Analysis of the Role of Indicator Technics in Quantitation of Valvular Regurgitation

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Homer R. Warner Regurgitation Analysis of the Role of Indicator Technics In Quantitation of Valvular 1524-4571 Copyright © 1962 American Heart Association. All rights reserved. Print ISSN: 0009-7330. Online ISSN: TX 72514 Circulation Research is published by the American Heart Association. 7272 Greenville Avenue, Dallas, doi: 10.1161/01.RES.10.3.519 Circulation Research 1962, 10:519-529 http://circres.ahajournals.org/content/10/3/519.citation located on the World Wide Web at: The online version of this article, along with updated information and services, is http://www.lww.com/reprints Reprints: Information about reprints can be found online at [e-mail] 410-528-8550. E-mail: Kluwer Health, 351 West Camden Street, Baltimore, MD 21202-2436. Phone: [phone]. Fax: Permissions: Permissions & Rights Desk, Lippincott Williams & Wilkins, a division of Wolters http://circres.ahajournals.org//subscriptions/ Subscriptions: Information about subscribing to Circulation Research is online at Downloaded from http://circres.ahajournals.org/ at University of Utah on January 19, 2012 Analysis of the Role of Indicator Technics In Quantitation of Valvular Regurgitation By Homer R. Warner, M.D., Ph.D. • Although the usefulness of certain indica-tor methods in the evaluation of patients with valvular regurgitation is now well established, many of the technics currently in use do not yield consistently accurate information. Since these failures may be due to lack of an ade-quate theoretical basis for interpretation of the indicator-dilution data obtained, further exploration into the logical foundation upon which these technics rest seems worth while. In this paper a mathematical model (fig. 1) of the left side of the heart is presented and used as a basis for predicting the time course of indicator concentration to be logically anticipated in the left atrium, left ventricle, and aorta following injection into each of these chambers or into a pulmonary artery in the presence or absence of mitral or aortic valvular regurgitation. Mathematical Representation of Left Side of Heart First I shall describe with a set of ordinary differential equations the time course of blood flow, volume and pressure in the chambers of the left side of the heart. The rate at which the volume (Vi) of the left atrium changes with time is the sum of the flow into the atrium from the pulmonary veins (Qi) and from the left ventricle (Qa) minus the flow out of the atrium into the ventricle (Q2) and is given by dt 1 = Qi + Q3 - Q2. (1) Qi varies with the respiratory cycle but is independent of the cardiac cycle. This is ex-pressed in Qi = A + B sine (cot + $) (2) Latter-day Saints Hospital and University of Utah, Established Investigator, American Heart Associa-tion. This investigation was supported in part by Research Grant H-4064 from the National Institutes of Health, United States Public Health Service. where A is the mean Qi; B is a parameter that defines the maximal change in Qx from the mean at any phase of the respiratory cy-cle, a is the frequency of the respiratory variations in intrathoraeic pressure, and $ is the phase angle between the maximal intra-thoraeic pressure and maximal Qj. Sinusoidal variations in intrathoraeic pressure are as-sumed for convenience. Q2 is zero during ventricular systole, and during diastole it is given by dQ2 dt + biQ2 = Pi - P2 = V! - KMV« (3) where ax is the pressure gradient required to accelerate the flow of blood across the mitral valve at a rate of 1 ml./sec.~2, bi is the re-sistance to flow across the mitral valve during diastole, and Km and K2lJ represent the ratio during diastole of pressure to volume in the left atrium and left ventricle respectively and are treated as constants in the first ap-proximation. These latter two parameters might, of course, be treated as functions of time or volume. Q3 is zero during diastole, and during systole it is given by a2 dt = p2 _ P l = (4) where a2 and b2 are the inertiance and resist-ance to flow across the mitral valve during systole and Kis and K2s represent the ratio of pressure to volume for the left atrium and left ventricle during systole. The rate of change of volume of the left ventricle (V2) is given by ~ = Q2 - Qs - Q4 + QB (5) where Q4 and Q5 represent flow across the aortic valve in systole and diastole respec-tively and are given by Circulation Research, Volume X, March 1962 519 Downloaded from http://circres.ahajournals.org/ at University of Utah on January 19, 2012 520 WARNER FIGURE 1 Diagram of model of left side of heart. Terms arc defined in the text. dt and (6) a4 ^25- + b4QB = P8 - P2 = K8VS - K2dVa (7) where b3 and b4 are the resistance to flow across the aortic valve in systole and diastole and Ks is the ratio of pressure to volume in the aorta. Q4 is zero during diastole and Qr, is zero during systole. The rate at which the volume of the aorta (V3) changes with time is given by where b-, is the resistance to forward flow out of the aorta (peripheral resistance). These eight differential equations must be solved simultaneously in order to express the course of each of these variables as a func-tion of time for any given set of system parameters. One analog-computer solution to these equations is shown in figure 2. Here is shown the predicted time course of flow and volume in the absence of valvular re-gurgitation. These wave forms represent flow from left ventricle to aorta (Q4) (which is zero during diastole), flow from left atrium to left ventricle (Q2) (which is zero during systole), and volume of left atrium (Vj), left ventricle (V2) and aorta (V3) as a func-tion of time. In figure 3 is shown the time course of flow and volume when "mitral and aortic regurgitation" is present. Q8 is baekflow across the mitral valve and Qr, across the aortic valve. The effect of changing any one parameter on the time course of each of these variables may be readily studied in such a model by simply adjusting the appropriate potentiometer. Now in order to define the expected time course of concentration of an indicator in the left atrium (Ci), left ventricle (Co) and aorta (C3) following injection into any of these chambers, it is only necessary to define the nature of the mixing process. Although, in reality, mixing is undoubtedly not in-stantaneous throughout the left atrium or ventricle,1'2 such an assumption is made here in order to examine the logical consequences to which this assumption leads. Also it is assumed that the concentration of indicator at the root of the aorta equals the left ventricular concentration during systole and remains constant during the succeeding dias-tole, that is, blood in the ascending aorta is completely replaced by new blood ejected with each systole. The mass of indicator in the atrium (Mj) and ventricle (Mo) is obtained by integra-tion of dt = Q1C0 - Q2C, + Q3C, (9) and dMo dt - (Q3 + Q4) Co + Qr,C3 (10) where Co is the concentration of dye in pul-monary- vein blood entering the left atrium. A term, liti, must be added to equation 9 in the case of left atrial injection, or to equa-tion 10 in the case of left ventricular injec-tion. 11 is the rate of injection of indicator and ti is the duration of injection. The con-centration terms follow from the definitions and _ M, Ma (11) (12) and must be generated after the integration Circulation Research, Volume X, March 1968 Downloaded from http://circres.ahajournals.org/ at University of Utah on January 19, 2012 SYMPOSIUM ON INDICATOR-DILUTION TECHNICS 521 of equations 9 and 10 since Vi and V2 are variables. As already stated, C3 equals C2 during systole and remains constant during the succeeding diastole. To solve these equations on an analog com-puter, relays are used to set the boundary conditions for systole and diastole as pre-scribed by the equations.3 These relays are controlled with a timing circuit set to corre-spond to the duration of systole and diastole that normally occurs at the particular heart rate being studied. These equations will now be used to ex-plore the logical conclusions to which the assumptions lead in the analysis of certain indicator technics that are currently em-ployed for the quantitative assessment of mitral and aortic valvular regurgitation. First to be considered is the injection of indicator into the left ventricle with detec-tion of concentration in the left atrium (Ci) and the left ventricle (C2) for the quantita-tive estimation of flow from ventricle to atrium in mitral regnrgitation. The curves shown in figure 4 represent a solution of equations 1 through 12 for the variables Cj and C2 resulting from a simu-lated injection of indicator into the left ventricle during diastole. It can be seen that C2 decreases with each diastole and remains constant during systole, while C.i, the indi-cator concentration in the left atrium, in-creases with systole and decreases during diastole. Lacy and associates'1 have suggested the use of S C,,, (13) Q2 2 C2a for estimation of the ratio of average back-flow (Q:i) from ventricle to atrium over a whole cycle to average forward flow (Q2) from atrium to ventricle over the whole cycle where Cn is the average concentration of indicator in the atrium during each ven-tricular diastole and C2s is the average con-centration of indicator in the left ventricle during each systole. Each of these concen-trations is summed for the number of heart cycles necessary to clear the indicator from Q. Q, V V2 V, FIGURE 2 Simultaneous solution of flow and volume equa-tions 1 through 8 obtained with an analog com-puter. Qs and Q5 are set to zero. atrium and ventricle. In fact, however, equa-tion 13 is not true in the general case unless either Q3 or Co is constant, during the course of systole and either C, or Qo is constant during diastole. It can be seen that C2 is constant during each systole, but neither Ci nor Q2 is constant in diastole. Recently, Sinclair and associates2 have used a modified form of this approach to assess experimentally produced mitral regurgitation in dogs. These authors measured the ratio of the area under a left atrial dye curve to the area under a dye curve obtained from a femoral artery following injection into the left ventricle. They found that the pi'edic-tion of regurgitant flow using this ratio correlated (r = 0.96) with regurgitant flow Circulation Research, Volume X, March 1968 Downloaded from http://circres.ahajournals.org/ at University of Utah on January 19, 2012 522 WARNER Q Q V, FIGURE 3 Solution of flow and volume equations in the presence of mitral regurgitation and aortic regur-gitaiion. The resistance to regurgitatit flow across the mitral valve is equal to 40 times the resistance to forward flow in this instance. Resistance to backfloxo across the aortic valve is equal to 1.4 times resistance to fonuard flow across the aortic valve. estimated by the hydraulic formula of Gorlin and Dexter5 using the pressure gradient measured during the experiment and the cross-sectional area of the defect as meas-ured at necropsy. From the theoretically derived curves shown in figure 4, prediction of the ratio of Qa to Q2 underestimates the actual ratio by 5.4 per cent when the ratio of the total area under the two dilution curves is used. That the error involved in using this approxi-mation is small may result from the fact that the systolic and diastolic time course of variation in Ci are fairly symmetrical. It is of special interest in regard to the practical application of this technic that Sinclair and co-workers found that the esti-mated regurgitant fraction in a given dog was not dependent upon the site of injection in the left ventricle and was dependent upon the site of sampling in the left atrium only when the sampling catheter was actually in a pulmonary vein or in the cephalad region of the atrium. Consistent ratios were obtained in the midatrium and near the mitral valve. Next to be considered is the possibility of measuring Q3 from an indicator-dilution curve recorded downstream from the injec-tion. In figure 5 is shown the time course of dye concentration in the left ventricle fol-lowing injection into the left ventricle with and without mitral regurgitation. The curve labeled "normal" was obtained with Q3 set to zero and the curve labeled "M.I." was obtained with Q3 equal to 0.64 times the net cardiac output. It can be seen that the down slope of the curve is very insensitive to the presence of Q8. In figure 6, end-systolic residual volume of the ventricle was varied from 50 to 100 ml. and produced a marked change in the shape of the curve. The time constant of the down slope in-creased to 1.5 times its original value when end-systolic residual left ventricular volume was increased from one half to two thirds of the end-diastolic ventricular volume as shown at the bottom of this figure. From these two results it is obvious that even in the ideal case, in which injection is made in a single diastole into the left ventricle and mixing is complete, the use of the down slope for measurement of Q3 would be unsatisfactory. In figure 7 is shown the time course of Ci and C3 when the con-centration of dye entering the left atrium from the pulmonary veins (Co) has the time course shown here, as it might have follow-ing an injection into the pulmonary artery. In such a case, it is not possible to measure Q3 from the aortic curve as Korner and Shillingford6 attempted to do, since no in-dependent measurement of the effect of left atrial and left ventricular volume can be made. In the case of left ventricular injec-tion and left ventricular or aortic sampling it would theoretically be possible to deter-mine Q3 since left ventricular end-diastolic volume may be measured from the concen-tration of indicator in the ventricle during the first systole following a diastolic injec- Circulation Research, Volume X, March 1962 Downloaded from http://circres.ahajournals.org/ at University of Utah on January 19, 2012 SYMPOSIUM ON INDICATOR-DILUTION TECHNICS 523 FIGURE 4 At the top is shown the time course of Qs with and without mitral regurgitation. Below is shoivn the time course of C2 and C1 following injection of indicator into the left ventricle during diastole. These tivo indicator-concentration curves are integrated and the ratio of the integrals is compared to the ratio of Q, to Qt as used by Sinclair and co-workers.' Qs is the difference between values for Qt with and without mitral insuf-ficiency. tiori. This has independently been pointed out by Polissar and Eapaport.7 However, in spite of these theoretical ob-jections, it must be said that downstream indicator-dilution curves have proved of value in providing semiquantitative, if indi-rect, information regarding the presence and severity of clinical mitral regurgitation. An example of such an index is shown in figure 8. Here is plotted the reciprocal of the time constant (T) of the exponential down slope of the indicator-concentration curve against the build-up time (tb) of the curve. It can be seen that there is a fair separation of the patients with mitral re-gurgitation from the patients without mitral regurgitation, but there are certain excep-tions as has been found with other such empiric indices. Unfortunately, the excep-tions are often the very cases in which the diagnosis of mitral regurgitation may be un- Circulalion Research. Volume X, March 196B certain on other grounds as well. This index is based on the observation that mitral re-gurgitation prolongs the descending limb of the curve more than the ascending limb. Such selective prolongation might occur if a relatively abrupt unsmeared curve were to enter a large left atrium or left ventricle. An extreme example of this is the case of injection of all the indicator into the left ventricle in a single diastole as illustrated in figure 4. In this case the peak concentra-tion is reached in the first heart cycle. In the case of injection into the left atrium the result is much the same, namely the build-up time of the aortic curve depends upon the time-course of indicator concentra-tion in blood entering the atrium while the down slope may be prolonged by a large left atrium or left ventricle. The ability of this index to detect mitral regurgitation must depend, then, upon the occurrence in Downloaded from http://circres.ahajournals.org/ at University of Utah on January 19, 2012 524 WARNER !:;jt;::i 't -f : : : : ••:ii!J:: I1!!!!!?! ^3 KI ^ I(M.I) . •. n • • • : : . . : : ; • . . . I • • - r i i i i fr • : ; 1 : : : t trflioB ••4 EFFECT* OF FjO i" INJECT INTO I 11:..?. "A iliiiiiii ;p!=:i:; ii •ft+HHH A sf\ :: • : - • = FIGURE 5 Comparison of the time course of Cs with and without mitral regurgitation in the presence of a constant mean left ventricular and left atrial volume. The time course of Q2 with and without mitral regurgitation is shoivn at the top. mitral regurgitation of left atrial or left ventricular enlargement, or both, out of proportion to the changes in the pulmonary circulation which "smear" the dilution curve by the time it enters the left atrium, or upon the occurrence of a peculiar mixing of indi-cator in the left atrium or left ventricle in mitral regurgitation. Militating against the latter argument is the observation that acute mitral regurgitation in dogs does not pro-duce the typical distortion of an indicator-dilution curve seen in patients with long-standing mitral regurgitation. Other indices have been proposed Avhose ability to separate patients with mitral re-gurgitation from patients with other cardiac defects is dependent upon the relationship of the amount of "smearing" of the dye curve as it passes through the pulmonary circulation and left side of the heart to the "smearing" that occurs as the indicator passes around the whole circulation or the right side of the heart and the systemic veins. One example of this is the CL/CR ratio proposed by Wood and Woodward.8 Cr, is defined as the minimal concentration of dye obtained during the descending limb of the curve before recalculation again in-creases the concentration, and Cu is the peak concentration achieved during the recircu-lation hump of the curve. Cr, is dependent only on events taking place as the indicator goes from the pulmonary artery to the sam-pling site in a systemic artery, and CR will be influenced by events occurring in the whole circulation. Perhaps the fact that this index is relatively successful in separating patients with mitral regurgitation from those without regurgitation is the result of a selective dilatation of the left ventricle, left atrium, and, possibly, pulmonary vascular bed as compared to the systemic veins and right side of the heart in patients with mitral regurgitation. Lange and Hecht9 have injected dye into a peripheral vein and recorded simultane-ously the concentration of dye in the pul-monary artery and a systemic artery. The Circulation Research, Volume X, March 19GS Downloaded from http://circres.ahajournals.org/ at University of Utah on January 19, 2012 SYMPOSIUM ON INDIOATOE-DILUTION TECHNICS 525 FIGURE 6 Effect of increasing end-syslolio residual volume of the left ventricle on the time course of Cs following left ventricular injection. difference in appearance time and mean circulation time between the two curves is used to estimate the severity of mitral re-gurgitation. This approach to the detection of mitral regurgitation onee again depends upon the relative "smearing" of indicator with passage through the pulmonary circu-lation and left side of the heart as com-pared to the effects of passage of indicator from a systemic vein to the pulmonary artery. Since this "smearing" is largely determined by the volume of the left atrium and left ventricle and not by the magnitude of regurgitant flow (Q3), this index, like the others just presented, cannot be expected to yield direct information regarding Q3.10 It is apparent that more theoretical and experimental work must be done to clearly define all the factors responsible for the observed alteration in contour of a dilution curve that results from its passage through the various component parts of the circula-tion. From such information and a better understanding of the pathologic physiology of mitral regurgitation, the use of indicator technics for quantitation of mitral regurgi-tation may attain the accuracy and relia-bility required for the solution of the prac-tical problems which face the clinician. Aortic Regurgitation Methods First to be considered is the possibility of measuring regurgitant flow across an aortic valve from a downstream curve follow-ing injection into the left ventricle. If the injection is made in diastole and mixing is complete in the left ventricle, the concen-tration of dye during the first systole, both in the left ventricle and in the aorta, will be equal to the amount of indicator injected divided by the end-diastolic value of V-j. This volume is the sum of the residual end-systolic volume of the left ventricle, the net stroke volume entering from the leiit atrium, and the regurgitant stroke volume entering from the aorta. During the next diastole, blood that enters the left ventricle from the aorta will have the same concentration of indicator as the blood remaining in the ven-tricle from the previous systole and will have the same effect on the subsequent Circulation Research, Volume X, March 1962 Downloaded from http://circres.ahajournals.org/ at University of Utah on January 19, 2012 526 WARNER !•• •• I • • • : l . FIGURE 7 Predicted time course of Cs with and ivithout mitral regurgitation following a simulated injection into the pulmonary artery. Co is the waive form chosen to represent the time course of dye concentration in blood entering the left atrium from the pulmonary veins. The scale factor on this curve is arbitrary. end-diastolic left ventricular concentration of dye as would have occurred had the resid-ual left ventricular volume been increased by an amount equal to the regurgitant stroke volume. Thus, the downstream dye curve in aortic regurgitation cannot permit the quan-titation of regurgitant flow across the aortic valve unless an independent measure of the end-systolic residual volume is available. Un-fortunately, this information cannot be ob-tained by means of the indicator-dilution principle, since the very presence of aortic regurgitation invalidates the premises upon which this teclmic depends. Injection of indicator into the aorta and simultaneous measurement of its concentra-tion in the left ventricle and in a peripheral artery have been used by Armelin and co-workers11 to estimate the backflow across the aortic valve in aortic regurgitation from ~ = -* = regurgitant fraction (14) Q4 a2 where Q5 is the mean flow over the whole heart cycle from aorta to left ventricle, Q4 is the mean flow from left ventricle to aorta over the whole heart cycle, ax is the area under the indicator-concentration curve re-corded from the left ventricle, and a2 is the area under the indicator-concentration curve recorded from a femoral artery. Since equation 14 is based upon the same prin-ciple as equation 13 for flow across the mitral valve, it is essential that the frac-tion of injected indicator that regurgitates into the left ventricle be representative of the fraction of the total forward flow of blood that regurgitates. To analyze this, the results of an injection timed with respect to the heart cycle will be considered. If the injection occurs early in diastole and is short (0.1 second), all of the dye might be carried back into the left ventricle, resulting in a regurgitant fraction of one, even if the severity of aortic regurgitation is minimal. Circulation Research, Volume X, March 1968 Downloaded from http://circres.ahajournals.org/ at University of Utah on January 19, 2012 SYMPOSIUM ON INDICATOR-DILUTION TECHNICS 527 10 8 6 3 .25 .2 .15 - I K IO £ .08 o 5> .06 .04 .03 .025 .02 .01 \ lndex = l /I.I. index=-^ V,\ oV o-M.I. • -No M.I. \ \ \ \ \ i i i i 11 i i i i 1.5 2 2.5 3 4 5 6 7 8 910 15 2O25 3 O 4 0 5O6O8OI0O BUILD-UP TIME( t b ) SECONDS FICURE 8 Comparison of the doiun slope (1/T) of the exponential descending limb of a femoral-artery dilution curve following pulmonary-artery injection of indicator to the build-up time (tb) in patients toith and without mitral regurgitation as proved at operation. Broken line indicates an index of one. All that is required for this to occur is that the labeled blood in the first few centi-meters of the aorta be replaced during dias-tole with unlabeled blood from farther down the aorta. Even if the injection were carried over the whole heart cycle, that fraction in-jected during diastole would be subject to the error just described. On the other hand, if the injection were carried out just over the duration of systole, an overestimate of backflow might still be expected since the concentration of dye expressed at the end of systole as a function of distance down the aorta from the aortic valve would not be uniform, but would depend upon the time course of flow velocity during systole past the injection site. The highest concen- Circulalion Research, Volume X, March 196Z tration of dye would be closest to the aortic valve, since flow velocity out of the ventricle is maximal early in systole. This may explain why Armelin and associates found no sig-nificant difference between the estimates of regurgitation with this technic made from dye injections carried out over the duration of systole, over the duration of diastole, and over the whole cycle, since b}r this technic an overestimate of regurgitant flow would be expected in all three eases. Another method for estimation of back-flow in aortic regurgitation involves the in-jection of indicator into the descending aorta and detection of indicator concentration in blood from the left radial artery'- (or use of an oximeter at the right ear18). Repeated Downloaded from http://circres.ahajournals.org/ at University of Utah on January 19, 2012 528 WARNER injections of! indicator are made into the aorta, each time at a distance 2 cm. farther from the origin of the subclavian artery until a point is reached at which injection no longer results in appearance of indicator at the left radial sampling site on the first circulation. The distance from the origin of the left subclavian artery to this point is taken as the distance over Avhich backflow in the aorta travels during a single diastole. This distance multipled by the cross-sectional area of the aorta would represent the volume of blood regurgitating from this segment of the vascular bed in one diastole. This esti-mate would be valid if the farthest-traveling particles of indicator were representative of the whole column of blood as is the case with the "bubble flowmeter." However, Warner and Toronto14 have recently shown that, in-creasing the heart rate results in a much more drastic decrease in aortic regurgita-tion estimated by this technic than could be explained by taking into account the change in the fraction of the heart cycle occupied by diastole at the increased rate and by reasonable assumptions regarding the inertia of the blood column. They con-cluded that the progressive development of laminar flow during diastole caused an apparent marked increase in aortic insuffi-ciency at slow heart rates. Thus, in using this technic as a practical semiquantitative index of aortic regurgitation, heart rate at the time of the study must be taken into consideration. Conclusions From the analysis here presented, the fol-lowing conclusions regarding the use of indi-cators for the quantitative evaluation of mitral and aortic regurgitation may be drawn: 1. Even with the assumption of complete mixing in the left atrium and left ventricle, large fluctuations in the time course of indi-cator concentration in the left atrium may be expected following sudden single injec-tion of: indicator into the left ventricle in the presence of mitral regurgitation. Despite these pulsatile variations in the time course of left atrial concentration of indicator and the simultaneous variation in the time course of flow across the mitral valve in diastole, it should be possible to estimate the magni-tude of the mitral regurgitant flow within about 5 per cent by using the modification of equation 13 employed by Sinclair and associates.2 Whether this accuracy is possi-ble with less complete mixing cannot be answered. 2. From the analysis based on this mathe-matical model of a pulsatile heart with com-plete mixing assumed in the left atrium and left ventricle, it has been demonstrated that detection and quantitation of mitral regurgi-tation from an indicator-dilution curve re-corded from the left ventricle following injection of indicator into the left ventricle is possible but difficult since the shape of the curve is quite insensitive to regurgitant flow, compared to its sensitivity to changes in volume of the left atrium and left ven-tricle. Moreover, direct quantitation of mitral regurgitation is impossible following injec-tion into the pulmonary artery or left atrium, since other much more critical determinants of the curve, namely left atrial and left ven-tricular volume, cannot be measured from such a curve. 3. Quantitation of aortic regurgitation from an indicator-concentration curve re-corded downstream from the left ventricle is not possible because the effect of the regurgitant stroke volume is indistinguish-able from the effect of increasing the end-systolic residual left ventricular volume by an identical amount. Furthermore, the deter-mination of left ventricular end-systolic vol-ume by means of an indicator-dilution tech-nic is not possible in the presence of aortic regurgitation. 4. Both the detection of indicator in the left ventricle following aortic injection and the determination of maximal backflow dis-tance that indicator particles travel up the aorta during a single diastole tend to over-estimate the severity of aortic regurgitation. The extent of the overestimate is directlv Circulation Research, Volume X, March 196& Downloaded from http://circres.ahajournals.org/ at University of Utah on January 19, 2012 SYMPOSIUM ON INDICATOR-DILUTION TECHNICS 529 related to the duration of diastole, at least with the latter teelmic. Some theoretical objections have been raised (in this paper) to the quantitative interpretation of information derived from the use of indicator technics for the evalua-tion of valvular regurgitation. It seems rea-sonable to expect, however, that further anal-ysis of the factors measured by the various indices of valvular regurgitation currently in use may increase the usefulness of these technics as tools for the practical evaluation of patients suspected of having valvular regurgitation. References 1. IRISAWA, H., WILSON, M. F., AND RUSHMER, R. !F.: Left ventricle as a mixing chamber. Circulation Res. 8: 183, 1960. 2. SINCLAIR, J. D., NEWCOMBE, C. P., DONALD, D. E., AND WOOD, E. H.: Experimental analysis of atrial sampling teelmic for qunntitating mitral rogurgitntion. Proc. Staff Meet., Mayo Clin. 35: 700, 1960. 3. WARNER, H. R.: The use of an analog computer for analysis of control mechanisms in the circulation. Proc. IRE 47: 1913, 1959. 4. LACY, W. W., GOODSON, W. H., WHEELER, W. G., AND NEWMAN, E. V.: Theoretical and practical requirements for the valid measurement of indicator-dilution of regurgitant flow across incompetent valves. Circulation Res. 7: 454, 1959. 5. GOBLIN, R., AND DEXTER, L.: Hydraulic formula for calculation of the cross-sectional area of the mitral valve during regurgitation. Am. Heart J. 43: 188, 1952. G. KORNER, P. I., AND SHILLINGFORD, J. P.: Further observations on the estimation of valvular incompetence from indicator dilution curves. Clin. Sc. 15: 417, 1956. 7. POLISSAR, M. J., AND RAPAPORT, E.: A mathe-matical pulsatile model of the human heart: Application to analysis of indicator curves. Presented at postdoctorate summer course, International School of Physics, Vareima, Italy, July, 1960. 8. WOOD, E. H., AND WOODWARD, E., JR. : A simple method for differentiating mitral regurgitation from mitral stenosis by means of indicator-dilution curves. Proc. Staff Meet., Mayo Clin. 32: 536, 1958. 9. LANGE, ~R. TJ., AND HECHT, H. H.: Quantitation of valvular regurgitation from multiple indi-cator- dilution curves. Circulation 18: 623, 395S. 10. MARSHALL, H. W., AVOODWARD, K., JR., AND WOOD, E. H.: Hcmoclyiininic methods for differentiation of mitral stenosis and rogurgi-tation. Am. J. Cardiol. 2: 24, 195S. 11. ARMELIN, E., MICHAELS, L., MARSHALL, TI. AV., DONALD, D. B., AND WOOD, K IT.: Detection of retrograde passage of indicator from aorta to left ventricle in dogs. (Abstr.) The Physiologist 3: 10 (Aug.) 1960. 12. WARNER, H. R., AND TORONTO, A. F.: Quantita-tion of bnckflow in patients with aortic in-sufficiency using an indicator teelmic. Circula-tion Res. 6: 29, 195S. 13. BRAUNWALD, E., AND MORROW, A. K.: A method for the detection and estimation of aortic regurgitant flow in man. Circulation 17: 505, 1958. 14. WARNER, H. R., AND TORONTO, A. I \ : Effect of heart rate on aortic insufficiency as measured by a dye-dilution technique. Circula-tion Res. 9: 413, 1961. Circulation Research, Volume X, March 196X Downloaded from http://circres.ahajournals.org/ at University of Utah on January 19, 2012