Wenchang Tan

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.

Growth, ageing and scaling laws of coronary arterial trees.

Despite the well-known design principles of vascular systems, it is unclear whether the vascular arterial tree obeys some scaling constraints during normal growth and ageing in a given species. Based on the micro-computed tomography measurements of coronary arterial trees in mice at different ages (one week to more than eight months), we show a constant exponent of 3/4, but age-dependent scaling coefficients in a length–volume scaling law ( Lc is the crown length, Vc is the crown volume, Klength–volume is the age-dependent scaling coefficient) during normal growth and ageing. The constant 3/4 exponent represents the self-similar fractal-like branching pattern (i.e. basic mechanism to regulate the development of vascular trees within a species), whereas the age-dependent scaling coefficients characterize the structural growth or resorption of vascular trees during normal growth or ageing, respectively. This study enhances the understanding of age-associated changes in vascular structure and function.

Morphometric and Hemodynamic Analysis of Atherosclerotic Progression in Human Carotid Artery Bifurcations

Although atherosclerosis has been widely investigated at carotid artery bifurcation, there is a lack of morphometric and hemodynamic data at different stages of the disease. The purpose of this study was to determine the lesion difference in patients with carotid artery disease compared with healthy control subjects. The three-dimensional (3D) geometry of carotid artery bifurcation was reconstructed from computed tomography angiography (CTA) images of Chinese control subjects (n = 30) and patients with carotid artery disease (n = 30). We defined two novel vector angles (i.e., angles 1 and 2) that were tangential to the reconstructed contour of the 3D vessel. The best-fit diameter was computed along the internal carotid artery (ICA) center line. Hemodynamic analysis was performed at various bifurcations. Patients with stenotic vessels have larger angles 1 and 2 (151 ± 11° and 42 ± 20°) and smaller diameters of the external carotid artery (ECA) (4.6 ± 0.85 mm) compared with control subjects (144 ± 13° and 36 ± 16°, 5.2 ± 0.57 mm) although there is no significant difference in the common carotid artery (CCA) (7.1 ± 1.2 vs. 7.5 ± 1.0 mm, P = 0.18). In particular, all patients with carotid artery disease have a stenosis at the proximal ICA (including both sinus and carina regions), while 20% of patients have stenosis at the middle ICA and 20% have stenosis expansion to the entire cervical ICA. Morphometric and hemodynamic analyses suggest that atherosclerotic plaques initiate at both sinus and carina regions of ICA and progress downstream.

Calcium waves initiating from the anomalous subdiffusive calcium sparks

The objective of the study is to investigate the propagation of Ca2+ waves in full-width cardiac myocytes and carry out sensitivity analysis to study the effects of various physiological parameters on global Ca2+ waves. Based on the anomalous subdiffusion of Ca2+ sparks, a mathematical model was proposed to characterize the Ca2+ waves. The computed results were in agreement with the experimental measurements using confocal microscopy. This model includes variables of current through the Ca2+ release unit (CRU; ICRU), duration of current flow through CRU (Topen), Ca2+ sensitivity parameter (K), the longitudinal and transverse spatial separation of CRUs (lx and ly, where x denotes longitudinal direction (x-axis) and y denotes transverse direction (y-axis)) and Ca2+ diffusion coefficients (Dx, Dy). The spatio-temporal mechanism of the anomalous Ca2+ sparks led to results that were different from those based on Ficks law. The major findings were reported as: ICRU affected the dynamic properties of Ca2+ waves more significantly than Topen; the effect of K on the properties of Ca2+ waves was negligible; ly affected the amplitude significantly, but lx affected the longitudinal velocity significantly; in turn, the limitation and significance of the study are discussed.

Hemodynamics of left internal mammary artery bypass graft: Effect of anastomotic geometry, coronary artery stenosis, and postoperative time

Although the left internal mammary artery (LIMA) bypass graft is the best choice for surgical revascularization, its hemodynamics are still complex and can result in long-term graft failure. Here, we performed a hemodynamic analysis of the LIMA-coronary artery with end-to-side/side-to-side anastomoses based on 15 patient-specific CTA images at various postoperative periods. We hypothesize that hemodynamic patterns are determined by the interplay of LIMA geometry, anastomotic configuration, and severity of native coronary artery stenosis, which are strongly affected by the postoperative time. A 3D finite volume method with the inlet pressure wave and outlet resistance boundary conditions was used to compute the distribution of pressure and flow, from which the time-averaged wall shear stress (TAWSS), oscillation shear index (OSI), time-averaged WSS gradient (TAWSSG), and transverse WSS (transWSS) were determined. To characterize the hemodynamic environment, we defined surface area ratios of low TAWSS (≤4dynes/cm(2)), high OSI (≥0.15), TAWSSG (≥500dynes/cm(3)), and transWSS (≥6dynes/cm(2)) in the LIMA graft and at the anastomosis between LIMA graft and coronary artery. These ratios were determined by the interplay of multiple morphometric parameters in the LIMA-coronary artery, but increased with postoperative time. These findings have significant implications for understanding LIMA graft patency.

Interplay of Proximal Flow Confluence and Distal Flow Divergence in Patient-Specific Vertebrobasilar System.

Approximately one-quarter of ischemic strokes involve the vertebrobasilar arterial system that includes the upstream flow confluence and downstream flow divergence. A patient-specific hemodynamic analysis is needed to understand the posterior circulation. The objective of this study is to determine the distribution of hemodynamic parameters in the vertebrobasilar system, based on computer tomography angiography images. Here, the interplay of upstream flow confluence and downstream flow divergence was hypothesized to be a determinant factor for the hemodynamic distribution in the vertebrobasilar system. A computational fluid dynamics model was used to compute the flow fields in patient-specific vertebrobasilar models (n = 6). The inlet and outlet boundary conditions were the aortic pressure waveform and flow resistances, respectively. A 50% reduction of total outlet area was found to induce a ten-fold increase in surface area ratio of low time-averaged wall shear stress (i.e., TAWSS ≤ 4 dynes/cm2). This study enhances our understanding of the posterior circulation associated with the incidence of atherosclerotic plaques.

A comparison of postoperative morphometric and hemodynamic changes between saphenous vein and left internal mammary artery grafts

There is higher long‐term failure of the saphenous vein graft (SVG) compared with the left internal mammary artery (LIMA) graft, which is affected by the hemodynamic environment. A comprehensive analysis of postoperative structure‐function changes is important to study the atherogenesis in the SVG. A comparison of morphometric and hemodynamic parameters was carried out between LIMA grafts and SVGs and between different time points postoperatively. Various parameters were obtained from the image reconstruction and flow simulation in patients, who underwent CT exams for ~1 year, 5 and 10 years after revascularization. Morphometric data showed a decrease in lumen size in the entire SVG and anastomosis of different patients in a sequence of ~1 year, 5 and 10 years postoperatively despite negligible changes of LIMA size. Computational results indicated the fourfold increased surface area ratio (SAR) of low time‐averaged wall shear stress (TAWSS) in the SVG and anastomosis at postoperative 10 years than that at postoperative ~1 year. The SAR of high TAWSS gradient (TAWSSG) at the distal anastomosis between SVG and coronary arteries was significantly higher (14 ± 9% vs. 6 ± 8%) than that in the LIMA group at postoperative ~1 year. There were strong correlations between morphometric and hemodynamic parameters in the SVG and distal anastomosis at various time points postoperatively, which showed deterioration relevant to persistent diffuse diseases at postoperative ~10 years.

Intraspecific Scaling Laws are Preserved in Ventricular Hypertrophy, but not in Heart Failure

It is scientifically and clinically important to understand the structure-function scaling of coronary arterial trees in compensatory (e.g., left and right ventricular hypertrophy, LVH and RVH) and decompensatory vascular remodeling (e.g., congestive heart failure, CHF). This study hypothesizes that intraspecific scaling power laws of vascular trees are preserved in hypertrophic hearts but not in CHF swine hearts. To test the hypothesis, we carried out the scaling analysis based on morphometry and hemodynamics of coronary arterial trees in moderate LVH, severe RVH, and CHF compared with age-matched respective control hearts. The scaling exponents of volume-diameter, length-volume, and flow-diameter power laws in control hearts were consistent with the theoretical predictions (i.e., 3, 7/9, and 7/3, respectively), which remained unchanged in LVH and RVH hearts. The scaling exponents were also preserved with an increase of body weight during normal growth of control animals. In contrast, CHF increased the exponents of volume-diameter and flow-diameter scaling laws to 4.25 ± 1.50 and 3.15 ± 1.49, respectively, in the epicardial arterial trees. This study validates the predictive utility of the scaling laws to diagnose vascular structure and function in CHF hearts to identify the borderline between compensatory and decompensatory remodeling.

Effects of rogue ryanodine receptors on Ca2+ sparks in cardiac myocytes

Ca2+ sparks and Ca2+ quarks, arising from clustered and rogue ryanodine receptors (RyRs), are significant Ca2+ release events from the junctional sarcoplasmic reticulum (JSR). Based on the anomalous subdiffusion of Ca2+ in the cytoplasm, a mathematical model was developed to investigate the effects of rogue RyRs on Ca2+ sparks in cardiac myocytes. Ca2+ quarks and sparks from the stochastic opening of rogue and clustered RyRs are numerically reproduced and agree with experimental measurements. It is found that the stochastic opening Ca2+ release units (CRUs) of clustered RyRs are regulated by free Ca2+ concentration in the JSR lumen (i.e. [Ca2+]lumen). The frequency of spontaneous Ca2+ sparks is remarkably increased by the rogue RyRs opening at high [Ca2+]lumen, but not at low [Ca2+]lumen. Hence, the opening of rogue RyRs contributes to the formation of Ca2+ sparks at high [Ca2+]lumen. The interplay of Ca2+ sparks and Ca2+ quarks has been discussed in detail. This work is of significance to provide insight into understanding Ca2+ release mechanisms in cardiac myocytes.

The Structure‐function remodeling in rabbit hearts of myocardial infarction

Animal models are of importance to investigate basic mechanisms for ischemic heart failure (HF). The objective of the study was to create a rabbit model through multiple coronary artery ligations to investigate the postoperative structure‐function remodeling of the left ventricle (LV) and coronary arterial trees. Here, we hypothesize that the interplay of the degenerated coronary vasculature and increased ventricle wall stress relevant to cardiac fibrosis in vicinity of myocardial infarction (MI) precipitates the incidence and progression of ischemic HF. Echocardiographic measurements showed an approximately monotonic drop of fractional shortening and ejection fraction from 40% and 73% down to 28% and 58% as well as persistent enlargement of LV cavity and slight mitral regurgitation at postoperative 12 weeks. Micro‐CT and histological measurements showed that coronary vascular rarefaction and cardiac fibrosis relevant to inflammation occurred concurrently in vicinity of MI at postoperative 12 weeks albeit there was compensatory vascular growth at postoperative 6 weeks. These findings validate the proposed rabbit model and prove the hypothesis. The post‐MI rabbit model can serve as a reference to test various drugs for treatment of ischemic HF.