A MATHEMATICAL-ANALYSIS ON THE BIOLOGICAL ZERO PROBLEM IN LASER-DOPPLER FLOWMETRY

The biological zero (BZ) problem is a critical issue inherent in laser Doppler flowmetry (LDF). It causes confusion when measuring low tissu e blood flows, Many experimental studies have been done on the questio n of whether the BZ flux should be subtracted from the normally measur ed flux in various situations. However this problem can only be solved after a proper mathematical analysis, Only then can we clearly define and formulate what flux is truly meaningful in blood perfusion measur ement and what movement generates the BZ Bur and how can we correctly remove it. Following this motivation, the movement of moving blood cel ls (MBC's) is decomposed into a net translation and a random wondering based on in vivo observations. This important step leads to a clear d efinition of the BZ and net perfusion flux and reveals that subtractio n of BZ flux from the normal flux will certainly cause an underestimat ion of the net flux, Using this decomposition, the relationship betwee n the net, BZ and normal flux is established which leads to the correc t formula to recover the net flux from the BZ and normal fluxes. This recovered net flux is shown to be bounded by the normal flux and the n ormal flux minus the BZ flux, numerical studies, preliminary phantom m odel and clinical evaluations manifest that the new approach is more a ccurate and reasonable at measuring low net fluxes, In contrast, subtr acting BZ flux causes a systematic underestimation of perfusion and is apparently inappropriate even from a methodological point of view. In addition to the novel BZ solution, a general density function of the speed of MBC's is given which is more faithful than the Maxwell densit y used in [4], This general density function offers new possibilities for further theoretical developments in LDF.