## From the paper submitted to the BioMed Research International Journal...

ULTRASONOGRAPHIC FETAL GROWTH CHARTS: A QUANTITATIVE EVALUATION OF THE IMPACT OF ETHNICITY ON DIAGNOSES BASED ON A PRELIMINARY REPORT PERFORMED ON SALENTINIAN POPULATION.

The study includes a population of about 500 Italian women undergoing ultrasound examination between the 11th and 41th weeks of gestation, between November 2012 and September 2013. All pregnant were enrolled in a previously defined area, the southeast of Italy, in the Vito Fazzi Hospital, in Italy, and Departments of Obstetrics and Gynecology assessed the investigation. Gestational age was established by US imaging during the first visit, at study enrolment. All patients received written and oral information about the study, and they signed the informed consent.

Assuming that, at each gestational age, the measurement of interest has a Gaussian distribution with a mean and a standard deviation (SD) and that, in general, both vary smoothly with gestational age, a centile curve has been calculated using the well-known formula:

Centile = mean + K * SD

where K is the corresponding centile of the standard Gaussian distribution (for instance, determination of 10th and 90th centile curves requires that K = ± 1.28), mean is the mean and SD is the standard deviation of the mean of the fetal measurements for each gestational age. The mean has been estimated by the fitted values from an appropriate polynomial regression curve of the measurement of interest on gestational age. Several curve-fitting and smoothing techniques have been tested for the mean estimation of the different biometric parameters and the goodness of fit for each regression model has been carefully assessed. The polynomial model that better satisfies the experimental data is the cubic one, since it better fulfils with respect to the fractional polynomial and to the logarithmic transformations.

y = a + (b * GA) + (c * GA2) + (d * GA3)

When the measurement has approximately a Gaussian distribution, the fitted values following regression of the “scaled absolute residuals” on age are estimate of the SD curve. These residuals are the differences between the measurements and the estimated curve for the mean with the sign removed and multiplied by a corrective constant equal to √π/2 = 1.253. Generally, if the scaled absolute residuals appear to show no trend with gestational age, the SD is estimated as the standard deviation of the unscaled residuals (measurements minus the estimated mean curve). If there is a trend, then polynomial regression analysis is needed to estimate an appropriate curve in the same way of the mean. For BPD, HC and AC biometric parameters, the residuals were regressed on gestational ages by using a linear model in the form of:

yBPD,HC,AC = a + (b * GA)

while, for the FL parameter, the quadratic regression seems to better fulfill with respect to the linear one. The adopted equation is:

yFL = a + (b * GA) + (c * GA2)

Finally, these predictive mean and SD equations allow calculating any required centile, replacing the value in the centile formula.

Full biometric measurements (AC, BPD, FL, HC) were obtained for about 500 fetuses. Data analysis showed that neither the use of fractional polynomials (the greatest power of the polynomials being 3) nor the logarithmic transformation improved the fitting of the curves. Therefore, the data were kept in their original scale. The best-fitted regression model to describe the relationships between HC, AC, BPD, FL and gestational age was a cubic one, whereas other studies proved that a simple quadratic model fitted BPD and FL. Models fitting the SD were straight lines for BPD, HC and AC and quadratic line for FL.

The corresponding regression equations, with the respective R2 index (which is the linear determination index that takes values between 0 and 1 and is approaching the more than 1 as the interpolating curve approaches to real data), for the mean and the standard deviation are illustrated below. The relevant centile (5th, 10th, 50th, 90th, 95th) representing respectively the HC, the BPD, the AC and the FL, are reported in Tables 2, 3, 4 and 5. In each table is also indicated the sample number, the mean and the standard deviation related to each gestational week.    In order to validate the system, authors have performed an initial technical test with a growth curve simulator able to respect the mean and the standard deviation that characterize the Gaussian distribution for a specific patient age. The generated data allowed authors to prove the correctness of the elaboration of the fetal growth curves model. After this preliminary analysis, authors have performed a test on the field considering about 500 US pictures related to Italian women undergoing ultrasound examination between the 11th and 41th weeks of gestation at Vito Fazzi Hospital - Lecce, between November 2012 and September 2013. Measurements of Biparietal Diameter (BPD), Head Circumference (HC), Abdominal Circumference (AC) and Femur Length (FL) were obtained by means of various obstetric US equipment. The obtained curves were then compared with those developed by Giorlandino et al. in 2009 as reference growth curves for the Italian population, and those developed by Johnsen et al. in 2006 as reference growth curves for the European population, in order to verify possible differences due to statistic methodology, selection criteria or, possibly, true genetic variability of the studied population. The AC and HC biometric parameters seem to follow more or less the same Italian and European trend according to the gestational age. In fact, no significant differences were observed in the values measured during the different growth stages. Considering the BPD and the FL parameters, instead, they present a little variability. As shown in Figure 2 and Figure 3, the Salentinian BPD values are always up for about 6 mm and FL ones are always greater then 7 mm.  The other biometric parameters are, instead, very similar.  This variability may be better presented by means of scatterplot of Salentinian samples overlapped with the centile curves to verify the amount and the density of the samples that are outside the considered range. Considering the Italian reference centile curves depicted in Figure 6, which represent respectively the 5th, 10th, 25th, 50th, 75th, 90th and 95th, the Salentinian samples are always above the upper limit especially in the last weeks of gestation. Similarly for the other biometric parameters:   Samples above the 95th centile are traditionally used to define large for gestational age (LGA), and the usage of such Italian reference curves on a Salentinian fetus could lead to misdiagnosis. To examine in a quick way one or more sets of data graphically box plots can be used. They can be useful to indicate the degree of dispersion (spread) and skewness in the data, and to identify outliers. Each plot depicts the five-number summaries for each biometric parameter, namely the minimum and maximum values, the upper (Q3) and lower (Q1) quartiles and the median. The variability present in the FL parameter can be also observed in this kind of graph, which consider more population groups.    This variability has to be medically investigated since it can be due to several reasons: equipment or measurement errors, genetic variability of the analysed population, racial factors, … In any case, the measured variability is useful to demonstrate the effectiveness of the proposed approach.

In order to quantify the impact of the adoption of wrong growth charts on fetal diagnoses, authors have analysed the samples’ trend for each biometric parameters and have then compared it with the Italian and European standard. Authors found significant differences between Salentinian FL growth plots and those reported by Giorlandino et al. for Italy and Johnsen et al. for Europe. Figure below (Fig. 14) describes this difference, representing the sample number and the percentage value for each biometric parameters (BPD, HC, AC and FL) which exceed the upper limit (95th centile) and the lower one (5th centile) considering the Italian and European reference curves. Our findings require that we should carefully re-examine the appropriateness of continued use of currently adopted reference growth curves to classify neonates SGA, LGA, and AGA. In fact, considering for example the Femur Length parameter, Salentinian fetuses present bigger values with respect to those of Italian (26% of Salentinian samples are upper the 95th centile) and European (46% of Salentinian samples are upper the 95th centile)