12,442 research outputs found
3D simulations of early blood vessel formation
Blood vessel networks form by spontaneous aggregation of individual cells
migrating toward vascularization sites (vasculogenesis). A successful
theoretical model of two dimensional experimental vasculogenesis has been
recently proposed, showing the relevance of percolation concepts and of cell
cross-talk (chemotactic autocrine loop) to the understanding of this
self-aggregation process. Here we study the natural 3D extension of the
computational model proposed earlier, which is relevant for the investigation
of the genuinely threedimensional process of vasculogenesis in vertebrate
embryos. The computational model is based on a multidimensional Burgers
equation coupled with a reaction diffusion equation for a chemotactic factor
and a mass conservation law. The numerical approximation of the computational
model is obtained by high order relaxed schemes. Space and time discretization
are performed by using TVD schemes and, respectively, IMEX schemes. Due to the
computational costs of realistic simulations, we have implemented the numerical
algorithm on a cluster for parallel computation. Starting from initial
conditions mimicking the experimentally observed ones, numerical simulations
produce network-like structures qualitatively similar to those observed in the
early stages of \emph{in vivo} vasculogenesis. We develop the computation of
critical percolative indices as a robust measure of the network geometry as a
first step towards the comparison of computational and experimental data.Comment: 25 pages, 9 figures Submitted to: JC
Multiscale modelling of vascular tumour growth in 3D: the roles of domain size & boundary condition
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
A Process-Oriented Architecture for Complex System Modelling
A fine-grained massively-parallel process-oriented model of platelets (potentially artificial) within a blood vessel is presented. This is a CSP inspired design, expressed and implemented using the occam-pi language. It is part of the TUNA pilot study on nanite assemblers at the universities of York, Surrey and Kent. The aim for this model is to engineer emergent behaviour from the platelets, such that they respond to a wound in the blood vessel wall in a way similar to that found in the human body -- i.e. the formation of clots to stem blood flow from the wound and facilitate healing. An architecture for a three dimensional model (relying strongly on the dynamic and mobile capabilities of occam-pi) is given, along with mechanisms for visualisation and interaction. The biological accuracy of the current model is very approximate. However, its process-oriented nature enables simple refinement (through the addition of processes modelling different stimulants/inhibitors of the clotting reaction, different platelet types and other participating organelles) to greater and greater realism. Even with the current system, simple experiments are possible and have scientific interest (e.g. the effect of platelet density on the success of the clotting mechanism in stemming blood flow: too high or too low and the process fails). General principles for the design of large and complex system models are drawn. The described case study runs to millions of processes engaged in ever-changing communication topologies. It is free from deadlock, livelock, race hazards and starvation em by design, employing a small set of synchronisation patterns for which we have proven safety theorems
A Review of Mathematical Models for the Formation of\ud Vascular Networks
Mainly two mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former consists of the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter consists of the sprouting of new vessels from an existing capillary or post-capillary venule. Similar phenomena are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis.\ud
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A number of mathematical approaches have analysed these phenomena. This paper reviews the different modelling procedures, with a special emphasis on their ability to reproduce the biological system and to predict measured quantities which describe the overall processes. A comparison between the different methods is also made, highlighting their specific features
The 'Sphere': A Dedicated Bifurcation Aneurysm Flow-Diverter Device.
We present flow-based results from the early stage design cycle, based on computational modeling, of a prototype flow-diverter device, known as the 'Sphere', intended to treat bifurcation aneurysms of the cerebral vasculature. The device is available in a range of diameters and geometries and is constructed from a single loop of NITINOL(®) wire. The 'Sphere' reduces aneurysm inflow by means of a high-density, patterned, elliptical surface that partially occludes the aneurysm neck. The device is secured in the healthy parent vessel by two armatures in the shape of open loops, resulting in negligible disruption of parent or daughter vessel flow. The device is virtually deployed in six anatomically accurate bifurcation aneurysms: three located at the Basilar tip and three located at the terminus bifurcation of the Internal Carotid artery (at the meeting of the middle cerebral and anterior cerebral arteries). Both steady state and transient flow simulations reveal that the device presents with a range of aneurysm inflow reductions, with mean flow reductions falling in the range of 30.6-71.8% across the different geometries. A significant difference is noted between steady state and transient simulations in one geometry, where a zone of flow recirculation is not captured in the steady state simulation. Across all six aneurysms, the device reduces the WSS magnitude within the aneurysm sac, resulting in a hemodynamic environment closer to that of a healthy vessel. We conclude from extensive CFD analysis that the 'Sphere' device offers very significant levels of flow reduction in a number of anatomically accurate aneurysm sizes and locations, with many advantages compared to current clinical cylindrical flow-diverter designs. Analysis of the device's mechanical properties and deployability will follow in future publications
Computational Simulations for Aortic Coarctation: Representative Results From a Sampling of Patients
Treatments for coarctation of the aorta (CoA) can alleviate blood pressure (BP) gradients(D), but long-term morbidity still exists that can be explained by altered indices of hemodynamics and biomechanics. We introduce a technique to increase our understanding of these indices for CoA under resting and nonresting conditions, quantify their contribution to morbidity, and evaluate treatment options. Patient-specific computational fluid dynamics (CFD) models were created from imaging and BP data for one normal and four CoA patients (moderate native CoA: D12 mmHg, severe native CoA: D25 mmHg and postoperative end-to-end and end-to-side patients: D0 mmHg). Simulations incorporated vessel deformation, downstream vascular resistance and compliance. Indices including cyclic strain, time-averaged wall shear stress (TAWSS), and oscillatory shear index (OSI) were quantified. Simulations replicated resting BP and blood flow data. BP during simulated exercise for the normal patient matched reported values. Greatest exercise-induced increases in systolic BP and mean and peak DBP occurred for the moderate native CoA patient (SBP: 115 to 154 mmHg; mean and peak DBP: 31 and 73 mmHg). Cyclic strain was elevated proximal to the coarctation for native CoA patients, but reduced throughout the aorta after treatment. A greater percentage of vessels was exposed to subnormal TAWSS or elevated OSI for CoA patients. Local patterns of these indices reported to correlate with atherosclerosis in normal patients were accentuated by CoA. These results apply CFD to a range of CoA patients for the first time and provide the foundation for future progress in this area
Including Aortic Valve Morphology in Computational Fluid Dynamics Simulations: Initial Findings and Application to Aortic Coarctation
Computational fluid dynamics (CFD) simulations quantifying thoracic aortic flow patterns have not included disturbances from the aortic valve (AoV). 80% of patients with aortic coarctation (CoA) have a bicuspid aortic valve (BAV) which may cause adverse flow patterns contributing to morbidity. Our objectives were to develop a method to account for the AoV in CFD simulations, and quantify its impact on local hemodynamics. The method developed facilitates segmentation of the AoV, spatiotemporal interpolation of segments, and anatomic positioning of segments at the CFD model inlet. The AoV was included in CFD model examples of a normal (tricuspid AoV) and a post-surgical CoA patient (BAV). Velocity, turbulent kinetic energy (TKE), time-averaged wall shear stress (TAWSS), and oscillatory shear index (OSI) results were compared to equivalent simulations using a plug inlet profile. The plug inlet greatly underestimated TKE for both examples. TAWSS differences extended throughout the thoracic aorta for the CoA BAV, but were limited to the arch for the normal example. OSI differences existed mainly in the ascending aorta for both cases. The impact of AoV can now be included with CFD simulations to identify regions of deleterious hemodynamics thereby advancing simulations of the thoracic aorta one step closer to reality
Simulations demonstrate a simple network to be sufficient to control branch point selection, smooth muscle and vasculature formation during lung branching morphogenesis
Proper lung functioning requires not only a correct structure of the
conducting airway tree, but also the simultaneous development of smooth muscles
and vasculature. Lung branching morphogenesis is strongly stereotyped and
involves the recursive use of only three modes of branching. We have previously
shown that the experimentally described interactions between Fibroblast growth
factor (FGF)10, Sonic hedgehog (SHH) and Patched (Ptc) can give rise to a
Turing mechanism that not only reproduces the experimentally observed wildtype
branching pattern but also, in part counterintuitive, patterns in mutant mice.
Here we show that, even though many proteins affect smooth muscle formation and
the expression of Vegfa, an inducer of blood vessel formation, it is sufficient
to add FGF9 to the FGF10/SHH/Ptc module to successfully predict simultaneously
the emergence of smooth muscles in the clefts between growing lung buds, and
Vegfa expression in the distal sub-epithelial mesenchyme. Our model reproduces
the phenotype of both wildtype and relevant mutant mice, as well as the results
of most culture conditions described in the literature.Comment: Initially published at Biology Ope
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