Immersed boundary method predictions of shear stresses for different flow topologies occuring in cerebral aneurysms

A volume-penalizing immersed boundary method is presented that facilitates the computation of incompressible fluid flow in complex flow domains. We apply this method to simulate the flow in cerebral aneurysms, and focus on the accuracy with which the flow field and the corresponding shear stress field are computed. The method is applied to laminar, incompressible flow in curved cylindrical vessels and in a model aneurysm. The time-dependent shear stress distributions over the vessel walls are visualized and interpreted in terms of the flow fields that develop. We compute shear stress levels at two different Reynolds numbers, corresponding to a steady and an unsteady flow. In the latter situation strong fluctuations in the shear stress are observed, that may be connected to raised risk-levels of aneurysm rupture

Simulation of Pulsatile Flow in Cerebral Aneurysms: From Medical Images to Flow and Forces

In this chapter we present a numerical model for the simulation of blood flow inside cerebral aneurysms. We illustrate the process of predicting flow and forces that arise in vessels and aneurysms starting from patient-specific data obtained using medical imaging techniques. Once the three-dimensional geometry is reconstructed, we discuss fluid properties of blood which allows to compute the flow. The flow of an incompressible Newtonian fluid in the human brain is simulated by using a volume penalizing immersed boundary method, in which the aneurysm geometries are represented by the so-called masking function. We impose pulsatile flow forcing, based on the direct measurement of the mean flow velocity in a vessel during a cardiac cycle and focus on effects due to changes in the flow regimes. In slow or very viscous flows the pulsatile forcing dominates the fluid dynamical response, while at faster or less viscous flows the intrinsic unsteadiness of natural incompressible flow is dominant over the pulsatile flow forcing effect. We consider a full range of physiologically relevant conditions and show high frequencies to emerge in the pulsatile response. The strong qualitative transitions in flow behavior and shear stress levels inside an aneurysm cavity at increased flow rates may contribute to the long-term risk of aneurysm rupture

Alkali and Alkaline Earth Metal Compounds: Core-Valence Basis Sets and Importance of Subvalence Correlation

Core-valence basis sets for the alkali and alkaline earth metals Li, Be, Na, Mg, K, and Ca are proposed. The basis sets are validated by calculating spectroscopic constants of a variety of diatomic molecules involving these elements. Neglect of $(3s,3p)$ correlation in K and Ca compounds will lead to erratic results at best, and chemically nonsensical ones if chalcogens or halogens are present. The addition of low-exponent $p$ functions to the K and Ca basis sets is essential for smooth convergence of molecular properties. Inclusion of inner-shell correlation is important for accurate spectroscopic constants and binding energies of all the compounds. In basis set extrapolation/convergence calculations, the explicit inclusion of alkali and alkaline earth metal subvalence correlation at all steps is essential for K and Ca, strongly recommended for Na, and optional for Li and Mg, while in Be compounds, an additive treatment in a separate `core correlation' step is probably sufficient. Consideration of $(1s)$ inner-shell correlation energy in first-row elements requires inclusion of $(2s,2p)$ `deep core' correlation energy in K and Ca for consistency. The latter requires special CCV$n$Z `deep core correlation' basis sets. For compounds involving Ca bound to electronegative elements, additional $d$ functions in the basis set are strongly recommended. For optimal basis set convergence in such cases, we suggest the sequence CV(D+3d)Z, CV(T+2d)Z, CV(Q+$d$)Z, and CV5Z on calcium.Comment: Molecular Physics, in press (W. G. Richards issue); supplementary material (basis sets in G98 and MOLPRO formats) available at http://theochem.weizmann.ac.il/web/papers/group12.htm

Unconventional computing using evolution-in-nanomaterio: neural networks meet nanoparticle networks

Recently published experimental work on evolution-in-materio applied to nanoscale materials shows promising results for future reconfigurable devices. These experiments were performed on disordered nano-particle networks that have no predefined design. The material has been treated as a blackbox, and genetic algorithms have been used to find appropriate configuration voltages to enable the target functionality. In order to support future experiments, we developed simulation tools for predicting candidate functionalities. One of these tools is based on a physical model, but the one we introduce in this paper is based on an artificial neural network. The advantage of this newly presented approach is that, after training the neural network to match either the real material or its physical model, it can be configured using gradient descent instead of a black-box optimisation. The experiments we report here demonstrate that the neural network can model the simulated nano-material quite accurately. The differentiable, neural network-based material model is then used to find logic gates, as a proof of principle. This shows that the new approach has great potential for partly replacing costly and time-consuming experiments with the real materials. Therefore, this approach has a high relevance for future computing, either as an alternative to digital computing or as an alternative way of producing multi-functional reconfigurable devices

Pulsatile flow in model cerebral aneurysms

We present an immersed boundary method based on volume penalization, with which pulsatile flow in a model cerebral aneurysm is simulated. The model aneurysm consists of a curved vessel merged with a spherical cavity. The dominant vortical structures arising in the time-dependent flow are discussed and the evolution of the maximal shear stress in the aneurysm is analyzed. We approximate flow properties of blood by those of an incompressible Newtonian fluid. The flow inside the aneurysm is simulated with the use of a skew-symmetric finite-volume discretization and explicit time-stepping. We focus on effects due to variations in the amplitude of the pulsatile flow as well as due to changes in the Reynolds number (Re) by studying flow at Re = 100, 250 and 500. At Re = 500 a complex time dependence in the shear stress levels is observed, reflecting the lively development of the flow in the model aneurysm in which vortices are created continuously inside the curved vessel and in the spherical cavity of the aneurysm. An increase in the amplitude of the pulsatile flow increases the shear stress levels somewhat, but at Re = 500 the flow is mainly dominated by its intrinsic unsteadiness. Reducing the Reynolds number yields a stronger contribution of the periodic pulsatile flow forcing: at Re = 100 we find a strong dominance of shear stress levels due to the forcing, while at Re = 250 the intrinsic and pulsatile unsteadiness are of comparable importance

Immersed boundary method for pulsatile transitional flow in realistic cerebral aneurysms

We adopt a volume penalizing immersed boundary method for the simulation of pulsatile blood flow inside cerebral aneurysms. We show that the flow undergoes a transition from an orderly state at low physiological Reynolds numbers, in which the pulsatile forcing is closely followed in time, to a complex response with strongly increased high-frequency components at higher physiological Reynolds numbers, i.e., at higher flow rates and larger aneurysm sizes. The flow is computed by solving the Navier–Stokes equations for incompressible flow. Geometric complexity of aneurysms in the cerebrovascular system is captured by defining the fluid and solid domains using a so-called binary ‘masking function’, which is a key element in the immersed boundary method. The pulsatile variation of the flow rate is represented in terms of measured cross-sectionally averaged velocities in the vicinity of the aneurysm, obtained by noninvasive Transcranial Doppler sonography. Transition of the flow is found to arise in qualitatively the same way at all locations near the aneurysm bulge, quite independent of the solution component that is monitored. The numerical reliability of the predicted transition is quantified on the basis of practical upper and lower bounding solutions, expressing the sensitivity of the flow to uncertainties in the aneurysm geometry. We compute the spectrum of the response of the flow at various locations and flow conditions and quantify the transition in local pressure and velocity. The significant increase of small-scale, high-frequency structures at higher Reynolds numbers may have potential for clinical screening application in the future

Development and application of a volume penalization immersed boundary method for the computation of blood flow and shear stresses in cerebral vessels and aneurysms

A volume-penalizing immersed boundary method is presented for the simulation of laminar incompressible flow inside geometrically complex blood vessels in the human brain. We concentrate on cerebral aneurysms and compute flow in curved brain vessels with and without spherical aneurysm cavities attached.We approximate blood as an incompressible Newtonian fluid and simulate the flow with the use of a skew-symmetric finite-volume discretization and explicit time-stepping. A key element of the immersed boundary method is the so-called masking function. This is a binary function with which we identify at any location in the domain whether it is ‘solid’ or ‘fluid’, allowing to represent objects immersed in a Cartesian grid. We compare three definitions of the masking function for geometries that are non-aligned with the grid. In each case a ‘staircase’ representation is used in which a grid cell is either ‘solid’ or ‘fluid’. Reliable findings are obtained with our immersed boundary method, even at fairly coarse meshes with about 16 grid cells across a velocity profile. The validation of the immersed boundary method is provided on the basis of classical Poiseuille flow in a cylindrical pipe.We obtain first order convergence for the velocity and the shear stress, reflecting the fact that in our approach the solid-fluid interface is localized with an accuracy on the order of a grid cell. Simulations for curved vessels and aneurysms are done for different flowregimes, characterized by different values of the Reynolds number (Re). The validation is performed for laminar flow at Re = 250, while the flow in more complex geometries is studied at Re = 100 and Re = 250, as suggested by physiological conditions pertaining to flow of blood in the circle of Willis

Application of an immersed boundary method to flow in cerebral aneurysms and porous media

We present the development and application of an immersed boundary (IB) method for the simulation of incompressible flow inside and around complex geometrical shapes and cavities. The IB method is based on a volume-penalization method that is applied throughout the domain, rendering the velocity in stationary solid parts negligibly small, while the flow in the open parts of the domain is governed by the Navier-Stokes equations. The flow solver is based on a skew-symmetric finite-volume discretization in combination with explicit time-stepping for the convective and viscous fluxes, and implicit time-stepping for the IB forcing term. The complex geometry is characterized in terms of a so-called ‘masking function’ which equals unity in the solid parts and zero in the open parts of the domain. The focus is on the accuracy with which gradients of the solution close to solid walls can be approximated using the IB methodology. We investigate this for flow through a model of an aneurysm as may develop in the circle of Willis in a human brain, and to flow in a structured porous medium composed of a regular spatial arrangement of square rods. The shear stress acting on the vessel walls in case of flow through an aneurysm and the permeability of the porous material were analyzed. The computational method converges as a first order method for Poiseuille flow, with a considerable influence derived from the precise definition of the masking function near solid-fluid interfaces. We identify the best masking function strategy and show that for plane Poiseuille flow even second order convergence may be obtained. Qualitatively reliable results are obtained already at modest resolutions of 8-16 grid cells across a characteristic opening in the flow domain, e.g., the vessel diameter or the size of the gap between individual square rods

A Systematic Review for the Design of In Vitro Flow Studies of the Carotid Artery Bifurcation

Purpose: In vitro blood flow studies in carotid artery bifurcation models may contribute to understanding the influence of hemodynamics on carotid artery disease. However, the design of in vitro blood flow studies involves many steps and selection of imaging techniques, model materials, model design, and flow visualization parameters. Therefore, an overview of the possibilities and guidance for the design process is beneficial for researchers with less experience in flow studies. Methods: A systematic search to in vitro flow studies in carotid artery bifurcation models aiming at quantification and detailed flow visualization of blood flow dynamics results in inclusion of 42 articles. Results: Four categories of imaging techniques are distinguished: MRI, optical particle image velocimetry (PIV), ultrasound and miscellaneous techniques. Parameters for flow visualization are categorized into velocity, flow, shear-related, turbulent/disordered flow and other parameters. Model materials and design characteristics vary between study type. Conclusions: A simplified three-step design process is proposed for better fitting and adequate match with the pertinent research question at hand and as guidance for less experienced flow study researchers. The three consecutive selection steps are: flow parameters, image modality, and model materials and designs. Model materials depend on the chosen imaging technique, whereas choice of flow parameters is independent from imaging technique and is therefore only determined by the goal of the study