Parturition is the act of giving birth. While not usually considered as catastrophic, it is arguably the major event in a life (apart from its termination) and it is interesting that our theoretical approach extends to this situation. This is maybe not so surprising in view of the commonalities with the previous examples.
Can we predict parturition? Notwithstanding the large number of investigations on the factors that could trigger parturition in superior mammals (monkeys and humans), we still do not have a clear signature in any of the measured variables. This is to be contrasted to the situation for inferior mammals such as cats, cows, etc, for which the secretion of a specific hormone can be linked unambiguously to the triggering of parturition.
Knowledge of precursors and predictors of human parturition would be important both for our understanding of the controlling mechanisms and for practical use for detection and diagnostic of various abnormalities of birth process. They involve a multitude of genetic, metabolic, nutritional, hormonal and environmental factors. Present research is however hindered by the lack of a clear recognized correlation between the time evolution of these various variables with the initiation of parturition.
In collaboration with a team of obstetricians, we have proposed [Sornette et al., 1994] a coherent logical framework which allows us to rationalize the various laboratory and clinical observations on the maturation, the triggering mechanisms of parturition, the existence of various abnormal patterns as well as the effect of external stimulations of various kinds. Within the proposed mathematical model, parturition is seen as a ``critical'' instability or phase transition from a state of quietness, characterized by a weak incoherent activity of the uterus in its various parts as a function of time (state of activity of many small incoherent intermittent oscillators), to a state of globally coherent contractions where the uterus functions as a single macroscopic oscillator leading to the expulsion of the baby. Our approach gives a number of new predictions and suggests a strategy for future research and clinical studies, which present interesting potentials for improvements in predicting methods and in describing various prenatal abnormal situations.
We have proposed to view the occurrence of parturition as an instability, in which the control parameter is a maturity parameter (MP), roughly proportional to time, and the order parameter is the amplitude of the coherent global uterine activity in the parturition regime. This idea is summarized by the concept of a so-called supercritical ``bifurcation''. This simple view is in apparent contradiction with the extreme complexity of the fetus-mother system, which can be addressed at several levels of descriptions, starting at the highest level from the mother, the fetus and their coupling through the placenta. For example, in the mother, the myometrium plays an important role in pregnancy, maturation and onset of labor. It is now well-established that the human myometrium is an heterogeneous tissue formed of several layers which differ in their embryological origin and which exhibit quite different histological and pharmalogical properties. In the uterine corpus, one must distinguish the outer (longitudinal) and the inner (circular) layers. These two layers composed mainly of smooth muscle cells are separated by an intermediate layer containing a large amount of vascular and connective tissues, but poor in smooth muscle cells. The inner and outer muscle layers have different patterns of contractility and differ in their response and sensitivity to contractile and relaxant agents. This is just an example of the complexity which goes on down to the molecular level, with the action of many substances providing positive and negative feedbacks evolving as a function of maturation. The basis of our simple theory relies on many recent works in a variety of domains (mathematics, hydrodynamics, optics, chemistry, biology, etc) which have shown that a lot of complex systems consisting of many nonlinear coupled subsystems or components may self-organize and exhibit coherent behavior of a macroscopic scale in time and/or space, in suitable conditions. The Rayleigh-B\'enard fluid convection experiment is one of the simplest paradigm for this type of behavior. The coherent behavior appears generically when the coupling between the different components becomes strong enough to trigger or synchronize the initially incoherent subsystems. There are many observations in human parturition where an increasing ``coupling'' is associated with maturation of the fetus leading to the cooperative synchronized action of all muscle fibers of the uterus characteristic of labor.
Perhaps, the most vivid illustration of the increasing coupling as maturation increases is provided by monitoring the uterine activity, using standard external tocographic techniques. Away from term, the muscle contractions during gestation are generally weak and characterized by local bursts of activity both in time and space. Increasing uterine activity is observed when the term is approaching, culminating in a complete modification of behavior where regular globally coherent contractions reflects the spatial and time coherence of all the muscles constituting the uterus. The transition between the premature regime and the parturition regime at maturity is characterized by a systematic tendency to increasing uterine activity, both in amplitude, duration of the bursts and spatial extension of the activated uterine domains. The susceptibility of the fetus-mother system (to influence the uterine response) to external perturbations or stimulations seems to increase notably on the approach of parturition, since important modifications and reactions of the uterus may result from relatively small stimulii from the mother or fetus.
The main prediction is that, on the approach to the critical instability, one expects a characteristic increase of the fluctuations of uterine activity. Other quantities that could be measured and which are related to the uterine activity are expected to present a similar behavior. The cooperative nature of maturation and parturition proposed here rationalizes the present inability to establish unequivocally predictive parameters of the biochemical events preceeding myometrical activity and/or cervical ripening involved in preterm labor. Our theory suggests a precise experimental methodology in order to obtain an early diagnosis, essential for the efficient treatment of prematurity, which still constitutes the major cause of neonatal morbidity and mortality. In particular, monitoring muscle tremors or vibrations as a function of time of muscle fibers of the uterus would provide quantitative tests of the theory with respect to the spatio-temporal build-up of contractile fluctuations. Our theory also correctly accounts for the observations that external factors affecting the mother such as heavy work and psychologic stress are able to modify the maturity of the uterus measured by the progressive modification of the cervix and more frequent uterine contractions. These external factors, in addition to produce direct contraction stimulations, could also be able to modify the post-maturity parameter and control the susceptibility of the fetus-mother system to small influences which can trigger the change from discordant contrations to concordant contractions of a premature or post-mature labor.
We note finally that the whole policy for the description of risk factors has been based on an implicit and unformalized hypothesis of a critical transition which is explicited in our theoretical framework. The prevention program for preterm deliveries [Papiernik et al., 1984] was also based on the hypothesis of such a critical transition and the understanding that a small reduction of a triggering factor could be enough to prevent the uterus from beginning its critical phase of activity. The high susceptibility of the fetus-mother system to various factors is also at the origin of the fact that the conventional system of calculation of the risk factors does not explain the real success of the prevention which has been observed [Papiernik et al., 1984] . Effectively applied in France, our system, which is based on this idea of a critical transition, was able to reduce significantly the rate of preterm births for all french women measured on Haguenau population of pregnant women from 1971 to 1982, or on randomized samples of all french births.
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