頸動脈粥樣硬化斑塊形成與斑塊薄壁壓力之Vivo核磁共振為基礎之二維/三維流固耦合模型
J Biomech.Author manuscript; available in PMC 2009 January 1.Published in final edited form as:
http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=18191138]J Biomech. 2008; 41(4): 727–736.
Published online 2008 January 11.
doi: 10.1016/j.jbiomech.2007.11.026.
PMCID: PMC2291514
NIHMSID: NIHMS43308
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A Negative Correlation between Human Carotid Atherosclerotic Plaque Progression and Plaque Wall Stress: In Vivo MRI-Based 2D/3D FSI Models
Dalin Tang,1* Chun Yang,2 Sayan Mondal,1 Fei Liu,3 Gador Canton,3 Thomas S. Hatsukami,3,4 and Chun Yuan3 1 Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester, MA 01609
2 Mathematics Department, Beijing Normal University, Beijing, China
3 Deparment of Radiology, University of Washington, Seattle, WA 98195
4 Division of Vascular Surgery, University of Washington, Seattle, WA. 98195
*Corresponding author: Dalin Tang, Mathematical Sciences Department, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, Phone: 508-831-5332, fax: 508-831-5824, e-mail: dtang@wpi.edu
http://www.pubmedcentral.nih.gov/corehtml/pmc/pmcgifs/rt-arrow.gif The publisher's final edited version of this article is available at http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&retmode=ref&cmd=prlinks&id=18191138]J Biomech.
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Abstract
It is well accepted that atherosclerosis initiation and progression correlate positively with low and oscillating flow wall shear stresses (FSS). However, this mechanism cannot explain why advanced plaques continue to grow under elevated FSS conditions. In vivo magnetic resonance imaging (MRI)-based 2D/3D multi-component models with fluid-structure interactions (FSI, 3D only) for human carotid atherosclerotic plaques were introduced to quantify correlations between plaque progression measured by wall thickness increase (WTI) and plaque wall (structure) stress (PWS) conditions. A histologically validated multi-contrast MRI protocol was used to acquire multi-year in vivo MRI images. Our results using 2D models (200–700 data points/patient) indicated that 18 out of 21 patients studied showed significant negative correlation between WTI and PWS at time 2 (T2). The 95% confidence interval for the Pearson correlation coefficient is (−0.443, −0.246), p < 0.0001. Our 3D FSI model supported the 2D correlation results and further indicated that combining both plaque structure stress and flow shear stress gave better approximation results (PWS, T2: R2 = 0.279; FSS, T1: R2 = 0.276; Combining both: R2 = 0.637). These pilot studies suggest that both lower PWS and lower FSS may contribute to continued plaque progression and should be taken into consideration in future investigations of diseases related to atherosclerosis. Keywords: Plaque progression, blood flow, atherosclerosis, plaque rupture, fluid-structure interaction
1. Introduction
Atherosclerotic plaque progression are believed to be related to multiple factors such as mechanical forces, plaque morphology and inflammation, vessel remodeling, and blood conditions, chemical environment, and lumen surface condition (Friedman, 1987, 1993; Giddens et al., 1993; Ku, 1997; Ku et al., 1985; Naghavi et al., 2003a, 2003b; Ravn and Falk, 1999; Ross, 1993). The role of mechanical factors in plaque progression using sequential patient tracking data, however, has not been well documented. The governing mechanisms are not well understood. The difficulty is partially due to the fact that atherosclerosis is a slow process and patient-specific data showing plaque progression takes a long time to acquire. It has been well accepted that low and oscillating flow shear stresses correlate positively with intimal thickening and atherosclerosis progression (Friedman, 1987, 1993; Giddens et al., 1993; Ku et al., 1985, 1992). This “low shear stress” (LSS) hypothesis has influenced the atherogenesis research field considerably in recent years. However, as plaque progression continues, stenosis becomes more severe and lumen narrowing will eventually occur which are often associated with elevated high shear stress conditions (Tang et al., 2001, 2004a, 2005b). The LSS hypothesis cannot explain why intermediate and advanced plaques continue to grow under elevated high shear stress conditions. Several research groups reported findings controversial to the LSS hypothesis and suggested the growing importance of searching for other mechanical factors such as plaque wall (structure) stresses (PWS) and new hypotheses for mechanisms governing plaque progression process (Joshi et al., 2004; Wentzel et al., 2003, 2005). The purpose of this investigation is to quantify possible correlation between human carotid atherosclerotic plaque progression and PWS conditions by using 2D and 3D multi-component plaque models based on in vivo magnetic resonance images (MRI) data taken from patients at multiple time points. MRI-based atherosclerotic plaque models have been introduced by several groups (Holzapfel, 2002; Huang et al., 2001; Kaazempur-Mofrad et al., 2002; Long et al., 1997, 2000; Steinman et al, 2002) and our group (Tang et al., 2004b, 2005b). In this paper, both 2D and 3D models were solved by a commercial finite element package ADINA (ADINA R & D, Inc., Watertown, MA) to obtain plaque stress/strain conditions (Bathe, 1996; Bathe, 2002). Linear regression analysis was performed to quantify correlations between plaque maximum principal stress (Stress-P1) and plaque progression measured by wall thickness increase (WTI). Statistically significant negative correlations were found in 18 out of 21 patients studied.
2. Methods
2.1 In vivo Serial MRI Data Acquisition and Segmentation
To quantify possible correlations between plaque progression and selected mechanical factors, the first step was to scan patients with atherosclerotic plaques multiple times (serial MRI) to obtain plaque progression data. Serial MRI data of carotid atherosclerotic plaques from twenty-one (numbered as Y1–Y21; age: 54–84, mean: 70.6; 19 males, 2 females) were acquired by the University of Washington (UW) group using protocols approved by the University of Washington Institutional Review Board with informed consent obtained. Scan time intervals were 18 months for Y1–Y20 and 10 months for Y21. MRI scans were conducted on a GE SIGNA 1.5-T whole body scanner using an established protocol outlined in the paper by Yuan and Kerwin (Yuan and Kerwin, 2004). A custom-designed carotid phased-array surface coil was used for all scans. Multi-contrast images in T1, T2, proton density(PD), time-of-flight (TOF), and contrast-enhanced (CE) T1 weighted images of atherosclerotic plaques were generated to characterize plaque tissue composition and luminal and vessel wall morphology (Cai et al., 2002; Yuan and Kerwin, 2004; Yuan et al., 2001a, 2001b). The multi-contrast MRI techniques for human carotid imaging have been used and validated by histological data by Yuan and his group with several publications (Cai et al., 2002; Kerwin et al., 2003; Liu et al., 2006; Yuan and Kerwin, 2004; Yuan et al., 2001a, 2001b). A custom-designed computer package CASCADE (Computer-Aided System for Cardiovascular Disease Evaluation) developed by the Vascular Imaging Laboratory (VIL) at the University of Washington (UW) was used to perform image analysis and segmentation (Kerwin et al., 2003). Upon completion of a review, an extensive report was generated and segmented contour lines for different plaque components for each slice were stored for 2D/3D computational model reconstructions. Fig. 1 shows 10 (selected from 24) MRI slices (T1W) obtained from a human carotid plaque sample, the segmented contour plots, and the re-constructed 3D geometry. Figure 2 gives a sample plaque re-constructed from serial MRI data showing plaque progression. http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=2291514&blobname=nihms43308f1.gifFigure 1 In vivo 3D MRI images of a human carotid plaque and 3D reconstruction. (a) 10 (out of 24) MRI (T1) slices; (b) segmented contour plots; (c) re-constructed 3D plaque geometry
http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=2291514&blobname=nihms43308f2.gifFigure 2 A plaque sample showing progression. Red: lumen; Yellow: necrotic core; Dark blue: calcification; Light blue: vessel outer wall.
2.2 In Vivo MRI-Based Multi-Component Plaque Models
2D multi-component models were used in this paper because they were less labor-intensive and the stress results provided reasonable accuracy for our correlation analysis. All segmented 2D slices were read into ADINA input file, pixel by pixel. To get a starting geometry from the in vivo MRI data, the original in vivo geometry was reduced by 8–10% before the data was read into ADINA so that the actual in vivo shape could be recovered when initial axial pre-stretch and pressurization were applied. The reduction rate varied from patient to patient and was numerically determined for an optimal match with in vivo shape after pressurization. The 2D geometry was then divided into many "areas" so that mesh could be made to curve-fit plaque components in the vessel wall. Computational meshes were made under ADINA computing environment. Finer mesh was used at the thin cap and other places as needed. A 3D FSI model was developed using Y21 data for validation purpose and the 3D correlation results showed good agreement with 2D models (details given in 3.2).
For 2D and 3D solid models, both artery wall (normal tissue) and plaque components (calcification, lipid core, and others) were assumed to be hyperelastic, isotropic, incompressible and homogeneous. The nonlinear modified Mooney-Rivlin model was used to describe the material properties of the vessel wall and plaque components (Bathe, 2002; Huang et al., 2001; Tang et al., 2004b). The strain energy function is given by,
http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=2291514&blobtype=equ&blobname=M1
(1)
http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=2291514&blobtype=equ&blobname=M2
(2)
where I1 and I2 are the first and second strain invariants, C = = XTX is the right Cauchy-Green deformation tensor, X = = [∂xi/∂aj], (xi) is current position, (ai) is original position, ci and Di are material parameters chosen to match experimental measurements and current literatures (Humphrey, 2002; Kobayashi et al., 2003). For the 3D FSI model, the flow was assumed to be laminar, Newtonian, viscous and incompressible. The incompressible Navier-Stokes equations with arbitrary Lagrangian-Eulerian (ALE) formulation were used as the governing equations. No-slip conditions, natural traction equilibrium boundary conditions and continuity of displacement were assumed on all interfaces between all components and the interface between solid and fluid. Inlet and outlet were fixed in longitudinal (axial) direction, but allowed to expand/contract with flow otherwise. The complete FSI model is given below: http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=2291514&blobtype=equ&blobname=M3
(3)
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(10)
where standard notations were used (Tang et al., 2004b). Material stress-stretch curves for fibrous tissue (vessel), lipid pool, and calcifications, prescribed inlet and outlet pressure conditions and the corresponding flow rates obtained from the FSI model are given by Fig. 3. Patient-specific maximum and minimum pressure values (by arm prior to MRI scan) were used to adjust the profile in Fig. 3 for each patient studied. The inlet pressure was prescribed in the lumen for all 2D models. Stress-P1 and flow shear stress values corresponding to maximum pressure were used in the correlation analysis.
http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=2291514&blobname=nihms43308f3.gifFigure 3 Material curves and pressure conditions for the multi-component plaque model. (a) Stress-stretch curves derived from the modified Mooney-Rivlin model. The parameters are (c2 = 0 for all materials): vessel and fibrous tissue: c1 = 368000, D1 = 144000, (more ...)
2.3 Solution Methods
The 2D (solid only) and 3D FSI models were solved by ADINA. ADINA uses unstructured finite element methods for both fluid and solid models. Nonlinear incremental iterative procedures are used to handle fluid-structure interactions. The governing finite element equations for both solid and fluid models were solved by Newton-Raphson iteration method. More details of the computational models and solution methods can be found from Tang et al. (2004b), Yang et al. (2007) and Bathe (2002).
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