The folks over at Children's National Medical Center, Washington, D.C. (CNMC) have fired up their digital echo database: in a four month period, they sorted through over 400 eligible normal echos, and served up the largest analysis of normal coronary artery dimensions to date.

Their approach to the data analysis included explorations of the independent variables of BSA and height (and height, raised to the 2.7 power). Analysis of the varying independent measures and relationships demonstrated that the "best fit" model was the exponential model using BSA, or what is also known as the allometric model. Landing on this manner of analysis is not just fortuitous happenstance- numerous other investigations have come to the same conclusion regarding the scaling of cardiovascular structures. It is interesting to note that other recently published z-score data landed on a unique and quite different model (nonlinear polynomial fit).

Considering their allometric model, the scaling exponents of each of the coronary arteries calculated in this analysis are quite similar, but are *not* identical. Also, the scaling exponents are all very near 0.4-- not 0.5 as might be predicted by the theory of dimensional consistency (*linear* measurement of the coronary artery scaled to body surface *area*, i.e., cm vs. cm^{2}). Actually, this comes as no surprise, given that the true nature of the relationship is (probably) a complex cascade between lean body mass, cardiac output, wall tension, and LV mass. Imperfect estimations of BSA are only peripherally related to some of these factors. It makes me wonder what the relationship would look like if we scaled/standardized the coronary artery diameters to LV mass instead of BSA.

Comparing this data to prior work, the authors note a very close correlation with the data from Boston, and they very politely admit some similarities to the data from Singapore (although, to be fair to the Singapore analysis it should be noted that they sought to make an internally standardized reference- indexing to the aorta- and thus their treatment of the relationship to BSA is not very robust). The authors have already done their own "smackdown" and their graphic comparison of the CNMC and Boston data is unsurprising. Moreover, the models and scaling exponents are remarkably similar. Here are the two LMCA prediction equations:

CNMC*:

Boston:

* note: the CNMC equation is the alternate/equivalent form of their published equation: ln(M) = beta_{1} + beta_{2} x ln(BSA)

If we discount the Boston y-intercept of -0.02887, as being so small as to be very nearly zero ( or, "not significantly different from zero"), the equations become all the more similar. We are then left with the primary difference between the z-score predictions being: the manner in which they deal with variance. The Boston group attempts to predict the standard deviation by a second regression equation, and the CNMC group takes the approach, now currently in vogue, of substituting the regression RMSE as the SD. The validity of either approach could(should?) probably be debated…

In the words of the authors:

Having a readily available Z-score calculator will be invaluable

Give it a go at ParameterZ.com.

I admit to taking a few liberties with this calculator: I convert the measurements to mm; I use the Haycock BSA formula rather than DuBois & DuBois (can't we just agree to do this already?); I use the 5th and 95th percentiles (± 1.65 SD's) for the limits on the range of normal values.

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