Mathematical models of brachial plexus development during the fetal period: clinical aspects

The brachial plexus is an important anatomical structure. It can be damaged in both the perinatal and postnatal periods as a result of injury. The available literature does not provide much discussion of the development of the brachial plexus in human fetuses.

The goal of the study was a mathematical analysis of fetal brachial plexus growth and geometry.

The study examined 220 human brachial plexuses, derived from 110 fetuses (including 50 females - 45.45%) aged 14-32 weeks of fetal life, with a crown-rump length (CRL) ranging from 80 to 233 mm. Anthropological methods, preparation, digital image acquisition, the Image J measurement tool, the Scion Image for Windows program and statistical methods were applied. In each fetus, somatic as well as linear parameters were observed: lengths, diameters and distances between the nerves making up the brachial plexus geometry.

In the majority of the linear parameters analyzed, no sexual dimorphism or asymmetry were observed. The following asymmetries and sexual dimorphisms appear to be significant from the clinical point of view: asymmetry in the length of the C7 and Th1 nerve left radix, asymmetry in the diameters of the musculocutaneous nerve on the left and the median and ulnar nerves on the right; as well as an increased distance between nerves roots in female fetuses. The weekly growth of individual parts of the plexus varied, as did the correlation ratios among them. The most rapid growth was observed between the 14th and 18th weeks, and the slowest between the 24th and 28th weeks. Four formulae were used in the mathematical growth model: linear regression, logarithmic function, the von Bertalanffy growth model and the Gompertz curve.

The prenatal development of the brachial plexus is not constant. The applied mathematical functions proved useful in describing its growth rate.