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Different methods are used for aortic root dilatation in different papers (eg.diastolic versus systolic measurement, inner to inner or leading edge to leading edge diameters). One should take into account these differences in using the appropriate formula to calculate Z-scores. Aortic root refers to the measurement at the sinuses of valsalva.

1. Theoretical and empirical derivation of cardiovascular allometric relationships in children. J Appl Physiol 99:445-457, 2005.  Sluysmans T and Colan SD.

2. Nomograms for Aortic Root Diameters in Children Using Two-Dimensional Echocardiography. Am J Cardiol 2010  105: (6) 888-894. Gautier M, Detaint D, Fermanian C, Aegerter P, Delorme G, Arnoult F, Milleron O,  Raoux F, Stheneur C, Boileau C, Vahanian A, Jondeau G.

For children ages 2-18, using leading edge to leading edge during diastole (includes aortic wall thickness).

BSA formula (Dubois and Dubois formula)
BSA (m²) = 0.007184 x H^0.725 x W^0.425 with H height in cm, W weight in kg

Z-scores for diameters at the sinuses of valsalva in diastole and leading edge to leading edge (up to age 18)
Boys Z = [ln(d) - 3.1 - 0.49 x ln(BSA)] / 0.1
Girls Z = [ln(d) - 3.1 - 0.44 x ln(BSA)] / 0.09
With d = diameter in mm

Dan Dyar, Pediatric Cardiac Sonographer, has created a website that includes several convenient z-score calculators.  A Calculator that uses this formula can be found here. 

3. Boston data based formula: Validation and re-evaluation of a discriminant model predicting anatomic suitability for biventricular repair in neonates with aortic stenosis.  J Am Coll Cardiol. 2006 May 2; 47(9) :1858-65.   Colan SD, McElhinney DB, Crawford EC, Keane JF, Lock JE.

For up to age 25, systole, inner to inner edge.

Body surface area (Haycock formula)
BSA= 0.024265*(H^0.3964)*(W^0.5378) with H height in cm, W weight in kg 

Mean aortic root (cm) for BSA
AR (cm) = 2.06611*(BSA^0.5)

SD for aortic root
SD (cm) = 0.09864+ (0.11796*BSA)

Z-score
Z = (AR - (2.06611*(BSA^0.5)))/(0.09864+0.11796*BSA)
With AR root in cm

Dan Dyar, Pediatric Cardiac Sonographer, has created a website that includes several convenient z-score calculators.  A calculator that uses this formula can be found here.

4. Cornell data-based formulae Two-dimensional echocardiographic aortic root dimensions in normal children and adults. Am J Cardiol 1989;64(8):507-512.  Roman MJ, Devereux RB, Kramer-Fox R, O’Loughlin J.

For children and adults in different ranges of age, measured in diastole – leading edge to leading edge

BSA formula (Dubois and Dubois formula)
BSA (m²) = 0.007184 x H^0.725 x W^0.425 with H height in cm, W weight in kg

Age up to 15:
Mean predicted AR (cm) for BSA = 1.02 + 0.98*BSA
SD (cm) = 0.18 cm
Z = (Measured root diameter – predicted AR)/0.18

Age 20 to 40:
Mean predicted AR (cm) for BSA  = 0.97 + 1.12*BSA 
SD (cm) = 0.24 cm
Z = (Measured root diameter – predicted AR)/0.24

Age >40
Mean predicted AR (cm) for BSA = 1.92 + 0.74*BSA 
SD (cm) = 0.37 cm
Z = (Measured root diameter – predicted AR)/0.37.

Nomograms:

5. Regression Equations for Calculation of Z Scores of Cardiac Structures in a Large Cohort of Healthy Infants, Children, and Adolescents: An Echocardiographic Study. J Am Soc Echocardiogr 2008;21:922-934.  Pettersen MD, Du W, Skeens ME, Humes RA.

6. Prevalence and Correlates of Aortic Root Dilatation in Normotensive and Hypertensive Adults: The Family Blood Pressure Program.  Circulation 2009;120 (suppl 2):s540.  Richard B Devereux, Richard Cooper, Alan Weder, Todd B Seto, Craig Hanis, Thomas H Mosley, Jr, D C Rao, Donna K Arnett

7. Marfan syndrome in children and adolescents: an adjusted nomogram for screening aortic root dilation. Heart 1998;78:69–72.  Rozendaal L, Groenink M, Naeff MS, Hennekam RC, Hart AA, van der Wall EE, Mulder BJM.

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