Simplified model of laser Doppler signals during reactive hyperaemia



Laser Doppler flowmetry (LDF) is a non-invasive method to measure tissue blood flow. During reactive hyperaemia, the LDF signal increases to a peak and then returns to a resting value. A simplified model is developed to explain these variations. The emphasis is on simulating the effects occurring rather than on trying to mimic the anatomical structure of the microcirculation. A single blood vessel is therefore analysed. The increasing value of blood velocity is studied, and vasodilatation as well as vasoconstriction are taken into account. The model parameters are calculated using wavelets. For a 2-min occlusion on a healthy subject, the radius of the vessel is initially 15 μm, increasing to 24.6 μm at the peak, reached 14 s after the release of the occlusion. The model shows that the high value of the LDF signal during the initial phase of reactive hyperaemia is produced by an increasing number of erythrocytes in a cross-section, due to vasodilatation rather than an increase in moving blood cell velocities. Moreover, the rapidity of the vasodilatation and vasoconstriction effects determine the rapidity of the signal variations. The paper aims to give a basic solution to develop a numerical model.


Laser Doppler flowmetry Model Reactive hyperaemia 


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  1. Abbot, N. C., andBeck, J. S. (1993): «Biological zero in laser Doppler measurements in normal, ischaemic and inflamed human skin»,Int. J. Microcirc: Clin. Exp.,12, pp. 89–98Google Scholar
  2. Berne, R. M., andLevy, M. N. (1996): «Overview of the circulation», inMosby (Ed.): «Principles of physiology», pp. 219–222Google Scholar
  3. Bonner, R., andNossal, R. (1981): «Model for laser Doppler measurements of blood flow in tissue»,Appl. Opt.,20, pp. 2097–2107Google Scholar
  4. Bonner, R. F., andNossal, R. (1990): «Principles of laser-Doppler flowmetry»,in Shepherg, A. P., andÖberg, P. Å. (Eds.): «Laser Doppler blood flowmetry» (Kluwer Academic Publishers) pp. 17–45Google Scholar
  5. Colantuoni, A., Bertuglia, S., andIntaglietta, M. (1984): «Quantitation of rhythmic diameter changes in arterial microcirculation»,Am. J. Physiol.,246 (Heart Circ. Physiol. 15), pp. H508-H517Google Scholar
  6. Colantuoni, A., Bertuglia, S., andIntaglietta, M. (1993): «Biological zero of laser Doppler fluxmetry: microcirculatory correlates in the hamster cheek pouch during flow and no flow conditions»,Int. J. Microcirc.: Clin. Exp.,13, pp. 125–136Google Scholar
  7. Colantuoni, A., Bertuglia, S., andIntaglietta, M. (1994): «Microvascular vasomotion: origin of laser Doppler flux motion»,Int. J. Microcirc.,14, pp. 151–158Google Scholar
  8. Fairs, S. L. E. (1988): «Observations of a laser Doppler flowmeter output made using a calibration standard»,Med. Biol. Eng. Comput.,26, pp. 404–406Google Scholar
  9. Gaehtgens, P., Dührssen, C., andAlbrecht, K. H. (1980): «Motion, deformation, and interaction of blood cells and plasma during flow through narrow capillary tubes»,Blood Cells,6, pp. 799–812Google Scholar
  10. Intaglietta, M., Silverman, N. R., andTompkins, W. R. (1975): «Capillary flow velocity measurementsin vivo andin situ by television methods»,Microvasc. Res.,10, pp. 165–179CrossRefGoogle Scholar
  11. Kvernebo, K., Slagsvold, C. E., andGoldberg, T. (1988): «Laser Doppler flux reappearance time (FRT) in patients with lower limb atherosclerosis and healthy controls»,Eur. J. Vasc. Surg.,2, pp. 171–176CrossRefGoogle Scholar
  12. Kvernmo, H. D., Stefanovska, A., Bracic, M., Kirkeboen, K. A., andKvernebo, K. (1998): «Spectral analysis of the laser Doppler perfusion signal in human skin before and after exercise»,Microvasc. Res.,56, pp. 173–182CrossRefGoogle Scholar
  13. Lipowsky, H. H., Kovalcheck, S., andZweifach, B. W. (1978): «The distribution of blood theological parameters in the microvasculature of cat mesentery»,Circ. Res.,43, pp. 738–749Google Scholar
  14. Mallat, S. G. (1989): «A theory for multiresolution signal decomposition: the wavelet representation»,IEEE Trans. Patt. Anal. Machine Intell.,11, pp. 674–693MATHCrossRefGoogle Scholar
  15. Nilsson, G. E. (1984): «Signal processor for laser Doppler tissue flowmeters»,Med. Biol. Eng. Comput.,22, pp. 343–348Google Scholar
  16. Nilsson, G. E., Tenland, T., andÖberg, P. Å. (1980a): «A new instrument for continuous measurement of tissue blood flow by light beating spectroscopy»,IEEE Trans.,BME-27, pp. 12–19Google Scholar
  17. Nilsson, G. E., Tenland, T., andÖberg, P. Å. (1980b): «Evaluation of a laser Doppler flowmeter for measurement of tissue blood flow»,IEEE Trans.,BME-27, pp. 597–604Google Scholar
  18. Ninet, J., andFronek, A. (1985): «Cutaneous postocclusive reactive hyperemia monitored by laser Doppler flux metering and skin temperature»,Microvasc. Res.,30, pp. 125–132CrossRefGoogle Scholar
  19. Ray, S. A., Buckenham, T. M., Belli, A. M., Taylor, R. S., andDormandy, J. A. (1999): «The association between laser Doppler reactive hyperaemia curves and the distribution of peripheral arterial disease»,Eur. J. Vasc. Endovasc. Surg.,17, pp. 245–248CrossRefGoogle Scholar
  20. Sacks, A. H., Ksander, G., O'Neill, H., andPerkash, I. (1988): «Difficulties in laser Doppler measurement of skin blood flow under applied external pressure»,J. of Rehab. Res., and Dev.,25, pp. 19–24.Google Scholar
  21. Schlichting, H. (1968): «Boundary-layer theory» (McGraw-Hill Book Company, New York)Google Scholar
  22. Sheng, C., Sarwal, S. N., Watts, K. C., andMarble, A. E. (1995): «Computational simulation of blood flow in human systemic circulation incorporating an external force field»,Med. Biol. Eng. Comput.,33, pp. 8–17Google Scholar
  23. Smye, S. W., andBloor, M. I. G. (1990): «A single-tube mathematical model of reactive hyperaemia»,Phys. Med. Biol.,35, pp. 103–113CrossRefGoogle Scholar
  24. Stern, M. D. (1975): «In vivo evaluation of microcirculation by coherent light scattering»,Nature,254, pp. 56–58CrossRefGoogle Scholar
  25. Szymanski, P. (1932): «Quelques solutions exactes des équations de l'hydrodynamique du fluide visqueux dans le cas d'un tube cylindrique»,J. Math. Pures. appl.,11, pp. 67–107MATHGoogle Scholar
  26. Watkins, D. W., andHolloway, G. A. (1978): «An instrument to measure cutaneous blood flow using the Doppler shift of laser light»,IEEE Trans.,BME-25, pp. 28–33Google Scholar
  27. Weidenhagen, R., Wichmann, A., Koebe, H. G., Lauterjung, L., Fürst, H., andMessmer, K. (1996): «Analysis of laser Doppler flux motion in man: Comparison of autoregressive modelling and fast Fourier transformation»,Int. J. Microcirc.,16, pp. 64–73Google Scholar
  28. Wilkin, J. K. (1986): «Periodic cutaneous blood flow during postocclusive reactive hyperemia»,Am. J. Physiol.,250, pp. H765-H768Google Scholar
  29. Wilkin, J. K. (1987): «Cutaneous reactive hyperemia: Viscoelasticity determines response»,J. Invest. Dermatol.,89, pp. 197–200CrossRefGoogle Scholar
  30. Zhong, J., Seifalian, A. M., Salerud, G. E., andNilsson, G. E. (1998): «A mathematical analysis on the biological zero problem in laser Doppler flowmetry»,IEEE Trans.,BME-45, pp. 354–364Google Scholar

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© IFMBE 2000

Authors and Affiliations

  1. 1.Groupe ISAIP-ESAIPSaint Barthélémy d'AnjouFrance
  2. 2.Service des Explorations VasculairesC.H.U. d'AngersAngersFrance
  3. 3.Ecole Nationale Supérieure des Arts et MétiersLaboratory of Advanced Instrumentation and RoboticsAngersfrance

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