646 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



the arterial pressure record or from the simultaneously 

 obtained ventricular and arterial tracings (16, 17, 81, 

 no, 151-153, 162-164). 



Estimation of the degree of stenosis in a specific 

 part of the circulation, particularly over the different 

 valves, has been attempted through the use of various 

 hydraulic formulas. Gorlin & Gorlin (84) derived a 

 hydraulic formula that could be used to calculate 

 valve areas. Dow and collaborators (52), and .Silber 

 and others (185) attempted to use a much simpler 

 formula, based on PoLseuille's law, and calculate 

 "valvular resistance." Rodrigo & Snellen (171), in 

 '953' published a critical study of the physical basis 

 of the method employed, and concluded that the 

 formula used for calculating valvular resistance be- 

 comes invalid if the blood flow is not laminar. The 

 "stenotic index" derived from this formula was found 

 to be directly proportional to the volume of flow. 

 Accordingly, any change in cardiac output will give 

 a change in the calculated resistance. They preferred 

 the valve area formula for the estimation of the 

 degree of stenosis. 



The general formula for calculation of the area of 

 certain orifices in the circulation deri\'ed b\' Gorlin 

 and Gorlin reads : 



C X 44-5 \/ft - Pi 



i'hcre 



In each case the rate of flow must be calculated for 

 that period when the particular valve in question is 

 open: ventricular diastole for atrioventricular and 

 ventricular systole for seinilunar \alves. Usually, 

 empirical constants have been derived for each vah'e 

 from a comparison of anatomically measured and 

 physiologically calculated areas. 



In mitral or tricuspid stenosis the general formula 

 is altered through the insertion of the following specific 

 values. 



Ml' A = 



CO/DFP 



CO/DFP 



0.7 X 44-5\/"?C"„ - 5 0.7 X 44.5\/i^m - LV„, 



where 



AtVA = mitral valve area, cm^ 



CO = cardiac output, ml/min 



DFP = diastolic filling period, sec/min 



0.7 = empirical constant, C 



44.5 = gravity acceleration factor 



LAr„ = left atrial mean pressure, mm Hg 



PC, = pulmonary capillary mean pressure, mm Hg 



LVmd = left ventricular diastolic mean pressure, mm Hg 



5 = assumed left sentricular diastolic mean pressure, 

 mm Hg 



For tricuspid valve area, left heart pressures are ex- 

 changed for right heart values. 



Rodrigo & Snellen (171) approved of the \ah'e 

 area formula of Gorlin and Gorlin, although the 

 "constant" used in the formula proved to be a variable 

 term. From mathematical considerations Rodrigo 

 states that the acceptance of the constant provides an 

 error of 20 per cent; when large deviations occur, 

 this error may be as great as 40 per cent. To this 

 mathematical error several biological sources of error 

 must be added. The use of pulmonary artery wedge 

 pressure instead of left atrial pressure may introduce 

 too high a figure for pressure gradient. Of greater 

 importance is the use of mean atrial pressure instead 

 of diastolic pressure, which may vary considerably. 

 To use an assumed value for left ventricular diastolic 

 pressure likewise may cause great error in the estima- 

 tion of valvular pressure gradient. The impossibilit\ 

 of judging exactly the presence and degree of mitral 

 regurgitation may invalidate the flow measurements 

 which usually estimate only the effecti\^e flow, not the 

 total flow (which includes that lost via regurgitation) 

 through the valve. 



Ferrer tt al. (71), in studying a case with tricuspid 

 stenosis, obtained exact data which they used to 

 check the formula. The results of calculation (0.5B 

 cm-) differed considerably from what was found at 

 autopsy (1.65 cm"). "The limitations of the method 

 of Gorlin are obsious, when one considers that the 

 engineer's formulas are applicable to hydraulic 

 systems with fixed orifices, which are similar to short 

 tubes and assume the absence of pulsatile flow." 

 Many others, including the present author, likewise 

 consider it unreliable and unsuitaljle for exact 

 measurements (31). 



In a recent appraisal of this formula Gorlin (83) 

 states that the two main values of the formula, as 

 expressed by those who are using it, were that it gave 

 a better understanding of stenotic valve disease and 

 that it was an aid in the occasional patient about 



