Photon transport through the entire adult human head

2.1.

Numerical Modelling

Monte Carlo ray-tracing simulations were performed using Monte Carlo eXtreme (MCX) to estimate the attenuation and distribution of light through the head. An open-source six-layer head volume mesh [Fig. 1(a)] derived from an averaged MRI²¹ was used with optical coefficients from Cassano et al.¹⁸ (at 810 nm) displayed in Table 1.

Table 1

Optical properties used in this study for the layers of the simulated volume mesh. The values are taken from Cassano et al.18 at 810 nm.

A uniformly distributed collimated disk source with 2 in. diameter was directed toward the side of the head $\sim 4\mathrm{cm}$ above the tip of the ear.

Figure 1(b) shows the attenuation of fluence inside the head from 1 cm to 15.5 cm depth is of order ${10}^{16}$ to ${10}^{18}$. The graph in Fig. 1(b) represents the sum of the fluence for voxels inside the head in sagittal slices that are increasingly further from the source. The values were normalized by the slice with the maximum total fluence. The increase in normalized fluence for slices up to 1 cm depth inside the head is due to the curvature of the head surface. Only voxels inside the head are used in the summation, and some areas of the source do not interact with the tissue until deeper slices. Section 1 in the Supplementary Material explains this in more detail with accompanying diagrams.

To overcome such high attenuation factors and adequately sample the time-of-flight (ToF) distribution at the detector, 362 simulations were performed across three computers with NVIDIA GeForce RTX 4090 graphics cards for a combined run time of $>850\mathrm{h}$. The graphics card memory could run $2\times {10}^{11}$ single-point precision photon packets per simulation, and the aggregated photon weights at the detector from a total of $7.24\times {10}^{13}$ launched photons were used to estimate the final distribution.

Analysis of the simulated fluence-rate distribution through the head in Fig. 1(c) shows that light explores all regions of the brain and persists mostly in areas with low scattering and absorption, such as the cerebrospinal fluid above and below the cortex.

2.2.

Experimental Methods

To demonstrate the feasibility of detecting photons that have experienced the longest trajectories, and therefore most likely to interact with the deepest layers of the head, an experiment was performed to detect light that has traveled diametrically from one side of the head to the other (i.e., across the widest point of the skull).

The experimental configuration is outlined in Fig. 2(a): a pulsed laser (1.2 W power, 800 nm wavelength, 140 fs pulse duration, 80 MHz repetition rate) is expanded to a uniformly distributed circular beam of 1 in. diameter and projected against the side of the head above the ear. Diametrically opposite the source, a demagnifying tapered fiber bundle (Edmund Optics, Barrington, New Jersey, United States, 25 to 8 mm fiber optic taper) is placed in close proximity to the scalp and redirects light to a photomultiplier tube (PMT, Hamamatsu, Japan, H7422P-50). The PMT operates in photon counting mode, such that the detection of a photon produces an electrical pulse that can be synchronized with the laser emission to produce a photon ToF distribution using a time-correlated single-photon counting (TCSPC) module (Becker & Hickl, Berlin, Germany, SPC-150N).

The combination of high laser power and a large-area single-photon sensitive detector is optimized to overcome the extreme attenuation of light through the head. Increasing the area of incident laser exposure allows the use of high powers without reaching the maximum permissible exposure of human skin. This is in contrast to typical fNIRS devices that use point-like emitters in an effort to maintain high spatial resolution, as well as low-power and small form-factor hardware.

The detector used in this work is chosen to maximize the etendue (product of light collection solid angle and sensor area) of light collection with a large-area detector (5 mm diameter). The demagnifying tapered fiber bundle is used to further increase the area of collection by $\sim 5\times$ at the sacrifice of $\sim 5\times$ reduction in solid angle of collection. Time-resolved DOT systems can be characterized using the basic instrument protocol outlined by Wabnitz et al.,²² which suggests that the maximum $A\mathrm{\Omega }$ product of a typical DOT fiber collection system is limited to $\sim 8{\mathrm{mm}}^2\mathrm{sr}$. In our configuration, the PMT sensor is recessed by the outer casing limiting the angle of collection to an equivalent of $\mathrm{NA}=0.52$. By the same calculation in the work by Wabnitz et al.,²² our configuration has $A\mathrm{\Omega }=16.68{\mathrm{mm}}^2\mathrm{sr}$, more than twice the estimated maximum of typical systems. The PMT used in this work is commonly used in the field of fNIRS due to its high sensitivity to near-infrared wavelengths (QE = 15% at 800 nm) and the timing characteristics and sensitivity are reported by Wabnitz et al.²² We measure our system to have a 300 ps (full width half maximum) impulse response function (IRF) and a dark count rate of 15 cps. An advantage of time-resolving measurements in this experiment using TCSPC allowed us to further overcome background photon counts and noise that is uncorrelated with the laser source.

To prevent light from reaching the detector from sources other than light transmitted through the head, the experiment was performed in a light-tight enclosure that surrounded the head. The enclosure was built using black foamboard and covered with two layers of black cloth and a laser safety curtain. The participant’s torso from the waist upward was also wrapped in two layers of black cloth, which was sealed to the enclosure using Velcro. To prevent light scattering from optics immediately after the laser and reflecting from objects around the lab, a separate light-tight enclosure was built and similarly covered with cloth and the laser safety curtain. A black silicone mold with a 1 in. inner diameter hole was used to press the source against the head and prevent back reflections from the skin reaching the detector. On the detector side, sponge wrapped in black cloth was used to make a comfortable seal against the head during measurements and isolate the area of the head diametrically opposite the source from any other spurious reflections in the light-tight enclosure reaching the detector. Similarly, the detector was enclosed in a custom-built foamboard box wrapped with black cloth inside a larger foamboard enclosure, which was also covered with cloth and the laser safety curtain. Light reaching the detector from reflections around the lab appeared as a time-delayed impulse response function with 300 ps full width half maximum. Improvements in the seals around the experiment that extinguished this signal were used to ensure the enclosure was light-tight. A picture of the enclosures can be found in the Supplementary Material.

3.1.

Experimental Photon Detection

The results in Fig. 2(b) show experimental ToF distributions for photons transmitted through an adult male head (15.5 cm diameter) with fair skin and no head hair, collected on two different days, 1 week apart. For each day, the time traces are the mean of 15 2-min exposures, resulting in 30 min of total acquisition time. In every five exposures, a background reading was recorded where the subject was in the same position, but the laser beam shutter was activated to prevent light from reaching the head. The average counts in the background readings were subtracted from the average counts in the signal recordings for each timebin, and the result was smoothed using a Savitzky–Golay filter (window = 251, order = 3). An example of the mean background–subtracted photon counts overlayed with the filtered signal is shown in Fig. 2(c). The standard error shown in Fig. 2(b) for each timebin was calculated using the 2 min exposures before filtering. The standard error was added to and subtracted from the filtered signal to estimate the upper and lower bounds of the counts in each timebin, respectively. The upper and lower bounds were smoothed with the same filter used for the signal. For detailed inspection, Fig. 2(b) is plotted over a log scale in Sec. 2 of the Supplementary Material.

The measured experimental attenuation was found to be of the order ${10}^{18}$, corresponding to a detection of around one photon per second for a 1.2 W source. The simulated ToF distribution for the experimental configuration was approximated using a 2 in. diameter uniformly distributed source and a detector area corresponding to the photons leaving the surface of the head mesh cropped to a depth 13.3 cm from the source onward, above the ear, and behind the temple. The source size is larger than in the experiments to account for the challenging repeatability of source placements between measurements. The underlying population distribution was approximated using kernel density estimation using kernel bandwidths determined by Silverman’s rule²³ to overcome subsampling. The distribution is then convolved with the experimental impulse response function. The simulated result shows good agreement with experimental results for the first two moments of the distribution, i.e., for both the peak delay time and width of the ToF distribution, indicating that the measured signal propagated through the head via similar migration pathways as seen in the numerical model. We attribute the discrepancy between the tails of the experimental distributions on different days to the challenging reproducibility of the source and detector placements between trials and the low number of photons measured, which results in a low signal-to-noise ratio. Despite this, we still see the strong overlap of the uncertainty bounds represented by the standard error on the mean photon counts in each timebin. Further analysis of the experimental data with the simulated time-resolved fluence data for increasing depths is shown in Sec. 3 of the Supplementary Material.

3.2.

Photon Migration Pathways

Despite considering photon propagation in the human head as a diffuse optics problem where it is typically expected that light is highly scattered in all directions, the heterogeneity of optical properties and complex geometry of different layers causes light to be guided through the head in preferred pathways. This phenomenon is caused by channels of low scattering and absorption (e.g., cerebrospinal fluid) surrounded by high scattering (e.g., skull and gray matter), such that light follows the path of least extinction. A general study of the fundamental mechanism of guided light in diffusive materials was recently explored by Mitchell et al.²⁴ In the context of fNIRS, light guided by cerebrospinal fluid has been observed in numerous previous studies and is typically considered an unwanted nuisance that decreases the depth of penetration of light and increases uncertainty when trying to locate brain activity.^25–27 By contrast, in this work, we argue that the role of light guided by weakly scattering channels is critical for localizing changes in light absorption in deep brain regions and can be exploited by optimized source and detector arrangements.

Analysis of 50 random detected photon packet trajectories for various source positions is shown in Fig. 3. Positioning the source high above the ear can cause light to be guided around the top of the brain in the CSF layer [Fig. 3(a)], whereas lower positions cause light to be transported under the brain [Fig. 3(c)]. Likewise, moving the source toward the back of the head or forward toward the temple can increase the likelihood of photon pathways reaching the occipital or frontal lobe regions, respectively [Figs. 3(d)–3(e)].

The position of the source in Figs. 3(b) and 3(e) closely approximates the configuration used in the experiment. A source launch area of 2 in. diameter was used to account for the uncertainty in position throughout the experiments. A detector with a radius of 4 cm was placed diametrically opposite the source and remained fixed for all source positions. Surprisingly, although it is likely that most of the experimentally detected photons propagated around the top of the head, Fig. 3(b) indicates that there are also trajectories under the cerebrum with similar order of magnitude attenuation.

The expectation value of the photon packet path lengths $⟨\text{path}⟩$ for the configuration in Figs. 3(b) and 3(e) is over 1 m propagation length. Normalizing the photon packet path lengths by the source-detector separation $\mathrm{SDD}=155\mathrm{mm}$ corresponds to a differential path length factor of $\mathrm{DPF}=\frac{⟨\text{path}⟩}{\mathrm{SDD}}=6.5$, which matches the measured and predicted values from conventional DOT systems for an adult human head.²⁸ Of the total DPF, the partial path length contributions for each layer are as follows: 17% from scalp, 35% from skull, 22% from cerebrospinal fluid, 19% from gray matter, 6% from white matter, and 1% from air cavities. Okada et al.²⁹ report typical partial path contributions for DOT with SDD = 50 mm to be: 65% from scalp and skull, 35% from the cerebrospinal fluid, and 5% in the gray matter. If the signal-to-noise ratio could be improved, a possible advantage of transmission geometry measurements is the increased proportion of the photon path interacting with gray matter compared with reflection geometries, which could lead to greater sensitivity to cerebral hemodynamics.

Unlike conventional systems, the large source-detector separation results in a much greater number of total transport mean free path lengths experienced by a photon. The weights of the detected photon packets $w_i$ in the $i$’th layer were used to calculate a weighted average of the reduced scattering $⟨{\mu }_s^{\prime }⟩=\sum _i^N{w}_i{\mu }_{s_i}^{\prime }/\sum _i^N{w}_i$ and the absorption coefficient $⟨{\mu }_a⟩$ for $N$ layers described in Table 1. The expected number of transport mean free paths experienced by a photon from the source to the detector is therefore $\mathrm{SDD}\times (⟨{\mu }_s^{\prime }⟩+⟨{\mu }_a⟩)=234$. Using typical values used in reflection geometries ($⟨{\mu }_s^{\prime }⟩=1{\mathrm{mm}}^{-1}$, $⟨{\mu }_a⟩=0.1{\mathrm{mm}}^{-1}$, SDD = 50 mm), we estimate most conventional DOT systems detect photons that have undergone $\sim 50$ transport mean free path lengths. We also show in Fig. 4, a sensitivity analysis that is obtained by calculating the Jacobian for the light rays, i.e., a map of how light intensity changes at the detector for small changes to the absorption coefficient at each voxel in the head.³⁰ The Jacobian for the source-detector arrangement approximating experimental conditions, Figs. 4(a) and 4(b), highlights that measurements in this configuration are indeed sensitive to changes in the absorption in deep regions of the brain reaching areas that are currently inaccessible for fNIRS devices, such as the midbrain, sulci, and deep regions of the cerebellum. Figure 4(c) shows that by repositioning the source 40 mm lower, the sensitivity map is isolated almost exclusively to regions under the cerebrum and demonstrates the potential to target deep brain regions with careful consideration of source-detector arrangements. These Jacobians are an extension of the typical “banana-like” sensitivity profiles found in fNIRS^1,31 in the limit of large source-detector separation, which here evolve into nontrivial shapes that could be used to reconstruct tomographic information.