Classification of Human Placental Stem Villi Review of Structural and Functional Aspects
Open Biomed Eng J. 2017; 11: 36–48.
Villous Tree Model with Active Contractions for Estimating Blood Flow Weather in the Human Placenta
Yoko Kato
1Faculty of Engineering science, Tohoku Gakuin Academy, Tagajo, Miyagi, Japan
Michelle L. Oyen
twoDepartment of Engineering, Academy of Cambridge, Cambridge, United kingdom
Graham J. Burton
3Center for Trophoblast Enquiry and Development Physiology, Section of Neuroscience, University of Cambridge, Cambridge, United kingdom of great britain and northern ireland
Received 2016 Oct thirty; Revised 2017 Jan 12; Accepted 2017 Feb 17.
Abstruse
Background:
In the human placenta, maternal and fetal bloods exchange substances through the surface of the villous trees: the fetal blood circulates in the villous trees, around which the maternal blood circulates. The blood flows directly influence fetal growth. Stem villi, the main supports of the villous tree, take contractile cells along the axes, whose contractions are expected to influence the blood circulations in the placenta. The displacement is neither measurable nor predictable while non-invasive measurements such as umbilical Doppler waveforms are helpful to predict the histological changes of the villous trees and vascularization in the placenta.
Objective:
The deportation caused past the contraction of the villous tree is necessary to predict the blood flows in the placenta. Hence, a computational villous tree model, which actively contracts, was developed in this study.
Method:
The villous tree model was based on the previous reports: shear moduli of the human being placenta; branching patterns in the stem villi. The displacement pattern in the placenta was estimated by the computational model when the shear elastic moduli were changed.
Results:
The results evidence that the displacement caused past the contraction was influenced by the shear rubberband moduli, but kept useful for the claret flows in the placenta. The characteristics agreed with the robustness of the blood flows in the placenta.
Conclusion:
The villous tree model, which actively contracts, was developed in this report. The combination of this computational model and non-invasive measurements volition be useful to evaluate the condition of the placenta.
Keywords: Human placenta, Villous tree, Stem villi, Contraction, Placental function, Blood flow
INTRODUCTION
The man placenta has both maternal and fetal blood circulations, which exchange gases, nutrients and waste through the surface of the villous tree without mixture [1]: the maternal blood from the uterine arteries flows slowly into the intervillous space and returns to the uterine veins while the fetal blood from the umbilical arteries flows into arteries within the chorionic plate, circulates through claret vessels in the villous tree, and returns to the umbilical veins. The influence of the maternal and fetal blood flows on the transport of substances has been reported previously [2, 3].
The villous tree is composed of stem villi, intermediate villi, terminal villi and mesenchymal villi. Stem villi are the master support of the villous tree between the two bounding surfaces of the placenta. The stem villi accept the contractile cells, which surround the arterial and venous vessels and run forth the longitudinal axis of the branch [4-11]. The contraction of the stem villi has been observed in vitro [v, 12-fourteen], which is expected to help the circulations of the maternal and fetal bloods. The maximum velocity of the contraction was much smaller than that of uterus, and the summit isometric tension was 1.39 kPa for electrical tetanus and ane.32 kPa for KCl exposure on average [fourteen]. The contraction directly assists the fetal blood flow in the vessels of the stem villi because the contractile cells surround the vessels axially. Still, the fetal blood in the capillary of the villous tree and the maternal blood in the intervillous space are not surrounded past the contractile cells directly, and similarity in the directions between the blood period and the contractile cells has not been clear. In the meantime, the mechanical backdrop of the human being placenta were evaluated by tensile, compression and shear [15]: The elastic moduli measured by shear were much smaller than those by tensile and compression. The shear stress was less than i kPa when the strain was 1 (strain velocity < 0.04 /s). Because that the blood vessels were aligned with the direction of the force [fifteen], the shear elastic moduli in the environment of the blood vessels would exist much less than 1 kPa. Comparison the tension of the contractile cell with the shear elastic moduli, the deportation and its propagation in the placenta would occur although neither directly measurement nor prediction for the displacement is possible.
The conditions of the placenta, concerning the blood flow, are non-invasively observed by ultrasound and magnetic resonance (MR). The velocity of the blood catamenia in the umbilical avenue is measured by ultrasound Doppler velocimetry and described every bit menstruation velocity waveforms (FVWs). The histological characteristics in the villous tree, including the distribution of the villous types and vascularization, tin can exist estimated past FVW at end diastolic: positive, absent-minded or reverse [16-xviii]. The oxygen environment, which is evaluated past oxygen-enhanced MRI and BOLD MRI [19], influenced the bifurcation pattern of the villous tree: hypoxia enhances the bifurcation [twenty, 21]. The magnitude of the perfusion in the placenta can be expressed equally relative values past 3-dimensional (3D) ability Doppler [22] and dissimilarity-enhanced MR images [23], only the direction is inappreciably measured.
In general, the normal mature placenta shows legions in some degree, such as infarctions, which can prevent the blood circulations in the placenta. 3D power Doppler indicated that the perfusion in the normal placenta was kept through the gestational ages, from xv to 40 weeks [24]. In the meantime, the bore, branching patterns and generation of the stalk villi were previously reported [1, 25] so that a computational model of the villous tree with active contractions can be developed. If the displacement caused by the contraction is corresponding to the perfusion evaluated by 3D power Doppler or MRI, the direction of the claret flow can be estimated by changing the distribution of the shear rubberband moduli as the pattern of the displacement in the placenta agrees with that of the perfusion. Assuming that the contraction force and shear elastic moduli of the region surrounding the stalk villi are representative of the placental weather condition, the results of the computation can be translated properly.
In this study, a computational model of the villous tree in the human placenta with agile contractions was developed for estimating the claret flow status. The shape of the stem villi was based on the previous reports [1, 25], and the surroundings of the stem villi were causeless as one continuum, where the displacement caused by the contraction propagated considering the branching pattern of the villi around the stem villi, and the shape of the intervillous infinite, which is the space surrounded by the villi and the maternal blood passes through, are complicated. Past using this model, it was examined whether or non the contraction could assist the fetal blood period in the capillary and the maternal claret flow in the intervillous space. Moreover, the influence of the mechanical properties in the villous tree on the pattern of the displacement was also examined.
COMPUTATIONAL MODEL
Stem Villi
The stem villi are categorized into the 3 groups: truncus chorii, adjacent to the chorionic plate; rami chorii, next to the truncus chorii; ramuli chorii, between the rami chorii and the basal plate [1, 25]. The bore gradually becomes smaller from the chorionic plate to the basal plate, and branches are found in all the groups except the truncus chorii. The branching pattern of the ramuli chorii is not equally dichotomous. The generations of branches in the rami chorii and ramuli chorii are upwardly to iv, and from 1 to thirty, respectively. Table one shows the size and branching pattern in the stem villi model. In this model, the chorionic and basal plates, and the boundaries between the categories (truncus chorii, rami chorii and ramuli chorii) were parallel to each other. Firstly, how to utilise the centripetal and centrifugal orders at the branch to describe the branching pattern in Table 1 is explained. Figs. ( 1a and 1b ) bear witness a uncomplicated branching design designated by the centripetal order and centrifugal order: the tip and trunk are designated as i and maximum, respectively, at the centripetal social club, and vice versa at the centrifugal club. The centripetal order is used to evaluate dichotomy [26, 27]. The bifurcation ratio, Rb , is divers as the post-obit equation:
Villous tree model developed in this study. The branching pattern in the stem villi of the model was indicated by the centripetal and centrifugal orders at the branches, whose case is indicated by (a) and (b), respectively. (c-e) show the side views of the model: the stem villi, white; the villi except the stem villi, blue; the intervillous space, which the maternal blood passes through, blueish. Equally (d) and (e) show, this model is between the chorionic and basal plates. The z axis of the Cartesian coordinate organisation is perpendicular to the chorionic plate. The size of this model is 34.viii × 34.8 × 24.5 [mm] (1200 × 1200 × 847 [pixels], 29 μm/pixel).
Table 1
Size and branching design in the stem villi model.
| Parameter | Truncus chorii | Rami chorii | Ramuli chorii | ||
|---|---|---|---|---|---|
| Branch | d [mm] | 1 - 3 | 0.5 - 1 | 0.iii - 0.5 | |
| z [mm] | 0 - 2.nine | two.9 - xiii.five | xiii.5 - 24.5 | ||
| Centrality | 50c [mm] | 0 (z = 2.9) | viii.99 (z = 13.five) | - | |
| Lb [mm] | - | 0 (z =ii.9) | * | ||
| 0.29 (z = 3.nine) | |||||
| 1.74 (z = 4.7) | |||||
| iv.64 (z = 5.8) | |||||
| r [mm] | - | (Lb < 1.74) 1.74 | - | ||
| (50b ≥one.74) 8.99 | |||||
| Rb | - | 2 | 2.22 - 6.02 | ||
| Cf | - | 4 | 4 - 20 | ||
The stem villi model was ready in the infinite, whose size was 34.viii × 34.8 × 24.5 [mm] (ten × y × z): the z coordinate shows the distance from the chorionic plate; d, the diameter of the branch; Lc , the distance from the eye of the space in each z coordinate (17.4 mm, 17.4 mm, z) to the axis of the branch at the boundary between the categories; Fiftyb , the distance from the center of the space in each z coordinate to the bifurcation; *, each co-operative bifurcated differently; r, the radius of curvature Rb , bifurcation ratio; Cf , the centrifugal society at the tip.
where Nu is the number of branches at the centripetal order u. If Rb is 2, the branching is as dichotomous. Bold that Rb is constant, Northwardu is a geometrical series given as:
where umax is the maximum centripetal order. Hence,
Rb of the branches was calculated by the method of least squares. Tabular array 1 shows that Rb in the rami chorii was two, only that in the ramuli chorii was not equal to 2. These values indicate that the branching patterns in the rami chorii and ramuli chorii are equally and unequally dichotomous, respectively. The centrifugal order at the tip, Cf , in Tabular array ( 1 ), corresponds to the generation of the branches. While Cf in the rami chorii was constant, that in the ramuli chorii was varied. That is considering the branches in the ramuli chorii were not symmetric.
The diameter range in each category was equally follows: truncus chorii, 900 – 3000 μm; rami chorii, 300 – 1000 μm; ramuli chorii, 50 – 500 μm [25]. Tabular array i shows that the diameter ranges concord with the same one. The change of the diameter at the truncus chorii was much larger than those at the rami chorii and ramuli chorii. For the smooth connection between the truncus chorii and rami chorii, the derivative of the radius with respect to the z coordinate should be zero at the boundary. Hence, the following equation was used to determine the radius of the branch at the truncus chorii:
(iv)
where rmax and rmin are the maximum and minimum radii in the truncus chorii, and ztr is the purlieus betwixt the truncus chorii and rami chorii (ztr = 2.9 mm). In the rami chorii, the radius was decreased as the distance along the centrality was longer. The radius of the branch in the ramuli chorii became larger as the centripetal order increased. The radii of the branches at the connecting indicate were modulated as all the branches showed the aforementioned radius.
The branches in the rami chorii were equally dichotomous too as symmetric, and xvi branches were connected to those in the ramuli chorii at the boundary. The branches in the ramuli chorii should be unequally dichotomous. For making unequally dichotomous branches, the 2D diffusion-limited aggregation (DLA) models [28] were made by the free-software, dla-nd, which was developed by the Dr. Mark J. Stock (http://markjstock.org/dla-nd/). Because the path between the branching points was non smoothen in this model, the line betwixt the branching points was prepare equally an axis of a branch.
Equally Tabular array ( 1 ) shows, the longest distance from the chorionic plate in the model was 24.5 mm. According to the previous reports, the thickness of the human placenta and chorioamniotic membrane, the surface of the placenta, were 25 mm [1] and 243 μm [29] on boilerplate, respectively. It is calculated that the distance betwixt the chorionic and basal plates is 24.8 mm. The longest distance from the chorionic plate in the model was close to the calculated distance betwixt the chorionic and basal plates, based on the previous reports [1, 29]. In the meantime, the cross section of the model, parallel to the chorionic plate, had the bounding rectangle, whose size was 23.8 mm × 22.6 mm (width × height). The previous report [1] indicated that the placenta at term, whose diameter was 220 mm, had 60 – 70 villous stems. The surface area based on this bore is 3.80 × x4 mm2 so that the boilerplate cantankerous department of the villous copse is 5.42 × 102 - six.33 × 102 mm2, whose respective bore is 26 – 28 mm. The size of the cross section in the model was close to that based on the previous report [one]. Figs. ( 1c - 1e ) show the villous tree model developed in this inquiry. The size was 34.eight × 34.viii × 24.5 [mm] (1200 × 1200 × 847 [pixels], 29 μm/pixel).The Cartesian coordinate system, whose z axis was perpendicular to the chorionic plate, was used to depict the position in the model. Its origin was besides on the chorionic plate.
Contraction Management
The contractile cells run forth the longitudinal centrality of the branch [4-eleven]. Each point at the boundary surface betwixt the stem villi and the surroundings has two tangential directions equally Fig. ( two ) shows. The tangential direction, closer to the axis of the branch than the other, was decided every bit the contraction direction.
Contraction directions at the branches of the rami chorii. Arrows show the directions of the contractions. Each branch in the stem villi contracts along its axis and toward the junction.
At the truncus chorii, the centrality of the co-operative was parallel to the z centrality and its radius was largely changed as Equation (four) shows. The angle between the z centrality and tangential direction (φo ) and the differentiation of Equation (4) by z are equally follows:
(vi)
Considering that the direction of the contraction at the axis of the co-operative was (0, 0, -1),
When the angle between the signal at the surface and the x centrality in the xy plane is θo , the tangential direction is (sinφocosθo , sinφosinθo , cosφo ). Comparing the rami chorii with the truncus chorii at Table ( 1 ), the bore change at the rami chorii was 25% of that at the truncus chorii. In addition, the rami chorii showed the range of the z coordinate, which was most 3.7 times larger than that at the truncus chorii. The change of the diameter at the rami chorii was much smaller than that at the truncus chorii. Hence, the tangential direction at the surface was parallel to the axis of the branch at the rami chorii. Because the change of the diameter was also small at the ramuli chorii, the tangential direction was adamant in the same way.
Displacement
As Figs. ( 1c - 1e ) show, assuming that the surround of the stalk villi were one continuum in this model, the propagation of the deportation in the placenta was evaluated by the model. A moving ridge equation is by and large described equally below:
(8)
where u is displacement vector, ρ is density, λl and μ are Lamé's abiding. μ as well shows a shear elastic modulus. Generally, biological tissue is incompressible, and so that the second term in Equation (eight) is zero. Hence,
Hence, the shear wave (transverse wave), whose propagation is normal to the vibration and carried out in solid, was evaluated in this computation. The displacement caused by the shear moving ridge is described as follows [30]:
where ξo is the amplitude, grand is the moving ridge number (m = 2π/λ, λ is wave length), r is the distance from the surface of the stem villi, t is time, and ω is angular frequency. ξo was 0.1 μm in all the computational weather condition. The shear elastic modulus, μ, is described every bit follows [31]:
Considering that thousand = 2π/λ and ω=2πν (ν, frequency),
ρ was 1.0 × x3 kg/10003 because of biological tissues [32]. ν was 1.0 Hz, and λ was 0.29, 0.58 or 1.45 mm (ten, 20 or fifty pixels) in the ciphering and so that the shear moduli were eight.41 × 10-5, iii.36 × x-four and 2.10 × ten-3 Pa. The displacement is attenuated by viscoelastic properties and then that the maximum distance for the propagation was 1.45, 2.ix and four.35 mm (50, 100 and 150 pixels). In order to simplify the problem, t was set for zero. That is, the computation did not consider the time upshot on the displacement. The maximum distance for the propagation was not dependent on the position. λ was kept constant in the surroundings, or became longer as the distance from the surface of the stem villi was longer. In the latter case, λ was increased from 0.29 mm to 1.45 mm every 1-third of the maximum altitude from the surface. Hence, in that location were 12 conditions in this computation.
RESULTS
Characteristic Positions and Visualization
The displacement of the environs of the stem villi is described by the polar coordinate organisation (magnitude, φ (0° ≤ φ ≤ 180°) and θ (-180° ≤ θ < 180°)) considering the coordinate system was useful to split the deportation into its magnitude and direction. Fig. ( 3 ) shows the results when λ and the maximum distance for the propagation were 1.45 mm and 4.35 mm, respectively. Fig. ( 3a ) shows that the displaced area was gradually increased as the z coordinate became larger. The long and steep slope was observed from the truncus chorii to the rami chorii. The same features were observed in all the computational weather. Figs. ( 3b , 3c and 3d ) prove the mean and standard departure (SD) of each parameter: magnitude, φ and θ. The hateful and SD were calculated for all the points in the displaced area, whose magnitude was more than zero. When the displacement is perpendicular to the chorionic plate, the value of θ cannot exist determined. Hence, such a critical betoken was not included for the calculation of the mean and SD in θ. Fig. ( 3b ) shows that the SD normalized by the hateful was calculated in order to evaluate the magnitude range of the displacement in each z coordinate. The peak of the normalized SD was observed around the boundary between the truncus chorii and rami chorii, which is named every bit zd . The mean and SD well-nigh the direction of the displacement in each z coordinate are shown in Figs. ( 4c and 4d ). As Fig. ( 4c ) shows, the mean of φ was kept around 90 degrees, but the SD of φ indicated two peaks, whose positions are named as zφ1 and zφ2 , respectively. Fig. ( 3d ) shows that the mean of θ slightly decreased around the boundary between the rami chorii and ramuli chorii, which is named as zθ , while the SD of θ was kept around ninety°. These characteristic z coordinates, zd , zφ1 , zφ2 , and zθ , were observed at all the computations. Fig. ( iv ) shows the images which visualizes the magnitude, φ, and θ in each characteristic z coordinate and the middle z coordinates of the truncus chorii (zt ), rami chorii (zr ), and ramuli chorii (zrl ) nether the same computational condition as Fig. ( 3 ) shows. The displaced area became larger as the z coordinate was increased. The magnitude of the displacement was near kept constant at every z coordinate although the magnitude in the limited surface area at zd was high. The distributions of φ and θ were largely changed along the z coordinate equally shown in Figs. ( 3c and 3d ) The visualization of the deportation and management similar Fig. ( iv ) is useful to find out critical points and of import points for analysis.
Displacement caused past the contraction of the stem villi. λ = 1.45 mm, and the maximum distance for the propagation = 4.35 mm. All the parameters at each z coordinate are shown. While (a) shows the displaced surface area, the magnitude (b) and direction (φ, θ) (c, d) of the displacement were described by the representative values, the mean and standard deviation (SD) for the displaced surface area. The solid and dotted lines in (c) and (d) are the mean and SD, respectively. The triangles show the characteristic positions, which were observed at all the computations. zd , zφ1 , zφ2 , and zθ are the z coordinates for these characteristic positions.
Displacement patterns in the characteristic positions. λ = 1.45 mm, and the maximum altitude for the propagation = 4.35 mm. In add-on to the characteristic positions in each parameter, zd , zφ 1, zφ2 , and zθ, the representative positions of the truncus chorii, rami chorii and ramuli chorii appear: zt , zr and zrl , which are the heart z coordinates of the truncus chorii, rami chorii, and ramuli chorii, respectively.
Magnitude of the Displacement
As Fig. ( 4 ) shows, the magnitude of the displacement was kept almost constant except the magnitude was loftier nigh the stem villi at zd . xc% of the displaced surface area showed that the magnitude relative to the maximum one was less than 0.17 for the maximum altitude for the propagation = one.45 mm and λ increasing as the distance from the surface of the stalk villi, and 0.06 for other results. The SD normalized by the hateful was large at zd , but the high magnitude was in the limited area. Hence, the maternal and fetal blood circulations in the villous tree and intervillous space would exist influenced by the abiding distribution of the displacement in the placenta. Because the shape of the stem villi direct influences the displacement pattern, the model whose shape near the loftier magnitude is changed will exist developed and used for the computation to examine whether or not such a high magnitude is inevitable.
Direction of the Displacement (φ and θ)
Figs. ( 5a - 5e ) prove the distribution of φ at the characteristic z coordinates (zφ1 , zφ2 ) and the middle z coordinate in each category (zt , zr , zrl ) for the same condition as shown in Fig. ( three ). The expanse fraction, which is the area for each φ normalized by all the displaced area, was used to evaluate the distribution of φ. The surface area fraction around φ = 90° (φ = 45° - 135°) was largest at zφ1 (Fig. 5b ) and smallest at zφ2 (Fig. 5d ). The aforementioned characteristics were observed in all the computations. For all the computational conditions, the hateful and SD of the expanse fraction at φ = 45° - 135° were calculated at each z coordinate. As the boilerplate values in Fig. ( 5f ) evidence, more xc% of the displaced area showed φ from 45° to 135° at zφ1 . The expanse with the same range of φ was effectually 10% at zφ2 . Because that the φ = 90° means the direction parallel to the xy aeroplane, near of the displacement was parallel to the xy plane at zφ1 , and parallel to the z axis at zφ2 . Fig. ( 5f ) shows that the mean of the expanse fraction at the other positions was around 0.three. Hence, φ did not have a preferred direction in that location. The displacement could help the maternal blood to go to the chorionic plate at zφ2 , spread parallel to the chorionic plate and the basal plate at zφ1 , and become toward the basal plate at zφ2 . In the meantime, the branches in the stem villi around zφ1 and zφ2 had the axes largely different from the directions of the displacement there: the axis of the co-operative in the truncus chorii is perpendicular to the chorionic plate, and that in the rami chorii was largely inverse considering of its curvature. The displacements at zφ1 and zφ2 could assist the fetal blood to pass through the vessels in the stem villi. Moreover, the maternal and fetal bloods could be homogenized by the displacement at zt , zr and zrl . The SD was largest at zt , and smallest at zφ1 . The SD at zrl was larger than that at zφ1 , but much smaller than those at the other characteristic positions. Because that λ and the maximum distance for the propagation are respective to the mechanical properties of the surroundings of the stalk villi, φ at zφ1 and zrl would be hardly influenced by the mechanical property of the surroundings, but φ at the truncus chorii would be vulnerable to information technology.
Distribution of φ in the characteristic positions for the displacement at λ = 1.45 mm and the maximum altitude for the propagation = 4.35 mm. (a-e) evidence the distributions of φ at the following feature positions, zt , zφ1 , zr , zφ2 and zrl . The area fraction of φ, from 45° to 90°, for all the computation results is indicated in (f).
Figs. ( 6a - 6d ) testify the distribution of θ at the characteristic z coordinates (zθ ) and the middle z coordinate in each category (zt , zr , zrl ) for the same status as Fig. ( 3 ) shows. The expanse fraction, the area for each θ normalized by all the displaced area, was used for describing the distribution. Figs. ( 6a and 6b ) bear witness that the similar distribution pattern was observed every 90° at zt and zr . The result agreed with the mean of θ at zt and zr , effectually zero. Fig. ( 6c ) shows the distribution of θ at zθ , where the area fraction at θ = -180° - 90° (the third quadrant) and θ = 0° - 90° (the first quadrant) was larger than that at θ = -90° - 0° (the 4th quadrant) and θ = 90° - 180° (the second quadrant). This event agreed with the subtract of the mean at zθ in Fig. ( 3d ). As Table ( one ) shows, the branches in the ramuli chorii were unequally dichotomous also every bit asymmetric while those in the rami chorii were equally dichotomous as well as symmetric. Because the rami chorii had 16 branches connecting to those in the ramuli chorii, 16 types of the branching pattern were used in the ramuli chorii. zθ was located around the boundary between the rami chorii and ramuli chorii. The branches of the ramuli chorii at zθ were about parallel to the z axis in the second and fourth quadrant, only those in the showtime and third quadrants were non. The bending of the branch at zθ would cause the characteristic distribution of θ at zθ . The similar distribution design was observed at zrl , but each peak was much smaller than that at zθ every bit Fig. ( 6d ) shows. Because zrl was placed on the middle of the ramuli chorii, the feature caused at zθ would be weakened past the branches which showed diverse angles. All the computational results showed the same characteristics as Figs. ( 6a - 6d ) show. The SD of the area fraction in each interval (each value of θ) (SDin ) was calculated in lodge to evaluate the uniformity of the distribution in θ for all the computations. Fig. ( 6e ) shows that the average value of SDin at zθ was largest and that at zrl was smallest, amid all the positions. The distribution of θ was virtually uniform at zrl , and most fluctuated at zθ in all the positions. The distribution of θ at zθ would be influenced by the angle of the branches in the ramuli chorii. Because θ at zrl did not have a preferred value, the maternal and fetal bloods could be homogenized. The SD values of SDin at zt and zθ was much larger than those of other ii positions, and that at zrl was smallest in all the positions. The results evidence that the mechanical properties of the villus tree would strongly influence θ at zt and zθ , but hardly influence that at zrl . Fifty-fifty if the mechanical properties of the villous tree are changed, the homogenization of the bloods around the ramuli chorii would be kept.
Distribution of θ for the displacement at λ = i.45 mm and the maximum altitude for the propagation = 4.35 mm. (a-d) show the distribution of θ in the feature positions, zt , zr , zθ and zrl . The SD of the expanse fraction in each class interval for all the computations (SDin ) is indicated in (due east).
Give-and-take
In this report, the computational villous tree model was developed, and used to evaluate the displacement in the man placenta caused past the contraction of the stem villi. The magnitude of the displacement was almost homogeneous, and the direction was useful for the fetal and maternal blood circulations. This trend was maintained fifty-fifty if the mechanical backdrop of the placenta were changed. The experimental results such as MRI and 3D ability Doppler angiography are described by scalar values then that the magnitude of the deportation could be direct compared with them. The resolution in the computation of this model was much college than that in MRI or 3D power Doppler. Hence, representative values such as hateful and SD will exist necessary if the comparison between the experimental information and the computational result is carried out.
In the computation, every point in the stalk villi contracted at the same time. Hence, the result in this study indicated that the displacement caused by the contraction would exist helpful for the blood circulations when each contractile cell in the stem villi contracts at the same time. How to control the timing of the contraction for the effective blood circulation in the placenta tin can be investigated by this villous tree model. This investigation will exist carried out in the future. The event of the displacement on the maternal and fetal claret flows would be influenced past the directions of these blood flows. A computational model and method are necessary to investigate this effect. Developing them, with considering the usage of FWVs, will be the important topic to evaluate the blood circulation in the placenta.
CONCLUSION
In this study, the computational model of the villous tree with agile contractions was adult. The results based on this model prove that the contraction could assist the maternal and fetal claret circulations in the placenta, and its outcome would maintain even if the mechanical circumstances are changed. The combination between this computational model and non-invasive measurements will be useful to evaluate the status of the placenta.
ACKNOWLEDGEMENTS
Declared none.
Conflict OF INTEREST
The author confirms that this commodity content has no conflict of interest.
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