J Clin Ultrasound 20:321327, June 1992 0 1992 by John Wiley & Sons, Inc. CCC 0091-2751/92/050321-07 $04.00

Mathematical Modeling of Fetal Splenic Growth: Use of the Rossavik Growth Model Toshiyuki Hata, MD, PhD,* Russell L. Deter, MD,? Showa Aoki, MD,* Ken Makihara, MD,* Kohkichi Hata, MD, PhD,* and Manabu Kitao, MD, PhD*

Abstract: Growth of the fetal spleen has been monitored by measurements of the maximal length (SL), profile circumference (SC), and profile area (SA) of the spleen, from 20 weeks to 41 weeks, menstrual age. Growth curves for these parameters have been determined using a specially developed growth curve model [P = c(tjk s'tll. R2 values of 94.3%, 94.9%, and 96.3%were obtained for SL, SC, and SA, respectively. Variability analysis indicated some progressive increase in variability with menstrual age for these three parameters. Variability data were used with the growth curve models to determine standard curves for SL, SC, and SA. These standard curves provide a superior means for evaluating the normal splenic growth in the fetus and for identifying splenic abnormalities in utero. Indexing Words: Fetus Normal growth * Splenic length Splenic circumference * Splenic area * Rossavik model +

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Fetal splenomegaly occurs in cases of congenital transplacental infections, hematologic diseases, immunological disorders, and lipidoses.' Moreover, a hypoplastic spleen is often found in cases of DiGeorge syndrome and sickle cell disease.2 Therefore, the measurements of fetal splenic size should be a useful diagnostic tool in the detection of congenital splenic abnormalities in utero. Rossavik and Deter3. have investigated a new model for the assessment of fetal growth that potentially has significant advantages over models studied in other investigations. To evaluate this model's ability to characterize the growth processes of fetal organs, we reinvestigated the growth of splenic parameters, namely the maximal length (SL), profile circumference (SC), and profile area (SA), using this model. MATERIALS AND METHODS

As described p r e v i ~ u s l y splenic ,~ measurements were obtained from 229 pregnant Japanese women whose menstrual age (MA) ranged from From the *Department of Obstetrics and Gynecology, Shimane Medical University, Izumo, Japan, and ?Department of Obstetrics and Gynecology, Baylor College of Medicine, Houston, Texas. For reprints contact Toshiyuki Hata, MD, PhD, Department of Obstetrics and Gynecology, Shimane Medical University, Izumo 693, Japan.

20 weeks to 41 weeks. All patients had regular menses and a known date of onset of the last menstrual period (LMP). The MA calculated from the first day of the LMP agreed with those determined from the crown-rump length6 in the first trimester, or biparietal diameter6 and femur diaphysis length7 in the early second trimester. Only one set of measurements from each fetus was used. All infants were delivered vaginally and birth weights were in the normal range (between the 10th and 90th percentiles) of the standard weight growth curve for the Japanese.' The methods used to obtain SL, SC, and SA measurements have been described in detail e l ~ e w h e r e .In ~ the transverse view of the fetal abdomen, the fetal spleen was identified as a well-circumscribed triangular or crescent figure, posterior to the stomach and lateral to the left adrenal gland. The echoes of the spleen were homogenous and hypoechoic. The SL, SC, and SA were measured using a microcomputer with a digitizer. These measurements were made by one of us (SA). The instruments used in this study were Aloka SSD-256 (3.5 MHz) and Aloka SSD650 (3.5 MZ). The coefficient of variation of SL, SC, and SA were 2.1%,3.3%, and 3.7%, respecti~ely.~ As described in detail by Rossavik and Deter,4 plotting of data, regression analysis, and calculation of descriptive statistics were carried out us321

HATA ET AL.

322

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g k

14.0t 10.5+ -

* 6

-

+4

-

e

Ef

-

0

k . . i

V V

. . i

c

l.O+ -

-

W 4

-

a

3.5+

wl

-

8 --+---------+---------+---------+---------+---------+----

20.0

24.0

28.0

32.0

36.0

40.0

Menstrual Age (weeks)

B

N

-e 0

c 0, 4

a wl

C

Menstrual Age (weeks)

FIGURE 1. (A) The splenic length ISL), (B) splenic circumference (SC), and ( C ) splenic area (SA). Plot of data points and regression curve. Single values are indicated by asterisks and multiple values by the appropriate numbers.

JOURNAL OF CLINICAL ULTRASOUND

MATHEMATICAL MODELING OF FETAL SPLENIC GROWTH

ing the Minitab statistical p r ~ g r a mFor . ~ the regression analysis the logarithmic form of the Rossavik equation [P = c(tjk '@'I was used: +

log, P

=

log, c

+ k log, t + st log,

t

in which P is anatomic parameter, k, c, and s the model coefficients, and t the duration of growth calculated from the estimated start point (SP) of the growth curve3:

t=MA-SP in which MA is duration of pregnancy in weeks calculated from first day of LMP. The SP chosen was 6 weeks from the LMP for SL, SC, and SA, based on embryological studies." RESULTS

Figures l A , lB, and 1C are plots showing the distributions of data points for SL, SC, and SA, respectively. Equations describing the change in SL, SC, and SA as a function of MA were obtained using the method of least squares (Table 1). High R2 values (94.3%, 94.9%, 96.3%) were found for these three parameters, indicating that the model adequately represents the experimental data. Coefficients of variation (CV = SD/ Mean x 100) were also calculated for k, s, and c for each parameter (Table 1). They showed that the estimates of the coefficients for these three functions were determined with similar accuracy. Student's t test showed that all the values of k, s, and c for these three parameters differed from zero ( p < 0.001). The weekly predicted values calculated using the equation's for SL, SC, and SA are given in Table 2.

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Differences (deviations) between measured values and the predicted values given by the regression equations for SL, SC, and SA are shown in Figure 2A. 2B. amd 2C, respectively. For all three parameters, variability slightly increases with MA (and increasing predicted values of SL, SC, and SA). This time dependency could be eliminated by expressing the deviations as a percentage of the expected values4 (Figures 3A, 3B, and 3C). The nearly uniform distribution of the percentage deviations thoughout pregnancy suggests that the limits of normal variability may be calculated using this ~ a r a m e t e rThe . ~ mean ? SD values of percent deviations for SL, SC and SA were 0.1% ? 7.3%, -0.6% 2 7.2%,and 0.7% 12.8%, respectively. Two standard deviations above and below the predicted value (PV), using the percent deviations, were chosen as the upper and lower limits of the normal range (Table 2). Limit values (LV) were calculated using the following expression4:

*

LV = PV 5 (PV) (2 SD)/100 = PV (1 k 2 SDi100) DISCUSSION

It is important that the growth of different parts of the fetal body are described by the same type of mathematical model because this makes quantitative comparisons of growth and shape changes p ~ s s i b l e The . ~ Rossavik model used in this investigation gave good fits for SL (R2 = 94.3%).SC (R2 = 94.9%),and SA (R2= 96.3%). By comparison, Aoki et al.5 required the use of three different types of mathematical models to characterize the growth of SL (R2 = 92.7%), SC (R2 = 93.9%),and SA (R2 = 95.2%).The results of Schmidt et a1.' were similar to those of Aoki et

TABLE 1 Characteristics of Rossavik Growth Equations for the Splenic Length (SL), Profile Circumference (SC), and Profile Area (SA) ~~

Parameter

Coefficient

Mean

SD

cv %

SL

k S C

2.3091 -0.01207 0.00531

+O.1321

1.9775 -0.008202 0.03039

+0.1284 t0.001295 +0.00265

6.5 - 15.8 8.7

3.8511 -0.014645 0.0000644

?0.2248

5.8 -15.5 5.5

+0.001331 +0.00032

S C

S C

"SP: start point. VOL. 20. NO. 5,JUNE 1992

*0.002266 +0.0000035

SP" wk

%

94.3