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Online Appendix for the following JCMG article
TITLE: Normalized End-Systolic Volume and Preload Reserve Predict Ventricular
Dysfunction Following Surgery for Aortic Regurgitation Independent of Body Size
AUTHORS: Thomas L. Gentles, FRACP, John K. French, MB, PHD, Irene Zeng, MSC,
Paget F. Milsom, FRACS, A. Kirsten Finucane, FRACS, Nigel J. Wilson, FRACP
APPENDIX
Functional Preload Index
The Functional Preload Index (FPI) attributes any difference in shortening relative to the
velocity of shortening, to preload status. For example, an individual with a SF 2 standard
deviations above the normal population mean and VCFc 1 standard deviation below the
normal population mean would have a FPI of +3. (1-4)
Z-scores
A z-score is a dimensionless number indicating the number of standard deviations from the
normal population mean a measurement lies with respect to body surface area or age. The
mean z-score for the normal population is 0 with a SD of 1.
Z-score Calculation
Z-scores were generated according to the formula: z-score = (measured – expected)/standard
deviation, where the expected value was calculated from the normal data following
logarithmic transformation of the index variable vs. body surface area in the case of chamber
size, or the linear relationship vs. age in the case of function and fiber stress (Table) as
illustrated by the following:
ESV z-score = (ln ESV – (ln[BSA^a *b])) / SEE
EF z-score = EF – (a * age + b) / SEE
In the above equations, the SEE was adjusted for the normal population size and distribution
according to the formula:
SEE = (Sy.x * ((ln BSA – mean x)^2 / Lxx + 1/n +1)^0.5
where mean x is the mean of lnBSA in the normal population (0.4594), Lxx is the corrected
sum of squares for lnBSA in the normal population (12.294), and n is the number in the
normal population (158), or
SEE = (Sy.x * ((Age – mean x)^2 / Lxx + 1/n +1)^0.5
where mean x is the mean age in the normal population (25.0), Lxx is the corrected sum of
squares for age in the normal population (33658.4), and n is the number in the normal
population (158).
Where there was no relationship between the index variable and body surface area or age the
expected value was the unadjusted population mean. For example:
FS z-score = (FS – population mean) / population SD
Appendix Table. Regression equations derived from normal population for calculation
of z-scores
Variable
Predicted
Sy.x or SD
EDD
y = 3.88*BSA0.40
0.071
ESD
y = 3.56*BSA0.41
0.096
EDth/D
0.166
0.024
SF
33.6
3.1
VCFc
1.02
0.09
ESFSc
0.81*Age + 171
28.8
SVIc
-0.0013*ESFSc + 1.28
0.092
EDV
64.7* BSA1.12
0.164
ESV
23.1*BSA1.19
0.204
-0.06 * Age + 64.4
4.03
EF
Abbreviations: EDD, end-diastolic dimension; ESD, end-systolic dimension; EDth/D, enddiastolic wall thickness/dimension ratio; SF, shortening fraction; VCFc, heart rate-corrected
mean velocity of circumferential fiber shortening; ESFSc, end-systolic circumferential fiber
stress; SVI, stress-velocity index; EDV, end-diastolic volume; ESV, end-systolic volume; EF,
ejection fraction; Sy.x, standard error; SD, standard deviation.
Appendix References
1.
Nixon JV, Murray RG, Leonard PD, Mitchell JH, Blomqvist CG. Effects of large
variations of preload on left ventricular performance characteristics in normal subjects.
Circulation. 1982;65(4):698-703.
2.
Borow KM, Neumann A, Marcus RH, Sareli P, Lang RM. Effects of simultaneous
alterations in preload and afterload on measurements of left ventricular contractility in
patients with dilated cardiomyopathy: Comparisons of ejection phase, isovolumetric and endsystolic force-velocity indexes. J Am Coll Cardiol. 1992;20:787-95.
3.
Colan SD, Borow KM, Nuemann A. Left ventricular end-systolic wall stress-velocity
of fiber shortening relation: A load independent index of myocardial contractility. J Am Coll
Cardiol. 1984;4:715-24
4.
Segar DS, Moran M, Ryan T. End-systolic regional wall stress-length and stress-
shortening relations in an experimental model of normal, ischemic and reperfused
myocardium. J Am Coll Cardiol. 1991;17:1651-60.