Non-Newtonian effects of blood flow on hemodynamics in distal vascular graft anastomoses

Non-Newtonian fluid flow in a stenosed coronary bypass is investigated numerically using the Carreau-Yasuda model for the shear thinning behavior of the blood. End-to-side coronary bypass anastomosis is considered in a simplified model geometry where the host coronary artery has a 75% severity stenosis. Different locations of the bypass graft to the stenosis and different flow rates in the graft and in the host artery are studied. Particular attention is given to the non-Newtonian effect of the blood on the primary and secondary flow patterns in the host coronary artery and the wall shear stress (WSS) distribution there. Interaction between the jet flow from the stenosed artery and the flow from the graft is simulated by solving the three-dimensional Navier-Stokes equation coupled with the non-Newtonian constitutive model. Results for the non-Newtonian flow, the Newtonian flow and the rescaled Newtonian flow are presented. Significant differences in axial velocity profiles, secondary flow streamlines and WSS between the non-Newtonian and Newtonian fluid flows are revealed. However, reasonable agreement between the non-Newtonian and the rescaled Newtonian flows is found. Results from this study support the view that the residual flow in a partially occluded coronary artery interacts with flow in the bypass graft and may have significant hemodynamic effects in the host vessel downstream of the graft. Non-Newtonian property of the blood alters the flow pattern and WSS distribution and is an important factor to be considered in simulating hemodynamic effects of blood flow in arterial bypass grafts.     

Uncertainty quantification in cerebral circulation simulations focusing on the collateral flow: Surrogate model approach with machine learning

Collateral circulation in the circle of Willis (CoW), closely associated with disease mechanisms and treatment outcomes, can be effectively investigated using one-dimensional–zero-dimensional hemodynamic simulations. As the entire cardiovascular system is considered in the simulation, it captures the systemic effects of local arterial changes, thus reproducing collateral circulation that reflects biological phenomena. The simulation facilitates rapid assessment of clinically relevant hemodynamic quantities under patient-specific conditions by incorporating clinical data. During patient-specific simulations, the impact of clinical data uncertainty on the simulated quantities should be quantified to obtain reliable results. However, as uncertainty quantification (UQ) is time-consuming and computationally expensive, its implementation in time-sensitive clinical applications is considered impractical. Therefore, we constructed a surrogate model based on machine learning using simulation data. The model accurately predicts the flow rate and pressure in the CoW in a few milliseconds. This reduced computation time enables the UQ execution with 100 000 predictions in a few minutes on a single CPU core and in less than a minute on a GPU. We performed UQ to predict the risk of cerebral hyperperfusion (CH), a life-threatening condition that can occur after carotid artery stenosis surgery if collateral circulation fails to function appropriately. We predicted the statistics of the postoperative flow rate increase in the CoW, which is a measure of CH, considering the uncertainties of arterial diameters, stenosis parameters, and flow rates measured using the patients’ clinical data. A sensitivity analysis was performed to clarify the impact of each uncertain parameter on the flow rate increase. Results indicated that CH occurred when two conditions were satisfied simultaneously: severe stenosis and when arteries of small diameter serve as the collateral pathway to the cerebral artery on the stenosis side. These findings elucidate the biological aspects of cerebral circulation in terms of the relationship between collateral flow and CH.     

Fluid–structure interaction (FSI) simulation for studying the impact of atherosclerosis on hemodynamics,arterial tissue remodeling,and initiation risk of intracranial aneurysms

The biomechanical and hemodynamic effects of atherosclerosis on the initiation of intracranial aneurysms (IA) are not yet clearly discovered. Also, studies for the observation of hemodynamic variation due to atherosclerotic stenosis and its impact on arterial remodeling and aneurysm genesis remain a controversial field of vascular engineering. The majority of studies performed are relevant to computational fluid dynamic (CFD) simulations. CFD studies are limited in consideration of blood and arterial tissue interactions. In this work, the interaction of the blood and vessel tissue because of atherosclerotic occlusions is studied by developing a fluid and structure interaction (FSI) analysis for the first time. The FSI presents a semi-realistic simulation environment to observe how the blood and vessels' structural interactions can increase the accuracy of the biomechanical study results. In the first step, many different intracranial vessels are modeled for an investigation of the biomechanical and hemodynamic effects of atherosclerosis in arterial tissue remodeling. Three physiological conditions of an intact artery, the artery with intracranial atherosclerosis (ICAS), and an atherosclerotic aneurysm (ACA) are employed in the models with required assumptions. Finally, the obtained outputs are studied with comparative and statistical analyses according to the intact model in a normal physiological condition. The results show that existing occlusions in the cross-sectional area of the arteries play a determinative role in changing the hemodynamic behavior of the arterial segments. The undesirable variations in blood velocity and pressure throughout the vessels increase the risk of arterial tissue remodeling and aneurysm formation.

     

Pulsatile flow through a constricted tube: effect of stenosis morphology on hemodynamic parameters

In this paper, we investigate pulsatile flow through a constricted tube with the aim of assessing the effect of stenosis morphology on hemodynamic parameters. The fluid-solid interaction of pulsatile flow through a compliant tube with elastic walls was simulated using an arbitrary Lagrangian-Eulerian (ALE) finite-element method. We consider blood flow through various mild stenoses of 25.8% severity in diameter with trapezoidal and bell-like morphologies at a fixed Womersley number of 7.75. The results show that the distribution of the time-averaged wall shear stress (TAWSS), which is the main factor affecting the hemodynamic parameters, strongly depends on the axial stretch of the stenosis; elongation of the stenotic region increases by 41.1% the maximum TAWSS for stenoses of trapezoidal morphology whereas the maximum TAWSS decreases by 14.8% for the corresponding stenoses of bell-like morphology. The present findings indicate that risk factors due to atherosclerosis may vary in a complicated manner as an atheromatous plaque gradually builds up and morphs with time.     

Influence of arterial wall compliance on the pressure drop across coronary artery stenoses under hyperemic flow condition

Hemodynamic endpoints such as flow and pressure drop are often measured during angioplasty procedures to determine the functional severity of a coronary artery stenosis. There is a lack of knowledge regarding the influence of compliance of the arterial wall-stenosis on the pressure drop under hyperemic flows across coronary lesions. This study evaluates the influence in flow and pressure drop caused by variation in arterial-stenosis compliance for a wide range of stenosis severities. The flow and pressure drop were evaluated for three different severities of stenosis and tested for limiting scenarios of compliant models. The Mooney-Rivlin model defined the non-linear material properties of the arterial wall and the plaque regions. The non-Newtonian Carreau model was used to model the blood flow viscosity. The fluid (blood)-structure (arterial wall) interaction equations were solved numerically using the finite element method. Irrespective of the stenosis severity, the compliant models produced a lower pressure drop than the rigid artery due to compliance of the plaque region. A wide variation in the pressure drop was observed between different compliant models for significant (90% area occlusion) stenosis with 41.0, 32.1, and 29.8 mmHg for the rigid artery, compliant artery with calcified plaque, and compliant artery with smooth muscle cell proliferation, respectively. When compared with the rigid artery for significant stenosis the pressure drop decreased by 27.7% and 37.6% for the calcified plaque and for the smooth muscle cell proliferation case, respectively. These significant variations in pressure drop for the higher stenosis may lead to misinterpretation and misdiagnosis of the stenosis severity.     

Structural adaptation increases predicted perfusion capacity after vessel obstruction in arteriolar arcade network of pig skeletal muscle

Arteriolar arcades provide alternate pathways for blood flow after obstruction of arteries or arterioles such as occurs in stroke and coronary and peripheral vascular disease. When obstruction is prolonged, remaining vessels adjust their diameters chronically in response to altered hemodynamic and metabolic conditions. Here, the effectiveness of arcades in maintaining perfusion both immediately following obstruction and after structural adaptation was examined. Morphometric data from a vascular casting of the pig triceps brachii muscle and published data were used to develop a computational model for the hemodynamics and structural adaptation of the arcade network between two feed artery branches, FA1 and FA2. The predicted total flow to capillaries (Q(TA)) in the region initially supplied by FA2 decreased to 26% of the normal value immediately after FA2 obstruction but was restored to 78% of the normal value after adaptation. After obstruction of 1-10 randomly selected arcade segments, Q(TA) was on average 18% higher in the arcade network than in a corresponding two-tree network without arcades. Structural adaptation increased Q(TA) by an additional 16% in the arcade network but had almost no effect in the two-tree network. These results indicate that arcades can partially maintain blood flow after vascular blockage and that this effect is substantially enhanced by structural adaptation.     

Adaptation of the uterine arcade in rats to pregnancy

In order to study the adaptation of the uterine arterial system to pregnancy we measured vascular dimensions and other growth related data (DNA content and [3H]thymidine incorporation rate) on excised uterine arcades, pressurized to 100 mmHg, of rats before and during pregnancy (day 8, 18 and 21 of gestation). The vascular conductance of the arcade was calculated using a numerical method. In order to investigate the response of the arcade to flow impairment during early pregnancy, the same measurements were repeated on uterine arcades from pregnant animals (day 21 of gestation), where the left uterine artery had been ligated on day 8 of pregnancy. In adult virgin rats, the uterine arcade was 0.3 +/- 0.05 mm wide and 50 +/- 5 mm long. With these vascular dimensions the vascular conductance of the arcade (2.5 microliters/(s x mmHg] was calculated to be inadequate for the blood supply to the pregnant uterus at term. During the course of pregnancy modest changes were seen: The arcade increased 80% in length, 30% and 80% in internal diameter at the ovarian and cervical origin respectively and 6 times in conductance. Weight of the arcades increased 2-3-fold, [3H]thymidine incorporation rate 7-fold whereas the DNA mass remained constant. Ligation of the uterine artery on day 8 caused a 2 times increase in internal diameter of the ovarian (open) origin of the arcade without change in weight, whilst the cervical (ligated) origin of the arcade had the same internal diameter as that of the control group. The calculated vascular conductance of the ligated arcade was the same as for controls.(ABSTRACT TRUNCATED AT 250 WORDS)     

Large deforming buoyant embolus passing through a stenotic common carotid artery: a computational simulation

Arterial embolism is responsible for the death of lots of people who suffers from heart diseases. The major risk of embolism in upper limbs is that the ruptured particles are brought into the brain, thus stimulating neurological symptoms or causing the stroke. We presented a computational model using fluid-structure interactions (FSI) to investigate the physical motion of a blood clot inside the human common carotid artery. We simulated transportation of a buoyant embolus in an unsteady flow within a finite length tube having stenosis. Effects of stenosis severity and embolus size on arterial hemodynamics were investigated. To fulfill realistic nonlinear property of a blood clot, a rubber/foam model was used. The arbitrary Lagrangian-Eulerian formulation (ALE) and adaptive mesh method were used inside fluid domain to capture the large structural interfacial movements. The problem was solved by simultaneous solution of the fluid and the structure equations. Stress distribution and deformation of the clot were analyzed and hence, the regions of the embolus prone to lysis were localized. The maximum magnitude of arterial wall shear stress during embolism occurred at a short distance proximal to the throat of the stenosis. Through embolism, arterial maximum wall shear stress is more sensitive to stenosis severity than the embolus size whereas role of embolus size is more significant than the effect of stenosis severity on spatial and temporal gradients of wall shear stress downstream of the stenosis and on probability of clot lysis due to clot stresses while passing through the stenosis.     

Shear stress paradigm for perinatal fractal arterial network remodeling in lambs with pulmonary hypertension and increased pulmonary blood flow

Congenital heart disease with increased blood flow commonly leads to the development of increased pulmonary vascular reactivity and pulmonary arterial hypertension by mechanisms that remain unclear. We hypothesized a shear stress paradigm of hemodynamic reactivity and network remodeling via the persistence and/or exacerbation of a fetal diameter bifurcation phenotype [parent diameter d(0) and daughters d(1) >or= d(2) with alpha < 2 in (d(1)/d(0))(alpha) + (d(2)/d(0))(alpha) and area ratio beta < 1 in beta = (d(1)(2)+ d(2)(2))/ d(0)(2)] that mechanically acts as a high resistance magnifier/shear stress amplifier to blood flow. Evidence of a hemodynamic influence on network remodeling was assessed with a lamb model of high-flow-induced secondary pulmonary hypertension in which an aortopulmonary graft was surgically placed in one twin in utero (Shunt twin) but not in the other (Control twin). Eight weeks after birth arterial casts were made of the left pulmonary arterial circulation. Bifurcation diameter measurements down to 0.010 mm in the Shunt and Control twins were then compared with those of an unoperated fetal cast. Network organization, cumulative resistance, and pressure/shear stress distributions were evaluated via a fractal model whose dimension D(0) approximately alpha delineates hemodynamic reactivity. Fetus and Control twin D(0) differed: fetus D(0)=1.72, a high-resistance/shear stress amplifying condition; control twin D(0) = 2.02, an area-preserving transport configuration. The Shunt twin (D(0)=1.72) maintained a fetal design but paradoxically remodeled diameter geometry to decrease cumulative resistance relative to the Control twin. Our results indicate that fetal/neonatal pulmonary hemodynamic reactivity remodels in response to shear stress, but the response to elevated blood flow and pulmonary hypertension involves the persistence and exacerbation of a fetal diameter bifurcation phenotype that facilitates endothelial dysfunction/injury.     

Hemodynamic, vascular, and reproductive impact of FMS-like tyrosine kinase 1 (FLT1) blockade on the uteroplacental circulation during normal mouse pregnancy

To investigate the role of FMS-like tyrosine kinase 1 (FLT1, also known as VEGFR1) signaling during pregnancy, mice were injected with anti-FLT1 neutralizing antibody (Ab) beginning on Gestational Day 8 or 12 and every other day thereafter until Day 18; vehicle-only injected mice served as controls. Uterine artery blood flow was measured with ultrasound on Days 13 and 18, and morphometric measurements of the uterine arcade were carried out on Day 19 to provide a measure of gestational vascular remodeling; reproductive performance was evaluated by determining litter size, resorption rates, and pup and placental weights. Ab injections beginning on Day 8 or Day 12 resulted in significant reductions of uterine artery peak systolic and diastolic flows at Days 13 and 18. In addition, normal reproductive function was compromised, as evidenced by a significant reduction in average number of viable pups along with enhanced resorption rates. Reproductive performance was also significantly compromised in this group, although less severely. There was no evidence of a reduction in main uterine artery diameters, though arterial distensibility was reduced, and the diameter of the main uterine vein was significantly smaller in the Ab-injected mice. Significant reductions in main uterine artery and segmental artery length were also noted. Placental and pup weights were similar in all the groups. FLT1 inhibition during murine pregnancy impaired blood flow to the fetal-placental unit, compromised several indices of vascular remodeling, reduced fecundity, and increased fetal reabsorptions. The effects of FLT1 inhibition are most pronounced when targeted during early pregnancy.     

Structural remodeling of mouse gracilis artery after chronic alteration in blood supply

The goals of this study were to determine the time course and spatial dependence of structural diameter changes in the mouse gracilis artery after a redistribution of blood flow and to compare the observations with predictions of computational models for structural adaptation. Diameters were measured 1, 2, 7, 14, 21, 28, and 56 days after resection of one of the two blood supplies to the artery. Overall average diameter, normalized with respect to diameters in untreated vessels, increased slightly during the first 7 days, then increased more rapidly, reaching a peak around day 21, and then decreased. This transient increase in diameter was spatially nonuniform, being largest toward the point of resection. A previously developed theoretical model, in which diameter varies in response to stimuli derived from local metabolic and hemodynamic conditions, was extended to include effects of time-delayed remodeling stimuli in regions of reduced perfusion. Predictions of this model were consistent with observed diameter changes, including the transient increase in diameters near the point of resection, when a remodeling stimulus with a time delay of approximately 7 days was included. The results suggest that delayed stimuli significantly influence the dynamic characteristics of vascular remodeling resulting from reduced blood supply.     

Analysis of blood flow in the entire coronary arterial tree

A hemodynamic analysis of coronary blood flow must be based on the measured branching pattern and vascular geometry of the coronary vasculature. We recently developed a computer reconstruction of the entire coronary arterial tree of the porcine heart based on previously measured morphometric data. In the present study, we carried out an analysis of blood flow distribution through a network of millions of vessels that includes the entire coronary arterial tree down to the first capillary branch. The pressure and flow are computed throughout the coronary arterial tree based on conservation of mass and momentum and appropriate pressure boundary conditions. We found a power law relationship between the diameter and flow of each vessel branch. The exponent is approximately 2.2, which deviates from Murray's prediction of 3.0. Furthermore, we found the total arterial equivalent resistance to be 0.93, 0.77, and 1.28 mmHg.ml(-1).s(-1).g(-1) for the right coronary artery, left anterior descending coronary artery, and left circumflex artery, respectively. The significance of the present study is that it yields a predictive model that incorporates some of the factors controlling coronary blood flow. The model of normal hearts will serve as a physiological reference state. Pathological states can then be studied in relation to changes in model parameters that alter coronary perfusion.     

Estimation of valvular resistance of segmented aortic valves using computational fluid dynamics

Aortic valve stenosis is associated with an elevated left ventricular pressure and transaortic pressure drop. Clinicians routinely use Doppler ultrasound to quantify aortic valve stenosis severity by estimating this pressure drop from blood velocity. However, this method approximates the peak pressure drop, and is unable to quantify the partial pressure recovery distal to the valve. As pressure drops are flow dependent, it remains difficult to assess the true significance of a stenosis for low-flow low-gradient patients. Recent advances in segmentation techniques enable patient-specific Computational Fluid Dynamics (CFD) simulations of flow through the aortic valve. In this work a simulation framework is presented and used to analyze data of 18 patients. The ventricle and valve are reconstructed from 4D Computed Tomography imaging data. Ventricular motion is extracted from the medical images and used to model ventricular contraction and corresponding blood flow through the valve. Simplifications of the framework are assessed by introducing two simplified CFD models: a truncated time-dependent and a steady-state model. Model simplifications are justified for cases where the simulated pressure drop is above 10 mmHg. Furthermore, we propose a valve resistance index to quantify stenosis severity from simulation results. This index is compared to established metrics for clinical decision making, i.e. blood velocity and valve area. It is found that velocity measurements alone do not adequately reflect stenosis severity. This work demonstrates that combining 4D imaging data and CFD has the potential to provide a physiologically relevant diagnostic metric to quantify aortic valve stenosis severity.     

Mesenteric resistance arteries in type 2 diabetic db/db mice undergo outward remodeling

Objective

Resistance vessel remodeling is controlled by myriad of hemodynamic and neurohormonal factors. This study characterized structural and molecular remodeling in mesenteric resistance arteries (MRAs) in diabetic (db/db) and control (Db/db) mice.

Methods

Structural properties were assessed in isolated MRAs from 12 and 16 wk-old db/db and Db/db mice by pressure myography. Matrix regulatory proteins were measured by Western blot analysis. Mean arterial pressure and superior mesenteric blood flow were measured in 12 wk-old mice by telemetry and a Doppler flow nanoprobe, respectively.

Results

Blood pressure was similar between groups. Lumen diameter and medial cross-sectional area were significantly increased in 16 wk-old db/db MRA compared to control, indicating outward hypertrophic remodeling. Moreover, wall stress and cross-sectional compliance were significantly larger in diabetic arteries. These remodeling indices were associated with increased expression of matrix regulatory proteins matrix metalloproteinase (MMP)-9, MMP-12, tissue inhibitors of matrix metalloproteinase (TIMP)-1, TIMP-2, and plasminogen activator inhibitor-1 (PAI-1) in db/db arteries. Finally, superior mesenteric artery blood flow was increased by 46% in 12 wk-old db/db mice, a finding that preceded mesenteric resistance artery remodeling.

Conclusions

These data suggest that flow-induced hemodynamic changes may supersede the local neurohormonal and metabolic milieu to culminate in hypertrophic outward remodeling of type 2 DM mesenteric resistance arteries.     

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.     

A longitudinal study of remodeling in a revised peripheral artery bypass graft using 3D ultrasound imaging and computational hemodynamics

We report a study of the role of hemodynamic shear stress in the remodeling and failure of a peripheral artery bypass graft. Three separate scans of a femoral to popliteal above-knee bypass graft were taken over the course of a 16 month period following a revision of the graft. The morphology of the lumen is reconstructed from data obtained by a custom 3D ultrasound system. Numerical simulations are performed with the patient-specific geometries and physiologically realistic flow rates. The ultrasound reconstructions reveal two significant areas of remodeling: a stenosis with over 85% reduction in area, which ultimately caused graft failure, and a poststenotic dilatation or widening of the lumen. Likewise, the simulations reveal a complicated hemodynamic environment within the graft. Preliminary comparisons with in vivo velocimetry also showed qualitative agreement with the flow dynamics observed in the simulations. Two distinct flow features are discerned and are hypothesized to directly initiate the observed in vivo remodeling. First, a flow separation occurs at the stenosis. A low shear recirculation region subsequently develops distal to the stenosis. The low shear region is thought to be conducive to smooth muscle cell proliferation and intimal growth. A poststenotic jet issues from the stenosis and subsequently impinges onto the lumen wall. The lumen dilation is thought to be a direct result of the high shear stress and high frequency pressure fluctuations associated with the jet impingement.     

The influence of artery wall curvature on the anatomical assessment of stenosis severity derived from fractional flow reserve: a computational fluid dynamics study

This study aims to investigate the influence of artery wall curvature on the anatomical assessment of stenosis severity and to identify a region of misinterpretation in the assessment of per cent area stenosis (AS) for functionally significant stenosis using fractional flow reserve (FFR) as standard. Five artery models of different per cent AS severity (70, 75, 80, 85 and 90%) were considered. For each per cent AS severity, the angle of curvature of the arterial wall varied from straight to an increasingly curved model (0°, 30°, 60°, 90° and 120°). Computational fluid dynamics was performed under transient physiologic hyperemic flow conditions to investigate the influence of artery wall curvature on the pressure drop and the FFR. The findings in this study may be useful in in vitro anatomical assessment of functionally significant stenosis. The FFR decreased with increasing stenosis severity for a given curvature of the artery wall. Moreover, a significant decrease in FFR was found between straight and curved models discussed for a given severity condition. These findings indicate that the curvature effect was included in the FFR assessment in contrast to minimum lumen area (MLA) or per cent AS assessment. The MLA or per cent AS assessment may lead to underestimation of stenosis severity. From this numerical study, an uncertainty region could be evaluated using the clinical FFR cutoff value of 0.8. This value was observed at 81.98 and 79.10% AS for arteries with curvature angles of 0° and 120° respectively. In conclusion, the curvature of the artery should not be neglected in in vitro anatomical assessment.     

Arterial wall remodeling under sustained axial twisting in rats

Blood vessels often experience torsion along their axes and it is essential to understand their biological responses and wall remodeling under torsion. To this end, a rat model was developed to investigate the arterial wall remodeling under sustained axial twisting in vivo. Rat carotid arteries were twisted at 180° along the longitudinal axis through a surgical procedure and maintained for different durations up to 4 weeks. The wall remodeling in these twisted arteries was examined using histology, immunohistochemistry and fluorescent microscopy. Our data showed that arteries remodeled under twisting in a time-dependent manner during the 4 weeks post-surgery. Cell proliferation, MMP-2 and MMP-9 expressions, medial wall thickness and lumen diameter increased while collagen to elastin ratio decreased. The size and number of internal elastic lamina fenestrae increased with elongated shapes, while the endothelial cells elongated and aligned towards the blood flow direction gradually. These results demonstrated that sustained axial twisting results in artery remodeling in vivo. The rat carotid artery twisting model is an effective in vivo model for studying arterial wall remodeling under long-term torsion. These results enrich our understanding of vascular biology and arterial wall remodeling under mechanical stresses.     

A mathematical model for the distribution of hemodynamic parameters in the human retinal microvascular network

To quantitatively assess the arteriovenous distribution of hemodynamic parameters throughout the microvascular network of the human retina, we constructed a retinal microcirculatory model consisting of a dichotomous symmetric branching system. This system is characterized by a diameter exponent of 2.85, instead of 3 as dictated by Murray’s law, except for the capillary networks. The value of 2.85 was the sum of a fractal dimension (1.70) and a branch exponent (1.15) of the retinal vasculature. Following the feeding artery (central retinal artery), each bifurcation was recursively developed at a distance of an individual branch length [L(r) = 7.4r ^1.15] by a centrifugal scheme. The venular tree was formed in the same way. Using this model, we evaluated hemodynamic parameters, including blood pressure, blood flow, blood velocity, shear rate, and shear stress, within the retinal microcirculatory network as a function of vessel diameter. The arteriovenous distributions of blood pressure and velocity in the simulation were consistent with in vivo measurements in the human retina and other vascular beds of small animals. We therefore conclude that the current theoretical model was useful for quantifying hemodynamics as a function of vessel diameter within the retinal microvascular network.     

Sequential venous anastomosis design to enhance patency of arterio-venous grafts for hemodialysis

Arterio-venous grafts (AVGs), the second best option as long-term vascular access for hemodialysis, face major issues of stenosis mainly due to development of intimal hyperplasia at the venous anastomosis which is linked to unfavorable hemodynamic conditions. We have investigated computationally the utility of a coupled sequential venous anastomotic design to replace conventional end-to-side (ETS) venous anastomosis, in order to improve the hemodynamic environment and consequently enhance the patency of AVGs. Two complete vascular access models with the conventional and the proposed venous anastomosis configurations were constructed. Three-dimensional, pulsatile blood flow through the models was simulated, and wall shear stress (WSS)-based hemodynamic parameters were calculated and compared between the two models. Simulation results demonstrated that the proposed anastomotic design provides: (i) a more uniform and smooth flow at the ETS anastomosis, without flow impingement and stagnation point on the artery bed and vortex formation in the heel region of the ETS anastomosis; (ii) more uniform distribution of WSS and substantially lower WSS gradients on the venous wall; and (iii) a spare route for the blood flow to the vein, to avoid re-operation in case of stenosis. The distinctive hemodynamic advantages observed in the proposed anastomotic design can enhance the patency of AVGs.