An analysis of the Pediatric Heart Network public database
Z-scores for the sinuses of Valsalva, sinotubular junction and ascending aorta from a model of about 3,200 healthy children in the Pediatric Heart Network public database, adjusted for height, build, age and sex, with side-by-side comparison to published pediatric references, including PHN, Mahgerefteh and Lauzon-Schnittka.
The same child and measurements under other published or derived normalization methods. Each method has its own reference group and age range. The PHN z-score uses the published PHN Echo Z-Score Project table for all ages; the Mahgerefteh values were recomputed in children 2 years and older. Lauzon-Schnittka comes from a large multicenter clinical cohort that included overweight and obese children; clinical measurements by many readers give a wider normal range than core-lab measurements.
CSA/ht = π × (diameter ÷ 2)² ÷ height (cm²/m). For the CSA/ht methods, the mean comes from the age-group table or from a regression on age and sex, and the SD always comes from the age-group table. The coefficients in the published supplement spreadsheet differ from a regression refit on the same public PHN data, so both are shown.
Every method here shares one limit, as does any z-score calculator built from healthy children: almost no reference child falls beyond z ±4. Past that point, z-scores depend on assumptions about the tail rather than on data, which is why the methods diverge for a severely dilated aorta. The percent of expected does not depend on those assumptions.
| Level | Expected diameter | Effect on z |
|---|
Effects are compared with a child of typical weight for the same height. Typical weight is the smoothed average weight for height in the PHN reference group (healthy, non-obese children). Children who are lean for their height have slightly smaller aortas; above typical weight, the expected diameter barely changes.
Each z-score answers one question: how unusual is this diameter for a healthy child of the same size, build, age and sex? The model answers it in three parts, the same three used to build growth charts (the LMS method): where the middle is, how wide the spread is, and what shape the distribution has. It is fit separately for each level of the aorta.
The median diameter comes from log height, weight for height, age and sex. Height enters as a smooth curve rather than a fixed exponent, so the model can follow growth that is slower than body length in toddlers (an exponent near 0.75) and close to proportional in adolescence (near 0.95). Weight for height compares the child's weight with the typical weight for their height in the same reference group: lean children have slightly smaller aortas, and weight above typical changes little. Once size is known, age and sex add only small effects. Every effect is multiplicative, so it changes the expected diameter by a percentage, the same at every size.
σ is close to a coefficient of variation: the typical scatter of healthy diameters as a fraction of the median, about 8 to 11%. It is a smooth function of height and is slightly larger in infants, partly because a 1 mm rounding step is a bigger fraction of a small aorta.
λ (the Box-Cox power) describes how the distribution stretches in its tails, and it is estimated from the data rather than assumed. λ = 0 means diameters are log-normal: being twice the median counts the same at any size. λ = 1 means each extra millimetre counts the same, the assumption behind ratio z-scores such as diameter ÷ BSA^0.5. λ = 2 is the scale of an area, such as CSA/ht. The data put the sinuses near 0 (log-normal) and the sinotubular junction and ascending aorta near 0.4, and rule out 2 for all three. Near the middle the choice barely matters; for a severely dilated aorta it can change z by a factor of two, which is why it is fitted here.
| Level | Children | λ | σ (spread) | Male vs female |
|---|
D is the measured diameter and M the predicted median. When λ is 0, the formula becomes ln(D ÷ M) ÷ σ. The second formula turns any z back into millimetres; it draws the scales and gives the normal range (z −2 to +2).
Percent of expected is 100 × D ÷ M, the same idea as percent predicted in pulmonary function testing and in the athlete equations of Herrera-Leaño et al. It does not depend on λ or σ, so it is the steadier number for describing and following severe dilation, where z-scores from different methods diverge.
Without a weight, the calculator uses the same kind of model built from height and sex only.
Healthy, non-obese children from birth to 18 years in the NIH/NHLBI Pediatric Heart Network Echo-Z/Normal ECG public use dataset (core-lab measurements, 19 centers). Data cleaning is described below.
In the reference group, z-scores have mean 0 and SD 1 in every height decile and age group, with no remaining trend against height, age, weight, BMI or sex, and 2.1 to 2.6% of children beyond ±2 on each side (2.3% expected). Royston–Wright Q-tests across height groups show the spread (σ), skewness (λ) and kurtosis behaving as intended at every size, except slightly heavy tails at the sinotubular junction.
Records were screened in two stages, and only clear errors were excluded, never values that were merely unusual.
Body size. Weight for height was computed for every child, and records far outside the reference range were reviewed. Five combinations that are not physiologically possible in a healthy child (for example, a newborn recorded at 71 cm, and a 7.7-year-old at 134 cm and 15 kg) were excluded from all three models.
Measurements. After a first fit, the largest |z| values at each level were reviewed. A reading was excluded only when it was implausible and isolated to one level while the other levels in the same child were normal: one sinotubular junction (13 mm in a 172 cm adolescent, z −6.6) and two ascending aortas (12 and 13 mm in children about 140 cm tall, z −4.0 to −4.7, with normal sinuses and sinotubular junction). A child who was large at all three levels (z about +3.5 throughout) was kept, because agreement across levels points to real anatomy.
In total, 5 of 3,215 records were excluded from all models, and 3 single measurements from one level each. Removing them did not change the main findings. They mattered most for the shape: the two ascending aorta readings alone moved λ from 0.48 to 0.37 and accounted for the skewness and kurtosis flags in the Q-tests.
Self-test. Running…
Fit in R with the gamlss package (Box-Cox Cole-Green family, P-spline smooths), exported as lookup tables and interpolated in the browser.
Calibration is close to exact out to about z ±2.5. Beyond ±3, about twice as many reference children fall in each tail as a normal distribution predicts (roughly 8 instead of 4 per tail), so z-scores there are approximate; past about ±4 they extend the fitted shape rather than the data, and the percent of expected is the more robust measure. The sinotubular junction has slightly heavier tails than this model assumes, so extreme STJ z-scores should be read with some care. The reference group excluded obesity, so results for children well outside the reference weight-for-height range are extrapolations. Diameters were recorded to the nearest millimetre; in newborns, 1 mm moves z by about 1. The dilation bands follow the AHA scientific statement on aortopathy in children (normal < 2, mild 2 to < 3.5, moderate 3.5 to < 5, severe ≥ 5), applied to this model's z. For research and education; it does not replace clinical judgment.