Material transport in the left ventricle with aortic valve regurgitation

This experimental in vitro work investigates material transport properties in a model left ventricle in the case of aortic regurgitation, a valvular disease characterized by a leaking aortic valve and consequently double-jet filling within the elastic left ventricular geometry. This study suggests that material transport phenomena are strongly determined by the motion of the counterrotating vortices driven by the regurgitant aortic and mitral jets. The overall particle residence time appears to be significantly longer with moderate aortic regurgitation, attributed to the dynamics resulting from the timing between the onset of the two jets. Increasing regurgitation severity is shown to be associated with higher frequencies in the time-frequency spectra of the velocity signals at various points in the flow, suggesting nonlaminar mixing past moderate regurgitation. Additionally, a large part of the regurgitant inflow is retained for at least one cardiac cycle. Such an increase in particle residence time accompanied by the occurrence and persistence of a number of attracting Lagrangian coherent structures presents favorable conditions and locations for activated platelets to agglomerate within the left ventricle, potentially posing an additional risk factor for patients with aortic regurgitation.

Figure 1

Schematic of the filling flow in a healthy left ventricle and one with aortic valve regurgitation. Here and in the following figures AV denotes aortic valve, MV mitral valve, and ROA regurgitant orifice area.

Figure 2

Symmetric left ventricular model used in this study.

Figure 3

Schematic of the left heart duplicator. As the piston pulls back, the left ventricle fills through the mitral valve directly from the left atrium (and reservoir). Once the piston attains its maximal backward position, the left atrium is compressed to inject additional fluid into the ventricle ($A$ wave filling). This begins the piston's forward stroke, compressing the ventricle in the hydraulic chamber and ejecting fluid through the aortic valve up to the reservoir.

Figure 4

(a) Mitral inflow waveform recorded just ahead of the reservoir generating a total cardiac output of 4.5 l/min with distinct $E$ and $A$ waves of filling observed in the velocity field just below the mitral valve (inset). (b) Ventricular and aortic pressure waveforms falling in the expected healthy range. Note that the quantity $t^{*}=t/T$ is defined in Sec. 3 and used thereafter, with $T=0.857$ s being the cycle period, therefore $t=0.857$ s in the above figures corresponds to $t^{*}=1$.

Figure 5

Intraventricular flow patterns at selected instants during the left ventricle's filling phase for all simulated cases of aortic regurgitation. Note the progression from a dominant mitral jet-driven vortex, imparting a clockwise swirl to the ventricular volume, to a dominant regurgitant jet-driven vortex, imparting a counterclockwise swirl.

Figure 6

Path followed by the vortex cores generated during the $E$ wave of filling, from the start to the end of the filling phase (i.e., from $t^{*}=0.438$ to $t^{*}=1$), for all cases simulated in this study. The mitral vortex core path is traced in black, while that of the regurgitant vortex core is traced in red. The advection of two circular blobs, one in the ventricle center and one in the apical region, is also illustrated, color coded according to the vortex core positions at specific time instants. The dashed lines show approximately the motion of the blob centroids as a visual aid. Note that the mitral vortex in the healthy ventricle is tracked for one complete cycle (i.e., from $t^{*}=0.438$ to $t^{*}=1.438$), while that in the case of mild regurgitation is tracked until $t^{*}=0.887$, where the vortex is sheared out.

Figure 7

Advection of virtual particles from the beginning of the filling phase ($t^{*}=0.438$) over two cycles for a healthy left ventricle (top row) and for one with mild aortic regurgitation having a regurgitant orifice area 3.3% of the fully open geometric aortic valve area (bottom row). Particles are colored black if they are ejected in the first beat, green if ejected in the second beat, and red if the particles remain after two beats. The first, third, and fifth columns represent the beginning of the filling phase (end of ejection) for consecutive cycles, while the second and fourth columns represent the beginning of the ejection phase (end of filling) for the respective cycles.

Figure 8

(a) Normalized particle residence time (${\tau }^{*}$) in the left ventricle at the start of the ejection phase ($t^{*}=0$) colored by time until ejection in beats; $\beta =0.438$ is the duration of the ejection phase normalized by the cycle period ($T=0.857$ s). (b) Percentage of ventricle area corresponding to the colored regions in (a).

Figure 9

(a) Normalized particle residence time (${\tau }^{*}$) in the left ventricle at the start of the ejection phase ($t^{*}=0$) colored by time since injection in beats; $\alpha =0.562$ is the duration of the filling phase normalized by the cycle period ($T=0.857$ s). (b) Percentage of ventricle area corresponding to the colored regions in (a).

Figure 10

(a) Left ventricular area at the start of the ejection phase ($t^{*}=0$) partitioned by blood that (1) has entered and ejected the ventricle in the same beat (direct flow), (2) was already present in the ventricle and was ejected in the current beat (delayed outflow), (3) has entered and remained in the ventricle in the current beat (retained inflow), and (4) was already present in the ventricle and not ejected in the current beat (residual volume). (b) Percentage of left ventricular area corresponding to the regions displayed in (a).

Figure 11

Left ventricular area at the start of the ejection phase ($t^{*}=0$) partitioned between aortic (blue) and mitral (red) inflows according to blood that (1) has entered and ejected the ventricle in the same beat (direct flow), (2) was already present in the ventricle and was ejected in the current beat (delayed outflow), (3) has entered and remained in the ventricle in the current beat (retained inflow), and (4) was already present in the ventricle and not ejected in the current beat (residual volume).

Figure 12

Time-frequency spectra of the $u$ component of velocity (right) at three points for the healthy and mild cases of aortic regurgitation. Here and in the following figures spectra marked with TR denote sample spectra for a single time-resolved velocity signal, while those marked with Mean denote the mean of ten spectra computed from the velocity signal of distinct acquisitions. The top two rows of spectra correspond to the healthy scenario, while the bottom two rows correspond to the mild scenario. The vorticity field (left) is also shown at $t^{*}=0.566$, the time at which the highest frequencies are present just downstream of the mitral inflow (point 2).

Figure 13

Time-frequency spectra of the $u$ component of velocity (right) at three points for the moderate cases of aortic regurgitation. The top two rows of spectra correspond to the moderate-1 scenario, while the bottom two rows correspond to the moderate-2 scenario. The vorticity field (left) is also shown at $t^{*}=0.566$.

Figure 14

Time-frequency spectra of the $u$ component of velocity (right) at three points for the severe cases of aortic regurgitation. The top two rows of spectra correspond to the severe-1 scenario, while the bottom two rows correspond to the severe-2 scenario. The vorticity field (left) is also shown at $t^{*}=0.566$.

Figure 15

Backward FTLE fields for six severities of aortic regurgitation (including the healthy scenario) at the same six time instants throughout the filling phase of the left ventricle. The backward FTLE fields were computed over an integration time of two cycles.

Figure 16

Forward FTLE fields for six severities of aortic regurgitation (including the healthy scenario) at the same six time instants throughout the filling phase of the left ventricle. The forward FTLE fields were computed over an integration time of two cycles.