(The equations are provided via an online supplement, supplied to me by the authors.)

Normalized end-systolic volume and pre-load reserve predict ventricular dysfunction following surgery for aortic regurgitation independent of body size.

Gentles TL, French JK, Zeng I, Milsom PF, Finucane AK, Wilson NJ.

JACC Cardiovasc Imaging. 2012 Jun;5(6):626-33.

Although the article describes equations for LV function and dimensions, I use only the dimensional z-scores. The form of these equations is that of an allometric relationship with BSA, with log-log transformation of both the measured value and the BSA.

The formula used for estimating BSA is not described within the article/supplement; I am awaiting a response from the authors on this. In the meantime, calculations are made using the Haycock formula.

### LVEDD and LVESD

The allometric equations for the LVEDD and LVESD use exponents of around 0.4, which is slightly less than what would be expected by the theory of geometric similarity: 0.5. Numerous other authors have discovered linear relationships when correcting/adjusting linear dimensions (cm) to body surface area (m^{2}). Additionally, the LVESD values seem a bit off when compared to other available sources:

(I have contacted the authors; awaiting their response)

### LVEDV and LVESV

Data for the left ventricular volumes is also in the form of an allometric relationship with BSA, with an exponent of around 1.1. Again, this differs somewhat from what would be predicted by geometric similarity, and by other empirical evidence. The closer the exponent is to 1.0, the more the relationship is strictly linear with BSA, which is unexpected, particularly since the authors recognize this peril:However, the relationship between body size and LV size is nonlinearYet, when you plot out the predicted values, it looks quite linear:

versus an allometric equation with an exponent of 1.38 (Lytrivi et al.):

Anyhow, given the paucity of ventricular volume z-score equations, these are now included among other pediatric echo z-score calculations at

### app.parameterz.com

***update Dec 2012***

The author has advised me that there was an error with the online supplement.The app now uses the updated value."The intercept for ESD should be 2.56 NOT 3.56 as is on the web"