The honored science and education member of the RANS, corresponding-member of the IAS of HS, Dr.S. (eng.). Professor, Pil E.A. Russia, Saint-Petersburg, Saint-Petersburg State Marine Technical University

BUILDING LIMITS OF EXISTENCE AREA OF A HEALTHY OR A DISEASED BODY WITH USE OF THE MS EXCEL PROGRAM

Every medical book always mentions a healthy and a diseased body, but there is no specific mention of the limits within which a healthy body exists. The limits are understood as any specific numeric values of one or several parameters according to which we can make a respective conclusion. This article deals with the issue of calculation of existence limits of both a healthy and a diseased body with the use of the MS Excel program and is based on the analysis of results of experimental research done in the cancer biophysics laboratory where the researchers studied the effect of different actions (Table 1) on 32 factors.

Table 1. Types of actions on study groups

№	Type of action
1.	Control (without tumor) with no action
2.	Injection of a chemotherapeutic agent intramuscularly (i.m.)
3.	Injection of a chemotherapeutic agent (i.m.) + adrenalin
4.	Injection of a chemotherapeutic agent into the lymph node (into ln)
5.	Injection of a chemotherapeutic agent (into ln) + magnetic field
6.	Injection of a chemotherapeutic agent intramuscularly (i.m.)
7.	Control + normal saline solution (to group 2)
8.	Control + adrenalin (to group 3)
9.	Control + magnetic field (to groups 5 and 6)
10.	Control (tumor without action) (to groups 2 to 9)
11.	Control (without tumor) + chemotherapeutic agent (i.m.)

Out of these 32 factors we took 24 presented in Table 2 based on which we built the existence areas of a healthy and a diseased body in relation to variable Х15, NADP of cortex (as it has a relatively big difference between the maximum and the minimum values of the correlation coefficient) with the use of the REGRESSION program [1, 2].

Table 2. Factors studied

№	Variables	Title
1.	Х15	NADP of cortex
2.	Х3	Weight of thymus per 100 g of animal mass
3.	Х4	Average surface of adrenal cortex
4.	Х5	Average surface of adrenal medulla
5.	Х6	Total cells in the standard surface of cortex
6.	Х7	Percentage of small lymphocytes in the standard surface of cortex
7.	Х8	Percentage of middle lymphocytes in the standard surface of cortex
8.	Х9	Number of macrophages in cortex
9.	Х10	Total cells in the standard surface of adrenal medulla
10.	Х11	Percentage of small lymphocytes of adrenal medulla
11.	Х12	Percentage of middle lymphocytes of adrenal medulla
12.	Х13	RNA/DNA of thymus of cortex
13.	Х14	NAD of cortex
14.	Х16	NADPH+ of cortex
15.	Х17	NADP of cortex
16.	Х18	Succinate dehydrogenase of cortex
17.	Х19	Lactate dehydrogenase of cortex
18.	Х20	Volume of cores of cortex thymocytes
19.	Х21	Volume of adrenal medulla thymocytes
20.	Х23	RNA/DNA of adrenal medulla
21.	Х24	NADPH+ of adrenal medulla
22.	Х25	NADP of adrenal medulla
23.	Х26	Succinate dehydrogenase of adrenal medulla
24.	Х27	Lactate dehydrogenase of adrenal medulla

Table 3 below shows resulting correlation coefficients R² placed in a way that from number 1 to 12 they ascend, and from 13 to 23 descend. On the basis of these data there was built a curve 1 (dashed line) presented in Fig. 1 and Fig. 2. The next Table 4 shows the maximum and minimum deviations of correlation coefficients R² from a healthy body for a group of a chemotherapeutic agent. The tables created this way had a number of unfilled cells which is due to these values being absent. In such cases where there was only one value for +R² or -R² it was inserted into cell +R²min or -R²max. That said, there may be points and even areas where curves of a diseased body are tangent to the curve of a healthy body by one or several factors, i.e. when for certain reasons we cannot deduce the limits of a diseased body. These areas were given the name of “areactive zones” in medicine.

Table 3. Correlation coefficients R²t for variable Х15 in ascending and descending order for thymus

№	Variables	R^2a	№	Variables	R^2a
1	Х7	0,203	13	X5	0,796
2	X16	0,367	14	X11	0,747
3	X19	0,391	15	X20	0,716
4	X21	0,435	16	X27	0,665
5	X26	0,524	17	X25	0,630
6	X14	0,614	18	X4	0,624
7	X18	0,625	19	X13	0,524
8	X8	0,658	20	X17	0,493
9	X24	0,680	21	X23	0,404
10	X12	0,742	22	X10	0,367
11	X3	0,747	23	X6	0,259
12	X9	0,898

Fig. 1. Dependence R2 = f(Xi) for thymus during chemotherapy

Here:

· +R²max - the maximum value of the correlation coefficient of a diseased body R²d differing from that of a healthy body R²h upwards;

· +R²2min - the minimum value of the correlation coefficient of a diseased body R²d differing from that of a healthy body R²h upwards;

· -R²max - the maximum value of the correlation coefficient of a diseased body R²d differing from that of a healthy body R²h downwards;

· -R²min - the minimum value of the correlation coefficient of a diseased body R²d differing from that of a healthy body R²h downwards.

In other words, all +R²max and +R²min values are placed above curve 1 while all -R²max and -R²min values are placed below curve 1.

On the basis of Table 4 we built Fig. 1 which shows that the whole zone can be divided into the following five areas: Ssu and Ssl are the upper and the lower areas where even a diseased body cannot exist; Sdu and Sdl are the upper and the lower areas of a diseased body (in Fig. 1 and Fig. 2 they are marked in grey); Shu is the existence area of a healthy body placed above curve 1; Shl is the existence area of a healthy body placed below curve 1.

Thus, we can note down the following formula (1)

Stl = Ssu + Sdu +Shu + Shl + Sdl + Ssl. (1)

However, as the upper part of a diseased body Sdu consists of 4 parts, i.e. Sdu1, Sdu2, Sdu3, Sdu4, hence it can be represented by the following formula (2) (ref. Fig. 1)

Sdu = Sdu1 + Sdu2 + Sdu3 + Sdu4. (2)

Similarly to the upper part Sdu, the lower part of a diseased body Sdl is calculated according to the formula (3)

Sdl = Sdl1 + Sdl2 + Sdl3 + Sdl4 + Sdl5 + Sdl6 + Sdl7. (3)

Fig. 2. Dependence for thymus for control

Calculations completed for these areas showed that they have the following surface values: Ssu = 3,109 unit², (14,132%); Sdu = 3,967 unit², (18,032%); Shu = 2,009 unit², (9,716%); Shl = 2,138 unit², (9,716%); Sdl = 3,048 unit², (13,85%); Ssl = 7,73 unit², (35,13%). As we see from the calculations presented, a healthy body can have the surface of Sh = 7,73 unit², (35,13%), a diseased body has the surface of Sd = 7,015 unit², (31,89%), and the area where neither a healthy, nor a diseased body can exist (Ssu + Ssl) makes 10,839 unit², (49,266%).

Similar calculations were made for the group of a healthy body for control + a chemotherapeutic agent. The data received are presented in Table 5 and on the basis of these data we built Fig. 2. Here we deduced the following values of the surfaces: Ssu = 6,057 unit², (27,53%); Sdu = 1,781 unit², (8,095%); Shu = 1,248 unit², (5,67%); Shl = 1,884 unit², (8,564%); Sdl = 2,864 unit², (13,02%); Ssl = 8,167 unit², (37,12%%). That said, a healthy body has the surface of Sh = 3,132 unit², (14,234%), a diseased body has the surface of Sd = 4,645 unit², (21,114%), and the area where neither a healthy, nor a diseased body can exist (Ssu + Ssl) makes 14,224 unit², (64,652%) [3].

Table 4. Maximum and minimum deviations of the correlation coefficient R² from a healthy body for the group of a chemotherapeutic agent

№	Variables	R^2a	+R^2max	+R^2min	-R^2max	-R^2min
1	Х7	0,203	0,679	0,467	0,180	-
2	X16	0,367	0,644	0,543	0,245	0,113
3	X19	0,391	0,968	0,488	0,284	-
4	X21	0,435	0,900	0,455	0,162	-
5	X26	0,524	0,849	0,528	0,448	0,312
6	X14	0,614	0,942	0,791	0,450	-
7	X18	0,625	0,943	0,632	0,615	0,324
8	X8	0,658	0,956	0,805	0,502	0,468
9	X24	0,680	0,832	0,691	0,650	0,383
10	X12	0,742	0,898	0,754	0,646	0,318
11	X3	0,747	0,848	0,803	0,770	0,623
12	X9	0,898	-	0,954	0,777	0,611
13	X5	0,796	0,909	0,838	0,729	0,540
14	X11	0,747	0,823	0,799	0,633	0,354
15	X20	0,716	0,882	0,746	0,675	0,575
16	X27	0,665	-	0,869	0,657	0,213
17	X25	0,630	0,929	0,640	-	-
18	X4	0,624	0,873	0,641	0,597	0,329
19	X13	0,524	-	0,829	0,416	0,169
20	X17	0,493	0,718	0,551	0,276	-
21	X23	0,404	0,934	0,586	0,168	-
22	X10	0,367	0,756	0,611	0,351	0,284
23	X6	0,259	0,591	0,273	0,213	0,107

Table 5. Maximum and minimum deviations of the correlation coefficient R² from a healthy body for control + a chemotherapeutic agent

№	Variables	R^2a	+R^2max	+R^2min	-R^2max	-R^2min
1.	Х7	0,203	0,551	0,299	-	-
2.	X16	0,367	0,806	0,398	0,254	-
3.	X19	0,391	0,769	0,452	0,384	-
4.	X21	0,435	0,810	0,479	-	-
5.	X26	0,524	0,922	0,662	0,338	-
6.	X14	0,614	-	0,665	0,439	0,432
7.	Х18	0,625	-	0,638	0,169	-
8.	Х8	0,658	-	0,722	0,635	-
9.	Х24	0,680	-	0,768	0,665	0,437
10.	Х12	0,742	-	0,845	0,734	0,452
11.	Х3	0,784	-	0,793	0,771	0,469
12.	Х9	0,898	-	-	0,877	0,344
13.	Х5	0,796	-	0,878	0,762	0,499
14.	Х11	0,747	-	-	0,729	0,321
15.	Х20	0,716	-	0,843	0,712	0,425
16.	Х27	0,665	0,773	0,735	0,336	-
17.	Х25	0,630	-	0,711	0,542	0,346
18.	Х4	0,624	0,784	0,693	0,340	-
19.	Х13	0,524	-	-	0,475	0,220
20.	Х17	0,493	0,749	0,539	0,486	0,410
21.	Х23	0,404	-	0,462	-	-
22.	Х10	0,367	-	0,368	0,317	0,312
23.	Х6	0,259	-	0,386	0,251	0,207

Note:

1. All experiments were made by Professor E.A. Sheyko, Rostov-on-Don, Russia.

2. All calculations were made by Professor E.A. Pil, St.-Petersburg, Russia.

BIBLIOGRAPHY

1. E.A. Pil, E.A. Sheyko. Analysis of Regression Dependences Found While Studying the Parameters of Blood and Thymus / Saint Petersburg Institute of Fine Mechanics and Optics. – 16 p., illustrated. – References: 1 title – Rus. Dep. in VINITI 07.12.93. N3037–В93

2. E.A. Pil, E.A. Sheyko. Use of a Personal Computer in Experimental Oncology / Oncology Problems. – 1993. – N3. – pp. 92–94

3. E.A. Pil, E.A. Sheyko. Defining the Existence Limits of a Healthy and a Diseased Body Based on the Analysis of their Correlation Coefficients, Saint Petersburg, REMO&Со, Saint Petersburg, 1997. – 19 p., illustrated.