Basic concept of dual slopes
The optical properties of tissue can be measured with FD-NIRS from the slopes of the logarithmic amplitude and phase. This requires collecting data at a minimum of two source-detector distances, r1 and r2. An accurate measurement of these slopes requires instrumental contributions (from source emission, detector sensitivity, optical coupling with tissue, etc.) to be exactly the same for the measurement at the two distances. This cannot be guaranteed in the case of measurements with a single source and two detectors (so-called single-slope measurements), since each detector contributes its individual instrumental factors. One way to address this problem is via calibration measurements on known phantoms. Another approach, which does not require any calibration, is with a combination of two sources (S1, S2) and two detectors (D1, D2) that are properly arranged. The key requirement is that the two detectors play opposite roles in the single-slope measurements obtained with source 1 and source 2; in other words, if detector 1 is closer to source 1 than source 2, then detector 2 must be farther from source 1 than source 2.
Fig. 1. Visual representation of the impact of an additional phase contribution from detector D1 in single slope 1 (yellow shading, obtained with S1, D1, D2) and single slope 2 (pink shading, obtained with S2, D1, D2). The dual slope obtained by averaging single slopes 1 and 2 (green shading) cancels out the additive phase contributions from detector D1.
A visual representation of the correction of instrumental contributions is shown in the left panel of Fig. 1 for phase slope measurements. The yellow-shaded panel shows a measurement of single slope 1 (using single source S1, and both detectors D1 and D2). If detector D1 (which contributes the short-distance measurement at r1) introduces an instrumental additional phase contribution, the measured slope will be shallower than the theoretical slope associated with the optical properties of tissue. Conversely, in the pink-shaded panel of single-slope 2, the same detector D1 now contributes the long-distance measurement at r2, and therefore its additional phase contribution results in a steeper measured slope than the theoretical slope. As long as these instrumental factors are additive and remain the same in the measurement of the two single-slope, they cancel out in the average of the two single slopes. This average, illustrated in the green panel of Fig. 1, represents the dual slope that is an accurate estimate of the theoretical slope and thus yields (when combined with the amplitude dual slope) a measurement of the tissue optical properties of tissue without any need for instrumental calibration.
An experimental demonstration of this basic concept is shown in the right panel of Fig. 1, where the optical coupling between the first detector (A) and a tissue phantom is varied during the experiment. This optical coupling change significantly impacts single-distance measurements and single-slope measurements, which are sensitive to changes in instrumental factors. By contrast, dual-slope measurements are insensitive to changes in optical coupling, which is a highly desirable feature in practical optical measurements in vivo.
- See also D. M. Hueber, S. Fantini, A. E. Cerussi, and B. Barbieri, “New Optical Probe Designs for Absolute (Self-calibrating) NIR Tissue Hemoglobin Measurements,” Proc. SPIE 3597, 618-631 (1999).