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Manuscript received August 19, 1991; revised manuscript received April 9, 1992, accepted April 22, 1992. -: Michael R. Zde, MD, Cardiology Divisionl hpaNnent of Medicine, Medical University of South Carolina, 171 Ashley Avenue, Charleston, South Carolina 29425. praventricular tachycardia caused a dilated cardiomyopathy with a 55% decrease in left ventricular ejection fraction. Res&. The left ventricular epicardial long -&short -axis dimension ratio remained constant throughout the cardiac cycle in each animal group. End -diastolic and end -systolic volumes calcu - lated with the simplified echocardiographic method correlated closely with angiographidy measured volumes; for end -diastolic volume, echocardiographic end -diastolic volume = 1 .O (angio- graphic end -diastolic volume) -1.8 ml, r = 0.96; for end -systolic volume, echocardiographic end -systolic volume = 0.98 (angb graphic end -systolic volume) -0.7 ml, r = 0.95. Conclusions. Thus the lefi ventricular epicardial long-d short-&is dimension ratio was constant throughout the cardiac cycle in a variety of animal species and age groups and in the presence of cardiac diseases that significantly altered left ventric - ular geometry and function. The simplified echocardiographic method examined provided an accurate determination of left ventricular volumes. (J Am Coll Cmdiol1992;20.986-93) that occur during the development and treatment of cardiac disease (1-5). Therefore, both the long (major) -axis dimen - sion and the short (minor) -axis dimension must be measured.

Although short -axis dimension is easily measured with echo - cardiographic techniques, these techniques have important limitations in the ability to measure changes in the long -axis dimension throughout the cardiac cycle. A variety of two - dimensional and M -mode echocardiographic methods have been developed to overcome these limitations; however, their complexity (multiple views, detailed mathematics or computer -based digitizing) has limited their clinical and research application (6-11). In the current study, we pro - pose a simplified echocardiographic method for determining volume that will minimize these limitations.

The method we propose is based on recent observations (12 -22) that, in contrast to endocardial measurements; the extent of shortening in the epicardial long -axis dimension is similar to that in the epicardial short -axis dimension. This similarity in the percent of epicardial axis shortening sug - gested the possibility that the ratio of the epicardial long -axis dimension to the epicardial short -axis dimension might be ' 01992 by tbe American College of Cardiology 0735-1097192135.00 JACC Vol. 20, No. 4 October 1992:986-93 constant throughout the cardiac cycle. If this were true, left ventricular endocardial long -axis dimension (and then vol - ume) at each point in the cardiac cycle could be calculated (rather than measured) by using echocardiographically mea - sured instantaneous left ventricular endocardial short -axis dimension and wall thickness and only a single measurement of left ventricular endocardial long -axis dimension made at any point in the cardiac cycle. Therefore, the purposes of this study were to test three hypotheses: 1) the left ventric - ular epicardial long -axislshort -axis dimension ratio is con - stant throughout the cardiac cycle; 2) this ratio remains constant throughout the cardiac cycle even in the presence of cardiac diseases that significantly alter left ventricular geometry and function; and 3) left ventricular volume at a given point in the cardiac cycle can be calculated from the instantaneous endocardial short -axis dimension and wall thickness and a constant that is derived at only one point in the cardiac cycle from the left ventricular epicardial long - axis/short-axis dimension ratio. Methods The proposed model was predicated on two assumptions: 1) the epicardial long -axislshort -axis dimension ratio is con - stant throughout the cardiac cycle; and 2) the ratio remains constant throughout the cardiac cycle in different animal species and different age groups and in the presence or absence of cardiac disease. These assumptions were vali - dated by using angiographically determined enddiastolic and end -systolic endocardial short -axis dimension, endocar - dial long -axis dimension, wall thickness and volume from eight groups of animals: a) 13 normal adult dogs; b) 8 normal puppies; c) 9 normal pigs; d) 13 dogs with acute mitral regurgitation; e) 12 dogs with chronic mitral regurgitation; f) 7 dogs that had undergone mitral valve replacement; g) 12 dogs with aortic stenosis; h) 6 pigs that had undergone rapid atrial pacing.

Comparisons were then made in six animals each in groups a, d, e and f between left ventricular volumes calculated from echocardiographic data and left ventricular volumes measured angiographically . Some angiographically measured volumetric data from these animals have been incorporated in previous studies (23 -26); however, the angiographic dimension, length and thickness data presented in this study have not been previously published. Proposed model. Left ventricular volume, assuming the geometry of a prolate ellipsoid, is calculated from the general formula:

where V = left ventricular volume, Dendo = left ventricular endocardial short (minor -)-axis dimension and Len&, = left ventricular endocardial long (major -)-axis dimension. In the proposed model, it is assumed that Dendo can be measured ZlLE ET AL. 987 ECHOCARDIOGRAPHICALLY DETERMINED VOLUME Lepi = Lend0 + h' h' = h(40%) Depi = Dendo + 2h Lend0 +h' Dendo+ 2h z= Figure 1. Prolate ellipsoid geometry used to model the left ventricle.

Epicardial (epi) and endocardial (endo) measurements of long -axis (L) and short -axis (D) dimensions and apical (h') and posterior wall thickness (h) were used to calculate the epicardial long -axis dimen - sion to short -axis dimension ratio (Z). throughout the cardiac cycle but Lcd0 can or will be measured only at one point in the cardiac cycle (for example, at end -diastole); V and Lcndo at any other point in the cardiac cycle will be calculated by using the following proposed model. Step 1. Let Z be the left ventricular epicardial long -axis (Lepi)/short-axis (Depi) dimension ratio.

As depicted in Figure 1, Lepi = left ventricular endocardial long -axis dimension (Len&,) plus the apical wall thickness (h'); Depi = left ventricular endocardial short -axis dimension (Dendo) plus 2 X posterior wall thickness (h). Thus endocardial measurements of long -axis dimension and short -axis dimension are used to calculate epicardial measurements of these dimensions and their ratio. Step 2. Apical wall thickness is normally less than ante - rior, posterior or septal wall thickness; however, it may be difficult to quantitate accurately and may vary among spe - cies and in diseases. Therefore, for the purpose of this study, we will assume that h' is equal to a percent (40%) of the posterior wall thickness. Forty percent was chosen because, as shown by the data in Table 1, Z was constant from end -diastole to end -systole when h' was assumed to be 20%, 40% and 80% of posterior wall thickness. In addition, previous studies (27,28) suggest that 40% may be a reason - able assumption; nonetheless, it must be acknowledged that it was made arbitrarily.

Step 3. The constant Z can be used to calculate Lcndo and left ventricular volume at a given point in the cardiac cycle ZILE ET AL. ECHOCARDIOCRAPHICALLY DETERMINED VOLUME 988 JACC Vol. 20, No. 4 October 1992:986-93 Table 1. Angiographic Left Ventricular Epicardial Long -Axis Dimension to Short -Axis Dimension Ratio End -Dias tole End -Systole 220 z, z, z, z, z, Nod adult dogs 1.2 f 0.03 1.2 f 0.03 1.2 ?I 0.03 1.2 f 0.03 1.2 f 0.03 1.3 f 0.03 Normal puppies 1.3 t 0.05 1.3 2 0.05 1.4 t 0.05: 1.2 f 0.08 1.2 f 0.08 1.3 2 0.07 Normal pigs 1.2 t 0.03 1.3 d 0.03 1.4 t 0.04* 1.2 f 0.03 1.3 t 0.03 1.5 f 0.03 Dogs with AS 1.2 t 0.03 1.2 t 0.03 1.3 f 0.03 1.2 f 0.03 1.2 f 0.03 1.3 f 0.03 Dogs with acute MR 1.2 f 0.02 1.2 f 0.02 1.2 f 0.02 1.2 f 0.03 1.2 f 0.03 1.3 t 0.03 Dogs with MVR 1.3 f 0.05 1.3 f 0.05 1.4 f 0.05' 1.3 2 0.05 1.3 t 0.05 1.4 f 0.05 Pigs with SVT 1.2 f 0.06 1.3 f 0.06 1.4 f: 0.06' 1.2 f 0.06 1.3 t 0.06 1.4 2 0.06 *p < 0.05 versus normal adult dogs. Data arc expressed as mean value f SEM. AS = aortic stenosis; MR = mitral regurgitation; MVR = mitral valve replacement; SVT = supraventricular tachycardia; Z = left ventricular epicardial long -axis to short -axis ratio; &, Z,, Z, = Z calculated assuming the left ventricular apical wall thickness (h') is 20%, 4@% or 80%, respectively, of the posterior wall thickness (h). 1.1 t 0.05' Dogs with chronic MR 1.0 f 0.02. 1.1 f 0.02 1.1 f 0.02 1.0 f 0.04* 1.1 t 0.04 by using instantaneous Dendo and h. For example, Z is calculated at end -diastole by using measurements of end- diastolic Dendo, Lendo and h in equation 3. To calculate end -systolic endocardial long -axis dimension (Lendo*): Led* + (0.4)h' Dendo* + ' Z= [41 where Dendo* = end -systolic left ventricular endocardial short -axis dimension and h* = end -systolic posterior wall thickness. Solving equation 4 for Lendo*: &* = Z De&* t h*(2Z - 0.4). PI Because Dendo* and h* are measured variables and Z can be calculated from equation 3, equation 5 permits the evalua - tion of Lendo and hence the evaluation of end -systolic volume by using equation 1. To test the hypothesis that Z is constant throughout the cardiac cycle, each of the eight groups of animals underwent left ventricular cineangiography. With use of the angiographic data (Table 2), 2 was calculated at end- diastole and at end -systole (Table 1). We reasoned that if there was a variation in 2 throughout the contraction, it would be most pronounced at the extremes of the cardiac cycle (end -systole and end -diastole). However, to prove that Z was constant throughout the cardiac cycle, frame by frame analysis of angiographic volumes was performed beginning at end -diastole and ending at end -systole in seven normal adult dogs and seven dogs with chronic mitral regurgitation. In addition to end -diastole and end -systole, 2 was calculated at 25%, 50% and 75% of the way through systole (that is, the period from end -diastole to end -systole) (Table 3). To test the accuracy of the proposed echocardiographic method, echocardiographically calculated left ventricular end -diastolic and end -systolic volumes were compared with angiographically measured left ventricular volumes (Table 3). The proposed model was compared with volume calcu - lated echocardiographically by the cubed rule, that is, Vol - ume = (minor [short -]-axis dimen~ion)~. Four groups of animals (normal adult dogs, dogs with acute mitral regurgi - tation, dogs with chronic mitral regurgitation and dogs that had undergone mitral valve replacement) underwent both left ventricular cineangiography and left ventricular M -mode and two -dimensional echocardiography . The methods used to create the animal models of cardiac disease and the methods used to perform angiography and echocardiography have been previously described in detail (23-26,29). A brief summary of each follows. Lefl ventricular cineangiography (23). A 5F pigtail cath - eter was inserted into the left ventricle from the femoral Table 2. Angiographic Data at End -Diastole and End -Systole End -Diastole End -Systole D (cm) h (cm) L (cm) v (d) D (cm) h (cm) L (cm) v (mu Normal adult dogs 4.4 t 0.1 0.9 f 0.02 6.8 2 0.1 68 t 4 3.2 t 0.1 1.1 t 0.03 6.1 t 0.2 33 f 3 Dogs with As 4.1 f 0.2 1.0 f 0.04 6.8 2 0.2 59 f 5 2.5 f 0.1 1.4 f 0.05 6.0 f 0.2 20 f 3 Dogs with chronic ha 5.7 t 0.1 0.8 f 0.03 7.4 f 0.2 130 t 9 4.2 f 0.2 1.1 f 0.05 6.3 t 0.2 59 t 5 Pigs with SVT 4.7 2 0.3 0.5 c 0.01 7.5 2 0.3 8656 4.1 t 0.2 0.6 f 0.03 7.1 f 0.2 6854 Normal puppies 2.9 2 0.1 0.5 f 0.03 5.0 f 0.2 23 f 3 1.7 f 0.1 0.9 f 0.03 3.6 t 0.3 621 19 t 1 Nod pigs 3.6 f 0.1 0.8 f 0.02 6.2 f 0.1 41 t 2 2.5 f 0.1 1.1 t 0.05 Dogs with acute MR 4.7 t 0.1 0.8 f 0.02 7.2 f 0.2 82 t 5 3.0 t 0.1 1.2 f 0.03 6.1 f 0.2 29 f 2 Dogs with MVR 4.8 t 0.1 0.8 t 0.02 7.9 t 0.3 96 2 6 3.8 t 0.2 1.0 f 0.05 7.1 0.2 55 t 6 5.7 f 0.1 Data are expressed as mean value c SEM. D = left ventricular endocardial short -axis dimensions; L = left ventricular endocardial long -axis dimension; v = left ventricular volume; other abbreviations as in Table 1. JACC Vol. 20, No. 4 October 1992:986-93 ZILE ET AL. ECHOCARDIOGRAPHICALLY DETERMINED VOLUME 989 Table 3. Angiographic Left Ventricular Epicardial Long -Axis Dimension to Short -Axis Dimension Ratio Normal Adult Dogs Dogs With Chronic MR Enddiastole 1.2 f 0.03 25% 1.2 5 0.04 50% 1.2 -c 0.02 75% 1.2 2 0.03 End-s y stole 1.2 2 0.05 1.1 f 0.02 1.1 f 0.03 1.1 2 0.05 1.1 f 0.04 1.1 c 0.02 Data are expressed as mean value f SEM. MR = mitral regurgitation; 25%, 50%, 75% = percent of time period from end -diastole to end -systole. artery. A ventriculogram was performed in the 30" right anterior oblique position at 60 frame&, with nonionic radio - graphic contrast medium, injected at 10 mUs for 1.5 s. Volumes were calculated by the area -length method, assum - ing a prolate ellipsoid geometry: V = 0.85 Az/L,~, [61 where A = left ventricular area and Len&, = left ventricular endocardial long -axis dimension. Left ventricular endocar - dial short -axis dimension (Dendo) was calculated as Dd = 4AIrLk. VI It should be noted that $Dendo in equation 7 was substituted for area (A) in equation 6, equation 7 would be identical to equation 1. The accuracy of angiographically determined volumes in our laboratory has been documented in previous studies (23,25,26). Close agreement was found between angiographically determined stroke volume and thermodilu- tiondetermined stroke volume. In addition, a good correla - tion was found between angiographic left ventricular mass and left ventricular mass weighted at autopsy. Angiographic determination of mass depends on accurate assessment of left ventricular cavity and myocardial volumes. This corre - lation in angiographic stroke volume and mass with ther - modilution stroke volume and weighted mass served to validate the accuracy of the angiographically measured volume. Left ventricular echocardiography (29). Two -dimensional and M -mode echocardiographic studies (ATL Ultramark VI, 2.25 MHz and 3.5 MHz transducers) were performed from the right parasternal area. Echocardiographic data were measured with use of the American Society of Echocardiog - raphy criteria, including the leading edge convention. Echo- cardiographic tracings were interpreted by investigators unaware of the angiographic data. Care was taken to obtain a true short (minor-)-axis dimension with echocardiographic techniques. No animal had segmental coronary disease or segmental wall motion abnormalities; therefore all left ven - tricles were symmetric in shape. In each animal, a two - dimensional parasternal long -axis view was recorded with special care taken not to foreshorten the apex. M -mode echocardiographic recordings obtained from this two - dimensional view were perpendicular to the long (major -)-axis dimension and above the papillary muscles. Dimension measurements were made from the interventric - ular septum near the aorta to the posterior left ventricular free wall near the base. In addition, in each animal a two -dimensional parasternal short -axis view was recorded with special care to ensure that each view was round and symmetric. In this view, dimension measurements were made from the ventricular septum to the posterior left ventricular free wall with the cursor directed between the papillary muscles. In this study, short -axis dimension refers to the minor-axis dimension, and long -axis dimension refers to the major-axis dimension, and these dimensional mea - surements should be distinguished from the long - and short - axis echocardiographic views used to measure them. Aortic banding (24). Pressure overload left ventricular hypertrophy was induced by banding mongrel puppies at 8 to 10 weeks of age. A 0.5 -cm wide umbilical tape band was placed around the ascending aorta distal to the coronary arteries. As the animals grew, the fixed band produced gradually increasing left ventricular pressure overload. After 3 months of banding, the dogs developed a left Ventricular to aorta gradient of 95 k 35 mm Hg and a 60% increase in left ventricular mass compared with that in normal control dogs. Creation of mitral regurgitation (23). In adult mongrel dogs, a urologic stone -grasping forceps was advanced through a sheath to the mitral valve apparatus. The forceps was used to grasp chordae tendineae, whose forcible retrac - tion caused chordal rupture. Enough grasps were made to produce severe mitral regurgitation. The average regurgitant fraction was 64 k 4%. After 3 months (chronic mitral regurgitation), end -diastolic volume increased by 46% and . left ventricular mass increased by 36%. Mitral valve replacement (25). Three months after cre - ation of mitral regurgitation, dogs underwent mitral valve replacement with a 21-, 23- or 25-mm pericardial xenograft prosthesis (Ionescu-Shiley). The effect of mitral valve re - placement was documented 3 months postoperatively with simultaneous echocardiography and cardiac catheterization.

Mitral valve replacement resulted in the elimination of the mitral regurgitation and a decrease in left ventricular end- diastolic volume to normal. Supraventricular tachycardia (26,29). In adult pigs, a shielded electrode was sutured to the left atrium, attached to a modified programmable pacemaker (Spectrax, Medtronic, Inc.) and placed in a subcutaneous pocket. After recovery from this procedure, the pigs underwent pacing -induced supraventricular tachycardia (left atrial pacing at 240 beats/ min) for 3 weeks. Supraventricular tachycardia resulted in a dilated, hypocontractile left ventricle with no change in left ventricular mass. Left ventricular enddiastolic and end- systolic volume tripled, systolic ejection fraction decreased to 20% and the left ventriclehody weight ratio was un- changed. Data analysis. To prove the hypothesis that the constant Z does not change during the cardiac cycle, Z was calculated from angiographic data at end -diastole and end -systole in eight groups of animals. Statistical differences between Z at __ 990 ZILE ET AL.

ECHOCARDIOGRAF’HICALLY DETERMINED VOLUME JACC Vol. 20. No. 4 October 1992:986-93 Table 4. Angiographic Versus Echocardiographic Volume Echocardiographic Angiographic Proposed Model Cubed Rule EDV ESV EDV ESV EDV ESV Normal adult dogs n+4 3622 n 4 3.1 3 102 IO* 39 2 8* Dogs with MVR 9926 4525 9722 47 t 8 110 t 9* 40 f 7* Dogs with acute MR 8123 2424 8123 2224 97 f It* 19 2 8* Dogs with chronic MR 120 f 6 53 f 6 120 2 5 49 t 6 170 f 12’ 65 f IO* *p < 0.05 versus angiographic values. Data are expressed as mean value f SEM. Cubed rule = echocardio- graphic short -axis (dimension)’; EDV = end -diastolic volume; ESV = end -systolic volume; proposed model = method described under Methods; other abbreviations as in Table 1. end -diastole and Z at end -systole were determined by using a paired Student t test. Comparisons of Z among the eight groups of animals, using normal dogs (group a) as a control group, was performed by using an unpaired Student t test.

To validate the accuracy of calculating left ventricular volume with the proposed echocardiographic method, angio - graphically measured end -diastolic and end -systolic volumes were compared with echocardiographically calculated vol - umes in the same animals. Differences were determined with a paired Student t test. Differences were considered signs - cant ifp < 0.05. Data are presented as mean value ? SEM. AU animals received humane care in compliance with the “Principles of Laboratory Animal Care” formulated by the National Society for Medical Research and the Guide for the Care and Use of Laboratory Animals prepared by the National Academy of Sciences and published by the Na - tional Institutes of Health (NIH publication 85 -23, revised 1985). Results Left ventricular epicardial long-axk dimension to short - axis dimension ratio. Angiographic left ventricular volume, endocardial short -axis dimension, endocardial long -axis di - mension and wall thickness data at end -diastole and end- systole for all eight groups of animals are presented in Table 2. These data were used to calculate Z (ratio of left ventric - ular epicardial long -axis dimension to short -axis dimension) presented in Table 1. Values of Z determined at end -systole were closely comparable to Z values determined at end - diastole. There were no statistically significant differences between end -diastolic and end -systolic values for Z in any of the eight groups examined. In addition, data presented in Table 3 demonstrate that Z was constant at five points throughout the cardiac cycle in normal dogs and in dogs with chronic mitral regurgitation. Thus Z appeared to be constant throughout the cardiac cycle. In addition, Z values in the normal adult dogs were closely comparable to Z values in all of the other seven groups examined. Z appeared to be relatively constant throughout species and age groups and in .the presence or absence of cardiac diseases that significantly alter left ventricular geometry and function. . Echorardiographically calculated versus angiographically measured volume. Table 4 and Figures 2 and 3 compare echocardiographically calculated and angiographically mea - sured end -diastolic and end -systolic volumes. There were no statistical differences between the echocardiographically cal - culated and angiographically measured values. In addition, there was a good correlation between echocardiographically calculated and angiographically measured end -diastolic vol - ume (Echocardiographic end -diastolic volume = 1 .O [Angio- graphic end -diastolic volume] - 1.8 ml; r = O.%, R2 = 0.93) and end -systolic volume (Echocardiographic end -systolic volume = 0.98 [Angiographic end -systolic volume] -0.7 ml; r = 0.95, R2 = 0.91). Discussion The principal findings of this study were that 1) the left ventricular epicardial long -axidshort -axis dimension ratio is Figure 2. Correlation between echocardiographically (ECHO) cal - culated and angiographically (ANGIO) measured left ventricular end -diastolic volume. Data are from normal dogs, dogs with acute or chronic mitral regurgitation and dogs that had undergone mitral valve replacement. 01 I I I 1 0 40 EO 120 160 END -DIASTOLIC VOLUME (mi) ANGiO JACC Vol. 20, No. 4 October 1992:986-93 ZILE ET AL. ECHOCARDIOGRAPHICALLY DETERMINED VOLUME 991 100 - g 80 5 ’g - - w 6 60 - 00 -1w 2 40 In > In P - 20 - Y 0.98 X - 0.65 r = 0.95 I I I I I 0 20 40 60 80 100 END -SYSTOLIC VOLUME (ml) ANGIO Figure 3. Correlation between echocardiographically (ECHO) cal - culated and angiographically (ANGIO) measured left ventricular end -systolic volume. Data are from normal dogs, dogs with acute or chronic mitral regurgitation and dogs that had undergone mitral valve replacement.

constant throughout the cardiac cycle; 2) this ratio remains constant throughout the cardiac cycle in a variety of animal species, age groups and in the presence of cardiac diseases that cause significant changes in left ventricular geometry and function; and 3) the echocardiographic method proposed in this study allows accurate calculation of left ventricular volume with echocardiographic techniques. Advantages of “proposed model.” There are three major advantages to calculating left ventricular volume with the approach presented in this study: 1) echocardiography is a noninvasive technique, 2) the left ventricle is modeled as a prolate ellipsoid, and 3) only a single measurement of left ventricular long axis (taken at any time during the cardiac cycle) is required. Noninvasive methods allow left ventric - ular volume and left ventricular volume -based indexes of left ventricular function to be measured serially during the development, treatment and recovery from a variety of cardiac diseases. Although the current study demonstrates that left ventricular epicardial geometry is relatively un- changed by cardiac disease, many cardiac diseases cause significant changes in left ventricular endocardial geometry, particularly the relation between left ventricular endocardial long - and short -axis dimensions. For example, pressure overload hypertrophy causes an increase in the left ventric - ular endocardial long-axishhort-axis dimension ratio, caus - ing the left ventricle to become more cylindric. In contrast, volume overload hypertrophy causes a decrease in this ratio, causing the left ventricle to become more spheric. Thus detection of serial changes in volume (an endocardial based measurement) must be performed by using methods that account for or incorporate these changes in geometry into their calculation.

For these reasons a prolate ellipsoid geom - etry is most frequently chosen. However, calculating vol - ume with an elliptic model requires measurement of both the endocardial long -axis and short -axis dimensions.

Echocardiographic determinations of left ventricular long -axis dimensions are best made with the transducer placed in the apical position (apical two - or four -chamber view). However, these views frequently do not allow assess - ment of the left ventricular short -axis dimension because the left ventricular endocardium is not readily seen (the echo - cardiographic beam is parallel to the endocardium of the interventricular septum and the posterior wall) (30,31). In contrast, when the transducer is placed in the parasternal position (parasternal long - or short -axis views), accurate left ventricular short -axis dimension and wall thickness mea - surements can be made. However, the long -axis dimension cannot be readily visualized throughout the cardiac cycle because of inability to visualize the apex (apical foreshort - ening, apical dropout) (32). The current method was devel - oped because of these difficulties in simultaneously measur - ing long -axis and short -axis dimensions throughout the cardiac cycle and because of an increasing reliance on volume -based indexes of left ventricular function (and their requirement of multiple coordinates of volume throughout the cardiac cycle).

The current method calculates volume by using an elliptic geometry but requires only one measurement of endocardial long -axis dimension during the cardiac cycle (for example, at an easily defined, reproducible point such as end -diastole). A single two -dimensional, apical view can be used to deter - mine the left ventricular endocardial long -axis dimension at a single point in the cardiac cycle. This measurement can be combined with a two -dimensional or two -dimensionally di - rected M -mode detemination of left ventricular endocardial short -axis dimension at the same point in the cardiac cycle.

The epicardial long -axislshort -axis dimension ratio, Z, can thus be determined. Then left ventricular volume at any point in the cardiac cycle can be calculated by measuring instantaneous left ventricular endocardial short -axis dimen - sion and wall thickness with two -dimensional or two- dimensionally directed M -mode echocardiography or by measuring left ventricular endocardial area with two - dimensional echocardiography. The accuracy of the pro - posed model was validated in this study over a wide range of left ventricular volumes, geometry and left ventricular func - tion. End -diastolic volume ranged from 50 to 150 ml, en- docardial end -diastolic long -axidshort -axis dimension ratio ranged from 2: 1 to 1.5: 1 and left ventricular ejection fraction ranged from 70% to 20%. As in previous studies, angiograph- ically determined volumes (32 -35) were slightly larger than echocardiographically measured volumes. Other echocardiographic models for calculating volume. Previous studies (1 1) have used four general echocardio - graphic methods to calculate left ventricular volume. Left ventricular volume was calculated by using M -mode mea- , 992 ZILE ET AL. ECHOCARDIOGRAPHICALLY DETERMINED VOLUME surements of left ventricular endocardial short -axis dimen - sion and the cubed -rule (1 1): Left ventricular volume = (short -axis dimen~ion)~ . [8] This method has many limitations, the most important of which is its inability to account for changes in geometry.

Left ventricular volume was calculated with two -dimen - sional echocardiography by measuring the left ventricular endocardial long -axis (major axis, L) and the two left ven - tricular endocardial short axes (minor axes, D, and D2) (8):

[91 L D1 D2 Left ventricular volume = 4/3 ?r - -. - . 222 As discussed, simultaneous measurement of L, D, and D, at multiple points in the cardiac cycle is problematic. Left ventricular volume was calculated from two -dimensional echocardiograms with the area -length method (6) (equation 6). The disadvantage of this method is that it requires digitizing the endocardial surface area at each point in the cardiac cycle that volume is determined. With this two - dimensional approach, the number of frames suitable for digitizing are limited by the relatively low recording fre - quency (30 to 60 times/s) required by two -dimensional tech - nology. In addition, digitizing requires computer -based ana - lytic methods. Lastly, left ventricular volume was calculated by using two -dimensional echocardiography and Simpson's rule, where left ventricular volume is calculated as the sum of the volume of multiple ventricular slices of a known thickness (7,9,10). With this method, each volume determi - nation requires that multiple cuts and multiple digitizing be performed. Although volumes determined with all of these methods have been shown to have a good correlation with angiographically determined volumes, each has limiting dis - advantages (8). The method presented in this study was designed in an attempt to avoid these disadvantages. Transmural and major-dminor-axis dimension shorten - ing gradients. Previous studies (12 -22) made it clear that there is a gradient in shortening extent across the left ventricular wall (from endocardium to epicardium) in both the short - and the long -axis dimension. Using contrast ventriculography, ultrasound dimension transducers, metal - lic markers and echocardiography, previous studies (12 -22) indicated that the average extent of left ventricular short - axis endocardial shortening was 35% (range 25% to 38%), midwall shortening 21% (range 20% to 25%) and epicardial shortening 10% (range 7% to 12%); left ventricular long -axis endocardial shortening averaged 15% (range 9% to 16%) and epicardial shortening 10% (range 5% to 11%). Thus previous data (12 -22) suggest that in the normal ventricle both long - and short -axis epicardial shortening averaged 10% and pre - dict that the epicardial long-axis/short-axis ratio should be constant throughout the cardiac cycle. Data from the current study regarding epicardial short - and long -axis shortening are consonant with these previous studies. Thus our study confirms these predictions in the normal left ventricle and JACC Vol. 20, No. 4 October 1992:986-93 both extends these findings to a variety of animal species and age groups and validates their application in patients with cardiac disease.

The demonstration that the left ventricular epicardial long -axidshort -axis dimension ratio is constant throughout the cardiac cycle has important physiologic implications.

The left ventricular epicardial silhouette changes by I 10% during contraction. In contrast, the left ventricular endocar - dial silhouette changes dramatically. The change in left ventricular endocardial silhouette and the resultant left ven - tricular volume displacement during contraction therefore primarily depends on the extent of left ventricular wall thickening. The change in the endocardium is most promi - nent in the short -axis dimension; the extent of shortening in this dimension is two to three times greater than that in the long -axis dimension. The change in short -axis dimension is caused by circumferential (intraventricular septum, anterior, lateral and posterior walls) wall thickening, whereas the change in long -axis dimension is caused only by apical wall thickening and the actions of the chordae tendineae. These differences in the distribution of wall thickening between the long and short axes cause the endocardial long-axislshort- axis dimension ratio to change significantly during contrac - tion and account for the fact that the majority of volume displacement is caused by changes in left ventricular wall thickening along the endocardial short axis.

Limitations. Particularly in the clinical setting where acoustic windows may be limited, care must be taken to obtain the true minor (short) -axis dimensions of the left ventricle. M -mode and two -dimensional measurements should be taken at the tips of the mitral valve leaflets with dimensions measured very close to the base of the left ventricle intersecting the septum near the aorta. This may be different in some clinical setting and may differ somewhat from patient to patient. Similarly, great care must be taken to avoid foreshortening the major (long) -axis dimension. Again, this may be different in some clinical settings and may limit the application of the methods described in this study.

The method described in this study will not work ade - quately in animals or patients with segmental coronary artery disease or segmental wall motion abnormalities, or both. However, it will work well in any symmetrically contracting ventricle. In chronic heart disease such as vol - ume overload hypertrophy, pressure overload hypertrophy or dilated cardiomyopathies, the use of the long -axis dimen - sion allows the ventricle to be modeled as a prolate ellipse rather than as a sphere. Therefore, accurate calculation of ventricular volume, taking into account changes in ventric - ular geometry, can be made during the progression and regression of these forms of chronic heart disease. In the current study correlations between echocardio - graphically calculated and angiographically measured vol - umes were presented only at end -diastole and at end -systole. No data were presented to confirm that this correlation exists throughout the cardiac cycle. However, two facts suggested that this assertion may be true: 1) the epicardial - 1 i i 1 I I I I i I I !

i I JACC Vol. 20, No. 4 October I W2:986-93 993 ZILE ET AL. ECHOCARDIOGRAPHICALLY DETERMINED VOLUME long -axidshort -axis dimension ratio was constant through - out the cardiac cycle; 2) as shown in Figure 2, there was.a good correlation over a large range of volumes (20 to 160 ml) between angiographically and echocardiographically deter - mined volumes. This range of volumes was comparable to the range observed in the left ventricle from end -diastole to end -s ystole.

Conclusions. The left ventricular epicardial long -axis/ short -axis dimension ratio was constant throughout the cardiac cycle in a variety of animal species and age groups and in the presence of cardiac diseases that significantly altered left ventricular geometry and function. The echocar - diographic method examined in this study provided an accurate determination of left ventricular volume. We thank Beverly Ksenzak for help in the preparation of the manuscript.

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