Maximal wall shear stress in arterial stenoses: application to the internal carotid arteries

Numerical modelling of the interaction between dialysis catheter, vascular vessel and blood considering elastic structural deformation

The dialysis catheter indwelling in human bodies has a high risk of inducing thrombus and stenosis. Biomechanical research showed that such physiological complications are triggered by the wall shear stress of the vascular vessel. This study aimed to assess the impact of CVC implantation on central venous haemodynamics and the potential alterations in the haemodynamic environment related to thrombus development. The SVC structure was built from the images from computed tomography. The blood flow was calculated using the Carreau model, and the fluid domain was determined by CFD. The vascular wall and the CVC were computed using FEA. The elastic interaction between the vessel wall and the flow field was considered using FSI simulation. With consideration of the effect of coupling, it was shown that the catheter vibrated in the vascular systems due to the periodic variation of blood pressure, with an amplitude of up to 10% of the vessel width. Spiral flow was observed along the catheter after CVC indwelling, and recirculation flow appeared near the catheter tip. High OSI and WSS regions occurred at the catheter tip and the vascular junction. The arterial lumen tip had a larger effect on the WSS and OSI values on the vascular wall. Considering FSI simulation, the movement of the catheter inside the blood flow was simulated in the deformable vessel. After CVC indwelling, spiral flow and recirculation flow were observed near the regions with high WSS and OSI values.

Humanized GPIbα-von Willebrand factor interaction in the mouse

The interaction of platelet glycoprotein Ibα (GPIbα) with von Willebrand factor (VWF) initiates hemostasis after vascular injury and also contributes to pathological thrombosis. GPIbα binding to the VWF A1 domain (VWFA1) is a target for antithrombotic intervention, but attempts to develop pharmacologic inhibitors have been hindered by the lack of animal models because of the species specificity of the interaction. To address this problem, we generated a knockin mouse with Vwf exon 28-encoding domains A1 and A2 replaced by the human homolog (VWF^h28). VWF^h28 mice (M1HA) were crossbred with a transgenic mouse strain expressing human GPIbα on platelets (mGPIbα^null;hGPIbα^Tg; H1MA) to generate a new strain (H1HA) with humanized GPIbα-VWFA1 binding. Plasma VWF levels in the latter 3 strains were similar to those of wild-type mice (M1MA). Compared with the strains that had homospecific GPIbα-VWF pairing (M1MA and H1HA), M1HA mice of those with heterospecific pairing had a markedly greater prolongation of tail bleeding time and attenuation of thrombogenesis after injury to the carotid artery than H1MA mice. Measurements of GPIbα-VWFA1 binding affinity by surface plasmon resonance agreed with the extent of observed functional defects. Ristocetin-induced platelet aggregation was similar in H1HA mouse and human platelet-rich plasma, and it was comparably inhibited by monoclonal antibody NMC-4, which is known to block human GPIbα-VWFA1 binding, which also inhibited FeCl₃-induced mouse carotid artery thrombosis. Thus, the H1HA mouse strain is a fully humanized model of platelet GPIbα-VWFA1 binding that provides mechanistic and pharmacologic information relevant to human hemostatic and thrombotic disorders.

Machine Learning Approach for Predicting Wall Shear Distribution for Abdominal Aortic Aneurysm and Carotid Bifurcation Models

Computer simulations based on the finite element method represent powerful tools for modeling blood flow through arteries. However, due to its computational complexity, this approach may be inappropriate when results are needed quickly. In order to reduce computational time, in this paper, we proposed an alternative machine learning based approach for calculation of wall shear stress (WSS) distribution, which may play an important role in mechanisms related to initiation and development of atherosclerosis. In order to capture relationships between geometric parameters, blood density, dynamic viscosity and velocity, and WSS distribution of geometrically parameterized abdominal aortic aneurysm (AAA) and carotid bifurcation models, we proposed multivariate linear regression, multilayer perceptron neural network and Gaussian conditional random fields (GCRF). Results obtained in this paper show that machine learning approaches can successfully predict WSS distribution at different cardiac cycle time points. Even though all proposed methods showed high potential for WSS prediction, GCRF achieved the highest coefficient of determination (0.930-0.948 for AAA model and 0.946-0.954 for carotid bifurcation model) demonstrating benefits of accounting for spatial correlation. The proposed approach can be used as an alternative method for real time calculation of WSS distribution.

Mining data from CFD simulation for aneurysm and carotid bifurcation models

Arterial geometry variability is present both within and across individuals. To analyze the influence of geometric parameters, blood density, dynamic viscosity and blood velocity on wall shear stress (WSS) distribution in the human carotid artery bifurcation and aneurysm, the computer simulations were run to generate the data pertaining to this phenomenon. In our work we evaluate two prediction models for modeling these relationships: neural network model and k-nearest neighbor model. The results revealed that both models have high prediction ability for this prediction task. The achieved results represent progress in assessment of stroke risk for a given patient data in real time.

One-dimensional model for propagation of a pressure wave in a model of the human arterial network: comparison of theoretical and experimental results

Pulse wave evaluation is an effective method for arteriosclerosis screening. In a previous study, we verified that pulse waveforms change markedly due to arterial stiffness. However, a pulse wave consists of two components, the incident wave and multireflected waves. Clarification of the complicated propagation of these waves is necessary to gain an understanding of the nature of pulse waves in vivo. In this study, we built a one-dimensional theoretical model of a pressure wave propagating in a flexible tube. To evaluate the applicability of the model, we compared theoretical estimations with measured data obtained from basic tube models and a simple arterial model. We constructed different viscoelastic tube set-ups: two straight tubes; one tube connected to two tubes of different elasticity; a single bifurcation tube; and a simple arterial network with four bifurcations. Soft polyurethane tubes were used and the configuration was based on a realistic human arterial network. The tensile modulus of the material was similar to the elasticity of arteries. A pulsatile flow with ejection time 0.3 s was applied using a controlled pump. Inner pressure waves and flow velocity were then measured using a pressure sensor and an ultrasonic diagnostic system. We formulated a 1D model derived from the Navier-Stokes equations and a continuity equation to characterize pressure propagation in flexible tubes. The theoretical model includes nonlinearity and attenuation terms due to the tube wall, and flow viscosity derived from a steady Hagen-Poiseuille profile. Under the same configuration as for experiments, the governing equations were computed using the MacCormack scheme. The theoretical pressure waves for each case showed a good fit to the experimental waves. The square sum of residuals (difference between theoretical and experimental wave-forms) for each case was <10.0%. A possible explanation for the increase in the square sum of residuals is the approximation error for flow viscosity. However, the comparatively small values prove the validity of the approach and indicate the usefulness of the model for understanding pressure propagation in the human arterial network.

Mining data from hemodynamic simulations via Bayesian emulation

Background:

Arterial geometry variability is inevitable both within and across individuals. To ensure realistic prediction of cardiovascular flows, there is a need for efficient numerical methods that can systematically account for geometric uncertainty.

Methods and results:

A statistical framework based on Bayesian Gaussian process modeling was proposed for mining data generated from computer simulations. The proposed approach was applied to analyze the influence of geometric parameters on hemodynamics in the human carotid artery bifurcation. A parametric model in conjunction with a design of computer experiments strategy was used for generating a set of observational data that contains the maximum wall shear stress values for a range of probable arterial geometries. The dataset was mined via a Bayesian Gaussian process emulator to estimate: (a) the influence of key parameters on the output via sensitivity analysis, (b) uncertainty in output as a function of uncertainty in input, and (c) which settings of the input parameters result in maximum and minimum values of the output. Finally, potential diagnostic indicators were proposed that can be used to aid the assessment of stroke risk for a given patient's geometry.

Transient integral boundary layer method to calculate the translesional pressure drop and the fractional flow reserve in myocardial bridges

Background

The pressure drop – flow relations in myocardial bridges and the assessment of vascular heart disease via fractional flow reserve (FFR) have motivated many researchers the last decades. The aim of this study is to simulate several clinical conditions present in myocardial bridges to determine the flow reserve and consequently the clinical relevance of the disease. From a fluid mechanical point of view the pathophysiological situation in myocardial bridges involves fluid flow in a time dependent flow geometry, caused by contracting cardiac muscles overlying an intramural segment of the coronary artery. These flows mostly involve flow separation and secondary motions, which are difficult to calculate and analyse.

Methods

Because a three dimensional simulation of the haemodynamic conditions in myocardial bridges in a network of coronary arteries is time-consuming, we present a boundary layer model for the calculation of the pressure drop and flow separation. The approach is based on the assumption that the flow can be sufficiently well described by the interaction of an inviscid core and a viscous boundary layer. Under the assumption that the idealised flow through a constriction is given by near-equilibrium velocity profiles of the Falkner-Skan-Cooke (FSC) family, the evolution of the boundary layer is obtained by the simultaneous solution of the Falkner-Skan equation and the transient von-Kármán integral momentum equation.

Results

The model was used to investigate the relative importance of several physical parameters present in myocardial bridges. Results have been obtained for steady and unsteady flow through vessels with 0 – 85% diameter stenosis. We compare two clinical relevant cases of a myocardial bridge in the middle segment of the left anterior descending coronary artery (LAD). The pressure derived FFR of fixed and dynamic lesions has shown that the flow is less affected in the dynamic case, because the distal pressure partially recovers during re-opening of the vessel in diastole. We have further calculated the wall shear stress (WSS) distributions in addition to the location and length of the flow reversal zones in dependence on the severity of the disease.

Conclusion

The described boundary layer method can be used to simulate frictional forces and wall shear stresses in the entrance region of vessels. Earlier models are supplemented by the viscous effects in a quasi three-dimensional vessel geometry with a prescribed wall motion. The results indicate that the translesional pressure drop and the mean FFR compares favourably to clinical findings in the literature. We have further shown that the mean FFR under the assumption of Hagen-Poiseuille flow is overestimated in developing flow conditions.

Multi-branching flows from one mother tube to many daughters or to a network

Multiply branching fluid flows are modelled in two contexts. The first (type I) is for one-to-many branching. Computations are described for flow through a channel, with fully developed motion upstream, which branches abruptly into a number of subchannels downstream. The differences in pressure between the upstream end of the channel and the downstream ends of the subchannels are substantial. Comparisons with recent analytical predictions show fair agreement for Reynolds numbers in the low tens and above. The second context (type II) has successive generations of bifurcation in a network. Modelling, computations and analysis include the effects of many bifurcations.

A one-dimensional viscous-inviscid strong interaction model for flow in indented channels with separation and reattachment

A new one-dimensional model is presented for the calculation of steady and unsteady flow through an indented two-dimensional channel with separation and reattachment. It is based on an interactive boundary layer approach, where the equations for the boundary layer flow near the channel walls and for an inviscid core flow are solved simultaneously. This approach requires no semi-empirical inputs, such as the location of separation and reattachment, which is an advantage over other existing one-dimensional models. Because of the need of an inviscid core alongside the boundary layers, the type of inflow as well as the length of the channel and the value of the Reynolds number poses some limitations on the use of the new model. Results have been obtained for steady flow through the indented channel of Ikeda and Matsuzaki. In further perspective, it is discussed how the present model, in contrast to other one-dimensional flow models, can be extended to calculate the flow in nonsymmetrical channels, by considering different boundary layers on each of the walls.