Нелинейные фракталы: приложения в физиологии и офтальмологии. Обзор
https://doi.org/10.18008/1816-5095-2014-1-4-11
Аннотация
Фрактальная геометрия и нелинейная динамика имеют приложения в области биологии и медицины. Многие сложные структуры живых систем проявляют фракталоподобную геометрию, и особое внимание привлекают вопросы нелинейности анатомических структур человека и его физиологических функций. Представлен обзор мультидисциплинарных исследований, демонстрирующих мультимасштабную нелинейную сложность физиологических функций и фрактальную геометрию анатомических структур здорового человека, включая сетчатку, которые упрощаются или усложняются при заболеваниях и в процессе старения человека. Патологические состояния часто вызывают развитие высоко периодичной динамики процессов, доминирующей на одном масштабе времени. В развитие приложений нелинейной динамики в физиологии зрительной системы и офтальмологии предложены исследования влияния фрактального мелькающего светового фона на электрогенез сетчатки и зрительной коры. Предполагается, что эти знания могут лечь в основу новых методов электрофизиологической диагностики и лечения заболеваний зрительной системы.
Ключевые слова
Об авторе
М. В. Зуева
ФГБУ «Московский НИИ глазных болезней им. Гельмгольца» Минздрава России
Россия
Россия
Список литературы
1. Mandelbrot B. B. 1982. The fractal geometry of nature. New York: Freeman, 1982.
2. Федер Е. Фракталы. М.: Мир, 1991.
3. Crownover R. M. Introduction to Fractals and Chaos, Jones and Bartlett Publishers: Boston — London, 1995, 306 p.
4. Iannaccone, P. M., Khokha, M. K. (Eds.). Fractal geometry in biological systems: an analytical approach. BocaRaton, FL:CRC Press, 1996.
5. Goldberger A. L., Rigney D. R., West B. J. Chaos and fractals in human physiology. Sci. Amer. 1990; 262: 42‑49.
6. Goldberger A. L. Giles F. Filley Lecture. Complex Systems. Proceed. Amer. Thor. Soc. 2006; 3: 467‑471.
7. Ayers S. The Application of Chaos Theory to Psychology. Theory & Psychol 1997; 7 (3): 373‑398.
8. Stewart I. Does God play Dice? The (new) mathematics of Chaos. Oxford: Basil Blackwell, 1989. — Cambridge, 1991 Blackwell Publishers (Basil or Willy) Wiley-Blackwell; 2 edition, 2002.
9. Belair J., Glass L., van der Heiden U., Milton J. Dynamical disease: mathematical analysis of human illness. New York: American Institute of Physics Press; 1995.
10. Bass G. Nonlinear Man. Chaos, fractal and homeostatic interplay in human physiology, 1997, available on-line at [http://www.tonleenders.nl / Pdf / chaos_and_man.PDF]
11. Beuter A., Glass L., Mackey M., Titcombe M. S. Nonlinear dynamics in physiology and medicine. New York: Springer-Verlag; 2003.
12. Fadel P. J., Barman S. M., Phillips S. W., Gebber G. L. Fractal fluctuations in human respiration. J. Appl. Physiol. 2004; 97: 2056‑2064.
13. Goldberger A. L., Amaral L. A. N., Hausdorff J. M., Ivanov P. Ch., Peng C.‑K., Stanley H. E. Fractal dynamics in physiology: Alterations with disease and aging. Proc. Natl. Acad. Sci. USA (PNAS) 2002; 99 (Suppl 1): 2466‑2472.
14. Ivanov P. Ch., Amaral L. A. N., Goldberger A. L., Stanley H. E. Stochastic feedback and the regulation of biological rhythms. Europhys. Lett. 1998; 43: 363‑368.
15. Peng C. K., Mietus J. E., Liu Y., Lee C., Hausdorff J. M., Stanley H. E., Goldberger A. L. Quantifying fractal dynamics of human respiration: age and gender effects. Ann. Biomed. Eng. 2002; 30: 683‑692.
16. Dingwell J. B., Cusumano J. P. Nonlinear time series analysis of normal and pathological human walking. Chaos 2000; 10: 848‑863.
17. Goldberger A. L. Fractal variability versus pathologic periodicity: complexity loss and stereotypy in disease. Perspect. Biol. Med. 1997; 40: 543‑561.
18. Terrier P., Dériaz O. Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking. Journal of NeuroEngineering and Rehabilitation 2011; 8 (12): 1‑13.
19. Lehnertz K. Non-linear time series analysis of intracranial EEG recordings in patient with epilepsy — an overview, Int. J. Psychophysiol. 1999; 34: 45‑52.
20. Babloyantz A. Estimation of Correlation Dimensions from Single and Multichannel Recordings — A Critical View. Brain Dynamics 1989; 2: 122‑130.
21. Schiff S. J., Jerger K., Duong D. H., Chang T., Spano M. L., Ditto W. L. Controlling chaos in the brain. Nature 1994; 370: 615‑620.
22. Korn H., Faure P. Is there chaos in the brain? II. Experimental evidence and related models. C R Biol. 2003; 326 (9): 787‑840.
23. Izhikevich E. M. Dynamical Systems in Neuroscience. The Geomentry of Excitability and Bursting. The MIT Press: Cambride, Massachusetts, 2007.
24. Das A. 2001. Brain and Chaos. When two giants meet, Brain & Mind, 14, November 2001, available on-line at [http://www.epub.org.br / cm / n14 / mente / chaos. html]
25. Saermark K., Lebech J.,Bak C. K., Sabers A. Magnetoencephalography and Attractor Dimension: Normal Subjects and Epileptic Patients. Brain Dynamics 1989; 2:149‑157.
26. Besthorn C., Sattel H., Geiger-Kabisch C., Zerfass R., Förstl H. Parameters of EEG dimensional complexity in Alzheimer’s disease. ElectroencephclinNeurophysiol 1995; 95: 84‑89.
27. Anninos P. A., Adamopoulos A. V., Kotini A., Tsagas N. Nonlinear analysis of brain activity in magnetic influenced Parkinson patients. Brain Topogr 2000; 13 (2):135‑44.
28. Kotini A., Anninos P. Detection of non-linearity in schizophrenic patients using magnetoencephalography. Brain Topogr 2002; 15 (2): 107‑113.
29. Abásolo D., Hornero R., Espino P., Poza J., Sánchez C. I., de la Rosa R. Analysis of regularity in the EEG background activity of Alzheimer’s disease patients with approximate entropy. ClinNeurophysiol 2005; 116: 1826‑1834.
30. Hornero R., AbásoloD., Escudero J., Gómes C. Nonlinear analysis of electroencephalogram and magnetoencephalogram recordings in patients with Alzheimer’s disease. Phil Trans R SocA 2009; 367 (1887): 317‑336.
31. Ризниченко Г. Ю. Лекции по математическим моделям в биологии. Москва —Ижевск: РХД, 2002.
32. Priplata AA, Niemi JB, Harry JD, Lipsitz LA, Collins JJ. Vibrating insoles and balance control in elderly people Lancett 2003; 362 (9390):1123‑1124.
33. Ross S. E. Noise-enhanced postural stability in subjects with functional ankle instability. Br J Sports Med. 2007; 41 (10): 656‑659.
34. Costa M., Priplata A. A., Lipsitz L. A., Wu Z., Huang N. E., Goldberger A. L., Peng C.‑K. Noise and Poise: Enhancement of postural complexity in the olderly with a stochastic-resonance-based therapy. EurophysLett. 2007. Author manuscript; available in PMC 2007 August 15.
35. Зуева М. В. Негативное ремоделирование сетчатки при ретинальных дегенерациях. Обзор литературы. Вестник Офтальмологии 2006; (5): 47‑50.
36. Jones B. W., Kondo M., Terasaki H., Lin Y., McCall M., Marc R. E. Retinal remodeling. Jpn J Ophthalmol 2012; 56: 289‑306.
37. Ly T., Gupta N., Weinreb R. N., Kaufman P. L., Yücel Y. H.. Dendrite plasticity in the lateral geniculate nucleus in primate glaucoma. Vision Res, 2011; 51 (2):243‑250.
38. Moolman D. L., Vitolo O. V., Vonsattel J. P., Shelanski M. L. Dendrite and dendritic spine alterations in Alzheimer models. J Neurocytol, 2004;33: 377‑387.
39. Avakian A., Kalina R. E., Sage E. H., Rambhia A. H., Elliott K. E., Chuang E. L., Clark J. I., Hwang J.‑N., Parsons-Winerter P. Fractal analysis of region-based vascular change in the normal and non-proliferative diabetic retina. Curr Eye Res 2002; 24 (4): 274‑280.
40. Daxer A. Characterisation of the neovascularisation process in diabetic retinopathy by means of fractal geometry: diagnostic implications. Graefe’s Arch Clin Exp Ophthalmol. 1993a; 231: 681‑686.
41. Daxer A. The fractal geometry of proliferative diabetic retinopathy: implications for the diagnosis and the process of retinal vasculogenesis. Current Eye Research. 1993b; 12: 1103‑1109.
42. Daxer A. Mechanisms in retinal vasculogenesis: an analysis of the spatial branching site correlation. Current Eye Research; 1995; 14: 251‑254.
43. Family F., Masters B. R., Platt D. E.. Fractal pattern formation in human retinal vessels. Physica D; 1989; 38: 98‑103.
44. Hooymans P. M., Merkus F,W. Current status of cardiac glycoside drug interactions. Clin Pharm; 1985; 4: 404‑413.
45. Landini G., Misson G. P., Murray P. I. Fractal analysis of the normal human retinal fluorescein angiogram. Current Eye Research; 1993; 12: 23‑27.
46. Landini G., Murray P. I., Misson G,P. Local connected fractal dimension and lacunarity analysis of 60 degree fluorescein angiograms. Invest Ophthalmol Vis Sci. 1995; 36: 2749‑2755.
47. Mainster M. A. The fractal properties of retinal vessels: embryological and clinical perspectives. Eye 1990; 4: 235‑241.
48. Masters B. R. Fractal analysis of the vascular tree in the human retina. Annu Rev Biomed Eng. 2004; 6: 427‑452.
49. Jelinek H., de Mendonça M., Oréfice F., Garcia C., Nogueira R., Soares J., Junior R. Fractal analysis of the normal human retinal vasculature. Int J Ophthalmol Vis Sci 2009; 8 (2). http://ispub.com / IJOVS / 8 / 2 / 9788
50. Tălu S. Fractal analysis of normal retinal vascular network. Oftalmologia 2011;55 (4):11‑16.
51. Wong T. Y. Retinal vessel diameter as a clinical predictor of diabetic retinopathy progression: time to take out the measuring tape. Arch Ophthalmol. 2011; 129 (1): 95‑96.
52. Ikram M. K., Cheung C. Y., Lorenzi M., Klein R., Jones T. L. Z., Wong T. Y. Retinal vascular caliber as a biomarker for diabetes microvascular complications. Diabetes Care 2013; 36 (3): 750‑759.
53. Klein R., Myers C. E., Lee K. E., Gangnon R., Klein B. E. K. Changes in retinal vessel diameter and incidence and progression of diabetic retinopathy. Arch Ophthalmol. 2012; 130 (6): 749‑755.
54. Cheung N., Rogers S. L., Donaghue K. C., Jenkins A. J., Tikellis G., Wong T. Y. Retinal arteriolar dilation predicts retinopathy in adolescents with type 1 diabetes. Diabetes Care 2008; 31 (9): 1842‑1846.
55. Benitez-Aguirre P., Craig M. E., Sasongko M. B., Jenkins A. J., Wong T. Y., Wang J. J., Cheung N., Donaghue K. C. Retinal vascular geometry predicts incident retinopathy in young people with type 1 diabetes: a prospective cohort study from adolescence. Diabetes Care 2011; 34 (7): 1622‑1627.
56. Sasongko M. B., Wong T. Y., Donaghue K. C., Cheung N., Jenkins A. J., Benitez-Aguirre P., Wang J. J. Retinal arteriolar tortuosity is associated with retinopathy and early kidney dysfunction in type 1 diabetes. Amer J Ophthalmol. 2012; 153 (1):176.e1–183.e1.
57. Cheung N., Donaghue K. C., Liew G., Rogers S. L., Wang J. J., Lim S. W., Jenkins A. J., Hsu W., Li Lee M., Wong T. Y. Quantitative assessment of early diabetic retinopathy using fractal analysis. Diabetes Care 2009; 32 (1): 106‑110.
58. Kunicki A. C., Oliveira A. J., Mandonça M. V., Barbosa C. T., Nogueira R. A. Can the fractal dimension be applied for the early diagnosis of non-proliferative diabetic retinopathy? Braz J Med Biol Res. 2009; 42 (10): 930‑934.
59. Lim S. W., Cheung N., Wang J. J., Donaghue K. C., Liew G., Islam F. M., Jenkins A. J., Wong T. Y. Retinal vascular fractal dimension and risk of early diabetic retinopathy: A prospective study of children and adolescents with type 1 diabetes. Diabetes Care. 2009; 32 (11): 2081‑2083.
60. Cheung C. Y., Lamoureux E., Ikram M. K., Sasongko M. B., Ding J., Zheng Y., Mitchell P., Wang J. J., Wong T. Y. Retinal vascular geometry in Asian persons with diabetes and retinopathy. J Diabetes Sci Technol. 2012; 6 (3): 595‑605.
61. Doubal F. N., MacGillivray T. J., Patton N., Dhillon B., Dennis M. S., Wardlaw J. M. Fractal analysis of retinal vessels suggests that a distinct vasculopathy causes lacunar stroke. Neurology. 2010; 74 (14): 1102‑1107.
62. Grauslund J., Green A., Kawasaki R., Hodgson L., Sjølie A. K., Wong T. Y. Retinal vascular fractals and microvascular and macrovascular complications in type 1 diabetes. Ophthalmology 2010; 117 (7): 1400‑1405.
63. Poon M., Craig M. E., Kaur H., Cusumano J., Sasongko M. B., Wong T. Y., Donaghue K. C. Vitamin D deficiency is not associated with changes in retinal geometric parameters in young people with type 1 diabetes. J Diabetes Res Volume 2013 (2013), Article ID 280691, 5 pages http://dx.doi.org / 10.1155 / 2013 / 280691 Epub 2013 Jul 7.
64. Yiu Y.‑F., Chan Y.‑H., Yiu K.‑H., Siu C. W., Li S. W., Wong L. Y., Lee S. W., Tam S., Wong E. W., Cheung B. M., Tse H. F. Vitamin D deficiency is associated with depletion of circulating endothelial progenitor cells and endothelial dysfunction in patients with type 2 diabetes. J Clin Endocr Metab. 2011; 96 (5): E830 — E835.
65. Rilk A. J. 2003. The Flicker Electroretinogram in Phase Space: Embeddings and Techniques. Inaugural-Dissertation zur Erlangung des Doktorgrades der Medizin. Tübingen: Aus der Universit.ats-Augenklinik Tübingen, http://tobias-lib.uni-tuebingen.de / volltexte / 2003 / 1029 / pdf / FlicERG.pdf
66. Schiff SJ, Jerger K, Duong DH, Chang T, Spano ML, Ditto WL. Controlling chaos in the brain. Nature. 1994; 370: 615‑620.
67. Regalado A. A gentle scheme for unleashing chaos. Science. 1995; 268 (5219): 1848.
68. Garfinkel A., Spano M. L., Ditto W. L., Weiss J. N. Controlling cardiac chaos. Science. 1992; 257: 1230‑1235.
Рецензия
Для цитирования:
Зуева М.В. Нелинейные фракталы: приложения в физиологии и офтальмологии. Обзор. Офтальмология. 2014;11(1):4-11. https://doi.org/10.18008/1816-5095-2014-1-4-11
For citation:
Zueva M.V. Nonlinear fractals: applications in physiology and ophthalmology. Ophthalmology in Russia. 2014;11(1):4-11. https://doi.org/10.18008/1816-5095-2014-1-4-11
Просмотров: 1340
Послать статью по эл. почте 