Flow patterns and wall shear stress distribution in human internal carotid arteries: the geometric effect on the risk for stenoses

It has been widely observed that atherosclerotic stenosis occurs at sites with complex hemodynamics, such as arteries with high curvature or bifurcations. These regions usually have very low or highly oscillatory wall shear stress (WSS). In the present study, 3D sinusoidally pulsatile blood flow through the models of internal carotid artery (ICA) with different geometries was investigated with computational simulation. Three preferred sites of stenoses were found along the carotid siphon with low and highly oscillatory WSS. The risk for stenoses at these sites was scaled with the values of time-averaged WSS and oscillating shear index (OSI). The local risk for stenoses at every preferred site of stenoses was found different between 3 types of ICA, indicating that the geometry of the blood vessel plays significant roles in the atherogenesis. Specifically, the large curvature and planarity of the vessel were found to increase the risk for stenoses, because they tend to lower WSS and elevate OSI. Therefore, the geometric study makes it possible to estimate the stenosis location in the ICA siphon as long as the shape of ICA was measured.     

Computing the ankle-brachial index with parallel computational fluid dynamics

The ankle-brachial index (ABI), a ratio of arterial blood pressure in the ankles and upper arms, is used to diagnose and monitor circulatory conditions such as coarctation of the aorta and peripheral artery disease. Computational simulations of the ABI can potentially determine the parameters that produce an ABI indicative of ischemia or other abnormalities in blood flow. However, 0- and 1-D computational methods are limited in describing a 3-D patient-derived geometry. Thus, we present a massively parallel framework for computational fluid dynamics (CFD) simulations in the full arterial system. Using the lattice Boltzmann method to solve the Navier–Stokes equations, we employ highly parallelized and scalable methods to generate the simulation domain and efficiently distribute the computational load among processors. For the first time, we compute an ABI with 3-D CFD. In this proof-of-concept study, we investigate the dependence of ABI on the presence of stenoses, or narrowed regions of the arteries, by directly modifying the arterial geometry. As a result, our framework enables the computation a hemodynamic factor characterizing flow at the scale of the full arterial system, in a manner that is extensible to patient-specific imaging data and holds potential for treatment planning.     

Merging computational fluid dynamics and 4D Flow MRI using proper orthogonal decomposition and ridge regression

Time resolved phase-contrast magnetic resonance imaging 4D-PCMR (also called 4D Flow MRI) data while capable of non-invasively measuring blood velocities, can be affected by acquisition noise, flow artifacts, and resolution limits. In this paper, we present a novel method for merging 4D Flow MRI with computational fluid dynamics (CFD) to address these limitations and to reconstruct de-noised, divergence-free high-resolution flow-fields. Proper orthogonal decomposition (POD) is used to construct the orthonormal basis of the local sampling of the space of all possible solutions to the flow equations both at the low-resolution level of the 4D Flow MRI grid and the high-level resolution of the CFD mesh. Low-resolution, de-noised flow is obtained by projecting in vivo 4D Flow MRI data onto the low-resolution basis vectors. Ridge regression is then used to reconstruct high-resolution de-noised divergence-free solution. The effects of 4D Flow MRI grid resolution, and noise levels on the resulting velocity fields are further investigated. A numerical phantom of the flow through a cerebral aneurysm was used to compare the results obtained using the POD method with those obtained with the state-of-the-art de-noising methods. At the 4D Flow MRI grid resolution, the POD method was shown to preserve the small flow structures better than the other methods, while eliminating noise. Furthermore, the method was shown to successfully reconstruct details at the CFD mesh resolution not discernible at the 4D Flow MRI grid resolution. This method will improve the accuracy of the clinically relevant flow-derived parameters, such as pressure gradients and wall shear stresses, computed from in vivo 4D Flow MRI data.     

Time-accurate,parallel, multi-zone,multi-block solver to study the human cardio-vascular system

A parallel, time-accurate flow solver is devised to study the human cardio-vascular system. The solver is capable of dealing with moving boundaries and moving grids. It is designed to handle complex, three-dimensional vascular systems. The computational domain is divided into multiple block subdomains. At each cross section the plane is divided into twelve sub-zones to allow flexibility for handling complex geometries and, if needed, appropriate parallel data partitioning. The unsteady, three-dimensional, incompressible Navier-Stokes equations are solved numerically. A second-order in time and third-order upwind finite volume method for solving time-accurate incompressible flows based on pseudo-compressibility and dual time-stepping technique is used. For parallel execution, the flow domain is partitioned. Communication between the subdomains of the flow on Riken's VPP/700E supercomputer is implemented using MPI message-passing library. A series of numerical simulations of biologically relevant flows is used to validate this code.     

Flow rates in perfusion bioreactors to maximise mineralisation in bone tissue engineering in vitro

In bone tissue engineering experiments, fluid-induced shear stress is able to stimulate cells to produce mineralised extracellular matrix (ECM). The application of shear stress on seeded cells can for example be achieved through bioreactors that perfuse medium through porous scaffolds. The generated mechanical environment (i.e. wall shear stress: WSS) within the scaffolds is complex due to the complexity of scaffold geometry. This complexity has so far prevented setting an optimal loading (i.e. flow rate) of the bioreactor to achieve an optimal distribution of WSS for stimulating cells to produce mineralised ECM. In this study, we demonstrate an approach combining computational fluid dynamics (CFD) and mechano-regulation theory to optimise flow rates of a perfusion bioreactor and various scaffold geometries (i.e. pore shape, porosity and pore diameter) in order to maximise shear stress induced mineralisation. The optimal flow rates, under which the highest fraction of scaffold surface area is subjected to a wall shear stress that induces mineralisation, are mainly dependent on the scaffold geometries. Nevertheless, the variation range of such optimal flow rates are within 0.5–5 mL/min (or in terms of fluid velocity: 0.166–1.66 mm/s), among different scaffolds. This approach can facilitate the determination of scaffold-dependent flow rates for bone tissue engineering experiments in vitro, avoiding performing a series of trial and error experiments.     

An approach to improve Wang-Smith chaotic simulated annealing

Previous research shows that Wang-Smith chaotic simulated annealing, which employs a gradually decreasing time-step, has only a scaling effect to computational energy of the Hopfield model without changing its shape. This makes the net has sensitive dependence on the value of damping factor. Considering Chen-Aihara chaotic simulated annealing with decaying self-coupling has a shape effect to computational energy of the Hopfield model, a novel approach to improve Wang-Smith chaotic simulated annealing, which reaps the benefits of Wang-Smith model and Chen-Aihara model, is proposed in this paper. With the aid of this method the improved model can affect on computational energy of the Hopfield model from scaling and shape. By adjusting the time-step, the improved neural network can also pass from a chaotic to a non-chaotic state. From numerical simulation experiments, we know that the improved model can escape from local minima more efficiently than original Wang-Smith model.     

Analysis of thoracic aorta hemodynamics using 3D particle tracking velocimetry and computational fluid dynamics

Parallel to the massive use of image-based computational hemodynamics to study the complex flow establishing in the human aorta, the need for suitable experimental techniques and ad hoc cases for the validation and benchmarking of numerical codes has grown more and more.     

A grid layout algorithm for automatic drawing of biochemical networks

MOTIVATION: Visualization is indispensable in the research of complex biochemical networks. Available graph layout algorithms are not adequate for satisfactorily drawing such networks. New methods are required to visualize automatically the topological architectures and facilitate the understanding of the functions of the networks. RESULTS: We propose a novel layout algorithm to draw complex biochemical networks. A network is modeled as a system of interacting nodes on squared grids. A discrete cost function between each node pair is designed based on the topological relation and the geometric positions of the two nodes. The layouts are produced by minimizing the total cost. We design a fast algorithm to minimize the discrete cost function, by which candidate layouts can be produced efficiently. A simulated annealing procedure is used to choose better candidates. Our algorithm demonstrates its ability to exhibit cluster structures clearly in relatively compact layout areas without any prior knowledge. We developed Windows software to implement the algorithm for CADLIVE. AVAILABILITY: All materials can be freely downloaded from http://kurata21.bio.kyutech.ac.jp/grid/grid_layout.htm; http://www.cadlive.jp/ SUPPLEMENTARY INFORMATION: http://kurata21.bio.kyutech.ac.jp/grid/grid_layout.htm; http://www.cadlive.jp/     

A software tool for modeling and simulation of numerical P systems

A P system represents a distributed and parallel bio-inspired computing model in which basic data structures are multi-sets or strings. Numerical P systems have been recently introduced and they use numerical variables and local programs (or evolution rules), usually in a deterministic way. They may find interesting applications in areas such as computational biology, process control or robotics. The first simulator of numerical P systems (SNUPS) has been designed, implemented and made available to the scientific community by the authors of this paper. SNUPS allows a wide range of applications, from modeling and simulation of ordinary differential equations, to the use of membrane systems as computational blocks of cognitive architectures, and as controllers for autonomous mobile robots. This paper describes the functioning of a numerical P system and presents an overview of SNUPS capabilities together with an illustrative example. Availability: SNUPS is freely available to researchers as a standalone application and may be downloaded from a dedicated website, http://snups.ics.pub.ro/, which includes an user manual and sample membrane structures.     

Solving the three dimensional quadratic assignment problem on a computational grid

The exact resolution of large instances of combinatorial optimization problems, such as three dimensional quadratic assignment problem (Q3AP), is a real challenge for grid computing. Indeed, it is necessary to reconsider the resolution algorithms and take into account the characteristics of such environments, especially large scale and dynamic availability of resources, and their multi-domain administration. In this paper, we revisit the design and implementation of the branch and bound algorithm for solving large combinatorial optimization problems such as Q3AP on the computational grids. Such gridification is based on new ways to efficiently deal with some crucial issues, mainly dynamic adaptive load balancing and fault tolerance. Our new approach allowed the exact resolution on a nation-wide grid of a difficult Q3AP instance. To solve this instance, an average of 1,123 computing cores were used for less than 12 days with a peak of around 3,427 computing cores.     

Numerical simulation of steady turbulent flow through trileaflet aortic heart valves—I. Computational scheme and methodology

A numerical simulation model and technique are described to simulate steady turbulent blood flow through trileaflet tissue valves of varying degrees of stenosis. The aortic trileaflet tissue valve design was chosen as the subject of this study, since it is the only popular valve in current clinical use which is approximately axisymmetric. An axisymmetric geometry is computationally more convenient since it involves only two dimensional equations. The geometry and dimensions of the aorta were designed from angiographic studies and measurements made from cadavers. The valve dimensions were obtained from tissue leaflet photography studies conducted on tissue bioprostheses of varying degrees of stenosis. The nonrectangular nature of this valve necessitated the use of a body conforming grid. Thompson's method coupled with a Chimera grid system was chosen for this purpose. The Chimera grid was used to avoid a grid with highly skewed cells. Turbulence was simulated by using the k- model with the wall function method. This decision was made after comparing the k- model's performance with that of lower order models, and after considering the increased computer time requirements and decreased stability of more complex models, such as the Reynolds stress model. The results of the study which are very encouraging and compare favorably with in vitro experimental data, are described in Part II of the paper.     

An Evaluation of Alternative Designs for a Grid Information Service

Computational grids consisting of large and diverse sets of distributed resources have recently been adopted by organizations such as NASA and the NSF. One key component of a computational grid is an information services that provides information about resources, services, and applications to users and their tools. This information is required to use a computational grid and therefore should be available in a timely and reliable manner. In this work, we describe the Globus information service, describe how this service is used, analyze its current performance, and perform trace-driven simulations to evaluate alternative implementations of this grid information service. We find that the majority of the transactions with the information service are changes to the data maintained by the service. We also find that of the three servers we evaluate, one of the commercial products provides the best performance for our workload and that the response time of the information service was not improved during the single experiment we performed with data distributed across two servers.     

Drug release from coronary eluting stents: A multidomain approach

In this paper, starting from a consistent mathematical model, a novel computational approach is proposed for assessing some biomechanical effects on drug release from coronary drug-eluting stents (DESs), related to tissue properties, local hemodynamics and stent design. A multiscale and multidomain advection–diffusion model is formulated for describing drug dynamics in the polymeric substrate covering the stent, into the arterial wall, and in the vessel lumen. The model accounts for tissue microstructure (anisotropic drug diffusion, porosity, drug retention induced by resident proteins), macrostructure (plaque between stent and tissue), and local hemodynamics. In the case of hydrophobic taxus-based compounds, several numerical analyses have been carried out on simplified geometries by using finite element simulations, performing significant comparisons with other recent studies and highlighting general conclusions for assessing effectiveness of some modelling features as well as useful hints for optimizing drug delivery design and technology.     

A general purpose parallel block structured open source incompressible flow solver

A general purpose incompressible flow solver, called caffa3d.MBRi, is presented which features a block structured framework to accommodate both a flexible approach to geometry representation and a straightforward implementation of parallel capabilities through the MPI library. Representation of complex geometries can be handled semi automatically through a combination of body fitted blocks of grids and the immersed boundary condition strategy over both Cartesian and body fitted grid blocks. The parallelization strategy is based on the same block structured framework, by means of encapsulated MPI calls performing a set of conceptually defined high level communication tasks. A set of real world applications ranging from bioengineering to microclimate scenarios is presented to demonstrate the capabilities of the solver, which is open source and freely available through the web page.     

An Agent-Based Model of the Response to Angioplasty and Bare-Metal Stent Deployment in an Atherosclerotic Blood Vessel

Purpose

While animal models are widely used to investigate the development of restenosis in blood vessels following an intervention, computational models offer another means for investigating this phenomenon. A computational model of the response of a treated vessel would allow investigators to assess the effects of altering certain vessel- and stent-related variables. The authors aimed to develop a novel computational model of restenosis development following an angioplasty and bare-metal stent implantation in an atherosclerotic vessel using agent-based modeling techniques. The presented model is intended to demonstrate the body’s response to the intervention and to explore how different vessel geometries or stent arrangements may affect restenosis development.

Methods

The model was created on a two-dimensional grid space. It utilizes the post-procedural vessel lumen diameter and stent information as its input parameters. The simulation starting point of the model is an atherosclerotic vessel after an angioplasty and stent implantation procedure. The model subsequently generates the final lumen diameter, percent change in lumen cross-sectional area, time to lumen diameter stabilization, and local concentrations of inflammatory cytokines upon simulation completion. Simulation results were directly compared with the results from serial imaging studies and cytokine levels studies in atherosclerotic patients from the relevant literature.

Results

The final lumen diameter results were all within one standard deviation of the mean lumen diameters reported in the comparison studies. The overlapping-stent simulations yielded results that matched published trends. The cytokine levels remained within the range of physiological levels throughout the simulations.

Conclusion

We developed a novel computational model that successfully simulated the development of restenosis in a blood vessel following an angioplasty and bare-metal stent deployment based on the characteristics of the vessel cross-section and stent. A further development of this model could ultimately be used as a predictive tool to depict patient outcomes and inform treatment options.     

FitEM2EM--tools for low resolution study of macromolecular assembly and dynamics

Studies of the structure and dynamics of macromolecular assemblies often involve comparison of low resolution models obtained using different techniques such as electron microscopy or atomic force microscopy. We present new computational tools for comparing (matching) and docking of low resolution structures, based on shape complementarity. The matched or docked objects are represented by three dimensional grids where the value of each grid point depends on its position with regard to the interior, surface or exterior of the object. The grids are correlated using fast Fourier transformations producing either matches of related objects or docking models depending on the details of the grid representations. The procedures incorporate thickening and smoothing of the surfaces of the objects which effectively compensates for differences in the resolution of the matched/docked objects, circumventing the need for resolution modification. The presented matching tool FitEM2EMin successfully fitted electron microscopy structures obtained at different resolutions, different conformers of the same structure and partial structures, ranking correct matches at the top in every case. The differences between the grid representations of the matched objects can be used to study conformation differences or to characterize the size and shape of substructures. The presented low-to-low docking tool FitEM2EMout ranked the expected models at the top.     

GENOCOP algorithm and hierarchical grid transformation for image warping of two dimensional gel eletrophoretic maps

Hierarchical grid transformation is a powerful approach to SDS 2DPAGE maps warping. The hierarchy of the warping transformation is able to model both global and local deformations of the gels and the algorithm can be stopped when a certain degree of accuracy in the image alignment is obtained. The numerical optimization of the position of the nodes of the grid that are responsible for the image warping is a multivariate task that can be solved efficiently using Genetic Algorithms. The use of Genetic Algorithms ensures that an optimal position of the nodes can be defined with a low computational cost with respect to other methods. The optimal positions of the nodes of the grid can be successfully used for defining a good warping of the gels.     

Investigation of left heart flow using a numerical correlation to model heart wall motion

A three-dimensional computational fluid dynamics (CFD) method has been developed to model the flow in the left heart including atrium and ventricle. Since time resolution of the medical scans does not fit the requirements of the CFD calculations, the main challenge in a numerical simulation of heart chambers is wall motion modeling. This study employs a novel three-dimensional approximation scheme to correlate the wall boundary and grid movement in systole and diastole. It uses a geometry extracted from medical images in the literature and deformed based on the reported flow rates. The opening and closing of the mitral (MV) and the aortic valve (AV) considered as simultaneous events. Unstructured tetragonal grids were used for the meshing of the domain. The calculation was performed by a Navier–Stokes solver using the arbitrary Lagrange–Euler (ALE) formulation. Results show that the proposed correlation for the wall motion could predict the main features of heart flows.     

Viscous flow simulation in a stenosis model using discrete particle dynamics: a comparison between DPD and CFD

Flow and stresses induced by blood flow acting on the blood cellular constituents can be represented to a certain extent by a continuum mechanics approach down to the order of the?μm level. However, the molecular effects of, e.g., adhesion/aggregation bonds of blood clotting can be on the order of nm. The coupling of the disparate length and timescales between such molecular levels and macroscopic transport represents a major computational challenge. To address this challenge, a multiscale numerical approach based on discrete particle dynamics (DPD) methodology derived from molecular dynamics (MD) principles is proposed. The feasibility of the approach was firstly tested for its ability to simulate viscous flow conditions. Simulations were conducted in low Reynolds numbers flows (Re = 25–33) through constricted tubes representing blood vessels with various degrees of stenosis. Multiple discrete particles interacting with each other were simulated, with 1.24–1.36 million particles representing the flow domain and 0.4 million particles representing the vessel wall. The computation was carried out on the massive parallel supercomputer NY BlueGene/L employing NAMD-a parallel MD package for high performance computing (HPC). Typical recirculation zones were formed distal to the stenoses. The velocity profiles and recirculation zones were in excellent agreement with computational fluid dynamics (CFD) 3D Navier–Stokes viscous fluid flow simulations and with classic numerical and experimental results by YC Fung in constricted tubes. This feasibility analysis demonstrates the potential of a methodology that widely departs from a continuum approach to simulate multiscale phenomena such as flow induced blood clotting.     

Computational study of the effect of geometric and flow parameters on the steady flow field at the rabbit aorto-celiac bifurcation

Arterial hemodynamic forces may play a role in the localization of early atherosclerotic lesions. We have been developing numerical techniques based on overset or "Chimera" type formulations to solve the Navier-Stokes equations in complex geometries simulating arterial bifurcations. This paper presents three-dimensional steady flow computations in a model of the rabbit aorto-celiac bifurcation. The computational methods were validated by comparing the numerical results to previously-obtained flow visualization data. Once validated, the numerical algorithms were used to investigate the sensitivity of the computed flow field and resulting wall shear stress distribution to various geometric and hemodynamic parameters. The results demonstrated that a decrease in the extent of aortic taper downstream of the celiac artery induced looping fluid motion along the lateral walls of the aorta and shifted the peak wall shear stress from downstream of the celiac artery to upstream. Increasing the flow Reynolds number led to a sharp increase in spatial gradients of wall shear stress. The flow field was highly sensitive to the flow division ratio, i.e., the fraction of total flow rate that enters the celiac artery, with larger values of this ratio leading to the occurrence of flow separation along the dorsal wall of the aorta. Finally, skewness of the inlet velocity profile had a profound impact on the wall shear stress distribution near the celiac artery. While not physiological due to the assumption of steady flow, these results provide valuable insight into the fluid physics at geometries simulating arterial bifurcations.