Tong Luo

Microstructural constitutive model of active coronary media.

Although vascular smooth muscle cells (VSMCs) are pivotal in physiology and pathology, there is a lack of detailed morphological data on these cells. The objective of this study was to determine dimensions (width and length) and orientation of swine coronary VSMCs and to develop a microstructural constitutive model of active media. The dimensions, spatial aspect ratio and orientation angle of VSMCs measured at zero-stress state were found to follow continuous normal (or bimodal normal) distributions. The VSMCs aligned off circumferential direction of blood vessels with symmetrical polar angles 18.7° ± 10.9°, and the local VSMC deformation was affine with tissue-level deformation. A microstructure-based active constitutive model was developed to predict the biaxial vasoactivity of coronary media, based on experimental measurements of geometrical and deformation features of VSMCs. The results revealed that the axial active response of blood vessels is associated with multi-axial contraction as well as oblique VSMC arrangement. The present morphological database is essential for developing accurate structural models and is seminal for understanding the biomechanics of muscular vessels.

Simplified Models of Non-Invasive Fractional Flow Reserve Based on CT Images.

Invasive fractional flow reserve (FFR) is the gold standard to assess the functional coronary stenosis. The non-invasive assessment of diameter stenosis (DS) using coronary computed tomography angiography (CTA) has high false positive rate in contrast to FFR. Combining CTA with computational fluid dynamics (CFD), recent studies have shown promising predictions of FFRCT for superior assessment of lesion severity over CTA alone. The CFD models tend to be computationally expensive, however, and require several hours for completing analysis. Here, we introduce simplified models to predict noninvasive FFR at substantially less computational time. In this retrospective pilot study, 21 patients received coronary CTA. Subsequently a total of 32 vessels underwent invasive FFR measurement. For each vessel, FFR based on steady-state and analytical models (FFRSS and FFRAM, respectively) were calculated non-invasively based on CTA and compared with FFR. The accuracy, sensitivity, specificity, positive predictive value and negative predictive value were 90.6% (87.5%), 80.0% (80.0%), 95.5% (90.9%), 88.9% (80.0%) and 91.3% (90.9%) respectively for FFRSS (and FFRAM) on a per-vessel basis, and were 75.0%, 50.0%, 86.4%, 62.5% and 79.2% respectively for DS. The area under the receiver operating characteristic curve (AUC) was 0.963, 0.954 and 0.741 for FFRSS, FFRAM and DS respectively, on a per-patient level. The results suggest that the CTA-derived FFRSS performed well in contrast to invasive FFR and they had better diagnostic performance than DS from CTA in the identification of functionally significant lesions. In contrast to FFRCT, FFRSS requires much less computational time.

IVUS Validation of Patient Coronary Artery Lumen Area Obtained from CT Images

Aims Accurate computed tomography (CT)-based reconstruction of coronary morphometry (diameters, length, bifurcation angles) is important for construction of patient-specific models to aid diagnosis and therapy. The objective of this study is to validate the accuracy of patient coronary artery lumen area obtained from CT images based on intravascular ultrasound (IVUS). Methods and Results Morphometric data of 5 patient CT scans with 11 arteries from IVUS were reconstructed including the lumen cross sectional area (CSA), diameter and length. The volumetric data from CT images were analyzed at sub-pixel accuracy to obtain accurate vessel center lines and CSA. A new center line extraction approach was used where an initial estimated skeleton in discrete value was obtained using a traditional thinning algorithm. The CSA was determined directly without any circular shape assumptions to provide accurate reconstruction of stenosis. The root-mean-square error (RMSE) for CSA and diameter were 16.2% and 9.5% respectively. Conclusions The image segmentation and CSA extraction algorithm for reconstruction of coronary arteries proved to be accurate for determination of vessel lumen area. This approach provides fundamental morphometric data for patient-specific models to diagnose and treat coronary artery disease.

Hemodynamic analysis of patient‐specific coronary artery tree

Local hemodynamic parameters, such as wall shear stress (WSS), oscillatory shear index and relative resident time (RRT), have been linked to coronary plaque initiation and progression. In this study, a left coronary artery tree model was reconstructed from computed tomography angiography images of a patient with multiple stenoses. The geometry of the coronary artery tree model was virtually restored by eliminating the lesions, essentially re-creating the virtually healthy artery anatomy. Using numerical simulations, flow characteristics and hemodynamic parameter distributions in the stenosed and virtually healthy models were investigated. In the virtually healthy artery model, disturbed flows were found at four locations, prone to initialization of plaque formation. Low WSS and high RRT were exhibited in three of the four locations, and high WSS and low RRT were exhibited in the fourth. These findings suggest that coronary plaque is more likely to form in locations with disturbed flow conditions characterized by low WSS and high RRT or high WSS and low RRT. In addition, clinical index of fractional flow reserve was found to significantly correlate with blood flow rate, rather than anatomic parameters, such as diameter stenosis, which implied the importance of hemodynamic environment in stenosis formation.

Mild anastomotic stenosis in patient-specific CABG model may enhance graft patency: a new hypothesis.

It is well known that flow patterns at the anastomosis of coronary artery bypass graft (CABG) are complex and may affect the long-term patency. Various attempts at optimal designs of anastomosis have not improved long-term patency. Here, we hypothesize that mild anastomotic stenosis (area stenosis of about 40–60%) may be adaptive to enhance the hemodynamic conditions, which may contribute to slower progression of atherosclerosis. We further hypothesize that proximal/distal sites to the stenosis have converse changes that may be a risk factor for the diffuse expansion of atherosclerosis from the site of stenosis. Twelve (12) patient-specific models with various stenotic degrees were extracted from computed tomography images using a validated segmentation software package. A 3-D finite element model was used to compute flow patterns including wall shear stress (WSS) and its spatial and temporal gradients (WSS gradient, WSSG, and oscillatory shear index, OSI). The flow simulations showed that mild anastomotic stenosis significantly increased WSS (>15 dynes⋅cm−2) and decreased OSI (<0.02) to result in a more uniform distribution of hemodynamic parameters inside anastomosis albeit proximal/distal sites to the stenosis have a decrease of WSS (<4 dynes⋅cm−2). These findings have significant implications for graft adaptation and long-term patency.

3D Reconstruction of Coronary Artery Vascular Smooth Muscle Cells.

Aims The 3D geometry of individual vascular smooth muscle cells (VSMCs), which are essential for understanding the mechanical function of blood vessels, are currently not available. This paper introduces a new 3D segmentation algorithm to determine VSMC morphology and orientation. Methods and Results A total of 112 VSMCs from six porcine coronary arteries were used in the analysis. A 3D semi-automatic segmentation method was developed to reconstruct individual VSMCs from cell clumps as well as to extract the 3D geometry of VSMCs. A new edge blocking model was introduced to recognize cell boundary while an edge growing was developed for optimal interpolation and edge verification. The proposed methods were designed based on Region of Interest (ROI) selected by user and interactive responses of limited key edges. Enhanced cell boundary features were used to construct the cell’s initial boundary for further edge growing. A unified framework of morphological parameters (dimensions and orientations) was proposed for the 3D volume data. Virtual phantom was designed to validate the tilt angle measurements, while other parameters extracted from 3D segmentations were compared with manual measurements to assess the accuracy of the algorithm. The length, width and thickness of VSMCs were 62.9±14.9μm, 4.6±0.6μm and 6.2±1.8μm (mean±SD). In longitudinal-circumferential plane of blood vessel, VSMCs align off the circumferential direction with two mean angles of -19.4±9.3° and 10.9±4.7°, while an out-of-plane angle (i.e., radial tilt angle) was found to be 8±7.6° with median as 5.7°. Conclusions A 3D segmentation algorithm was developed to reconstruct individual VSMCs of blood vessel walls based on optical image stacks. The results were validated by a virtual phantom and manual measurement. The obtained 3D geometries can be utilized in mathematical models and leads a better understanding of vascular mechanical properties and function.

Area stenosis associated with non-invasive fractional flow reserve obtained from coronary CT images

Fractional flow reserve (FFR) determined by invasive angiography is the gold standard to assess the severity of coronary artery disease (CAD). FFRCT can be obtained non-invasively by combining computed tomography (CT) images and Computational Fluid Dynamics (CFD) method. In this study, FFRCT was computed for 6 models of patient-specific left coronary artery trees reconstructed from CT images. A total of 12 stenoses were observed. FFR values obtained for 7 of the 12 stenoses during invasive angiography were used as the gold standard for comparison. On a per-stenosis basis, the sensitivity, specificity, positive predictive value and negative predictive value were 50%, 100%, 100% and 83.3% respectively for FFRCT. A weak correlation was found between percent lumen diameter stenosis and FFRCT (r=0.431; p>0.05). However, the correlation between percent lumen area stenosis and FFRCT was significant (r=0.853; p<;0.05). Therefore, non-invasive FFRCT appears to be a promising index to assess the severity of CAD and lumen area has distinct advantages over diameter measurement in terms of anatomy assessment.

Computed tomography-based diagnosis of diffuse compensatory enlargement of coronary arteries using scaling power laws

Glagovs positive remodelling in the early stages of coronary atherosclerosis often results in plaque rupture and acute events. Because positive remodelling is generally diffused along the epicardial coronary arterial tree, it is difficult to diagnose non-invasively. Hence, the objective of the study is to assess the use of scaling power law for the diagnosis of positive remodelling of coronary arteries based on computed tomography (CT) images. Epicardial coronary arterial trees were reconstructed from CT scans of six Ossabaw pigs fed on a high-fat, high-cholesterol, atherogenic diet for eight months as well as the same number of body-weight-matched farm pigs fed on a lean chow (101.9±16.1 versus 91.5±13.1 kg). The high-fat diet Ossabaw pig model showed diffuse positive remodelling of epicardial coronary arteries. Good fit of measured coronary data to the length–volume scaling power law ( where Lc and Vc are crown length and volume) were found for both the high-fat and control groups (R2 = 0.95±0.04 and 0.99±0.01, respectively). The coefficient, KLV, decreased significantly in the high-fat diet group when compared with the control (14.6±2.6 versus 40.9±5.6). The flow–length scaling power law, however, was nearly unaffected by the positive remodelling. The length–volume and flow–length scaling power laws were preserved in epicardial coronary arterial trees after positive remodelling. KLV < 18 in the length–volume scaling relation is a good index of positive remodelling of coronary arteries. These findings provide a clinical rationale for simple, accurate and non-invasive diagnosis of positive remodelling of coronary arteries, using conventional CT scans.

A validated 3D microstructure-based constitutive model of coronary artery adventitia

A structure-based model that accurately predicts micro- or macromechanical behavior of blood vessels is necessary to understand vascular physiology. Based on recently measured microstructural data, we propose a three-dimensional microstructural model of coronary adventitia that incorporates the elastin and collagen distributions throughout the wall. The role of ground substance was found to be negligible under physiological axial stretch λz = 1.3, based on enzyme degradation of glycosaminoglycans in swine coronary adventitia (n = 5). The thick collagen bundles of outer adventitia (n = 4) were found to be undulated and unengaged at physiological loads, whereas the inner adventitia consisted of multiple sublayers of entangled fibers that bear the majority of load at higher pressures. The microstructural model was validated against biaxial (inflation and extension) experiments of coronary adventitia (n = 5). The model accurately predicted the nonlinear responses of the adventitia, even at high axial force (axial stretch ratio λz = 1.5). The model also enabled a reliable estimation of material parameters of individual fibers that were physically reasonable. A sensitivity analysis was performed to assess the effect of using mean values of the distributions for fiber orientation and waviness as opposed to the full distributions. The simplified mean analysis affects the fiber stress-strain relation, resulting in incorrect estimation of mechanical parameters, which underscores the need for measurements of fiber distribution for a rigorous analysis of fiber mechanics. The validated structure-based model of coronary adventitia provides a deeper understanding of vascular mechanics in health and can be extended to disease conditions.

Fast Marching and Runge–Kutta Based Method for Centreline Extraction of Right Coronary Artery in Human Patients

The CT angiography (CTA) is a clinically indicated test for the assessment of coronary luminal stenosis that requires centerline extractions. There is currently no centerline extraction algorithm that is automatic, real-time and very accurate. Therefore, we sought to (i) develop a hybrid approach by incorporating fast marching and Runge–Kutta based methods for the extraction of coronary artery centerlines from CTA; (ii) evaluate the accuracy of the present method compared to Van’s method by using ground truth centerline as a reference; (iii) evaluate the coronary lumen area of our centerline method in comparison with the intravascular ultrasound (IVUS) as the standard of reference. The proposed method was found to be more computationally efficient, and performed better than the Van’s method in terms of overlap measures (i.e., OV: