Numerical and experimental investigations of pulsatile blood flow pattern through a dysfunctional mechanical heart valve

ARTICLE IN PRESS Journal of Biomechanics 43 (2010) 1565–1572

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Numerical and experimental investigations of pulsatile blood flow pattern through a dysfunctional mechanical heart valve O. Smadi a, I. Hassan c, P. Pibarot b, L. Kadem a,n a

Laboratory of Cardiovascular Fluid Dynamics, Department of Mechanical and Industrial Engineering, Concordia University, 1455 de Maisonneuve Blvd W, Montreal, QC, Canada H3G 1M8 b Que´bec Heart & Lung Institute, Laval University, Quebec, Canada c Energy and Heat Transfer Laboratory, Department of Mechanical and Industrial Engineering, Concordia University, Sir George Williams Campus, 1515 St. Catherine W., EV4-213 Montreal, Quebec, Canada H3G 2W1

a r t i c l e in fo

abstract

Article history: Accepted 5 January 2010

Around 250,000 heart valve replacements are performed every year around the world. Due their higher durability, approximately 2/3 of these replacements use mechanical prosthetic heart valves (mainly bileaflet valves). Although very efficient, these valves can be subject to valve leaflet malfunctions. These malfunctions are usually the consequence of pannus ingrowth and/or thrombus formation and represent serious and potentially fatal complications. Hence, it is important to investigate the flow field downstream of a dysfunctional mechanical heart valve to better understand its impact on blood components (red blood cells, platelets and coagulation factors) and to improve the current diagnosis techniques. Therefore, the objective of this study will be to numerically and experimentally investigate the pulsatile turbulent flow downstream of a dysfunctional bileaflet mechanical heart valve in terms of velocity field, vortex formation and potential negative effect on blood components. The results show that the flow downstream of a dysfunctional valve was characterized by abnormally elevated velocities and shear stresses as well as large scale vortices. These characteristics can predispose to blood components damage. Furthermore, valve malfunction led to an underestimation of maximal transvalvular pressure gradient, using Doppler echocardiography, when compared to numerical results. This could be explained by the shifting of the maximal velocity towards the normally functioning leaflet. As a consequence, clinicians should try, when possible, to check the maximal velocity position not only at the central orifice but also through the lateral orifices. Finding the maximal velocity in the lateral orifice could be an indication of valve dysfunction. & 2010 Elsevier Ltd. All rights reserved.

Keywords: CFD In vitro model Dysfunctional mechanical heart valve Platelet activation Doppler-echocardiography

1. Introduction Dysfunction of Bileaflet Mechanical Heart Valve (BMHV) is a serious and potentially fatal complication. The incidence of dysfunction with this type of prosthesis is 0.2–6% patients/year (Montorsi et al., 2003). The restriction of the motion of the leaflet(s) may be due to pannus ingrowth (prevalence 0.14–0.65% patients/year (Sakamoto et al., 2006)) and/or thrombus formation. Several non-invasive medical imaging modalities, including Doppler-echocardiography, magnetic resonance, computed tomography, and cinefluoroscopy may be used to detect BMHV dysfunction and quantify its severity. However, these modalities have important limitations from theoretical, technical, and logistic standpoints. In particular, it is often difficult or impossible to discriminate with the currently available diagnosis techniques,

n

Corresponding author. Tel.: + 1 514 848 2424x3143; fax: + 1 514 848 3175. E-mail address: [email protected] (L. Kadem).

0021-9290/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2010.01.029

a normally functioning BMHV from a dysfunctional BMHV with mild severity that may become life-threatening in the short-term (Pibarot and Dumesnil, 2009). Moreover, the potential impact of a dysfunctional BMHV on blood components (red blood cells, platelets and coagulation factors) remains relatively unexplored. Most previous numerical and experimental studies of BMHVs have focused on normally functioning valves with an emphasis on the velocity field, transvalvular pressure drop and blood components damage. In previous numerical studies, the flow downstream of a normal BMHV was investigated under steady state flow conditions (Ge et al., 2003) and pulsatile flow conditions with or without Fluid Structure Interaction (FSI) (Grigioni et al., 2005; Pedrizzetti and Domenichini, 2006; Alemu and Bluestein, 2007). It should be noted that in most studies where FSI was considered, the flow through the BMHV was assumed to be laminar (Guivier et al., 2007; Redaelli et al., 2004; Dumont et al., 2007). Recently, Direct Numerical Simulation (DNS) with fully FSI was performed by Dasi et al. (2007) and Nobili et al. (2008). It should be noted, however, that application

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of DNS to clinical problems is limited due to its high computational cost. Most numerical and experimental studies on BMHV showed that the flow is characterized by trailing vortices arising from the leaflets and high levels of turbulent and wall shear stresses, usually many times higher than the physiological ones (Ge et al., 2005, 2008; Dasi et al., 2007), potentially leading to blood component damage. The disturbances of flow downstream of a normal BMHV should be magnified in the presence of leaflet prosthesis dysfunction. There are very few in silico or in vitro studies examining the effect of BMHV dysfunction on flow pattern. Baumgartner et al. (1993) showed, in vitro, that a defective BMHV (Carbomedics valve with one leaflet blocked) leads to an increase in the energy loss through the valve and a significant difference between Doppler and catheter gradients. This was confirmed numerically in a recent study performed by Smadi et al. (2009). The objective of this study is to numerically and experimentally investigate the pulsatile turbulent flow downstream of a dysfunctional BMHV in terms of velocity field, vortex formation and potential negative effect on blood components.

25 mm St. Jude Medical Hemodynamic Plus valve. The inner diameter was, therefore, 22.3 mm. The hinge mechanism of the valve was neglected and this valve has been chosen since it is the most commonly implanted in humans. The simulations were performed under unsteady conditions with an experimental pulsatile flow as inlet condition (Fig. 1) and ambient pressure at the outlet. The mean cardiac output was 5 L/min and the heart rate was 70 bpm (systolic phase duration 0.3 s). Blood was simulated as a Newtonian fluid with a density of 1080 kg/m3 and a dynamic viscosity of 0.0035 Pa s. The assumption of a Newtonian fluid behavior is realistic for blood flow in large arteries as the aorta and through mechanical heart valves (De Tullio et al., 2009; Nobili et al., 2008; Dasi et al., 2007). Inlet conditions corresponded to Remax =8023; Reaverage =3820 and Womersley number= 16.2. The Wilcox’s low-Reynolds k o model (Wilcox, 1998; Bluestein et al., 2000) was used to simulate the flow during the complete cardiac cycle. As FSI was not considered, the opening and closure dynamics were not simulated properly in this study. As a consequence, the vortex structures developed during opening and closure processes are not accurately represented. Therefore, only the fully opening period (from 60 to 250 ms) (Nobili et al., 2008) was analyzed in the results section. Commercial available software (Fluent 6.3.26 – Fluent Inc.; Lebanon; NH; USA) was used to perform the numerical simulations. All results were converged to residuals of o 10 4, unsteady simulation in general required 15–25 iterations per time step. Moreover, additional care was taken close to the wall and leaflet surfaces to maintain y + 51 (y+ = 0.25). The time step was set to 0.25 ms to satisfy time step independency. Three cycles were simulated before starting extraction of the results in order to reach the periodicity. 2.2. Discrete phase model

2. Models and methods 2.1. Numerical method Five 2D numerical models were created for the purpose of this study. The restriction of the leaflet motion was applied only on one of the two leaflets. This is because it is the most frequent situation in the clinical setting and that it is more difficult to detect when compared to the situation where both leaflets have restricted motion (Montorsi et al., 2003). The position of the leaflet was varied from fully opened position (opening angle =851; normal function) to fully closed position (angle= 301; 100% dysfunction) with three equally spaced intermediate positions 71.251 (25% dysfunction), 57.51 (50% dysfunction) and 43.751 (75% dysfunction). Non-symmetric sinuses were modeled based on the in vivo study performed by Reul et al. (1990) and used in vitro by Grigioni et al. (2001) (Fig. 1). For the upstream and downstream sections, the lengths were 10 D and 4 D, respectively (where D is the inlet diameter). The BMHV was modeled based on a

Turbulent flows are mainly characterized by vortices of different length scales. Small vortices, with a length scale similar to the size of blood components are responsible for blood components damage (hemolysis) and thrombus formation (platelets activation). These vortices induce a repetitive contact between platelets and activator molecules. The activation of platelets is mediated by von Willebrand factor (vWF). This factor will promote platelets adhesion to the subendothelium initiating thrombus formation. Numerically, the level of platelet activation is calculated by finding the summation of the shear stress magnitude times the residential time at each time instant (SsnDt) across different paths, a Lagrangian approach of particulate two phase flow was used. Particle paths under turbulent condition were calculated based on stochastic model (Gosman et al., 1981). This model has been used and described in detail by Bluestein et al. (2000). The calculations were carried out during the deceleration phase (100 – 150 ms after the peak). Therefore, the results did not depict platelet activations in the entire diastolic phase but rather wherein flow conditions predispose to platelet aggregation (Alemu and Bluestein, 2007).

Velocity (m/s)

1.5

1

0.5

0

0

0.2

0.4

0.6

0.8

1 2 3 4 X 5

Time (s) Fig. 1. Models for the five different cases: (1) 0% malfunction; (2) 25% malfunction; (3) 50% malfunction; (4) 75% malfunction; (5) 100% malfunction. Mesh quality for the sinuses and leaflets is shown and the cardiac cycle which was adapted as the inlet flow condition is also shown.

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Table 1 Calculations of discretization error.

/ = Maximumvelocity in the entire field(m/s) N1, N2, N3 ( The number of elements) r21 (Refinement factor N2/N1) r32 (Refinement factor N3/N2)

f1 f2 f3 p (The apparent order)

f21 ext (The extrapolated values)

300,000, 178,000, 100,000 1.299 1.330 2.844 2.849 2.879 5.892 2.842

e21 a (Approximate relative error)

0.190%

e21 ext (Extrapolated relative error)

0.072%

GCI 21 fine (the fine-grid convergence index)

0.090%

2.3. Numerical uncertainties Prior to unsteady simulations, steady flow simulations were conducted to establish grid density. The uncertainty and error in the study was calculated following the recommendations suggested in (ASME J. Fluids Eng., 130, pp. 078001-1-078001-4). Table 1 and Fig. 2 show the calculations for the discretization error of the maximum velocity value in the entire field and velocity profile at the vicinity of the valve, respectively. According to the maximum velocity in the entire field, the fine-grid convergence index (GCIfine) was 0.09% (this does not account for modeling errors). The maximum descritization uncertainty was 6% in the area close to the defective leaflet.

3. Experimental method The mock flow circulation model used in this in vitro study has been already described and validated (Garcia et al., 2003) (Fig. 3a). The fluid was composed of 2/3 water and 1/3 of glycerol so that its density (1080 kg/m3) and viscosity (3.5 cP) were similar to that of blood under high shear rate conditions. The flow rate was measured by an electromagnetic flowmeter, the pressure with Millar catheters and Doppler echocardiographic velocities using a Sonos 5500 machine. For all experiments (normal leaflets and one dysfunctional leaflet), the transvalvular flow rate was maintained at 5 L/min, corresponding to a stroke volume of approximately 70 mL for a heart rate of 70 bpm (ejection phase: 0.3 s). Systolic and diastolic pressures were maintained under normal conditions: 120 mmHg and 80 mmHg, respectively. A small stop pin was used to adjust the opening angle of the valve (Fig. 3a). To minimize the number of experimental conditions, only three different degrees of dysfunction were tested (0%; 50% and 100%). Dysfunction severities were determined through processing of images of the BMHV taken by a digital camera.

4. Results Fig. 4 shows velocity magnitude profiles downstream of the BMHV for different time instants and degrees of dysfunction. For the sake of clarity, only three cases are depicted (0, 50 and 100% dysfunctions). For 0% dysfunction (Fig. 4a), a uniform three-jet configuration can be noticed (through central and lateral orifices) with a maximum velocity of 1.47 m/s at the peak of systolic phase (90 ms). The three jets, at each time instant, have almost the same maximal velocity which is consistent with the experimental work of Grigioni et al. (2001). In the meantime, for 50% dysfunction (Fig. 4b), three jets were still able to develop with a little upward shift in the central jet except for the instant corresponding to the acceleration phase (60 ms). The maximum velocity at peak systole was higher than for the healthy case and as high as 2.22 m/s. With completely defective leaflet (100% dysfunction) (Fig. 4c),

Fig. 2. (a) Velocity profile at the vicinity of the valve for different grid solutions. (b) Fine-grids solution with discretization error bars.

significant changes in the flow dynamics, downstream of the valve, were noticed. Only two major jets developed, one of them through the central orifice and the second one through the upper lateral orifice (unobstructed orifice), while the velocity jet through the lower lateral orifice almost vanished. The maximum velocity at the peak of the systolic phase was as high as 3.51 m/s. Fig. 4d shows the comparison between the velocity profiles at the same location downstream of the BMHV at peak systole for the three different degrees of dysfunction. 4.1. Vortex formation The vortex formation is depicted in Figs. 5 and 6 by both vorticity magnitude and l2 criterion (Jeong and Hussain, 1995), respectively. In the healthy model, the shear layers at the upper

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and lower walls rolled up in the sinus region and started forming a vortex. At the peak of the systolic phase a single vortex was formed; this is consistent with the numerical and experimental work of Dasi et al. (2007). During early stage of the deceleration phase, a single vortex structure still exists, while in the middle stage of the deceleration phase, the single vortex breaks down

into two major vortices with other small scale vortices. On the other hand, in the wake of the valve leaflets, periodic vortex shedding (Von Karman vortex streets) was observed, which is consistent with the findings of Bluestein et al. (2000) and Nobili et al. (2008). In a partially defective leaflet (50%), the flow behavior is dramatically changed. During acceleration phase, vortices were formed between the valve leaflets and in the sinus area. These vortices appeared earlier during the systolic phase when compared with the healthy case. In addition, vortex shedding in the wake of the valve occurred earlier for the defective leaflet when compared with the healthy case. In a completely defective leaflet (100%), similar to the partially defective leaflet, vortices were formed between the valve leaflets but this time shifted toward the sinus area. Multiple vortical structures were also observed downstream of the valve. The significant difference between partially (50%) and completely closed (100%) cases was the development of a vortex structure upstream from the valve, just before the completely closed leaflet.

4.2. Doppler-echocardiographic measurements

Fig. 3. (a) Schematic representation of the mock flow model. (b) Alteration of the lower leaflet opening position using a small stop pin.

Fig. 7a shows the maximum velocity magnitude at the peak of systolic phase for different degrees of dysfunction using Dopplerechocardiographic velocity measurements and numerical simulation.

Fig. 4. Velocity profiles at the vicinity of the valve at different time instants and degrees of dysfunction. (a) 0% dysfunction (b) 50% dysfunction (c) 100% dysfunction (d) at the peak instant for different degrees of dysfunction.

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Fig. 5. Vorticity distributions downstream of a healthy and a dysfunctional mechanical valve at different time instants.

Fig. 6. Coherent structures downstream of a healthy and a dysfunctional mechanical valve at different time instants (using the l2 criterion).

In the healthy model, there was a good agreement between numerical and experimental results with percentage of difference less than 1.3%. When a dysfunction was induced on the lower leaflet, a discrepancy, proportional to the severity of the dysfunction, appeared between the experimental (Doppler-echo) and numerical results for maximum velocity. This difference reached up to 15% for 100% dysfunction. Fig. 7b shows the maximum transvalvular pressure gradient (TPGmax) and mean transvalvular pressure gradient (TPGmean), for different percentage of dysfunction. The TPGs were determined using the standard simplified Bernoulli equation (TPG =4 V2). TPGmax is a function of the square of maximum velocity (TPG= 4 V2max). Therefore, the TPGmax numerical and experimental results have the same trend as for the maximum velocity but with a magnification of the percent difference (2.6–32.2%). On the

other hand, in both 0% and 50% dysfunctions, the numerical TPGmean magnitude was lower than the echo-Doppler TPGmean magnitude. This could be explained as a result of the absence of FSI in the current numerical simulation. For 100% dysfunction, the FSI effect was limited and as a consequence the numerical TPGmean magnitude was higher than that of the echo-Doppler one. It is important to notice, at this point, that Dopplerechocardiographic measurements are extracted from 3D experimental measurements and compared to 2D numerical simulations. This approach is, however, reasonable since: (1) pressure and velocity field downstream of mechanical heart valves obtained using 2D and 3D simulations are comparable (Cheng et al. (2004)); (2) mean and maximum transvalvular pressure gradients measured using Doppler-echocardiography are evaluated using simplified Bernoulli equation (1D steady state formulation).

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4.3. Platelet activation

Fig. 7. Comparisons between numerical and Doppler-echocardiographic results; (a) maximum velocity; (b) the mean and the maximum transvalvular pressure gradients (TPG).

Fig. 8 shows estimated platelet trajectories for different percentages of dysfunction downstream of the BMHV during the deceleration phase: 100–150 ms after the peak of the systolic phase. Eighteen equally spaced positions across the valve were selected to inject the platelets at 100 ms after the peak and the results were depicted after 50 ms from the injection time (150 ms after the peak). Platelet paths changed significantly with increasing the percentage of BMHV malfunction. The platelets on the normal leaflet side travel farther in the domain (due to a higher velocity), except for 100% dysfunction. In this case the interaction between the upperlateral jet and the recirculation zone developed downstream of the valve thus limits the displacement of the platelets by redirecting them to the regions of lower turbulent shear stresses. Fig. 9a and b shows the level of platelet activation as calculated by (SsnDt) for particles released near the outer edge of the upper leaflet (normal leaflet) (Fig. 9a) and near the inner edge of the bottom leaflet (dysfunctional leaflet) (Fig. 9b). For the particles released near the outer edge of the upper leaflet, the highest level of activation was obtained for a 75% dysfunction (8.7 dyn/ s cm2). This value is five times higher than that of the healthy case and it is higher than that of a fully closed leaflet. This can be explained by the fact that in a partially blocked leaflet, the platelets were trapped in the wake of the trailing edge where the level of shear stress is relatively high. On the other hand, in the fully defective leaflet, the platelets escaped away from the wake of the leaflet region to the core of the flow where the shear stress is relatively lower. For the particles released near the inner edge of the bottom leaflet, the highest level of activation was found for 50% of dysfunction. Indeed, for 50% malfunction a significant amount of blood is still capable to pass through the malfunctioning orifice. The interaction between the jet coming from this orifice and the jet from the central orifice generates not only very high shear stresses but also leads to a rolling of fluids elements (increasing the residential time). This results in a significant increase in platelet activation. For higher malfunctions, the flow is mainly directed towards the Valsalva sinus (75% malfunction) or not allowed to pass through the lower orifice (100% malfunction). In both cases less interaction between the jets exists.

Fig. 8. Comparison of platelet paths downstream of the valve during the deceleration phase (100–150 ms after the peak) for different percentages of malfunction.

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of the valve. For this reason, the effect of neglecting FSI on TPGmean is less significant with higher percentage of dysfunction. Consequently, clinicians should pay attention to seek for the maximum velocity by shifting the Doppler beam from central to lateral, and this should be done on both sides. 5.2. TSS and residential time (platelet activation)

Fig. 9. Platelets level of activation during the deceleration phase (100–150 ms after the peak) for different percentages of dysfunction. (a) Particles released from the upper valve orifice. (b) Particles released from the lower valve orifice.

5. Discussion 5.1. Clinical diagnosis In the clinical setting, the evaluation of BMHV function is usually performed using Doppler-echocardiography. Maximum velocity of the forward flow is measured by positioning the ultrasound wave beam through the valve. Only the instantaneous maximum velocity is used to determine the transvalvular pressure gradient and effective orifice area (EOA). However, in order to get accurate measurements, it is very important to align the ultrasound beam with the flow direction (Doppler Effect). Furthermore, clinicians usually tend to position the axis of the Doppler beam within the center of the valve. In the case of normally functioning BHMV, the maximum velocity is similar in the 3 orifices (Fig. 4). However, in the case of a completely defective leaflet, the flow is shifted towards the normal leaflet and the maximal velocity is through the lateral orifice along the wall. The Doppler beam aligned on the central orifice may miss the maximum velocity that is displaced laterally. This may explain the discrepancy between peak gradient measured by Dopplerechocardiography and that obtained by numerical simulation in the case of severe prosthesis dysfunction (Fig. 7). In contrast, the difference in TPGmean was the highest in the healthy case. This could be explained by the fact that the fluid-structure interaction has not been simulated in this study, and as the TPGmean is calculated through the whole systolic phase, as a result, a percentage of error is expected during the opening and closure

Elevated turbulent shear stresses can lead to hemolysis and to platelet activation. However, the threshold for hemolysis is so high that it is unlikely to happen with current mechanical heart valves during systolic phase. This study shows that turbulent shear stress level and position will change in the case of a dysfunctional BMHV. In 50% dysfunction of one leaflet, the relatively high shear stress areas covered most of the domain downstream of the valve. Therefore, the number of blood elements that will be exposed to high shear stress level is higher in the case of partially defective leaflet than in the case of normal function or of a leaflet blocked in the fully closed position. Furthermore, the increase in the number and scale of vortices downstream of the valve will lead to an increase in the residential time of blood elements in these high shear stress regions. As a result, the level of platelet activation and thrombus formation can increase significantly. Interestingly, this study shows that the level of platelet activation is markedly increased at moderate levels of dysfunction, which may predispose to worsening of thrombosis or de novo thrombosis. Hence, this could lead to a vicious cycle where the abnormal flow pattern caused by mild or moderate degrees of dysfunction creates favorable conditions for thrombus formation on the valve, which in turn worsens the valve dysfunction. It should be noted, however, that the evaluation of shear stresses used to determine the level of platelet activation is based on 2D simulations. Under such conditions, Reynolds shear stresses are underestimated (De Tullio et al., 2009) compared to 3D simulations. However, this should not modify the clinical consequence since the threshold for platelet activation, using the 2D simulations, has been exceeded under both normal and malfunction conditions. In conclusion, this study showed that the flow upstream and downstream of a dysfunctional mechanical heart valve was highly influenced by malfunction severity and this resulted in discrepancies between the Doppler echocardiographic and numerical derived transvalvular pressure gradients. Moreover, the flow downstream of the dysfunctional valve was characterized by abnormally elevated shear stresses and large scale vortices, these characteristics can predispose to blood components damage. Finally, from a clinical point of view, clinicians should try, when possible, to check the maximal velocity position not only at the central orifice but also through the lateral orifices. Finding the maximal velocity in the lateral orifice could be an indication of valve dysfunction.

Conflicts of interest None

Acknowledgement This work was supported by a FQRNT Etablissement de Nouveaux Chercheurs grant. References Alemu, Y., Bluestein, D., 2007. Flow-induced platelet activation and damage accumulation in a mechanical heart valve: numerical studies. Artificial Organs 31 (9), 677–688.

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