T he Japan Society of Ultrasonics in Medicine (JSUM) published standard values of ultrasonic measurements of Japanese fetuses in 2003 [1]. Te pub- lished regression formulae for the standard values of bi-parietal diameter (BPD), abdominal circumference (AC), femur length (FL), and estimated fetal body weight (EFBW) have been widely used in the practice of medicine. Te regression formulae are cubic functions of time, but the biological or biomathematical reasons behind those functions remain unclear. When the ges- tational days beyond the domain of defnition are applied to the published formulae, the EFBW can be less than zero. Tis means that the formulae do not explain the biological phenomena but merely show the regression. We believe that phenomena in nature should be described by mathematics as much as possible. Te phenomena in medicine should thus be described by mathematical formulae such as diferential equations Acta Med. Okayama, 2018 Vol. 72, No. 2, pp. 115-119 CopyrightⒸ 2018 by Okayama University Medical School. http: // escholarship.lib.okayama- u.ac.jp / amo/ Original Article Formulae Based on Biomathematics to Estimate the Standard Value of Fetal Growth of Japanese Yasunari Miyagi a,b ＊ , Katsuhiko Tada c , Riko Takayoshi d , Nobutsugu Oguni d , Yasushi Sato d , Maki Shibata d , Machiko Kiyokawa d , Tadashi Hashimoto d , Tomoyoshi Takada d , Takashi Oda d , and Takahito Miyake d a Department of Gynecology, Miyake Ofuku Clinic, Okayama 701-0204, Japan, b Medical Data Labo, Okayama 703-8267, Japan, c Department of Obstetrics and Gynecology, Okayama Medical Center, Okayama 701-1192, Japan, d Department of Obstetrics and Gynecology, Miyake Clinic, Okayama 701-0204, Japan We devised biomathematics-based formulae to estimate the standard values of fetal growth of Japanese afer 22 weeks’ gestation. Te growth rates of bi-parietal diameter (BPD), abdominal circumference (AC), femur length (FL), and estimated fetal body weight (EFBW) at the time of gestation were assumed to be proportional to the product of the value at the time and the rest value of an unknown maximum value, respectively. Te EFBW was also assumed to follow a multiple logistic function of BPD, AC and FL to ft the standard values of Japanese fetuses published by the Japan Society of Ultrasonics in Medicine. Te Mann-Whitney test was used for statisti- cal analysis. Te values as a function of gestational day, t, were as follows: BPD(t) = 99.6/(1 + exp (2.725 − 0.01837 ＊ t)) (mm); AC(t) = 39.7/(1 + exp (2.454 − 0.01379 ＊ t)) (cm); FL(t) = 79.6/ (1 + exp (2.851 − 0.01710 ＊ t)) (mm); EFBW(t) = 8045.1/(1 + exp (6.028 − 0.06582 ＊ BPD(t) − 0.1469 ＊ AC(t)+ 0.07377 ＊ FL(t))) (g). EFBW as a function of BPD, AC and FL was as follows: EFBW = 8045.1/(1 + exp (4.747 + 0.02584 ＊ BPD + 0.1010 ＊ AC − 0.1416 ＊ FL)) (g). When the BPD, AC and FL were at −2 standard deviation (SD), −1SD, mean and + 2SD, the EFBW values calculated by the formula were statistically closer to the standard values than conventional formulas with p-values of 4.871 × 10 −7 , 4.228×10 −7 , 9.777×10 −7 and 0.028, respec- tively. Te formulae based on biomathematics might be useful to estimate the fetal growth standard values. Key words: fetal growth, formulae, biomathematics, Japanese, ultrasound Received July 7, 2017 ; accepted November 6, 2017. ＊ Corresponding author. Phone : +81-86-281-2020; Fax : +81-86-281-7575 E-mail : ymiyagi@mac.com (Y. Miyagi) Confict of Interest Disclosures: No potential confict of interest relevant to this article was reported.