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Time-varying effective mitral valve area: prediction and validation using cardiac MRI and Doppler echocardiography in normal subjects

Cardiovascular ¹Biophysics and ²Magnetic Resonance Laboratories, Cardiovascular Division, School of Medicine, Washington University in St. Louis, Missouri 63110

Submitted 17 March 2004 ; accepted in final form 13 May 2004

	ABSTRACT

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Precise knowledge of the volume and rate of early rapid left ventricular (LV) filling elucidates kinematic aspects of diastolic physiology. The Doppler E wave velocity-time integral (VTI) is conventionally used as the estimate of early, rapid-filling volume; however, this implicitly requires the assumption of a constant effective mitral valve area (EMVA). We sought to evaluate whether the EMVA is truly constant throughout early, rapid filling in 10 normal subjects using cardiac magnetic resonance imaging (MRI) and contemporaneous Doppler echocardiography, which were synchronized via ECG. LV volume measurements as a function of time were obtained via MRI, and transmitral flow values were measured via Doppler echocardiography. The synchronized data were used to predict EMVA as a function of time during early diastole. Validation involved EMVA determination using 1) the short-axis echocardiographic images near the mitral valve leaflet tips, 2) the distance between leaflet tips in the echocardiographic parasternal long-axis view, and 3) the distance between leaflet tips from the MRI LV outflow tract view. Predicted EMVA values varied substantially during early rapid filling, and observed EMVA values agreed well with predictions. We conclude that the EMVA is not constant, and its variation causes LV volume to increase faster than is reflected by the VTI. These results reveal the mechanism of early rapid volumetric increase and directly affect the significance and physiological interpretation of the VTI of the Doppler E wave. Application to subjects in selected pathophysiological subsets is in progress.

diastolic function; magnetic resonance imaging; E wave; transmitral flow

(1)

where LV(t) refers to the LV volume as a function of time, LV_m is the LV volume before the mitral valve opens, EMVA is the (constant) effective mitral valve area, and E(t) is the echocardiographic Doppler E wave velocity as a function of time. However, to determine LV volume as a function of time during the filling process, this approach is accurate if and only if the EMVA remains constant throughout filling (15, 16).

We previously evaluated left heart function in healthy, young adult volunteers in a study that combined Doppler echocardiographic flow data with cardiac magnetic resonance imaging (MRI) volume data, which were synchronized via ECG (4). This study noted that contrary to what is expected from Eq. 1, by the time the peak velocity of transmitral early rapid filling (Doppler E-wave maximum) is attained, the majority of the MRI-determined, early filling volume has already entered the left ventricle (Fig. 1)! Consequently, the maximum rate of volume increase identified via MRI precedes the peak of the E wave obtained via echocardiography, which is also in apparent conflict with Eq. 1. The discord between these observations and Eq. 1 may be resolved if the EMVA is permitted to vary as a function of time. Indeed, the apparent discrepancy between Eq. 1 and the findings in Fig. 1 motivates the present study. Accordingly, we evaluated EMVA as a function of time during diastolic early rapid filling in young, healthy adults using a combined MRI-echocardiographic approach. We sought improved characterization of the time dependence of EMVA during diastole to gain additional insight into the physiology of LV diastolic function and into the interpretation of the commonly used methods of measuring LV volume change during early rapid filling.

View larger version (28K): [in this window] [in a new window]   Fig. 1. Example of left ventricular (LV) volume data (from MRI; A) with transmitral flow data (from Doppler echocardiography; B) for a representative normal subject, synchronized by the ECG QRS complex (solid gray line). Note how the majority of the E-wave filling volume enters the left ventricle by the peak of the E wave (solid black line). Also shown are the onset of the transmitral Doppler E wave (dashed gray line), and E wave end (dashed black line).

	METHODS

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The initial four-chamber view was used to plan a short-axis cine-stack protocol of between 18 and 20 slices (9 mm thick with zero gap) that spanned the apex of the ventricles through the superior-posterior wall of the left atrium. Image slices were obtained during 10-s breathholds per slice, and each cine loop was divided into 20 cardiac phases triggered from the ECG R wave, which covered the entire cardiac cycle. For the short-axis stack image acquisition, the repetition time, echo time, and flip angle were 4.0 ms, 1.47 ms, and 50°, respectively. In-plane resolution of 1.41 mm was obtained with a field of view of 36 cm and a matrix size of 192 x 256 that was interpolated to 256 x 256.

Upon completion of the exam, the data were archived to 4.1-GB magnetooptical disks. All image analysis was performed off-line on a remote personal computer using eFilm 1.5.3 (eFilm Medical; Toronto, Ontario, Canada), Paint Shop Pro 7 (Jasc Software; Minnetonka, MN), and Scion Image (Scion; Frederick, MD) software.

In all subjects, the LV endocardial contours were manually traced in each slice at each phase of the three-dimensional dataset (Fig. 2), and the corresponding segmental volumes were determined. For each phase, the segmental volumes of the traces were summed via Simpson's rule and evaluated over the cardiac cycle. Intraobserver variability of MRI segmental volume measurements using this method was previously reported as <4% (4).

View larger version (117K): [in this window] [in a new window]   Fig. 2. Typical balanced fast field echo MRI image (short-axis view) shows endocardial trace of the LV at end diastole.

As previously reported (4), once the chamber volumes were determined from the MRI images, chamber volume data (from MRI) and flow (from echocardiography) were synchronized using the ECG QRS complex as a fiducial marker (as shown in Fig. 1). Care was taken to pick representative images of the transmitral flow profile at heart rates as similar as possible to those obtained during the MRI scan.

EMVA prediction. If the EMVA is permitted to vary as a function of time, Eq. 1 can be rewritten more precisely as

(2)

where EMVA(t) is the (variable) EMVA as a function of time. Rearranging Eq. 2 and solving for EMVA(t) yields

(3)

In this study, the d[LV(t)/dt] term is derived from the MRI volumetric data, and the E(t) term is calculated from the echocardiographic transmitral flow data.

To differentiate the LV volume curve obtained via MRI, a third-order spline was fit through the LV volume data points that occurred during the Doppler E wave using MatLab 5.3 (MathWorks; Natick, MA). The derivative of the LV volume spline fit was numerically calculated, and the values of the derivative at the same discrete points as the MRI LV volume points were used to calculate the EMVA in Eq. 3.

In each subject, three transmitral Doppler E waves were selected and fit using model-based image processing, a previously validated technique (9, 14) written in LabView 6 (National Instruments; Austin, TX), to yield a numerical representation of the continuous contour of each E wave (Fig. 3). These fits were averaged for each subject (10), and the average fit was used to determine the value of E(t) at the desired time points used in Eq. 3.

View larger version (77K): [in this window] [in a new window]   Fig. 3. Representative transmitral Doppler E wave with superimposed fit from model-based image processing. See text for details.

View larger version (53K): [in this window] [in a new window]   Fig. 4. Determination of effective mitral valve area (EMVA, dark lines) via measuring the area from echocardiography in a basal short-axis view at the level of the mitral leaflet tips (A), measuring the diameter from the echocardiographic parasternal long-axis view (B), and measuring the diameter from the MRI LV outflow tract view (C).

	RESULTS

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View larger version (11K): [in this window] [in a new window]   Fig. 5. LV volume curve (MRI measured) for a normal subject during diastole () superimposed with a predicted LV volume curve (gray line) using the velocity-time integral of the E wave and assuming a constant EMVA. Note how the predicted LV volume curve systematically underestimates the actual LV volume at every data point. Values on the time axis refer to the time (in ms) from the peak of the ECG QRS complex.

View larger version (33K): [in this window] [in a new window]   Fig. 6. Alternative imaging views of measured EMVA vs. predicted EMVA as a function of time (A) temporally linked with a transmitral flow image for one subject (B). Measured EMVA from the basal short-axis echocardiographic images near the mitral valve (), EMVA calculated from the distance between the mitral leaflet tips from the echocardiographic parasternal long-axis view (), and EMVA calculated from the distance between the mitral leaflet tips from the MRI LV outflow tract view () are shown. Predicted EMVA (based on Eq. 3) is also indicated (, dashed line). Note the similarity of predicted and measured shapes, which consist of an early, phasic, rapid increase and subsequent decrease in EMVA. Peak of the ECG QRS complex (gray vertical line) and beginning and end of the Doppler E wave (two black vertical lines) are also shown.

Interestingly, the EMVA derived from Eq. 3 predicts in all subjects that the maximum EMVA is obtained before the peak of the Doppler E wave. To evaluate this phenomenon more carefully and to remove the potential of systematic error due to differences between imaging modalities, we examined the same events using a single imaging modality. Accordingly, transmitral E waves and Doppler M-mode images of the mitral valve were synchronized relative to the R wave. In 9 of 10 subjects, relative to the R wave, the peak displacement of the anterior mitral leaflet occurred before the peak velocity of the E wave (Fig. 7). On average, the E wave reached its peak 20 ± 16 ms after the maximum displacement of the anterior mitral valve leaflet.

View larger version (56K): [in this window] [in a new window]   Fig. 7. ECG synchronized (gray vertical line) transmitral Doppler E wave (A) with Doppler M-mode (B) of the mitral valve leaflets for a representative subject. Note that the maximum displacement of the anterior leaflet (dashed black vertical line) occurs before the peak of the E wave (solid black vertical line).

	DISCUSSION

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View larger version (91K): [in this window] [in a new window]   Fig. 8. MRI short-axis velocity phase-encoded image of transmitral flow during early diastole in one of the subjects in this study. Note that the area of the flow jet in a plane at the leaflet tips is measured to be 12.1 cm2 in this example. MV, mitral valve; TV, tricuspid valve.

In previous studies modeling mitral valve mechanics, researchers postulated that at a certain transmitral threshold velocity, the valve attains its maximum effective cross-sectional area and remains at that area until transmitral flow decreases below this threshold velocity (1). Our results illustrate that the EMVA changes throughout early rapid filling. However, due to the short time intervals involved in the duration of the E wave coupled with the finite (30–50 ms) temporal resolution of the MRI method, it may be difficult to precisely determine any transmitral threshold velocity for maximum valve opening that may exist using our methods.

The existence of a time-varying EMVA is physiologically attractive and potentially significant because of its functional implications. In terms of the physiology of diastolic function and LV filling, our results provide insight into the robustness of the design of the human heart. In functional terms, it is desirable for the left ventricle to fill as rapidly as possible. One way to facilitate such rapid filling would be to allow the largest opening for the passage of blood (the EMVA) to occur essentially at the same time as the development of the maximum atrioventricular pressure gradient. Once the peak of the E wave is reached, the transmitral pressure gradient driving the forward flow has diminished to zero (6); thus the driving force for LV filling has ended. The remainder of the E wave, i.e., the deceleration portion, is generated by a reversal of the atrioventricular pressure gradient and reflects a combination of inertial and chamber stiffness effects (16).

Additionally, a commonly used clinical index for diastolic function is the Doppler E wave deceleration time (DT). Our results suggest that the volume of blood that enters the left ventricle during the E wave DT is less than half of the total E wave filling volume, although the deceleration portion of the E wave usually accounts for more than half of the total E wave duration (in healthy subjects). This, in conjunction with the reversal of the transmitral pressure gradient at the peak of the E wave, underscores that LV filling during the E wave DT is dominated by inertial forces and has less impact on the total E wave filling volume than might be indicated by the E wave VTI, assuming a constant EMVA. Studies to evaluate the significance of these findings in the setting of abnormal transmitral filling patterns are presently in progress.

Limitations. Because the MRI scan and echocardiographic study were contemporaneous but not simultaneous, we were unable to assure the maintenance of an absolutely constant heart rate in our subjects. Because the MRI imaging involved frequent breathholds, the measured heart rate of some subjects was found to be different during the MRI scan than during the echocardiography study (from 60 to 80 beats/min). However, during such minor changes in heart rate, the change in duration of systole is minimal, and the change in duration of diastolic early rapid filling is similarly minimal because the change in the cardiac cycle (R-R interval) duration is primarily accounted for by change in the duration of diastasis, the interval between the Doppler E and A waves when no significant transmitral flow occurs. Additionally, we note that the timing of events during systole and early diastole was consistent between the echocardiographic measurements and the MRI measurements even when the heart rates of subjects varied somewhat between the two studies. However, we also note that the use of breathholds during the MRI exam and its absence during the echocardiographic exam may introduce some differences in the transmitral pressure gradients present during the two studies. Because all of the subjects were young, were in good physical condition, and performed short (10 s) breathholds, such differences in pressure gradients were likely minimal.

As stated above, the temporal resolution of the MRI scans ranged from 30–50 ms, which corresponds to a frame rate of 20–33 frames/s. Although faster frame rates are achievable using other MRI protocols, this rate was selected to balance the simultaneous needs of subject comfort, breathhold duration, scan duration, and spatial resolution. Accordingly, the average temporal resolution of the MRI scans (39 ms) closely mirrors the temporal resolution of the echocardiographic cine loops (33 ms). Furthermore, the data presented in Figs. 5 and 6A clearly show that multiple data points during early rapid filling were obtained via all methods, which consistently demonstrates how the EVMA varies throughout early rapid filling.

Because the MRI volumetric data were acquired using 9-mm-thick slices, there is the possibility of systematic error in the volumes reported in this study. However, the technique employed in this study is the present MRI research standard. Manual tracings of the chambers may also raise concern, but it has also been the standard approach for chamber volume determination. A recently developed automated edge detection method for volume measurement showed excellent agreement relative to the present gold standard, which consists of manually traced segmental volumes (27).

To calculate the derivative of the LV volume curve during early rapid filling, the LV volume data points were fit with a third-order spline to render the LV data more continuous. Limitations of curve fitting in this manner are obvious and could lead to some inappropriately large derivatives. To minimize these errors, care was taken to select data points for use in Eq. 3 that were not too close in time to the onset of the Doppler E wave (which, in conjunction with errors arising from calculating MRI volumes using 9-mm-thick slices as well as limitations in the temporal resolution of MRI data in the setting of averaged, continuous E wave data, may yield a predicted EMVA larger than the cross-sectional LV area). However, in some cases, the initial data point for the predicted EMVA was still exorbitantly large. We note that even in these cases, subsequent predicted EMVA data points closely mirrored the calculated EMVA values.

We also note that the data indicate that the MRI-determined LV volume begins to increase before the beginning of the Doppler E wave (see Fig. 1). The shape of the LV volume curve is similar in all subjects in this study and is consistent with other published MRI-derived volume curves (4, 27), all of which indicate a single data point of minimum LV volume even in scans with sufficient temporal resolution to image multiple time points during isovolumic relaxation. This slight rise in volume before mitral valve opening and the onset of the E wave is likely an artifact of the MRI-volume measurement method. The rotational/torsional and slight geometric changes in the shape of the left ventricle during isovolumic relaxation may lead to the appearance of mildly increasing volume in the imaging plane employed in this study. The slice thickness of 9 mm may also mask small longitudinal motions of the mitral valve that serve to conserve LV volume during diastolic isovolumic wall relaxation. Consistently, however, the data show that at the onset of the Doppler E wave, the rate of LV filling (measured via MRI) increases dramatically, which thereby reinforces our confidence in the accuracy of the temporally aligned datasets (4).

We note that the calculated EMVAs via the echocardiographic PSL and MRI LVOT methods agreed with one another better than the EMVA calculated via the echocardiographic short-axis method. This is not surprising, because the PSL and LVOT views are essentially identical. The similar results obtained from these views further underscore the reliability of using both echocardiographic and MRI data to quantitate cardiac events. However, the echocardiographic short-axis-view data may have diverged from the other data, because the imaging plane may not have been precisely at the level of the mitral leaflet tips. Furthermore, the mitral valve annulus (to which the leaflets are attached) exhibits longitudinal motion during diastole as the mitral valve plane moves away from the apex during LV filling (which generates the Doppler tissue imaging-based E' wave). This motion may further exacerbate any misalignment of the imaging plane. Because the echocardiographic PSL and MRI LVOT are both long-axis views, the tips of the mitral leaflets can be visualized at all times, which eliminates the misalignment and through-plane motion issues inherent in short-axis views.

A full MRI mitral valve flow study protocol using velocity phase encoding was not performed on all of the subjects. Our goal was to precisely determine EMVA as a function of time, and although the phase-encoded velocity images can illustrate how large the cross-sectional area of the jet of mitral flow may be (see Fig. 8), it is difficult or impossible to measure anatomical features (such as mitral valve leaflet tips) with the precision that we required using this method. Similarly, EMVA was not calculated using the Doppler M-mode of the mitral valve, because in most images, the posterior leaflet was insufficiently well seen to make reliable measurements. Additionally, there was the short-axis misalignment concern as previously discussed. Nonetheless, due to the superior temporal and spatial resolution of M-mode Doppler, it was used to compare the timing of maximal anterior leaflet displacement with the peak Doppler E wave velocity. It may appear possible that the measured difference in time between the peak displacement of the anterior mitral leaflet and the peak of the E wave (see Fig. 7) is an artifact of different processing times between the two imaging modalities of the echocardiography machine. However, we note that the onset of the E wave (via the transmitral view) is virtually simultaneous with the opening of the valve (via M-mode) in all subjects (data not shown), which reinforces our confidence that the measurement reflects real physiology and is not a result of a systematic error due to either imaging modality or hardware-related image-processing times.

It was not the intention of this study to evaluate flow across the mitral valve in the sense of fluid dynamics, because such studies have been previously reported (2, 5, 19, 21, 24). It was our intention to predict and measure, using standard clinical imaging modalities, the size of the EMVA during early rapid filling. We also want to underscore that the majority of the early rapid filling volume enters the left ventricle during the initial component (about the first 80–100 ms) of early rapid filling. This is made possible by the generation of the largest EMVA during this interval of transmitral flow.

We conclude that during early rapid LV filling, the EMVA is not constant but rather is time dependent and often reaches areas larger than those previously reported in anatomical or pathological studies. The valve area is largest early during transmitral flow and decreases as flow diminishes. This facilitates rapid filling of the left ventricle in the shortest amount of time and leads to >50% of the E wave volume entering the left ventricle by the peak of the E wave. Data also indicate that the maximum EMVA occurs before the peak of the E wave, which likely mirrors the magnitude of the transmitral pressure gradient. These results highlight the limitations in calculating LV filling volume as a function of time using only the VTI of the Doppler E wave and an assumed constant EMVA. Application of these methods to hearts with abnormal transmitral filling patterns is in progress.

	GRANTS

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This work is supported in part by the Heartland Affiliate of the American Heart Association (Dallas, TX), the Whitaker Foundation (Roslyn, VA), the National Institutes of Health (Grants HL-54179 and HL-04023; Bethesda, MD), the Alan A. and Edith L. Wolff Charitable Trust (St. Louis, MO), and Philips Medical Systems (Best, The Netherlands).

	ACKNOWLEDGMENTS

 
The authors thank Shelton Caruthers for technical direction, Mary Watkins and Todd Williams for expert MRI image acquisition, Peggy Brown for expert echocardiographic image acquisition, and members of the Cardiovascular Biophysics Laboratory for helpful comments regarding manuscript preparation.

	FOOTNOTES

 

Address for reprint requests and other correspondence: S. J. Kovács, Cardiovascular Biophysics Laboratory, Washington Univ. Medical Center, Box 8086, 660 S. Euclid Ave., St. Louis, MO 63110 (E-mail: sjk{at}wuphys.wustl.edu)

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.

	REFERENCES

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1. Baccani B, Domenichini F, and Pedrizzetti G. Model and influence of mitral valve opening during the left ventricular filling. J Biomech 36: 355–361, 2003.[CrossRef][Web of Science][Medline]
2. Bakalyar DM, Hauser AM, and Timmis GC. A theoretical description of blood flow through the mitral orifice. J Biomech Eng 111: 141–146, 1989.[Medline]
3. Bowman AW and Kovács SJ. Assessment and consequences of the constant-volume attribute of the four-chambered heart. Am J Physiol Heart Circ Physiol 285: H2027–H2033, 2003.[Abstract/Free Full Text]
4. Bowman AW and Kovács SJ. Left atrial conduit volume is generated by deviation from the constant-volume state of the left heart: a combined MRI-echocardiographic study. Am J Physiol Heart Circ Physiol 286: H2416–H2424, 2004; 10.1152/ajpheart.00969.2003.[Abstract/Free Full Text]
5. Cooke J, Hertzberg J, Boardman M, and Shandas R. Characterizing vortex ring behavior during ventricular filling with Doppler echocardiography: an in vitro study. Ann Biomed Eng 32: 245–256, 2004.[CrossRef][Web of Science][Medline]
6. Courtois M, Kovács SJ Jr, and Ludbrook PA. Transmitral pressure-flow velocity relation. Importance of regional pressure gradients in the left ventricle during diastole. Circulation 78: 661–671, 1988.[Abstract/Free Full Text]
7. Gorlin R and Gorlin SG. Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts. I. Am Heart J 41: 1–29, 1951.
8. Gorlin R and Haynes FW. Physiologic method for calculation of cross-sectional area of the mitral valve (Abstract). J Clin Invest 29: 817, 1950.[Web of Science][Medline]
9. Hall AF and Kovács SJ. Automated method for characterization of diastolic transmitral Doppler velocity contours: early rapid filling. Ultrasound Med Biol 20: 107–116, 1994.[CrossRef][Web of Science][Medline]
10. Hall AF, Nudelman SP, and Kovács SJ. Beat averaging alternatives for transmitral Doppler flow velocity images. Ultrasound Med Biol 24: 971–979, 1998.[CrossRef][Web of Science][Medline]
11. Hatle L and Angelsen B. Doppler Ultrasound in Cardiology: Physical Principles and Clinical Applications. Philadelphia, PA: Lea and Febiger, 1982, p. 83.
12. Hatle L, Angelsen B, and Tromsdal A. Noninvasive assessment of atrioventricular pressure half-time by Doppler ultrasound. Circulation 60: 1096–1104, 1979.[Abstract/Free Full Text]
13. Hatle L, Brubakk A, Tromsdal A, and Angelsen B. Noninvasive assessment of pressure drop in mitral stenosis by Doppler ultrasound. Br Heart J 40: 131–140, 1978.[Abstract/Free Full Text]
14. Kovács SJ Jr, Barzilai B, and Pérez JE. Evaluation of diastolic function with Doppler echocardiography: the PDF formalism. Am J Physiol Heart Circ Physiol 252: H178–H187, 1987.[Abstract/Free Full Text]
15. Kovács SJ, Meisner JS, and Yellin EL. Modeling of diastole. Cardiol Clin 18: 459–487, 2000.[CrossRef][Medline]
16. Lisauskas JB, Singh J, Bowman AW, and Kovács SJ. Chamber properties from transmitral flow: prediction of average and passive left ventricular diastolic stiffness. J Appl Physiol 91: 154–162, 2001.[Abstract/Free Full Text]
17. Little WC, Ohno M, Kitzman DW, Thomas JD, and Cheng CP. Determination of left ventricular chamber stiffness from the time for deceleration of early left ventricular filling. Circulation 92: 1933–1939, 1995.[Abstract/Free Full Text]
18. Marino P, Destro G, Barbieri E, and Zardini P. Early left ventricular filling: an approach to its multifactorial nature using a combined hemodynamic-Doppler technique. Am Heart J 122: 132–141, 1991.[CrossRef][Web of Science][Medline]
19. McQueen DM, Peskin CS, and Yellin EL. Fluid dynamics of the mitral valve: physiological aspects of a mathematical model. Am J Physiol Heart Circ Physiol 242: H1095–H1110, 1982.[Abstract/Free Full Text]
20. Ormiston JA, Shah PM, Tei C, and Wong M. Size and motion of the mitral valve annulus in man. I. A two-dimensional echocardiographic method and findings in normal subjects. Circulation 64: 113–120, 1981.[Abstract/Free Full Text]
21. Peskin CS and McQueen DM. Fluid dynamics of the heart and its valves. In: Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology, edited by Othmer HG, Adler FR, Lewis MA, and Dallon JC. Englewood Cliffs, NJ: Prentice-Hall, 1996, p. 309–337.
22. Schiller NB, Shah PM, Crawford M, DeMaria A, Devereux R, Feigenbaum H, Gutgesell H, Reichek N, Sahn D, Schnittger I, Silberman NH, and Tajik AJ. Recommendations for quantitation of the left ventricle by two-dimensional echocardiography. American Society of Echocardiography Committee on Standards, Subcommittee on Quantitation of Two-Dimensional Echocardiograms. J Am Soc Echocardiogr 2: 358–367, 1989.[Medline]
23. Sondergaard L, Stahlberg F, and Thomsen C. Magnetic resonance imaging of valvular heart disease. J Magn Reson Imaging 10: 627–638, 1999.[CrossRef][Web of Science][Medline]
24. Thomas JD and Weyman AE. Fluid dynamics model of mitral valve flow: description with in vitro validation. J Am Coll Cardiol 13: 221–233, 1989.[Abstract]
25. Tsakiris AG, Gordon DA, Mathieu Y, and Lipton I. Time-motion of both mitral leaflets in early diastole. In: The Mitral Valve: A Pluridisciplinary Approach, edited by Kalmanson MD. Acton, MA: Publishing Sciences Group, 1976, p. 27–32.
26. Tsakiris AG, Gordon DA, Padiyar R, and Frechette D. Relation of mitral valve opening and closure to left atrial and ventricular pressures in the intact dog. Am J Physiol Heart Circ Physiol 234: H146–H151, 1978.[Abstract/Free Full Text]
27. Tseng WYI, Liao TY, and Wang JL. Normal systolic and diastolic functions of the left ventricle and left atrium by cine magnetic resonance imaging. J Cardiovasc Magn Reson 4: 443–457, 2002.[CrossRef][Web of Science][Medline]
28. Weyman AE. Principles and Practice of Echocardiography. Philadelphia, PA: Lea and Febiger, 1994, p. 99–103, 109–110, 288–289.
29. Wu CC, Skalak TC, Schwenk TR, Mahler CM, Anne A, Finnerty PW, Haber HL, Weikle RM II, and Feldman MD. Accuracy of the conductance catheter for measurement of ventricular volumes seen clinically: effects of electric field homogeneity and parallel conductance. IEEE Trans Biomed Eng 44: 266–277, 1997.[CrossRef][Web of Science][Medline]
30. Yang SS, Bentivoglio LG, Maranhao V, and Goldberg H. From Cardiac Catheterization Data to Hemodynamic Parameters. Philadelphia, PA: F. A. Davis, 1988, p. 128.

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