Lapitan D.G. - Research Scientist, Laboratory of Medical Physics Research, Moscow Regional Scientific and Research Clinical Institute named after M.F. Vladimirsky (MONIKI) E-mail: lapitandenis@mail.ru

Laser Doppler Flowmetry (LDF) is technology in modern medicine which allows to non-invasively investigate the blood microcircu-lation system. It is based on the tissue illumination by laser light and detection the backscattered from tissue radiation. The total signal backscattered both from moving red blood cells with Doppler frequency shift and from motionless scatterers on the initial radiation frequency is registered. Signal processing algorithm in LDF is based on the model of Bonner and Nossal, in which the blood flow is calculated with the use of the first-order moment of the power spectral density of a flowmeter-s output electrical signal. The basic theory of LDF was constructed with a large number of assumptions one of them is stationary amplitude of the reference beam scattered on motionless elements in tissues. But in practice, the fluctuations of this beam are observed due to the action of various rhythmic processes involved in the mechanisms of regulation of microcirculation system. The total amplitude of the backscattered flux strongly and nonlinear depends on the blood volume in the tested tissue. So the aim of this work is to study theoretically the effect of amplitude modulation of light flux incident on a photodetector applied to LDF. The Doppler scattering model taking into account the fluctuations of blood volume level in the tissue due to various rhythmic processes in the blood microcirculation system was developed. Based on modified model of Kubelka-Munk the simple analytical expressions for intensity of backscattered from tissue reference and Doppler fluxes depending on the blood volume level of tissue were obtained. The influence of modulation depth of blood volume on the modulation depth of amplitudes of reference and Doppler optical fields was investigated. The analytical expression for the photocurrent autocorrelation function which differs from the classical expression by the addition of components caused by amplitude modulation of blood volume. The analytical expression for a power spectral density of the photocurrent detected in LDF was obtained. It represents the sum of three components: amplitude-modulated, Doppler and beatings of amplitude-modulated and Doppler signals. It was shown that the ratio of the contribution of the amplitude-modulated signal in the spectrum to the Doppler signal is proportional to the square of the modulation depth of blood volume level. Using the numerical simulation the influence of low-frequency amplitude-modulated signal on the output perfusion signal registered in LDF was investigated. It was shown that this signal makes a significant contribution to the output signal that is not taken into consideration in the classical model of LDF and in the existing instruments implementing it. So the developed model is more universal compared to classical model and allows to simulate Doppler signal both in the presence and in the absence of the effect of amplitude modulation of tissue blood volume and for various optical properties of the medium of light propagation.

 

1. Rajan V., Varghese B., Leeuwen T.G., Steenbergen W. Review of methodological developments in laser Doppler flowmetry // Lasers Med. Sci. 2009. V. 24. P. 269-283.
2. Edwards R.V., Angus J.C., French M.J., Dunning Jr. J.W. Spectral analysis of the signal from the laser doppler flowmeter: Time-independent systems // Journal of Applied Physics. 1971. V. 42. № 2. P. 837-850.
3. Bonner R.F., Nossal R. Model for laser Doppler measurements of blood flow in tissue // Appl. Opt. 1981. V. 20. P. 2097-2107.
4. Sianoudis I., Drakaki E. Non invasive and real time analysis of skin pigmentation and cutaneous hemoglobin oxygenation: An experimental and theoretical approach // e-Journal of Science & Technology (e-JST) of TEI Athens. 2008. V. 3. № 1. P. 1-9.
5. Stromberg T., Karlsson H., Fredriksson I., Nystrom F.H., Larsson M. Microcirculation assessment using an individualized model for diffuse reflectance spectroscopy and conventional laser Doppler flowmetry // Journal of Biomedical Optics. 2014. V. 19. № 5. P. 057002-1-057002-6.
6. Rajan V., Varghese B., Van Leeuwen T.G., Steenbergen W. Effect of speckles on the depth sensitivity of laser Doppler perfusion imaging // Optics express. 2007. V. 15. № 17. P. 10911-10919.
7. Dunaev A.V., Zherebtsov E.A., Rogatkin D.A., Stewart N.A., Sokolovski E.U. Substantiation of medical and technical requirements for noninvasive spectrophotometric diagnostic devices // Journal of Biomedical Optics. 2013. V. 18. № 10. P. 107009-1-107009-9.
8. Lapitan D.G., Rogatkin D.A. Evaluation of the Doppler component contribution in the total backscattered flux for noninvasive medical spectroscopy // Proc. of SPIE. 2014. V. 9129. P. 91292X-1-91292X-8.
9. Lapitan D.G., Rogatkin D.A. Peremennoe krovenapolnenie biotkani kak istochnik shuma vo vkhodnom opticheskom signale medicinskogo lazernogo doplerovskogo floumetra // Opticheskijj zhurnal. 2016. T. 83. № 1. S. 41-46.
10. Dunaev A.V., Sidorov V.V., Krupatkin A.I., Rafailov I.E. / Palmer S.G., Sokolovski S.G., Rafailov E.U. The study of synchronization of rhythms of microvascular blood flow and oxygen saturation during adaptive changes // SPIE BiOS. - International Society for Optics and Photonics. 2014. P. 89350A-89350A-9.
11. Binzoni T., Leung T.S., Van De Ville D. The photo-electric current in laser-Doppler flowmetry by Monte Carlo simulations // Phys. Med. Biol. 2009. V. 54. P. 303-318.
12. Binzoni T., Leung T.S., Seghier M.L., Delpy D.T. Translational and Brownian motion in laser-Doppler flowmetry of large tissue volumes // Phys. Med. Biol. 2004. V. 49. P. 5445-5458.
13. Rogatkin D.A. Fizicheskie osnovy opticheskojj oksimetrii // Medicinskaja fizika. 2012. № 2. S. 97-114.
14. Aleksandrov E.B., Golubev JU.M., Lomakin A.V., Noskin V.A. Spektroskopija fluktuacijj intensivnosti opticheskikh polejj s negaussovojj statistikojj // Uspekhi fizicheskikh nauk. 1983. T.140. № 4. S. 547-582.
15. Rogatkin D.A. Ob osobennosti v opredelenii opticheskikh svojjstv mutnykh biologicheskikh tkanejj i sred v raschetnykh zadachakh medicinskojj neinvazivnojj spektrofotometrii // Medicinskaja tekhnika. 2007. № 2. S. 10-16.
16. Dmitriev M.A., Feducova M.V., Rogatkin D.A. On one simple backscattering task of the general light scattering theory // Proc. SPIE. 2004. V. 5475. P. 115-122.
17. Nilsson G.E., Tenland T., Oberg P.A. A new instrument for continuous measurement of tissue blood flow by light beating spectroscopy // Biomedical Engineering, IEEE Transactions on. 1980. V. 27. № 1. P. 12-19.
18. Cummins H.Z., Swinney H.L. III Light Beating Spectroscopy // Progress in Optics 8 (C). 1970. P. 133-200.
19. Zhong J., Nilsson G. On generalized photocurrent spectral moments and the recovery of speed distribution in laser Doppler flowmetry // Biomedical Engineering, IEEE Transactions on. 1993. V. 40. № 6. P. 595-597.
20. Bi R., Dong J., Poh C.L., Lee K. Optical methods for blood perfusion measurement - theoretical comparison among four different modalities // JOSA A. 2015. V. 32. № 5. P. 860-866.
21. Nilsson G.E., Tenland T., Oberg P.A. Evaluation of a laser Doppler flowmeter for measurement of tissue blood flow // Biomedical Engineering, IEEE Transactions on. 1980. V. 27. № 10. P. 597-604.
22. Fredriksson I., Fors C., Johansson J. Laser Doppler Flowmetry - a Theoretical Framework. Department of Biomedical Engineering, Linköping University (SWE). Linköping: 2007. 22 p.
23. Saidi I.S. Transcutaneous optical measurement of hyperbilirubinemia in neonates // Doctor of Philosophy dissertation. Houston: Rice University. 1992. 234 p.
24. Koelink M.H., De Mul F.F.M., Leerkotte B., Greve J. / Jentink H.W., Graaff R., Dassel A.C.M., Aarnoudse J.G. Signal processing for a laser-Doppler blood perfusion meter // Signal processing. 1994. V. 38. № 2. P. 239-252.
25. Rogatkin D.A., Lapitan D.G., Kolbas JU.JU., SHumskijj V.I. Individualnaja variabelnost parametrov mikrocirkuljacii krovi i problemy funkcionalnojj diagnostiki sistemy mikrocirkuljacii // Funkcionalnaja diagnostika. 2012. № 4. S. 24-29.
26. Dunaev A.V., Novikova I.N., ZHerebcova A.I., Krupatkin A.I. / Sokolovskijj S.G., Rafailov EH.U. Analiz fiziologicheskogo razbrosa parametrov mikrocirkuljatorno-tkanevykh sistem // Biotekhnosfera. 2013. № 5 (29).   S. 44-53.