Nigel B. Wood

Progress towards patient-specific computational flow modeling of the left heart via combination of magnetic resonance imaging with computational fluid dynamics.

A combined computational fluid dynamics (CFD) and magnetic resonance imaging (MRI) methodology has been developed to simulate blood flow in a subject-specific left heart. The research continues from earlier experience in modeling the human left ventricle using time-varying anatomical MR scans. Breathing artifacts are reduced by means of a MR navigator echo sequence with feedback to the subject, allowing a near constant breath-hold diaphragm position. An improved interactive segmentation technique for the long- and short-axis anatomical slices is used. The computational domain is extended to include the proximal left atrium and ascending aorta as well as the left ventricle, and the mitral and aortic valve orifices are approximately represented. The CFD results show remarkable correspondence with the MR velocity data acquired for comparison purposes, as well as with previously published in vivo experiments (velocity and pressure). Coherent vortex formation is observed below the mitral valve, with a larger anterior vortex dominating the late-diastolic phases. Some quantitative discrepancies exist between the CFD and MRI flow velocities, owing to the limitations of the MR dataset in the valve region, heart rate differences in the anatomical and velocity acquisitions, and to certain phenomena that were not simulated. The CFD results compare well with measured ranges in literature.© 2003 Biomedical Engineering Society.

Computational flow modeling of the left ventricle based on in vivo MRI data: initial experience.

AbstractA combined computational fluid dynamics (CFD) and magnetic resonance imaging (MRI) methodology has been developed to simulate blood flow in heart chambers, with specific application in the present study to the human left ventricle. The proposed framework employs MRI scans of a human heart to obtain geometric data, which are then used for the CFD simulations. These latter are accomplished by geometrical modeling of the ventricle using time-resolved anatomical slices of the ventricular geometry and imposition of inflow/outflow conditions at orifices notionally representing the mitral and aortic valves. The predicted flow structure evolution and physiologically relevant flow characteristics were examined and compared to existing information. The CFD model convincingly captures the three-dimensional contraction and expansion phases of endocardial motion in the left ventricle, allowing simulation of dominant flow features, such as the vortices and swirling structures. These results were qualitatively consistent with previous physiological and clinical experiments on in vivo ventricular chambers, but the accuracy of the simulated velocities was limited largely by the anatomical shortcomings in the valve region. The study also indicated areas in which the methodology requires improvement and extension.

Fluid-Wall Modelling of Mass Transfer in an Axisymmetric Stenosis: Effects of Shear-Dependent Transport Properties

Mechanical forces, such as low wall shear stress (WSS), are implicated in endothelial dysfunction and atherogenesis. The accumulation of low density lipoprotein (LDL) and hypoxia are also considered as main contributing factors in the development of atherosclerosis. The objective of this study was to investigate the influences of WSS on arterial mass transport by modelling the flow of blood and solute transport in the lumen and arterial wall. The Navier-Stokes equations and Darcy’s Law were used to describe the fluid dynamics of the blood in the lumen and wall respectively. Convection-diffusion-reaction equations were used to model LDL and oxygen transport. The coupling of fluid dynamics and solute dynamics at the endothelium was achieved by the Kedem-Katchalsky equations. A shear-dependent hydraulic conductivity relation extracted from experimental data in the literature was employed for the transport of LDL and a shear-dependent permeability was used for oxygen. The integrated fluid-wall model was implemented in Comsol Multiphysics 3.2 and applied to an axisymmetric stenosis. The results showed elevated LDL concentration and reduced oxygen concentration in the subendothelial layer of the arterial wall in areas where WSS is low, suggesting that low WSS might be responsible for lipid accumulation and hypoxia in the arterial wall.

Combined MR imaging and CFD simulation of flow in the human descending aorta

A combined MR and computational fluid dynamics (CFD) study is made of flow in the upper descending thoracic aorta. The aim was to investigate further the potential of CFD simulations linked to in vivo MRI scans. The three‐dimensional (3D) geometrical images of the aorta and the 3D time‐resolved velocity images at the entry to the domain studied were used as boundary conditions for the CFD simulations of the flow. Despite some measurement uncertainties, comparisons between simulated and measured flow structures at the exit from the domain demonstrated encouraging levels of agreement. Moreover, the CFD simulation allowed the flow structure throughout the domain to be examined in more detail, in particular the flow separation region in the distal aortic arch and its influence on the downstream flow during late systole. Additional information such as relative pressure and wall shear stress, which could not be measured via MRI, were also extracted from the simulation. The results have encouraged further applications of the methods described. J. Magn. Reson. Imaging 2001;13:699–713.

Analysis of Flow Patterns in a Patient-Specific Aortic Dissection Model

Aortic dissection is the most common acute catastrophic event affecting the thoracic aorta. The majority of patients presenting with an uncomplicated type B dissection are treated medically, but 25% of these patients develop subsequent aneurysmal dilatation of the thoracic aorta. This study aimed at gaining more detailed knowledge of the flow phenomena associated with this condition. Morphological features and flow patterns in a dissected aortic segment of a presurgery type B dissection patient were analyzed based on computed tomography images acquired from the patient. Computational simulations of blood flow in the patient-specific model were performed by employing a correlation-based transitional version of Menters hybrid k-epsilon/k-omega shear stress transport turbulence model implemented in ANSYS CFX 11. Our results show that the dissected aorta is dominated by locally highly disturbed, and possibly turbulent, flow with strong recirculation. A significant proportion (about 80%) of the aortic flow enters the false lumen, which may further increase the dilatation of the aorta. High values of wall shear stress have been found around the tear on the true lumen wall, perhaps increasing the likelihood of expanding the tear. Turbulence intensity in the tear region reaches a maximum of 70% at midsystolic deceleration phase. Incorporating the non-Newtonian behavior of blood into the same transitional flow model has yielded a slightly lower peak wall shear stress and higher maximum turbulence intensity without causing discernible changes to the distribution patterns. Comparisons between the laminar and turbulent flow simulations show a qualitatively similar distribution of wall shear stress but a significantly higher magnitude with the transitional turbulence model.

Effects of elastic compression stockings on wall shear stress in deep and superficial veins of the calf.

The purpose of this study was to estimate wall shear stress (WSS) in individual vessels of the venous circulation of the calf and quantify the effects of elastic compression based on change of vessel geometry and velocity waveform. The great saphenous vein and either a peroneal or posterior tibial vein have been imaged in four healthy subjects using magnetic resonance imaging, with and without the presence of a grade 1 medical stocking. Flow through image-based reconstructed geometries was numerically simulated for both a range of steady flow rates and ultrasound-derived transient velocity waveforms, scaled to give a standardized time averaged flow rate. For steady flow, the stocking produced an average percentage increase in mean WSS of approximately 100% in the great saphenous vein across a range of 0.125-1.25 ml/s. The percentage increase in the peroneal/posterior tibial veins varied from 490 to 650% across a range of 0.5-5 ml/s. In addition, application of the stocking eliminated periods of very low or zero flow from the transient waveforms. The average minimum value of WSS in all vessels without the stocking was <0.1 Pa. With the stocking, this was increased to 0.7 Pa in the great saphenous and 0.9 Pa in the peroneal/posterior tibial veins. The pathophysiological effects of these changes are discussed. In conclusion, the flight stocking was effective in raising venous WSS levels in prone subjects, and this effect was much more pronounced in the deep vessels. The stocking also tended to prevent cessation of flow during periods of increased downstream pressure produced by respiration.

Computational Modeling of LDL and Albumin Transport in an In Vivo CT Image-Based Human Right Coronary Artery

Low wall shear stress (WSS) is implicated in endothelial dysfunction and atherogenesis. The accumulation of macromolecules is also considered as an important factor contributing to the development of atherosclerosis. In the present study, a fluid-wall single-layered model incorporated with shear-dependent transport parameters was used to investigate albumin and low-density lipoprotein (LDL) transport in an in vivo computed tomographic image-based human right coronary artery (RCA). In the fluid-wall model, the bulk blood flow was modeled by the Navier-Stokes equations, Darcys law was employed to model the transmural flow in the arterial wall, mass balance of albumin and LDL was governed by the convection-diffusion mechanism with an additional reaction term in the wall, and the Kedem-Katchalsky equations were applied at the endothelium as the interface condition between the lumen and wall. Shear-dependent models for hydraulic conductivity and albumin permeability were derived from experimental data in literature to investigate the influence of WSS on macromolecular accumulation in the arterial wall. A previously developed so-called lumen-free time-averaged scheme was used to approximate macromolecular transport under pulsatile flow conditions. LDL and albumin accumulations in the subendothelial layer were found to be colocalized with low WSS. Two distinct mechanisms responsible for the localized accumulation were identified: one was insufficient efflux from the subendothelial layer to outer wall layers caused by a weaker transmural flow; the other was excessive influx to the subendothelial layer from the lumen caused by a higher permeability of the endothelium. The comparison between steady flow and pulsatile flow results showed that the dynamic behavior of the pulsatile flow could induce a wider and more diffuse macromolecular accumulation pattern through the nonlinear shear-dependent transport properties. Therefore, it is vital to consider blood pulsatility when modeling the shear-dependent macromolecular transport in large arteries. In the present study, LDL and albumin accumulations were observed in the low WSS regions of a human RCA using a fluid-wall mass transport model. It was also found that steady flow simulation could overestimate the magnitude and underestimate the area of accumulations. The association between low WSS and accumulation of macromolecules leading to atherosclerosis may be mediated through effects on transport properties and mass transport and is also influenced by flow pulsatility.

Initial findings and potential applicability of computational simulation of the aorta in acute type B dissection

OBJECTIVE Type B aortic dissection can be acutely complicated by rapid expansion, rupture, and malperfusion syndromes. Short-term adverse outcomes are associated with failure of the false lumen to thrombose. The reasons behind false lumen patency are poorly understood, and the objective of this pilot study was to use computational fluid dynamics reconstructions of aortic dissection cases to analyze the effect of aortic and primary tear morphology on flow characteristics and clinical outcomes in patients with acute type B dissections. METHODS Three-dimensional patient-specific aortic dissection geometry was reconstructed from computed tomography scans of four patients presenting with acute type B aortic dissection and a further patient with sequential follow-up scans. The cases were selected based on their clinical presentation. Two were complicated by acute malperfusion that required emergency intervention. Three patients were uncomplicated and were managed conservatively. The patient-specific aortic models were used in computational simulations to assess the effect of aortic tear morphology on various parameters including flow, velocity, shear stress, and turbulence. RESULTS Pulsatile flow simulation results showed that flow rate into the false lumen was dependent on both the size and position of the primary tear. Linear regression analysis demonstrated a significant relationship between percentage flow entering the false lumen and the size of the primary entry tear and an inverse relationship between false lumen flow and the site of the entry tear. Subjects complicated by malperfusion had larger-dimension entry tears than the uncomplicated cases (93% and 82% compared with 32% and 55%, respectively). Blood flow, wall shear stress, and turbulence levels varied significantly between subjects depending on aortic geometry. Highest wall shear stress (>7 Pa) was located at the tear edge, and progression of false lumen thrombosis was associated with prolonged particle residence times. CONCLUSIONS Results obtained from this preliminary work suggest that aortic morphology and primary entry tear size and position exert significant effects on flow and other hemodynamic parameters in the dissected aorta in this preliminary work. Blood flow into the false lumen increases with increasing tear size and proximal location. Morphologic analysis coupled with computational fluid dynamic modeling may be useful in predicting acute type B dissection behavior allowing for selection of proper treatment modalities, and further confirmatory studies are warranted.

Computational analysis of oxygen transport in the retinal arterial network.

Purpose: The retina has a high oxygen consumption, making it particularly vulnerable to vascular insults, impairing oxygen and nutrient supply. The aim of this study was to develop a detailed computational model for quantitative analysis of blood flow and oxygen transport in physiologically realistic retinal arterial networks. Such a model will allow us to examine the effect of topological changes in retinal vasculature on hemodynamics and oxygen distribution in the retinal circulation. Materials and Methods: The Navier-Stokes equations for blood flow and the convection-diffusion equation for oxygen transfer were solved numerically to obtain detailed blood flow and oxygen distribution patterns in a retinal arterial tree. The geometrical outlines of the central retinal artery and its major branches were extracted from retinal images acquired from a healthy young adult by a Zeiss FF450+ fundus camera. The reconstructed subject-specific retinal arterial network geometry was combined with a structured tree model for the distal peripheral vessels. The non-Newtonian rheological properties of blood were incorporated by using an empirical viscosity model to account for the Fahraeus-Lindqvist effect. Results: The model predicted pressure drops in the range of 11–14.6 mmHg between the inlet and outlets of the reconstructed network and non-uniform oxygen tension, which varied with the vessel diameter and distance from the optic disc. The mean oxygen saturation in retinal arteries was 93.1% for vessels larger than 50 μm in diameter and 82.2% for smaller arterioles. Conclusions: Our numerical results are in good agreement with in vivo measurements reported in the literature, demonstrating the potential of our model for prediction of oxygen distribution and intravascular oxygen tension profiles in the retinal arterial network. This paves the way for investigating the effects of parameter variation, simulating cases not available from experimental studies.

FLUID-STRUCTURE INTERACTION ANALYSIS OF WALL STRESS AND FLOW PATTERNS IN A THORACIC AORTIC ANEURYSM

In this study, fluid-structure interaction (FSI) simulation was carried out to predict wall shear stress (WSS) and blood flow patterns in a thoracic aortic aneurysm (TAA) where haemodynamic stresses on the diseased aortic wall are thought to lead to the growth, progression and rupture of the aneurysm. Based on MR images, a patient-specific TAA model was reconstructed. A newly developed two-equation laminar-turbulent transitional model was employed and realistic velocity and pressure waveforms were used as boundary conditions. Analysis of results include turbulence intensity, wall displacement, WSS, wall tensile stress and comparison of velocity profiles between MRI data, rigid and FSI simulations. Velocity profiles demonstrated that the FSI simulation gave better agreement with the MRI data while results for the time-averaged WSS (TAWSS) and oscillatory shear index (OSI) distributions showed no qualitative differences between the simulations. With the FSI model, the maximum TAWSS value was 13% lower, whereas the turbulence intensity was significantly higher than the rigid model. The FSI simulation also provided results for wall mechanical stress in terms of von Mises stress, allowing regions of high wall stress to be identified.