Flow patterns in three-dimensional porcine epicardial coronary arterial tree

Computing pulsatile blood flow of coronary artery under incomplete boundary conditions

BACKGROUND

Accurate measurement of pulsatile blood flow in the coronary arteries enables coronary wave intensity analysis, which can serve as an indicator for assessing coronary artery physiology and myocardial viability. Computational fluid dynamics (CFD) methods integrating coronary angiography images and fractional flow reserve (FFR) offer a novel approach for computing mean coronary blood flow. However, previous methods neglect the inertial effect of blood flow, which may have great impact on pulsatile blood flow calculation. To improve the accuracy of pulsatile blood flow calculation, a novel CFD based method considering the inertia term is proposed.

METHODS

A flow resistance model based on Pressure-Flow vs.Time curves is proposed to model the resistance of the epicardial artery. The parameters of the flow resistance model can be fitted from the simulated pulsating flow rates and pressure drops of a specific mode. Then, pulsating blood flow can be calculated by combining the incomplete pressure boundary conditions under pulsating conditions which are easily obtained in clinic. Through simulation experiments, the effectiveness of the proposed method is validated in idealized and reconstructed 3D model of coronary artery. The impacts of key parameters for generating the simulated pulsating flow rates and pressure drops on the accuracy of pulsatile blood flow calculation are also investigated.

RESULTS

For the idealized model, the previously proposed Pressure-Flow model has a significant leading effect on the computed blood flow waveform in the moderate model, and this leading effect disappears with the increase of the degree of stenosis. The improved model proposed in this paper has no leading effect, the root mean square error (RMSE) of the proposed model is low (the left coronary mode:≤0.0160, the right coronary mode:≤0.0065) for all simulated models, and the RMSE decreases with an increase of stenosis. The RMSE is consistently small (≤0.0217) as the key parameters of the proposed method vary in a large range. It is verified in the reconstructed model that the proposed model significantly reduces the RMSE of patients with moderate stenosis (the Pressure-Flow model:≤0.0683, the Pressure-Flow vs.Time model:≤0.0297), and the obtained blood flow waveform has a higher coincidence with the simulated reference waveform.

CONCLUSIONS

This paper confirms that ignoring the effect of inertia term can significantly affect the accuracy of calculating pulsatile blood flow in moderate stenosis lesions, and the new method proposed in this paper can significantly improves the accuracy of calculating pulsatile blood flow in moderate stenosis lesions. The proposed method provides a convenient clinical method for obtaining pressure-synchronized blood flow, which is expected to facilitate the application of waveform analysis in the diagnosis of coronary artery disease.

Study of the mechanism of action of sand therapy on atherosclerosis based on the two-phase flow-Casson model

BACKGROUND

Sand therapy is a non-pharmacological physiotherapy method that uses the natural environment and resources of Xinjiang to treat through the heat transfer and magnetic effects of sand.

OBJECTIVE

Employing the two-phase flow-Casson blood flow model, we investigate the mechanism of atherosclerosis prevention via sand therapy, offering a biomechanical theoretical rationale for the prevention of atherosclerosis through sand therapy via the prism of computational fluid dynamics (CFD).

METHODS

Sand therapy experiments were conducted to obtain popliteal artery blood flow velocity, and blood was considered as a two-phase flow composed of plasma and red blood cells, and CFD method was applied to analyze the hemodynamic effects of Casson's blood viscosity model before and after sand therapy.

RESULTS

(1) The blood flow velocity increased by 0.24 m/s and 0.04 m/s at peak systolic and diastolic phases, respectively, after sand therapy; the axial velocity of blood vessels increased by 28.56% after sand therapy. (2) The average red blood cell viscosity decreased by 0.00014 Pa ⋅ s after sand therapy. (3) The low wall shear stress increased by 1.09 Pa and the high wall shear stress reached 41.47 Pa after sand therapy. (4) The time-averaged wall shear stress, shear oscillation index and relative retention time were reduced after sand therapy.

CONCLUSION

The increase of blood flow velocity after sand therapy can reduce the excessive deposition of cholesterol and other substances, the decrease of erythrocyte viscosity is beneficial to the migration of erythrocytes to the vascular center, the increase of low wall shear stress has a positive effect on the prevention of atherosclerosis, and the decrease of time-averaged wall shear stress, shear oscillation index and relative retention time can reduce the occurrence of thrombosis.

Noninvasive computed tomography derived fractional flow reserve simulation based on microvascular tree model reconstruction

To establish a novel method for noninvasive computed tomography derived fractional flow reserve (CT-FFR) simulation based on microvascular tree model reconstruction and to evaluate the feasibility and diagnostic performance of the novel method in coronary artery disease compared with invasive fractional flow reserve (FFR). Twenty patients (20 vessels) who underwent coronary computed tomography angiography (CCTA) and invasive FFR were retrospectively studied. The anatomic epicardial coronary artery model was reconstructed based on CCTA image, and the microvascular tree model was simulated based on patient-specific anatomical structures and physiological principles. Numerical simulation was subsequently performed using the CFD method with full consideration of the variation of viscosity in microvascular. Two patients with the FFR value of .80 were selected for adjusting the parameters of the model, while the remaining 18 patients were selected as a validation cohort. After simulation, CT-FFR was compared with invasive FFR with a threshold of .80. Eleven (55%) patients had an abnormal FFR that was less than or equal to .80. Compared with invasive FFR, sensitivity, specificity, positive predictive value, negative predictive value, and accuracy of CT-FFR with an optimal threshold of .80 were 100%, 77.8%, 81.8%, 100%, 88.89%, respectively. There were a good correlation and consistency between CT-FFR and invasive FFR. Time per patient of CT-FFR analysis was less than 15 min. CT-FFR based on microvascular tree model reconstruction is feasible with good diagnostic performance. It requires a short processing time with excellent accuracy. Large multicenter prospective studies are required for further demonstrating the diagnostic performance of this novel model in myocardium ischemia evaluation.

Hemodynamics of vascular shunts: trends, challenges, and prospects

Vascular bypass surgery takes a significant place in the treatment of vascular disease. According to various assessments, this type of surgery is associated with almost 20 % of all vascular surgery episodes (up to 23 % according to the Federal Neurosurgical Center of Novosibirsk). Even though the problem of using of vascular grafts is obvious and natural, many problems associated with them are not still elucidated. From the mechanics' point of view, a vascular bypass is a converging or diverging tee, and the functioning of such structures still does not have strict mathematical formulations and proofs in the general case, which forces many researchers to solve specific engineering problems associated with shunting. Mathematical modeling, which is the gold standard for virtual simulations of industrial and medical problems, faces great difficulties and limitations in solving problems for vascular bypasses. Complications in the treatment of the vascular disease may follow the difficulties in mathematical modeling, and the price can be a cardiac arrest or a stroke. This work is devoted to the main aspects of the medical application of vascular bypasses and their functioning as a mechanical system, as well the mathematical aspects of their possible setup.

A spatiotemporal analysis of the left coronary artery biomechanics using fluid-structure interaction models

Biomechanics plays a critical role in coronary artery disease development. FSI simulation is commonly used to understand the hemodynamics and mechanical environment associated with atherosclerosis pathology. To provide a comprehensive characterization of patient-specific coronary biomechanics, an analysis of FSI simulation in the spatial and temporal domains was performed. In the current study, a three-dimensional FSI model of the LAD coronary artery was built based on a patient-specific geometry using COMSOL Multiphysics. The effect of myocardial bridging was simulated. Wall shear stress and its derivatives including time-averaged wall shear stress, wall shear stress gradient, and OSI were calculated across the cardiac cycle in multiple locations. Arterial wall strain (radial, circumferential, and longitudinal) and von Mises stress were calculated. To assess perfusion, vFFR was calculated. The results demonstrated the FSI model could identify regional and transient differences in biomechanical parameters within the coronary artery. The addition of myocardial bridging caused a notable change in von Mises stress and an increase in arterial strain during systole. The analysis performed in this manner takes greater advantage of the information provided in the space and time domains and can potentially assist clinical evaluation.

The Need to Shift from Morphological to Structural Assessment for Carotid Plaque Vulnerability

Degree of luminal stenosis is generally considered to be an important indicator for judging the risk of atherosclerosis burden. However, patients with the same or similar degree of stenosis may have significant differences in plaque morphology and biomechanical factors. This study investigated three patients with carotid atherosclerosis within a similar range of stenosis. Using our developed fluid-structure interaction (FSI) modelling method, this study analyzed and compared the morphological and biomechanical parameters of the three patients. Although their degrees of carotid stenosis were similar, the plaque components showed a significant difference. The distribution range of time-averaged wall shear stress (TAWSS) of patient 2 was wider than that of patient 1 and patient 3. Patient 2 also had a much smaller plaque stress compared to the other two patients. There were significant differences in TAWSS and plaque stresses among three patients. This study suggests that plaque vulnerability is not determined by a single morphological factor, but rather by the combined structure. It is necessary to transform the morphological assessment into a structural assessment of the risk of plaque rupture.

Uncertainty quantification of a three-dimensional in-stent restenosis model with surrogate modelling

In-stent restenosis is a recurrence of coronary artery narrowing due to vascular injury caused by balloon dilation and stent placement. It may lead to the relapse of angina symptoms or to an acute coronary syndrome. An uncertainty quantification of a model for in-stent restenosis with four uncertain parameters (endothelium regeneration time, the threshold strain for smooth muscle cell bond breaking, blood flow velocity and the percentage of fenestration in the internal elastic lamina) is presented. Two quantities of interest were studied, namely the average cross-sectional area and the maximum relative area loss in a vessel. Owing to the high computational cost required for uncertainty quantification, a surrogate model, based on Gaussian process regression with proper orthogonal decomposition, was developed and subsequently used for model response evaluation in the uncertainty quantification. A detailed analysis of the uncertainty propagation is presented. Around 11% and 16% uncertainty is observed on the two quantities of interest, respectively, and the uncertainty estimates show that a higher fenestration mainly determines the uncertainty in the neointimal growth at the initial stage of the process. The uncertainties in blood flow velocity and endothelium regeneration time mainly determine the uncertainty in the quantities of interest at the later, clinically relevant stages of the restenosis process.

Vertebral Artery Stenoses Contribute to the Development of Diffuse Plaques in the Basilar Artery

Vertebral artery (VA) stenosis is relevant to a high early risk of recurrent stroke and basilar artery (BA) is the most common intracranial site of atherosclerotic lesions. It is important to show predictive risk factors for transient ischemic attack (TIA) or posterior infarctions. The aim of the study is to investigate morphometry and hemodynamics in intracranial vertebral and basilar arteries of health and diseased patients to enhance the risk assessment. Based on the geometrical model reconstructed from CTA images in 343 patients, a transient three-dimensional computational model was used to determine the hemodynamics. Patients were classified in symmetric, asymmetric, hypoplastic, and stenotic groups while patients in the stenotic group were divided into unilateral, bilateral, bifurcation, and tandem stenotic sub-groups. Patients in bilateral, bifurcation, and tandem stenotic sub-groups had significantly lower basilar artery diameters than other groups. Patients in the stenotic group had significantly higher surface area ratio (SAR) of high time-averaged wall shear stress gradient (TAWSSG) and higher incidence of TIAs or posterior infarctions than other groups while patients in the tandem stenotic sub-group had the highest values (SAR-TAWSSG of 57 ± 22% and TIAs or posterior infarction incidence of 54%). The high SAR-TAWSSG is predisposed to induce TIAs or posterior infarction.

The improvement of the shear stress and oscillatory shear index of coronary arteries during Enhanced External Counterpulsation in patients with coronary heart disease

Background

Enhanced External Counterpulsation (EECP) can chronically relieve ischemic chest pain and improve the prognosis of coronary heart disease (CHD). Despite its role in mitigating heart complications, EECP and the mechanisms behind its therapeutic nature, such as its effects on blood flow hemodynamics, are still not fully understood. This study aims to elucidate the effect of EECP on significant hemodynamic parameters in the coronary arterial tree.

Methods

A finite volume method was used in conjunction with the inlet pressure wave (surrogated by the measured aortic pressure) before and during EECP and outlet flow resistance, assuming the blood as newtonian fluid. The time-average wall shear stress (TAWSS) and oscillatory shear index (OSI) were determined from the flow field.

Results

Regardless of the degree of vascular stenosis, hemodynamic conditions and flow patterns could be improved during EECP. In comparison with the original tree, the tree with a severe stenosis (75% area stenosis) demonstrated more significant improvement in hemodynamic conditions and flow patterns during EECP, with surface area ratio of TAWSS risk area (SAR-TAWSS) reduced from 12.3% to 6.7% (vs. SAR-TAWSS reduced from 7.2% to 5.6% in the original tree) and surface area ratio of OSI risk area (SAR-OSI) reduced from 6.8% to 2.5% (vs. SAR-OSI of both 0% before and during EECP in the original tree because of mild stenosis). Moreover, it was also shown that small ratio of diastolic pressure (D) and systolic pressure (S) (D/S) could only improve the hemodynamic condition mildly. The SAR-TAWSS reduction ratio significantly increased as D/S became larger.

Conclusions

A key finding of the study was that the improvement of hemodynamic conditions along the LMCA trees during EECP became more significant with the increase of D/S and the severity degree of stenoses at the bifurcation site. These findings have important implications on EECP as adjuvant therapy before or after percutaneous coronary intervention (PCI) in patients with diffuse atherosclerosis.

The structural properties of carotid arteries in carotid artery diseases - a retrospective computed tomography angiography study

Purpose

Aim of the study was to find answers to the following questions: What haemodynamic changes may occur in patients with stenotic, aneurysmal, dissection of the carotid artery and its branches? How do these changes differ in patients with normal and carotid disease?

Material and methods

In order to achieve this aim, the cranio-cervical CT angiography images of patients who were referred to our clinic for any reason and received the diagnosis of carotid stenosis, carotid dissection, and extra or intracranial aneurysm were reviewed retrospectively.

Results

Significant differences were detected in the carotid arteries of normal patients and those with aneurysm and dissection. When normal and aneurismal patients were compared, right and left ICA diameters (p = 0.000, p = 0.002, respectively), total ICA diameters (p = 0.000), carotid left Ø diameters (p = 0.026), right and left total Ø diameters (p = 0.024), and Murray’s and our cosine values of Ø angles (p = 0.001 and p = 0.022, respectively) were found to be different. Also, in a comparison made between normal patients and patients with dissection, right CCA (p = 0.000), ICA (p = 0.001), ECA (p = 0.004) diameters, total CCA (p = 0.001), ICA (p = 0.009), and ECA (p = 0.003) diameters were also found to be different.

Conclusions

This study showed that the presence of aneurysm plays an important role in the remodelling of the carotid arteries. Also, it is understood that Murray’s laws are still valid for the detection of structural deterioration in carotid artery diseases. Hence, it is believed that these data can be used in artificial intelligence studies.

Computational fluid dynamics of a novel perfusion strategy during hybrid thoracic aortic repair

BACKGROUND AND AIM

To mitigate the risk of perioperative neurological complications during frozen elephant trunk procedures, we aimed to computationally evaluate the effects of direct cerebral perfusion strategy through a left carotid-subclavian bypass on hemodynamics in a patient-specific thoracic aorta model.

METHODS

Between July 2016 and March 2019, 11 consecutive patients underwent frozen elephant trunk operation using the left carotid-subclavian bypass with a side graft anastomosis and right-axillary cannulation for systemic and brain perfusion. A multiscale model realized coupling three-dimensional computational fluid dynamics was developed and validated with in vivo data. Model comparison with direct antegrade cannulation of all epiaortic vessels was performed. Wall shear stress, wall shear stress spatial gradient, and localized normalized helicity were selected as hemodynamic indicators. Four cerebral perfusion flows were tested (6 to 15 mL/kg/min).

RESULTS

Direct cerebral perfusion of the left subclavian bypass resulted in higher flow rates with augmented speeds in all epiaortic vessels in comparison with traditional perfusion model. At the level of the left vertebral artery (LVA), a speed of 22.5 vs 21 mL/min and mean velocity of 3.07 vs 2.93 cm/s were registered, respectively. With a cerebral perfusion flow of 15 mL/kg, lower LVA wall shear stress (1.596 vs 2.030 N/m² ), and wall shear stress gradient (1445 vs 5882 N/m³ ) were observed. A less disturbed flow considering the localized normalized helicity was documented. No patients experienced neurological/spinal cord damages.

CONCLUSIONS

Direct perfusion of a left carotid bypass proved to be cerebroprotective, resulting in a more physiological and stable anterior and posterior cerebral perfusion.

PAK2 links cell survival to mechanotransduction and metabolism

Campbell et al. show that force stimulates PAK2 activation at cell–cell junctions, where it protects cells under force from death and plays a key role in linking force-induced mechanotransduction, metabolism, and cell survival.

Too little or too much force can trigger cell death, yet factors that ensure the survival of cells remain largely unknown. Here, we demonstrate that E-cadherin responds to force by recruiting and activating p21-activated protein kinase 2 (PAK2) to allow cells to stiffen, metabolize, and survive. Interestingly, PAK2 activation and its control of the apoptotic response are specific for the amplitude of force applied. Specifically, under low amplitudes of physiological force, PAK2 is protected from proteolysis, thereby ensuring cell survival. In contrast, under higher amplitudes of physiological force, PAK2 is left unprotected and stimulates apoptosis, an effect that is prevented by cleavage-resistant forms of the protein. Finally, we demonstrate that PAK2 protection is conferred by direct binding of AMPK. Thus, PAK2 mediates the survival of cells under force. These findings reveal an unexpected paradigm for how mechanotransduction, metabolism, and cell survival are linked.

Stenosis Indicators Applied to Patient-Specific Renal Arteries without and with Stenosis

Pulsatile flow in the abdominal aorta and the renal arteries of three patients was studied numerically. Two of the patients had renal artery stenosis. The aim of the study was to assess the use of four types of indicators for determining the risk of new stenosis after revascularization of the affected arteries. The four indicators considered include the time averaged wall shear stress (TAWSS), the oscillatory shear index (OSI), the relative reference time (RRT) and a power law model based in platelet activation modeling but applied to the endothelium, named endothelium activation indicator (EAI). The results show that the indicators can detect the existing stenosis but are less successful in the revascularized cases. The TAWSS and, more clearly, the EAI approach seem to be better in predicting the risk for stenosis relapse at the original location and close to the post-stenotic dilatation. The shortcomings of the respective indicators are discussed along with potential improvements to endothelial activation modeling and its use as an indicator for risks of restenosis.

Knockdown of P120 catenin aggravates endothelial injury under an impinging flow by inducing breakdown of adherens junctions

At present, the mechanisms underlying intracranial aneurysm (IA) development remain unclear; however, hemodynamics is considered a crucial factor in the induction of IA. To elucidate the association between hemodynamics and endothelial cell (EC) functions, a modified T chamber system was designed to simulate the adjustable hemodynamic conditions of an artery bifurcation. Normal human umbilical vein ECs (HUVECs) and HUVECs with P120 catenin (P120ctn) knockdown were cultured on coverslips and placed in the chamber. A flow rate of 250 or 500 ml/min impinged on the cell layer. Subsequently, the expression levels of P120ctn and other proteins, and EC morphological alterations, were examined. In normal HUVECs, after 3 h under a flow rate of 500 ml/min, the expression levels of P120ctn, vascular endothelial (VE)‑Cadherin, Kaiso and α‑catenin were decreased, whereas matrix metalloproteinase‑2 (MMP‑2) was increased. In HUVECs with P120ctn knockdown, the period during which ECs adhered to the coverslip was reduced to 1 h under a flow rate of 500 ml/min. In addition, the expression levels of VE‑Cadherin, Kaiso and α‑catenin in ECs were decreased, whereas those of MMP‑2 were increased after 1 h; more prominent alterations were detected under a 500 ml/min flow rate compared with a 250 ml/min flow rate. Adherens junctions (AJs) are critical to the maintenance of normal morphology and EC functioning in the vascular wall, and P120ctn is an important regulator of AJs. Loss of P120ctn may be induced by hemodynamic alterations. In response to changes in hemodynamic conditions, a loss of P120ctn may aggravate AJs between ECs, thus inducing inflammation in the vascular wall. Clinically, hemodynamic alterations may result in a loss of P120ctn and endothelial injury; therefore, P120ctn may have a critical role in inducing intracranial aneurysms.

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.

Bifurcation Asymmetry of Small Coronary Arteries in Juvenile and Adult Mice

Background: Microvascular bifurcation asymmetry is of significance for regulation of coronary flow heterogeneity during juvenile and adult growth. The aim of the study is to investigate the morphometric and hemodynamic variation of coronary arterial bifurcations in mice of different ages.

Methods: Pulsatile blood flows were computed from a Womersley-type model in the reconstructed left coronary arterial (LCA) trees from Micro-CT images in normal mice at ages of 3 weeks, 6 weeks, 12 weeks, 5-6 months, and >8 months. Diameter and flow ratios and bifurcation angles were determined in each bifurcation of the LCA trees.

Results: The blood volume and inlet flow rate of LCA trees increase and decrease during juvenile and adult growth, respectively. As vessel diameters decrease, the increased ratios of small to large daughter vessel diameters (D_s/D_l) result in more uniform flows and lower velocities. There are significant structure-functional changes of LCA trees in mice of >8 months compared with mice of < 8 months. As D_s/D_l increases, the variation trend of bifurcation angle during juvenile growth is different from that during adult growth.

Conclusions: Although inlet flows are different in adult vs. juvenile mice, the adult still have uniform flow and low velocity. This is accomplished through a decrease in diameter. The design ensures ordered dispersion of red cells through asymmetric branching patterns into the capillaries.

Hepatic Hemangiomas Alter Morphometry and Impair Hemodynamics of the Abdominal Aorta and Primary Branches From Computer Simulations

Background: The formation of hepatic hemangiomas (HH) is associated with VEGF and IL-7 that alter conduit arteries and small arterioles. To our knowledge, there are no studies to investigate the effects of HH on the hemodynamics in conduit arteries. The aim of the study is to perform morphometric and hemodynamic analysis in abdominal conduit arteries and bifurcations of HH patients and controls.

Methods: Based on morphometry reconstructed from CT images, geometrical models were meshed with prismatic elements for the near wall region and tetrahedral and hexahedral elements for the core region. Simulations were performed for computation of the non-Newtonian blood flow using the Carreau-Yasuda model, based on which multiple hemodynamic parameters were determined.

Results: There was an increase of the lumen size, diameter ratio, and curvature in the abdominal arterial tree of HH patients as compared with controls. This significantly increased the surface area ratio of low time-averaged wall shear stress (i.e., SAR-TAWSS =Surface  areaTAWSS≤4 dynes·cm−2Total  surface  area× 100%) (24.1 ± 7.9 vs. 5 ± 6%, 11.6 ± 12.8 vs. < 0.1%, and 44.5 ± 9.2 vs. 21 ± 24% at hepatic bifurcations, common hepatic arteries, and abdominal aortas, respectively, between HH and control patients).

Conclusions: Morphometric changes caused by HH significantly deteriorated the hemodynamic environment in abdominal conduit arteries and bifurcations, which could be an important risk factor for the incidence and progression of vascular diseases.

Fluid-structure interaction modeling of aneurysmal arteries under steady-state and pulsatile blood flow: a stability analysis

Tortuous aneurysmal arteries are often associated with a higher risk of rupture but the mechanism remains unclear. The goal of this study was to analyze the buckling and post-buckling behaviors of aneurysmal arteries under pulsatile flow. To accomplish this goal, we analyzed the buckling behavior of model carotid and abdominal aorta with aneurysms by utilizing fluid-structure interaction (FSI) method with realistic waveforms boundary conditions. FSI simulations were done under steady-state and pulsatile flow for normal (1.5) and reduced (1.3) axial stretch ratios to investigate the influence of aneurysm, pulsatile lumen pressure and axial tension on stability. Our results indicated that aneurysmal artery buckled at the critical buckling pressure and its deflection nonlinearly increased with increasing lumen pressure. Buckling elevates the peak stress (up to 118%). The maximum aneurysm wall stress at pulsatile FSI flow was (29%) higher than under static pressure at the peak lumen pressure of 130 mmHg. Buckling results show an increase in lumen shear stress at the inner side of the maximum deflection. Vortex flow was dramatically enlarged with increasing lumen pressure and artery diameter. Aneurysmal arteries are more susceptible than normal arteries to mechanical instability which causes high stresses in the aneurysm wall that could lead to aneurysm rupture.

IMPACT OF COMPETITIVE FLOW ON HEMODYNAMICS OF LIMA-LAD GRAFTING WITH DIFFERENT STENOSIS: A NUMERICAL STUDY

Background and Aims: Competitive flow exists in the native coronary artery when using artery graft in the coronary artery bypass graft (CABG), and it is a major factor affecting the long-term patency of the arterial grafts. The purpose of this study is to investigate the effects of the competitive flow on hemodynamic characteristics of left internal mammary artery (LIMA). Materials and methods: Seven three-dimensional (3D) LIMA-left anterior decending (LAD) grafting models with different diameter stenoses at the trunk of LAD were reconstructed, including 25%, 40%, 50%, 60%, 75%, 90% and 100%. The boundary conditions of these models were provided by the same lumped parameter model (LPM; 0D sub-model) of cardiovascular circulatory system, which is based on 0D/3D coupling method. Results: The simulation results show that competitive flow decreases when the stenosis rate increases and backflow exists in LIMA during systole when the degree of stenosis is below 50%; the wall shear stress (WSS) of the graft increases from 0.85[Formula: see text]Pa to 1.79[Formula: see text]Pa with the increase of the native coronary stenosis degree, while the oscillatory shear index (OSI) decreases from 0.1557 to 0.00213. Conclusions: Competitive flow may produce adverse hemodynamic effects on artery graft, especially when the stenosis degree is below 50%, competitive flow will significantly lead the long-term patency of the artery graft worse because of the backflow, low WSS and high OSI, and the effect of OSI is more obvious than WSS.

Vascular Adaptation to Exercise in Humans: Role of Hemodynamic Stimuli

On the 400th anniversary of Harvey's Lumleian lectures, this review focuses on "hemodynamic" forces associated with the movement of blood through arteries in humans and the functional and structural adaptations that result from repeated episodic exposure to such stimuli. The late 20th century discovery that endothelial cells modify arterial tone via paracrine transduction provoked studies exploring the direct mechanical effects of blood flow and pressure on vascular function and adaptation in vivo. In this review, we address the impact of distinct hemodynamic signals that occur in response to exercise, the interrelationships between these signals, the nature of the adaptive responses that manifest under different physiological conditions, and the implications for human health. Exercise modifies blood flow, luminal shear stress, arterial pressure, and tangential wall stress, all of which can transduce changes in arterial function, diameter, and wall thickness. There are important clinical implications of the adaptation that occurs as a consequence of repeated hemodynamic stimulation associated with exercise training in humans, including impacts on atherosclerotic risk in conduit arteries, the control of blood pressure in resistance vessels, oxygen delivery and diffusion, and microvascular health. Exercise training studies have demonstrated that direct hemodynamic impacts on the health of the artery wall contribute to the well-established decrease in cardiovascular risk attributed to physical activity.

Heterogeneous mechanics of the mouse pulmonary arterial network

Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure-radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.

Hemodynamics in Coronary Arterial Tree of Serial Stenoses

Serial segmental narrowing frequently occurs in humans, which alters coronary hemodynamics and further affects atherosclerotic progression and plaque formation. The objective of this study was to understand the distribution of hemodynamic parameters in the epicardial left main coronary arterial (LMCA) tree with serial stenoses reconstructed from patient computer tomography angiography (CTA) images. A finite volume method was used in conjunction with the inlet pressure wave and outlet flow resistance. The time-averaged wall shear stress (TAWSS) and oscillatory shear index (OSI) were determined from the flow field. A stenosis at a mother vessel mainly deteriorated the hemodynamics near the bifurcation while a stenosis at a daughter vessel affected the remote downstream bifurcation. In comparison with a single stenosis, serial stenoses increased the peak pressure gradient along the main trunk of the epicardial left anterior descending arterial tree by > 50%. An increased distance between serial stenoses further increased the peak pressure gradient. These findings have important implications on the diagnosis and treatment of serial coronary stenoses.

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.

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.

Nitinol Stent Oversizing in Patients Undergoing Popliteal Artery Revascularization: A Finite Element Study

Nitinol stent oversizing is frequently performed in peripheral arteries to ensure a desirable lumen gain. However, the clinical effect of mis-sizing remains controversial. The goal of this study was to provide a better understanding of the structural and hemodynamic effects of Nitinol stent oversizing. Five patient-specific numerical models of non-calcified popliteal arteries were developed to simulate the deployment of Nitinol stents with oversizing ratios ranging from 1.1 to 1.8. In addition to arterial biomechanics, computational fluid dynamics methods were adopted to simulate the physiological blood flow inside the stented arteries. Results showed that stent oversizing led to a limited increase in the acute lumen gain, albeit at the cost of a significant increase in arterial wall stresses. Furthermore, localized areas affected by low Wall Shear Stress increased with higher oversizing ratios. Stents were also negatively impacted by the procedure as their fatigue safety factors gradually decreased with oversizing. These adverse effects to both the artery walls and stents may create circumstances for restenosis. Although the ideal oversizing ratio is stent-specific, this study showed that Nitinol stent oversizing has a very small impact on the immediate lumen gain, which contradicts the clinical motivations of the procedure.

Three-dimensional virtual surgery models for percutaneous coronary intervention (PCI) optimization strategies

Percutaneous coronary intervention (PCI), especially coronary stent implantation, has been shown to be an effective treatment for coronary artery disease. However, in-stent restenosis is one of the longstanding unsolvable problems following PCI. Although stents implanted inside narrowed vessels recover normal flux of blood flows, they instantaneously change the wall shear stress (WSS) distribution on the vessel surface. Improper stent implantation positions bring high possibilities of restenosis as it enlarges the low WSS regions and subsequently stimulates more epithelial cell outgrowth on vessel walls. To optimize the stent position for lowering the risk of restenosis, we successfully established a digital three-dimensional (3-D) model based on a real clinical coronary artery and analysed the optimal stenting strategies by computational simulation. Via microfabrication and 3-D printing technology, the digital model was also converted into in vitro microfluidic models with 3-D micro channels. Simultaneously, physicians placed real stents inside them; i.e., they performed “virtual surgeries”. The hydrodynamic experimental results showed that the microfluidic models highly inosculated the simulations. Therefore, our study not only demonstrated that the half-cross stenting strategy could maximally reduce restenosis risks but also indicated that 3-D printing combined with clinical image reconstruction is a promising method for future angiocardiopathy research.

Image-based computational simulation of sub-endothelial LDL accumulation in a human right coronary artery

Accumulation of low density lipoproteins (LDL) in the vessel wall is suggested as the initiator of atherosclerosis and coronary stenosis. This process is associated with the performance of endothelium layer that regulates entering of macromolecules to the vessel wall. Therefore, the present study aims to investigate sub-endothelial accumulation of LDL molecules in a coronary tree and predict atherosclerosis prone sites. Non-Newtonian blood flow is simulated for normal and hypertensive conditions through the lumen of a right coronary artery reconstructed from computed tomography (CT) images. A three-pore model is implemented as the endothelium boundary condition and hence, plasma flow and LDL transport are simulated within the arterial wall. Based on the pore model, endothelium pathways divide into normal junctions, vesicles and leaky junctions. Most of LDL molecules pass through the leaky junctions that arise at locations with low wall shear stress (WSS). Results indicate that increase in the number of leaky junctions at branch points with low WSS can lead to both elevated levels of sub-endothelial LDL accumulation and atherosclerosis risk. Findings reveal that at the branch points with disturbed flow, sub-endothelial concentration of LDL for the hypertensive condition is higher than the normal condition, however for the rest of regions with uniform geometry and unidirectional flow, this is reversed. Comparisons of non-Newtonian and Newtonian flows show mean increases of 34% and 13% in the sub-endothelial concentrations of Newtonian flows during the normal and hypertensive conditions, respectively.

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.

Stability of carotid artery under steady-state and pulsatile blood flow: a fluid-structure interaction study

It has been shown that arteries may buckle into tortuous shapes under lumen pressure, which in turn could alter blood flow. However, the mechanisms of artery instability under pulsatile flow have not been fully understood. The objective of this study was to simulate the buckling and post-buckling behaviors of the carotid artery under pulsatile flow using a fully coupled fluid-structure interaction (FSI) method. The artery wall was modeled as a nonlinear material with a two-fiber strain-energy function. FSI simulations were performed under steady-state flow and pulsatile flow conditions with a prescribed flow velocity profile at the inlet and different pressures at the outlet to determine the critical buckling pressure. Simulations were performed for normal (160 ml/min) and high (350 ml/min) flow rates and normal (1.5) and reduced (1.3) axial stretch ratios to determine the effects of flow rate and axial tension on stability. The results showed that an artery buckled when the lumen pressure exceeded a critical value. The critical mean buckling pressure at pulsatile flow was 17-23% smaller than at steady-state flow. For both steady-state and pulsatile flow, the high flow rate had very little effect (&lt;5%) on the critical buckling pressure. The fluid and wall stresses were drastically altered at the location with maximum deflection. The maximum lumen shear stress occurred at the inner side of the bend and maximum tensile wall stresses occurred at the outer side. These findings improve our understanding of artery instability in vivo.

Tortuosity of coronary bifurcation as a potential local risk factor for atherosclerosis: CFD steady state study based on in vivo dynamic CT measurements

The purpose of the present study was to determine whether in vivo bifurcation geometric factors would permit prediction of the risk of atherosclerosis. It is worldwide accepted that low or oscillatory wall shear stress (WSS) is a robust hemodynamic factor in the development of atherosclerotic plaque and has a strong correlation with the local site of plaque deposition. However, it still remains unclear how coronary bifurcation geometries are correlated with such hemodynamic forces. Computational fluid dynamics simulations were performed on left main (LM) coronary bifurcation geometries derived from CT of eight patients without significant atherosclerosis. WSS amplitudes were accurately quantified at two high risk zones of atherosclerosis, namely at proximal left anterior descending artery (LAD) and at proximal left circumflex artery (LCx), and also at three high WSS concentration sites near the bifurcation. Statistical analysis was used to highlight relationships between WSS amplitudes calculated at these five zones of interest and various geometric factors. The tortuosity index of the LM-LAD segment appears to be an emergent geometric factor in determining the low WSS amplitude at proximal LAD. Strong correlations were found between the high WSS amplitudes calculated at the endothelial regions close to the flow divider. This study not only demonstrated that CT imaging studies of local risk factor for atherosclerosis could be clinically performed, but also showed that tortuosity of LM-LAD coronary branch could be used as a surrogate marker for the onset of atherosclerosis.

Numerical simulation and clinical implications of stenosis in coronary blood flow

Fractional flow reserve (FFR) is the gold standard to guide coronary interventions. However it can only be obtained via invasive angiography. The objective of this study is to propose a noninvasive method to determine FFRCT by combining computed tomography angiographic (CTA) images and computational fluid dynamics (CFD) technique. Utilizing the method, this study explored the effects of diameter stenosis (DS), stenosis length, and location on FFRCT. The baseline left anterior descending (LAD) model was reconstructed from CTA of a healthy porcine heart. A series of models were created by adding an idealized stenosis (with DS from 45% to 75%, stenosis length from 4 mm to 16 mm, and at 4 locations separately). Through numerical simulations, it was found that FFRCT decreased (from 0.89 to 0.74), when DS increased (from 45% to 75%). Similarly, FFRCT decreased with the increase of stenosis length and the stenosis located at proximal position had lower FFRCT than that at distal position. These findings are consistent with clinical observations. Applying the same method on two patients' CTA images yielded FFRCT close to the FFR values obtained via invasive angiography. The proposed noninvasive computation of FFRCT is promising for clinical diagnosis of CAD.

Perspective on CFD studies of coronary artery disease lesions and hemodynamics: a review

Coronary artery disease (CAD) is the most common cardiovascular disease. Early diagnosis of CAD's physiological significance is of utmost importance for guiding individualized risk-tailored treatment strategies. In this paper, we first review the state-of-the-art clinical diagnostic indices to quantify the severity of CAD and the associated invasive and noninvasive imaging technologies in order to quantify the anatomical parameters of diameter stenosis, area stenosis, and hemodynamic indices of coronary flow reserve and fractional flow reserve. With the development of computational technologies and CFD methods, tremendous progress has been made in applying image-based CFD simulation techniques to elucidate the effects of hemodynamics in vascular pathophysiology toward the initialization and progression of CAD. So then, we review the advancements of CFD technologies in patient-specific modeling, involving the development of geometry reconstruction, boundary conditions, and fluid-structure interaction. Next, we review the applications of CFD to stenotic sites, in order to compute their hemodynamic parameters and study the relationship between the hemodynamic conditions and the clinical indices, to thereby assess the amount of viable myocardium and candidacy for percutaneous coronary intervention. Finally, we review the strengths and limitations of current researches of applying CFD to CAD studies.

Numerical investigation of blood flow in three-dimensional porcine left anterior descending artery with various stenoses

Coronary heart disease causes obstruction of coronary blood flow and is the leading cause of death worldwide. The effect of focal stenosis on downstream flow pattern in the coronary arterial tree is not well understood. Here, the blood flows in normal and diseased porcine left anterior descending (LAD) arterial tree were modeled and compared to determine the effects of stenosis on the blood flow distribution and hemodynamic parameters. The anatomical model of LAD was extracted from a porcine heart by computed tomography (CT), which was comprised of a main trunk and nine side branches. Stenoses with various severities were imposed into the main trunk between the first and second side branches, and the boundary condition at each outlet accounted for the effect of stenosis on the flow rate in the downstream vasculature. It was found that only significant stenosis (≥75% area reduction) considerably altered pressure drop and total flow rate distribution in branches and at each bifurcation. The effect of significant stenosis on bifurcations, however, diminished at downstream locations. As demonstrated by distributions of oscillatory shear index and relative residence time, non-significant stenosis (<75% area reduction) has the potential to induce atherosclerosis near the ostium of downstream side branch, while significant stenosis can promote atherosclerosis in its wake.

Effects of stenosis on the porcine left anterior descending arterial tree

In this study, hemodynamics in the normal and diseased left anterior descending (LAD) arterial trees were compared to estimate the effects of stenosis on the flow rate distribution, detailed flow field and wall shear stress (WSS) distributions on both transient and steady flow conditions. The anatomical model was reconstructed from computed tomography (CT) images of a normal porcine heart. Stenosis was imposed at the trunk of LAD tree with different area stenosis ratios (25%, 50%, 75% and 90%) to study the effect of stenosis. It has been found that the steady-state simulation is competent to demonstrate the prominent flow features of transit flow. Only significant stenosis altered the flow rate considerably, and its effects diminished at the downstream bifurcations. Based on the WSS distribution, non-significant stenosis potentially led to the development of atherosclerosis near the ostium of the downstream side branch and significant stenosis might promote atherosclerosis in its wake.

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.

Blood pressure regulation VIII: resistance vessel tone and implications for a pro-atherogenic conduit artery endothelial cell phenotype

Dysfunction of the endothelium is proposed as the primary initiator of atherosclerotic peripheral artery disease, which occurs mainly in medium- to large-sized conduit arteries of the lower extremities (e.g., iliac, femoral, popliteal arteries). In this review article, we propose the novel concept that conduit artery endothelial cell phenotype is determined, in part, by microvascular tone in skeletal muscle resistance arteries through both changes in arterial blood pressure as well as upstream conduit artery shear stress patterns. First, we summarize the literature supporting the involvement of sympathetic nerve activity (SNA) and nitric oxide (NO) in the modulation of microvascular tone and arterial blood pressure. We then focus on the role of elevated blood pressure and shear stress profiles in modulating conduit artery endothelial cell phenotype. Last, we discuss findings from classic and emerging studies indicating that increased vascular resistance, as it occurs in the context of increased SNA and/or reduced NO bioavailability, is associated with greater oscillatory shear stress (e.g., increased retrograde shear) in upstream conduit arteries. The ideas put forth in this review set the stage for a new paradigm concerning the mechanistic link between increased microvascular tone and development of conduit artery endothelial dysfunction and thus increased risk for peripheral artery disease. Indeed, a vast amount of evidence supports the notion that excessive blood pressure and oscillatory shear stress are potent pro-atherogenic signals to the endothelium.

Effect of the degree of LAD stenosis on "competitive flow" and flow field characteristics in LIMA-to-LAD bypass surgery

The long-term patency of the left internal mammary artery (LIMA) in left anterior descending (LAD) coronary stenosis bypass surgery is believed to be related to the degree of competitive flow between the LAD and LIMA. To investigate the effect of the LAD stenosis severity on this phenomenon and on haemodynamics in the LIMA and anastomosis region, a numerical LIMA-LAD model was developed based on 3D geometric (obtained from a cast) and hemodynamic data from an experimental pig study. Proximal LAD pressure was used as upstream boundary condition. The model counted 13 outlets (12 septal arteries and the distal LAD) where flow velocities were imposed in systole, while myocardial conductance was imposed in diastole via an implicit scheme. LAD stenoses of 100 (total occlusion), 90, 75 and 0 % area reduction were constructed. Low degree of LAD stenosis was associated with highly competitive flow and low wall shear stress (WSS) in the LIMA, an unfavourable hemodynamic regime which might contribute to WSS-related remodelling of the LIMA and suboptimal long-term LIMA bypass performance.

Which diameter and angle rule provides optimal flow patterns in a coronary bifurcation?

The branching angle and diameter ratio in epicardial coronary artery bifurcations are two important determinants of atherogenesis. Murray's cubed diameter law and bifurcation angle have been assumed to yield optimal flows through a bifurcation. In contrast, we have recently shown a 7/3 diameter law (HK diameter model), based on minimum energy hypothesis in an entire tree structure. Here, we derive a bifurcation angle rule corresponding to the HK diameter model and critically evaluate the streamline flow through HK and Murray-type bifurcations. The bifurcations from coronary casts were found to obey the HK diameter model and angle rule much more than Murray's model. A finite element model was used to investigate flow patterns for coronary artery bifurcations of various types. The inlet velocity and pressure boundary conditions were measured by ComboWire. Y-bifurcation of Murray type decreased wall shear stress-WSS (10%-40%) and created an increased oscillatory shear index-OSI in atherosclerosis-prone regions as compared with HK-type bifurcations. The HK-type bifurcations were found to have more optimal flow patterns (i.e., higher WSS and lower OSI) than Murray-type bifurcations which have been traditionally believed to be optimized. This study has implications for changes in bifurcation angles and diameters in percutaneous coronary intervention.

A validated predictive model of coronary fractional flow reserve

Myocardial fractional flow reserve (FFR), an important index of coronary stenosis, is measured by a pressure sensor guidewire. The determination of FFR, only based on the dimensions (lumen diameters and length) of stenosis and hyperaemic coronary flow with no other ad hoc parameters, is currently not possible. We propose an analytical model derived from conservation of energy, which considers various energy losses along the length of a stenosis, i.e. convective and diffusive energy losses as well as energy loss due to sudden constriction and expansion in lumen area. In vitro (constrictions were created in isolated arteries using symmetric and asymmetric tubes as well as an inflatable occluder cuff) and in vivo (constrictions were induced in coronary arteries of eight swine by an occluder cuff) experiments were used to validate the proposed analytical model. The proposed model agreed well with the experimental measurements. A least-squares fit showed a linear relation as (Δp or FFR)(experiment) = a(Δp or FFR)(theory) + b, where a and b were 1.08 and -1.15 mmHg (r(2) = 0.99) for in vitro Δp, 0.96 and 1.79 mmHg (r(2) = 0.75) for in vivo Δp, and 0.85 and 0.1 (r(2) = 0.7) for FFR. Flow pulsatility and stenosis shape (e.g. eccentricity, exit angle divergence, etc.) had a negligible effect on myocardial FFR, while the entrance effect in a coronary stenosis was found to contribute significantly to the pressure drop. We present a physics-based experimentally validated analytical model of coronary stenosis, which allows prediction of FFR based on stenosis dimensions and hyperaemic coronary flow with no empirical parameters.