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Study and Validation of a Model
of Fetoplacental Circulation

> Abstract

The fetoplacental blood circulation has been object of interest for several years. The placenta can support life and feeding of the fetus during the pregnancy: it grows up with it, and concludes its functions at the childbirth. In particular it replaces the breathing organs, it allows the exchange of food and of waste substances, also driving the temperature of the fetus, when the central nervous system still cannot provide this function. Anyway final answers to many questions are still pending.
For instance the microscopic structure of the placenta during the pregnancy and the internal distribution of the blood flow have not yet been totally clarified.
More complex questions, clearly not yet easy to analyse, regard the exchange of organic substances. Answers to these questions, if reliable enough, could clarify the disputes concerned with the fetal blood oxygenation and about the causes of many pathologies of pregnancy, still with unknown aetiology.
Presently the knowledge concerning problems as IUGR (Intra-Uterine Growth Retardation), toxicology and teratology, is still lacking in sound experimental confirmations. Moreover the clinic research doesn't allow to stride along this direction because, for ethical reasons, invasive experiments over the fetus are not proposable.
Speaking about indirect measurements, the Doppler velocimetry made it possible to describe the blood flow characteristics of the fetal side and of the maternal side of the placenta, but the presently available instruments can afford measurements affected by tolerances reaching 35% and, quite important, the reliability of the results is depending by the competence of the operator.
Research adopting direct measurement techniques, drugs and radio-active substances have been done on animals, but the results are not convincing: it was better discovered that each animal species developed a different type of circulation, during the evolution. Anyway a certain resemblance between the human and the ovine placenta has been observed.

The target of this work is to study the fetoplacental circulation through a model that has been designed mainly on the basis of the actual knowledge about the placental vessels. The most interesting point is the possibility to apply the model to modern systems of clinical analysis, to perform medical examinations able to early detect some pathologies of the pregnancy. This study was supported by the design and realization of perfusion techniques that allowed the verification of the hypothesis that were introduced into the theoretical model.
The experimentation involves technical problems, also because the placenta is the junction of two different but partially interdependent organisms, and each of them can influence its functioning.
Anyway, during the experimentation, several clinical variables can be easily controlled: this allows to neglect some of them, simplifying the starting hypothesis, and to analyse separately some other ones. Figure n.1 shows the variables involved for the mass exchange during the pregnancy.

Figure 1
However, the clinical application of the data previously obtained through the experimentation came across several problems: technical limitations and too heavy simplifications of the conditions leaded to results affected by a high level of uncertainty.
The lack of data in the scientific literature, both regarding the placental morphology and the physical, mechanical characteristics of the tissue, is an other encountered problem.
A contribution in this direction was the possibility to perform in vitro experimentation. It regards the study, the set-up and the verification of systems able to keep the placenta alive after the child-birth, to be able to perform a measurement of the morphological parameters simulating the presence of a physiologic fluidodynamical condition.
Then two techniques of placental perfusion (using bovine blood and formaline) will be described. The description regards both the instrumentation and the testing protocol, such that all the laboratory trials are reproducible.
The goals of these two series of experiments are different. The first one, with blood, is aimed at the study of the fluidodynamics of placental vessels, while the second one wants to "fix" the vessel structure to prepare it for a following morphometrical examination.
Afterwards a critical comparison between the obtained data and already available data is done, to realise and verify a model of circulation of the fetal placenta.
A model allows to define relationships among the involved variables. As the complexity of a biological system could hinder its detailed description, a model generally starts analysing only a part of it. Some partial models are introduced, then they are verified through experimental observations and eventually corrected, in order to be completed taking in consideration other variables, firstly not considered.
The possibility of foreseeing serious fetal pathologies from the variation of some variables is a need of the medical field. Sometimes a model can help the medical staff to express well-timed diagnosis before the child-birth.

This thesis is composed by four parts:
The first part briefly describes the placental physiology and some pathological conditions, and the diagnosis instruments.
The second part takes in examination the realized perfusion systems, dwelling on the testing protocol. Our experimentation has been carried out at the gynaecology and obstetrics ward of the San Paolo hospital, Milan, in collaboration with the medical staff.
The third part is dedicated to the analysis of a simulation model of the placenta.
To be clearer on problems that are not common to medicine and to engineering, we deemed it necessary to add a glossary in the fourth part, to explain the technical terms, with some conversion tables for units of measure currently used in medicine.

The goal of the study was not simply limited to the development of a model, but it took advantage of a prior huge experimentation that contributed to verify the hypothesis of placental working, suggesting methods of analysis and measurement of the vascular characteristics, up to now performed only in extremely partial way.
The first part is introductory, it is aimed to introduce the elemental concepts on placental physiology and morphology. In the second part of this work the experimentation executed at S. Paolo hospital, Milan, is described. It has been developed during about 50 sessions, and it permitted to develop and set-up a reliable and accurate method of research. This allowed to study and verify the characteristics of the human placenta fluidodynamics. Soon after the child-birth and the drawing the placenta was connected to a perfusion set, able to simulate the physiological perfusion condition at the 38st week of gestation. An oxygenator maintained the concentrations of oxygen and carbon dioxide of the blood at physiological level.
The circuit realized in this way allowed to perform a controlled perfusion, with known parameters about input and output flow. The perfusion fluid was bovine blood, with physical characteristics similar to the fetal blood ones, instead of alkaline solution, as done by other researchers.

Figure 2
The experiments, performed in this way, averaged a correct perfusion of the placental vessels during about 15 minutes, generally showing a first period of stability of the measured data.
The input flows of the tests ranged 100 to 220 cc/min (the physiological value is about 300 cc/min). The measured arterial pressure was quite variable from test to test: from 49 mmHg to 187 mmHg per 100cc/min, with an average of 99 mmHg/100cc/min. The venous pressure was close to the physiological value: 15 to 20 mmHg.
During the beginning of our experimentation the main difficulty we met with came from the attempt to supply the umbilical arteries with a flow close to the physiological one, because a very high pressure was generated for a condition of general constriction of the placental vessels. This phenomenon had already been observed by all the other researchers who attended to placental in vitro perfusion: they could not reach our flow values, not even using alkaline solution instead of blood. Moreover, as it is not possible to simulate the situation of the intervillous space, increasing the input flow (and the arterial pressure too) a sudden settling of the capillaries was obtained, breaking off the test.
The placenta showed also a strong reactivity to the carbon dioxide concentration: a value lower than the physiological one (40 mmHg) in the fetal side produces a sudden constriction, that breaks off the perfusion within less than 5 minutes from the beginning. Also the concentration of carbon-dioxide in the maternal side can produce important effects, so the experimentation cannot proceed correctly if the placenta floats in normal water.
A kind of transudation of serum is an additional reason of interest. It is evidenced by the progressive haematocrite increasing showed by the perfused blood. This phenomenon confirms that a placenta is also a "dialyzer" for its perfusion fluids.

Our perfusion circuit has been utilised also to perform a successive set of tests, using a solution with formaldehyde and glutaraldehyde instead of blood. This type of 'fixing' perfusion has been extended averaging 23 minutes, with a flow ranging 100 to 250 cc/min, measuring an arterial pressure always lower than 120 mmHg. The analysis, performed with the microscope, of the placentas that have been fixed in this way confirmed the very high quality of the perfusion, and finally the accurate measurement of the gauge of placental in-pressure vessels was possible. The obtained data, regarding the first orders of vessels, don't match the data of the medical literature. In particular the latter group of figures is burdened with deficiency errors. These miscorrelations are essentially due to the adopted methods of measurement.
So, the developed device can be a valid support for a morphometric and anatomic study of the placental vascular net, unlike the previous studies, where the vessels have almost always been fixed and analysed at rest, that is a not-physiological situation.
The obtained values are part of the data that have been used to design the model. This is described in the third part of this work.
Preliminarily an extensive search for the required quantitative information about the morphology of the vessels has been held. The comparison of these data with the obtained ones allowed to define the size of each order of vessels. Finally we elaborated a table to determine the resistances and of the hydraulic capacitances of the model of fetoplacental circulation.
The model, realised using an equivalent electric circuit, was firstly applied to study the fluidodynamics of the fetoplacental circulation in the physiological situation, then in pathological situations, associated to infarction of vessels in rising percentage. The obtained graphs, relating to the flow in umbilical arteries and in fetal aorta, in physiological condition, are extremely interesting, because the match exactly the actual Doppler velocimetry waveforms: they are in favour of the choices that have been made to develop the mathematical model. So, the model revealed itself to be useful about a physical interpretation of the Doppler waves and about the various types of empirical pulsatility index used in the medical field.
The flow diagrams obtained simulating pathological situations give remarkable discussion points. There is a strong likeness between the result of the model and the collected medical data (variations of the typical data regarding waveforms and adimensional indexes). Moreover some effects and peculiarities of the flow modifications are emphasized. They have not yet been investigated enough: they can give prospects of development if experimentally verified.
In particular, increasing the degree of simulated pathology, the model doesn't show a decrease of pulsatility in the umbilical arteries, as wrongly showed by the previous models. On the contrary the waveform persists nearly unchanged, and the decrease of the instant flow at the end of the diastole (minimal value) happens more quickly than the corresponding decrease of the mean flow, as in the clinical data. The variations on the mentioned flow parameters are quite weak (lower than the accuracy of the currently used instruments) in case of slight pathological situations (15% of infarction), and the adimensional index PI, A/B and RI are not able to express well-timed diagnosis, as their significant shifting from the physiological-considered values happens only in case of pathologies reaching 30, 40% of the placental vessels. They produce a decrease of the mean flow greater than 10%, corresponding to pathologies that are already effective and compromising the functionality of the placenta.
Moreover we noticed an extremely interesting decrease of time delay between heart beat and systolic peak in the umbilical arteries when the pathology worsens. The course of this delay is quasi-linear. It assumes sizeable values (-7%) already with 15% of occluded vessels, thus even before similar variations in the characteristics of the Doppler flow waveforms occur. This phenomenon has not yet been observed in the medical field, but it can be checked by the current instrumentation set, and it is independent by the insonation angle and by the vessel gauge.

The model shows a substantial correspondence with the vascular structure of the fetoplacental cardiocirculatory system. It allows not only to make comparisons with already known results and methods, but it gives way to bring an original contribution suggesting more accurate and suitable diagnosis methods.

The flexibility and the powerful computational skill of the program suggest important possible developments for various types of analysis: more localised pathologies, pathologies altering the histological structure of the vessels (if able to change their elastic constant), physiological situations not at term.
The introduction of the tuning system for the cardiac flow versus the arterial pressure is an interesting investigation, that may offer valuable results. To remove the hypothesis of fixed flow does not involve any difficulty for the modification of the equivalent electric net, and it allows to introduce an optimisation work in order to obtain closer to the real situation results.

During the two years we spent since when the outline of this work was traced, we referred to a big number of people, often taking advantage of their patience, to get information, materials and favours.
Among them we should like to mention dott. Alessandra Pavesi, who followed the experimentation providing the essential link between the medical staff and us, and dott. Gaetano Bulfamante, the pathologist who performed the tests vouching for the validity of the experiments.

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Last updated: October 1, 2003.