Depth sensitivity of FD-NIRS signals from two-layered media

Frequency-domain near-infrared spectroscopy (FD-NIRS) allows for measurements of the amplitude and phase of photon-density waves in highly scattering media. FD-NIRS, in combination with the dual-slope (DS) technique, allows one to expand upon traditional single-distance (SD) measurements and yields various data-types with complementary spatial information about the medium being measured. The differing spatial sensitivities of DS FD-NIRS data-types can tell us more about the spatial distribution of tissue hemodynamics, or may allow for preferential sensitivity to specific tissue regions. The spatial sensitivity of a given measured data \(M\) is defined in terms of the relative effects on \(M\) from a local absorption perturbation at position \(\mathbf{r} (∆μa(r))\) and from a uniform absorption perturbation throughout the medium \((∆μa0)\). Specifically, the sensitivity of \(M\) to an absorption perturbation at \(\mathbf{r}\) can be expressed as follows:

 \(S_M\left(\mathbf{r}\right)=\frac{\partial M/\partial\mu_a(\mathbf{r})}{\partial M/\partial\mu_{a0}}\)

 Two-layered media provide a better representation of biological tissues than homogenous media, as they can model superficial tissue layers (skin, adipose tissue layer, skull, etc.). The characterization of two-layered media requires specifying the optical properties of the top and bottom layers, as well as the thickness of the top layer. Figure 1 shows the ratio of ∆M_∆μa,bot, the change in the measured data \(M\) that results from an absorption change in the bottom layer, to ∆M_∆μa,top, the change in the measured data \(M\) that results from the same absorption change in the top layer. Figure 1 is obtained from diffusion theory for a two-layered medium with optical properties specified in the figure. Besides the obvious finding that the relative sensitivity to the bottom vs. top layer decreases with top layer thickness, Fig. 1 shows that dual-slope phase data have the greatest relative sensitivity of bottom vs. top layer, followed by dual-slope intensity, single-distance phase, and single-distance intensity. This type of quantitative analysis is important to better understand the data collected from layered tissue, and is relevant for non-invasive optical measurements of cerebral and skeletal muscle hemodynamics.