HyperTRCSS: A hyperspectral time-resolved compressive sensing spectrometer for depth-sensitive monitoring of cytochrome-c-oxidase and blood oxygenation

Abstract. Significance Hyperspectral time-resolved (TR) near-infrared spectroscopy offers the potential to monitor cytochrome-c-oxidase (oxCCO) and blood oxygenation in the adult brain with minimal scalp/skull contamination. We introduce a hyperspectral TR spectrometer that uses compressive sensing to minimize acquisition time without compromising spectral range or resolution and demonstrate oxCCO and blood oxygenation monitoring in deep tissue. Aim Develop a hyperspectral TR compressive sensing spectrometer and use it to monitor oxCCO and blood oxygenation in deep tissue. Approach Homogeneous tissue-mimicking phantom experiments were conducted to confirm the spectrometer’s sensitivity to oxCCO and blood oxygenation. Two-layer phantoms were used to evaluate the spectrometer’s sensitivity to oxCCO and blood oxygenation in the bottom layer through a 10 mm thick static top layer. Results The spectrometer was sensitive to oxCCO and blood oxygenation changes in the bottom layer of the two-layer phantoms, as confirmed by concomitant measurements acquired directly from the bottom layer. Measures of oxCCO and blood oxygenation by the spectrometer were highly correlated with “gold standard” measures in the homogeneous and two-layer phantom experiments. Conclusions The results show that the hyperspectral TR compressive sensing spectrometer is sensitive to changes in oxCCO and blood oxygenation in deep tissue through a thick static top layer.

The temporal stability of the system with both lasers was characterized following a 1 h warmup period-this is the typical time required to warm up a TR system 66,89 .DTOFs were acquired consecutively over 55 minutes, each with a collection time of 1 s.A variable neutral density filter (NDC-50C-40M, Thorlabs Inc., USA) was used to limit the photon count rate to 1% of the laser repetition rate.Figure S1 shows the temporal stability results; the YSL laser results are on the left panel (originally reported in Ref. 56) and those for the NKT laser are displayed on the right.Noticeably, the MTOF, peak intensity, FWHM, and peak position of both lasers' DTOFs were quite stable after the warm-up period.We compared the spectral stability of the lasers from startup by acquiring spectra every 30 seconds for 55 minutes using a commercial CW spectrometer (Maya2000Pro, Ocean Insight, USA). Figure S2 displays the spectral stability of the YSL laser (data from Ref. 56) and the NKT laser.The YSL laser showed remarkable spectral stability from startup while the shape of the NKT laser spectrum was only stable after 30 minutes of warm-up.Nevertheless, when the NKT laser spectral shape stabilized, it remained consistent for the remaining 20 minutes of the test.

Monte Carlo Simulations
For each oxygenation level, 236 wavelengths were simulated to cover the 675-910 nm wavelength range which includes the spectral range of HyperTRCSS as well as the suggested ideal window for monitoring oxCCO. 16,22 or all simulations, the refractive index, wavelength-dependent anisotropy factor, and wavelength-dependent scattering coefficient were assigned the same values in both layers and were consistent at each oxygenation level.The refractive index was set to 1.33 in accordance with previous blood-yeast phantom literature. 60A wavelength-dependent anisotropy factor for Intralipid-based phantoms was used. 90The wavelength-dependent scattering coefficient was determined by fitting baseline acquisitions from an experimental phantom using the method described in Ref. 55.The scattering coefficients obtained for the baseline acquisitions were averaged and the result was fit to Eq. (S1) to recover the scattering amplitude a and the scattering power b-800 nm was used as the reference wavelength: The recovered a and b were used in Eq. (S1) to generate the scattering coefficient at each wavelength in the simulated range.The absorption coefficients of the bottom layer at each oxygenation level were calculated according to the absolute chromophore concentrations in Table S1 and Eq.(S2): where Hb, HbO, H 2 O, oxCCO, and redCCO are the concentrations of water, deoxyhemoglobin, oxyhemoglobin, oxidized cytochrome-c-oxidase, and reduced cytochrome-c-oxidase, respectively.µ a (λ) is the wavelength-dependent absorption coefficient.ε Hb (λ), ε HbO (λ), ε H 2 O (λ), ε oxCCO (λ), and ε redCCO (λ) are the wavelength-dependent specific extinction coefficients. 71Note that the top layer absorption coefficients were calculated using the concentrations in the first row of Table S1.A total hemoglobin concentration of 12 µM was used, based on previous work with blood-yeast phantoms, 56 and the total CCO concentration was estimated based on literature values for the rat brain as we could not find estimates for yeast. 91The saturation of hemoglobin and CCO was varied to capture the full range of chromophore concentration changes reported in Ref. 56, as we expected the experiments in this work to produce changes within that range.
Table S1 Absolute chromophore concentrations and changes (∆) in chromophore concentration relative to simulation #1.H 2 O is the water fraction, Hb is the concentration of deoxyhemoglobin, HbO is the concentration of oxyhemoglobin, oxCCO is the concentration of oxidized cytochrome-c-oxidase, and redCCO is the concentration of reduced cytochrome-c-oxidase.The units of concentration for Hb, HbO, oxCCO, and  Optimizing the Wavelength Range for TR Analysis Data from the MC simulations were used to determine the optimal wavelength range for recovering ∆Hb and ∆oxCCO from experimental TR data.We first tested the section of the "gold standard" range 16,22 captured by HyperTRCSS (780-875 nm), but found that the estimation of ∆Hb using this spectral range was poor.We then expanded the range to 680-875 nm to better capture the Hb spectral feature. 7,24 he upper bound was then adjusted from 875 nm to 870 nm, 860 nm, 850 nm, then 840 nm.Since the estimation of both chromophores became more accurate with the exclusion of the longer wavelengths, the optimal wavelength range for the TR analysis was determined to be 680-840 nm.
Light Source Spectral Instability in Homogeneous Phantom Experiments It is expected that ∆A(λ) would return to 0 at the end of the reoxygenation period, as this represents the return of the phantom to baseline conditions.However, if there is a change in the spectral shape of the light source, ∆A(λ) will be non-zero despite the phantom returning to baseline conditions.This confounding effect is apparent in repetition 2 of the homogeneous phantom experiment.In repetition 2 (NKT laser), ∆A(λ) did not return to a flat line after reoxygenation (Fig. S3), suggesting a change in the spectral shape of the light source.In contrast, in repetition 1 (YSL laser), ∆A(λ) was relatively flat but non-zero at the end of reoxygenation (Fig. S3), indicating a change in the intensity of the light source but no alteration of its spectral shape.

Fig
Fig S1 Temporal stability of the YSL (left column) and NKT (right column) lasers.Relative measures are shown to allow for comparison between the lasers.(A) and (B): Mean time of flight (MTOF) in picoseconds relative to the MTOF of the first measurement in the acquisition period.(C) and (D): Peak intensity normalized by the peak intensity of the first DTOF in the acquisition period.(E) and (F): Full-width half-maximum (FWHM) in picoseconds relative to the FWHM of the first measurement in the acquisition period.(G) and (H): DTOF peak temporal position relative to the temporal position of the peak in the first DTOF in the acquisition period.The width of one time bin is ∼ 12 ps.

Fig
Fig S2 Spectral stability of the YSL laser (A) and the NKT laser (B).The spectra were normalized by their area under the curve to display the spectral shape.

Fig
Fig S3 Changes in attenuation ∆A(λ) relative to baseline (0; black dotted line) following hemoglobin reoxygenation in repetition 1 (blue solid line) and 2 (orange dashed line) of the homogeneous phantom experiment.