Computational and Mathematical Methods in Medicine

Volume 2019, Article ID 8276715, 13 pages

https://doi.org/10.1155/2019/8276715

## A Mathematical Model Relating Pitocin Use during Labor with Offspring Autism Development in terms of Oxytocin Receptor Desensitization in the Fetal Brain

1700 Shattuck Avenue, #114, Berkeley, CA 94709, USA

Correspondence should be addressed to Mark M. Gottlieb; moc.liamg@0102beilttog.kram

Received 16 January 2019; Accepted 7 June 2019; Published 11 July 2019

Academic Editor: Anna Tsantili-Kakoulidou

Copyright © 2019 Mark M. Gottlieb. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper develops a mathematical model describing the potential buildup of high oxytocin concentrations in the maternal circulation during labor in terms of continuous Pitocin infusion rate, half-life, and maternal weight. Oxytocin override of the degradation of oxytocin by placental oxytocinase is introduced to model the potential transfer of oxytocin from the maternal circulation across the placenta into the fetal circulation and from there into the brain of the fetus. The desensitization unit *D* equal to 1.8*E*6 (pg·min)/ml is employed to establish a desensitization threshold and by extension, a downregulation threshold as a function of oxytocin override concentration and continuous Pitocin infusion time, that could be a factor in the subsequent development of autism among offspring. Epidemiological studies by Duke University [1], Yale University [2], and Harvard University [3] are discussed regarding Pitocin use and offspring autism development for an explanation of the weak correlations they identified. The findings of the Harvard epidemiological study are reinterpreted regarding Pitocin use and its conclusion questioned. Further evaluations of the findings of these three epidemiological studies are called for to incorporate medical information on quantity of Pitocin used, continuous Pitocin infusion rate, length of labor, and maternal weight to determine if a correlation can be established with offspring autism development above an empirically determined desensitization threshold for Pitocin use. Suggestions for research are discussed, including an alternative to continuous Pitocin infusion, pulsatile infusion of Pitocin during labor induction, which may mitigate possible offspring autism development.

#### 1. Introduction

An epidemiological study by Duke University published in 2013 that was conducted in North Carolina found a modest association between labor induction and labor augmentation with the incidence of autism among the offspring [1]. This study also found a weak correlation between the use of Pitocin, artificial oxytocin, during labor and offspring autism development. Oxytocin receptor (OTR) desensitization followed by downregulation by oxytocin in the fetal brain was proposed as a possible cause of the offspring autism development. An epidemiological study in Denmark by Yale University published in 2015 found a mild association in males between use of Pitocin during labor augmentation and the incidence of autism among the offspring [2]. More recently, an epidemiological study by Harvard University published in 2016 investigated the association between labor induction and autism in Sweden and initially identified a weak correlation that could point to the use of Pitocin as a cause of the offspring autism development [3]. However, using a novel statistical approach involving a family model relating the incidence of autism with labor induction among the offspring of mothers with multiple offspring, the Harvard study concluded that there was no correlation between labor induction, and by inference, the use of Pitocin, and the incidence of autism among the offspring.

The objective of this paper is to provide a mathematical model relating the desensitization of oxytocin receptors (OTRs) in the brain of the fetus to the continuous infusion of Pitocin during labor and, by this mathematical model, demonstrate that for long labors having long Pitocin infusion times with high Pitocin infusion rates, desensitization of OTRs in the brain of the fetus may occur. Oxytocin receptor desensitization may be followed by downregulation of oxytocin receptors [4], which was a concern of the Duke University study as a possible factor causing the development of autism in offspring [1]. This paper demonstrates that autism attributable to OTR desensitization arising from the use of Pitocin would be shown not to occur for labor inductions that have usual time frames, which can go from six hours [5] to 12 hours or more for continuous Pitocin infusion [6].

However, this mathematical model does indicate that OTR desensitization may occur in some cases of long labor induction and long labor augmentation, in which high Pitocin infusion rates are administered over long labors with long Pitocin infusion times. OTR desensitization and subsequent downregulation may be associated with the development of autism [1]. Hence, the conclusion of the Harvard study may be in error, in that the outcome that they claim does not occur, no correlation of autism with labor induction, and may occur for high infusion rates of Pitocin with long Pitocin infusion times during long labor inductions. Extrapolating data from these epidemiological studies to the population of the United States, it is possible to infer from the findings of this study that several hundred to one thousand or more offspring a year may be at risk of developing autism, following the use of large quantities of Pitocin by their mothers at high infusion rates during long labors. This comes to 0.5% to 1.0% of the number of cases of autism occurring each year in the United States.

This model was developed by the author to follow an earlier paper [7], in which it was shown that doses of Pitocin of 6 mU/min administered during 12-hour labors were a factor of 10 below the OTR desensitization limit, and hence, autism attributable to OTR desensitization would not occur. However, the earlier paper did not consider the effects of high continuous infusion rates over the course of long labors with long Pitocin infusion times on OTR desensitization with possible offspring autism development, which this paper does.

#### 2. Development and Exposition of Mathematical Model

##### 2.1. Explanation of Figure 1

To understand the buildup of Pitocin in the maternal circulation from a mathematical perspective, it is important to note that the concentration of Pitocin in the maternal circulation increases as a function of the half-life of Pitocin. The half-life of Pitocin in the maternal circulation is an indication of the relative efficiency of the liver and kidneys in removing Pitocin from the maternal circulation. Higher half-lives indicate lower Pitocin removal efficiency. The graph in Figure 1 indicates the relationship of the half-life of oxytocin in the blood with the percent oxytocin removal by the liver and kidneys and the percent oxytocin remaining in the blood after the removal. The indicated removal and retention of oxytocin is for a one-minute cycle of the blood circulation.