Fetal Cerebellar Growth Curves Based on Biomathematics in Normally Developing Japanese Fetuses and Fetuses with Trisomy 18

We used biomathematics to describe and compare cerebellar growth in normally developing and trisomy 18 Japanese fetuses. This retrospective study included 407 singleton pregnancies with fetuses at 14-39 weeks of gestation and 33 fetuses with trisomy 18 at 17-35 weeks. We used ultrasonography to measure fetal transverse cerebellar diameter (TCD) and anteroposterior cerebellar diameter (APCD). We hypothesized that cerebellar growth is proportional to cerebellar length at any given time point. We determined the formula L(t) ≒Keat+r, where e is Napier’s number, t is time, L is cerebellar length, and a, K, and r are constants. We then obtained regression functions for each TCD and APCD in all fetuses. The regression equations for TCD and APCD values in normal fetuses, expressed as exponential functions, were TCD(t)=27.85e0.02788t−28.62 (mm) (adjusted R2=0.997), and APCD(t)=324.29e0.00286t−322.62 (mm) (adjusted R2=0.995). These functions indicated that TCD and APCD grew at constant rates of 2.788%/week and 0.286%/week, respectively, throughout gestation. TCD (0.0153%/week) and APCD (0.000430%/week) grew more slowly in trisomy 18 fetuses. This study demonstrates the potential of biomathematics in clinical research and may aid in biological understanding of fetal cerebellar growth.