Development of mathematical methods for calculation of the pubic arch angle

Hypothesis/aims of study. The frequency of adverse intranatal outcomes is significantly increased when the pubic arch angle (PAA) is less than 90°. The accuracy of the manual method for determining PAA depends on a large number of parameters, such as obesity of a woman, as well as stereometric sensation and the experience of a doctor. Determination of PAA using ultrasound and X-ray pelviometry is generally available and reliable; however, it requires special training. The aim of this study was to develop mathematical methods for calculation of PAA.

Study design, materials and methods. The study included a retrospective and prospective analysis of 120 birth histories based on the Regional Clinical Hospital Perinatal Center (the Chita city, the years 2017/2018), which were divided into three equal groups. Group 1 consisted of patients with body weight deficit, group 2 included patients with normal body mass index, and group 3 comprised patients with alimentary constitutional obesity. On the eve of the birth, external pelviometry, the manual method for determining PAA, and ultrasound pelviometry by translabial access were performed.

Results. PAA determined by the manual method was 99.6 ± 11.3° in group 1, 100.1 ± 14.2° in group 2, and 98.2 ± 10.7° in group 3. When ultrasound pelviometry was performed, the value of PAA was 97.4 ± 10.7° in group 1, 104.8 ± 13.8° in group 2, and 104.1 ± 12.3° in group 3. The error of the manual method was 2.2% in group 1, 4.5% in group 2, and 7.6% in group 3. On the basis of mathematical modeling of external pelviometry data, a pattern is defined, which is expressed by the formula: PAA = 180° – arccos (0,5 ∙ S₁S₂/S₁P) – arccos (0,5 ∙ B₁B₂/(B₂S₁ – S₁P), where PAA is the pubic arch angle (°); S₁S₂, Distantia spinarum; S₁P, the distance between the anterior superior spine of the ilium to the lower edge of the symphysis; B₂S₁, the distance between the anterior superior spine of the ilium to the tuberosity of the opposite ischium; B₁B₂, the transverse size of the output plane. The coefficient of determination (R-squared) is 0.82. Thus, mathematical modeling allows determining PAA with a high degree of reliability.