It has been shown by the method of statistic data simulation that using samples of small volume characterizing reference state of biological systems results in overstatement of difficulty degree of state integral estimation. It was stated that using asymptotic integral estimations obtained at unlimited increase of modeling reference sample volume is effective as integral estimation of biological system stat

Fokin, V. A.

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Introduction Analysis of biomedical data, development of methods of data extraction form them, formation of integralestimations of biosystem state represent actively developing directions of modern information technologies inmedical science and practice of public health [1–4]. Inmathematical formulation the problem comes to construction of algorithms and functional reflection of attribute space characterizing biosystem in onedimensional space of estimations of this system states determined by a value of specified integral test.Construction of integral tests of state estimation mayresult in obtaining efficient estimations however their usesupposes accumulation of rather high volumes of reference data that is not may be always implemented in state ofsingle experimental investigations. Therefore, statisticdata simulation may be considered as efficient method ofstudying biosystem properties the results of which allow,on the one hand, estimating numerically statistic properties of the test itself and, on the other hand, allow determining conditions put on sampling volume required forobtaining robust generalized state estimations.Type of test of state estimation System S state is estimated with respect to a certainreference state S0 of this system. The state of the systemcorresponding, in particular, to a healthy organism maybe selected, for example, as such state. Let S0 and S bespecified reference and estimated states characterized bysets of objects {b6i |i∈NS0} and {b6j |j∈NS} respectively. HereNS0 and NS are the sampling volumes. The value of quantitative estimation of certain object state b6i∈S may becharacterized by its extent of proximity to reference stateS0 selecting which one should take into account the configuration of area in attribute space occupied by reference state, positioning of object b6j relative to this area as wellas positional relationship of objects representing systemreference state. Taking into account these conditions thetest of integral estimation of object b6i proximity to thestate S0 may be specified in the following way [5]:(*)where d(b6i,S0) is the certain extent of object b6i proximity to the set S0; DS0 is the extent of compactness of thearea occupied in attribute space by objects referring tothe state S0.Normalization to value DS0 in expression (*) allows taking into account contribution of both configuration ofarea S0 and positional relationship of objects in it to theobtained estimation. Let us specify the extent of compactness DS0 of reference state S0 in the following form:that is as an averaged value of average distances fromeach object referring to the state S0 to the rest of them.Value DS0 determined in this way represents intramultiple distance [6] concrete kind of which is determined bya way of specifying distances in attribute space. Thegeneralized distance is efficiently to be used as an extentof objects proximity in attribute space in biomedicaltasks [7] as in this case interconnection of features characterizing studied bioobjects is naturally taken into account. The generalized distance between k and i objectsis determined in the following way:Here C0 is the matrix of covariation of features characterizing state S0. Quantitative estimation of area compactness extent characterizing state S0 in generalizedmetric equals to double dimension of attribute space [5]:and expression for integral estimation of object b6i proximity to state S0 takes a form:where d(b6i,S0) is calculated as an averaged generalizeddistance from object b6i to S0,calculated using covariation matrix corresponding to reference state S0.Statistic simulation The main problem when using tests based on multidimensional methods of data analysis stipulated by lowvolumes of samplings characterizing reference state thatresults in significant variability of estimations obtainedat their use. Specific character of biomedical data is reflected in it and first of all their wide intra and interin00011( , ) ( , ),SNi M i jjSd b S d b bN == ∑G G G0 01( ) ( , ),2S i iI b d b Sm=G G0 0* 2 ,S SD D m= =10( , ) ( ) ( ).TM k i k i k id b b b b b b−= − −CG G G G G G0 000 011 11 1 ( , ),1S SN NS k jk jS SD d b bN N−= == −∑ ∑G G000( , )( ) ,iS iSd b SI bD=GGBulletin of the Томsк Pоlytеchnic University. 2007. V. 311. № 5120UDC 519.23:578.087.1STATISTIC DATA SIMULATION AT ESTIMATION OF BIOLOGICAL SYSTEM STATEV.A. FokinHPE SEI Siberian state medical university, TomskEmail: fokin@ssmu.tomsk.ruIt has been shown by the method of statistic data simulation that using samples of small volume characterizing reference state of biological systems results in overstatement of difficulty degree of state integral estimation. It was stated that using asymptotic integral estimations obtained at unlimited increase of modeling reference sample volume is effective as integral estimation of biological system state.dividual variability the consequence of which is the factthat repeat measurement at one and the same samplingmay result in different quantitative values of estimatedcharacteristics. Estimation of statistic features of integral test (*) suggested before represents nontrivial problem the solution of which using only analytical approaches is stipulated by significant difficulties and in somepractical cases is impossible.In this case investigation of statistic features of integral test may be efficiently implemented by the methodsof statistic simulation the results of which allow, on theone hand, estimating numerically statistic features ofthe test and, on the other hand, allow determining conditions put on conditions of forming reference samplings required for obtaining robust estimators.Statistic features of integral test were estimated in twostages. At the first stage M of sample set Xk (k=⎯1,M⎯) ofspecified volume corresponding to statistic features of reference state S0, represented by a certain sample set of objects X:{b6i|i∈1,⎯NS0⎯} was simulated. The obtained sequences of values imitate taking samplings from one and thesame set and, therefore, are free of errors stipulated by theinfluence of intra and interindividual variabilities of biological data. Then for each set Xk values of estimationsIS0,k(b6) the distribution of which was further used for studying statistic features of integral test were computed.Here vector b6characterizes object for which the estimation is carried out. In particular, vector corresponding tosample representative of state S, for example, vector corresponding to the centre of class may be examined as it.Control, computer engineering and information science121Fig. 1. Frequency histograms IS0 for different volumes NS0 of reference state. On abscissa – the value  IS0 on ordinate axis – the frequency value. The curve – approximation by normal distribution0 20 40 60 80 100020406080Ðàê æåëóäêàNS0=500 20 40 60 80 1000306090120NS0=1000 20 40 60 80 1000306090120NS0=4000 20 40 60 80 1000306090120NS0=10000 10 20 30 40 50 60050100150200Ðàê ëåãêèõNS0=500 10 20 30 40 50 60050100150200NS0=1000 10 20 30 40 50 60050100150200NS0=4000 10 20 30 40 50 60050100150200NS0=10000 20 40 60 80020406080100NS0=50Ðàê îáëàñòè ãîëîâû è øåè0 20 40 60 800306090120NS0=1000 20 40 60 800306090120NS0=4000 20 40 60 800306090120NS0=100040 60 80 100 120 140 16002040608010040 60 80 100 120 140 1600306090120Ðàê òîíêîé êèøêèNS0=5040 60 80 100 120 140 1600306090120NS0=100NS0=40040 60 80 100 120 140 1600306090120 NS0=1000Stomach cancerCancer of regions of head and neck Small intestine cancerLung cancerAt the second stage the influence of such factors assampling volume, ratio between sampling volume andquantity of jointly analyzed indices on the value of estimations was studied. Depending on the fact whether thelaw of multidimensional data distribution for statistic simulation of sets of their values is known or not differenttechniques may be applied [8–10]. Statistic features ofintegral test were estimated by calculating of average value of integral indexof average square deviationTo estimate integral test variability the variation coefficient was calculatedand (1–p).100 % confidence interval as the intervalcontaining values IS0 being between p/2.100 % and(1–p/2).100 % number of all values of integral test in aranged estimation row. Here p is the proper level of statistical significance. Such nonparametric way of estimation of confidence interval allows estimating it withoutany suppositions relative to the form of distribution lawand statistic features of integral test.Results of simulation Data of scanning electron microscopy (SEM) of surface architectonics of red blood cells obtained by composite authors [11–13] by the results of examination of patients at some cancer localizations of II–III stages as wellas healthy people served as the initial data for formingmodel samplings and statistic estimations of suggested integral test. As a form of red blood cells and their capacityto deformation is a sequence of a complex of violations offeatures, organization and metabolism of single components of red blood cells stipulated by presence of proper pathologic process then SEM data may be used forintegral estimation of degree of changes occurring in redblood system by selected complex of features.Statistic estimation of IS0 was carried out using thedeveloped computer program [14] simulating samplingscorresponding to volumes NS0 equal 50, 100, 200, 400,600, 800 and 1000 of observations with the assumptionthat reference sampling data satisfy multidimensionalnormal distribution law. Each sampling was simulatedfrom 100 to 1000 times with a pitch 100 according towhich statistic estimations of test value variability werecalculated. The results of simulation of statistic characteristics of integral test IS0 and its variability for estimating the state of red blood system by SEM data at different cancer localizations for certain values of NS0 and Mare given in Fig. 1 and 2.It follows form the analysis of the obtained resultsthat the value of reference sampling volume NS0 influences significantly the obtaining of robust estimators. Inparticular, at low volumes of samplings the wide variability of value IS0 is observed. The variation coefficient atNS0=50 amounts at the average to 20...25 % for all examined states decreasing to 4...8 % at sampling volumesNS0=1000. The dependence of computed average magnitudes of integral test values IS0 on model sampling volume for oncological disease of different localizationcorresponding to a number of model samplings M=500is given in Fig. 2.Fig. 2. Dependence of integral test value IS0 on model samplingvolume NS0 of reference stateFor other volumes of model samplings dependenceshave the similar form. Confidence intervals corresponding to 95 % are indicated by sections. Interesting resultof statistic simulation is the fact that the value of estimation depends on the volume of reference sampling andsmall volumes of samplings result in high estimations ofintegral test average value. Therefore, examination ofasymptotic estimations obtained at unlimited increaseof the volume of simulated reference sampling may be ofinterest.Conclusion 1. Statistic simulation of the data of biological systemreference state is the efficient method of formingsamplings of multidimensional data allowing decreasing the variability of integral estimation of the examined system state in conditions of low volumes ofinitial experimental data.2. Volume of reference sampling is a significant parameter for quantitative estimation of biological system state and low volumes of reference samplingsalong with great variability of the obtained integralestimation also result in overrating of average valueof the obtained integral estimation.3. It is efficient to use the asymptotic integral estimation obtained at unlimited increase of the volume ofmodel reference sampling as integral estimation ofbiological system state.0 200 400 600 800 1000020406080100120IS0NS0M=500 ??????????? ???????????????? ???????????? ?????? ? ??????????Lungs Small intestine Region of head and neckStomachCancer localizationl0( ) 100 %( )ISbVI bσ= ⋅GGl002,11( ) ( ( ) ( )) .MSI S kkb I b I bMσ== −∑G G G0 0 ,11( ) ( ),MS S kkI b I bM == ∑G GBulletin of the Томsк Pоlytеchnic University. 2007. V. 311. № 5122REFERENCES1. Bogomolov A.V., Gridin L.A., Kukushkin Yu.A., Ushakov I.B. Diagnostics of man state: mathematical approaches. – Moscow: Meditsina, 2003. – 464 p.2. Genkin A.A. New information technology of medical data analysis(ОМИС software). – St.Petersburg: Politekhnika, 1999. – 191 p.3. Dyuk V., Emannuel V. Information technologies in biomedical investigations. – St.Petersburg: Piter, 2003. – 528 p.4. Armitage P., Berry G. Statistical Methods in Medical Research. –3rd ed. – Oxford: Blackwell Scientific Publication, 1994. – 620 p.5. Fokin V.A. Estimation criterion of complex biosystem state // Bulletin of the Tomsk Polytechnic University. – 2004. – V. 307. – № 5. –P. 136–138.6. Tu J., Gonsales R. Principles of pattern recognition. – Moscow: Mir,1978. – 416 p.7. Konradov A.A. Statistic approaches to the analysis of multidimensional heterogeneous biological systems // Radiatsionnaya Biologiya, Radioecologiya. – 1994. – V. 34. –Issue 6. – P. 877–886.8. Ermakov S.M., Mikhailov G.A. Statistic simulation. 2d issue. –Moscow: Nauka, 1982. – 296 p.9. Efron B. The Jackknife, the Bootstrap and Other Resampling Plans.// CBMSNSF Regional Conference Series in Applied Mathematics, Monograph. 38. – Philadelphia: SIAM, 1982. – 92 p.10. Manly B.F.J. Randomization, Bootstrap and Monte Carlo Methodsin Biology. – London: Chapman and Hall/CRC, 1997. – 424 p.11. Novitskiy V.V., Ryazantseva N.V., Stepovaya E.A., Bystritskiy L.D.,Tkachenko S.B. Atlas. Clinical pathomorphism of red blood cells. –Moscow: GEOTARMED, 2003. – 208 p.12. Novitskiy V.V., Stepovaya E.A., Goldberg V.E., Kolosova M.V., Koreshkova K.G., Sokolova I.B., Bulavina Ya.V. Reversible aggregationand surface architectonics of red blood cells of peripheral blood ofpatients with lung cancer before and during antineoplastic polychemotherapy // Experimental and clinical pharmacology. – 1999. –V. 62. – № 5. – P. 28–30.13. Novitskiy V.V., Stepovaya E.A., Goldberg V.E., Kolosova M.V., Ryazantseva N.V., Korchin V.I. Red blood cells and malignant growths.– Tomsk: STT, 2000. – 288 p.14. Certificate № 2006614010 the RF. Computer program «StatSys» /V.A. Fokin, I.S. Khakimov, O.Yu. Nikiforova; Application№ 2006613281; Stated 29.09.2006; Published 22.11.2006.Received on 04.10.2007Control, computer engineering and information science123Rapid development of computer science and microtechnology during last decades made it possible to applydiagnostic equipment allowing recording continuouslyand processing wide range of physiological indices. Itgave, in its turn, a possibility to specialists to investigatein detail life activity of human body in different statesincluding sleep [1–3]. At the present the majority of scientists and doctors pay much attention to sleep qualityand man state in this period of his life. It is known thatin sleep many chronic and pathologic diseases whichcan be poorly diagnosed or often can not be diagnosedat all at wakefulness appear. Man health and efficiencydepends on sleep quality. The importance of sleep forhealthy living is a conventional fact. The first attemptsof recording physiological indices by primitive equipment were made more than 100 years ago. Since that time a number of standards and agreements was developed in this field. In particular, in 1968 a manualRechtschaffen & Kales (R&K) was published and wasaccepted as a standard [4]. Sleep stages and typical features of each of them were described in it in detail. It wassuggested to divide sleep into five stages: stages withslow eye movement I, II, III, IV and stage of rapid eyemovement (REM). When studying sleep a wide set ofphysiological indices is recorded. They are different intheir nature:• electroencephalogram (EEG) – brain transistance;• electrocoulogram (ECG) – eyebulb movement intwo derivations relative to counterlateral referents;• electromyogram (EMG) – muscle tonus;• electrocardiogram (ECG);UDC 681.3.06:518.5.001.57:612.821.7TECHNIQUE OF AUTOMATED HYPNOGRAM CONSTRUCTIONE.S. Zakharov, P.P. Kravchenko*, A.A. Skomorokhov«Medikom MTD», TaganrogEmail: office@medicommtd.com*Technological institute of Southern federal university, TaganrogEmail: kravch@tsure.ruThe technique of automated sleep stage recognition and hypnogram construction has been considered. For partition of initial polysomnogram by segments obtained as a result of patient sleep monitoring the signal energy is analyzed using nonlinear energy controller. Frequency weighted energy is calculated for all registered signals then averaging and segmentation occur according to monitored signals behavior.Secondary index vector which is used at transition from segments to fixed duration periods is formed for segments. One or another sleepstage is finally assigned to the period by correlation analysis. Accuracy of the developed algorithm is connected with quantity of consideredsecondary indices, maximally detailed description of sleep stage characteristics and realization of training by manually prepared examples.

Statistic data simulation at estimation of biological system state

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