INTRODUCTION

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THE FLUID DYNAMICS of diastolic filling are essentially unexplored for the right ventricle (RV) (10, 11), although in the context of the left ventricle (LV), they have been shown to hold great importance for proper evaluations of diagnostic studies and in pathophysiological investigations of ventricular function (17, 18, 21, 22). The elegant, classic experimental in vitro findings on mechanical left heart models and their analytical interpretation reported by Bellhouse (1) have shown that ventricular dilatation, common in heart failure, induces a decrease in the diastolic filling vortex strength. The diastolic filling vortices of interest here are "global" or "macroscopic" in the sense that they occupy a sizeable region within the chamber. They are "large-scale" structures in contrast to "microscopic" high-frequency disturbances (eddies) within the turbulent regime downstream of a stenotic valve. Knowledge concerning diastolic RV flow field characteristics under normal conditions and changes induced by chamber dilatation should improve application and interpretation of noninvasive diagnostic studies (Doppler color flow mapping, velocity-encoded cine magnetic resonance imaging, etc.) under these conditions. They should also lead to better insights into factors limiting the accuracy of indicator dilution measurements in RV dilatation, and point toward new research areas on aspects of intracardiac flow that could be implicated in the pathophysiology of failure characterized by chamber dilatation and remodeling and their sequelae.

For these reasons, RV intraventricular diastolic filling flow patterns were investigated under normal conditions and during volume overload with or without paradoxic septal motion (PSM) as an extension of our previously published work (15). Functional imaging of the diastolic RV flow field involving computational fluid dynamic simulations in individual animals was carried out, utilizing three-dimensional (3-D) real-time echocardiography (RT3D) for dynamic RV chamber reconstructions, which were validated by simultaneous sonomicrometry, as described in a recent publication (15). The simulations yielded high spatial and temporal resolution data on the filling vortex and the evolution of the RV diastolic flow field throughout the E-wave, and quantitative visualizations elucidated its detailed dynamic characteristics in the hearts of lightly sedated, awake dogs under control conditions and in experimentally induced chamber dilatation.

	METHODS

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Instrumentation and data acquisition. Because of the complicated dynamic RV geometry, this investigation required application of a recently developed functional imaging method (15), which comprises real-time 3-D cardiac imaging and computational fluid dynamics. Figure 1 summarizes the method.

View larger version (49K): [in this window] [in a new window]   Fig. 1.   Schematic summary of the functional imaging method, which comprises three parts. First, a semiautomated segmentation aided by intraluminal contrast medium locates the right ventricular (RV) endocardial surface. Second, a geometric scheme for dynamic RV chamber reconstruction applies a time interpolation procedure to the 3-dimensional real-time echocardiography (RT3D) data to quantify wall geometry and motion at 400 Hz. Finally, RV endocardial border motion information is used for mesh generation on a computational fluid dynamics solver to simulate development of the early RV diastolic inflow field. Boundary conditions (tessellated endocardial surface nodal velocities) for the solver are directly derived from the endocardial geometry and motion information. Method is independent of digital imaging modality used. IR, isovolumic relaxation; RF, rapid filling period; D, diastasis; A, atrial filling period.

3-D real-time echocardiography and image segmentation. Real-time 3-D images of the RV were obtained using the RT3D ultrasound scanner (Volumetrics Medical Imaging; Durham, NC). Endocardial border detection involved proprietary software, which displayed one RV frame at a time. A two-dimensional "(2-D) Swath" algorithm (15) located the most likely position of the endocardial border. The individual points were converted into 3-D cartesian coordinates and stored in a file. Each file was a four-dimensional (4-D) matrix containing a sequence of 3-D RV chamber "volumes" ordered chronologically. Each "volume" was a succession of endocardial border layers from apex to base (Fig. 1, inset 1).

Reconstruction of endocardial border points. The data representing the extracted endocardial edges were in layered form and were further processed to generate the desired coordinates in 3-D. To obtain RV diastolic flow field simulations at a temporal resolution of 400 Hz, it was necessary to approximate the 3-D RV geometry at time instants between successive RT3D images. Under steady-state conditions, RV geometry was calculated at these instants as a quadratic weighted average of the dynamic geometry in contiguous RT3D frames. Representative RV reconstructions are depicted in Fig. 1, inset 2.

Mesh generation and determination of boundary conditions. A combination of FIDAP (8, 9) and custom software (15) generated the mesh representing the 3-D domain for simulation of RV intraventricular diastolic flow (Fig. 1, inset 4). The instantaneous geometry defined the external nodal points of the mesh, to which were assigned boundary conditions, i.e., nodal velocity vectors describing direction and speed of instantaneous motion (Fig. 1, inset 4).

Computer simulations and flow visualization. Simulations were carried out using the CRAY T-90 supercomputer running FIDAP on the UNICOS operating system (Cray; Mendota Heights, MN) at the North Carolina Supercomputing Center. They had to be completed through consecutive runs, each advancing the solution by two to four 2.5-ms time steps. It was assumed that blood is a Newtonian, incompressible fluid with kinematic viscosity of 0.04 Stokes and mass density of 1.05 g/cm³ and that flow is governed by the Navier-Stokes equations. The flow field was visualized using the FIDAP postprocessing module, which extracts the field variables on any specified visualization plane or "cut" within the field (Fig. 1, inset 5; Figs. 2 and 3).

View larger version (96K): [in this window] [in a new window]   Fig. 2.   Representative fanlike frontal plane RV flow velocity fields during early stage of filling (top) and at E-wave peak volumetric inflow rate 136 cm3/s for normal wall motion (NWM) and 216 cm3/s for paradoxical septal motion (PSM) (bottom). Left, NWM; right, chamber dilatation with PSM in the same dog.

View larger version (117K): [in this window] [in a new window]   Fig. 3.   Frontal plane RV flow velocity fields (top), and color maps (middle) near end of E-wave, from same dog as Fig. 2. Instantaneous inflow rate was 39.0 cm3/s for NWM (left) and 71 cm3/s for PSM (right). Both visualization planes and color coding are identical to those in Fig. 2. Bottom, simultaneous transverse "cut" color maps in a plane 2.5 cm below the inflow orifice show to advantage the higher axial core velocities in the normal and the larger core cross-sectional area in the volume-overloaded chamber (cf. Fig. 5).

	RESULTS

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Wall motion patterns. All seven lightly sedated, awake animals exhibited normal wall motion (NWM) at control; three also had normal and four exhibited diastolic PSM in volume overload with chamber dilatation. PSM and NWM differ qualitatively from each other in the direction of septal movement. In PSM, the septum moves toward the LV in diastole. The NWM condition exhibits the opposite scenario in which the septum functions as part of the LV and moves into the right ventricle.

RV diastolic flow field simulations. The functional imaging simulations allowed examination of the dynamic evolution of the RV diastolic flow field throughout the E-wave in individual dog hearts under control and failure conditions characterized by RV dilatation. By taking the time derivative of the instantaneous RV volume calculated with the RT3D-based dynamic reconstruction method, the RV diastolic filling rate could be calculated. Representative plots of instantaneous RV volumetric filling rate (dV/dt) and volume (V) are shown in Fig. 1, insets 3a and b, respectively. Both control and volume overload simulations extended throughout the E-wave (cf. arrows in Fig. 4). RV flow field information was extracted from the databases obtained through the individual simulations. Scientific visualization of each simulated RV flow field disclosed the existence of large-scale vortical motions inside the filling right ventricles of the individual dog hearts both at control and under volume overload conditions.

View larger version (33K): [in this window] [in a new window]   Fig. 4.   As blood fans away from the central stream toward the endocardial walls, the convective deceleration effect tends, by the Bernoulli mechanism, to elevate downstream pressure opposing ventricular inflow (top right). There is an additional convective pressure decrease normal to the curved fanning streamlines (top left), which tends to decrease pressure in the direction of the chamber's base and away from the endocardial walls (long arrows crossing streamlines, lower left). During the upstroke of the E-wave, these combined adverse convective pressure effects are opposed by the local acceleration gradient, which favors forward flow. During the E-wave downstroke, they are joined in sense and augmented by the local deceleration gradient and can now reverse the flow. This leads to disruption of the boundary between oncoming blood and endocardial walls, or "flow separation," and to the formation of a toroidal vortex that surrounds the central core. Center inset, volumetric filling rate calculated by numerical differentiation of RV chamber volume obtained from dynamic representations using RT3D measurements; small arrows point to representative beginning and ending points of simulations.

Intraventricular flow field. In the following sections, illustrative functional imaging visualizations from the individual simulations are considered together in the context of the filling process throughout the entire E-wave, for a comparison of the RV diastolic flow field characteristics in ventricular dilatation with PSM to those with NWM. We examine snapshots of the RV flow field at the following three informative points of the E-wave: early in the upstroke, at peak volumetric inflow, and late in the downstroke.

Early upstroke through the peak of the E-wave. Figure 2 illustrates typical RV flow fields developing during the early upstroke of the E-wave soon after the onset of filling (top) and at peak volumetric inflow rate (bottom). Figure 2, left, shows the flow fields applying at control with NWM and, right, the fields applying under conditions of RV dilatation with PSM in the same animal. The velocity fields are visualized on an RV coronal (frontal) plane. The arrows indicate both direction and magnitude of the flow velocity at each node within the plane. Such arrow maps are effective in revealing the spatial organization of flow within the entire flow field. Flow velocity is encoded in the length of an arrow, whereas its color is assigned according to the z component of the velocity vector. A negative z component (i.e., the blue-green region of the spectrum) maps flow toward the apex, whereas a positive one (red-orange region) represents a velocity pointing toward the RV base (see color scale inset in Fig. 2).

Late downstroke of the E-wave. Figure 3, top, illustrates representative simulation plots of velocity vectors in the frontal plane. These results were obtained in the same dog as those in Fig. 2 but at instants close to the end of the E-wave. Figure 3, left, shows the flow field applying at control with NWM; the right shows the field applying under conditions of RV dilatation with PSM. The instantaneous volumetric inflow velocity was 39 cm³/s at control (NWM) and 71 cm³/s in the dilated chamber.

Color mapping. Figure 3, middle and bottom, shows color maps of the velocity fields at the same instants as the corresponding velocity plots of the top panels. Such mappings are familiar to echocardiographers and suitable for revealing the global organization of the flow. The regions with red and orange colors represent blood flow toward the base of the right ventricle, whereas regions with blue and green colors represent blood flow toward the apex. Comparison between NWM and PSM simulations showed that the vortical motion was stronger in the former, with a high intensity in the region surrounding the main incoming stream below the inflow orifice. This effectively encroaches on the available central core area beyond the inflow orifice that is available for flow toward the apex. The encroaching effect was more pronounced in the simulations under control conditions than in the dilated volume-overloaded ventricles (cf. Fig. 5). This is responsible for the higher velocity vector magnitudes present within the normal flow field, referred to in the preceding paragraph. As illustrated in the representative case shown in Fig. 3, the vortical motion generated in the dilated ventricles with PSM had a more even spatial distribution. In addition, the space available for flow toward the apex, marked by the blue, green, and yellow zones, was significantly greater for the volume-overloaded situation.

View larger version (28K): [in this window] [in a new window]   Fig. 5.   Although applying instantaneous volumetric inflow rate at control was much smaller than with volume overload, higher core velocities were present in the control flow field after vortex development. Visualization of simulation results from NWM and PSM (cf. Fig. 3) showed that the vortical motion was stronger in the former. Vortex ring encroaches on the available central core area for flow toward the apex: more substantially so in NWM (A) than in the dilated ventricle (B). Width of each arrow is proportional to the central core area beyond the inflow orifice that is available for flow toward the apex; the length, to linear inflow velocity in the central core.

	DISCUSSION

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We have recently developed a comprehensive software environment that is able to model complex diastolic intracardiac flows in individual animal or human hearts (15). The integrated software system can accept data from RT3D and other digital imaging sources, such as computed tomography or magnetic resonance imaging, to generate dynamic geometric reconstructions of the cardiac chambers, which are then passed on to an automatic finite element mesh generator and a finite element solver. The flow fields of interest are then displayed using scientific visualization techniques. In the present investigation, simulations using this functional imaging system have yielded important information about the detailed diastolic RV flow fields of specific hearts in lightly sedated, awake dogs under control and volume overload conditions.

This research produced for the first time finite element 3-D simulations of diastolic blood flow into the RV chamber using in vivo, real-time 3-D dynamic RV geometric data. Completed, for the first time, were simulations of the evolution of the RV diastolic flow field throughout the entire E-wave in individual animal hearts under control and volume overload conditions associated with surgically induced experimental chronic tricuspid insufficiency. Simulations through the entire duration of the E-wave have allowed us to demonstrate the existence of large-scale 3-D vortical motions, which develop inside the RV chamber during diastole both at control and volume overload.

This study has also provided strong and important evidence regarding the impact of the applying chamber size and wall motion patterns on the development of the RV velocity field during diastole. The functional imaging approach can also be used to study the flow field in the left ventricle.

Reynolds number and distribution of nodal points. The local Reynolds number, Re  D × v, of the RV diastolic inflow field (6, 12) constitutes a very important parameter in our computational fluid dynamic analysis. The characteristic length, D, in Re is proportional to the square root of flow cross-sectional area, whereas the velocity, v, in a diverging flow field decreases linearly as the area increases. Because the RV endocardial surface area is much larger than the tricuspid orifice area (area of walls/area of orifice  10), blood entering the chamber especially during the upstroke of the E-wave (before the flow breaks down into the vortical pattern, see Fig. 4) experiences powerful convective deceleration (6, 12). The net effect of a rapidly decreasing velocity v and a slowly increasing characteristic length D is a decrease in Re away from the orifice along the streamlines of the blood flow. The drop in Re is proportional to the square root of upstream to downstream flow cross-sectional areas. The local Re is therefore highest near the tricuspid orifice.

The RV diastolic vortex. In all simulations conducted in the seven dog hearts under control and volume overload conditions, development of large-scale vortical motions was observed during the downstroke of the E-wave. During this period, inflow velocity decreases and the pressure level rises within the flow field. As one moves away from the central stream toward the endocardial wall, convective pressure rise by the Bernoulli mechanism raises the pressure energy opposing ventricular inflow along any streamline. An adverse convective (11, 12) pressure gradient develops, and this is augmented by the local deceleration (11, 12) gradient during the downstroke of the E-wave. As is shown diagrammatically in Fig. 4, bottom left, the fanning streamlines are curved. This implies that the streaming blood is acted upon by a centripetal force and that the convective pressure gradient has a component normal to the concave streamlines also, which tends to drive the blood toward the base of the chamber (Fig. 4). Ultimately, the combined adverse pressure gradient forces arrest forward flow and deflect the direction of blood near the endocardial surface toward the base, leading to flow separation, roll up, and recirculating vortical motions within the chamber. Large-scale vortices form, as shown in Figs. 3 and 4.

Physiological significance. With the use of functional imaging (15), this study is the first to show the existence of vortical motion inside the right ventricle. The physiological repercussions of the vortical motion are most intriguing. Bellhouse (1), who conducted experimental studies on the LV diastolic vortex in the context of cardiac physiology in the early 1970s, proposed that vortical motion might assist in valve closure. Others (25) have suggested that the presence of LV diastolic vortical motions helps in the ensuing process of ejection, by conversion of vortex kinetic energy into kinetic energy of outflow after aortic valve opening. According to this view, vortices within the ventricle would act as energy-preserving flow structures (4). It is well known in fluid mechanics, however, that large vortices never unwind smoothly. Instead, they break up into smaller eddies, and this process is continued, until the vortices are reduced to micron-size eddies and at that level (Kolmogorov "microscale") they dissipate under the action of viscous forces (19). The process is known as the vortical cascade mechanism. This implies that vortices are essentially "traps" or "sinks of energy." Whatever kinetic energy is trapped in the recirculating motion of a vortex is bound to be converted to heat and lost from the motion and therefore cannot in fact aid ejection.

Clinical impact of RV size and wall motion patterns. Using functional imaging, we have demonstrated that not just quantitative but qualitative important alterations in the intraventricular velocity field result from changes in applying RV dynamic geometry and wall motion patterns. As shown by the results presented, the impact of abnormal chamber dilatation and wall motion patterns on RV flow is manifested throughout the entire E-wave. In this study, we have been able to characterize extensively the resultant alterations of the diastolic flow field. Our functional imaging simulation findings are in agreement with the classic studies of Bellhouse (1), who reported reduced vortex strength and extent in dilated ventricles.

View larger version (80K): [in this window] [in a new window]   Fig. 6.   Rotation in the intraventricular blood stream may naturally encourage a gentle scouring (shear) of the endocardial lining of the chamber (left); vortical spinning may promote chemical mixing and keep formed and unformed blood elements suspended as sugar and tea leaves are kept suspended by vigorous stirring, which sets up secondary vortical motions in a tea cup (right). P, pressure: acts perpendicularly; WS, wall shear: acts tangentially on the endocardial lining.