Physiological flow simulation in residual human stenoses after coronary angioplasty

Impact of the stent footprint on endothelial wall shear stress in patient-specific coronary arteries: A computational analysis from the SHEAR-STENT trial

BACKGROUND AND OBJECTIVE

Wall shear stress (WSS) has been known to play a critical role in the development of several complications following coronary artery stenting, including in-stent restenosis and thrombosis. Computational fluid dynamics is often used to quantify the post-stenting WSS, which may potentially be used as a predictive metric. However, large-scale studies for WSS-based risk stratification often neglect the footprint of the stent due to reconstruction challenges. The primary objective of this study is to statistically evaluate the impact of the stent footprints (Xience and Resolute stents) on the computed endothelial WSS and quantitatively identify the relationship between these local hemodynamic alterations and the global properties of the vessel, such as curvature, on WSS. The ultimate goal is to evaluate whether and when it is worth including the footprint of the stent in an in-silico study to compute the WSS reliably.

METHODS

A previously developed semi-automated reconstruction approach for patient-specific coronaries was employed as a part of the SHEAR-STENT trial. A subset of patients was analyzed (N=30), and CFD simulations were performed with and without the stent to evaluate the impact of the stent footprint on WSS. Due to the computationally expensive nature of transient analyses, a sub-cohort of ten patients were used to assess the reliability of WSS obtained from steady computations as a surrogate for the time-averaged results. Global and local vessel curvature data were extracted for all cases and evaluated against stent-induced alterations in the WSS. The differences between the Xience and Resolute stent platforms were also examined to quantify each stent's unique WSS footprint.

RESULTS

Results from the surrogate analysis indicate that steady WSS serves as an excellent approximation of the time-averaged computations. The presence of either stent footprint causes a statistically significant decrease in the space-averaged WSS, and a significant increase in the endothelial regions exposed to very low WSS as well (<0.5 Pa). Negative correlations were observed between vessel curvature and WSS differences, indicating that macroscopic vessel characteristics play a more prominent role in determining endothelial WSS at higher curvature values. In our pool of cases, comparison of Xience and Resolute stents revealed that the Resolute platform seems to lead to lower space-averaged WSS and an increase in areas of very low WSS.

CONCLUSION

These results outline (1) the necessity of including the stent footprint for accurate in-silico WSS analysis; (2) the global features of stented arteries serving as the dominant determinant of WSS past a certain curvature threshold; and (3) the Xience stent resulting in a milder presence of hemodynamically unfavorable WSS regions compared to the Resolute stent.

Impact of stent malapposition on intracoronary flow dynamics: An optical coherence tomography-based patient-specific study

Percutaneous coronary intervention with stent implantation has emerged as a popular approach to treat coronary artery stenosis. Stent malapposition (SM), also referred as incomplete stent apposition, could reduce stent tissue coverage and hence increase the risk of late stent thrombosis. The objective of this study was to investigate the impact of SM on intracoronary flow dynamics by combining optical coherence tomography (OCT) image-based model reconstruction and computational analysis. Firstly, a stenosed coronary artery model was reconstructed from OCT and angiography imaging data of a patient. Two structural analyses were carried out to simulate two types of coronary artery stent implantations: a fully-apposed (FA) case and a SM case. Then, based on the two deformed coronary geometries, two computational fluid dynamics (CFD) analyses were performed to evaluate the differences of hemodynamic metrics between the FA and the SM cases, including wall shear stress (WSS), time-averaged WSS (TWSS), oscillatory shear index (OSI), WSS gradient (WSSG), time-averaged WSSG (TWSSG), and relative residence time (RRT). The results indicated that maximum flow velocity was higher in the SM case than that of the FA case, due to the incomplete expansion of the stent and artery. Moreover, the SM case had a lower percentage of areas of adverse WSS (< 0.5 Pa) and RRT (> 10/Pa) but a higher percentage of areas of adverse OSI (> 0.1) and WSSG (> 5000 Pa/m). Specifically, the differences of OSI, WSSG, and RRT between the two cases were relatively small. It was suggested that SM might not be responsible for negative hemodynamic metrics which would further result in stent thrombosis on the basis of the present specific model.

Influence of renal artery stenosis morphology on hemodynamics

OBJECTIVE

Currently, the clinical classification of the severity of renal artery stenosis (RAS) solely depends on the degree of stenosis. In addition, when the stenosis degree is between 50% and 70%, the clinical strategy is decided based on whether the RAS is hemodynamically significant. In this study, the influence of RAS morphological parameters on hemodynamics was numerically analyzed to provide a theoretical basis for clinical treatment.

METHODS

Idealized RAS models were established to investigate the hemodynamic effects of the stenosis length, asymmetric stenosis, and direction of the opening of the renal artery.

RESULTS

The longer the stenosis length, the greater is the ratio of the low time-averaged wall shear stress (WSS) and high oscillatory shear index (OSI) area distal stenosis (when the stenosis area is the same). In addition, asymmetric stenosis leads to a significant increase in the ratio of the renal artery peak systolic velocity (R-PSV) and the abdominal aorta peak systolic velocity (A-PSV) when the stenosis area is 60-70%. Furthermore, the fraction flow reserve (FFR) of the RAS model with 12 mm stenosis length, upward eccentricity and upward direction of renal artery opening was approximately equal to the cumulative value of the influence of different stenosis morphologies on FFR.

CONCLUSION

An assessment of the severity of RAS should consider the stenosis area and other morphological parameters, including the length and asymmetry of RAS as well as the direction of the opening of renal artery, particularly when the stenosis degree of RAS is between 50% and 70%.

Influence of near-wall PIV data on recirculation hemodynamics in a patient-specific moderate stenosis: Experimental-numerical comparison

BACKGROUND

Recirculation zones within the blood vessels are known to influence the initiation and progression of atherosclerotic lesions. Quantification of recirculation parameters with accuracy remains subjective due to uncertainties in measurement of velocity and derived wall shear stress (WSS).

OBJECTIVE

The primary aim is to determine recirculation height and length from PIV experiments while validating with two different numerical methods: finite-element (FE) and -volume (FV). Secondary aim is to analyze how FE and FV compare within themselves.

METHODS

PIV measurements were performed to obtain velocity profiles at eight cross sections downstream of stenosis at flow rate of 200 ml/min. WSS was obtained by linear/quadratic interpolation of experimental velocity measurements close to wall.

RESULTS

Recirculation length obtained from PIV technique was 1.47 cm and was within 2.2% of previously reported in-vitro measurements. Derived recirculation length from PIV agreed within 6.8% and 8.2% of the FE and FV calculations, respectively. For lower shear rate, linear interpolation with five data points results in least error. For higher shear rate either higher order (quadratic) interpolation with five data points or lower order (linear) with lesser (three) data points leads to better results.

CONCLUSION

Accuracy of the recirculation parameters is dependent on number of near wall PIV data points and the type of interpolation algorithm used.

Numerical study to identify the effect of fluid presence on the mechanical behavior of the stents during coronary stent expansion

In this study, structural analysis and one-way fluid-structure interaction (FSI) analysis were performed to identify the effect of fluid presence on the mechanical behavior of the stents during stent expansion. An idealized vessel model with stenosis was used for simulation, and stents made of metal and polymer were assumed, respectively. The bilinear model was applied to the stents, and the Mooney-Rivlin model was applied to the arterial wall and plaque. The blood used in the FSI analysis was assumed to be a non-Newtonian fluid. As a result of all numerical simulations, the von Mises stress, the first principal stress and the displacement were calculated as the mechanical behaviors. Through the comparison of the results of the structural analysis with those of the one-way FSI analysis, our results indicated the fluid had no significant influence on the expansion of the metal stent. However, it was found that the expansion of the polymer stent affected by the presence of fluid. These findings meant the one-way FSI technique was suggested to achieve an accurate analysis when targeting a polymer stent for numerical simulation.

Structural and Hemodynamic Analyses of Different Stent Structures in Curved and Stenotic Coronary Artery

Coronary artery stenting is commonly used for the treatment of coronary stenosis, and different stent structures indeed have various impacts on the stress distribution within the plaque and artery as well as the local hemodynamic environment. This study aims to evaluate the performance of different stent structures by characterizing the mechanical parameters after coronary stenting. Six stent structures including three commercially-shaped stents (Palmaz-Schatz-shaped, Xience Prime-shaped, and Cypher-shaped) and three author-developed stents (C-Rlink, C-Rcrown, and C-Astrut) implanted into a curved stenotic coronary artery were investigated. Structural analyses of the balloon-stent-plaque-artery system were first performed, and then followed by hemodynamic analyses. The results showed that among the three commercially-shaped stents, the Palmaz-Schatz-shaped had the least stent dogboning and recoiling, corresponding to the greatest maximum plastic strain and the largest diameter change, nevertheless, it induced the highest maximum von Mises stress on plaque, arterial intima and media. From the viewpoint of hemodynamics, the Palmaz-Schatz-shaped displayed smaller areas of adverse low wall shear stress (<0.5 Pa), low time-averaged wall shear stress (<0.5 Pa), and high oscillating shear index (>0.1). Compared to the Cypher-shaped, the C-Rcrown and C-Astrut had smaller recoiling, greater maximum plastic stain and larger diameter change, which indicated the improved mechanical performance of the Cypher-shaped stent. Moreover, both C-Rcrown and C-Astrut exhibited smaller areas of adverse low wall shear stress, and low time-averaged wall shear stress, but only the C-Rcrown displayed a smaller area of adverse high oscillating shear index. The present study evaluated and compared the performance of six different stents deployed inside a curved artery, and could be potentially utilized as a guide for the selection of suitable commercially-shaped stent for clinical application, and to provide an approach to improve the performance of the commercial stents.

The influence of artery wall curvature on the anatomical assessment of stenosis severity derived from fractional flow reserve: a computational fluid dynamics study

This study aims to investigate the influence of artery wall curvature on the anatomical assessment of stenosis severity and to identify a region of misinterpretation in the assessment of per cent area stenosis (AS) for functionally significant stenosis using fractional flow reserve (FFR) as standard. Five artery models of different per cent AS severity (70, 75, 80, 85 and 90%) were considered. For each per cent AS severity, the angle of curvature of the arterial wall varied from straight to an increasingly curved model (0°, 30°, 60°, 90° and 120°). Computational fluid dynamics was performed under transient physiologic hyperemic flow conditions to investigate the influence of artery wall curvature on the pressure drop and the FFR. The findings in this study may be useful in in vitro anatomical assessment of functionally significant stenosis. The FFR decreased with increasing stenosis severity for a given curvature of the artery wall. Moreover, a significant decrease in FFR was found between straight and curved models discussed for a given severity condition. These findings indicate that the curvature effect was included in the FFR assessment in contrast to minimum lumen area (MLA) or per cent AS assessment. The MLA or per cent AS assessment may lead to underestimation of stenosis severity. From this numerical study, an uncertainty region could be evaluated using the clinical FFR cutoff value of 0.8. This value was observed at 81.98 and 79.10% AS for arteries with curvature angles of 0° and 120° respectively. In conclusion, the curvature of the artery should not be neglected in in vitro anatomical assessment.

Changes in the reference lumen size of target lesions before and after coronary stent implantation: Evaluation with frequency domain optical coherence tomography

Objective

In optical coherence tomography (OCT)-guided percutaneous coronary intervention (PCI), stent size is usually determined according to the pre-PCI lumen size of either the distal or proximal reference site. However, the effect of the OCT imaging catheter crossing the target lesion on the reference lumen measurements has not been studied. We evaluated changes in the reference lumen size before and after PCI using frequency domain OCT.

Methods

For 100 consecutive patients with PCI, mean lumen diameter (LD) and lumen area (LA) were measured at the proximal and distal reference sites before and after coronary stent implantation with OCT.

Results

Mean LD and LA of the distal reference site were significantly increased after PCI with stent implantation (2.57 ± 0.6 to 2.62 ± 0.64 mm, p < 0.01 and 5.20 ± 2.66 to 5.41 ± 2.54 mm², p < 0.01, respectively). By contrast, these indices at the proximal reference site were significantly decreased. ROC curve analysis selected MLA of 1.50 mm² as the best cutoff value for changes in mean LD. Distal mean LD was markedly increased after PCI in lesions with MLA < 1.50 mm (2.28 ± 0.48 to 2.40 ± 0.17 mm, P < 0.001), but did not change in lesions with MLA > 1.50 mm². Tissue characteristics were not correlated with changes in reference lumen size.

Conclusions

When we select the stent size during OCT-guided PCI, we need to pay attention to the decrease in the luminal measurement of the reference sites, especially in lesions with tight stenosis.

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.

Diagnostic Uncertainties During Assessment of Serial Coronary Stenoses: An In Vitro Study

Currently, the diagnosis of coronary stenosis is primarily based on the well-established functional diagnostic parameter, fractional flow reserve (FFR: ratio of pressures distal and proximal to a stenosis). The threshold of FFR has a “gray” zone of 0.75–0.80, below which further clinical intervention is recommended. An alternate diagnostic parameter, pressure drop coefficient (CDP: ratio of trans-stenotic pressure drop to the proximal dynamic pressure), developed based on fundamental fluid dynamics principles, has been suggested by our group. Additional serial stenosis, present downstream in a single vessel, reduces the hyperemic flow, Q˜h, and pressure drop, Δp˜, across an upstream stenosis. Such hemodynamic variations may alter the values of FFR and CDP of the upstream stenosis. Thus, in the presence of serial stenoses, there is a need to evaluate the possibility of misinterpretation of FFR and test the efficacy of CDP of individual stenoses. In-vitro experiments simulating physiologic conditions, along with human data, were used to evaluate nine combinations of serial stenoses. Different cases of upstream stenosis (mild: 64% area stenosis (AS) or 40% diameter stenosis (DS); intermediate: 80% AS or 55% DS; and severe: 90% AS or 68% DS) were tested under varying degrees of downstream stenosis (mild, intermediate, and severe). The pressure drop-flow rate characteristics of the serial stenoses combinations were evaluated for determining the effect of the downstream stenosis on the upstream stenosis. In general, Q˜h and Δp˜ across the upstream stenosis decreased when the downstream stenosis severity was increased. The FFR of the upstream mild, intermediate, and severe stenosis increased by a maximum of 3%, 13%, and 19%, respectively, when the downstream stenosis severity increased from mild to severe. The FFR of a stand-alone intermediate stenosis under a clinical setting is reported to be ∼0.72. In the presence of a downstream stenosis, the FFR values of the upstream intermediate stenosis were either within (0.77 for 80%–64% AS and 0.79 for 80%–80% AS) or above (0.88 for 80%–90% AS) the “gray” zone (0.75–0.80). This artificial increase in the FFR value within or above the “gray” zone for an upstream intermediate stenosis when in series with a clinically relevant downstream stenosis could lead to misinterpretation of functional stenosis severity. In contrast, a distinct range of CDP values was observed for each case of upstream stenosis (mild: 8–10; intermediate: 47–54; and severe: 130–155). The nonoverlapping range of CDP could better delineate the effect of the downstream stenosis from the upstream stenosis and allow for the accurate diagnosis of the functional severity of the upstream stenosis.

Influence of Variable Native Arterial Diameter and Vasculature Status on Coronary Diagnostic Parameters

In current practice, diagnostic parameters, such as fractional flow reserve (FFR) and coronary flow reserve (CFR), are used to determine the severity of a coronary artery stenosis. FFR is defined as the ratio of hyperemic pressures distal (p˜rh) and proximal (p˜ah) to a stenosis. CFR is the ratio of flow at hyperemic and basal condition. Another diagnostic parameter suggested by our group is the pressure drop coefficient (CDP). CDP is defined as the ratio of the pressure drop across the stenosis to the upstream dynamic pressure. These parameters are evaluated by invasively measuring flow (CFR), pressure (FFR), or both (CDP) in a diseased artery using guidewire tipped with a sensor. Pathologic state of artery is indicated by lower CFR (<2). Similarly, FFR lower than 0.75 leads to clinical intervention. Cutoff for CDP is under investigation. Diameter and vascular condition influence both flow and pressure drop, and thus, their effect on FFR and CDP was studied. In vitro experiment coupled with pressure-flow relationships from human clinical data was used to simulate pathophysiologic conditions in two representative arterial diameters, 2.5 mm (N1) and 3 mm (N2). With a 0.014 in. (0.35 mm) guidewire inserted, diagnostic parameters were evaluated for mild (∼64% area stenosis (AS)), intermediate (∼80% AS), and severe (∼90% AS) stenosis for both N1 and N2 arteries, and between two conditions, with and without myocardial infarction (MI). Arterial diameter did not influence FFR for clinically relevant cases of mild and intermediate stenosis (difference < 5%). Stenosis severity was underestimated due to higher FFR (mild: ∼9%, intermediate: ∼ 20%, severe: ∼ 30%) for MI condition because of lower pressure drops, and this may affect clinical decision making. CDP varied with diameter (mild: ∼20%, intermediate: ∼24%, severe: by 2.5 times), and vascular condition (mild: ∼35%, intermediate: ∼14%, severe: ∼ 9%). However, nonoverlapping range of CDP allowed better delineation of stenosis severities irrespective of diameter and vascular condition.

Particle depositions and related hemodynamic parameters in the multiple stenosed right coronary artery

BACKGROUND

Blood flow analysis of the human right coronary artery (RCA) has been carried out to investigate the effects of serial stenosis on coronary hemodynamics. A 3-D model of a serial stenosed RCA was reconstructed based on multislice computerized tomography images.

METHODS

A velocity waveform in the proximal RCA and a pressure waveform in the distal RCA of a patient with a severe stenosis were acquired with a catheter delivered wire probe and applied as boundary conditions. The numerical analysis examines closely the effect of a multiple serial stenosis on the hemodynamic characteristics such as flow separation, wall shear stress (WSS) and particle depositions.

RESULTS AND CONCLUSIONS

Energy loss associated with such flow expansion after each constriction will be large and consequently the pressure drop will be higher. Overall pressure drop increased from 1700 Pa (12.75 mmHg) at the end diastole to 11000 Pa (82.5 mmHg) at the peak systole. At the peak systole the WSS values reached 110 Pa in the stenosis with 28% diameter reduction and 210 Pa in the stenosis with 54% diameter reduction, which is high enough to damage the endothelial cells. However at the end of one cardiac cycle a percent of 1.4% (15 from 1063 particles release at the inlet section) remain inside the stenosed RCA.

Effect of guidewire on contribution of loss due to momentum change and viscous loss to the translesional pressure drop across coronary artery stenosis: an analytical approach

Background

Guidewire (GW) size and stenosis dimensions are the two major factors affecting the translesional pressure drop. Studying the combined effect of these parameters on the mean pressure drop (Δp) across the stenosis is of high practical importance.

Methods

In this study, time averaged mass and momentum conservation equations are solved analytically to obtain pressure drop-flow, Δp-Q, curves for three different percentage area blockages corresponding to moderate (64%), intermediate (80%), and severe (90%) stenoses. Stenosis is considered to be axisymmetric consisting of three different sections namely converging, throat, and diverging regions. Analytical expressions for pressure drop are obtained for each of these regions separately. Using this approach, effects of lesion length and GW insertion on the mean translesional pressure drop and its component (loss due to momentum change and viscous loss) are analyzed.

Results and Conclusion

It is observed that for a given percent area stenosis (AS), increase in the throat length only increases the viscous loss. However, increase in the severity of stenosis and GW insertion increase both loss due to momentum change and viscous loss. GW insertion has greater contribution to the rise in viscous loss (increase by 2.14 and 2.72 times for 64% and 90% AS, respectively) than loss due to momentum change (1.34% increase for 64% AS and 25% decrease for 90% AS). It also alters the hyperemic pressure drop in moderate (48% increase) to intermediate (30% increase) stenoses significantly. However, in severe stenoses GW insertion has a negligible effect (0.5% increase) on hyperemic translesional pressure drop. It is also observed that pressure drop in a severe stenosis is less sensitive to lesion length variation (4% and 14% increase in Δp for without and with GW, respectively) as compared to intermediate (10% and 30% increase in Δp for without and with GW, respectively) and moderate stenoses (22% and 48% increase in Δp for without and with GW, respectively). Based on the contribution of pressure drop components to the total translesional pressure drop, it is found that viscous losses are dominant in moderate stenoses, while in severe stenoses losses due to momentum changes are significant. It is also shown that this simple analytical solution can provide valuable information regarding interpretation of coronary diagnostic parameters such as fractional flow reserve (FFR).

Coupled fluid-wall modelling of steady flow in stenotic carotid arteries

Arterial stenoses may cause critical blood flow and wall conditions leading to clinical complications. In this paper computational models of stenotic carotid arteries are proposed and the vessel wall collapse phenomenon is studied. The models are based on fluid-structure interactions (FSI) between blood and the arterial walls. Coupled finite element and computational fluid dynamics methods are used to simultaneously solve for stress and displacement in the solid, and for pressure, velocity and shear stress in the fluid domain. Results show high wall shear stress at the stenosis throat and low (negative) values accompanied by disturbed flow patterns downstream of the stenosis. The wall circumferential stress varies abruptly from tensile to compressive along the stenosis with high stress concentration on the plaque shoulders showing regions of possible plaque rupture. Wall compression and collapse are observed for severe cases. Post-stenotic collapse of the arterial wall occurs for stenotic severity as low as 50%, with the assumption that a given amount of blood flow needs to pass the stenotic artery; whereas if constant pressure drop should be maintained across a constriction, then collapse happens at severity of 75% and above. The former assumption is based on the requirement of adequate blood supply to the downstream organs/tissue, while the latter stems from the fact that the pumping mechanism of the body has a limited capacity in regulating blood pressure, in case a stenosis appears in the vasculature.

Right ventricular inefficiency in repaired tetralogy of Fallot: proof of concept for energy calculations from cardiac MRI data

Repaired tetralogy of Fallot (rTOF) patients develop right ventricular (RV) dilatation and dysfunction. To prevent their demise, pulmonary valve replacement is necessary, though appropriate timing for it is challenged by a paucity of reliable diagnostic parameters. In this pilot study, we hypothesized that stroke work (SW) and energy calculations would delineate the inefficiency of RV performance in rTOF. RV SW was calculated for both an rTOF and a normal subject by utilizing RV pressure and volume measurements obtained during cardiac catheterization and MRI studies. Energy transfer rate and ratio were computed at the main pulmonary artery (PA). Compared to the normal RV, the rTOF RV had higher operating pressure, lower computed SW (0.078 J vs. 0.115 J for normal), and higher negative energy transfer at the PA (0.044 J vs. 0.002 J for normal). Furthermore, the energy transfer ratio was nearly twice as high for the normal RV (1.06) as for the rTOF RV (0.56). RV SW and energy transfer ratio delineate important operational efficiency differences in blood flow from the RV to the PA between rTOF and normal subjects. Our pilot data suggest that the rTOF RV is significantly less efficient than normal.

Hemodynamic diagnostics of epicardial coronary stenoses: in-vitro experimental and computational study

BACKGROUND

The severity of epicardial coronary stenosis can be assessed by invasive measurements of trans-stenotic pressure drop and flow. A pressure or flow sensor-tipped guidewire inserted across the coronary stenosis causes an overestimation in true trans-stenotic pressure drop and reduction in coronary flow. This may mask the true severity of coronary stenosis. In order to unmask the true severity of epicardial stenosis, we evaluate a diagnostic parameter, which is obtained from fundamental fluid dynamics principles. This experimental and numerical study focuses on the characterization of the diagnostic parameter, pressure drop coefficient, and also evaluates the pressure recovery downstream of stenoses.

METHODS

Three models of coronary stenosis namely, moderate, intermediate and severe stenosis, were manufactured and tested in the in-vitro set-up simulating the epicardial coronary network. The trans-stenotic pressure drop and flow distal to stenosis models were measured by non-invasive method, using external pressure and flow sensors, and by invasive method, following guidewire insertion across the stenosis. The viscous and momentum-change components of the pressure drop for various flow rates were evaluated from quadratic relation between pressure drop and flow. Finally, the pressure drop coefficient (CDPe) was calculated as the ratio of pressure drop and distal dynamic pressure. The pressure recovery factor (eta) was calculated as the ratio of pressure recovery coefficient and the area blockage.

RESULTS

The mean pressure drop-flow characteristics before and during guidewire insertion indicated that increasing stenosis causes a shift in dominance from viscous pressure to momentum forces. However, for intermediate (approximately 80%) area stenosis, which is between moderate (approximately 65%) and severe (approximately 90%) area stenoses, both losses were similar in magnitude. Therefore, guidewire insertion plays a critical role in evaluating the hemodynamic severity of coronary stenosis. More importantly, mean CDPe increased (17 +/- 3.3 to 287 +/- 52, n = 3, p < 0.01) and mean eta decreased (0.54 +/- 0.04 to 0.37 +/- 0.05, p < 0.01) from moderate to severe stenosis during guidewire insertion.

CONCLUSION

The wide range of CDPe is not affected that much by the presence of guidewire. CDPe can be used in clinical practice to evaluate the true severity of coronary stenosis due to its significant difference between values measured at moderate and severe stenoses.

Theoretical modeling of micro-scale biological phenomena in human coronary arteries

This paper presents a mathematical model of biological structures in relation to coronary arteries with atherosclerosis. A set of equations has been derived to compute blood flow through these transport vessels with variable axial and radial geometries. Three-dimensional reconstructions of diseased arteries from cadavers have shown that atherosclerotic lesions spiral through the artery. The theoretical framework is able to explain the phenomenon of lesion distribution in a helical pattern by examining the structural parameters that affect the flow resistance and wall shear stress. The study is useful for connecting the relationship between the arterial wall geometries and hemodynamics of blood. It provides a simple, elegant and non-invasive method to predict flow properties for geometrically complex pathology at micro-scale levels and with low computational cost.

Developing pulsatile flow in a deployed coronary stent

A major consequence of stent implantation is restenosis that occurs due to neointimal formation. This patho-physiologic process of tissue growth may not be completely eliminated. Recent evidence suggests that there are several factors such as geometry and size of vessel, and stent design that alter hemodynamic parameters, including local wall shear stress distributions, all of which influence the restenosis process. The present three-dimensional analysis of developing pulsatile flow in a deployed coronary stent quantifies hemodynamic parameters and illustrates the changes in local wall shear stress distributions and their impact on restenosis. The present model evaluates the effect of entrance flow, where the stent is placed at the entrance region of a branched coronary artery. Stent geometry showed a complex three-dimensional variation of wall shear stress distributions within the stented region. Higher order of magnitude of wall shear stress of 530 dyn/cm2 is observed on the surface of cross-link intersections at the entrance of the stent. A low positive wall shear stress of 10 dyn/cm2 and a negative wall shear stress of -10 dyn/cm2 are seen at the immediate upstream and downstream regions of strut intersections, respectively. Modified oscillatory shear index is calculated which showed persistent recirculation at the downstream region of each strut intersection. The portions of the vessel where there is low and negative wall shear stress may represent locations of thrombus formation and platelet accumulation. The present results indicate that the immediate downstream regions of strut intersections are areas highly susceptible to restenosis, whereas a high shear stress at the strut intersection may cause platelet activation and free emboli formation.

Guidewire flow obstruction effect on pressure drop-flow relationship in moderate coronary artery stenosis

To evaluate the local hemodynamic effects of coronary artery balloon angioplasty, computational fluid dynamics was applied to representative stenoses geometry post-angioplasty (minimal lesion diameter d(m) = 1.8mm which produced 64% mean area stenoses) based on a group of patients and measured values of coronary flow reserve (CFR) returning to a normal range (3.6+/-0.3). The computations were at mean flow rates (Q) of 50, 100, 150 and 170 ml/min. The study indicates changes in the hemodynamic conditions due to insertion of a guidewire, which can be used to determine the mean pressure drop (Deltap ) and fall in distal mean coronary pressure (p(r)), and thus give quantitative estimate of uncertainty expected in diagnosis of moderate lesions. The guidewire to minimal lesion diameter ratio is 0.26, causing tighter "artifactual" mean area stenoses of 65.5%. During hyperemia, p(m) dropped to 72 mmHg as compared to 75 mmHg under patho-physiological condition without guidewire. Q(h) (subscript h: hyperemia) decreased from 180 without guidewire to 170 ml/min with the guidewire present. Thus, there was a significant approximately 43% increase in Deltap(h) and a approximately 51% increase in the hyperemic flow resistance (R(h) = Deltap(h)/Q(h)) over the patho-physiological condition. This could cause an overestimation of the severity of the moderate stenoses. Transient and steady flow guidewire surface shear stress was 35-50% higher than corresponding values for arterial wall shear stress. The non-dimensional data given in tabular form may be useful in interpretation of clinical guidewire measurements for moderate lesions of similar geometry and size.

Characterizing momentum change and viscous loss of a hemodynamic endpoint in assessment of coronary lesions

Myocardial fractional flow reserve (FFR(myo)) and coronary flow reserve (CFR), measured with guidewire, and quantitative angiography (QA) are widely used in combination to distinguish ischemic from non-ischemic coronary stenoses. Recent studies have shown that simultaneous measurements of FFR(myo) and CFR are recommended to dissociate conduit epicardial coronary stenoses from distal resistance microvascular disease. In this study, a more comprehensive diagnostic parameter, named as lesion flow coefficient, c, is proposed. The coefficient, c, which accounts for mean pressure drop, Delta p, mean coronary flow, Q, and percentage area stenosis, can be used to assess the hemodynamic severity of a coronary artery stenoses. Importantly, the contribution of viscous loss and loss due to momentum change for several lesion sizes can be distinguished using c. FFR(myo), CFR and c were calculated for pre-angioplasty, intermediate and post-angioplasty epicardial lesions, without microvascular disease. While hyperemic c decreased from 0.65 for pre-angioplasty to 0.48 for post-angioplasty lesion with guidewire of size 0.35 mm, FFR(myo) increased from 0.52 to 0.87, and CFR increased from 1.72 to 3.45, respectively. Thus, reduced loss produced by momentum change due to lower percentage area stenosis decreased c. For post-angioplasty lesion, c decreased from 0.55 to 0.48 with the insertion of guidewire. Hence, increased viscous loss due to the presence of guidewire decreased c compared with a lesion without guidewire. Further, c showed a linear relationship with FFR(myo), CFR and percentage area stenosis for pre-angioplasty, intermediate and post-angioplasty lesion. These baseline values of c were developed from fluid dynamics fundamentals for focal lesions, and provided a single hemodynamic endpoint to evaluate coronary stenosis severity.

Delineating the guide-wire flow obstruction effect in assessment of fractional flow reserve and coronary flow reserve measurements

Hemodynamic analysis was conducted to determine uncertainty in clinical measurements of coronary flow reserve (CFR) and fractional flow reserve (FFR) over pathophysiological conditions in a patient group with coronary artery disease during angioplasty. The vasodilation-distal perfusion pressure (CFR-p(rh)) curve was obtained for 0.35- and 0.46-mm guide wires. Our hypothesis is that a guide wire spanning the lesions elevates the pressure gradient and reduces the flow during hyperemic measurements. Maximal CFR-p(rh) was uniquely determined by the intersection of measured CFR and calculated p(rh) of native and residual epicardial lesions in patients without microvascular disease, during angioplasty. Extrapolation of the linear curve gave a zero-coronary flow mean pressure (p(zf)) of approximately 20 mmHg and a corresponding p(rh) of 55 mmHg in the native lesions, which coincided with the level that causes ischemia in human hearts. On this linear curve, values of CFR and FFRmyo (pathophysiological condition) and CFRg and FFRmyog (in the presence of the guide wire) were obtained in native and residual lesions. A strong linear correlation was found between CFR and CFRg [CFR = CFRg x 0.689 + 1.271 (R2= 0.99) for 0.46 mm and CFR = CFRg x 0.757 + 1.004 (R2= 0.99) for 0.35 mm] and between FFRmyo and FFRmyog [FFRmyo = FFRmyog x 0.737 + 0.263 (R2= 0.99) for 0.46 mm and FFRmyo = FFRmyog x 0.790 + 0.210 (R2= 0.99) for 0.35 mm]. This study establishes a strong correlation between CFR and CFRg and between FFRmyo and FFRmyog, which could be used to obtain the true state of occlusion in the coronary artery during angioplasty.

Blood flow patterns in an anatomically realistic coronary vessel: influence of three different reconstruction methods

Many clinical studies suggest that local blood flow patterns are involved in the location and development of atherosclerosis. In coronary diseases, this assumption should be corroborated by quantitative information on local hemodynamic parameters such as pressure, velocity or wall shear stress. Nowadays, computational fluid dynamics (CFD) algorithms coupled to realistic 3-D reconstructions of such vessels make these data accessible. Nevertheless, they should be carefully analysed to avoid misinterpretations when the physiological parameters are not all considered. As an example, we propose here to compare the flow patterns calculated in a coronary vessel reconstructed by three different methods. In the three cases, the vessel trajectory respected the physiology. In the simplest reconstruction, the coronary was modelled by a tube of constant diameter while in the most complex one, the cross-sections corresponded to the reality. We showed that local pressures, wall shear rates and velocity profiles were severely affected by the geometrical modifications. In the constant cross-section vessel, the flow resembled to that of Poiseuille in a straight tube. On the contrary, velocity and shear rate exhibited sudden local variations in the more realistic vessels. As an example, velocity could be multiplied by 5 as compared to Poiseuille's flow and area of very low wall shear rates appeared. The results obtained with the most complex model clearly outlined that, in addition to a proper description of the vessel trajectory, the section area changes should be carefully taken into account, confirming assumptions already highlighted before the rise of commercially available and efficient CFD softwares.