New Coronary Artery Z-Score Calculator

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. cm²). 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) = beta₁ + beta₂ 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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Coronary Artery Z Score Regression Equations and Calculators Derived From a Large Heterogeneous Population of Children Undergoing Echocardiography.

Laura Olivieri, Bob Arling, Mark Friberg, Craig Sable. Journal of the American Society of Echocardiography December 2008 (Article in Press DOI: 10.1016/j.echo.2008.11.003)

Theoretical and empirical derivation of cardiovascular allometric relationships in children.

Sluysmans T, Colan SD. J Appl Physiol. 2005 Aug;99(2):445-57. Epub 2004 Nov 19.

Allometric analysis of the association between cardiac dimensions and body size variables in 464 junior athletes.

George K, Sharma S, Batterham A, Whyte G, McKenna W. Clin Sci (Lond). 2001 Jan;100(1):47-54.

Derivation of a size-independent variable for scaling of cardiac dimensions in a normal adult population.

Neilan TG, Pradhan AD, Weyman AE. J Am Soc Echocardiogr. 2008 Jul;21(7):779-85. Epub 2008 Mar 10.

Does size matter? Clinical applications of scaling cardiac size and function for body size.

Dewey FE, Rosenthal D, Murphy DJ Jr, Froelicher VF, Ashley EA. Circulation. 2008 Apr 29;117(17):2279-87. Review.

Regression Equations for Calculation of Z Scores of Cardiac Structures in a Large Cohort of Healthy Infants, Children, and Adolescents: An Echocardiographic Study.

Pettersen MD, Du W, Skeens ME, Humes RA. J Am Soc Echocardiogr. 2008 Aug;21(8):922-34. Epub 2008 Apr 11.

A Novel Method of Expressing Left Ventricular Mass Relative to Body Size in Children.

Foster BJ, Mackie AS, Mitsnefes M, Ali H, Mamber S, Colan SD. Circulation. 2008 May 27;117(21):2769-75. Epub 2008 May 19.

Coronary artery involvement in children with Kawasaki disease: risk factors from analysis of serial normalized measurements.

McCrindle BW, Li JS, Minich LL, Colan SD, Atz AM, Takahashi M, Vetter VL, Gersony WM, Mitchell PD, Newburger JW; Pediatric Heart Network Investigators.
Circulation. 2007 Jul 10;116(2):174-9. Epub 2007 Jun 18.

Coronary normograms and the coronary-aorta index: objective determinants of coronary artery dilatation.

Tan TH, Wong KY, Cheng TK, Heng JT. Pediatr Cardiol. 2003 Jul-Aug;24(4):328-35. Epub 2002 Sep 25.