Computational Simulations of Provisional Stenting of a Diseased Coronary Artery Bifurcation Model.

Although stenting of non-branched arterial segments has acceptable clinical outcomes, in-stent restenosis (ISR) and stent thrombosis remain clinically significant issues for vascular bifurcations (15-28% restenosis). Local fluid and solid stresses appear to play an important role in restenosis and thrombosis. The combined role of wall shear stress (WSS) and circumferential wall stresses (CWS) is unclear in the case of stenting at vascular bifurcations. Using numerical simulations, we computed the fluid shear, solid stresses and the stress ratio at the the bifurcation region. Stenting of main vessel increased the maximum CWS in the the side branch (SB), resulting in a nearly two-fold increase of stress ratio in the SB compared to the MB (5.1 × 105 vs. 9.2 × 105). The existence of plaque decreased WSS and increased CWS near the carina, increasing the stress ratio at the SB. The changes of stress ratio were highly consistent with clinical data on bifurcation stenting. Fluid dynamics and solids mechanics should be considered in planning of stenting for a specific bifurcation, as their combined biomechanical effect may play an important role in stent restenosis and thrombosis.

Search for an Optimal Design of a Bioprosthetic Venous Valve: In silico and in vitro Studies.

OBJECTIVE/BACKGROUND: Valve incompetence is a progressive disease of the venous system that may eventually lead to venous hypertension, pain, and ulcers. There is a need for a venous valve prosthesis to replace incompetent valves. Computational and experimental investigations on venous valve design and associated haemodynamics will undoubtedly advance prosthesis design and treatments. Here, the objective is to investigate the effect of venous valve on the fluid and solid mechanics. The hypothesis is that there exists a valve geometry that maximises leaflet shear stress (LSS) but minimises leaflet intramural stress (LIS; i.e., minimise stress ratio = LIS/LSS). METHODS: To address the hypothesis, fully dynamic fluid-structure interaction (FSI) models were developed. The entire cycle of valve opening and closure was simulated. The flow validation experiments were conducted using a stented venous valve prosthesis and a pulse duplicator flow loop. RESULTS: Agreement between the output of FSI simulations and output of pulse duplicator was confirmed. The maximum flow rates were within 6% difference, and the total flow during the cycle was within 10% difference. The simulated high stress ratio region at the leaflet base (five times the leaflet average) predicted the disease location of the vast majority of explanted venous valves reported in clinical literature. The study found that the reduced valve height and leaflet dome shape resulted in optimal performance to provide the lowest stress ratio. CONCLUSION: This study proposes an effective design of venous prostheses and elaborates on the correlations of venous valve with clinical observations.

Hemodynamics of venous valve pairing and implications on helical flow.

BACKGROUND: It has been shown that venous valves have pairing arrangements with specific relative orientation and spacing that contribute to helical flows. The studies to date have not quantified the hemodynamic impact of helical flow formation. A computational model allows various valve orientations and spacings to be studied to better understand the hemodynamic effect of valve pairing. METHODS: Simulations were performed for paired valves at physiologically relevant spacing and orientations to study the flow features and hemodynamics associated with valve pairing configurations. The wall shear stress (WSS), residence time, and pressure drop were evaluated for the various valve pairing cases. RESULTS: It was found that the WSS on the lumen flow side (front) of the leaflet is several times higher than on the valve pocket side (back). With orthogonal paired valves, the WSS at the critical back side is increased. Helical flow was clearly observed only with orthogonal valve pairing. The residence time was reduced to less than half (0.47 vs 1.16 seconds) in the orthogonal valve case compared with the parallel valve cases. The farther spaced valves (6 cm) had the highest residence time. CONCLUSIONS: This simulation study shows that helical flow in the veins of lower extremities is strongly dependent on the relative orientation and spacing of the valves. For optimal orientation (∼90 degrees) and spacing (∼4 cm), strong helical flow is seen, which enhances WSS and reduces the flow resistance and residence time. These findings demonstrate a structure-function relation that optimizes flow patterns in normal physiology, which can be compromised in venous valve disease. The results of this study provide valuable insights that improve the current understanding of blood flow patterns around venous valves and the design of future multiple paired prosthetic valves.

Biomechanical impact of provisional stenting and balloon dilatation on coronary bifurcation: clinical implications.

In-stent restenosis (ISR) and stent thrombosis remain clinically significant problems for bifurcations. Although the role of wall shear stress (WSS) has been well investigated, the role of circumferential wall stresses (CWS) has not been well studied in provisional stenting with and without final kissing balloon (FKB). We hypothesized that the perturbation of CWS at the SB in provisional stenting and balloon dilatation is an important factor in addition to WSS, and, hence, may affect restenosis rates (i.e., higher CWS correlates with higher restenosis). To test this hypothesis, we developed computational models of stent, FKB at bifurcation, and finite element simulations that considered both fluid and solid mechanics of the vessel wall. We computed the stress ratio (CWS/WSS) to show potential correlation with restenosis in clinical studies (i.e., higher stress ratio correlates with higher restenosis). Our simulation results show that stenting in the main branch (MB) increases the maximum CWS in the side branch (SB) and, hence, yields a higher stress ratio in the SB, as compared with the MB. FKB dilatation decreases the CWS and increases WSS, which collectively lowers the stress ratio in the SB. The changes of stress ratio were correlated positively with clinical data in provisional stenting and FKB. Both fluid and solid mechanics need to be evaluated when considering various stenting techniques at bifurcations, as solid stresses also play an important role in clinical outcome. An integrative index of bifurcation mechanics is the stress ratio that considers both CWS and WSS.NEW & NOTEWORTHY Although the role of wall shear stress (WSS) has been well investigated, the role of circumferential wall stresses (CWS) has not been well studied in provisional stenting with and without final kissing balloon. Both fluid and solid mechanics need to be evaluated when considering various stenting techniques at bifurcations. An integrative index of bifurcation mechanics is the stress ratio that considers both CWS and WSS.

Role of vessel-to-prosthesis size mismatch in venous valve performance.

BACKGROUND: Efforts to treat chronic venous insufficiency have focused on the development of prosthetic venous valves. The role of prosthetic valve-to-vessel size matching has not been determined. The purpose of this investigation was to assess the effect of size mismatching on venous valve function and to establish a mismatch limit that affects valve hemodynamic performance and venous wall stress to improve future valve designs and implants. METHODS: Flow dynamics of prosthetic venous valves were studied in vitro using a pulse duplicator flow loop. Valve performance based on flow rate and pressure measurements was determined at oversizing ratios ranging from 4.2% to 25%. Valve open area ratios at different size mismatching ratios were investigated by image analysis. Finally, a wall stress analysis was used to determine the magnitude of circumferential (hoop) stress in the venous wall at various degrees of oversizing. RESULTS: Our findings indicate that valve regurgitate volume, closing time, and pressure difference across the valve are significantly elevated at mismatch ratios greater than ∼15%. This is supported by increases in regurgitate velocity and open area relative to valves tested at near-nominal diameters. At this degree of size mismatch, the wall stress is increased by a factor of two to three times relative to physiologic pressures. CONCLUSIONS: These findings establish a relationship between valve size matching and valve hemodynamic performance, including vessel wall stress, which should be considered in future valve implants. The size of the prosthetic valve should be within 15% of maximum vein size to optimize venous valve hemodynamic performance and to minimize the hoop wall stress.

Impact of bifurcation dual stenting on endothelial shear stress.

Despite advances in percutaneous coronary interventions and the introduction of drug eluding stents, in-stent restenosis and stent thrombosis remain a clinically significant problem for bifurcations. The aim of this study is to determine the effect of dual bifurcation stenting on hemodynamic parameters known to influence restenosis and thrombosis. We hypothesized that double stenting, especially with a longer side branch (SB) stent, likely has a negative effect on wall shear stress (WSS), WSS gradient (WSSG), and oscillatory shear index (OSI). To test this hypothesis, we developed computational models of dual stents at bifurcations and non-Newtonian blood simulations. The models were then interfaced, meshed, and solved in a validated finite-element package. Longer and shorter stents at the SB and provisional stenting were compared. It was found that stents placed in the SB at a bifurcation lowered WSS, but elevated WSSG and OSI. Dual stenting with longer SB stent had the most adverse impact on SB endothelial WSS, WSSG, and OSI, with low WSS region up to 50% more than the case with shorter SB stent. The simulations also demonstrated flow disturbances resulting from SB stent struts protruding into the main flow field near the carina, which may have implications on stent thrombosis. The simulations predict a negative hemodynamic role for SB stenting, which is exaggerated with a longer stent, consistent with clinical trial findings that dual-stenting is comparable or inferior to provisional stenting.

Prosthetic venous valve patient selection by validated physics-based computational models.

BACKGROUND: There is significant interest in a venous prosthesis to replace insufficient valves. The aim of the current study was to select the patients with hemodynamic conditions most likely to benefit from a valve implant. The hypothesis is that the venous valve prosthesis is most suitable for patients with significant reflux, such as in chronic venous insufficiency (CVI), right heart hypertrophy (RHH), and right heart failure (RHF). Conversely, a prosthetic valve is likely to be of least benefit for deep venous thrombosis (DVT) patients with low flow. METHODS: To address this hypothesis, fully coupled fluid and solid mechanics computational models were developed and validated in five acute canine implants. The animal-validated simulations were then carried out for the CVI, RHH, RHF, and DVT patients based on literature hemodynamic data. A mechanical stress ratio of leaflet wall stress to fluid wall shear stress was defined to combine the effects of both fluid mechanics and solid mechanics on leaflet function, for which a lower stress ratio is hemodynamically desirable. RESULTS: The simulation results of mean valve flow velocity and percentage valve opening were found to be within 10% of the measurements in canines. The simulations show that the patients in the CVI classes 4 to 6, RHH patients, and RHF patients may have a significant reduction in stress ratio with virtual implant of a prosthetic valve. The DVT patient simulations demonstrate a minimal reduction in the stress ratio. After thrombus removal where flow is restored, however, the prosthetic valve may be helpful for post-thrombotic patients. CONCLUSIONS: For patient selections of the venous valve prosthesis, the most suitable patients are the CVI classes 4 to 6, RHH, and RHF patients. The least suitable patients are the DVT patients because a valve is not effective under low-flow conditions. The present study demonstrates a physics-based approach to patient selection that can be tested in future clinical trials.

Biomechanical comparison between mono-, bi-, and tricuspid valve architectures.

BACKGROUND: An understanding of the relationship between venous valve architecture and associated fluid and solid mechanical forces will undoubtedly advance prosthesis design and treatments. The objective of the current study was to compare three valve architectures (mono-, bi-, and tricuspid) and the implications of these designs on the fluid and solid mechanics of the valve leaflets. The hypothesis is that the bi-cuspid valve has the lowest mechanical cost, defined as the ratio of leaflet wall stress and fluid wall shear stress (WSS), for the venous environment as compared with mono- and tricuspid valves. METHODS: To address this hypothesis, fully coupled, two-way fluid-structure interaction computational models were developed and simulated for the three types of valves. RESULTS: The numerical simulations showed that the mean fluid WSS of the bicuspid valve was generally higher than the tri-cuspid valve, which was further higher than the monocuspid valve. The mean leaflet wall stress of the bicuspid valve was lower than the tricuspid valve, which was further lower than the monocuspid valve. Therefore, the mechanical cost, which was defined as solid wall stress/fluid WSS, of the bicuspid valve was the lowest. CONCLUSIONS: The lower mechanical cost may be a reason why the bicuspid valve is the dominant design in the venous system. This knowledge provides guidance for the design of novel venous prosthetic valves and may shed light on venous valve disease when the architecture of the valve is altered.

Hemodynamic coupling of a pair of venous valves.

BACKGROUND: In vivo studies have shown that valves in veins are paired in an orthogonal configuration. The aim of this study is to characterize the flow interaction of paired valves under controlled in vitro bench conditions. METHODS: A bench top in vitro experiment was set up at physiological flow conditions to simulate the flow inside a venous valve. Two bicuspid bioprosthetic valves paired in 0° and 90° orientations were tested in a 12-mm-diameter tube, and the two-dimensional velocity fields around the valve were measured by particle image velocimetry. The distance between the two valves was varied from 3 to 5 cm, and the corresponding velocities and vorticities were determined. RESULTS: Velocity field shows the flow exit from the orthogonal valve-pairing configurations forced the main jet stream to turn to the outer region of the tube. Flow patterns between the valves show significantly less stagnation region from the 90° valve pairing over a 0° valve pairing case. The variation in valves distance shows that the coupling effect of the two valves extends to a range beyond four times of the tube diameter, albeit the ability to alter the flow decreases at larger distances. CONCLUSIONS: The findings suggest that the 90° valve pairing configuration regulates the flow between the valves, and the separation distance affects the hemodynamic efficiency of the two valves by reducing the total reverse flow volume.

Impact of stent mis-sizing and mis-positioning on coronary fluid wall shear and intramural stress.

Stent deployments with geographical miss (GM) are associated with increased risk of target-vessel revascularization and periprocedural myocardial infarction. The aim of the current study was to investigate the underlying biomechanical mechanisms for adverse events with GM. The hypothesis is that stent deployment with GM [longitudinal GM, or LGM (i.e., stent not centered on the lesion); or radial GM, RGM (i.e., stent oversizing)] results in unfavorable fluid wall shear stress (WSS), WSS gradient (WSSG), oscillatory shear index (OSI), and intramural circumferential wall stress (CWS). Three-dimensional computational models of stents and plaque were created using a computer-assisted design package. The models were then solved with validated finite element and computational fluid dynamic packages. The dynamic process of large deformation stent deployment was modeled to expand the stent to the desired vessel size. Stent deployed with GM resulted in a 45% increase in vessel CWS compared with stents that were centered and fully covered the lesion. A 20% oversized stent resulted in 72% higher CWS than a correct sized stent. The linkages between the struts had much higher stress than the main struts (i.e., 180 MPa vs. 80 MPa). Additionally, LGM and RGM reduced endothelial WSS and increased WSSG and OSI. The simulations suggest that both LGM and RGM adversely reduce WSS but increase WSSG, OSI, and CWS. These findings highlight the potential mechanical mechanism of the higher adverse events and underscore the importance of stent positioning and sizing for improved clinical outcome.

Impact of main branch stenting on endothelial shear stress: role of side branch diameter, angle and lesion.

In-stent restenosis and stent thrombosis remain clinically significant problems for bifurcation lesions. The objective of this study is to determine the haemodynamic effect of the side branch (SB) on main branch (MB) stenting. We hypothesize that the presence of a SB has a negative effect on MB wall shear stress (WSS), wall shear stress gradient (WSSG) and oscillatory shear index (OSI); and that the bifurcation diameter ratio (SB diameter/MB diameter) and angle are important contributors. We further hypothesized that stent undersizing exaggerates the negative effects on WSS, WSSG and OSI. To test these hypotheses, we developed computational models of stents and non-Newtonian blood. The models were then interfaced, meshed and solved in a validated finite-element package. Stents at bifurcation models were created with 30° and 70° bifurcation angles and bifurcations with diameter ratios of SB/MB = 1/2 and 3/4. It was found that stents placed in the MB at a bifurcation lowered WSS dramatically, while elevating WSSG and OSI. Undersizing the stent exaggerated the decrease in WSS, increase in WSSG and OSI, and disturbed the flow between the struts and the vessel wall. Stenting the MB at bifurcations with larger SB/MB ratios or smaller SB angles (30°) resulted in lower WSS, higher WSSG and OSI. Stenosis at the SB lowered WSS and elevated WSSG and OSI. These findings highlight the effects of major biomechanical factors in MB stenting on endothelial WSS, WSSG, OSI and suggests potential mechanisms for the potentially higher adverse clinical events associated with bifurcation stenting.

Mis-sizing of stent promotes intimal hyperplasia: impact of endothelial shear and intramural stress.

Stent can cause flow disturbances on the endothelium and compliance mismatch and increased stress on the vessel wall. These effects can cause low wall shear stress (WSS), high wall shear stress gradient (WSSG), oscillatory shear index (OSI), and circumferential wall stress (CWS), which may promote neointimal hyperplasia (IH). The hypothesis is that stent-induced abnormal fluid and solid mechanics contribute to IH. To vary the range of WSS, WSSG, OSI, and CWS, we intentionally mismatched the size of stents to that of the vessel lumen. Stents were implanted in coronary arteries of 10 swine. Intravascular ultrasound (IVUS) was used to size the coronary arteries and stents. After 4 wk of stent implantation, IVUS was performed again to determine the extent of IH. In conjunction, computational models of actual stents, the artery, and non-Newtonian blood were created in a computer simulation to yield the distribution of WSS, WSSG, OSI, and CWS in the stented vessel wall. An inverse relation (R(2) = 0.59, P < 0.005) between WSS and IH was found based on a linear regression analysis. Linear relations between WSSG, OSI, and IH were observed (R(2) = 0.48 and 0.50, respectively, P < 0.005). A linear relation (R(2) = 0.58, P < 0.005) between CWS and IH was also found. More statistically significant linear relations between the ratio of CWS to WSS (CWS/WSS), the products CWS × WSSG and CWS × OSI, and IH were observed (R(2) = 0.67, 0.54, and 0.56, respectively, P < 0.005), suggesting that both fluid and solid mechanics influence the extent of IH. Stents create endothelial flow disturbances and intramural wall stress concentrations, which correlate with the extent of IH formation, and these effects were exaggerated with mismatch of stent/vessel size. These findings reveal the importance of reliable vessel and stent sizing to improve the mechanics on the vessel wall and minimize IH.

Fluid-structure interaction in aortic cross-clamping: implications for vessel injury.

Vascular cross-clamping is applied in many cardiovascular surgeries such as coronary bypass, aorta repair and valve procedures. Experimental studies have found that clamping of various degrees caused damage to arteries. This study examines the effects of popular clamps on vessel wall. Models of the aorta and clamp were created in Computer Assisted Design and Finite Element Analysis packages. The vessel wall was considered as a non-linear anisotropic material while the fluid was simulated as Newtonian with pulsatile flow. The clamp was applied through displacement time function. Fully coupled two-way solid-fluid interaction models were developed. It was found that the clamp design significantly affected the stresses in vessel wall. The clamp with a protrusion feature increased the overall Von Mises stress by about 60% and the compressive stress by more than 200%. Interestingly, when the protrusion clamp was applied, the Von Mises stress at the lumen (endothelium) side of artery wall was about twice that of the outer wall. This ratio was much higher than that of the plate-like clamp which was about 1.3. The flow reversal process was demonstrated during clamping. Vibrations, flow and wall shear stress oscillations were detected immediately before total vessel occlusion. The commonly used protrusion clamp increased stresses in vessel wall, especially the compressive stress. This design also significantly increased the stresses on endothelium, detrimental to vessel health. The present findings are relevant to surgical clamp design as well as the transient mechanical loading on the endothelium and potential injury. The deformation and stress analysis may provide valuable insights into the mode of tissue injury during cross-clamping.

A simulation of vessel-clamp interaction: transient closure dynamics.

Cross-clamping of aorta is routinely performed in cardiac surgery. The objective of this study was to simulate cross-clamping of the aorta to elucidate the perturbation of stresses in the wall (solid mechanics) and lumen of the vessel (fluid mechanics). Models of the aorta and clamp were created in Computer Assisted Design and Finite Element Analysis packages. The vessel wall was considered as a non-linear anisotropic material while the fluid was simulated as Newtonian with pulsatile flow. The clamp was applied to produce total occlusion in approximately 1 s. A cylindrical and rectangular geometry for the clamp were considered. High jet speed and flow reversal were demonstrated during clamping. It was found that the clamp design and vessel wall anisotropy affected both the fluid wall shear stress (WSS) and solid stresses in vessel wall. The maximum wall stresses increased by about 170 and 220% during closure in the cases of plate and cylindrical clamps, respectively. The plate clamp design was superior for reduction of both solid stresses as well as fluid shear stresses. The cylindrical clamp causes much larger stresses than the plate clamp in each of the stress components; e.g., radial compression of -180 vs. -50 kPa. Vibrations, flow and WSS oscillations were detected immediately before total vessel occlusion. The present findings provide valuable insights into the mode of tissue injury during clamping and may also be useful for improving surgical clamp designs.

Effects of stent sizing on endothelial and vessel wall stress: potential mechanisms for in-stent restenosis.

Stent sizing and apposition have been shown to be important determinants of clinical outcome. This study evaluates the mechanical effects of undersizing and oversizing of stents on endothelial wall shear stress (WSS) and vessel wall stress to determine a possible biomechanical mechanism of in-stent restenosis and thrombosis. Three-dimensional computational models of stents, artery, and internal fluid were created in a computer-assisted design package, meshed, and solved in finite element and computational fluid dynamic packages. The simulation results show that the effects of various degrees of undersizing on WSS, WSS gradient, and oscillatory shear index were highly nonlinear. As the degree of undersizing increased, the heterogeneity of WSS became smaller. The WSS distribution for the 20% undersizing was smooth and uniform, whereas the 5% case was very heterogeneous. The combination of lower WSS and higher WSS gradient and oscillatory shear index in the 5% undersized case may induce neointimal hyperplasia or thrombosis. Additionally, the oversizing simulation results show that the maximum intramural wall stress of the 20% oversizing case is significantly larger than the maximum stress for the 10% and zero oversizing cases. Edge stress concentration was observed, consistent with the restenosis typically observed in this region. This study demonstrates that proper sizing of stent is important for reducing the hemodynamic and mechanical disturbances to the vessel wall. Furthermore, the present findings may be used to improve stent design to reduce endothelial flow disturbances and intramural wall stress concentrations.

A rate-insensitive linear viscoelastic model for soft tissues.

It is well known that many biological soft tissues behave as viscoelastic materials with hysteresis curves being nearly independent of strain rate when loading frequency is varied over a large range. In this work, the rate-insensitive feature of biological materials is taken into account by a generalized Maxwell model. To minimize the number of model parameters, it is assumed that the characteristic frequencies of Maxwell elements form a geometric series. As a result, the model is characterized by five material constants: micro(0), tau, m, rho and beta, where micro(0) is the relaxed elastic modulus, tau the characteristic relaxation time, m the number of Maxwell elements, rho the gap between characteristic frequencies, and beta=micro(1)/micro(0) with micro(1) being the elastic modulus of the Maxwell body that has relaxation time tau. The physical basis of the model is motivated by the microstructural architecture of typical soft tissues. The novel model shows excellent fit of relaxation data on the canine aorta and captures the salient features of vascular viscoelasticity with significantly fewer model parameters.