Anatomical and hemodynamic changes in the vascular bed of umbilical cord during intranatal period

Introduction 

The umbilical cord is formed in the early stages of the embryonic period. It is an important morphofunctional structure throughout the entire intrauterine development [1]. It is the only link between the mother and the fetus [2]. The structure of the vascular bed of the umbilical cord largely controls the possibility of a proper fetus development and affects the perinatal outcome [1]. Impaired fetoplacental circulation is an important predictor of adverse outcomes for children in the first year of their life, specifically, disorders of their physical and psychomotor development [3]. Chronic placental insufficiency (CPI) is becoming the most common cause of antenatal fetal death, intrauterine hypoxia and deficient growth. The literature also contains data on disorders in the immune system of the mother and fetus in CPI [4]. In addition to the period of intrauterine development, the fetus must go through the stage of labor and adapt to the effects of intrauterine pressure, which occurs as a result of uterine contraction caused by the interaction of hormonal and mechanical factors [2]. Currently, the assessment of the impact of labor and the increasing external pressure on the anatomical and hemodynamic parameters in the umbilical cord vessels is of utmost importance for clinical practice. In connection with the development of new computer technology and the introduction of digitalization in medical practice, one of the relevant methods for resolving this issue is the 3D modeling of the umbilical cord and its vessels [5].

Objective – analysis of anatomical and hemodynamic transformations in the vascular bed of the umbilical cord during labor via computer modeling of physiological processes and the associated change in the external pressure gradient.

Materials and Methods

Biological material was collected at the Clinical Perinatal Center in Ufa, Russia, with the written consent of the patients. On October 23, 2024, the Ethics Committee of the Bashkir State Medical University of the Russian Federation Ministry of Healthcare attested that the scientific research complied with generally accepted ethical standards, requirements for the observance of the rights, interests and personal dignity of the study participants in accordance with the Federal Standard R 52379-2005, Good Clinical Practice. We selected umbilical cords with a conventional anatomical structure in terms of number of vessels, viz., those with two arteries and a vein. The clinical criterion for inclusion the mother in the study was the absence of severe somatic pathology, pregnancy complications (such as preeclampsia or gestational diabetes mellitus) and infectious diseases. In relation to the fetus, the inclusion criteria were full-term gestational age and the Apgar test score of 7-8 pts. as assessed by neonatologist. The umbilical cord was collected for the study immediately after its cutting off. 

In our study, we used and processed 20 umbilical cords to perform a morphological study, make corrosion cast specimens of umbilical cord vessels, and prepare a database for Ansys Fluent 2021 software.

The vessels of the umbilical cord were rinsed in the running water to prevent the formation of blood clots. The biomaterial was transported in a physiological solution of sodium chloride for 12 h from the moment of collection. The next stage of the study was carried out at the Department of Human Anatomy of Bashkir State Medical University of the Russian Federation Ministry of Healthcare. The collected umbilical cord was divided into three equal segments (proximal, median, and distal) with a scalpel. The proximal segment was used to create a corrosion cast specimen, which is shown in Figure 1a. The vessels were filled with Belakril-M XO dental material by pumping the mixture with a syringe and cannula until they were filled, followed by dissolving the organic tissues in a potassium hydroxide solution. This is an original method protected by a patent (D.V. Shaduro, V.S. Pikalyuk: Method for Manufacturing Anatomical Corrosion Cast Specimens) [6]. 

The 3D models were built at the Laboratory of Additive Manufacturing Technology of Bashkir State Medical University. A proximal segment of 10 cm in length was used to create 3D models of the umbilical cord vessels. This size was chosen based on the dimensional technical limitations of the RangeVision Spectrum stationary 3D scanner (Russia) and of the rotary table. Data processing was performed using the ScanCenter NG 2022 software. For further work with 3D models, we employed professional open-source software, Blender 4.2.

3D modeling of circulation in the umbilical vessels under external pressure was performed in the universal program of finite element analysis, Ansys Fluent 2021, at Ufa University of Science and Technology, Ufa, Russia, using the Fluid Flow (Fluent) and Transient Structural packages of hydrodynamic and strength analysis.

The first stage of our study involved the modeling of a single straight artery isolated from other umbilical cord structures based on an actual artery in STL format.

To more accurately approximate the computer model to the biological material, we specified additional parameters in the Ansys software: Young’s modulus (longitudinal elastic modulus) and the equation of the bulk modulus of elasticity, in which the Poisson’s ratio plays a key role. These parameters characterize the elastic properties and represent the elasticity of the vessel wall [7].

The wall deformation under external pressure was determined using the formulas built into Ansys Mechanical. After analyzing published sources, we concluded that the optimal level of external pressure applied in our study is 120 mm Hg, which reflects the average pressure during the active phase of labor. The mean velocity of blood flow was specified based on the ultrasound data. The data were automatically converted for use in Ansys. The mean blood flow velocity was 0.3 m/s in the artery and 0.1 m/s in the vein.

The dynamic viscosity of the blood was calculated based on the empirical Carreau-Yasuda model, which ius one of the common non-Newtonian blood models used to describe arterial blood flow.

When conducting the study, we chose laminar blood flow, since the blood in most vessels flows in this mode, including the umbilical cord vessels [8]. 

The second stage of the study was 3D modeling of the umbilical vessel complex surrounded by embryonic mucous connective tissue (EMCT) in Ansys Fluent 2021. 3D modeling of the umbilical vessel complex surrounded by EMCT was based on an actual umbilical cord in STL format.

Young’s modulus was assumed at the level of 1.08 MPa, and the Poisson’s ratio in the equation was assumed equal to 0.49. The vessel walls in this case are elastic, and the presented data will not impose large errors into the calculations [9]. 

It is known that the density of blood is approximately 1,060 kg/m³ [10], viscosity measured in kg/m is determined by the Carreau property calculated by the formula, the time constant is 3.313 s, the power in the model is 0.3568, the viscosity at zero deformation is 0.056 kg/m×s, and the viscosity at infinite deformation is 0.0035 kg/m×s. The calculation method is shear rate-dependent viscosity. The intravascular pressure was selected from published sources: 88 mm Hg for arteries and 41 mm Hg for veins [11].

The parameters specified in the Ansys program for the EMCT were: 4 kPa for Young’s modulus, Poisson’s ratio was 0.47, and density was 1.63 g/cm³ [12]. The applied external pressure was also 120 mm Hg. Next, we calculated the intravascular hemodynamic changes using the Ansys Fluent 2021 software, and the changes in the umbilical cord anatomy and its vessels were analyzed against the background of external pressure.

Statistical data processing was performed using the Statistica 10 software. The data are presented in counts and percentages (%). The significance of differences was assessed using the Wilcoxon test. The critical significance level was chosen at the level of p<0.05.

Results

We began the development of a 3D model of the umbilical cord and its vessels with its representation in the Ansys Fluent 2021 software as a 3D mesh. Figure 1A illustrates the collected biological material of the umbilical cord of a rectilinear (straight) shape. This variant of the umbilical artery anatomy is not pathological: we obtained it as a result of physiological uncomplicated childbirth. Figure 1B shows a photograph of a corrosion cast specimen made on the basis of the aforementioned umbilical cord. Two umbilical arteries are shown in pink, while the vein is shown in blue-brown. Figure1C demonstrates a mesh of a straight umbilical artery in the Ansys Fluent 2021 software interface.

The thickness of the vessel wall, along with the internal diameter of the arteries and veins, were determined based on our data from a morphometric study conducted on biological material via the ImageJ software. The internal diameter of the vein was 4.4 mm, the internal diameter of the arteries was 2.7 mm. The thickness of the walls of the umbilical vessels was 0.3 mm and 0.5 mm, respectively.

As a result of computer calculations using the Ansys Fluent 2021 software, we established that in a straight artery, when exposed to external pressure (120 mm Hg), the blood flow velocity increased by 85.5% and was 0.56 m/s. Intravascular pressure increased by 38.5%, from 88 mm Hg to 122 mm Hg.

As for the anatomical characteristics, the walls of the arterial vessel were deformed, as a result of which its lumen narrowed in the frontal or sagittal planes, depending on the direction of the external pressure vector. Figure 2A demonstrates a change in the longitudinal configuration of the umbilical artery under the impact of an external force. Figure 2B shows a change in the cross-section of the vessel lumen with a change in intravascular blood flow velocity. Figure 2С illustrates the change in the cross-section of the umbilical artery lumen with a change in intravascular pressure.

Figure 3 presents the second stage of the study, during which we modeled the blood flow in the vascular bed of the intact umbilical cord. Figure 3A shows a mesh of two arteries, a vein and EMCT built in the Ansys Fluent 2021 software. Figure 3B demonstrates a spiral right-handed course of arteries inside the EMCT with a step of 0.28 twists/cm. The values of physiological parameters specified in the computer program are described above in the Materials and Methods section.

As a result of 3D computer modeling in the Ansys Fluent 2021 software, we established that when external pressure is applied to the umbilical vessels surrounded by EMCT, morphofunctional changes are manifested to a much lesser extent. For instance, the blood flow velocity in the spiral umbilical arteries increased by 20% and amounted to 0.36 m/s, while intravascular pressure increased by 8% (95 mm Hg). In the umbilical vein, the blood flow velocity increased by 24% (0.12 m/s), while intravascular pressure increased by 10% (44 mm Hg), which is slightly higher than in the umbilical arteries. We hypothesize that this is due to the less elastic vascular wall and the linear structure of the umbilical vein.

According to the Wilcoxon criterion, hemodynamic changes in the vascular bed of the umbilical cord against the background of the external pressure are statistically significant (p<0.05).

In a 3D model without the effect of external pressure, the cross-sectional area of the umbilical cord was 1.9 cm². The cross-sectional areas of the arteries, veins and EMCT were 0.12 cm², 0.15 cm² and 1.48 cm², respectively.

The cross-sectional areas of the umbilical cord, EMCT, umbilical arteries and vein did not change, despite the external deformation of the umbilical cord, vascular wall and changes in the lumen of the vessels in the frontal or sagittal planes (depending on the direction of the external pressure vector).

Discussion

Our study showed that dynamic changes in vascular circulation do not always comply with the conventional laws of hydrodynamics. According to Bernoulli’s principle, at points where fluid velocity increases, its pressure decreases, and vice versa [13]. In our study, under the impact of external pressure (presumably intrauterine), along with an increase in both blood flow velocity and intravascular pressure, is noted. Apparently, this is due to the fact that the circulatory system is morphologically and functionally complex. Pressure and flow velocity of the blood are affected by many factors (such as vascular resistance, blood volume, the state of the cardiovascular system, and neuroendocrine processes). The spiral structure of the umbilical arteries helps maintain a steadier blood flow and adapts hemodynamics to external changes. In our study, we attempted to develop a 3D model of the umbilical cord vessels (similar to the actual original biological structure), taking into account, as much as possible, the physical, anatomical and functional features of the umbilical cord. We therefore believe that with a change in external pressure, both the pressure and flow velocity of the blood inside the umbilical vessels increase. There is published evidence that an increase in the number of umbilical cord twists affects an increase in intravascular pressure [14]. At the same time, the spiral structure of the umbilical cord provides some protection of the vessels from compression and changes in blood flow conditions and minimizes disorders in the shear stress of the vascular wall [15, 16]. The presence of vascular spirality weakens the extreme pressure in the arteries [17]. 

It is also worth noting that the factor of tortuosity of the umbilical arterial vessels is not unique in nature. E.g., experimental and clinical studies of collateral circulation revealed the phenomenon of tortuosity of the forming pathways of bypass flow during occlusion of the main circulation. In particular, V.N. Tonkov, studying the dynamics of collateral formation in various parts of the body, described the spiral course of vessels as a functional factor in adaptation to varying conditions of circulation [18]. Hence, the spiral type of vessel orientation can contribute to adequate blood redistribution, which is especially important in dynamically changing blood flow conditions.

As a result of our study, the important protective role of the EMCT was confirmed, because when external pressure was applied to an isolated vessel, we observed its deformation, lumen narrowing, and changes in hemodynamic parameters to a greater extent than when applied via the EMCT.

The EMCT tightly surrounds the umbilical vessels [1]. It is a spongy structure with pores filled with hyaluronic acid, proteoglycans, and hydrophilic molecules. Due to its structure, the EMCT resists compression, thereby protecting the umbilical vessels from mechanical compression [19]. Based on the above, we conclude that it is incorrect to consider the effect of external pressure on the umbilical vessels out of context: it is necessary to take into account the complex of the vein, two arteries and the EMCT closely adjacent to them. 

The novelty of our study lies in the computer modeling of the umbilical cord vessels and EMCT, based on both original morphological analysis and published data related to the intranatal period. 

Conclusion

The proposed 3D model developed on the basis of corrosion cast specimens of umbilical vessels is an adequate tool for morphofunctional study of fetoplacental circulation. Anatomical and hemodynamic parameters in the umbilical vessels undergo transformations of varying severity during the intranatal period. These changes involve an increase in intravascular velocity and blood flow pressure, deformation of the umbilical cord and vascular wall and narrowing of the lumen of the vessels, while maintaining the cross-sectional area of the umbilical cord and its vessels against the background of external pressure. We believe that our study has clinical significance and indicates the need to use ultrasound imaging of the umbilical cord and study of fetoplacental circulation during labor. 

Author contributions: M.Yu. Klyavlina – the concept of the study, data collection and, manuscript preparation; R.T. Nigmatullin – data analysis, text editing; D.Yu. Rybalko – text editing; A.V. Maslennikov – the concept of the study; A.A. Kasatkin – data collection; N.A. Vorontsova – data collection. 

Conflict of interest. None declared.