2.1.

Monte Carlo Simulations

The MC code used for the study was described in detail earlier.^35–37 The algorithm allows for efficient simulations of DTOFs at different source-detector separations for different combinations of absorption properties of the layered medium. The statistical moments of the DTOFs related to the absorption coefficient change resulting from simulated inflow and washout of the ICG to two layers of the model (lower and upper) mimicking intra and extracerebral tissue compartments were analyzed. The temporal changes in absorption of the dye, ${\mu }_{\mathrm{a}}$, were simulated independently for both layers of the medium according to the functions proposed by Leung et al.^36,38 Initial optical properties of the medium were as follows: absorption coefficient of the medium ${\mu }_{\mathrm{a}}=0.015{\mathrm{mm}}^{-1}$, reduced scattering coefficient of the medium ${\mu }_{\mathrm{s}}^{\prime }=1{\mathrm{mm}}^{-1}$, and refractive index $n=1.4$. Initially, the superficial layer was assumed to be 1 cm thick and the deeper layer was 1 m thick (which simulates semi-infinite medium). Amplitudes of the changes of the absorption coefficient $\mathrm{\Delta }{\mu }_{\mathrm{a}}$ in the upper and lower layers were chosen in the range from 0.002 to $0.004{\mathrm{mm}}^{-1}$. The DTOFs were obtained at 67 source-detector separations (from 0.1 to 6.7 cm). Because at the largest source-detector separations only a small number of photons are re-emitted, the simulations were carried out for a large total number of photon packages $N=2\times {10}^9$.

2.2.

Instrumentation

Time-resolved laboratory system based on eight photomultiplier tubes (PMT, R7400U−02, Hamamatsu Photonics, Japan) and eight time-correlated single photon counting (TCSPC) cards (SPC-134, Becker and Hickl, Berlin, Germany)^39–41 was used in combination with femtosecond MaiTai laser (Spectra Physics),^33,42 allowing the measurement of 16 DTOFs simultaneously. Laser pulses were generated at a wavelength of 760 nm with a frequency of 80 MHz. The wavelength used in the experiments was selected close to the maximum of the absorption spectrum of ICG and with consideration of the properties of filters used in order to block the fluorescence light.^21,36 The laser light was coupled into two fibers (1.5 and 3 m long, $\phi =1\mathrm{mm}$, $\mathrm{NA}=0.39$) used to deliver the light to the phantom or the head of the healthy volunteer. Two beam expanders (F810SMA-780 and F220SMA-B, Thorlabs, Sweden) were applied on the tips of the source fibers in order to distribute the laser light on large areas of the tissue (15 and 8 mm diameter). This solution allowed us to keep the laser power density on the surface of the head below the safety limits ($2\mathrm{mW}/{\mathrm{mm}}^2$). The laser light powers at the tips of the source fibers were 200 and 20 mW, respectively. Eight fiber bundles of diameter 7 mm with active area of diameter 4 mm ($\mathrm{NA}=0.54$, Loptek, Germany) were used to deliver the light re-emitted for the phantom or tissue to the photodetectors. The short-pass filters (NT47−586, Edmund Optics) with cut-off wavelength of $\lambda =800\mathrm{nm}$ were mounted in front of the PMTs in order to block the fluorescence light.

The combination of the two source positions and eight detection spots allowed for monitoring of optical signals for 16 source-detector separations in the range $r_{\mathrm{SD}}=10$ to 67.5 mm. The laser beam (output from MaiTai laser) was split into two light paths, which were coupled into two optical fibers. In this way, the laser pulses transmitted into the tissue or phantom using these two fibers were delayed by $\approx 3\mathrm{ns}$.

2.3.

Phantom Experiments

The phantom consisted of a fish tank ($41\mathrm{cm}\times 26\mathrm{cm}\times 30\mathrm{cm}$) filled with a $1:3$ mixture of milk (fat content 3.2%) and water with small amount of ink (Black Indian Ink, Winsor & Newton). The solution of milk, water, and ink was used to obtain optical properties corresponding to properties of human tissue (${\mu }_{\mathrm{a}}\approx 0.035{\mathrm{cm}}^{-1}$ and ${\mu }_{\mathrm{s}}^{\prime }\approx 12.5{\mathrm{cm}}^{-1}$). The optical properties of the medium were obtained by time-resolved measurements and by analysis of the statistical moments of the measured DTOFs.⁴³

The measurements were carried out on the homogeneous phantom in which two transparent PVC tubes (inner diameter$=3\mathrm{mm}$ and outer diameter$=3.8\mathrm{mm}$) were located at different depths (0 and 2 cm) with respect to the surface of the phantom. The measurements were carried out at 16 source-detector separations (see Fig. 1) by positioning the optodes holder equipped with two source fibers and eight detecting fiber bundles on the surface of the phantom.

Fig. 1

The optode holder used in the phantom and in vivo studies. Red rings mark the positions of the beam expanders (source positions) and blue rings reflect locations of the tips of the detection fiber bundles.

In order to mimic dynamic inflow of the dye through the tubes located deeper and more superficial, a laboratory setup equipped with a peristaltic pump⁴⁴ was applied in order to pump through the tubes the same solution of milk, water, and ink that filled out the phantom. Furthermore, two independent boluses of ICG were injected into the two tubes located at different depths with a defined delay between them. First, the bolus was injected into the tube located deeper, which mimics realistic sequence of inflow of the bolus to the intra and extracerebral tissue compartments.

2.4.

In Vivo Measurements

The in vivo measurements were carried out on three healthy volunteers (mean age 36, the coauthors of the paper). The measurements protocol was approved by the Ethics Committee of the Medical University of Warsaw. In each case, a written informed consent was obtained from the subject. The subjects were examined in supine position. The optodes were fixed on the surface of the head with the use of rubber foam and Velcro stripes. The optodes were positioned on the right frontal area of the head below the line of hairs. A dose of 10 mg of ICG (Pulsion, Germany) dissolved in 5 mL of aqua pro injectione was administrated into the left forearm vein.

2.5.

Data Analysis

In the preprocessing phase in the measured DTOFs, the background signal was subtracted and correction of nonlinearity of the TCSPC electronics was applied. The statistical moments of the simulated and measured DTOFs (number of photons $N$, mean time of flight $⟨t⟩$, and variance $V$) were derived from the parts of the distributions limited by 3% of their maxima.⁴³ Time-courses of the statistical moments calculated for different source-detector separations were normalized and the time-to-peak (TTP) corresponding to the maximum of amplitude change caused by the ICG inflow was calculated. Typically the TTP values decrease with the order of the statistical moment (${\mathrm{TTP}}_N>{\mathrm{TTP}}_{⟨t⟩}>{\mathrm{TTP}}_V$) as shown in Fig. 2.

Fig. 2

Presentation of the data processing principle [time-to-peak (TTP) parameter calculation from the time-courses of the statistical moments of distribution of time of flights of photons (DTOFs)] on the data obtained by Monte Carlo (MC) simulations.

In the next step, $\mathrm{\Delta }\mathrm{TTP}$ values for each statistical moment were calculated. In the case of MC simulations, $\mathrm{\Delta }\mathrm{TTP}$ was estimated as the difference between the calculated TTP values and reference value, which was ${\mathrm{TTP}}_0$ obtained for simulated inflow function for the lower layer of the model.³⁸ In the phantom studies and in vivo measurements, the reference value ${\mathrm{TTP}}_0$ was determined for each of the experiments as the minimal value of ${\mathrm{TTP}}_V$. In the case of MC simulations, ${\mathrm{TTP}}_{\mathrm{MAX}}$ was obtained by the analysis of the simulated inflow function for the upper layer of the model. In the phantom studies and in vivo measurements, the reference value ${\mathrm{TTP}}_{\mathrm{MAX}}$ was determined for each experiment as the maximal value of ${\mathrm{TTP}}_N$.

3.1.

Monte Carlo Simulations

Results of the analysis of $\mathrm{\Delta }\mathrm{TTP}$ obtained for different statistical moments of DTOFs calculated by MC simulations for different thickness of the upper layer (from 6 to 12 mm) are presented in Fig. 3. In these simulations, the reduced scattering coefficient was assumed to be ${\mu }_{\mathrm{s}}^{\prime }=10{\mathrm{cm}}^{-1}$. It should be noted that $\mathrm{\Delta }\mathrm{TTP}$ approaches zero when the simulated signal perfectly reveals the inflow of the dye to the deeper layer of the model. It can be observed that for thin extracerebral tissue compartment, all statistical moments can provide information corresponding to the deeper tissue compartment even for source-detector separations $<3\mathrm{cm}$. However, increase in the thickness of the upper layer causes the $\mathrm{\Delta }\mathrm{TTP}$ obtained from the signals of the total number of photons $N$ to be strongly overestimated. This effect, with lesser extent, can be observed for higher-order statistical moments. Only small discrepancy between the estimated and expected value of $\mathrm{\Delta }\mathrm{TTP}$ can be observed ($<0.2\mathrm{s}$) for source-detector separations $r_{\mathrm{SD}}\ge 4\mathrm{cm}$ when the variance $V$ of the DTOF is analyzed.

Fig. 3

Analysis of the results of the MC simulations. Changes in $\mathrm{\Delta }\mathrm{TTP}$ obtained at different source-detector separations and different upper layer thickness for three moments of DTOFs: total number of photons $N$, mean time of flight $⟨t⟩$, and variance of the DTOF $V$. The reduced scattering coefficient was assumed to be ${\mu }_{\mathrm{s}}^{\prime }=10{\mathrm{cm}}^{-1}$.

Results of the second series of MC simulations are presented in Fig. 4. Analysis of $\mathrm{\Delta }\mathrm{TTP}$ was carried out for media of different reduced scattering coefficient ${\mu }_{\mathrm{s}}^{\prime }$. It can be observed that scattering properties of the medium strongly influence the sensitivity of the moments to the inflow of the dye to the deeper layer of the model. The increase in ${\mu }_{\mathrm{s}}^{\prime }$ leads to strong discrepancy between the estimated and expected value of $\mathrm{\Delta }\mathrm{TTP}$ when the total number of photons $N$ is analyzed. This effect can also be observed for higher-order statistical moments, but this discrepancy remains relatively small ($<1\mathrm{s}$) for all values of ${\mu }_{\mathrm{s}}^{\prime }$ and large source-detector separations ($r_{\mathrm{SD}}>3\mathrm{cm}$) when the variance $V$ of the DTOF is analyzed.

Fig. 4

Analysis of the results of the MC simulations. Changes in $\mathrm{\Delta }\mathrm{TTP}$ obtained at different source-detector separations and different reduced scattering coefficient of the medium for three moments of DTOFs: total number of photons $N$, mean time of flight $⟨t⟩$, and variance of the DTOF $V$. The thickness of the upper layer was assumed to be 10 mm.

Results of the last series of MC simulations are presented in Fig. 5. Analysis of $\mathrm{\Delta }\mathrm{TTP}$ was carried out for different relations between amplitudes of changes in absorption of the dye ${\mu }_{\mathrm{a}}$ for both layers of the model. It can be observed that increase in the amplitude of change in the absorption coefficient ${\mu }_{\mathrm{a}}$ in the upper layer of the model results in increase in discrepancy of $\mathrm{\Delta }\mathrm{TTP}$ estimation. When the amplitude of change in the upper layer of the model is two times larger than that in the lower layer, the uncertainty of $\mathrm{\Delta }\mathrm{TTP}$ estimation is $<1\mathrm{s}$ only for $V$ signal obtained at source-detector separation $>4\mathrm{cm}$.

Fig. 5

Analysis of results of the MC simulations obtained for different amplitudes of change in absorption coefficient in the upper layer of the model. (a) Dynamic changes in absorption coefficient in upper and lower layer of the model and (b) corresponding changes in $\mathrm{\Delta }\mathrm{TTP}$ at different source-detector separations calculated for: total number of photons $N$, mean time of flight $⟨t⟩$and variance $V$of the DTOFs. The thickness of the upper layer was assumed to be 10 mm and the reduced scattering coefficient was assumed to be ${\mu }_{\mathrm{s}}^{\prime }=1{\mathrm{mm}}^{-1}$.

3.2.

Phantom Experiments

The results of the phantom experiments are presented in Fig. 6. Obtained results show trends similar to those presented in the MC simulations. For larger delays between bolus appearance in the tubes located deeper and superficially, $\mathrm{\Delta }\mathrm{TTP}$ changes quickly with source-detector separation. Moreover, as expected, the uncertainty of $\mathrm{\Delta }\mathrm{TTP}$ estimation is lower when the delay in appearance of the boluses in the deeper and superficial tubes is larger.

Fig. 6

Results obtained during phantom experiments. Changes in $\mathrm{\Delta }\mathrm{TTP}$ obtained at different source-detector separations for three delays $\mathrm{\Delta }t$ between the appearances of the boluses of indocyanine green (ICG) in the tubes located superficially and deeper in the medium. Results of the analysis of three moments of DTOFs: total number of photons $N$, mean time of flight $⟨t⟩$, and variance $V$ of the DTOF.

3.3.

In Vivo Measurements

The DTOFs were obtained for 16 source-detector separations (from 1 to 6.75 cm) during in vivo (see Fig. 7) tests carried out in healthy volunteers. As presented in Fig. 7, results of these experiments confirm the trends that were observed in MC simulations and phantom experiments.

Fig. 7

Analysis of results of the in vivo experiments carried out on three healthy volunteers. Changes in $\mathrm{\Delta }\mathrm{TTP}$ obtained at different source-detector separations by analysis of three moments of DTOFs: total number of photons $N$, mean time of flight $⟨t⟩$, and variance of the DTOF $V$.

As expected, the uncertainty of $\mathrm{\Delta }\mathrm{TTP}$ estimation is lowest when the $V$ signal is analyzed. However, the decrease in the discrepancy observed in $\mathrm{\Delta }\mathrm{TTP}$ depends strongly on the subject measured.

Additionally, in order to assess repeatability of the measurement, the analysis of moments of DTOFs obtained in consecutive injections in a single subject was performed (see Fig. 8). It can be observed that the pattern of changes in $\mathrm{\Delta }\mathrm{TTP}$ does not dependent significantly on the ICG concentration in the injected bolus (5, 8, and 10 mg of ICG dissolved in 5 mL of aqua pro injectione). Moreover, it can be observed that the largest delay between signals of moments obtained at different source-detector separations does not depend significantly on the dose of ICG injected.

Fig. 8

Changes in $\mathrm{\Delta }\mathrm{TTP}$ obtained at different source-detector separations for three consecutive ICG injections in a single healthy volunteer. Different concentrations of the ICG in the bolus $C_{\mathrm{ICG}}$ were applied.