We investigated the relationship between chromophore concentrations in two-layered scattering media and the apparent chromophore concentrations measured with broadband optical spectroscopy in conjunction with commonly used homogeneous medium inverse models. We used diffusion theory to generate optical data from a two-layered distribution of relevant tissue absorbers, namely, oxyhemoglobin, deoxyhemoglobin, water, and lipids, with a top-layer thickness in the range 1–15 mm. The generated data consisted of broadband continuous-wave (CW) diffuse reflectance in the wavelength range 650–1024 nm, and frequency-domain (FD) diffuse reflectance at 690 and 830 nm; two source-detector distances of 25 and 35mm were used to simulate a dual-slope technique. The data were inverted using diffusion theory for a semi-infinite homogeneous medium to generate reduced scattering coe±cients at 690 and 830nm (from FD data) and effective absorption spectra in the range 650–1024nm (from CW data). The absorption spectra were then converted into effective total concentration and oxygen saturation of hemoglobin, as well as water and lipid concentrations. For absolute values, it was found that the effective hemoglobin parameters are typically representative of the bottom layer, whereas water and lipid represent some average of the respective concentrations in the two layers. For concentration changes, lipid showed a significant cross-talk with other absorber concentrations, thus indicating that lipid dynamics obtained in these conditions may not be reliable. These systematic simulations of broadband spectroscopy of two-layered media provide guidance on how to interpret effective optical properties measured with similar instrumental setups under the assumption of medium homogeneity.

The concept of region of sensitivity is central to the field of diffuse optics and is closely related to the Jacobian matrix used to solve the inverse problem in imaging. It is well known that, in diffuse reflectance, the region of sensitivity associated with a given source–detector pair is shaped as a banana, and features maximal sensitivity to the portions of the sample that are closest to the source and the detector. We have recently introduced a dual-slope (DS) method based on a special arrangement of two sources and two detectors, which results in deeper and more localized regions of sensitivity, resembling the shapes of different kinds of nuts. Here, we report the regions of sensitivity associated with a variety of source–detector arrangements for DS measurements of intensity and phase with frequency-domain spectroscopy (modulation frequency: 140MHz) in a medium with absorption and reduced scattering coe±cients of 0.1 and 12 cm-1, respectively. The main result is that the depth of maximum sensitivity, considering only cases that use sourcedetector separations of 25 and 35 mm, progressively increases as we consider single-distance intensity (2.0 mm), DS intensity (4.6 mm), single-distance phase (7.5 mm), and DS phase (10.9 mm). These results indicate the importance of DS measurements, and even more so of phase measurements, when it is desirable to selectively probe deeper portions of a sample with diffuse optics. This is certainly the case in non-invasive optical studies of brain, muscle, and breast tissue, which are located underneath the superficial tissue at variable depths.

We have recently introduced a new technique, coherent hemodynamics spectroscopy (CHS), which aims at characterizing a specific kind of tissue hemodynamics that feature a high level of covariation with a given physiological quantity. In this study, we carry out a detailed analysis of the significance of coherence and phase synchronization between oscillations of arterial blood pressure (ABP) and total hemoglobin concentration ([Hbt]), measured with near-infrared spectroscopy (NIRS) during a typical protocol for CHS, based on a cyclic thigh cuff occlusion and release. Even though CHS is based on a linear time invariant model between ABP (input) and NIRS measurands (outputs), for practical reasons in a typical CHS protocol, we induce finite “groups” of ABP oscillations, in which each group is characterized by a different frequency. For this reason, ABP (input) and NIRS measurands (output) are not stationary processes, and we have used wavelet coherence and phase synchronization index (PSI), as a metric of coherence and phase synchronization, respectively. PSI was calculated by using both the wavelet cross spectrum and the Hilbert transform. We have also used linear coherence (which requires stationary process) for comparison with wavelet coherence. Themethod of surrogate data is used to find critical values for the significance of covariation between ABP and [Hbt]. Because we have found similar critical values for wavelet coherence and PSI by using five of the most used methods of surrogate data, we propose to use the data-independent Gaussian random numbers (GRNs), for CHS. By using wavelet coherence and wavelet cross spectrum, and GRNs as surrogate data, we have found the same results for the significance of coherence and phase synchronization between ABP and [Hbt]: on a total set of 20 periods of cuff oscillations, we have found 17 coherent oscillations and 17 phase synchronous oscillations. Phase synchronization assessed with Hilbert transform yielded similar results with 14 phase synchronous oscillations. Linear coherence and wavelet coherence overall yielded similar number of significant values. We discuss possible reasons for this result. Despite the similarity of linear and wavelet coherence, we argue that wavelet coherence is preferable, especially if one wants to use baseline spontaneous oscillations, in which phase locking and coherence between signals might be only temporary.

A recently proposed analytical hemodynamic model1 [S. Fantini, NeuroImage 85, 202–221 (2014)] is able to predict the changes of oxy, deoxy, and total hemoglobin concentrations (model outputs) given arbitrary changes in blood flow, blood volume, and rate of oxygen consumption (model inputs). One assumption of this model is that the capillary compartment is characterized by a single blood transit time. In this work, we have extended the original model by considering a distribution of capillary transit times and we have compared the outputs of both models (original and extended) for the case of sinusoidal input signals at different frequencies, which realizes the new technique of coherent hemodynamics spectroscopy (CHS). For the calculations with the original model, we have used the mean value of the distribution of capillary transit times considered in the extended model. We have found that, for distributions of capillary transit times having mean values around 1 s and a standard deviation less than about 45% of the mean value, the original and extended models yield the same CHS spectra (i.e., model outputs versus frequency of oscillation) within typical experimental errors. For wider capillary transit time distributions, the two models yield different CHS spectra. By assuming that Poiseuille's law is valid in the capillary compartment, we have related the distribution of capillary transit times to the distributions of capillary lengths and capillary speed of blood flow to calculate the average capillary and venous saturations. We have found that, for standard deviations of the capillary transit time distribution that are less than about 80% of the mean value, the average capillary saturation is always larger than the venous saturation. By contrast, the average capillary saturation may be less than the venous saturation for wider distributions of the capillary transit times.

A novel hemodynamic model has been recently introduced, which provides analytical relationships between the changes in cerebral blood volume (CBV), cerebral blood flow (CBF), and cerebral metabolic rate of oxygen (CMRO₂), and associated changes in the tissue concentrations of oxy- and deoxy-hemoglobin (△O and △D) measured with near-infrared spectroscopy (NIRS) [S. Fantini, Neuroimage 85, 202–221 (2014)]. This novel model can be applied to measurements of the amplitude and phase of induced hemodynamic oscillations as a function of the frequency of oscillation, realizing the novel technique of coherent hemodynamics spectroscopy (CHS) [S. Fantini, Neuroimage 85, 202–221 (2014); M. L. Pierro et al., Neuroimage 85, 222–233 (2014)]. In a previous work, we have demonstrated an in vivo application of CHS on human subjects during paced breathing [M. L. Pierro et al., Neuroimage 85, 222–233 (2014)]. In this work, we present a new analysis of the collected data during paced breathing based on a slightly revised formulation of the hemodynamic model and an efficient fitting procedure. While we have initially treated all 12 model parameters as independent, we have found that, in this new implementation of CHS, the number of independent parameters is eight. In this article, we identify the eight independent model parameters and we show that our previous results are consistent with the new formulation, once the individual parameters of the earlier analysis are combined into the new set of independent parameters.

Hemodynamic low-frequency (~0.1 Hz) spontaneous oscillations as detected in the brain by nearinfrared spectroscopy have potential applications in the study of brain activation, cerebral autoregulation, and functional connectivity. In this work, we have investigated the phase lag between oscillations of cerebral deoxy- and oxy-hemoglobin concentrations in the frequency range 0.05-0.10 Hz in a human subject during a mental workload task. We have obtained a measure of such phase lag using two different methods: (1) phase synchronization analysis as used in the theory of chaotic oscillators and (2) a novel cross-correlation phasor approach. The two methods yielded comparable initial results of a larger phase lag between low-frequency oscillations of deoxy- and oxyhemoglobin concentrations during mental workload with respect to a control, rest condition.

We have examined ten human subjects with a previously developed instrument for near-infrared diffuse spectral imaging of the female breast. The instrument is based on a tandem, planar scan of two collinear optical fibers (one for illumination and one for collection) to image a gently compressed breast in a transmission geometry. The optical data collection features a spatial sampling of 25 points/cm² over the whole breast, and a spectral sampling of 2 points/nm in the 650– 900nm wavelength range. Of the ten human subjects examined, eight are healthy subjects and two are cancer patients with unilateral invasive ductal carcinoma and ductal carcinoma in situ, respectively. For each subject, we generate second-derivative images that identify a network of highly absorbing structures in the breast that we assign to blood vessels. A previously developed paired-wavelength spectral method assigns oxygenation values to the absorbing structures displayed in the second-derivative images. The resulting oxygenation images feature average values over the whole breast that are significantly lower in cancerous breasts (69±14%, n = 2) than in healthy breasts (85±7%, n = 18) (p < 0.01). Furthermore, in the two patients with breast cancer, the average oxygenation values in the cancerous regions are also significantly lower than in the remainder of the breast (invasive ductal carcinoma: 49±11% vs 61±16%, p < 0.01; ductal carcinoma in situ: 58±8% vs 77±11%, p < 0.001).

We have applied functional near-infrared spectroscopy (fNIRS) to the human forehead to distinguish different levels of mental workload on the basis of hemodynamic changes occurring in the prefrontal cortex. We report data on 3 subjects from a protocol involving 3 mental workload levels based on to working memory tasks. To quantify the potential of fNIRS for mental workload discrimination, we have applied a 3-nearest neighbor classification algorithm based on the amplitude of oxyhemoglobin (HbO2) and deoxyhemoglobin (HbR) concentration changes associated with the working memory tasks. We have found classification success rates in the range of 44%–72%, which are significantly higher than the corresponding chance level (for random data) of 19.1%. This work shows the potential of fNIRS for mental workload classification, especially when more parameters (rather than just the amplitude of concentration changes used here) and more sophisticated classification algorithms (rather than the simple 3-nearest neighbor algorithm used here) are considered and optimized for this application.