350 rub
Journal Science Intensive Technologies №5 for 2015 г.
Article in number:
Self-similarity and fractal dimension of instantaneous cardiac rhythm scattergram
Keywords: instantaneous cardiac rhythm scattergram fractal dimension self-similarity
Authors:
A.N. Kudinov - Dr. Sc. (Phys.-Math.), Professor, Tver State University. E-mail: mathlab@yandex.ru D.Y. Lebedev - Post-graduate Student, Tver State University. E-mail: dangerr27@mail.ru V.N. Ryzikov - Ph. D. (Phys.-Math.), Associate Professor, Tver State University. E-mail: vlr@yandex.ru V.P. Tsvetkov - Dr. Sc. (Phys.-Math.), Professor, Tver State University. E-mail: tsvet@tversu.ru I.V. Tsvetkov - Dr. Sc. (Eng.), Professor, Tver State University. E-mail: tsvet@tversu.ru A.P. Ivanov - Dr. Sc. (Med.), Professor, Research advisor of Tver Cardiologic Dispensary. E-mail: ivanovcardio2010@yandex.ru
Abstract:
In this work, the new instantaneous cardiac rhythm (ICR) scattergram fractal dimension calculation algorithm based on appearance of fractal lattices in was developed and implemented. This algorithm makes possible to improve the ICR scattergram measuring accuracy essentially. Based on the method developed, the ICR scattergram fractal dimensions for two patients of the Tver Cardiology Health Center with different symptoms were determined. These values were found as equal to: D1 = 1,326 and D2 = 1,113. The self-similarity of sets of points under investigation of ICR scattergrams within the accuracy of at least 1% was shown. The study undertaken demonstrates the perspectiveness of application of fractal properties of ICR scatterrams as a cardiovascular system state marker.
Pages: 57-63
References

 

  1. Baevskijj R.M. Prognozirovanie sostojanijj na grani normy i patologii. M.: Medicina. 1979. 205 s.
  2. Kudinov A.N., Lebedev D.JU., Cvetkov V.P., Cvetkov I.V.Matematicheskaja model multifraktalnojj dinamiki i analiz serdechnykh ritmov // Matematicheskoe modelirovanie. 2014. T. 26. № 10. S. 127−136.
  3. Lebedev D.JU., Ivanov A.P., Ryzhikov V.N., Cvetkov V.P. Fraktalnye svojjstva skatterogrammy mgnovennogo serdechnogo ritma // Tezisy dokl. mezhdunar. molodezhnojj konf. «Sovremennye problemy prikladnojj matematiki i informatiki» (Dubna, 25−29 avgusta 2014). Dubna: OIJAI. 2014. S. 89−92.
  4. Kudinov A.N., Lebedev D.JU., Ivanov A.P., Ryzhikov V.N., Cvetkov V.P., Cvetkov I.V.Samopodobie skatterogrammy mgnovennogo merdechnogo ritma // Vestnik Tverskogo gosudarstvennogo universiteta. Ser. Prikladnaja matematika. 2014. № 3.
  5. German V.A., Potapov A.A.Obrabotka medicinskikh rentgenovskikh izobrazhenijj fraktalnymi metodami // Nelinejjnyjj mir. 2011. № 5. S. 275−279.
  6. Richard M. Kronover FRAKTALY I KHAOS v dinamicheskikh sistemakh. Osnovy teorii. M.: Postmarket. 2000. 352 s.
  7. Damodar N. Gujarati, Dawn C. Porter. Basic Econometrics (Fifth ed.). New York: McGraw-Hill Irwin. 2009. P. 73−78.