Nikos Stergiopulos

Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation

A three-dimensional finite element model of the carotid artery bifurcation was constructed in order to determine the stress field and assess the modification of the stress field when residual strain is taken into account. Residual strain in the carotid bifurcation was characterized by experimental observations. According to these observations, a geometrical model of the carotid artery was constructed to exhibit a state free of strain. Appropriate boundary conditions were applied to yield the correct geometry in the unloaded state, and physiological levels of pressure and axial stretching were applied. The model took into account the varying thickness of the arterial wall along the bifurcation. For modeling purposes, the material was considered to be hyperelastic, incompressible, homogenous and isotropic. For comparison, a similar model of the carotid artery which does not include the effects of residual strain was also created. The results demonstrate that in the model of the carotid artery bifurcation with residual strain, the distribution of maximum principal stress along the inner wall and the circumferential stress throughout the wall is much more uniform than in the model without residual strain. The ratio between the stress at the inner and the outer walls is highest at the lateral wall of the carotid sinus; this is the same location known to be a site of low and oscillatory fluid wall shear stress, and the principal location of early intimal thickening. These results suggest that the localization of atherosclerosis in the carotid artery may be due to local variations in both fluid wall shear stress and solid wall stress.

Total arterial inertance as the fourth element of the windkessel model

In earlier studies we found that the three-element windkessel, although an almost perfect load for isolated heart studies, does not lead to accurate estimates of total arterial compliance. To overcome this problem, we introduce an inertial term in parallel with the characteristic impedance. In seven dogs we found that ascending aortic pressure could be predicted better from aortic flow by using the four-element windkessel than by using the three-element windkessel: the root-mean-square errors and the Akaike information criterion and Schwarz criterion were smaller for the four-element windkessel. The three-element windkessel overestimated total arterial compliance compared with the values derived from the area and the pulse pressure method ( P = 0.0047, paired t-test), whereas the four-element windkessel compliance estimates were not different ( P = 0.81). The characteristic impedance was underestimated using the three-element windkessel, whereas the four-element windkessel estimation differed marginally from the averaged impedance modulus at high frequencies ( P = 0.0017 and 0.031, respectively). When applied to the human, the four-element windkessel also was more accurate in these same aspects. Using a distributed model of the systemic arterial tree, we found that the inertial term results from the proper summation of all local inertial terms, and we call it total arterial inertance. We conclude that the fourelement windkessel, with all its elements having a hemodynamic meaning, is superior to the three-element windkessel as a lumped-parameter model of the entire systemic tree or as a model for parameter estimation of vascular properties.In earlier studies we found that the three-element windkessel, although an almost perfect load for isolated heart studies, does not lead to accurate estimates of total arterial compliance. To overcome this problem, we introduce an inertial term in parallel with the characteristic impedance. In seven dogs we found that ascending aortic pressure could be predicted better from aortic flow by using the four-element windkessel than by using the three-element windkessel: the root-mean-square errors and the Akaike information criterion and Schwarz criterion were smaller for the four-element windkessel. The three-element windkessel overestimated total arterial compliance compared with the values derived from the area and the pulse pressure method (P = 0.0047, paired t-test), whereas the four-element windkessel compliance estimates were not different (P = 0.81). The characteristic impedance was underestimated using the three-element windkessel, whereas the four-element windkessel estimation differed marginally from the averaged impedance modulus at high frequencies (P = 0.0017 and 0.031, respectively). When applied to the human, the four-element windkessel also was more accurate in these same aspects. Using a distributed model of the systemic arterial tree, we found that the inertial term results from the proper summation of all local inertial terms, and we call it total arterial inertance. We conclude that the fourelement windkessel, with all its elements having a hemodynamic meaning, is superior to the three-element windkessel as a lumped-parameter model of the entire systemic tree or as a model for parameter estimation of vascular properties.

Use of pulse pressure method for estimating total arterial compliance in vivo

We determined total arterial compliance from pressure and flow in the ascending aorta of seven anesthetized dogs using the pulse pressure method (PPM) and the decay time method (DTM). Compliance was determined under control and during occlusion of the aorta at four different locations (iliac, renal, diaphragm, and proximal descending thoracic aorta). Compliance of PPM gave consistently lower values (0.893 +/- 0.015) compared with the compliance of DTM (means +/- SE; r = 0.989). The lower compliance estimates by the PPM can be attributed to the difference in mean pressures at which compliance is determined (mean pressure, 81.0 +/- 3.6 mmHg; mean diastolic pressure, over which the DTM applies, 67.0 +/- 3.6 mmHg). Total arterial compliance under control conditions was 0.169 +/- 0. 007 ml/mmHg. Compliance of the proximal aorta, obtained during occlusion of the proximal descending aorta, was 0.100 +/- 0.007 ml/mmHg. Mean aortic pressure was 80.4 +/- 3.6 mmHg during control and 102 +/- 7.7 mmHg during proximal descending aortic occlusion. From these results and assuming that upper limbs and the head contribute as little as the lower limbs, we conclude that 60% of total arterial compliance resides in the proximal aorta. When we take into account the inverse relationship between pressure and compliance, the contribution of the proximal aorta to the total arterial compliance is even more significant.We determined total arterial compliance from pressure and flow in the ascending aorta of seven anesthetized dogs using the pulse pressure method (PPM) and the decay time method (DTM). Compliance was determined under control and during occlusion of the aorta at four different locations (iliac, renal, diaphragm, and proximal descending thoracic aorta). Compliance of PPM gave consistently lower values (0.893 ± 0.015) compared with the compliance of DTM (means ± SE; r = 0.989). The lower compliance estimates by the PPM can be attributed to the difference in mean pressures at which compliance is determined (mean pressure, 81.0 ± 3.6 mmHg; mean diastolic pressure, over which the DTM applies, 67.0 ± 3.6 mmHg). Total arterial compliance under control conditions was 0.169 ± 0.007 ml/mmHg. Compliance of the proximal aorta, obtained during occlusion of the proximal descending aorta, was 0.100 ± 0.007 ml/mmHg. Mean aortic pressure was 80.4 ± 3.6 mmHg during control and 102 ± 7.7 mmHg during proximal descending aortic occlusion. From these results and assuming that upper limbs and the head contribute as little as the lower limbs, we conclude that 60% of total arterial compliance resides in the proximal aorta. When we take into account the inverse relationship between pressure and compliance, the contribution of the proximal aorta to the total arterial compliance is even more significant.

Shear stress, vascular remodeling and neointimal formation

The role of shear stress in atherosclerosis has been well documented. However, its role in restenosis was underexposed. In this paper a novel in vivo measuring technique and several of its applications related to restenosis will be described. The technique consists of a combination of 3D reconstruction of blood vessels and computational fluid dynamics (CFD). The 3D imaging techniques use either of 3D intravascular ultrasound (IVUS) as a stand-alone technique or a fusion of biplane angiography and IVUS (ANGUS). CFD is applied in order to relate local shear stress distribution to the morphology of the vessel wall. In the applications of these techniques it will be demonstrated that shear stress plays a role in the prediction of neointimal formation in in-stent restenosis and in vascular remodeling after balloon angioplasty. Attempts to locally increase shear stress by a newly developed flow divider indicate that shear stress reduce in-stent neointimal formation by 50%.

A model for geometric and mechanical adaptation of arteries to sustained hypertension

This study aimed to model phenomenologically the dynamics of arterial wall remodeling under hypertensive conditions. Sustained hypertension was simulated by a step increase in blood pressure. The arterial wall was considered to be a thick-walled tube made of nonlinear elastic incompressible material. Remodeling rate equations were postulated for the evolution of the geometric dimensions of the hypertensive artery at the zero-stress state, as well as for one of the material constants in the constitutive equations. The driving stimuli for the geometric adaptation are the normalized deviations of wall stresses from their values under normotensive conditions. The geometric dimensions are modulated by the evolution of the deformed inner radius, which serves to restore the level of the flow-induced shear stresses at the arterial endothelium. Mechanical adaptation is driven by the difference between the area compliance under hypertensive and normotensive conditions. The predicted time course of the geometry and mechanical properties of arterial wall are in good qualitative agreement with published experimental findings. The model predicts that the geometric adaptation maintains the stress distribution in arterial wall to its control level, while the mechanical adaptation restores the normal arterial function under induced hypertension.

Validation of a patient-specific one-dimensional model of the systemic arterial tree

The aim of this study is to develop and validate a patient-specific distributed model of the systemic arterial tree. This model is built using geometric and hemodynamic data measured on a specific person and validated with noninvasive measurements of flow and pressure on the same person, providing thus a patient-specific model and validation. The systemic arterial tree geometry was obtained from MR angiographic measurements. A nonlinear viscoelastic constitutive law for the arterial wall is considered. Arterial wall distensibility is based on literature data and adapted to match the wave propagation velocity of the main arteries of the specific subject, which were estimated by pressure waves traveling time. The intimal shear stress is modeled using the Witzig-Womersley theory. Blood pressure is measured using applanation tonometry and flow rate using transcranial ultrasound and phase-contrast-MRI. The model predicts pressure and flow waveforms in good qualitative and quantitative agreement with the in vivo measurements, in terms of wave shape and specific wave features. Comparison with a generic one-dimensional model shows that the patient-specific model better predicts pressure and flow at specific arterial sites. These results obtained let us conclude that a patient-specific one-dimensional model of the arterial tree is able to predict well pressure and flow waveforms in the main systemic circulation, whereas this is not always the case for a generic one-dimensional model.

Estimation of local aortic elastic properties with MRI

Aortic compliance and pulse wave velocity (PWV) are important determiners of heart load, and are clinically useful indices of cardiovascular risk. Most direct methods to derive them require invasive pressure measurement. In this work a noninvasive technique to evaluate aortic compliance and PWV using MRI is proposed. MRI magnitude and phase images to measure area and flow in the ascending aorta were acquired in a group of 13 young healthy subjects. Assuming that the early systolic part of the wave was unidirectional and reflectionless, PWV was determined as the ratio between flow and area variations at early systole. Our results were compared to pulse wave velocities derived from a direct transit time, and to one using ascending aortic area and peripheral brachial pulse pressure. The new method proved to be accurate and in good agreement with the transit time method, as well as with previously published results. Magn Reson Med 47:649–654, 2002.

Augmentation of Wall Shear Stress Inhibits Neointimal Hyperplasia After Stent Implantation Inhibition Through Reduction of Inflammation

Background—Low wall shear stress (WSS) increases neointimal hyperplasia (NH) in vein grafts and stents. We studied the causal relationship between WSS and NH formation in stents by locally increasing WSS with a flow divider (Anti-Restenotic Diffuser, Endoart SA) placed in the center of the stent. Methods and Results—In 9 rabbits fed a high-cholesterol diet for 2 months to induce endothelial dysfunction, 18 stents were implanted in the right and left external iliac arteries (1 stent per vessel). Lumen diameters were measured by quantitative angiography before and after implantation and at 4-week follow-up, at which time, macrophage accumulation and interruption of the internal elastic lamina was determined. Cross sections of stent segments within the ARED (S+ARED), outside the ARED (S[minus]ARED), and in corresponding segments of the contralateral control stent (SCTRL) were analyzed. Changes in WSS induced by the ARED placement were derived by computational fluid dynamics. Computational fluid dynamics analysis demonstrated that WSS increased from 0.38 to 0.82 N/m2 in the S+ARED immediately after ARED placement. This augmentation of shear stress was accompanied by (1) lower mean late luminal loss by quantitative angiography ([minus]0.23±0.22 versus [minus]0.58±0.30 mm, P =0.02), (2) reduction in NH (1.48±0.58, 2.46±1.25, and 2.36±1.13 mm2, P <0.01, respectively, for S+ARED, S[minus]ARED, and SCTRL), and (3) a reduced inflammation score and a reduced injury score. Increments in shear stress did not change the relationship between injury score and NH or between inflammation score and NH. Conclusions—The newly developed ARED flow divider significantly increases WSS, and this local increment in WSS is accompanied by a local reduction in NH and a local reduction in inflammation and injury. The present study is therefore the first to provide direct evidence for an important modulating role of shear stress in in-stent neointimal hyperplasia.

Effect of Flow Diverter Porosity on Intraaneurysmal Blood Flow

AbstractBackground and Purpose:Growth and rupture, the two events that dominate the evolution of an intracranial aneurysm, are both dependent on intraaneurysmal flow. Decrease of intraaneurysmal flow is considered an attractive alternative for treating intracranial aneurysms by minimally invasive techniques. Such modification can be achieved by inserting stents or flow diverters alone. In the present paper, the effect of different commercial and innovative flow diverters’ porosity was studied in intracranial aneurysm models.Material and Methods:Single and stent-in-stent combination of Neuroform II as well as single and stent-in-stent combination of a new innovative, low-porosity, intracranial stent device (D1, D2, D1 + D2) were inserted in models of intracranial aneurysms under shear-driven flow and inertia-driven flow configurations. Steady and pulsating flow rates were applied using a blood-like fluid. Particle image velocimetry was used to measure velocity vector fields in the aneurysm midplane along the vessel axis. Flow and vorticity patterns, velocity and vorticity magnitudes were quantified and their value compared with the same flows in absence of the flow diverter.Results:In absence of flow diverters, a solid-like rotation could be observed in both shear-driven and inertia-driven models under steady and pulsatile flow conditions. The flow effects due to the insertion of low-porous devices such as D1 or D2 provoked a complete alteration of the flow patterns and massive reduction of velocity or vorticity magnitudes, whereas the introduction of clinically adopted high-porous devices provoked less effect in the aneurysm cavity. As expected, results showed that the lower the porosity the larger the reduction in velocity and vorticity within the aneurysm cavity. The lowest-porosity device combination (D1 and D2) reached an averaged reduction of flow parameters of 80% and 88% under steady and pulsatile flow conditions, respectively. The reduction in mean velocity and vorticity was much more significant in the shear-driven flows as compared to the inertia-driven flows.Conclusion:Although device porosity is the main parameter influencing flow reduction, other parameters such as device design and local flow conditions may influence the level of flow reduction within intracranial aneurysms.ZusammenfassungHintergrund und Ziel:Die zwei wichtigsten Faktoren für die Entwicklung intrazerebraler Aneurysmen, nämlich Wachstum und Ruptur, hängen vom intraaneurysmatischen Blutfluss ab. Eine Verminderung des intraaneurysmatischen Blutflusses durch minimalinvasive Techniken wird als attraktive Behandlungsmethode erachtet. Eine solche Modifikation des Blutflusses kann durch das Einbringen eines Stents oder „flow diverter“ allein erzielt werden. In der vorliegenden Arbeit untersuchten die Autoren den Effekt der Porosität verschiedener handelsüblicher und innovativer „flow diverters“ an Modellen intrakranieller Aneurysmen.Material und Methodik:Sowohl einzelne oder Stent-in-Stent-Kombinationen des Neuroform II (NF) als auch einzelne oder Stent-in-Stent-Kombinationen von neuen innovativen, niedrigporösen intrakraniellen Stents (D1, D2, D1 + D2) wurden in Modellen intrakranieller Aneurysmen mit Eigenschaften von „shear-driven“ und „inertia-driven“ Fluss platziert. Flächen mit Geschwindigkeitsvektoren in der mittleren Ebene des Aneurysmas parallel zur Achse des Gefäßes wurden mit Hilfe der „particle image velocimetry“ (PIV) ermittelt. Eigenschaften von Fluss und Verwirbelungen, Geschwindigkeit und Ausmaß von Verwirbelungen wurden gemessen und mit Messwerten des gleichen Modells ohne „flow diverter“ verglichen.Ergebnisse:Ohne „flow diverter“ konnte eine beständige Rotation in beiden – „shear-driven“ und „inertia-driven“ – Flussmodellen beobachtet werden. Die Auswirkungen nach Platzierung eines niedrigporösen Modells wie D1 oder D2 riefen eine komplette Änderung der Flusseigenschaften und eine massive Verringerung der Geschwindigkeit und des Ausmaßes von Verwirbelungen hervor, wohingegen die Platzierung klinisch angewendeter hochporöser Modelle geringere Auswirkungen auf die Kavität des Aneurysmas hatte. Erwartungsgemäß haben die Ergebnisse gezeigt: Je kleiner die Porosität ist, desto größer sind die Auswirkungen auf Blutflussgeschwindigkeit und Verwirbelungen im Aneurysma. Die Kombination mit der geringsten Porosität (D1 und D2) erzielte eine durchschnittliche Reduktion der Flussparameter um 80% bzw. 88% bei konstanten und pulsatilen Flüssen. Die Verminderung von mittlerer Geschwindigkeit und von Verwirbelungen war beim „shear-driven“ Fluss deutlich signifikanter als beim „inertia-driven“ Fluss.Schlussfolgerung:Obwohl die Porosität der wichtigste Parameter zur Senkung des Flusses ist, können andere Parameter wie das Design des jeweiligen Modells oder lokale Flusseigenschaften die Wirksamkeit der Flussreduktion in intrakraniellen Aneurysmen beeinflussen.

Physical basis of pressure transfer from periphery to aorta: a model-based study

We propose a new method to derive aortic pressure from peripheral pressure and velocity by using a time domain approach. Peripheral pressure is separated into its forward and backward components, and these components are then shifted with a delay time, which is the ratio of wave speed and distance, and added again to reconstruct aortic pressure. We tested the method on a distributed model of the human systemic arterial tree. From carotid and brachial artery pressure and velocity, aortic systolic and diastolic pressure could be predicted within 0.3 and 0.1 mmHg and 0.4 and 1.0 mmHg, respectively. The central aortic pressure wave shape was also predicted accurately from carotid and brachial pressure and velocity (root mean square error: 1.07 and 1.56 mmHg, respectively). The pressure transfer function depends on the reflection coefficient at the site of peripheral measurement and the delay time. A 50% decrease in arterial compliance had a considerable effect on reconstructed pressure when the control transfer function was used. A 70% decrease in arm resistance did not affect the reconstructed pressure. The transfer function thus depends on wave speed but has little dependence on vasoactive state. We conclude that central aortic pressure and the transfer function can be derived from peripheral pressure and velocity.