Study and Validation of a Model
of Fetoplacental Circulation

> Part 4 - Appendices

4.1. Level Control for the Reservoir |
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As mentioned in the Part 2 of this thesis, this electronic circuit controls the level of the blood in the reservoir of the oxygenator: it must never get completely empty (this can happen in case of leakage of the perfusion circuit or of the placenta) in order to avoid to pump air into the vessels.
Figure 96 is the electric diagram of the tool, functionally composed by 3 parts: voltage regulator, oscillator, control.
The voltage regulator supplies 9V to the node B, and about 12 V to the node A, used to drive the relay without influencing the rest of the circuit with spikes. The relay of our circuit drives a 220V/8W valve, but the tool can easily drive other types of valves, probably more effective than our one.
The external probe is connected to a square-wave oscillator (about 250 Hz): the frequency can be modified through the 47k resistor and the 100nF capacitor. The 220nF capacitors filters the DC component, the 22nF capacitors filters the spikes of the node 2. The voltage applied to the probes is alternate, to avoid electrolysis in the blood.

Fig.96: Electric diagram of the regulator

Connecting the probe to the 'min' input the signal reaches the NAND port, working as an inverter. The diodes connected to the port input are protections for ESD and overvoltages. The 1MW resistance is a pulldown for node 4 when the signal is missing, i.e. when the level is lower than the minimum expected. The capacitor at the input decouples the probe from the DC voltage introduced by the resistor.
With the signal at the 'min' probe, the node 5 is at high level due to the filtering done by the 1MW resistance
in parallel with the 100nF capacitor; the transistor connected to the second NAND drives a buzzer.
The other 2 NAND ports are a Set/Reset flip-flop driving the relay. In this way the valve is driven only when the level cannot reach the 'min' probe, up to the reaching of the 'max' probe.
The probes are stainless steel wires fixed to the holes at the top of the reservoir, as shown by the picture in the chapter on the perfusion with blood.
The push-button of the 'min' signal is used to reload the max quantity of blood without waiting for the reservoir to be empty.
For the circuit we developed a fiber-glass PCB (figures 97 and 98). The probes are connected through a 3-pole connector: they can be easily replaced without disassembling the circuit. The plastic box has a tool to be applied to the oxygenator bar, and is waterproof: the switch, the buzzer, the fuse and the hole to connect other types of valve (if necessary) are placed on the bottom part.
The valve has been fixed externally, in order to facilitate maintenance work.

Fig.97: Mask for PCB

Fig.98: Circuit assembly

4.2. Relationships and Calculations for Morphometrical Data of the Vessels |
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In order to calculate the dimensions of the vessels we used mainly data obtained by Kaufmann [20] and by Arts [25]. The only values directly available, on the vessels of the cotyledons, were the following:

Volume of the placenta | 488 cm3
Total volume of the villi | 240 cm3
% trunci vs total vol. | 2
% rami vs total vol. | 3.8
% ramuli vs total vol. | 21.4
% interm. mature villi vs total vol. | 26.2
% terminal villi vs total vol. | 36.5

Also the mean percentages of "lumina" of trunci, rami and ramuli (26%), interm. mature villi (21%) and terminal villi (45.2%) were available.
The lengths of the vessels of the trunci, of the 4 orders of rami, of the mature interm. and terminal villi, of the 10 orders of ramuli were available too.
The number of vessels in parallel per each type and order of villi has been obtained, knowing the numbar of trunci and of terminal villi, considering dichotomic splitting where not differently mentioned by the description of 3.1.7. paragraphs.
The dymensions of the chorionic vessels have been obtained by the previous literature [45][25].
The table for the values to be used for the model was absolutely incomplete:

|  |  |  | Vessels |  |  |  | stem | villi | ® |
|  | Arteries |  | cor. |  |  |  |  | rami |  |
|  | funicolus | I | II | III | IV | trunci | I | II | III | IV
N |  | 2 | 2 |  |  |  | 50 | 400 |  |  |
r° | m m | 1750 |  |  |  |  | 325 | 275 |  |  |
l | mm | 520 | 30 | 30 | 30 | 30 | 5 | 10 | 20 |  |

|  |  |  | ¬ | stem | villi |  |  |  |  |  | villi |
|  |  |  |  | ramuli |  |  |  |  |  | interm |  |
| I | II | III | IV | V | VI | VII | VIII | IX | X | mature | term. | sinus.
Nx1000 |  |  |  |  |  |  |  |  |  |  |  | 45000 | --
r° |  |  |  |  |  |  |  |  |  |  | 14 | 7.2 | 25
l | 1.1 | 1.1 | 1.1 | 1.1 | 1.1 | 1.1 | 1.1 | 1.1 | 1.1 | 1.1 | 0.45 | 1 | 0.1

Tab.39 (A and B): Morphometric data about the placental vessels directly available in literature.

We calculated the diameters of the missing vessels considering the hypothesis of unchanged total area for the chorionic vessels (0.19 cm2) [25][45].
For the stem villi this hypothesis is no longer available: we calculated the areas of rami e ramuli with the following formula:

. .
The values increase from 0.17 cm2 (trunci) to 70 cm2 (interm. mature villi).
Within the splittings of rami and ramuli we made the hypothesis of linear increasing: for the rami we imposed that the mean area does not change,
with x = increment between adjacent levels.
The increment y of the areas of adjacent levels of ramuli has been computed that the area should be 0.17+4x+0.5y at ramuli of the I order, and 70-0.5y at ramuli of the X order. We verified that the weighted average of the so computed areas is compatible with the correspondent data already obtained.
From the total areas of the sections we calculated the diameters of each type and order of vessels.

4.3. Units of Measure |
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For the model the SI units have been used:

Quantity | Unit | Symbol | LMTI
Voltage | Volt | V | L 2 MT-3 I-1
Current | Ampère | A | I
Charge | Coulomb | C | TI
Time | second | s | T
Capacitance | Farad | F | L-2 M-1 T 4 I 2
Resistance | Ohm | W | L 2 MT-3 I-2
Inductance | Henry | H | L 2 MT-2 I-2

Tab.40: SI units

Some of the units that are used in medicine do not belong to this system: to make a correspondance between hydraulic and electric quantities we have to convert them.

Quantity | Symbol | Unit | Relationship
Length | l , r | cm | = 10-2 m
Viscosity | m | cP | =10-3 Pa.s
Pressure | P , k | mmHg | =133.3 Pa
Flow | Q | cc/min | =6-1×10-7 m 3/s

Considering that to convert the obtained data into SI units, they must be multiplied by the following constants:

R : 103
C : 10-6/133.3
L : 0.1
V : 133.3.

4.4. Glossary |
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aberration, chromatic | iridescence of image outlines caused by the different rifraction of each color.
abruptio (placentae) | premature detachment of the placenta
accuracy | matching level between a measurement and the real value being measured
air chamber | closed reservoir, with pressurised air, connected to a pipe: it works as a damper
amnios | thin membrane surrounding the fetus
analogic | signal that can assume any value within a range
anastomosis | confluence of two vessels
aneurism | weakening of the wall of a vessel, generating a bulge
bypass | vessel bypassing a vascular district
capillary (vessel) | very thin vessels (from latin capilla = hair)
chorion | external membrane around the embryo
collapse | sudden decrease of pressione
cotyledon | lobe of the placenta
decidua | part of the uterine mucosa enveloping the ovule
diffraction | phenomenon of wave propagation: a wave interferes with itself when running into an obstacle with dimensions comparable with its wavelength
digital | signal whose amplitude can have a finite number of values
endometrius | inner layer of the uterus
(a)etiology | study of the causes of disease
FFT | method for the calculation of the Fourier transform
hemolysis | breaking of the membrane of the herythrocites
heparin | anticoagulant
mesenchima | connective tissue
perfusion | continuous introduction of a liquid into a vessel
precision | ratio between the measurement and the error introduced by the meter
previa, placenta | placenta positioned in the low part of the uterus, prevents the normal birth
rheology | science studying the deformation of materials and related strains
sensitivity | ratio between the result of the measurement and the correspondent input signal
sinusoid (of the terminal villi) | enlargement of a capillary of the terminal villi
spectrum | series of frequences forming a signal
stenosis | abnormal narrowing of a vessel or meatus
strain-gauge | strain sensor used as transducer to measure strains or deformations
tolerance | range of variation of the result of a measure
transducer | tool able to make a conversion between different phisical quantities
ultrasound | sound at high frequency, above the upper limit of human hearing.
villus | final parts of the ramification of the placental vessels

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Last updated: October 1, 2003