Study and Validation of a Model
of Fetoplacental Circulation

3.3. Conclusioni Results |
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Il lavoro descritto ha lo scopo di portare alla definizione di un valido strumento diagnostico in grado di rilevare, più tempestivamente di altre metodologie, patologie fetali e placentari. Tali variazioni possono essere simulate e valutate con l'ausilio di un modello, per poi venire confrontate con i risultati di ecografie, abbastanza precise e diffuse, anche se limitatamente alle sole arterie ombelicali e aorta.
L'obiettivo dello studio non si é limitato alla realizzazione di un modello, ma si é avvalso di una vasta sperimentazione che ha contribuito a verificare ipotesi di funzionamento della placenta proponendo metodi di analisi e misurazione della caratteristiche vascolari.
La sperimentazione condotta presso l'ospedale S. Paolo di Milano, sviluppata durante circa 50 sedute di prova, ha dato modo di realizzare un metodo di indagine preciso per verificare le caratteristiche della fluidodinamica della placenta.
Il circuito di perfusione realizzato ha permesso di attuare una perfusione controllata della placenta, con parametri di portata di ingresso e di uscita noti, impiegando sangue bovino come fluido di perfusione.
Le portate d'ingresso con cui sono state svolte le prove erano comprese tra 100 e 220 cc/min. La pressione arteriosa rilevata è risultata variabile: da 49 mmHg a 187 mmHg per ogni 100cc/min, per una durata media di 15 minuti.
La principale difficoltà incontrata nasce dal tentativo di alimentare le arterie ombelicali con portate fisiologiche, poiché si generano pressioni molto elevate. Il fenomeno è stato riscontrato da tutti gli altri ricercatori, i quali non hanno potuto raggiungere i nostri valori di portata, neppure utilizzando soluzione fisiologica.
Si è anche evidenziata una notevole reattività della placenta alla concentrazione di anidride carbonica.
Un ulteriore motivo di interesse si é incontrato nel trasudamento di siero verso l'esterno della placenta.
Il nostro circuito è stato quindi impiegato per una successiva serie di esperimenti, usando una soluzione di formaldeide e glutaraldeide. L'analisi al microscopio delle placente così fissate ha confermato l'ottima qualità della perfusione, ed ha reso finalmente possibile una misurazione precisa dei calibri dei vasi in pressione.
Il dispositivo messo a punto si propone dunque come valido ausilio per uno studio morfometrico della rete vascolare placentare, a differenza degli studi precedenti nei quali i vasi sono sempre stati fissati a riposo.
Le misure raccolte sulle placente così perfuse hanno costituito parte dei dati sui quali é stato basato il modello.
Preliminarmente si è svolto un'ampia ricerca nella letteratura medica per ottenere tutte le informazioni quantitative sulla morfologia dei vasi, che confrontata con quanto ottenuto dalle nostre osservazioni, ha permesso di definire le geometrie di ogni ordine di vaso. Infine si é realizzata una tabella per il dimensionamento delle resistenze e delle capacità idrauliche del modello del circolo feto-placentare.
Il modello, realizzato attraverso un circuito elettrico equivalente, é stato impiegato per studiare la fluidodinamica della circolazione feto-placentare nella situazione fisiologica e in situazioni patologiche. I grafici ottenuti sono esattamente coincidenti con le flussimetrie esistenti.
I grafici relativi alle situazioni patologiche offrono argomenti di discussione: vengono evidenziati effetti e peculiarità delle modificazioni dei flussi finora non indagati, offrendo prospettive di sviluppo qualora questi venissero verificati sperimentalmente. In particolare, all'aumentare del grado della patologia simulata, non si è osservata la diminuzione di pulsatilità della portata nelle arterie ombelicali erroneamente evidenziata da modelli precedenti. Le variazioni nei parametri di portata citati sono molto deboli (inferiori alla precisione degli strumenti oggi in uso) in caso di situazioni patologiche lievi, e gli indici adimensionali PI, A/B e RI non risultano adatti per la formulazione di diagnosi precoci.
Ci é inoltre parso di estremo interesse la rilevazione della diminuzione, all'aggravarsi della patologia, del ritardo temporale tra battito cardiaco e picco sistolico nelle arterie ombelicali. L'andamento di tale ritardo è quasi lineare, ed assume valori apprezzabili già con lieve occlusione del dei vasi. Il fenomeno ancora non è stato osservato in ambito clinico, ma risulta facilmente controllabile con i mezzi attuali, ed è indipendente dall'angolo di insonazione e dalla misura del diametro del vaso.
La versatilità del programma utilizzato ha suggerito inoltre sviluppi per analisi di vario tipo: patologie più localizzate, patologie che alterano la struttura istologica dei vasi cambiandone la costante elastica, situazioni fisiologiche non a termine.

3.3. Results |
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The aim and the achievement of this work have been to aid the outlining of a valid diagnostic tool, capable to detect fetal and placental pathologies, more immediately then other already applied techniques. In fact these pathologies cause variations of some parameters in comparison to the physiologic situation. Such variations can be simulated and evaluated using a model, to be then compared with the results of blood flow velocity waveforms, that are accurate enough and already practised in the medical field, even if useful only to analyse umbilical vessels and aorta.
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 to engineers. 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 setup a reliable and accurate method of research. This allowed to study and verify the characteristics of the human placenta fluidodynamics. Soon after the childbirth and the drawing the placenta was connected to a perfusion set, able to simulate the physiological perfusion condition at the 38th 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.
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 experimentation the main difficulty we met with comes from the attempt to supply the umbilical arteries with a flow close to the physiological one, because a very high pressure is generated for a condition of general constriction of the placental vessels. This phenomenon has 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) cause a quick constriction, that breaks off the perfusion within less than 5 minutes from the beginning.
A kind of transudation of serum is an additional reason of interest. It is proved 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 placentae 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.
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 index). 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 prenatal 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 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 skills of the program used for the analysis of the electrical net suggest important possible developments for various types of investigation: 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 results closer to the real situation.

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