoma derived cell lines (HEPG2 cells) has been well characterized but implementations of multiscale models integrating this known metabolism have not been previously reported. We therefore extend a previously published multiscale model of vascular tumour growth, and integrate it with an experimentally verified network of central metabolism in HEPG2 cells. This resultant combined model links spatially heterogeneous vascular tumour growth with known metabolic networks within tumour cells and accounts for blood flow, angiogenesis, vascular remodelling and nutrient/growth factor transport within a growing tumour, as well as the movement of, and interactions between normal and cancer cells. Model simulations report for the first time, predictions of spatially resolved time courses of core metabolites in HEPG2 cells. These simulations can be performed at a sufficient scale to incorporate clinically relevant features of different tumour systems using reasonable computational resources. Our results predict larger than expected temporal and spatial heterogeneity in the intracellular concentrations of glucose, oxygen, lactate pyruvate, f16bp and Acetyl-CoA. The integrated multiscale model developed here provides an ideal quantitative framework in which to study the relationship between dosage, timing, and scheduling of anti-neoplastic agents and the physiological effects of tumour metabolism at the cellular level. Such models, therefore, have the potential to inform treatment decisions when drug response is dependent on the metabolic state of individual cancer cells.

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