Morphometric Features of Different Types of Bifurcations in the Splenic Intraorgan Arterial System in Individuals of Different Gender and Age

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LIST OF ABBREVIATIONS

CI — confidence interval

INTRODUCTION

The spleen is one of essential organs of the immune system [1]. Extirpation of the spleen leads to disruption of many functions of this system. In the context of increasing number of traumatic injuries of the spleen, there is much concern about organ-saving operations (partial resection of damaged tissues) [2]. Besides, the problem of early objective diagnosis of spleen pathology based on the search for quantitative criteria of norm is actively discussed. The development of such methods is impossible without a thorough theoretical study, in particular, a morphological investigation of the intraorgan arterial bed of spleen [3, 4].

A promising direction that has recently emerged in morphology is investigation of the arterial bed of various human organs as fractal or quasi-fractal systems [5, 6]. Conceptual models have been developed that permit to quantitatively describe the peculiarities of the vascular bed. In the opinion of the authors of this work, this approach will help create a morphometric standard of the intraorgan vascular bed, which will be useful in objective diagnosis of probable deviations from the normal structure [7]. One of such models is a dichotomous model, which presents the arterial bed as a structure consisting of interconnected bifurcations. This model is also interesting from the point of view of the fact that arterial lesions most commonly occur in the points of their branching [8, 9].

As shown earlier, bifurcations structurally differ from each other. There are distinguished different groups [7] and types [10] of bifurcations. However, the presented morphological variants do not cover the entire structural diversity of bifurcations. Speculatively, bifurcations of the intraorgan arterial bed of spleen can be divided into three types: type 1 — open bifurcations (the inner diameter of the mother arterial segment (D) is less than the sum of the inner diameters of the daughter arterial segments (dmax и dmin), D < dmax + dmin)); type 0 — neutral bifurcations (the inner diameter of the mother arterial segment (D) equals the sum of the inner diameters of the daughter arterial segments, D = dmax + dmin); type 2 — closed bifurcations (the inner diameter of the mother arterial segment (D) is greater than the sum of the inner diameters of the daughter arterial segments, D > dmax + dmin).

The aim of this study to identify morphometric features of different types of bifurcations of the intraorgan arterial bed of spleen in individuals of different gender and age.

MATERIALS AND METHODS

This paper investigated the characteristics of the intraorgan arterial bed of spleen of 67 people who died suddenly or from accidental causes at the age from 21 to 60. The study was performed on corrosion preparations. The study was carried out in compliance with the ethical principles, including those stated in the World Medical Association’s Declaration of Helsinki. The study was approved by Ethics Committee of the Medical Institute of Kadyrov Chechen State University (Protocol No. 258/24-77 of October 16, 2022). The work used age periodization accepted at VII All-Union Conference of 1965 on Problems of Age-Related Morphology, Physiology and Biochemistry.

To make corrosion preparations, the section material was collected according to the following criteria: spleens obtained at autopsy from people of both genders aged 21 to 60 years who died from occasional causes (33 men, 34 women; 34 people belonged to the first period of adulthood, 33 — to the second period) not associated with pathology of spleen and vascular bed). Mass of spleen 150 g–190 g, no external damages. Exclusion criteria: age of victims below 21 and above 60; mechanical damages to the spleen; history of spleen disease, visible deformations and anomalies of the vascular bed of the spleen.

The recorded information was gender, age, date of death, date of autopsy, date of experiment, weight of the organ, No. of autopsy protocol, cause of death. Corrosion preparations of the intraorgan arterial bed of spleen were prepared according to the standard procedure [11].

The vascular bed was presented as connected graphs where the vertices corresponded to the points of branching of arteries, and edges — to arterial segments. The vertices of the graph were numbered arbitrarily and identically for all the study cases [7]. The parameters of each arterial segment of corrosion preparations of the splenic intraorgan arterial bed were measured using a gradual stepwise decomposition of the cast, namely: the diameter (D) of the arterial segment in its central part (in the middle of the distance between the nearest branches) in mm and the length (L) of the arterial segment in mm determined as the shortest distance between two branches with the measurement accuracy up to 0.01 mm. The minimal diameter of casts of arterial segments measured by this method was 0.1 mm. The obtained data were entered into special tables (Excel, Microsoft Office, USA): the first column of the database was protocol number; 2 — age group (1 — the first period of adulthood, 2 — the first period of adulthood); 3 — gender (1 — male, 2 — female); 4 — conventional address of the beginning of segment; 5 — conventional address of the end of segment; 6 — D (mm), 7 — L (mm).

To characterize this structure, the values of the following parameters were determined based on the morphometry data [7]:

1. Gr — generation number — the ordinal number of the newly formed group of arteries to which the given segment belonged. Here, the ‘artery’ was understood as a linear structure consisting of daughter segments with a larger inner diameter;
2. i — division level — a newly formed series of arterial segments;
3. FF1 — form factor, $FF1=\frac{2L}{D}$
4. ƞ — branching factor, $7\eta =\frac{d_{max}^2+d_{min}^2}{D^2}$
5. γ — asymmetry factor, $\gamma ={\left(\frac{d_{min}}{d_{max}}\right)}^2$

To obtain a representative sample, the method of multistage cluster sampling according to G G Avtandilov was used [12]. The optimal sample size was determined using the equation:

$N=2x(A+B){}^{2}x\frac{S^2}{DIF{F}^2}$

where N is the recommended sample size for each group; S is the mean square deviation of the analyzed attribute; DIFF is the effect value (differences between the average values) supposed to be identified; A = 1.96 is a constant depending on the significance level; В = 0.84 is a constant depending on the power of the criterion; at significance level 5% A = 1.96) and power 80% (В = 0.84).

 

Fig. 1. Examples of corrosion preparations of the spleen: (a) a man, 31 years old; (b) a man, 60 years old.

 

In total, 6,840 arterial bifurcations were examined which were located at 20 levels of division and presented 8 generations.

The distribution of the values of the study parameters was checked for correspondence to the normal distribution law using Kolmogorov–Smirnov test. The distribution type of all the study parameters, absolute and relative was found to differ from the normal distribution law (Table 1).

 

Table 1. Results of Check of Distribution of Values of Study Parameters for Correspondence to Normal Distribution Law (n = 6,840, n₁ = 67)

Parameters	Results of Analysis
	Kolmogorov–Smirnov Test	p
Gr	0.188	0.0001
i	0.094	0.001
D, mm	0.210	0.0001
dmax, mm	0.225	0.0001
dmin, mm	0.291	0,0001
L, mm	0.140	0,0001
lmax, mm	0.144	0.0001
lmin, mm	0.155	0.0001
FF1	0.142	0.0001
ƞ	0.200	0.0001
γ	0.232	0.0001

Notes: D — proximal segment diameter; dmax — larger distal segment diameter; dmin — smaller distal segment diameter; L — proximal segment length; lmax — larger distal segment length; lmin — smaller distal segment length; FF1 — form factor (length-to-radius ratio); γ — кasymmetry factor of distal branches; p — significance level of Kruskal–Wallis test for independent samples, n — number of bifurcations, n1 — number of corrosive preparations

 

For assessing the differences in the groups, Kruskal–Wallis test for independent samples was used. In the work, medians, 95% confidence interval (CI) of median (Me) and relative number of categorical values were determined on different generations and division levels. The statistical analysis was performed using the R language.

RESULTS

According to the aim of the study, all bifurcations were divided into 3 types: type 1 — open bifurcations; type 0 — neutral; type 2 — closed. It was established that in the structure of the intraorgan arterial bed of spleen (Figure 2a), the neutral type (0) bifurcations predominated (n = 51%). The least represented were type 2 bifurcations (9%). Open bifurcations (1) took the intermediate position.

 

Fig. 2. The relative number of bifurcations of the intraorgan arterial bed of spleen: total (a), depending on gender (b), depending on age (c).

 

The results of a comparative analysis of the relative number of various types of bifurcations in persons of different gender and age groups (first and second periods of adulthood) are shown in Figures 2b, 2c. The relative number of open bifurcations in the intraorgan arterial bed of spleen was slightly higher in men (46%) than in women (35%). In contrast, the number of neutral bifurcations was higher in the group of women (55%) than of men (46%). The relative number of closed bifurcations differed insignificantly: 8% in men and 10% in women. Neutral bifurcations predominated in the groups of the first and second periods of adulthood with a small difference: 54% in the second period and 48% in the first. The relative number of open and closed bifurcations was higher in the first adult period (42% and 10%, respectively) than in the second (38% and 8%).

At the next stage of the work, the morphometric parameters of different types of bifurcations of the intra-organ arterial beds of spleen were determined (Table 2).

 

Table 2. Parameters (Me (95% CI)) of Different Types of Studied Bifurcations of Intraorgan Arterial Bed of Spleen (n = 6,840, n1 = 67)

Parameters	Morphofunctional Type of Bifurcation			p
	open (1), D < dmax + dmin	neutral (0), D = dmax + dmin	closed (2), D > dmax + dmin
Gr	3 (3; 4)	3 (3; 4)	3 (3; 4)	0.0001
i	7 (7; 8)	8 (8; 9)	8 (8; 9)	0.0001
D, mm	0.9 (0.9; 1.0)	0.3 (0.6; 0.7)	0.6 (0.6; 0.7)	0.0001
dmax, mm	0.7 (0.7; 0.8)	0.2 (0.2; 0.3)	0.3 (0.3; 0.4)	0.0001
dmin, mm	0.4 (0.4; 0.5)	0.1 (0.1; 0.1)	0.1 (0.1; 0.1)	0.0001
L, mm	3.1 (3.1; 3.2)	2.7 (2.7; 2.9)	3.0 (3.0; 3.2)	0.0001
lmax, mm	2.7 (2.7; 2.9)	2.2 (2.2; 2.3)	2.0 (2.0; 2.1)	0.0001
lmin, mm	2.6 (2.6; 2.7)	2.0 (2.0; 2.1)	1.8 (1.7; 2.0)	0.0001
FF1, mm	7.0 (6.9; 7.4)	17.0 (16.7; 18.0)	9.4 (8.6; 10.0)	0.0001
ƞ, mm	0.91 (0.91; 0.94)	0.50 (0.50; 0.50)	0.36 (0.36; 0.39)	0.0001
γ, mm	0.44 (0.44; 0.51)	1.0 (1.0; 1.0)	0.25 (0.25; 0.44)	0.0001

Notes: D — proximal segment diameter; dmax — larger distal segment diameter; dmin — smaller distal segment diameter; L — proximal segment length; lmax — larger distal segment length; lmin — smaller distal segment length; FF1 — form factor (length-to-radius ratio); ƞ — branching factor; γ — asymmetry factor of distal branches; n — number of bifurcations, n1 — number of corrosion preparations; Ме — median; CI — confidence interval; p — significance level of Kruskal–Wallis test for independent samples

 

Thus, the largest diameter of mother segments was found in open bifurcations, the smallest — in neutral ones (Table 2). The maximal segment lengths were characteristic of open bifurcations, the minimal — of neutral ones. The maximal value of FF1 form factor was observed in neutral bifurcations and the minimal — in open ones. The maximal branching factor was noted in open bifurcations, and the minimal — in closed ones. The highest symmetry factor was typical of neutral bifurcations, the smallest one — of closed.

At the final stage, the distribution of different types of bifurcations was analyzed for different generation numbers and division levels of the intraorgan arterial bed of spleen. With an increase in the generation number and division level, the relative number of neutral bifurcations increased, of open bifurcations decreased and of neutral ones practically did not change (Figure 3).

 

Fig. 3. Distribution of various morphological types of bifurcations by division levels (a) and generation numbers (b).

 

DISCUSSION

The problem of searching for a morphological, to be more exact, a morphometric, standard and, based on it, a morphometric criterion for the norm of the vascular bed of the internal organs of a person is one of the key tasks of modern medicine. Today, there have finally formed two main directions, similar to and different from each other.

The arterial bed of the internal organs (including spleen) is known to have a tree-like configuration [6] and branches out in the depth or on the surface of organs relatively uniformly. To this end, the vascular tree has a fractal (self-similar), or, more exactly, quasi-fractal geometry, which permits to model and, consequently, to quantify these structures using fractal analysis [13]. This direction was initiated by Benoit Mandelbrot in 1975 to designate irregular, but self-similar structures [14, 15].

The main quantitative characteristics of a fractal object is its fractal dimensionality — a measure of the filling of a space with the studied structure, in the given case — with vessels [16]. The value of this dimensionality is proposed to be used as a morphometric standard of normal structure. The calculation of this value does not present any special difficulties. The evaluation of the fractal geometry of the arterial bed can be performed with the minimal participation of a diagnostician and can serve as a method of preclinical diagnosis of circulatory disorders. The main disadvantage of this approach is impossibility to exactly understand the physical sense of the values obtained. For this reason, its use in further practical and theoretical investigations is limited.

A different approach to the study of the arterial bed of internal organs is proposed by the authors of conceptual models of vascular beds (segmental, dichotomous, trunk models) [6, 7], where the vascular bed is presented as a system consisting of self-similar, and in a certain way, interconnected structural elements — vascular segments, bifurcations, trunks. This approach allows not only to determine the morphometric standard, but also to completely restore the structure of the arterial bed to the hemomicrocirculatory bed level by its initial parts through numerical modeling and knowledge of the basic morphofunctional principles of the structure.

The main models of the vascular bed:

Segmental model

The main morphofunctional unit is an arterial segment, and the vascular bed is represented as a structure consisting of various segments forming rows — division levels. At the same time, an arterial segment is defined as a part of the arterial bed located between two adjacent division levels.

Dichotomous model

The arterial bed is considered as a structure consisting of interconnected dichotomous branches. Arterial branching is a more complex element of the system compared to the arterial segment and includes a mother vascular segment, two daughter branches and a point of bifurcation.

Trunk model

The arterial bed is considered as a system consisting of interconnected trunks — arteries. According to this model, the artery is a linear structure that includes daughter segments with a large diameter from a given point to the microcirculatory bed level.

The most widespread is the dichotomous model. There are widely known works of B Py, C D Murray, H B M Uylings, M Zamir, and others devoted to this issue [17–20]. We believe that there is no special need to repeat this once again. However, it would be appropriate to recall that the authors of the above-mentioned works considered the arterial bed as a system consisting of ideal — ‘optimal’ — bifurcations focused on passing blood at minimal ‘cost’. Nevertheless, further studies have shown that the intraorgan vascular bed of the heart [10] and kidney [7] consists of structurally different groups (‘optimal’ and ‘suboptimal’) and types (complete asymmetry, lateral asymmetry, unilateral symmetry and complete symmetry) of bifurcations.

The given study considers three morphologically different types of bifurcation: type 1 — open bifurcations where the inner diameter of the mother arterial segment (D) is less than the sum of inner diameters of daughter arterial segments (dmax и dmin), D < dmax + dmin; type 0 — neutral bifurcations where the inner diameter of the arterial segment equals the sum of inner diameters of the daughter segments, D = dmax + dmin; type 2 — closed bifurcations where the inner diameter of mother arterial segment is greater than the sum of inner diameters of the daughter segments, D > dmax + dmin.

The results obtained strongly evidence the existence of all the three types. It has been shown that the relative number of various types of bifurcations is not the same and differs depending on gender and age. It is noticeable that females of the second period of adulthood have a higher relative number of neutral bifurcations and a lower number of open bifurcations than men and individuals of the first period of adult-hood. This fact can probably be used as a favorable sign in prognosis of survival. Apparently, neutral bifurcations are more labile in terms of adaptation of the intraorgan arterial bed of spleen to the constantly changing physiological conditions of the existence of an organism as a whole.

The diameters and lengths of arterial segments of neutral bifurcations are significantly smaller, and the form factor and asymmetry factor are noticeably greater than those of open and closed bifurcations, that is, neutral bifurcations, in general, turn out to be the smallest and the most symmetrical.

The arrangement of various types of bifurcations by division levels and generation numbers confirms the said above. It is clearly seen that with increase in the division level and generation number, the relative number of neutral bifurcations increases, of open bifurcations noticeably decreases and of closed bifurcations remains approximately constant. The fifth division level and the second-generation number are the key point where the relative numbers of neutral and open bifurcations are equal. Most likely that this topographic point plays a key role in the functioning of the entire intraorgan arterial bed of spleen and can be the main diagnostic object. The morphometric characteristics of bifurcations at the given point, as well as its location, can probably be used as a morphometric reference. That is, displacement of the intersection points of the curves describing the relative number of neutral and open bifurcations can be interpreted as a deviation of the structure of the intraorgan arterial bed of spleen from the norm.

Probable limitations of the study and prospects for further investigation.

The described facts are probably manifested only in the intraorgan arterial bed of a human spleen. It is known that different parenchymal organs perform different functions and, therefore, the structure of the intraorgan vascular beds and structural elements constituting them, may be different. It can be suggested that the functions of various types of bifurcations of the intraorgan arterial bed of spleen are not limited by passage of blood at the lowest ‘cost’. The above said suggests conducting a comparative quantitative investigation of the total possible spectrum of functions performed by different types of bifurcations, for example, passage and distribution of blood and a supporting function. It is required that similar investigations be conducted in relation to the intraorgan vascular beds of other parenchymal organs, such as kidney and liver.

CONCLUSIONS

1. The intraorgan arterial bed of spleen is a quasi-fractal system consisting of three types of bifurca- tions — open (40%), neutral (51%) and closed (9%).
2. The relative number:
3. a) of open bifurcations in the splenic intraorgan arterial bed is greater in men (46%) than in women (35%); of neutral bifurcations is greater in the group of women (55%) compared to men (46%); of closed bifurcations is less in men (8%) than in women (10%);
4. b) of neutral bifurcations is higher (54%) in the splenic arterial bed in the individuals of the second period of adulthood, and of open (38%) and closed (8%) bifurcations is less than in the individuals of the first period of adulthood: 48%, 42% and 10%, respectively;
5. c) of neutral bifurcations increases and of closed ones decreases with increase in the generation number and division level, and the number of closed bifurcations practically does not change.
6. The following was established:
7. a) the difference in the relative number of various type of bifurcations in individuals of different gender and age was identified;
8. b) the predominant arrangement of various types of bifurcations by generation number and division level was shown;
9. c) the difference in the values of form factor, branching factor and asymmetry factor in various types of bifurcations was identified that should be taken into account in the quantitative modeling of the structure of the intraorgan arterial bed of spleen of humans of the respective gender and age, and of the structure of various types of bifurcations.

ADDITIONALLY

Funding. This study was not supported by any external sources of funding.

Conflict of interests. The authors declare no conflicts of interests.

Contribution of authors: A. S. Dadashev — collection and processing of material, writing the text; O. K. Zenin — research conception and design, editing; I. S. Miltykh — processing of material, statistical processing; E. S. Kafarov — research conception and design, editing. The authors confirm the correspondence of their authorship to the ICMJE International Criteria. All authors made a substantial contribution to the conception of the work, acquisition, analysis, interpretation of data for the work, drafting and revising the work, final approval of the version to be published and agree to be accountable for all aspects of the work.

Финансирование. Авторы заявляют об отсутствии внешнего финансирования при проведении исследования.

Конфликт интересов. Авторы заявляют об отсутствии конфликта интересов.

Вклад авторов: Дадашев А. Ш. — сбор и анализ данных, написание текста; Зенин О. К. — концепция исследования, дизайн исследования и редактирование; Милтых И. С. — обработка материала, статистический анализ; Кафаров Э. С. — концепция исследования, дизайн исследования и редактирование. Авторы подтверждают соответствие своего авторства международным критериям ICMJE (все авторы внесли существенный вклад в разработку концепции, проведение исследования и подготовку статьи, прочли и одобрили финальную версию перед публикацией).

About the authors

Ali Sh. Dadashev

Kadyrov Chechen State University

Email: mukulatura95@mail.ru
ORCID iD: 0000-0001-8502-0841
Russian Federation, Grozny

Oleg K. Zenin

Penza State University

Author for correspondence.
Email: zen.olegz@gmail.com
ORCID iD: 0000-0002-5447-1989

MD, Dr. Sci. (Med.), Professor

Russian Federation, Penza

Ilia S. Miltykh

Penza State University

Email: contact@miltykh.com
ORCID iD: 0000-0002-9130-3255
Russian Federation, Penza

Edgar S. Kafarov

Kadyrov Chechen State University

Email: Edgar-kafaroff@yandex.ru
ORCID iD: 0000-0001-9735-9981

MD, Dr. Sci. (Med.), Professor

Russian Federation, Grozny

References

Supplementary files