Elsevier

Journal of Biomechanics

Volume 48, Issue 4, 26 February 2015, Pages 585-591
Journal of Biomechanics

Unraveling the relationship between arterial flow and intra-aneurysmal hemodynamics

https://doi.org/10.1016/j.jbiomech.2015.01.016Get rights and content

Abstract

Arterial flow rate affects intra-aneurysmal hemodynamics but it is not clear how their relationship is. This uncertainty hinders the comparison among studies, including clinical evaluations, like a pre- and post-treatment status, since arterial flow rates may differ at each time acquisition. The purposes of this work are as follows: (1) To study how intra-aneurysmal hemodynamics changes within the full physiological range of arterial flow rates. (2) To provide characteristic curves of intra-aneurysmal velocity, wall shear stress (WSS) and pressure as functions of the arterial flow rate. Fifteen image-based aneurysm models were studied using computational fluid dynamics (CFD) simulations. The full range of physiological arterial flow rates reported in the literature was covered by 11 pulsatile simulations. For each aneurysm, the spatiotemporal-averaged blood flow velocity, WSS and pressure were calculated. Spatiotemporal-averaged velocity inside the aneurysm linearly increases as a function of the mean arterial flow (minimum R2>0.963). Spatiotemporal-averaged WSS and pressure at the aneurysm wall can be represented by quadratic functions of the arterial flow rate (minimum R2>0.996). Quantitative characterizations of spatiotemporal-averaged velocity, WSS and pressure inside cerebral aneurysms can be obtained with respect to the arterial flow rate. These characteristic curves provide more information of the relationship between arterial flow and aneurysm hemodynamics since the full range of arterial flow rates is considered. Having these curves, it is possible to compare experimental studies and clinical evaluations when different flow conditions are used.

Introduction

Hemodynamics influences the arterial wall behavior and regulates the blood coagulation process (Wootton and Ku, 1999, Reneman et al., 2006). In cerebral aneurysms, hemodynamics has been related to their initiation, development and rupture (Gao et al., 2008, Xiang et al., 2011, Meng et al., 2013) and is known to affect endovascular therapies, such as flow divertion (Mut et al., 2014a, Pereira et al., 2013a).

To understand intra-aneurysmal hemodynamics, vascular morphology and arterial flow conditions have to be considered. Morphology defines unique characteristics of the studied system (arterial calibers, aneurysm size and shape, etc.), those measurable from medical images. Several morphological features have been described like size, shape, aspect ratio, and correlated with aneurysmal rupture (Ujiie et al., 2001, Xiang et al., 2011). In contrast, it is not clear how arterial flow conditions alter intra-aneurysmal hemodynamics.

Through computational fluid dynamics (CFD) simulations, it has been shown that intra-aneurysmal hemodynamics depends on the arterial flow rates. Inside aneurysms, flow patterns and quantitative variables, such as velocity and wall shear stress (WSS), vary if flow conditions change (Jiang and Strother, 2009, Marzo et al., 2011, McGah et al., 2014). Moreover, CFD-based studies have highlighted the importance of imposing patient-specific flow rates and have quantified the errors when derived boundary conditions are used (Marzo et al., 2011, McGah et al., 2014). Nevertheless, patient-specific measurements are limited to the temporal frame of the examination. In other words, patient-specific flow conditions are time-dependent measurements, because arterial flow rates change during patient׳s lifetime. An example of such flow rate variation is when resting or exercising (Poulin et al., 1999).

In the lack of flow measurements, a wide range of possible boundary conditions is available from the literature. Some of those conditions are based on the geometry, like an area–inflow relation (Cebral et al., 2008) or based on physiological conditions, like a WSS of 1.5 Pa at the inlet of the model (Reneman et al., 2006). Other flow conditions can be obtained from mean values over young and elder populations (Hoi et al., 2010, Ford et al., 2005). The variety of boundary conditions makes unfeasible the comparison among experimental studies, particularly those conducted with CFD.

Indeed, a better understanding of the relationship “arterial flow-aneurysm hemodynamics” is required. In clinical practice for example, the uncertainties in this relationship hinder the comparison among medical image sequences, since flow conditions may differ among image acquisition times (Chien and Viñuela, 2013, Pereira et al., 2013a). More precisely, an evaluation of endovascular device performance by functional imaging could be done during clinical interventions (Bonnefous et al., 2012), or to assess longitudinal studies with several follow-ups if the relationship arterial flow-aneurysm hemodynamics is known.

The purpose of this work is to unravel the relationship between arterial flow and intra-aneurysmal hemodynamics when the full physiological range of arterial flow rates is covered. Quantitative characterizations of the averaged intra-aneurysmal velocity, WSS and pressure are pursuit. A clear relationship “artery-aneurysm flow” allows the comparison among experimental studies and clinical observations under different flow conditions.

Section snippets

Materials

Fifteen aneurysms from ten patients were studied. All aneurysms were located in one of the internal carotid arteries (ICA), between the carotid siphon and the ICA bifurcation. Two aneurysms were terminal and 13 lateral. Depending or their size, four aneurysms were classified as small (size<3mm), five as medium (size between 3 mm and 5 mm) and six as large aneurysms (size>5mm). To visualize these aneurysms, volumetric images were acquired by an X-ray system (Allura Xper FD20 system of Philips

Results

Fig. 2A depicts temporal-averaged WSS distribution for 3 cases (3 aneurysms) for some Q¯s. Temporal-averaged WSS magnitude increases with Q¯ in all the vascular models, including the aneurysm walls. OSI distributions in 7 aneurysm models (3 cases) are shown in Fig. 2B. For these aneurysms, OSI seems to be stable from Q¯>Q¯3, excepting for terminal aneurysms (case 2). Maximum OSI values in case 10 were located around the aneurysm bleb.

Spatiotemporal-averaged variables (vel¯sa, WSS¯sa and pre¯sa

Discussion

The influence of the arterial flow rates on intra-aneurysmal hemodynamics was analyzed. vel¯sa, WSS¯sa and pre¯sa increase with higher flow rates (Fig. 2). Nevertheless, this study revealed that these variables can be characterized as functions of the arterial flow rate for each aneurysm. A good fitting (minimum R2>0.96) was found for all characteristic curves. These curves are generic and do not depend on the shape of the waveform.

vel¯sa linearly increases with arterial flow rate and can be

Conclusions

vel¯sa, WSS¯sa and pre¯sa can be characterized as functions of the mean arterial flow rate, which can be obtained with few measurements. Characterizing these variables within the full physiological range of flow rates provides a complete view of intra-aneurysmal hemodynamics compared to a single-flow condition assessment. These curves go beyond any patient-specific temporal-dependent flow conditions and provide a complete view for comparison of experimental and clinical studies under any

Conflict of interest statement

None declared.

Acknowledgments

Authors would like to thank the Department of Medical Imaging and Information Sciences, Interventional Neuroradiology Unit, University Hospitals of Geneva, Switzerland, for providing the medical images from which vascular models were extracted. Authors would like to thank Dr. Laurence Rouet and Dr. Cécile Dufour from Medisys – Philips Research Paris, France, for the revision of this paper.

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