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Division of Cardiac and Thoracic Surgery, 1 Department of Surgery, and 2 Center for Emerging Cardiovascular Technologies, Duke University Medical Center, Durham, North Carolina 27710
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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We describe a novel functional imaging approach for quantitative analysis of right ventricular (RV) blood flow patterns in specific experimental animals (or humans) using real-time, three-dimensional (3-D) echocardiography (RT3D). The method is independent of the digital imaging modality used. It comprises three parts. First, a semiautomated segmentation aided by intraluminal contrast medium locates the RV endocardial surface. Second, a geometric scheme for dynamic RV chamber reconstruction applies a time interpolation procedure to the RT3D data to quantify wall geometry and motion at 400 Hz. A volumetric prism method validated the dynamic geometric reconstruction against simultaneous sonomicrometric canine measurements. Finally, the 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. The new functional imaging approach may yield important kinematic information on the distribution of instantaneous velocities in the RV diastolic flow field of specific normal or diseased hearts.
cardiac image analysis; ventricular function; cardiac fluid dynamics; right ventricle; heart chamber volume
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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QUANTITATIVE ANALYSIS of three-dimensional (3-D) digital cardiac images has become increasingly important given the recent advances in the digital cardiac imaging techniques of 3-D echocardiography, magnetic resonance imaging, computed tomography, and digital fluoroscopy (1, 24, 26). The growth of these digital imaging techniques is accompanied by an increasing usage of image manipulation tools, providing more elaborate image analysis and measurement and quantitative evaluation and leading to more refined diagnostic accuracy than visual interpretation alone. Moreover, complex mathematical procedures are being used to localize and highlight important changes in cardiac function that cannot be visually detected directly from the original images. With the concurrent development of high-performance computers and analytical software, a functional sort of imaging can now evolve, geared toward the creation of physiological images that are the result of a mathematical simulation derived from a set of images. Such functional imaging will allow visualization and understanding of the evolution of any dynamic process of interest (filling, ejection) within the heart. Accordingly, it should allow better insights into cardiac physiology and pathophysiology and may possibly detect warning signs of diseases not yet overt.
This study developed innovative dynamic geometric chamber reconstruction models for use in functional imaging analyses of right ventricular (RV) filling dynamics and physiology. With the use of a new volumetric "prism method," it is first shown that the geometric chamber reconstructions provide accurate and reliable dynamic instantaneous RV chamber geometry and volumes throughout the cardiac cycle. The method is then applied to functional imaging of the early RV inflow field under normal and experimental volume overload conditions.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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As depicted in Fig. 1, there are
three major phases to our image-based, dynamic blood flow simulation.
The input is the real-time, 3-D echocardiographic (RT3D) images of the
heart, including the RV chamber. The segmentation phase takes this
imaging data and extracts the RV chamber border. The output of the
segmentation phase is successive geometric snapshots of the RV chamber
boundary. The second phase, geometric reconstruction and wall motion
analysis, takes as input these snapshots through the cardiac cycle and
computes the 3-D motion of the endocardial boundary. The final phase,
computational fluid dynamics (CFD) simulation, applies boundary
conditions from the endocardial border motion data to a finite element
method (FEM)-based fluid dynamics software. The output is the
full 3-D field of intraventricular blood flow.
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Experimental animals and instrumentation. RT3D images of the right ventricle were obtained on seven awake, large (23-30 kg) adult dogs of either sex, chronically instrumented with sonomicrometric crystals for volume measurements using the shell subtraction (SSM) model (6, 7, 14, 22, 25) both under control conditions and during subacute, surgically induced (chordal rupture) volume overload. Cardiac chamber casts were obtained in another eight dogs of comparable size and characteristics at the end of unrelated surgical experiments. All procedures and animal care were in accordance with institutional guidelines, conforming to the "Position of the American Heart Association on Research Animal Use," American Heart Association, November 11, 1984.
The physiological characteristics, tricuspid chordal rupture procedure, and instrumentation for sonomicrometric data acquisition have been recently published (2, 22, 23, 25). The cardiac period was 0.550 ± 0.012 s (means ± SD) at control and 0.530 ± 0.014 s in the volume overload condition. In brief, the right external jugular vein was exposed with the animal under local anesthesia with 1% lidocaine, and an 8-Fr 25-cm introducer sheath was positioned into the right ventricle under fluoroscopy. A 6-Fr urological biopsy forceps (Circon Instruments; Santa Barbara, CA) was inserted into the right ventricle via the sheath, and multiple passes were taken to sever chordae until 3-4+ regurgitation developed (2, 22, 23, 25). Regurgitation was such as to yield both complete contrast medium filling of the atrium within several cycles and an elevation of peak right atrial pressures (v wave) to over 15 mmHg with obliteration of the x-y descent. Imaging data were collected between the second and third weeks after chordal rupture.Real-time 3-D echocardiography.
RV images were obtained by a Volumetrics (Volumetrics; Durham, NC)
phased-array RT3D ultrasound scanner (16, 26, 28). With the use of the stored image data, endocardial border detection systems extract and compute the coordinates of points constituting the
RV endocardial borders (16, 26, 28, 29). The scanner was
initially set to the multiple-scanning mode, enabling
observation of images on two mutually orthogonal B-mode scans
as well as several parallel horizontal C-scan planes (Fig.
2). The maximum depth of scanning was set
at either 12 or 14 cm, depending on thoracic size and geometry. At
these settings, framing rate was either 21.9 or 19.3 frames/s, axial
resolution 1-1.5 mm, and lateral resolution was 1.5-2 mm.
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Endocardial border detection and RV chamber geometry.
The imaging data stored on a 1.2-GB magneto-optical disk (Sony
Electronics; Montvale, NJ) were first transferred into the local memory
of a Silicon Graphics Reality Engine (Silicon Graphics; Mountain View,
CA) at the Imaging and Visualization Facility of the Duke Center for
Emerging Cardiovascular Technologies. The data were read by interactive
endocardial border detection software (16, 26, 28, 29),
which displayed the echocardiographic RV volumes individually. The
software displays all horizontal cross sections in an apex-to-base
order, along with the two mutually orthogonal B-mode images. With the
use of the reference record taken during the experiment, the cross
sections at the levels of the tricuspid valve and apex were first
determined. A semiautomated interactive computer module then located
the endocardial border. The putative border is represented by a moving
stack of contours in a set of two-dimensional (2-D) slices. An operator
initiates the moving endocardial border stack by entering a rough
initial contour on a single slice. This contour then adapts
automatically to the endocardial border using the "2-D swath"
algorithm (16, 26, 28, 29). The swath algorithm follows
the moving endocardial border through all the slices of the frame (Fig.
3, top), as well as successive
time frames. Each contour in the moving stack was converted to its
elliptical Fourier series allowing for evenly spaced endocardial border
coordinates. The elliptical Fourier series is useful in representing
cardiac shapes and in automated methods for finding boundaries
(27, 29). These representations provide a frequency-based
decomposition of an object and describe its overall shape efficiently
using relatively few harmonic coefficients.
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Echocardiographic RV instantaneous chamber volume adjustment.
The RV chamber volume was also calculated from the instantaneous
sonomicrometric dimensions by the standard SSM formulas (6, 7,
14, 22, 25). The volumetric inflow rate through the tricuspid
orifice was obtained digitally as the time derivative of the RV chamber
volume by using the central difference method. The calculated rate of
volume change over time (dV/dt) signal was smoothed using
the first 20 harmonics of its Fourier decomposition, and tricuspid
inflow rate values were sampled at 800 Hz; representative tracings of RV chamber volume and its time derivative signal
obtained in this way are presented in Fig.
4. These values were used for adjusting
the instantaneous volume and velocity boundary conditions in the CFD
simulations of the RV diastolic flow field, as needed, according to the
following scheme.
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t is
the time increment (2.5 ms) between these two instants, and
dV/dt is the rate of change of volume at t + 1.25 ms.
For RT3D-derived meshes of which the instantaneous volume differed from
that calculated using the previous equation, a uniform expansion/contraction method was applied to obtain a new mesh with the
desired volume while preserving the geometric similarity. For an
arbitrary boundary point (x0,
y0, z0) in the original
mesh, the coordinates of its corresponding point (x,
y, z) in the adjusted mesh were
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Validation of RV chamber geometric reconstruction.
To validate the geometric representation of the RV chamber, a
volumetric approach was applied. Dynamic noninvasive RV volumes obtained by RT3D were compared with simultaneously determined sonomicrometric ones by using SSM in the chronically instrumented awake
dogs under control and volume overload conditions. To calculate the
chamber volume enclosed by the endocardial border, a volumetric "prism method" was developed, which represents a simple adaptation of the Archimedean method of exhaustion for computing areas and volumes
of various geometric objects (11). Advantages of the prism
method are that its individual steps can be easily automated, and,
unlike "disk summation" using Simpson's or other integral algorithms, the vertices of the tetrahedral tessellation can accurately follow endocardial surface details corresponding to local
"features" (Fig. 5,
bottom), such as papillary
muscles. The primary steps are shown graphically in Fig. 5 and include
the following: 1) Connect the corresponding points of
adjacent layers, forming a slice. 2) With the use of the
"pseudocenters" defined by the means of the x- and
y-coordinates separately for the points of the top and
bottom layers, divide each slice into n wedges, where
n is the number of points within each layer. 3)
Decompose each wedge into three tetrahedra in the manner illustrated in
Fig. 5. 4) For an arbitrary tetrahedron with vertices
O, A, B, and C, calculate its volume using the scalar triple
product
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RV chamber cast measurements.
The volumetric "prism method" was itself validated first on RV
chamber casts. At the end of unrelated surgical experiments, eight dogs
(comparable in size and characteristics to the chronically instrumented
animals) were euthanized with intravenous KCl (1 to 2 mmol/kg) to
result in diastolic cardiac arrest. The heart was quickly excised with
the stumps of the great vessels. After being thoroughly cleaned,
cardiac chamber casts were immediately prepared under physiological
diastolic hydrostatic loading. Left and right ventricles, in that
order, were filled with molten paraffin retrogradely through the aorta
and pulmonary artery. Paraffins with a low melting point (115°F) were
employed to minimize heat introduction. Once set, the casts were
removed, and surface points corresponding to endocardial landmarks were
noted. A representative RV cast is shown in Fig.
6, inset.
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Statistical comparisons. Bland and Altman's (4, 5) approach was applied to assess the agreement between measurement modes. The mean of the methods is treated as the best estimate of true value (4). Alternate methods were visually compared for agreement, any bias due to systematic error, and to spot any possible relationship between imprecision and chamber size. ANOVA and standard statistical analyses were performed by using SAS (SAS; Cary, NC) and Statgraphics Plus (Manugistics Group; Rockville, MD).
Functional imaging. With the use of the prism model with RT3D data, RV chamber dynamic geometry and boundary conditions (RV endocardial velocities) were obtained for solution of the Navier-Stokes equations (8-10, 18, 19) in CFD simulations of RV filling characteristics. Blood was assumed to be a Newtonian, incompressible fluid with a kinematic viscosity of 0.04 Stokes and mass density of 1.05 g/cm3. We used a combination of custom software and FIDAP (Fluid Dynamics International; Evanston, IL). FIDAP is a general-purpose computer program that uses FEM to simulate fluid flows (9, 10). In FEM the flow domain represented by the filling RV chamber is tessellated into small "finite elements," forming a mesh (8). The definition of the elements is accomplished by identifying the locations of the element corners in space. These identified points are called "nodes." The partial differential Navier-Stokes equations covering the flow domain as a whole are replaced by ordinary differential equations for the unsteady flow analyses at hand. The resulting system of equations has matrix coefficients that are derived by approximating the continuum equations on each element (8-10). The boundary condition assigned to each external nodal point was the time-dependent velocity vector describing the direction of instantaneous motion of the nodal point (see Fig. 9, top). This nonlinear system of equations was solved by numerical techniques to determine velocity distributions at each node in every element throughout the "discretized" (8) flow field.
FIDAP performed the numerical computations involved in solving the Navier-Stokes equations governing the evolution of the flow field. Numerical simulations were carried out using the CRAY T90 supercomputer running FIDAP on the UNICOS operating system (Cray; Mendota Heights, MN) at the North Carolina Supercomputing Center (Research Triangle Park, NC).| |
RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Validation on casts of RV geometric reconstruction and volumetric prism method. Fixing the number of layers along the z-axis of each RV chamber cast to 25, we first assessed the impact of varying the number of Fourier harmonics representing the endocardial border of a 2-D layer on the accuracy of the geometric reconstruction for the 3-D chamber. Each layer was fitted with 3, 5, 7, and 10 harmonics. A representative fit using 7 harmonics is shown in Fig. 6. ANOVA showed no significant difference among the volumes measured (F = 0.01, P = 0.99). When the linear model was used for calibrating each prism method calculation against direct water displacement, on the basis of standar error of estimate (SEE) and root mean square (RMS) error of the residuals, the best fit was obtained using five harmonics.
A possible relationship between the number of successive 2-D layers interpolated along the z-axis, and the accuracy of the geometric reconstruction was then explored. Each layer was represented using five harmonics. Accuracy tests were performed for 10, 15, 25, 35, and 50 layers along the z-axis. The volumes of all eight RV casts obtained by the prism method for each of these numbers of z-axis layers were compared with the volumes obtained by water displacement. Again, ANOVA showed no significant difference between the six sets (viz., the computed 10, 15, 25, 35, and 50 axial layer volumes and direct water displacement), and linear calibrations versus water displacement showed no significant differences in SEE and RMS error. The agreement between the prism method, using the first 5 harmonics for 2-D smoothing and 25 z-axis layers, and water displacement was examined by the method of Bland and Altman (4, 5). As shown in Fig. 7, the measurement points follow the identity line very closely (top left). The difference plot (Fig. 7, top right) shows the variance of the observations to be small and constant across the sampling range and the lack of bias or systematic error in the prism calculations. The bias was
0.19%, so on average volumes of the RV geometric
reconstructions were 0.19% lower than the direct measurements of
cast volume by water displacement.
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Volumetric validation of the dynamic RV chamber geometric
reconstruction in conscious dogs.
The panel labeled as CL in Fig. 8 shows a
representative comparison of instantaneous RV chamber volumes obtained
in an awake chronically instrumented dog heart by using SSM with
simultaneous volumes calculated by applying the prism method to the
RT3D imaging data under the control condition. The panel labeled VO is
similar but under volume overload, which produced considerable
increases in operating RV chamber volume levels.
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Functional imaging results.
Figure 9 shows representative functional
imaging results (comparative fluid dynamics) of the commencing
diastolic RV inflow field. Simulations of the RV inflow field in its
earliest stages were performed on all seven animals under control and
volume overload conditions. Simulation data shown in Fig. 9,
left, exemplify normal conditions, in which the septum moves
toward the RV free wall, and those on the right diastolic PSM, in which
the septum moves toward the left ventricle. The flow fields are
illustrated at instants just after the onset of the upstroke of the E
wave at which the average inflow velocities were comparable.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Our goal was to couple noninvasive digital imaging technology with innovative computer modeling and simulation techniques to contribute to the development of a fluid dynamic functional imaging approach to the study of intracardiac flow patterns and pathophysiology. Modeling is the geometric counterpart to simulation in that the goal is not to describe function but to quantitatively capture dynamic chamber anatomy in space and time. From the locations of endocardial border points in space, modeling defines connections between these points to derive instantaneous tessellated RV chamber surfaces and volumes. Our dynamic reconstruction approach defines RV chamber anatomy by means of discrete points joined to form polygonal tessellating elements such as tetrahedra. There is a natural synergy between modeling and simulations in that the CFD simulations require a geometric description of the flow domain for which the discretized FEM mesh is generated.
Physiological simulation is the quantitative description of biophysical behavior in terms of mathematical equations. The reasons for performing CFD simulations include our desire to visualize cardiac fluid dynamic function, leading to improved utilization of information available in contemporary and emerging new diagnostic imaging modalities, and as a tool to investigate conditions that are difficult or even impossible to create experimentally.
Results from the present volumetric animal study show that, using RT3D imaging, our RV chamber geometric reconstruction method computes dynamic RV volumes throughout the cardiac cycle, which agree closely with those by SSM, both under control and volume overload conditions. The accuracy of the invasive SSM in normal and volume-overloaded canine hearts has been verified in previous publications from our laboratory (6, 7). In addition, the prism method was shown on casts to compute RV chamber volumes that closely coincide to those by water displacement.
Prism volumetric method. The dynamic RV reconstruction scheme was shown to be accurate by using the prism method. In common with other volumetric methods (13, 15, 17) based on geometric reconstruction of images, the prism method places no geometric assumption on the chamber whose volume is to be measured. It can be used with other noninvasive digital imaging modalities, including magnetic resonance and computed tomography scanning, in addition to 3-D echocardiography.
Advantages of the prism method are that its individual steps can be easily automated and, unlike "disk summation" using Simpson's or other integral algorithms, the vertices of the tetrahedral tessellation can accurately follow endocardial surface details corresponding to local "features" (Fig. 5), such as papillary muscles. Because it remains difficult to extract the RV chamber directly by automated endocardial border recognition from RT3D frames, we currently feel it is more appropriate to segment the chamber slice by slice, isolating the endocardium, and then tessellate the surface from the layered 2-D contour stack. On the basis of our results, it is recommended to use five to seven harmonic 2-D layer Fourier representations and no more than 25 z-axis layers. This represents the best balance between the tightness of fit of each 2-D layer, the smoothness of each regenerated layer, and the accuracy of the geometric reconstruction. With continuing advances in spatiotemporal resolution and accuracy of imaging technologies, however, it should become possible to extract the chamber automatically and then obtain the Fourier transform to the volume image (constructed of voxels instead of pixels) in the 3-D frequency space directly.Functional imaging of RV inflow with normal wall motion and PSM. Our method can analyze intraventricular blood flow patterns in any individual heart because it drives the CFD simulations using actual RV chamber dynamic geometric reconstruction and wall motion as boundary conditions. The comparative fluid dynamics of the commencing diastolic RV inflow field with normal wall motion (NWM) and with diastolic paradoxical septal motion, shown in Fig. 9, are interesting. The PSM case exhibits a flow field that is qualitatively different from that of NWM: with NWM there is blood flow toward the free wall in the septal region, whereas with PSM there is very little blood flow in that region. Compared with normal, wall motion abnormalities yield conspicuously different velocity profiles at the tricuspid anulus. This result suggests that presence of diastolic wall motion abnormalities may be detected by clinical Doppler evaluation of diastolic inflow velocity profiles in the earliest stage of diastolic inflow. At that stage the flow field is irrotational (8, 18-21). From the fluid dynamic standpoint, irrotational flow patterns in regions such as the ventricular chamber ("simply connected") are exclusively dependent on the instantaneous velocity of the boundary. Alternatively, different patterns of motion by the endocardial surface (including interventricular septum) are transmitted instantaneously throughout the flow field, including at the tricuspid orifice.
In both cases, highest velocities are concentrated in the vicinity of the inflow orifice. This reflects the strong convective deceleration ensuing as blood moves from the orifice to the periphery of the chamber. It is analogous and exactly the converse of the strong convective acceleration of the intraventricular ejection flow in the immediate vicinity of the outflow orifice, which has previously been demonstrated in cardiac catheterization and CFD studies (3, 8-10, 18-21). Because the RV endocardial surface area is much larger than the tricuspid orifice area (endocardial surface/orifice area
10), blood
entering the irrotational flow field of early diastole experiences convective deceleration (18). The magnitude of blood
velocities below the inflow orifice falls off more gradually in the
normal case reflecting a lower convective deceleration than in the
volume-overloaded ventricle with diastolic paradoxical septal motion,
where the transition from higher to lower flow velocities is abrupt.
The larger the end-systolic size of the chamber relative to the inflow valve anulus, the higher is the diastolic convective deceleration. This
reveals a subtle but important influence on filling dynamics of an
"inflow, or diastolic, ventriculoannular disproportion," ensuing
with chamber dilatation in volume overload. The concept is the
counterpart of the "outflow, or systolic ventriculoannular disproportion," introduced and elaborated in earlier publications (8, 10, 18, 19).
In conclusion, a novel functional imaging approach has been developed
for the investigation of blood flow patterns in the right ventricle of
specific experimental animals (and human subjects) using information
derived from RT3D images. The method is independent of imaging modality
used, e.g., ultrasound, magnetic resonance, and digital
ventriculography. Boundary conditions are directly derived from dynamic
endocardial geometry, which allows for the first time an
animal-specific ventricular blood flow simulation under normal or
abnormal wall motion patterns. It is hoped that the method of combining
dynamic modeling of the cardiac chambers throughout the cardiac cycle
in combination with computational fluid dynamics will become
increasingly valuable for understanding the detailed nature of 3-D flow
patterns in the heart. It is likely that improvements in RT3D imaging
will allow this type of analysis for all cardiac chambers and in
diverse physiological and disease states.
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APPENDIX |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Under steady-state conditions, RV chamber geometry was interpolated between successive RT3D images as the weighted average of the changing endocardial border outline obtained using RT3D. It was sufficient to obtain the set of Fourier coefficients representing the geometry. For an arbitrary instant t* within a cardiac cycle, a given Fourier coefficient (f*) was calculated using the following algorithm.
Obtain the time intervals between t* and
t1,
t2, ... ,tn, where
t1,
t2, ... ,tn are RT3D
frame sampling instants within a steady-state cardiac cycle of length
T. Let the time intervals be t1,
t2, ... ,tn,
where
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ACKNOWLEDGEMENTS |
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This work was supported in part by National Heart, Lung, and Blood Institute Grant R01 HL-50446 (to A. Pasipoularides), the Duke/National Science Foundation Engineering Research Center for Emerging Cardiovascular Technologies, and the North Carolina Super Computing Center/Cray Research (to A. Pasipoularides and M. Shu).
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FOOTNOTES |
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Address for reprint requests and other correspondence: D. D. Glower, Division of Cardiac and Thoracic Surgery, PO Box 3851 Med. Ctr., Duke Univ., Durham, NC 27710.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
First published September 12, 2002;10.1152/ajpheart.00577.2002
Received 11 July 2002; accepted in final form 30 August 2002.
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REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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10 ms from onset) of the E-wave. With NWM there is
blood flow toward the free wall in the septal region, whereas with PSM
there is very little blood flow in that region. Note the different
velocity profiles at the tricuspid orifice, and the abrupt transition
(deceleration) from red-yellow-green to black in the dilated chamber
(PSM) compared with the more gradual transition through blue hues in
the normal.