The use of modern information technology in biomedical research permits to obtain a holistic cybernetic view of the cell. The method of constructing correlation portraits of different fields of hormone-producing cells' activity has significantly expanded the approaches to studying the relationships between their ultrastructures in different conditions. However, the significance of the portrait nodal points for cell activity remains unclear. This paper first presents a step-by-step study of the nodal points of correlation portraits of follicular thyrocytes' transport capability, which consists in elucidating their connection filling, the studied correlations between their constituent elements, analyzing the effect of the established transport features of hormonal product by intraorganic microcapillary bed under the effect of organic and inorganic iodine. It is established that the nodal points of correlation portraits are mathematical results of stabilizing and adapting changes in hormonal cells, the study of which will permit to better understand the functional dependencies that occur in the cell during its activity.
deficiency mathematical methods in cytology, correlation analysis, correlation portrait, thyroid gland, follicular thyrocyte, thyroid hormone transport, organic iodine, inorganic iodine, iodine
This work is a continuation of a series of our studies prioritized in this field of science, previously
presented at IDDM’2018 [
We base our concept of cytological research on the approach to the cell as a cybernetic
selfregulatory system. Based on these ideas, the animal cell is subject to many different external and
internal influences, with internal influences being divided into influences of other cells of the same
organ and influences of different body systems cells. The point of application of influences in the cell
are cellular ultrastructures, which are strictly functionally specialized and implement a specific field
of the cell activity [
2021 Copyright for this paper by its authors.
One of the prerequisites for the functioning of the biological system is its diversity – the number of
states that it can acquire under certain conditions [
The task of biomedical diagnostics is to establish the dependence of the diagnosis on many state parameters of the studied system. Then the task of medical diagnosis is to find a expression ∗ = ( 1∗, 2∗, 3∗, … , ∗ ) → ∈ = ( 1, 2, 3, … , ) , (1) where X* is a set of a particular patient’s state parameters, and D is a set of diagnoses inherent in the given field of medicine.
However, the main mathematical methods used to solve diagnostic problems (Bayesian [
= ( 1, 2, 3, … , ) , (2) where fd is some function that establishes a relationship between the variables xi, i = 1, n and d.
The variables x1 xn and the function d can be quantitative, qualitative or expressed using special scales, for example, by a scoring system. This makes it possible to take into account the qualitative staining of the condition, which significantly expands the possibilities of establishing a correct diagnosis, but provides a strict determinism of the diagnosis on the input data, which is difficult to achieve when studying the cell.
Traditional methods of cytological examination are based on the use of either quantitative data
about the object under study, or qualitative information that describes the state of this object.
Quantitative definitions that can be subjected to mathematical transformation can not establish and
analyze all the nuances of the cell’s state as a biological system, while qualitative information about
it, which is given in words of the language used and is able to note the slightest changes in its state
under various influences, can not be calculated, and hence objectified. This does not permit to
analyze, compare, summarize the data obtained and draw sound conclusions. Thus, approaches to the
formalization of qualitative and binary information about the cell, despite its importance for medical
science, remain undeveloped. In our previous publications, in particular [
The purpose of the presented work was to study the significance of the nodal points of correlation portraits as places that connect and unite the ultrastructures of the follicular thyrocytes’ transport activity. The task of the study was to establish the value of nodal points for the transport of hormonal product by intraorgan microcapillary bed in the following model conditions: optimal supply of iodine to rats, uncorrected alimentary iodine deficiency, taking the minimum effective dose of organic and inorganic iodine.
The study was performed on 40 white nonlinear male rats with an initial body weight of 140–160g, which were kept in standard vivarium conditions for 30 days. Group 1 rats consuming common feed were universal controls for rats of other groups. Rats of groups 2, 3, 4 were on an isocaloric starchcasein diet; iodine-containing compounds were eliminated from the salt mixture to create a model of alimentary iodine deficiency. Adjustment of iodine starvation in rats of group 3 was performed with organic iodine (iodine-protein components), rats of group 4 – with inorganic iodine (potassium iodide), which they consumed in the minimum histologically confirmed dose of 21 μg/kg body weight. Iodine compounds were not added to the diet of group 2 rats, which were an additional control for animals of groups 3 and 4. During observation and euthanasia, the principles of bioethics were observed in compliance with the European Convention for the Protection of Vertebrate Animals Used in Experiments (Strasbourg, 1986) and Council of Europe Directive 2018/63/ CV.
The study methods used in this work have already been partially presented in detail by us at
IDDM’2020 [
Reference points for the construction of correlation portraits in all groups were moderate folding of the follicular thyrocytes’ basal cytoplasmic membranes (P2), moderate width of the microvessels’ pericapillary space (Q2), unchanged (normal) endotheliocytes (R2), no features (normal) microcapillary bed (S1). The main nodal points of correlation portraits were considered to be the points through which the most correlations pass, the additional nodal points are points with fewer correlations.
The actual features of the correlation portrait were P2, Q1, Q5, R2, R4, S1, between which the following correlations were observed: very high (1.00≥| r |≥ 0.91) – 2; high (0.90≥| r |≥ 0.71) – 0; salient (0.70≥| r |≥ 0.51) – 2; moderate (0.50≥| r |≥ 0.31) – 6 (all indirect). The main nodal points of the portrait were moderate folding of the basal cytoplasmic membranes of follicular thyrocytes (P2) and no features (normal) microcapillary bed (S1), which had 4 connections; additional nodal points of the portrait were an insignificant width of the pericapillary space (Q1), no additional inclusions in the pericapillary space (Q5), unchanged (normal) endotheliocytes (R2) and small pseudopodia of endotheliocytes (R4), which had 3 connections. Under conditions of optimal iodine supply of rats, the number of very high direct connections passing through the nodal points was 2, the number of high – 0, the number of salient direct connections – 2, while the number of moderate indirect connections was 6 (Fig. 1).
The connective filling of the correlation portrait nodal points of the intact rats’ follicular thyrocytes transport capability profile is presented in Tab. 2.
point nodal points with indication of their signs quality
no additional inclusions in the pericapillary space
insignificant width of pericapillary space
points elements
P2—Q5 Сorrelation coefficient (r)
0.612 P2—R4 P2—R2 P2—Q1 S1—Q1 S1—Q5 S1* Q5 R2 no features (normal) microcapillary bed unchanged (normal) endotheliocytes no features (normal) microcapillary bed small pseudopodia of endotheliocytes no additional inclusions of pericapillary space small pseudopodia of endotheliocytes unchanged (normal) endotheliocytes insignificant width of pericapillary space
R2—Q1 −0.408 1.000
Nodal point P2, through its direct connections (r=0.612) with Q5 and R4, contributes to the harmonization of indirect connections (r=−0.408) with Q1 and R2, which have a certain disharmonious potential. Nodal point S1 harmonizes indirect connections (r=−0.408) traced between Q1, Q5, R2, R4, which can cause instability of the transport system. At the same time, a certain instability of the system, which is indicated by indirect connections S1, may be a sign of its ability to adapt. Under conditions of optimal odine supply to rats, the correct transport of the hormonal product by the microcapillary bed occurs in the presence of 2 main components: the relationship "Q1—R2 (insignificant width of the pericapillary space - normal endotheliocytes)" and "Q5—R4 (no inclusions in the pericapillary space - small pseudopodia of endotheliocytes)", very high direct connections (r=1.000) which provide functional balance in the transport system.
The actual features of the studied portrait were P3, Q1, Q2, Q5, R2, R3, R5, S1, between which very high connections (1.00≥| r |≥ 0.91) – 1 (indirect), high connections were traced (0.90≥| r |≥ 0.71) – 1, salient connections (0.70≥| r |≥ 0.51) – 5 (indirect 4), moderate connections (0.50≥|r |≥ 0.31) – 7 (indirect 4). The main nodal points of the portrait were normal (R2) and hypertrophied endotheliocytes (R3), which had 5 conneсtions each; additional nodal points were a significant fold of the basal cytoplasmic membranes of follicular thyrocytes (P3), an insignificant width of the pericapillary space (Q1), no additional inclusions in the pericapillary space (Q5), small pseudopodia of endotheliocytes (R4), no features (normal) microcapillary bed (S1), which had 3 connections. Under conditions of alimentary iodine deficiency, the following connections passed through the nodal points of the correlation portrait: very high – 1 indirect, high – 1 direct, salient – 5 (indirect 4), moderate – 8 (indirect 5) - see Fig. 2.
The connective filling of the nodal points of the follicular thyrocytes transport capability correlation portrait profile of rats, which were in conditions of alimentary iodine deficiency, are presented in Tab. 3.
Nodal point R2 through direct communication (r=0.408) R2 with S1 stabilizes indirect connections R2 with R4 (r=−0.612), and with P3 (r=−0.408), which indicate a functional mismatch in the transport of hormonal product by intraorgan microcapillary bed. Another area of the nodal point R2 influence on the activity of thyrocytes is the adaptation of the intraorgan microcapillary bed to the transport of thyroid hormones in conditions of iodine deficiency. Manifestations of this are the following connections: direct with Q1 (r=0.408) and indirect with Q5 (r=−0.612).
The nodal point R3 also has a stabilizing effect on hormone transport. Thus, the direct connection of R3 with S1 (r=0.612) helps to reduce the adverse (unbalancing) effects of indirect connections (r=−0.408) R3 with Q1, Q5, R4 and a direct connection of the same force with P3. Nevertheless, a very high indirect connection between the nodal points P3 and Q1 (r=−1.000) indicates that the system is generally in an unstable state.
The actual features of the studied portrait were P3, Q2, Q3, Q5, R2, R3, R5, S1, between which the following correlations were established (Fig. 3): very high (1.00≥| r |≥0.91) – 3 (of which indirect – 2), salient connections (0.70≥| r |≥0.51) – 11 (6 indirect), moderate connections (0.50≥| r |≥ 0.31) – 7 (of which indirect 5). The main nodal points of the portrait were a significant folding of basal cytoplasmic membranes of follicular thyrocytes (P3), unchanged (normal) endotheliocytes (R2), hypertrophied endotheliocytes (R3), medium (normal) pseudopodia of endotheliocytes (R5), which had 6 connections each. Additional focal points of the portrait were Q2, Q3, S1, which had 5 connections, and Q5, which had 3 connections.
The connective filling of the nodal points of the transport capability profile correlation portrait of rat follicular thyrocytes, for which the alimentary iodine deficiency was corrected with the minimum effective dose of organic iodine (21μg/kg body weight), is presented in Tab. 4. R2* R2* R2* R2* R3* R3* R3* R3* R5* R5* R5* Q3 S1 Q5 unchanged (normal) endotheliocytes hypertrophied endotheliocytes unchanged (normal) endotheliocytes moderate width of pericapillary space unchanged (normal) endotheliocytes significant width of pericapillary space unchanged (normal) endotheliocytes medium (normal) pseudopodia of endotheliocytes unchanged (normal) endotheliocytes no features (normal) microcapillary bed hypertrophied endotheliocytes significant width of pericapillary space hypertrophied endotheliocytes medium (normal) pseudopodia of endotheliocytes hypertrophied endotheliocytes moderate width of pericapillary space hypertrophied endotheliocytes no features (normal) microcapillary bed medium (normal) pseudopodia of endotheliocytes no features (normal) microcapillary bed medium (normal) pseudopodia of endotheliocytes significant width of pericapillary space medium (normal) pseudopodia of endotheliocytes moderate width of pericapillary space significant width of pericapillary space no additional inclusions in pericapillary space no features (normal) microcapillary bed no additional inclusions of pericapillary space no additional inclusions of pericapillary space moderate width of pericapillary space R2—Q2 R2—Q3 R2—R5 R2—S1 R3—Q3 R3—R5 R3—Q2 R3—S1 R5—S1 R5—Q3 R5—Q2 Q3—Q5 S1—Q5 Q5—Q2 0.612 −0.612 −0.667 −0.408
Analysis of the correlations in the discussed portrait showed that their combination at the node point P3 improves the transport direction of the thyroid gland. Thus, a very high direct connection of P3 with R2 (r=1.000) and connections of P3 with Q2 (r=0.612) and S1 (r=−0.408) balance the indirect connections of P3 with R3 (r=−1.000), Q3 (r=−0.612) and R5 (r=−0.667), which indicate certain difficulties in transporting the hormonal product.
The connections at the R2 node point indicate an improved transport of thyroid hormones. This is indicated by the direct relationship R2 with Q2 (r=0.612) and the indirect relationship R2 with S1 (r=−0.408) and R5 (r=−0.667). The node point R3 has the same adaptive effect, in which the correlations R3 are connected: direct with Q3 (r=0.612) and R5 (r=0.667), and indirect with S1 (r=−0.408). In turn, the correlations that form the R5 nodal point have a certain stabilizing effect on the transport direction of thyrocytes. These include direct connections R5 with S1 (r=0.612), R3 (r=0.667), Q3 (r=0.408), and indirect connections R5 with R2 (r=−0.667) and P3 (r=−0.667). Peculiarities of correlations in nodal points Q2, Q3, Q5, S1 have already been considered in the study of other nodal points of the discussed correlation portrait.
The actual characteristics of the correlation portrait were P1, P2, Q2, Q3, Q5, R2, R3, R4, R5, S3, S5, S6, between which the following correlations were established (Fig. 4): very high (1.00≥| r | ≥0.91) – 8 (of which indirect - 4), high (0.90≥| r |≥0.71) – 2 (all direct), salient 0.70≥| r |≥0.51) – 25 (17 of them are indirect), moderate 0,50≥| r |≥0,31 – 6 (of which indirect - 1).
The main nodal points of the portrait were a moderate width of pericapillary space (Q2) and hypertrophied endotheliocytes (R3), which had 10 connections each. Additional nodal points of the portrait were P1 – 8 connections; Q3, R5, S3, S5, S6, which had 7 connections each; Q5 and R4 – 5 connections each; R2 – 4 connections. The connection filling of the nodal points correlation portrait of the transport capability profile of rat follicular thyrocytes, for which the alimentary iodine deficiency was corrected with the minimum effective dose of inorganic iodine (21μg/kg body weight), is presented in Tab. 5. Q2* R3* R3* R3* R3* R3* R3* R3* R3* R3* P1 P1 P1 P1 P1 P1 P1 P1 Q3 Q3 Q3 Q3 R5 R5 moderate width of pericapillary space unchanged (normal) endotheliocytes moderate width of pericapillary space small pseudopodia of endotheliocytes hypertrophied endotheliocytes medium (normal) pseudopodia of endotheliocytes hypertrophied endotheliocytes significant width of pericapillary space hypertrophied endotheliocytes no additional inclusions in pericapillary space hypertrophied endotheliocytes presence of erythrocytes in microcapillary bed hypertrophied endotheliocytes presence of mast cells in microcapillary bed hypertrophied endotheliocytes presence of fibrin threads in microcapillary bed hypertrophied endotheliocytes moderate folding of basal cytoplasmic membranes hypertrophied endotheliocytes unchanged (normal) endotheliocytes hypertrophied endotheliocytes small pseudopodia of endotheliocytes insignificant folding of basal cytoplasmic membranes significant width of pericapillary space insignificant folding of basal cytoplasmic membranes unchanged (normal) endotheliocytes insignificant folding of basal cytoplasmic membranes small pseudopodia of endotheliocytes insignificant folding of basal cytoplasmic membranes presence of erythrocytes in microcapillary bed insignificant folding of basal cytoplasmic membranes presence of mast cells in microcapillary bed insignificant folding of basal cytoplasmic membranes presence of fibrin threads in microcapillary bed insignificant folding of basal cytoplasmic membranes moderate folding of basal cytoplasmic membranes insignificant folding of basal cytoplasmic membranes no additional inclusions in pericapillary space significant width of pericapillary space presence of erythrocytes in microcapillary bed significant width of pericapillary space presence of mast cells in microcapillary bed significant width of pericapillary space presence of fibrin threads in microcapillary bed significant width of pericapillary space medium (normal) pseudopodia of endotheliocytes medium (normal) pseudopodia of endotheliocytes unchanged (normal) endotheliocytes medium (normal) pseudopodia of endotheliocytes presence of erythrocytes in microcapillary bed Q2—R4 R3—R5 R3—Q3 R3—Q5 R3—S3 R3—S5 R3—S6 R3—P2 R3—R2 R3—R4 P1—Q3 P1—R2 P1—R4 P1—S3 P1—S5 P1—S6 P1—P2 P1—Q5 Q3—S3 Q3—S5 Q3—S6 Q3—R5 R5—R2 R5—S3 R5 S3 S3 S6 Q5 Q5 R4 medium (normal) pseudopodia of endotheliocytes presence of mast cells in microcapillary bed medium (normal) pseudopodia of endotheliocytes presence of fibrin threads in microcapillary bed presence of erythrocytes in microcapillary bed presence of mast cells in microcapillary bed presence of erythrocytes in microcapillary bed presence of fibrin threads in microcapillary bed presence of fibrin threads in microcapillary bed presence of mast cells in microcapillary bed no additional inclusions in pericapillary bed moderate folding of basal cytoplasmic membranes no additional inclusions in pericapillary space small pseudopodia of endotheliocytes small pseudopodia of endotheliocytes moderate folding of basal cytoplasmic membranes R5—S6 S3—S5 S3—S6 S6—S5 Q5—P2 Q5—R4 R4—P2 −0.645 1.000
Correlations that pass through the nodal point Q2 significantly reduce the functional stress caused by iodine deficiency. These include the direct Q2 connections with R3 (r=1.000), R5 (r =0.791), Q3 (r=0.612), (r=0.612), R2 (r=0.408), and R4 (r=0.408). In general, indirect bonds (r=−0.612) Q2 with P2, S3, S5 and S6 indicate difficulties in hormone transport. However, we believe that in combination with other connections that form the discussed node Q2, they are an indication that inorganic iodine improves the transport capability of the intraorgan microcapillary bed.
The nodal point R3 had a similar effect. Thus, the complex of direct connections R3 with R5 (r=0.791), Q3 (r=0.612), Q5 (r=0.612), R2 (r=0.408), R4 (r=0.408) is aimed at stabilizing the functional capability of the microcapillary bed. Indirect connections R3 with S3 (r=−0.612), S5 (r=−0.612), S6 (r=−0.612), and P2 (r=−0.612), which generally indicate a certain inconsistency in the transport of the hormone under iodine deficit, are largely offset by other correlations that pass through the discussed node point.
Node point P1 harmonizes other correlations that pass through it. This is indicated by the complex of indirect connections of P1 with such indices of the state of endotheliocytes and microcapillary bed as R2 (r=−0.612), R4 (r=−0.612), S3 (r=−0.612), S5 (r=−0.612), S6 (r=−0.612), Q5 (r=−0.408). This aspect of the influence of the nodal point is evidenced by the direct connections of P1 with Q3 (r=0.612) and P2 (r=0.408). The nodal point S3, through its ultrastructural element S3, was connected by very high direct correlations (r=1,000) with S5 and S6.
Given the ability of erythrocytes to bind thyroid hormones to their membranes and distribute them to the bloodstream after binding to plasma proteins, we consider these connections to be an adaptive mechanism aimed at improving the transport of the hormonal product. Other connections that passed through the nodal point S3 were indirect connections S3 with P1 (r=−0.612), Q2 (r=−0.612), Q3 (r=−1.000), R3 (r=−0.612), R5 (r=−0.645), which also indicated that one of the means of transporting thyroid hormones by the microcapillary bed was erythrocytes.
Thus, the study of the nodal points connection content of correlation portraits and nomenclatures of these correlations made it possible to better understand the essence of the interactions of ultrastructures of the studied profile and to determine the general direction of their action in different study conditions. Thus, with optimal provision of the body of rats with iodine system-forming nodal points of the follicular thyrocytes transport capability correlation portrait were moderate folding of the basal follicular thyrocytes cytoplasmic membranes (P2) and no features (normal) microcapillary bed (S1), provide both activity and balance in the system of “transportation of the produced hormonal product by the intraorganic microcapillary bed”.
On the other hand, in the conditions of alimentary iodine deficiency, nodal points became especially important, the basis of which is significant folding of basal follicular thyrocytes cytoplasmic membranes (P3), normal endotheliocytes (R2), hypertrophied endotheliocytes (R3) and medium (normal) pseudopodia of endotheliocytes (R5). Through the connections of these systemforming nodal points, the hormone was transported under adverse conditions of iodine deficiency.
When correcting alimentary iodine deficiency with organic iodine, the transport of thyroid hormones provided stabilizing connections of nodal points, the system-forming basis of which was significant folding of basal cytoplasmic membranes of follicular thyrocytes (P3), unchanged and hypertrophied endotheliocytes (R2 and R3).
At the same time, when taking a similar dose of inorganic iodine, the transport of hormones was provided by a complex system of nodal points with stabilizing complexes of correlations. In this case, the system-forming basis of nodal points was an insignificant folding of the follicular thyrocytes’ basal cytoplasmic membranes (P1), moderate width of the pericapillary space (Q2), hypertrophied endotheliocytes (R3) and the presence of erythrocytes in the microcapillary bed (S3).
We noticed that the nodal point S1, the system-forming basis of which no features (normal) microcapillary bed, is a frequent component of correlation portraits of the studied direction of follicular thyrocytes. Because many indirect connections pass through it, we consider it an important stabilizing element of the intraorgan system of thyroid hormone transport. Comparison of the structural organizations of the correlation portraits’ nodal points studied in the presented work showed that the closest to the indices of intact rats (norms) were the data of rats that consumed organic iodine. The results are presented in the final Tab. 6.
Thus, the performed study became the basis for a certain revision of our previous views on the correlation portraits’ nodal points as exclusively places of accumulation of correlations. Taking into account the obtained data, we believe that the nodal points of the correlation portraits of the transport direction largely indicate changes in the activity of thyrocytes as hormone-producing cells.
1. Nodal points of correlation portraits are mathematical resultants of changes in cells. This permits to study the functional dependencies that occur during the activity of hormone-producing cells.
2. The interaction of correlations in the nodal points of correlation portraits has a stabilizing and adaptive effect on the studied activity of the cell, which makes the nodal points important elements of the regulating system.
3. A large number of nodal points in the correlation portrait may be a sign of a certain instability of the whole system.
4. When several correlations of a correlation portrait pass through one nodal point, their mutual potentiation or mutual weakening is possible, and the effect is directly proportional to the number of connections.
5. In the study of the transport direction of follicular thyrocytes, the most informative is the study of the main nodal points of correlation portraits.
6. The presence of additional nodal points in the correlation portraits of the follicular thyrocytes transport direction indicates significant reserve capability of follicular thyrocytes as hormoneproducing cells.
7. Analysis of the described nomenclature of the correlation portraits’ nodal points showed the variety of activities, stability and adaptation of the hormonal product transportation system in the correction of iodine deficiency with organic and inorganic iodine. This proves that the thyrocyte is a cybernetic self-regulatory system.
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