혈관 번역(한국어 원본)최근 computing resources and numerical algorithms의 발전에 힘입어 Fluid-Structure interaction (FSI)과 같은 coupled field에 대한 numerical analysis가 활발히 이뤄 지고 있다. FSI method는 fluid dynamics를 위한 CFD와 structural analysis를 위한 FEM을 동시에 사용하는 방법으로 structure의 motion과 flow의 characteristics를 함께 고려하는 analysis에 적합하며, 특히 structure가 유연하고 structure의 motion이 flow에 미치는 영향이 클수록 그 활용도가 높아진다. American Heart Association의 보고에 따르면 blood vessel은 rigid body가 아닌 flexible body와 유사하며 carotid artery의 경우 약 3~15%정도의 luminal strain이 발생한다(Bella et al., 1999). 또한 Caro et al. (1974)의 cardiovascular physiology research에 의하면 aorta는 elastic body와 유사한 behavior를 보이며 elastic modulus는 약 0.2~1.2 MPa 정도의 range를 가지는 것으로 보고했다. 이처럼 FSI method는 blood vessel과 같이 유연한 structure와 blood flow의 characteristics를 동시에 고려해야 하는 analysis에서 고유한 강점을 가지며 carotid artery, abdominal aortas, cerebral aneurysms, and coronary artery등에서 이를 이용한 연구 또한 활발히 진행되고 있다(Figueroa et al., 2006), (Torri et al., 2006), (Koshiba et al., 2007), (Scotti et al., 2008), (Tezduyar et al., 2008), (Zeng et al., 2008).
Arterial biomechanics에서 FSI method을 적용하기 위해서는 blood와 vessel의 geometry, material properties, grid system, boundary condition 산정 등과 같이 합리적인 analysis model의 생성이 요구된다. Blood vessel의 geometry는 일반적으로 개개인의 MRI나 CT사진을 이용하여 생성하거나 (Tang et al. 2004a, 2004b, 2005), (Kock et al., 2008) generalized model을 이용하여 (Tada and Tarbell, 2005) numerical analysis를 수행하며 blood flow는 MRI 등으로 measurement하거나 이를 모사한 pulsatile을 사용하는 것이 일반적이다(Kim et al., 2008), (Gijsen et al., 1999), (Leung et al., 2006).
Blood vessel의 material properties의 경우 elastic model 이나 hyperealstic model을 이용한 연구가 활발히 진행되고 있다. Perktold and Rappitsch (1995)는 0.361 MPa의 elastic modulus를 적용하여 carotid artery bifurcation에서 flow characteristics를 연구했으며 이를 통해 bifurcation에서 radius 대비 최대 16% displacement가 발생하고 apex region에 maximum stress가 발생한다고 보고했다. 또한 Zhao et al. (2002)은 MRI를 이용하여 생성한 5가지 carotid bifurcation model에 0.24~0.43 MPa의 elastic modulus를 적용시켜 연구를 수행하였으며 연구 결과로 모든 경우에서 atherosclerotic plaque가 생긴 부분에서 low wall shear stress and high mechanical stress가 함께 발생한다고 보고했다. Tada and Tarbell. (2005)은 elastic modulus가 0.5 MPa인 common carotid bifurcation에서 stress phase angle과 shear stress의 relationship을 연구하였으며 plaque에서 circumferential stress/strain (CS)과 fluid wall shear stress (WSS)사이에 large negative phase angle이 나타난다고 보고했다.
Blood vessel을 hyperelasticity 특성을 가진 model로 각정한 경우, Younis et al. (2004) studied the inter-individual variations in flow dynamics and wall mechanics at the carotid artery bifurcation, and its effects on atherogenesis, in three healthy humans. 여기서 vessel wall은 strain-density function을 이용하여 모사하였으며, 연구 결과로 largest contiguous region of low WSS는 carotid bulb에서 나타나며 cyclic strain (CS)은 apex에서 최대로 발생하며 wall distensibility 는 oscillatory shear index (OSI) 의 effect를 받는다고 보고했다. 또한 Tang et al. (2004a, b), Gao and Long. (2008)는 Mooney-Rivlin model을 이용하여 stenosis과 lipid pool을 고려한 atherosclerotic plaques 연구를 수행하였으며 Leach et al. (2009) 는 Demiray-type strain energy density function을 이용하여 arterial wall을 모사하여 two-stage approach를 통해 효율적으로 atherosclerotic arteries의 image-based FSI model을 생성할 수 있다고 보고했다. |
혈관 번역(영어 번역본)Aided by advances in computing resources and numerical algorithms, many recent studies performing numerical analysis on coupled fields, such as fluid-structure interaction (FSI), have been produced. The FSI method simultaneously uses CFD and FEM for fluid dynamics and structural analysis respectively. It is suitable for analyses that consider both the motion of structures and flow characteristics, and especially useful when the structure is flexible and the impact of structural motion on flow is large. According the study by the American Heart Association, blood vessels are closer to flexible bodies than to rigid bodies, and in the case of the carotid artery, there is a luminal strain of approximately 3 to 15% (Bella et al., 1999). In addition, Caro et al (1974) have reported in their cardiovascular physiological research that the aorta shows behavior resembling that of an elastic body, with the elastic modulus range of 0.2 to 1.2 MPa. As the FSI method is particularly well-suited for the analysis of flexible structures such as blood vessels where both structural and blood flow characteristics must be considered, there have been a number of recent studies using this method on carotid artery, abdominal aortas, cerebral aneurysms, and coronary artery (Figueroa et al., 2006; Torri et al., 2006; Koshiba et al., 2007; Scotti et al., 2008; Tezduyar et al., 2008; Zeng et al., 2008).
In order to apply the FSI method on arterial biomechanics, rational analytical models on material properties, grid system, boundary conditions of blood and vessel are required. The geometry of blood vessel is usually acquired through MRI and CT images of individuals (Tang et al. 2004a, 2004b, 2005; Kock et al., 2008), or through numerical analysis of generalized models (Tada and Tarbell, 2005). Blood flow is typically measured using MRI or modeled using pulsatiles (Kim et al., 2008; Gijsen et al., 1999; Leung et al., 2006).
There is ongoing research on the material properties of blood vessels, using elastic models and hyperelastic models. Perktold and Rappitsch (1995) studied flow characteristics in carotid artery bifurcation, applying the elastic modulus of 0.361 MPa, and found that there was a maximum displacement of 16% from the radius in bifurcation, and that the maximum stress occurred in the apex region. Zhao et al. (2002) conducted a study applying elastic modulus of 0.24-0.43 MPa on 5 carotid bifurcation models acquired using MRI, and they reported that in all cases low wall shear stress and high mechanical stress occurred together where there was atherosclerotic plaque. Tada and Tarbell (2005) the relationship between stress phase angle and shear stress in common carotid bifurcation with an elastic modulus of 0.5 MPa, and found that large negative phase angles appeared between circumferential stress/strain (CS) and fluid wall shear stress (WSS) in plaques.
Among the cases where hyperelastic models were used for blood vessels, Younis et al. (2004) studied the inter-individual variations in flow dynamics and wall mechanics in carotid artery bifurcation and its effects on altherogenesis in three healthy human subjects. Younis et al. used the strain-density function to model vessel walls, and reported that the largest contiguous region of low WSS occurred at the carotid bulb and the highest cyclic strain (CS) at the apex. They also found that wall distensibility was affected by oscillatory shear index (OSI). Tang et al. (2004a, 2004b), and Gao and Long (2008) investigated atherosclerotic plaques using the Mooney-Rivlin model to take stenosis and lipid pool into account. Leach et al. (2009) used the Demiray-type strain energy density function to model arterial walls to construct efficiently an image-based FSI model of atherosclerotic arteries through a two-stage approach. |
