Construction of computer model in tissue morphometry

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Morphometry of tissues is usually conducted by direct microscopy [1-3]. All tissue elements are counted in the microscope field which is moved by a researcher «by eye’s estimation» with inevitable overlapping of fields which significantly influences the results. It is rarely possible to look through all microscope fields due to a high labor intensity of the process.

The surface area of the studied elements is not calculated or is assessed approximately with use of a reticle eyepiece. The section area of the entire preparation is calculated by application of millimeter paper onto the micro-preparation. In this case it is impossible to distinguish between different kinds of tissues (for example, between muscle tissue and stroma), and a significant error exists.

With manual microscopy and analysis, processing of one micropreparation takes up to 4-6 hours. Here, one cannot exclude mistakes that are difficult to detect. Correction of mistakes requires time comparable with that used for the primary analysis of micropre-parations [1].

Aim of work: partial automatization of histomorphological method for objective assessment of the condition of the studied tissues and for acceleration of histomorpho-logical examinations.

Materials and Methods

We examined mammary glands of normal rats and of rats with cystic breast [2, 4]. Morphometric analysis of 253 microprepara-tions of rats’ mammary glands was conducted by 23 parameters [3].

I. Taking photos of micropreparations.

Micromed-2 microscope with x40 magnification was used. Photos of microprepa-rations were taken using video eyepiece for Toup Cam 9.0 mp microscope (resolution 9 megapixels). It appeared to have excessive resolution while for the required quality of photos 3 megapixel resolution was sufficient. Here, photos partially overlapped. This did not influence the final model since all the basic parameters were calculated relative to the total area of photos and not to the area of the section of the micropreparation. There were made 10-30 photos of each micropreparation which took about 2-3 minutes. To study 253 micro-preparations, in total about 5,000 photos were taken which required about 12 hours.

II. Counting of tissue elements on photographs.

The obtained histomorphological photos were downloaded into a graphic editor (for example, Photoshop) and were processed layer-by-layer with calculation of the required parameters. For example, at the first stage everything not related to the micropreparation was eliminated, and the area of the whole tissue was calculated, at the second stage everything not related to stroma was eliminated with calculation of the area of stroma, and so on. The area of remained or eliminated elements of tissue in pixels (px) could be viewed in the extended «Histogram» window (shows the area of the highlighted figure). Besides the area, any other elements could be counted, for example, ducts of mammary glands or vessels. All calculated areas and values were recorded in Excel table.

This simplified method of computer morphometry resembles manual morpho-metry, but it is much faster and more convenient, since the calculation is carried out on a large screen of a computer with the probability for emphasizing the elements and for application of filters which is impossible with direct microscopy of the examined tissues.

III. Construction of computer model.

All values of parameters for each photo of a micropreparation were summated («summation» function), and final values for each micropreparation were obtained.

After that calculations were made using formulas (taken from the section «formulas» or written by the researchers themselves).

The areas of histomorphological elements were converted from px to µm². Resolution of the studied data was 800/600 px. With x40 magnification of the microscope: 1 mm=275 px, 1 mm²=75,625 px, 1 µm²≈0.0746 px, 1 px≈13.22 µm².

The area of pixels was calculated using the formula

$1 px=r\frac{S1}{S2}$

where r is pixel resolution of a certain photoin µm², S1 – surface area of a certain photo, S2 – surface area of a new photo.

Accordingly, with resolution 872/654 px:$1 px=13.22*\frac{800*600}{872*654}$ ≈11.12 µm². If magnification is changed, the value is multiplied by the ratio of the previous magnification to a new one.

Then a scheme was constructed in which all values were subject to a series of mathematical transformations to obtain the values of each parameter. This is a mathematical model of the conducted experiment that was presented in Excel in the form of successive columns in each of which a specific parameter was calculated. With this, at any moment it is possible to take any value from any column and use it for calculations (Fig. 1).

  

Fig. 1. Algorithm of construction of computer model in Excel

 

If in the experiment several groups of objects (for example, of animals) are studied which should be differentiated against each other, an additional stage is included to find the average values for each group with automatic calculation of mean square deviation.

In our case 23 groups of experimental animals were studied, therefore the average parameters were calculated for each group. On the basis of the average values for each group conclusions were made for the results of the work.

In the experiment 23 morphometric parameters were calculated:

• AHS (mm²) – area of histoto-pographic section of mammary gland.
• Q (in pieces) – total quantity of ducts in a section.
• QS (in pieces) – quantity of single ducts in the maximal cross section of mammary gland.
• QDG (in pieces) – quantity of ducts arranged in groups.
• QG (in pieces) – quantity of groups of ducts.
• P (in pieces per mm²) – density of glandular field = Q/AHS.
• DG – density of groups of ducts, equals QG/AHS.
• ADG – average quantity of ducts in one group, equals QDG/QG.
• %S – percentage of single ducts, equals QS/Q·100%.
• %G – percentage of grouped ducts of all ducts = 100%-%S.

11) %AGF – percentage of area of glandular field, equals percentage of the area of ducts of the area of mammary gland tissue.

12) %AS – percentage of the area of stroma, equals 100% - % of the area of ducts.

13) AGF – area of glandular field in mm², equals AHS·%AS.

14) AS – area of stroma in mm², equals AHS – AGF.

15) DV – degree of vascularization, equals the quantity of vessels/AS.

16) ADD – average dimension of one duct, equals AGF/Q in µm².

17)  CS – cellularity of periductal stroma.

18)  %C – percentage of cells.

19)  HE (in µm) – heigh to fepithelium. Assessment of the height of epithelium (thickness around ducts) in µm.

20)  AADE (in thousands of µm²) – average area of ductal epithelium.

21)  ADL (in thousands of µm²) – average area of a duct lumen, equals ADD-AADE.

22)  ADEM (in thousands of µm²) – area of ductal epithelium in maximal section, equals AADE·Q.

23)  AGL (in thousands of µm²) – area of glandular lumen, equals AGF-ADEM.

It should be noted that parameters P, ADD, ADL are considered the most important for assessment of a degree of cystic breast.

Results and Discussion

For calculation of practically all morphometric parameters 6 basic parameters are required: area of section, area of stroma, area of glandular tissue, area of lumens, quantity of ducts, quantity of vessels. Earlier the basic parameters (ADD, ADL) were calculated by indirect methods using formulas, with a high degree of error. Application of computer morphometry permitted to significantly improve accuracy of calculation of these parameters.

Visualization and assessment of relationships between the studied parameters permitted to detect some mathematical inaccuracies of the morphometry of mammary glands that was difficult to detect earlier without computer modeling. In particular, it appeared that division by the quantity of ducts often gives false-high and false-low results. This is due to the fact that ducts of mammary glands normally are practically invisible, and in result the number of ducts (denominator in many above described parameters) appears very low which makes the final result higher. And, vice versa, in case of prominent cystic breast all ducts are visible which makes the results false-low in comparison with partial regression of cysts when the total area of ducts practically remains unchanged, but minimally dilated ducts become invisible.

In our opinion, for more adequate evaluation of the condition of mammary gland tissue the following parameter may be used which will be especially effective in assessment of the extent of evidence of cystic breast condition: %DD (degree of dilation of lumens of ducts relative to the area of stroma). It equals ADL/AS. This parameter is helpful in the general assessment of the condition of ducts irrespective of the quantity of ducts (Q). Here it is possible to see what part of stroma is taken by dilated ducts which vividly reflects the extent of evidence of cystic breast. With manual morphometry, it is very difficult to calculate this parameter without high error.

After having obtained a computer model in Excel further research is conducted, in particular:

1. Statistical processing of results using Student’s and other methods (exist in Excel).
2. Visualization of results of work in graphic charts and diagrams.
3. Use of the obtained values at any stage for additional research activities (for example, use of machine training tools for establishment of relationships between the studied morphometric parameters).
4. Calculation of new parameters required for improvement of the model or of the method in general.

In our opinion, the advantages of a computer model are:

1. The given model is suitable for analysis of any tissue and not only of mammary glands.
2. All results are in the same place, and it is possible to visualize any parameter. This permits to see the results of the work in whole which facilitates formulation of conclusions and search for errors.
3. In case separate values or formulas are changed, the whole model is immediately recalculated which considerably accelerates research work.
4. The results may be checked at any level of research which simplifies search formistakes and improves transparency of the procedure of the scientific work.
5. The speed of morphometry is approximately 2-3 times that of direct microscopy even without use of machine training methods.
6. The obtained data may be used to establish generalities including those for construction of combined models to be used for description of the processes occurring in the organism, from different points of view.

The main conditions for creation of a computer model are possessing certain experience in using such programs as Photoshop and Excel (or their analogs) and availability of video-eyepiece for a microscope.

Computer modeling in morphometry of tissues that was carried out in cystic breast condition, may be as well used in other diseases of mammary glands [5] and in investigations of other organs and tissues.

Conclusions

1. Computer modeling in morphometry of tissues provides many possibilities for fast conduction of high-quality scientific work.
2. Computer modeling has a number of advantages over direct microscopy in analysis of the results of histomorphological examination of tissues.
3. In future, construction and improvement of computer models will permit to create combined models that could be usedfor description of functioning of an organism at different levels of its organization from different positions simultaneously.
4. For a more precise assessment of the condition of the mammary gland tissue a new parameter is proposed: (%DD) – the degree of dilation of ducts which effectively shows the condition of the mammary gland tissue in cystic breast condition.

About the authors

Anton S. Vasin

Ryazan State Medical University

Author for correspondence.
Email: anto-vasin@inbox.ru
ORCID iD: 0000-0003-3790-4620
SPIN-code: 2387-3689
ResearcherId: A-7261-2018

PhD Student of the Department of Pathophysiology

Russian Federation, 9, Vysokovoltnaja, Ryazan, 390026

Viktor V. Davidov

Ryazan State Medical University

Email: anto-vasin@inbox.ru
ORCID iD: 0000-0001-6479-7504
SPIN-code: 1356-7511
ResearcherId: S-3209-2016

MD, PhD, Professor, Professor of the Department of Pathophysiology

Russian Federation, 9, Vysokovoltnaja, Ryazan, 390026

Janna A. Svirina

Ryazan State Medical University

Email: anto-vasin@inbox.ru
ORCID iD: 0000-0001-5895-231X
ResearcherId: D-2931-2018

MD, PhD, Assistant of the Department of Pathophysiology

Russian Federation, 9, Vysokovoltnaja, Ryazan, 390026

References

Supplementary files