The present study elucidates the flow features evolving within the ventricle of a beating left heart model with two mechanical heart valves (MHVs) fixed in mitral and aortic positions. This configuration represents the clinical case of double valve replacement (DVR). Two types of MHVs were used – bi-leaflet mechanical heart valve (BMHV) and mono-leaflet mechanical heart valve (MMHV). Leaflets of MHVs in the mitral position were aligned to mimic closely that of the anatomical mitral valve, whereas in the aortic position their alignment was varied in two different orientations. A 2D Particle Image Velocimetry (PIV) technique was used to explore flow details in the mid-coronal plane of the left ventricle (LV) for 50 cardiac cycles. The heartbeat was simulated at the rate of 60 cycles per minute maintaining the ejection fraction of 45%. In BMHV cases, both the orientations of the aortic valve (AV) produced entirely different non-physiological flow patterns. But in MMHV cases both the orientations of the aortic valve produced flow patterns similar to the physiological flow patterns. The LV contraction during systole exhibited a strong dependence on the AV orientation. Energy loss (EL) due to viscous dissipation, obtained from the strain rate, shows that phase-wise distribution over a complete cardiac cycle is affected by the AV orientation, but the net integrated values show only a marginal difference for BMHV whereas a significant difference for MMHV. Based on the findings, this study suggests that consideration of the AV orientation is important for better LV performance in the DVR conditions and hence for post-surgical cardiac health.
Research Article
PIV visualization of flow pattern in left heart ventricle model with double valve replacement
https://doi.org/10.21203/rs.3.rs-1996035/v1
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During diastole, the blood flow from the mitral valve (MV) appears to make a clockwise or counterclockwise vortex while filling the left ventricle (LV) is subject to the choice of the cardiac chamber view. Physiologically with the opening of the MV, the blood flow proceeds along the posterior wall of the LV toward the apex and turns back clockwise toward the aortic valve (AV) according to the apical 3-chamber view and counterclockwise according to the apical 4-chamber view. Such vortex forms due to the interaction of flow with the constrained enclosure's structural boundary. Another type of vortex, characteristic of the LV filling with the opening of the MV, forms around the free jet in the azimuthal plane parallel to the MV annulus. This vortex is associated with the E-wave and is known as a vortex ring, which induces the enhanced blood flow into the LV for efficient filling. Subsequently, just before the closure of the MV, contraction of the left atrium (LA) results in the A-wave and the associated second vortex ring having a slight tilt caused by the MV's anterior leaflet. Tilting of the vortex ring favorably directs the blood for the smooth outflow. The contribution of vortices to the performance of the LV is not straightforward to assess and needs more exploration via in vivo and in vitro investigations for deeper understanding.
Several researchers have focused on vortex dynamics during LV filling through their in vitro (Reul et al. 1981; Domenichini et al. 2005; Gharib et al. 2006; Jeyhani et al. 2017; Meschini et al. 2018; Maraouch et al. 2021) and in vivo (Kheradvar et al. 2007; Töger et al. 2012; Le et al. 2012; Elbaz et al. 2014; Martínez-Legazpi et al. 2014; Calkoen et al. 2015; Elbaz et al. 2017; Hu et al. 2022; Charonko et al. 2013; Hong et al. 2008; Faludi et al. 2010) studies. Gharib et al. (2006) first reported the visual clinical evidence of vortex ring formation in the LV of a healthy subject during the diastole phase of the cardiac cycle. They hypothesized that analysis of a well-formed vortex could be an index of cardiac health. However, a lack of unanimity on such a quantitative index renders it an unsettled issue.
Diseased and repaired MV and LV result in disturbed LV vortex and altered flow patterns in LV (Hong et al. 2008; Calkoen et al. 2015; Yoshida et al. 2018; Morichi et al. 2022). Diseased heart valves, when found irreparable, are replaced with Prosthetic Heart Valves (PHVs) of various types of which Mechanical Heart Valves (MHVs) are known for their better longevity (Bloomfield 2002; Yoganathan et al. 2004). Bileaflet Mechanical Heart Valves (BMHVs) and Monoleaflet Mechanical Heart Valves (MMHVs) are two popular and commonly used MHVs. Particularly, BMHVs have shown better long-term performance in clinical studies (Nishida et al. 2015). Worldwide, millions of heart valve replacement surgeries take place every year (Hammermeister et al. 2000; Rahimtoola 2010) of which about 10% are Double Valve Replacements (DVRs) - a condition where both Mitral and Aortic Valves (MV and AV) are replaced by PHVs (David et al. 1997; Davierwala et al. 2013; Amirtharaj et al. 2019; Husso et al. 2021; Egger et al. 2022). It has been observed from the clinical studies that MHVs are preferred over Bio-PHVs or a combination of Bio-PHVs and MHVs for DVR (Brown et al. 1993).
Flow through BMHV in mitral position has been investigated by various researchers in vivo (Faludi et al. 2010; Mächler et al. 2004; Pedrizzetti et al. 2010), in vitro (Meschini et al. 2018; Chandran KB et al. 1989; Pierrakos et al. 2004; Akutsu and Saito 2006; Querzoli et al. 2010; Wang et. Al. 2016; Saaid et al. 2018; Saaid et al. 2019; Vu et al. 2019) and in silico (Choi et al. 2014; Su et al. 2015) for the last few decades on various aspects such as flow pattern, turbulence, and shear distribution. Similarly, several in vitro (Chandran KB et al. 1989, Mouret et al. 2005; Querzoli et al. 2010; Vuki ́cevi ́c et al. 2012 and Wang et al. 2016) and in vivo (Pop et al. 1989) studies have been conducted to analyze the flow dynamics aspects of MMHVs in the mitral position. As the geometry of MHVs significantly differs from that of the native MV and produces multiple jets, a few attempts have been made to study the influence of MHV orientation on LV flow dynamics. The flow patterns in clinical studies (Faludi et al. 2010; Pedrizzetti et al. 2010) were significantly different with the reversal of vortex flow direction when a BMHV replaced the native mitral valve with its leaflets opening parallel to the posterior wall matching the anatomical orientation. However, in vitro studies (Pierrakos et al. 2004; Vu et al. 2019) did not show any evidence of vortex formation in the mid-plane during LV filling with a BMHV orienting its leaflets perpendicular to the posterior wall (non-anatomical alignment). Surprisingly, the flow patterns created by MMHV were similar to that of the native mitral valve when its larger orifice faced the posterior wall, and the jet flow produced a clockwise vortex in an apical 3-chamber view (K B Chandran et al. 1989; Pop et al. 1989). The LV flow changed the direction of rotation to counterclockwise for the larger orifice turning towards the anterior wall.
From the various investigations comprising in vivo, in vitro, and CFD, it is clear that for the efficient functioning of a heart, a quick diastolic LV filling aided by the formation of vortex rings, streamlined flow propelling the blood to the apex region, and a smooth unhindered return of the blood to the outflow tract for ejection are essential requirements. However, it is noticed that none of the in vitro studies, so far, has paid attention to the nature of outflow from LV. The test setup either consisted of a simple opening (Pierrakos et al. 2004; Choi et al. 2014) or a bio-prosthetic valve (Chandran KB et al. 1989; Vu et al. 2019), or a ball-and-cage valve (Akutsu and Fukuda 2005; Akutsu and Saito 2006) at AV position for the main focus was always to examine the effect of BMHV in MV position on the inflow during LV filling. Further, to the best of our knowledge, no in vitro study has been carried out to investigate the LV flow with the DVR condition using MHV at MV and AV positions except for Mouret et al. 2005 and Saaid et al. 2018 who did not consider the effect of the AV orientation.
The literature reflects the growing consensus among researchers that the health and functionality of a heart correlate, though not reached unanimity on quantification so far, with the flow pattern in LV. DVR, particularly in the left ventricle, is a high-risk-proposition considering mid-term morbidity and mortality, but it is the only option as no other treatment exists.
The present in vitro study aims to investigate, using a laser-based advanced diagnostic facility, the flow patterns for four cases of DVR in the LV model with the implantation of MHVs consisting of BMHVs in the first two cases and MMHVs in the remaining two cases. In the first case, BMHV implantation in the MV position is kept in anatomical orientation with the shut line of leaflets parallel to the posterior wall, and in the AV position, it is oriented perpendicular to the anterior wall. In the second case, the orientation of BMHV is kept unaltered in the MV position, and in the AV position, it is rotated to orient its shut line of leaflets parallel to the anterior wall. In the third case, MMHVs are oriented with the larger orifice facing the posterior wall in the MV position, and the smaller orifice facing the anterior wall in the AV position. In the fourth case, MMHV is oriented in the MV position having its larger orifice facing the posterior wall, and in the AV position, the larger orifice facing the anterior wall. The flow patterns include phase averaged plots of velocity distribution with velocity vector field and vorticity distribution with streamlines.
A. Experimental setup
A transparent left heart model was fabricated consisting of the aorta, Left Atrium (LA) component, and flexible LV to simulate aortic and LV flows together with the LV's anatomical inlet and outlet geometries. A photograph of the experimental setup and its schematic view are shown in Figs. 1a and 1b, respectively. The left heart (labeled as “2” in Fig. 1) components were made in three different parts, (i) LA, aortic sinus, and LV base with adjoining MV and AV seats making an angle of 135o between their planes (refer Fig. 2a) as reported in a clinical study (Veronesi et al. 2009), (ii) LV sac (refer Fig. 2b) and (iii) aortic arch from sino-tubular junction to descending aorta including three branches having averaged dimensions obtained from the literature (Bierbach et al. 2010; Kahraman et al. 2006; Roman et al. 1989). The LA was approximated in a spherical shape with anatomical volume. All the components of the left heart, except the LV sac, were 3D printed. The axisymmetric LV sac with a uniform wall thickness of 2 mm was molded from transparent silicone rubber (MS-1003, Dow Corning) in a semi-ellipsoidal shape as shown in Fig. 2b. The molded LV sac has a 70 mm minor axis and 60 mm semi-major axis following the previous study (Domenichini et al. 2005) making about 145 ml diastolic volume. St. Jude mitral BMHV (27MJ-501) and St. Jude aortic BMHV (27AGN-751), both 27 mm in size, and Medtronic 21 mm MMHV and Bjork-Shiley 27 mm MMHV were used in the assembly of the left heart model and are shown in Figs. 2c and 2d.
The left heart model was mounted inside a transparent acrylic chamber and the aorta outflow and the LA inflow were connected with the reservoir and collecting tank, appropriately, to complete the recirculation loop. A mixture of 40% glycerin and 60% water by volume was used as the test fluid to completely fill the acrylic chamber and the left heart model. This fluid has viscosity and density similar to that of hematocrit blood (Hochareon et al. 2003). Flow control valves were used downstream of the branches of the aorta in order to allow about a third of aortic flow.
A constant head maintained in the reservoir and the resistance manipulated by the aortic arch along with branches and control valves simulated the preload and afterload, respectively. A peristaltic pump of Vi-Vitro SuperPump AR series was connected with the test chamber to simulate pulsatile flow in the LV with the desired frequency and stroke volume through a controller. The periodic displacement of test fluid in the chamber causes contraction and expansion of the LV sac to actuate the flow circulation through non-return valves. During the systole, the LV squeezes to push the flow out through AV and aorta to the collecting tank and during the diastole, the MV opens to supply the fluid inside the LV from the reservoir through LA. A small air gap, close to the atmosphere, was kept in the test chamber to adjust the left ventricle compliance (Maraouch et al. 2021). Thus, the entire system mimics the simple cardiac flow at a varying rate based on the waveform fed as input to the controller.
Properties of test fluid are given in Table. I. The test fluid has its refractive index matching with that of the LV material and the chamber wall.
Table I. Properties of Test Fluid for Experiments
|
S.No. |
Property |
Value |
|---|---|---|
|
1 |
Density (\(\rho\)) |
1100 kg/m3 |
|
2 |
Viscosity (\(\mu\)) |
0.0035 Pa.s |
|
3 |
Specific Gravity |
1.1 |
|
4 |
Refractive Index |
1.4 |
Orientation of the BMHV having a shut line of leaflets aligned with a vertical cross-sectional plane cutting through centers of AV and MV is termed as 0o. Orientation of the MMHV having its major (larger) orifice facing the posterior wall of LV is termed as 180 o whereas, in the aortic position, the MMHV having its major orifice facing the anterior wall of the aorta is termed as 0 o and the posterior wall of the aorta is termed as 180 o. Figure 3 schematically depicts various orientations of BMHVs and MMHVs – BMHV 90o at MV with 0o at AV (BM90-A0 ) for Case 1, 90o at MV with 90o at AV (BM90-A90) for Case 2, MMHV 180o at MV with 0o at AV (MM180-A0) for Case 3, and 180o at MV with 180o at AV (MM180-A180) for Case 4, and definition sketch of anterior and posterior walls of the LV.
A TSI make 2D PIV system with Nd: YLF laser sheet, vertically oriented, was focused from the outside of a side wall of the chamber to illuminate the mid-plane of the LV cutting through the centers of AV and MV. A Phantom VEO 710 high-speed camera was orthogonally positioned in the front such that the flow field in the vertical mid-plane of the LV could be captured in an apical 3 chamber view. The PIV interrogation window, enframing the LV measured 130 mm x 80 mm (width x height). Spherical polyamide particles of 20 \(\mu m\) diameter and 1030 kg/m3 density from Dantec Dynamics were used to seed the flow inside the left heart excluding the chamber. The specific gravity of the seed particles nearly matched that of the test fluid making them neutrally buoyant.
The physiological cardiac cycle was simplified as a waveform which is shown in Fig. 4a with diastole and systole phases in a ratio of 60:40 (de Heer et al. 2011). This waveform was based on earlier studies (Kheradvar and Gharib 2009) and was used as input to the controller of SuperPump along with the heart beat rate of 60 bpm. The displacement volume of the pump was set to 65 ml mimicking the Stroke Volume (SV) with the Ejection Fraction (EF) of about 45% which is in the range of left ventricle ejection fraction (LVEF) post DVR surgery (Skudicky et al. 1997, Gupta et al. 2017). Flow through descending aorta outlet was maintained at 66% of inflow and the outflow through ascending aorta branches was maintained at 17% for RCCA, 8.5% for LCA, and 8.5% for LSA (Antman EM et al. 1980).
B. Data acquisition
Laser pulse and high speed camera were synchronized to acquire a pair of data image frames at the rate of 100 Hz. The time between two frames of the pair was kept 2 ms. Thus, 100 image pairs were acquired in a single cardiac cycle with the time gap of 10 ms. For each case, involving 50 cardiac cycles, a total of 5000 image pairs were acquired. Since a pair of images is used to obtain the velocity field using correlation method, a single image pair corresponds to one time step of cardiac cycle. Every 5th image pair of the entire data set was chosen for post processing, thereby leaving a time gap of 50 ms between two successive pairs. Thus, a complete cardiac cycle consists of twenty phases with a time step of 50 ms as shown in Fig. 4b. From phase 1 to phase 6 represent accelerating filling of the LV while 6 to 12 represent decelerating filling. Similarly, phase 12 to phase 16 represent accelerating ejection of fluid from the LV and 16 to 20 represent decelerating ejection. Thus, phases 6 and 16 represent peaks of diastole and systole, respectively.
C. Data analysis
For the PIV data analysis, a MATLAB based open source code PIVLab (Thielicke 2019) was used. Flow details were calculated using PIV cross correlation approach with a 50% overlap multi-pass approach starting from one 32 x 32 pixel interrogation followed by 16 x 16 pixel interrogation pass.
The phase average technique was used for data from 50 cycles for BMHV cases and 16 cycles for MMHV cases to obtain the velocity (V), vorticity (\(\omega\)), and strain rate (\(ϵ\)) fields using the following expressions.
$$V=\sqrt{(}{u}^{2}+{v}^{2})$$
1
,
$$\omega =(\frac{dv}{dx}-\frac{du}{dy})$$
2
,
and
$$ϵ=(\frac{dv}{dx}+\frac{du}{dy}).$$
3
The method first used by Hayashi et al. (2015) to estimate the energy loss (EL) in the ventricle for each phase of a cardiac cycle involved the calculation from the strain rate using the following expression.
$$EL=\mu \int \int \int (\frac{du}{dy}+\frac{dv}{dx}{)}^{2}dx.dy.dz$$
4
The EL thus determined from in vivo echocardiography was validated against the in vitro measurements (Stugaard et al. 2015). Since the PIV measurements are planar covering the mid-cross-sectional area of LV, the energy loss was calculated using strain field as Watt per meter from the following equation.
$$EL/m=\mu \int \int (\frac{du}{dy}+\frac{dv}{dx}{)}^{2}dx.dy$$
5
Flow patterns in LV in terms of phase averaged velocity distribution, velocity vector field, vorticity distribution, and streamlines for the four cases are presented here. Out of 20 phases of a cardiac cycle, flow field details of Early Diastole (ED, phase 1), Mid-Diastole (MD, phase 7), Late Diastole (LD, phase 11), Early Systole (ES, phase 13), Mid-Systole (MS, phase 16) and Late Systole (LS, phase 19) are selected for discussion. In the figures showing the flow details, the top right of LV is the region below MV and the top left is that below AV (Fig. 3).
A. BMHV Case 1: MV90o-AV0o
Figure 5a shows the velocity field obtained from phase averaging of 50 cardiac cycles at various stages of a cardiac cycle for MV at 90o and AV at 0o orientations. The phase averaging technique can filter out the noise and capture the coherent part of the flow. A similar technique has been used earlier by Fortini et al. (2010). The asymmetric compression of an axisymmetric sac of uniform thickness under the influence of uniform surrounding pressure is rather perplexing and remains to be explained. The leaflets of an open BMHV form a central orifice and two peripheral orifices thereby producing three co-flowing non-circular jets inclined towards the long axis. Therefore, a usually expected jet ensuing with the opening of MV and a growing vortex ring around it are found to be missing during early and peak diastolic phases. Instead, relatively high-velocity flow is seen at ED to impinge and turn along the Anterior (septal) wall of the LV forming a large-scale counterclockwise vortex in the mid-region and a partially visible small clockwise vortex in the basal region below AV. The corresponding streamlines in Fig. 5b display the flow path more discernibly. A large vortical region in the middle of the LV does not allow the flow from the MV to directly reach the central part of the LV, instead, it first fills the upper mid-region and the basal region pushing outwardly the anterior wall. With the continuous filling, the LV is seen to regain its regular shape at MD wherein not only a high-speed jet is seen to hit the posterior wall in the basal region but also the flow along the anterior wall fills the apical region while turning counterclockwise. However, the corresponding streamlines in Fig. 5b show the vortical region decreased in size and confined between a saddle point close to the posterior wall in the mid-region and a point of confluence close to the posterior wall in the apical region. The majority of the flow coming from the MV is seen to fill the LV outside the vortical region, and a small part of it makes its way to the vortex from the point of confluence. Further, with a lapse of time and the reduced filling rate at LD before the closing of the MV, the entire basal region is occupied by the three jets from the MV – a jet flow from the anterior peripheral orifice tending to turn toward the outflow tract, a jet flow from the central orifice toward the long axis, and a jet flow from the posterior orifice forming the counterclockwise vortex next to the posterior wall. Interestingly, the flow returning from the apex region and rising along the posterior wall meets the flow from the MV in the mid-region and results in a fully formed counterclockwise vortex. The corresponding streamlines show a well-grown counterclockwise vortex with the point of confluence shifted along the apical wall toward the anterior side and a pair of contra-rotating vortices above next to the posterior wall.
As the contraction of the LV sac commences with the compression stroke of the SuperPump marking the beginning of the systole, the MV closes while the AV opens to facilitate ejection of the LV fluid. The image of ES in Fig. 5a displays the mid-section of the anterior wall pushing the fluid with higher velocity, which quickly gets diverted in opposite directions toward the apex and the AV. Further, the flow from the basal region appears to curvaceously move toward the outflow tract, and that from the apical region joins it in a circuitous fashion along the posterior wall. The corresponding streamlines in ES in Fig. 5b present a complex flow field marked by multiple foci and saddle points. Here, two foci spiraling out (source plus vortex) counterclockwise are unstable and the one spiraling inward (sink plus vortex) clockwise is stable according to the topological features of flow pattern (Perry AE 1986). The stability dictates the state of the flow as stable and unstable relate to the laminar and turbulent flows, respectively. On attaining the peak ejection rate at the MS, the anterior wall caves in with hardly any push-flow along it in the mid-region. However, the outflow in the basal region and the one joining it from the apex region appears to gain strength. The low-velocity islands in somewhat triangular formation occupying the central part of the LV present an unusual pattern hitherto unseen during the systole from ES to MS. Just before the closing of the AV when the outflow rate reduces during the LS, the flow from the basal region hits the anterior wall and diverts toward the apex completing a longish counterclockwise vortex. At this stage contraction of the LV is near to its maximum, and the flow pattern assumes the inception of the diastole as can be judged from the comparison with the ED. The corresponding streamlines show centrally located vortical structure in MS and LS of Fig. 5b, which is surprisingly growing in spite of increased compression at LS. These vortical structures have two distinct zones demarcated by bandlike clustering of the streamlines – the inner zone has streamlines spiraling inward, whereas the outer zone has streamlines spiraling outward. It is worth noting that these are sectional planar images of a highly complex 3D flow evolving from the combination of contra-spiraling flows having a common focal point.
The vorticity field, shown in Fig. 5b, depicts the dominance of counterclockwise vorticity in all the phases of both the diastole and systole. Though the streamlines show remarkable vortical structures, the overall magnitude of the vorticity is rather low as it depends on the velocity gradient and not on the absolute velocity. However, the region below the MV close to the posterior wall is marked with spots of relatively higher vorticity of the opposite signs in MD and LD as expected in the shear flow of the jet.
B. BMHV Case 2: MV90o-AV90o
Figure 6 shows the flow patterns in the LV for Case 2, wherein the BMHV at the AV position is rotated by 90° to change the orientation of its leaflets parallel to the anterior wall. What is most surprising and unexpected to observe is the shift in caving in of the LV from the anterior wall (seen in Fig. 5) to the posterior wall during the systole. For changing the orientation of the BMHV at the AV position, the LV sac was required to be removed, which was carefully refitted in the same position, as it was. Therefore, we surmise that the dynamics of the outflow during the systole creates a non-uniform pressure field, and the region of higher differential pressure tends to cave in.
Velocity vector fields, depicted in Fig. 6a, show three representative stages of the diastole and systole phases. The beginning of the diastole, ED, is marked by a single jet flow along the long axis from the basal region, and almost no flow in the region below the MV, which could be attributed to the peculiar shape of the posterior wall. The corresponding streamlines in Fig. 6b depict a system of co-rotating counterclockwise vortices in the region of very low velocities along the posterior wall. Compared to Case 1, the contrasting feature noted here is the flow from the MV reaching directly to the apex. With an increasing rate of filling, at the peak diastole MD, the central jet, created jointly from the central and anterior orifices, spreads and reaches the apical region and turns counterclockwise along the posterior wall. The posterior-orifice jet flow separately impinges on the posterior wall which is recovering from the caved-in state. The corresponding image MD in Fig. 6b shows the streamlines from the MV directly hitting the apex. Such smooth access of the flow to the
apex during the LV filling is physiologically a healthy sign. Spiraling inward streamlines, indicative of the laminar flow, exhibit two vortical structures of opposite signs. Toward the end of the diastole at LD, in completely inflated LV, the posterior-orifice jet with higher velocity entraps a small counterclockwise vortex against the posterior wall, as seen in Fig. 6a, and then turns clockwise but gets interrupted by the flow from the basal region. However, a fully-formed counterclockwise vortex is seen just below. This flow pattern is elucidated more clearly by the streamlines in the corresponding Fig. 6b, wherein the flow field is broadly divided into two parts demarcated by a bunch of streamlines emerging from the MV and impinging on the anterior wall in the apical region. The region above this demarcation is occupied by a clockwise vortical structure and the one below is occupied by a large-scale counterclockwise vortical structure, which has spiraling outward streamlines. The change in streamlines of foci from spiraling inward at the peak of diastole (MD) to spiraling outward for late diastole (LD) reflects the complex dynamics of the flow within a pulsating finite volume.
In all stages of the systole from early (ES) to late (LS), well-directed streamlines toward the AV suggest a rather relatively smooth ejection of the outflow. At the time of closing and opening of the valves, the transient flow has a connection between the systole and diastole, for example, the impressions of the LS and LD flow patterns become the precursor to that of the ED and ES, respectively. The vorticities of opposite signs show a nearly balanced distribution with overall low magnitudes except for some spots of higher values in the region below the MV at the LD and ES.
C. MMHV Case 3: MV180o-AV0o
Figure 7 shows phase averaged velocity and vorticity distributions along with velocity vectors and streamlines superimposed, respectively, for various stages of diastole and systole phases of a cardiac cycle for Case 3 wherein MMHVs are fitted at 180o orientation in MV position (major orifice facing the posterior wall) and at 0o orientation in AV position (major orifice facing the anterior wall). Caving in of the posterior wall during the late systole and early diastole is evident here also. Compared to the BMHV the effective orifice area of the MMHV is smaller, therefore magnitudes of both velocity and vorticity are expected to be higher as seen in the color-coded scales. On completion of the systole when diastole commences with the opening of the MV, the filling of the LV begins with a well-spread diffused jet flow along the posterior wall whose concave surface deflects it straight to the apical region as seen in ED of Fig. 7a. This flow then hits the anterior wall and turns around clockwise to form a well-defined vortex below the basal region. Similar observations are reported in the literature by several researchers (Mouret et al. 2005; Querzoli et al. 2010; Vuki ́cevi ́c et al. 2012 and Wang et al. 2016). The finer details of the flow, missed in the low-velocity regions, are clearly depicted by the streamlines in the corresponding Fig. 7b. During the peak diastole, the mitral jet velocity significantly increases and subsequently creates two contra-rotating vortices on both sides (see MD of Fig. 7a). These vortices are, actually, a cross-section of a vortex ring that is seen to descend and tilt while growing in size as clearly seen not only in LD but its impression is also seen in ES wherein a clockwise vortex facilitates smooth outflow. With the further contraction of the LV when the posterior wall caves in at the peak of the systole (MS) and pushes perpendicularly the fluid in contact. This movement of the posterior wall destroys the neighboring counterclockwise vortex, but it results in acceleration of the outflow along the anterior wall. Further, near the end of the systole (LS), the LV volume reduces to its minimum with a clockwise vortex below the basal region. The streamline plots show large vortical structures, all of them clockwise with the flow spiraling out at all the instants of the diastole and systole phases. This phenomenon clearly explains the advantage of the physiological clockwise vortex in LV flow dynamics. The vorticity distribution shows higher strength for the clockwise vorticity which concurs with the general flow pattern.
D. MMHV Case 4: MV180o-AV180o
Figure 8 shows flow patterns for Case 4 where the minor orifice of the MMHV at the AV position faces the anterior wall. It is surprising to note the absence of the caving in of the LV wall. But the rear wall did cave in which is not visible in the present view, however, its effect on the posterior wall, in the form of a slight bulge from the mid systole to the early diastole (MS, LS, and ED), is visible. Overall, there is a good similarity between the flow patterns seen in Figs. 8 except for some minor features seen in MS and LS. The LV filling in Fig. 7 is comparatively more efficient as the flow appears to reach the apex more closely, which is physiologically favorable.
Figure 9 summarizes the main features of the flow patterns observed in all four cases. Here, the flowlines are drawn to display the mid-diastole and mid-systole stages. Flowlines in the region of the opaque base of the model, just below the MV and AV, are extrapolated from what is seen in the LV. In the case of BMHVs, as the flow takes a longer counterclockwise (anti-physiological) path to fill the LV during the diastole, the exiting flow during the systole needs to find a circuitous route instead of straight from the central region of the LV as two streamlines cannot cross each other. A change in the BMHV orientation at the AV position, despite altering the caving in of the LV wall from the anterior to posterior sides, does not seem to affect the outflow. In the case of MMHVs, the filling process during the diastole is executed smoothly wherein the flow takes the clockwise vortical path along the posterior wall akin to the physiological flow pattern. As the flow direction is naturally towards the outflow tract, the ejection of flow during the systole is more efficient. However, the final exit of the flow from the AV is affected by the orientation of the leaflet. When the MMHV at the AV position is fitted at 0°, the open leaflet is aligned with the approaching flow which will exit with less resistance. However, with the change in the orientation of the MMHV to 180°, the exiting flow is likely to impinge on the face of the open leaflet thereby experiencing some rise in the resistance.
E. Energy loss
A plot of dissipative energy loss (EL) per meter, calculated using Eq. 5 from the strain rate fields of all the cases, is shown in Fig. 10 for all the phases of a cardiac cycle. For better clarity of the difference in magnitudes with low values, a logarithmic scale is used. The peak EL value of about 4–5 mW/m is observed around the mid-diastole for MMHV cases, whereas for BMHVs it is about 1 mW/m towards the late diastole. This can be attributed to the higher local velocities between MD and LD phases near the MV region which resulted in higher velocity gradients and hence higher strain rates for the MMHVs. However, the ascending trend of the EL during diastole reaching its peak and then continuous decline till the late systole is consistently the same for all the cases. This trend matches with those reported in both in vitro (Hayashi et al. 2015) and in vivo (Stugaard et al. 2015) studies with varying magnitude depending on various factors associated with ejection fraction, beat rate and health condition.
The area under each curve was estimated to obtain the net energy loss per meter over a complete cardiac cycle. Case 4 for MMHVs fitted in the MV position with its major orifice facing the posterior wall and in the AV position with its minor orifice facing the anterior wall (M180-A180) registered the highest EL, which was used to normalize the net EL values of other cases. The normalized net energy loss, thus obtained, is plotted in the inset of Fig. 10. The energy loss for the BMHVs is reduced by a huge margin of about 80%, but it is due to the entirely different valve design. What is more surprising is that by merely changing the orientation of the MMHV at the AV position by 180° (M180-A0), a significant reduction in the EL by about 25% is obtained.
The present in vitro study, carried out using the PIV technique, reveals the flow features of the LV with DVR both qualitatively and quantitatively. The former deals with the visualization of the LV flow pattern and the latter with the estimate of velocity, vorticity, strain rate, and energy loss. Though the MMHVs mimicked the physiological flow patterns, they resulted in much higher energy loss in comparison with the BMHVs that generated the anti-physiological flow patterns but much less turbulence and strain. In the case of DVR with BMHVs, the orientation of the leaflets in the AV position makes a negligible difference in the EL but alters the LV contraction significantly. However, with MMHVs the orientation of the major orifice at the AV position not only alters the LV contraction but also results in a considerable variation in the energy loss, thereby suggesting scope for optimization of orientation.
Limitations
The in vitro research study presented here, a comparison of flow patterns between two types of MHVs with varying orientations in AV position, assumed LV sac dimensions in diastolic condition. Hence, various squeezing patterns of the LV sac were observed in the cases studied. This might differ if the LV sac dimensions follow systolic condition, and the cardiac cycle begins from the diastole. Since the aim of this investigation is to study the flow pattern, the pressure measurements were not made during the experiments. The 2D flow patterns studied were obtained from the vertical mid-plane of the LV sac. The 3D nature of the flow could be obtained from integrating such 2D planes along various vertical cross sections. Lastly, material properties of the 3D printed transparent LV base visibly disturbed the laser sheet, therefore, the PIV measurements could not be made in the region close to the valves.
Acknowledgement
The authors would like to acknowledge the Central Facility for PIV at Indian Institute of Technology Bombay.
Ethical Approval
Not applicable
Competing Interests
The authors have no competing interests to declare that are relevant to the content of this article.
Authors’ Contributions
Satheesh Kumar Harikrishnan conducted the experiments, wrote the main manuscript text and prepared the figures. Shailendra D. Sharma supervised the experiments and edited the manuscript/figures. All authors reviewed the manuscript.
Funding
The authors did not receive support from any organization for the submitted work.
Availability of Data and Materials
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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No competing interests reported.