Novel data types in FD-NIRS

Time-domain near-infrared spectroscopy (TD-NIRS) measures the time-of-flight distribution of detected photons. Instead of using the entire distribution of time-of-flight, selected moments of the distribution are often used to streamline the measurement of optical properties or to achieve preferential sensitivity to deeper tissues. Frequency-domain NIRS (FD-NIRS) measures the DC intensity, AC amplitude, and phase \((\phi)\) of the detected modulated optical signal at angular frequency \(\omega (\omega=2\pi f)\). It is known that \(\phi\) is a surrogate of the 1st order moment in TD \((t)\), since \(\phi\approx\omega\left\langle t\right\rangle\). Like \(\left\langle t\right\rangle\) in TD, \(\phi\) in FD is known to be more sensitive to deeper tissue than AC or DC. Instead of using only the traditional data types measured directly in FD (DC, AC, \(\phi)\), we have proposed to enrich the space of FD data types by using specific combinations of AC, DC and \(\phi\). If we consider the arrival time \(t\) of detected photons as a random variable, its characteristic function X_t(ω) is given by: 

where \(\widetilde{R}=ACe^{i\phi}\) is the complex FD-NIRS reflectance and t^k is the moment of order \(k\) of the time-of-flight distribution. From Eq. (1) it follows that:

where \(\mathfrak{R}\) and \(\mathfrak{I}\) indicate the real and imaginary part. Sensitivity features of t^k can be studied in TD as guidance for defining new FD data types such as:

and the modulation depth (1-AC/DC) which is a surrogate of variance (var(\(t)\)).

Figure 1 shows the sensitivity of these novel FD-NIRS data types in single-distance and dual-slope configurations for absorption perturbations at a depth of 11.5 mm. These sensitivities need to be considered together with noise levels to evaluate contrast-to-noise ratios for detection of absorption perturbations in tissue.
 

Fig. 1. Sensitivity profiles of phase (ø) and new FD-NIRS data types in single-distance (left) and dual-slope (right) configurations.