Fluid waves in renal tubules.

Autoregulation of renal blood flow is ineffective when arterial pressure perturbations occur at frequencies above 0.05 Hz. To determine whether wave propagation velocity to the macula densa is rate limiting, we estimated compliances of the proximal tubule and the loop of Henle, and used these values in a model of pressure and flow as functions of time and distance in the nephron. Compliances were estimated from measurements of pressures and flows in early proximal, late proximal, and early distal tubules in rats under normal and Ringer-loaded conditions. A model of steady pressure and flow in a compliant, reabsorbing tubule was fitted to these results. The transient model was a set of nonlinear, hyperbolic partial differential equations with split, nonlinear boundary conditions, and was solved with finite difference methods. The loop of Henle compliance was larger than the proximal tubule compliance, and impulses in glomerular filtration rate were attenuated in magnitude and delayed in time in the loop of Henle. Simulated step forcings revealed a similar pattern. Periodic variations of GFR were attenuated at frequencies greater than 0.05 Hz, and there was a delay of 5 s between variations in GFR and macula densa flow rate. The high compliance of the loop slows wave propagation to the macular densa and reduces the amplitude of high frequency waves originating in the glomerulus, but other parts of the signal chain also contribute to the slow response of macula densa feedback.     

Influence of heart rate on fractional flow reserve, pressure drop coefficient, and lesion flow coefficient for epicardial coronary stenosis in a porcine model

A limitation in the use of invasive coronary diagnostic indexes is that fluctuations in hemodynamic factors such as heart rate (HR), blood pressure, and contractility may alter resting or hyperemic flow measurements and may introduce uncertainties in the interpretation of these indexes. In this study, we focused on the effect of fluctuations in HR and area stenosis (AS) on diagnostic indexes. We hypothesized that the pressure drop coefficient (CDP(e), ratio of transstenotic pressure drop and distal dynamic pressure), lesion flow coefficient (LFC, square root of ratio of limiting value CDP and CDP at site of stenosis) derived from fluid dynamics principles, and fractional flow reserve (FFR, ratio of average distal and proximal pressures) are independent of HR and can significantly differentiate between the severity of stenosis. Cardiac catheterization was performed on 11 Yorkshire pigs. Simultaneous measurements of distal coronary arterial pressure and flow were performed using a dual sensor-tipped guidewire for HR < 120 and HR > 120 beats/min, in the presence of epicardial coronary lesions of <50% AS and >50% AS. The mean values of FFR, CDP(e), and LFC were significantly different (P < 0.05) for lesions of <50% AS and >50% AS (0.88 ± 0.04, 0.76 ± 0.04; 62 ± 30, 151 ± 35, and 0.10 ± 0.02 and 0.16 ± 0.01, respectively). The mean values of FFR and CDP(e) were not significantly different (P > 0.05) for variable HR conditions of HR < 120 and HR > 120 beats/min (FFR, 0.81 ± 0.04 and 0.82 ± 0.04; and CDP(e), 95 ± 33 and 118 ± 36). The mean values of LFC do somewhat vary with HR (0.14 ± 0.01 and 0.12 ± 0.02). In conclusion, fluctuations in HR have no significant influence on the measured values of CDP(e) and FFR but have a marginal influence on the measured values of LFC. However, all three parameters can significantly differentiate between stenosis severities. These results suggest that the diagnostic parameters can be potentially used in a better assessment of coronary stenosis severity under a clinical setting.     

A finite-element model of blood flow in arteries including taper, branches, and obstructions

A nonlinear mathematical model of arterial blood flow, which can account for tapering, branching, and the presence of stenosed segments, is presented. With the finite-element method, the model equations are transformed into a system of algebraic equations that can be solved on a high-speed digital computer to yield values of pressure and volume rate of flow as functions of time and arterial position. A model of the human femoral artery is used to compare the effects of linear and nonlinear modeling. During periods of rapid alternations in pressure or flow, the nonlinear model shows significantly different results than the linear model. The effect of a stenosis on pressure and flow waveforms is also simulated, and the results indicate that these waveforms are significantly altered by moderate and severe stenoses.     

在正常和冠状动脉狭窄犬中扩张胃对冠脉血流动力学的影响

饱餐和扩张胃对心血管的影响早已引起人们的注意,但结论是不一致的。以往的实验都是在正常冠脉的动物上进行。本文在造成冠脉狭窄的情况下进行观察。在22条开胸狗的左旋支上,用微米狭窄器造成临界狭窄和重度狭窄。把一个气球送入胃中并充气600ml连续观察30min。正常冠脉组在扩张胃的最初15min内(前期)冠脉流量增多,主动脉压升高,血管总阻力下降,冠脉扩张;在扩张胃后15分钟(后期)无显著变化。冠脉临界狭窄组,前期冠脉流量增多,血管总阻力下降,冠脉扩张;后期流量减少,壁内血管阻力增加,冠脉收缩。冠脉重度狭窄组,前期冠脉流量无明显增加;后期流量显著减少,血管总阻力及心外膜、壁内血管阻力均增加,提示左旋支血管各段都发生收缩。 我们认为,餐后心绞痛的发作可能主要是在原有冠脉狭窄基础上冠脉流量进一步减少的结果。     

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.     

Study of the collateral capacity of the circle of Willis of patients with severe carotid artery stenosis by 3D computational modeling

This numerical study aims to investigate the capacity of the circle of Wills (CoW) to provide collateral blood supply for patients with unilateral carotid arterial stenosis. The basic 3D geometry of the CoW was reconstructed based on a magnetic resonance angiogram of a normal human subject. A total of 52 computational fluid dynamics simulations were performed for four geometry configurations of the CoW with an artificially inserted axisymmetric stenosis of different luminal area reductions in an internal carotid artery (ICA) under a variety of boundary conditions. The CoW geometric configurations included (a) a normal CoW with all communicating arteries; (b) as model (a) but with enlarged communicating arterial diameters; (c) as (a) but with the ipsilateral posterior communicating artery missing, and (d) as (c) but with enlarged communicating arteries. It is found that the blood perfusion pressure drop between the ipsilateral ICA and the middle cerebral artery (MCA) only becomes significant when the degree of stenosis is greater than 86%. The cerebral autoregulation range varied significantly between the different CoW configurations for the severe stenosis cases. Without causing the flow rates to decrease at the efferent arterial ends, the mean perfusion pressure in the ipsilateral ICA can drop from 100 to 73, 67, 92 and 84mmHg for the CoW models (a)-(d) with 96% luminal area reduction stenosis, respectively. The additional pathways are able to raise the ipsilateral MCA pressure significantly without reducing the total flow perfusion. Cerebral autoregulation effects were not directly included in the study. Therefore, the findings in the study should be interpreted with cautions when comes to the biological and clinical significance.     

Mechanism of reversible (99m)Tc-sestamibi perfusion defects during pharmacologically induced vasodilatation

Reversible perfusion defects on (99m)Tc-sestamibi imaging during hyperemia are thought to occur due to myocardial blood flow (MBF) "mismatch" between regions with and without stenosis. We have recently shown that myocardial blood volume (MBV) distal to a stenosis decreases during hyperemia, resulting in a reversible perfusion defect on myocardial contrast echocardiography (MCE). In this study, we hypothesized that a reversible perfusion defect on (99m)Tc-sestamibi imaging during hyperemia results from the same mechanism. We tested our hypothesis under the following conditions: 1) increases in MBF in the absence of changes in MBV by using direct intracoronary infusion of adenosine (group I, n = 10 dogs); 2) decrease in MBV despite an increase in MBF by left main infusion of adenosine proximal to a noncritical coronary stenosis placed on either coronary artery (group II, n = 13 dogs); and 3) reduction in both resting MBF and MBV by placement of a severe stenosis (group III, n = 7 dogs). In group I dogs, no difference in MBV or (99m)Tc-sestamibi uptake was found between the two coronary beds despite an up to fourfold increase in MBF in one bed with adenosine. In group II dogs, MBV distal to the stenosis decreased during hyperemia despite a twofold increase in mean MBF. A good correlation was found between (99m)Tc-sestamibi uptake and MBV ratios from the stenosed versus normal bed (r = 0.91, P < 0.001). In group III dogs, both MBF and MBV were decreased in the stenosed bed at rest with a good correlation noted between (99m)Tc-sestamibi uptake and MBV ratios from the stenosed versus normal bed (r = 0.92, P = 0.004). We conclude that reversible defects on (99m)Tc-sestamibi during vasodilator stress imaging are related to decreases in MBV distal to a stenosis and not to "flow mismatch" between beds. The decrease in MBV results in reduced (99m)Tc-sestamibi uptake during hyperemia.     

Computer modeling of the human systemic arterial tree

A model of the human systemic arterial tree has been devised, based on a lumped-parameter-circuit approximate form. This model has been set up and studied on an analog computer. A feature of this simulation is the division of the arterial system into sections whose lengths are inversely proportional (approximately) to their cross-sectional area-or what is termed ‘equal-volume’ modeling.

Great care was exercised in the determination of the model parameters, using expressions for these parameters from a recent paper by Rideout and Dick on fluid flow in distensible tubes, with numerical values based on measurements reported in the medical literature.

The simulated pressure and flow waveforms obtained with the model compare favorably with data recorded from the normal adult human, and exhibit such well-known features as distal delay and peaking of pressure pulses. The aortic input impedance vs. frequency curve checks well against measurements on the human. The model also provides a simple means for determination of cardiac output, cardiac work and cardiac power under various assumed conditions such as variation of heart rate.     

Abnormal arterial flows by a distributed model of the fetal circulation

Modeling the propagation of blood pressure and flow along the fetoplacental arterial tree may improve interpretation of abnormal flow velocity waveforms in fetuses. The current models, however, either do not include a wide range of gestational ages or do not account for variation in anatomical, vascular, or rheological parameters. We developed a mathematical model of the pulsating fetoumbilical arterial circulation using Womersley's oscillatory flow theory and viscoelastic arterial wall properties. Arterial flow waves are calculated at different arterial locations from which the pulsatility index (PI) can be determined. We varied blood viscosity, placental and brain resistances, placental compliance, heart rate, stiffness of the arterial wall, and length of the umbilical arteries. The PI increases in the umbilical artery and decreases in the cerebral arteries, as a result of increasing placental resistance or decreasing brain resistance. Both changes in resistance decrease the flow through the placenta. An increased arterial stiffness increases the PIs in the entire fetoplacental circulation. Blood viscosity and peripheral bed compliance have limited influence on the flow profiles. Bradycardia and tachycardia increase and decrease the PI in all arteries, respectively. Umbilical arterial length has limited influence on the PI but affects the mean arterial pressure at the placental cord insertion. The model may improve the interpretation of arterial flow pulsations and thus may advance both the understanding of pathophysiological processes and clinical management.     

Compliance characteristics of the hind-limb arterial system of normal and hypertensive rabbits

Pressure transients resulting from square-wave changes in abdominal aortic blood flow rate were used to derive effective arterial compliance and peripheral resistance of the hind-limb circulation of anaesthetized rabbits. The model for deriving these parameters proved applicable if step changes in flow were kept less than 35% of mean flow. Under resting conditions, the effective hind-limb arterial compliance of normal rabbits averaged 3.46 X 10(-3) mL/mmHg (1 mmHg = 133.322 Pa). Hind-limb arterial compliance decreased with increasing pressure at low arterial pressures, but unlike compliance of isolated arterial segments, compliance did not vary at and above normal resting pressures. Baroreflex destimulation (bilateral carotid artery occlusion) caused an increase in effective hind-limb vascular resistance at 48.4% and a decrease of arterial compliance of 50.7%, so that the constant for flow-induced arterial pressure changes (resistance times compliance) was largely unchanged. Similarly, the arterial time constant for rabbits with chronic hypertension was similar to that for controls because threefold increases in hind-limb vascular resistance were offset by decreases in compliance. Reflex-induced decreases in arterial compliance are probably mediated by sympathetic nerves, whereas decreases associated with hypertension are related to wall hypertrophy in conjunction with increased vasomotor tone. Arterial compliance decreased with increasing pressure in hypertensive animals, but this effect was less pronounced than in normotensive rabbits.     

Modelling pulse wave propagation in the rabbit systemic circulation to assess the effects of altered nitric oxide synthesis

Pulse wave propagation in the mature rabbit systemic circulation was simulated using the one-dimensional equations of blood flow in compliant vessels. A corrosion cast of the rabbit circulation was manufactured to obtain arterial lengths and diameters. Pulse wave speeds and inflow and outflow boundary conditions were derived from in vivo data. Numerical results captured the main features of in vivo pressure and velocity pulse waveforms in the aorta, brachiocephalic artery and central ear artery. This model was used to elucidate haemodynamic mechanisms underlying changes in peripheral pulse waveforms observed in vivo after administering drugs that alter nitric oxide synthesis in the endothelial cells lining blood vessels. According to our model, these changes can be explained by single or combined alterations of blood viscosity, peripheral resistance and compliance, and the elasticity of conduit arteries.     

Pulsatile pressure and flow in arterial stenoses simulated in a mathematical model

This paper presents the detailed pulsatile pressure and flow velocity patterns inside an axis symmetric stenosis model with 75% constriction. The pressure and velocities have been calculated by solving the Navier-Stokes equations by the finite element method, the velocity profile in a straight tube caused by a pulsating driving pressure has been calculated first and then used as a boundary condition for the stenosis calculations. The results of the mathematical simulations of the stenosis model have been obtained in terms of velocity vectors, streamlines and isobars at 16 different instances in time, each 15 degrees apart during a cardiac cycle. The calculated velocity field shows that a vortex is developed at the wall distal to the stenosis as the velocity decreases from the peak systolic value. At the site of the vortex, a local pressure minimum is found due to the conversion of pressure to kinetic energy. When the flow is reversed, the reversal occurs first along the wall, thus forcing the vortex toward the the centre of the tube. As the reverse flow velocity increases, a vortex is also developed at the proximal site of the stenosis.     

Arterial vasodilatory and ventricular diastolic reserves determine the stroke volume response to exercise in elderly female hypertensive patients

Elderly female hypertensives with arterial stiffening constitute a majority of patients with heart failure with preserved ejection fraction (HFpEF), a condition characterized by inability to increase cardiac stroke volume (SV) with physical exercise. As SV is determined by the interaction between the left ventricle (LV) and its load, we wished to study the role of arterial hemodynamics for exertional SV reserve in patients at high risk of HFpEF. Twenty-one elderly (67 ± 9 yr) female hypertensive patients were studied at rest and during supine bicycle stress using echocardiography including pulsed-wave Doppler to record flow in the LV outflow tract and arterial tonometry for central arterial pressure waveforms. Arterial compliance was estimated based on an exponential relationship between pressure and volume. The ratio of aortic pressure-to-flow in early systole was used to derive characteristic impedance, which was subsequently subtracted from total resistance (mean arterial pressure/cardiac output) to yield systemic vascular resistance (SVR). It was found that patients with depressed SV reserve (NoRes; reserve <15%; n = 10) showed decreased arterial compliance during exercise, while patients with SV reserve ≥15% (Res; n = 11) showed increased compliance. Exercise produced parallel increases in LV end-diastolic volume and arterial volume in Res patients while NoRes patients exhibited a lesser decrease in SVR and a drop in effective arterial volume. Poor SV reserve in elderly female hypertensives is due to simultaneous failure of LV preload and arterial vasodilatory reserves. Abnormal arterial function contributes to a high risk of HFpEF in these patients.     

Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements

A numerical model based on the nonlinear, one-dimensional (1-D) equations of pressure and flow wave propagation in conduit arteries is tested against a well-defined experimental 1:1 replica of the human arterial tree. The tree consists of 37 silicone branches representing the largest central systemic arteries in the human, including the aorta, carotid arteries and arteries that perfuse the upper and lower limbs and the main abdominal organs. The set-up is mounted horizontally and connected to a pulsatile pump delivering a periodic output similar to the aortic flow. Terminal branches end in simple resistance models, consisting of stiff capillary tubes leading to an overflow reservoir that reflects a constant venous pressure. The parameters required by the numerical algorithm are directly measured in the in vitro set-up and no data fitting is involved. Comparison of experimental and numerical pressure and flow waveforms shows the ability of the 1-D time-domain formulation to capture the main features of pulse wave propagation measured throughout the system test. As a consequence of the simple resistive boundary conditions used to reduce the uncertainty of the parameters involved in the simulation, the experimental set-up generates waveforms at terminal branches with additional non-physiological oscillations. The frequencies of these oscillations are well captured by the 1-D model, even though amplitudes are overestimated. Adding energy losses in bifurcations and including fluid inertia and compliance to the purely resistive terminal models does not reduce the underdamped effect, suggesting that wall visco-elasticity might play an important role in the experimental results. Nevertheless, average relative root-mean-square errors between simulations and experimental waveforms are smaller than 4% for pressure and 19% for the flow at all 70 locations studied.     

Increase in Ultrasonic Intensity of Blood Speckle across Moderate Coronary Artery Stenosis Is an Independent Predictor of Functional Coronary Artery Stenosis Measured by Fractional Flow Reserve: Pilot Study

Background and Aims

The degree of coronary artery stenosis should be assessed both anatomically and functionally. We observed that the intensity of blood speckle (IBS) on intravascular ultrasound (IVUS) is low proximal to a coronary artery stenosis, and high distal to the stenosis. We defined step-up IBS as the distal minus the proximal IBS, and speculated that this new parameter could be used for the functional evaluation of stenosis on IVUS. The aims of this study were to assess the relationships between step-up IBS and factors that affect coronary blood flow, and between step-up IBS and fractional flow reserve (FFR).

Methods and Results

This study enrolled 36 consecutive patients with angina who had a single moderate stenosis in the left anterior descending artery. All patients were evaluated by integrated backscatter IVUS and intracoronary pressure measurements. FFR was calculated from measurements using a coronary pressure wire during hyperemia. Conventional gray-scale IVUS images were recorded, and integrated backscatter was measured in three cross-sectional slices proximal and distal to the stenosis. Step-up IBS was calculated as (mean distal integrated backscatter value) − (mean proximal integrated backscatter value). Stepwise multiple linear regression analysis showed that the heart rate (r = 0.45, P = 0.005), ejection fraction (r = −0.39, P = 0.01), and hemoglobin level (r = −0.32, P = 0.04) were independently correlated with step-up IBS, whereas proximal and distal IBS were not associated with these factors. There was a strong inverse correlation between step-up IBS and FFR (r = −0.84, P < 0.001), which remained significant on stepwise multiple linear regression analysis.

Conclusions

The newly defined parameter of step-up IBS is potentially useful for the functional assessment of coronary artery stenosis.     

A novel servo-control system that imposes desired aortic input impedance on in situ rat heart

To clarify the pathophysiological role of dynamic arterial properties in cardiovascular diseases, we attempted to develop a new control system that imposes desired aortic impedance on in situ rat left ventricle. In 38 anesthetized open-chest rats, ascending aortic pressure and flow waveforms were continuously sampled (1,000 Hz). Desired flow waveforms were calculated from measured aortic pressure waveforms and target impedance. To minimize the difference between measured and desired aortic flow waveforms, the computer generated commands to the servo-pump, connected to a side branch of the aorta. By iterating the process, we could successfully control aortic impedance in such a way as to manipulate compliance and characteristic impedance between 60 and 160% of their respective native values. The error between desired and measured aortic flow waveforms was 70 +/- 34 microl/s (root mean square; 4.4 +/- 1.4% of peak flow), indicating reasonable accuracy in controlling aortic impedance. This system enables us to examine the importance of dynamic arterial properties independently of other hemodynamic and neurohumoral factors in physiological and clinical settings.     

Measurement of total pulmonary arterial compliance using invasive pressure monitoring and MR flow quantification during MR-guided cardiac catheterization

Pulmonary hypertensive disease is assessed by quantification of pulmonary vascular resistance. Pulmonary total arterial compliance is also an indicator of pulmonary hypertensive disease. However, because of difficulties in measuring compliance, it is rarely used. We describe a method of measuring pulmonary arterial compliance utilizing magnetic resonance (MR) flow data and invasive pressure measurements. Seventeen patients with suspected pulmonary hypertension or congenital heart disease requiring preoperative assessment underwent MR-guided cardiac catheterization. Invasive manometry was used to measure pulmonary arterial pressure, and phase-contrast MR was used to measure flow at baseline and at 20 ppm nitric oxide (NO). Total arterial compliance was calculated using the pulse pressure method (parameter optimization of the 2-element windkessel model) and the ratio of stroke volume to pulse pressure. There was good agreement between the two estimates of compliance (r = 0.98, P < 0.001). However, there was a systematic bias between the ratio of stroke volume to pulse pressure and the pulse pressure method (bias = 61%, upper level of agreement = 84%, lower level of agreement = 38%). In response to 20 ppm NO, there was a statistically significant fall in resistance, systolic pressure, and pulse pressure. In seven patients, total arterial compliance increased >10% in response to 20 ppm NO. As a population, the increase did not reach statistical significance. There was an inverse relation between compliance and resistance (r = 0.89, P < 0.001) and between compliance and mean pulmonary arterial pressure (r = 0.72, P < 0.001). We have demonstrated the feasibility of quantifying total arterial compliance using an MR method.     

On the choice of outlet boundary conditions for patient-specific analysis of aortic flow using computational fluid dynamics

Boundary conditions (BCs) are an essential part in computational fluid dynamics (CFD) simulations of blood flow in large arteries. Although several studies have investigated the influence of BCs on predicted flow patterns and hemodynamic wall parameters in various arterial models, there is a lack of comprehensive assessment of outlet BCs for patient-specific analysis of aortic flow. In this study, five different sets of outlet BCs were tested and compared using a subject-specific model of a normal aorta. Phase-contrast magnetic resonance imaging (PC-MRI) was performed on the same subject and velocity profiles extracted from the in vivo measurements were used as the inlet boundary condition. Computational results obtained with different outlet BCs were assessed in terms of their agreement with the PC-MRI velocity data and key hemodynamic parameters, such as pressure and flow waveforms and wall shear stress related indices. Our results showed that the best overall performance was achieved by using a well-tuned three-element Windkessel model at all model outlets, which not only gave a good agreement with in vivo flow data, but also produced physiological pressure waveforms and values. On the other hand, opening outlet BCs with zero pressure at multiple outlets failed to reproduce any physiologically relevant flow and pressure features.     

Steady flow and wall compression in stenotic arteries: a three-dimensional thick-wall model with fluid-wall interactions.

Severe stenosis may cause critical flow and wall mechanical conditions related to artery fatigue, artery compression, and plaque rupture, which leads directly to heart attack and stroke. The exact mechanism involved is not well understood. In this paper a nonlinear three-dimensional thick-wall model with fluid-wall interactions is introduced to simulate blood flow in carotid arteries with stenosis and to quantify physiological conditions under which wall compression or even collapse may occur. The mechanical properties of the tube wall were selected to match a thick-wall stenosis model made of PVA hydrogel. The experimentally measured nonlinear stress-strain relationship is implemented in the computational model using an incremental linear elasticity approach. The Navier-Stokes equations are used for the fluid model. An incremental boundary iteration method is used to handle the fluid-wall interactions. Our results indicate that severe stenosis causes considerable compressive stress in the tube wall and critical flow conditions such as negative pressure, high shear stress, and flow separation which may be related to artery compression, plaque cap rupture, platelet activation, and thrombus formation. The stress distribution has a very localized pattern and both maximum tensile stress (five times higher than normal average stress) and maximum compressive stress occur inside the stenotic section. Wall deformation, flow rates, and true severities of the stenosis under different pressure conditions are calculated and compared with experimental measurements and reasonable agreement is found.     

Inlet boundary conditions for blood flow simulations in truncated arterial networks

In the context of patient-specific cardiovascular applications, hemodynamics models (going from 3D to 0D) are often limited to a part of the arterial tree. This restriction implies the set up of artificial interfaces with the remaining parts of the cardiovascular system. In particular, the inlet boundary condition is crucial: it supplies the impulsion to the system and receives the reflected backward waves created by the distal network. Some aspects of this boundary condition need to be properly defined such as the treatment of backward waves (reflected or absorbed) and the value of the imposed hemodynamic wave (total or forward component). Most authors prescribe as inlet boundary condition (BC) the total measured variable (pressure, velocity or flow rate) in a reflective way. We show that with this type of inlet boundary condition, the model does not produce physiological waveforms. We suggest instead to prescribe only the forward component of the prescribed variable in an absorbing way. In this way, the computed reflected waves superpose with the prescribed forward waves to produce the total wave at the inlet. In this work, different inlet boundary conditions are implemented and compared for a 1D blood flow model. We test our boundary conditions on a truncated arterial model presented in the literature as well as on a patient-specific lower-limb model of a femoral bypass. We show that with this new boundary condition, a much better fitting is observed on the shape and intensity of the simulated pressure and velocity waves.