Photon penetration depth in human brain for light stimulation and treatment : A realistic Monte Carlo simulation study

Ting Li*, Chang Xue, Pengbo Wang, Yan Li and Lanhui Wu *Institute of Biomedical Engineering Chinese Academy of Medical Science and Peking Union Medical College 300192, Tianjin, P. R. China State Key Lab Elect Thin Film & Integrated Device and Department of Biomedical Engineering University of Electronic Science & Technology of China Chengdu 610054, P. R. China Design Center Avic Beijing Keeven Aviation Instrument Co., Ltd China Aviation Industry Corporation Beijing 100098, P. R. China litinghaha9@126.com


Introduction
The medical photonics research has come to the foreground in recent years.Light stimulation has been applied into medical treatment study, such as low-level laser therapy and photodynamic therapy, have experienced a rapid development from experimental stage to practical stage. 1,2While the temperature variation or heat generation e®ect has been well studied in the research of light therapy, the quantitative knowledge of light propagation and penetration depth is rare. 3There is no doubt that for those light stimulation and treatment ¯elds, the penetration depth of light is critical for both research and clinical application, especially on the issue for precision of personal medicine, quantitative-guide treatment, optimization of the light therapy parameters, and safety control.There is sparse experiment study on light penetration depth for human structured tissues, only semi-in¯nite phantom or layered phantom study were published. 4owever, it is undoable to measure, by experiment, light penetration depth within human head or mimicking head model with the complex geometry and structure.The alternative way is precise modeling of light propagation within realistic human head model.The di®use equation method and Monte Carlo modeling are the main ways to obtain the computation of light propagation.Compared to the recent developed analytical approximation method, 5 Monte Carlo method is more °exible and reliable, especially for nonin¯nite medium.There are several widely used Monte Carlo simulation techniques o®ered in our ¯eld, such as the one for layered tissue model (MCML), 6 the one for medical image depicted tissue model (tMCimg), 7 the one for mathematical geometry depicted tissue model (MCLS), 8 and the one for 3D voxelized media (MCVM). 9Although these methods have been accepted in biomedical ¯eld in accurate light propagation computation, the MCML and MCLS are only applicable layered tissue model or the model depicted with cube, sphere, or cylinder.Only tMCimg and MCVM are capable of modeling light propagation within realistic structure tissue model.MCVM is most fully tested. 63][14] While the other parts of human body, like breast, leg, arm, and belly, are simple in structure which mostly can be treated as layered model, the head is of complicate three-dimensional (3D) structure and complex geometry of cerebral tissue.It is not convincing to use layered head model to study light penetration depth.Realistic human brain structure model is required to provide reliable enough estimation of light penetration depth.
Recently, there was some realistic Monte Carlo simulation study which analyzed the factors a®ecting light propagation in realistic human brain, however most of them were not focused on the penetration depth and failed in o®ering quantitative comparison or answers, not to mention the e®ect of treatment light properties on light penetration depth. 8,10,11,15There was only one Monte Carlo study on light penetration depth on realistic head model, 13 which uses a MRI head model in which precision is not high enough.A more realistic and precised head model was recommended to model light propagation. 11isible human projects of the world provided us the realistic structured human brain model. 16hereinto, Visible Chinese human (VCH) is famous in highest-resolution structure image dataset, ¯nest and professional segmentation of VCH into di®erent types of tissues. 16,17VCH head dataset is capable to provide us the highest realistic human model for us to study particle propagation, 11,15,18 which delight us to study light penetration depth with VCH head model.Of note, the VCH model is a 3D voxelized model, requiring us to simulate light transportation within human head with a Monte Carlo approach which is compatible to voxelized media.
Our study aims to obtain quantitative evaluation of light penetration depth for light stimulation and therapy.We managed to use the most-realistic human head model, VCH, and the most reliable 3D Monte Carlo modeling technique which is compatible for the VCH voxelized model, MCVM to modeling 3D light propagation in human head.The important illumination parameters, such as the wavelength, pro¯le, and beam size of the treatment light, are interrogated to study the quantitative e®ect of those parameters to light penetration depth.The data of those parameters are set in the range of commonly used. 15The percentage of light °uence in di®erent-depth tissues, the contoured pseudo color map of °uence distribution, the sampled °uence decline with penetration depth, and the accumulated number of light-penetrated voxels are used to scale the light penetration depth.
This study ¯nally provided numeric evaluation of light penetration depth and quantitative comparison of the commonly-used treated light properties on light penetration.The ¯ndings showed deep penetration of light within gray matter and white matter, which support the capabilities of light stimulation and treatment in cerebral tissue volume.Plus the quantitative comparison on the illumination parameters based on our MCVM.VCH modeling exampled a reliable, fast, low-cost, and no-animal-test way to obtain light penetration depth value estimates for light stimulation and light therapy, compared to previous simplistic phantom study, simulation studies, animal therapeutic e®ect measurement studies.

Methods and Materials 2.1. VCH brain model
The VCH head model we used contains various types of tissues in a Chinese male human whole body frozen in the standing posture, and was horizontally sectioned at 0.02 cm interval.0.01 cm-perpixel-resolution photographs were obtained with digital color, which is higher than CT and MRI.The sections of VCH are performed by color photographs (see Fig. 1(a)).Distinct tissues in each slice were visibly distinguished, segmented and labeled with a series of speci¯ed number (see Fig. 1(b)).These precisely segmented and labeled sections and high-resolution colored photographs make it more realistic for studying human brain.Besides, compared to CT and MRI, which require lying posture, the upstanding posture in VCH is more close to the natural and real geometry of brain surface for the research about light penetration prediction. 10n the analysis of the color photographs and the numbered sections, the head model was segmented into eight types of tissue, including scalp, skull, CSF, muscle, visible artery, vein blood vessels, gray and white matter.We chose every four continuous pixels in both anterior-posterior and left-right directions in two continuous slices to form voxels of 0:04 Â 0:04 Â 0:04 cm 3 .This was the voxel size used to balance the computation parts in the simulation and get it more precise and real.Finally, we got a 450 Â 400 Â 150 voxel-size three-dimension matrix which contains a numerical scale, a list of various tissue types.The list describes the optical features of each speci¯c tissue for each voxel.The optical features of these tissues at 660, 810 and 980 nm 10,15,19,20 are listed in Table 1.Photon penetration depth in human brain 1743002-3

MCVM
The software we used was MCVM programmed by Ting Li, which applied to 3D voxelized media.The detailed algorithm has been described in Ref. 6. Brie°y, photon propagation in the head was determined by several factor such as scattering coe±cient, absorption coe±cient, phase function, re°ections and refractions in the 3D arbitrary surface of the tissue and complex interfaces between di®erent types of tissue.This program checked whether a photon could travel through a boundary between di®erent tissues once encountered a substep.Re°ection and refraction were also considered in this program.Each actual substep was relative to a single voxel and a single absorption coe±cient, and thus the absorption related with such substep was recorded precisely to the local voxel by pseudo continuous absorption weighting.So it is with scattering coe±cients.It proves that MCVM has been validated well with both theoretical data and experimental data.
In the simulation, we set up the input and output ¯le name, the illumination position and directions, number of photons as well as the optical properties of each type of tissue included.After the runs of MCVM simulation, the outputted 3D light °uence distribution were extracted out for analysis.

Simulation
The input data based on Table 1, was set in MCVM simulations.After computation, the results about the light absorption within di®erent voxels were output and extracted out.After simulations, we calculated the °uence distribution, divided the output light absorption distribution by the absorption coe±cient distribution in the tissue.With statistical analysis on the characteristic parameters on the 3D °uence distribution, we obtained the evaluation of light penetration depth at di®erent values of beam types, wavelengths and sizes.The position in the center of forehead, which is 1 cm above the eyebrow, is ideal to place the center of beam and the inject direction of it is just the normal direction of the forehead.The comparison within those results were performed to address the e®ect of wavelengths, beam types and beam sizes.
The wavelength, beam type and beam size are the main factors a®ecting light °uence distribution in human brain in consideration of this study.We chose three wavelengths: 660, 810 and 980 nm with the same beam size, two beam types: Gaussian beam and Top-hat beam and three kinds of beam size di®erent in diameters: 2, 4 and 6 cm with the same wavelength of 810 nm, totally 12 simulations.The number of photons in each simulation are 10 7 in total, which means the beams in our simulation study have same power density (normalized to be 1 W).Each simulation was repeated for 10 times and the result was obtained in average for data analysis to increase the signal-to-noise ratio.

Data analysis
The results of 10 times simulation of the 3D °uence distribution at di®erent combinations of treated light parameters were averaged by 10 to eliminate random e®ect.Then, the percentage of light °uence in di®erent-depth tissues were analyzed with pie chart.The contoured pseudo color map of °uence distribution were displayed to analyze the penetration depth visibly in space.In those photographs, di®erent colors, such as red, orange, yellow, blue and purple, represent the output light absorption distribution according to their intensity.The red means the highest absorption distribution, the orange means second high and so on.The sampled °uence decline at the light source emitting direction were extracted to show its decrease with penetration depth.The number of light-penetrated voxels are accumulated to investigate the penetrated depth scale especially in gray and white matter.The slice numbered 269 was exactly where the beam source center was placed, which is 1 cm above the eyebrow.Therefore, when analyzing the ¯nal results, we chose the color photographs of this slice in presentation.To make our research more accurate and intuitive, we accumulated all the °uence in brain and then calculated the proportion of each tissue in the form of percentage, and made a pie chart about the °uence distribution in brain tissues according to those research.

Light °uence distribution
The pie chart (Fig. 2) suggests the percentages of °uence in each tissue that we detected in brain, such as scalp, scull, CSF, etc., which were close to the simulation results shown in Ref. 15.It supported the reliability of the simulation.Moreover, the percentage of °uence in gray and white matter proved the light penetration is deep into cerebral tissue.
Figure 3 intuitively showed the abilities of each type of light in penetration into brain.From the results, we can get some idea of the approximate area of the light penetration inside human brain, which includes white matter and gray matter.In Fig. 3(a), it is obvious that wavelength plays a more important role in determining light penetration depth than beam type.It is obviously found that 810 nm is more suitable than 660 nm and 980 nm in transcranial LLLT for more deeply and widely penetration.Clearly, for 810 nm, red colored °uence has reached the gray matter and yellow colored °uence has even well reached the interior white matter.On the contrary, for 660 nm, yellow colored °uence only reached the gray matter and indigo colored °uence reached the white matter.While for 980 nm, only blue and purple parts could reach the white matter.Besides, It is found that for 810 nm, light could reach more widespread region in human brain compared to the other two wavelengths.For 980 nm, penetrated light is most concentrated but could not reach very deeply in brain, and thus it is ideal for light acupuncture, which requires highly focused and precisely located penetrating beam.For phototherapy, if doctors need to stimulate deeply into cerebral tissue, they would better choose 810 nm.Compared to the other two, 660 nm is basically a modest choice.
Another important ¯nding is that beam type plays a less important role in a®ecting the penetration depth of light in human brain.There is slight di®erence between Gaussian and Top-hat beams in a®ecting light °uence distribution.It is showed that Gaussian beams was able to penetrate a little more deeply than Top-hat beams, but the di®erence is very slight.For example, for 810 nm, it could be distinguished that for the photograph of Top-hat beam, yellow part took more area of white matter compared to Gaussian beam.
The result of simulations based on two beam types (Gaussian and Top-hat) and three diameters (2, 4 and 6 cm) is shown in Fig. 3

(b).
There is a tendency that as the beam size decreases, beam could penetrate more widely and deeply inside human brain.On the other hand, it could be found that when beam size is the same, beam type hardly causes di®erence between these two simulations.Accordingly, compared to beam type, beam size has more in°uence on the penetration depth of light.Another interesting phenomenon in those photographs is that as the beam size increases, the area beams could reach increase slightly, but the di®erence is not signi¯cant and the quantitative analysis were o®ered below.

Penetration depth
Figures 4 and 5 provide researchers sampled °uence decline with penetration depth and the exact penetration depth of several commonly used beams, and they also provide comparison among those beams.The horizontal dotted line, corresponding to, represents the penetration depth most equipment available now that could measure accurately.And the horizontal dotted line, corresponding to, represents the limiting penetration depth which the most advanced equipment could measure so far.
In Fig. 4, for beams of the same wavelength, Gaussian beams was able to penetrate more deeply than Top-hat beams, although the di®erence is relatively small, which is coincident with the above ¯gures.For example (as shown in Tables 2 and 3), the penetration depth of Top-hat beams is approximately 3.81 cm while the penetration depth of Gaussian beams is approximately 4.13 cm at the dotting line scales.The di®erences for 980 nm (although it is not very obvious on this chart) and 660 nm are the same in this photograph.Besides, for beams of the same beam type, the penetration depth of 810 nm is the greatest, which reaches 4.13 cm.660 nm takes the second in rank, reaching 3.45 cm in depth.980 nm obtained the smallest penetration depth, which is only about 1.45 cm.
In Fig. 5, the penetrated °uence attenuation of those six types of beams in light incidence direction were extracted precisely.If carefully observing the positions of those intersection points of those colored lines and the dotted line, it could be found that for both beam type, the penetration depth of light decreases as the beam size increases.Besides, it is hard to distinguish the di®erence between the penetration depths of beams with the same beam size but di®erent beam types.

Number of light penetrated voxels in cerebral tissues
The number of penetrated voxels by light is an overall parameter to re°ect the capability of beam penetration in human brain.As shown in Fig. 6, white bars represented the number of voxels in the gray matter reached by light and black bars represented the number of voxels in the white matter reached by light.It is obvious that for 810 nm, the numbers of light penetrated voxels within cerebral tissues were much larger than the other two wavelengths.This simulation results could also verify that 810 nm-light could penetrate most deeply and widely within cerebral tissue.Additionally, for both 810 nm and 660 nm, Top-hat beam showed a slightly (1-2%) better performance in penetrating inside brain, but for 980 nm, the opposite.Besides, the di®erent e®ects beam type brings are obviously very slight, which is the same with our previous ¯ndings.Di®erent from Figs. 6(a) and 6(b) showed that Top-hat beam always performed better in penetrating within cerebral tissue, compared to Gaussian beam.Plus, as beam diameter increases, the number of penetrated voxels increases as well, and  for 4 cm and 6 cm sizes of beams, there is no obvious di®erence between the numbers of light penetrated voxels.

Conclusion and Discussion
The main goal of this research is to obtain quantitative analysis of near-infrared light penetration depth and to make comparison of light penetration depths at some commonly-used treated light properties for transcranial light stimulation and therapy.The whole research was conducted in the way of 3D Monte Carlo simulation with the use of the most realistic human head model, VCH, which could provide the highest realistic human model with highest-resolution structure image dataset for us to study precise light propagation, and the most reliable 3D Monte Carlo modeling technique, which could help simulate light transportation inside human head realistically.The result we got is relatively more accurate and realistic than the previous related reports with simplistic structured or low-resolution MRI slice-based head models or light propagation computation with those method not for highly realistic head model.The light penetration depth were extracted and scaled by pie chart of accumulated °uence statistics, the light distribution of °uence in structured head pro¯le, the sampled decline curve of °uence at light incidence direction, and voxel numbers of irradiant voxels in di®erent types of tissues.All of the result provided successful quantitative analysis of light penetration depth for transcranial LLLT.
We explored the percentage of light °uence in di®erent-depth tissues in the way of simulation, measured the whole number of penetrated voxels in every experimental group and compare them in histograms, etc.The numeric evaluation of light penetration depth and quantitative comparison of those beams were analyzed in two aspects: the penetration depth of single beam and the total  number of penetrated voxels.To ¯nd the e®ects of factors such as wavelength, beam size and beam type, we chose di®erent but frequently-used wavelengths (660, 810 and 980 nm), beam diameters (2, 4 and 6 cm) and beam types (Gaussian and Top-hat beams) and divided them into two groups, each had six simulations of two beam types and three wavelengths or beam sizes.
In this study, we made quantitative investigation on stimulated/treated light penetration depth, which were mostly qualitatively studied by previous report and accordingly rarely reliable quantitative evaluation were reported.Our study showed that 810 nm was shown to be the most ideal choice for transcranial LLLT treatment for the widest and deepest penetration.980 nm is shown to be suitable for light acupuncture since the light at this wavelength is more concentrated and penetrates lightly.As for beam diameter, 2 cm size of light also performs better than those of 4 cm and 6 cm in penetrating within brain, but the di®erence between them is not quite signi¯cant.The similar ¯nding was also reported by others before, 15 however, in this research we went further by quantitative study.We observed the exact penetration depth of each beam and the total number of penetrated voxels.For example, the number of voxels penetrated by 660-nm-light is about 4/5 of 810 nm, and that of 980-nm-light is about 1/5 of that of 880-nm-light.Taken together of all quantitative analysis of all results in this study, it is distinct that wavelength takes the largest e®ect on penetration depth, the second is beam size and the third is beam type.
Limited by undoable experimental test of light penetration depth for clinical transcranial LLLT, we were not allowed to verify our simulation results but compare it with some other researchers' report.However, the simulation method, we used is of high accuracy and has been fully tested.MCVM is capable of precise modeling light propagation in 3D structured media; and the VCH is the top realistic human model with highest resolution and ¯nest segmentation referring to tissue type.In the future, we may perform relevant experiments on animals to measure photon penetration depth for light stimulation and therapy for brain diseases and address to current issues on light distribution 21 /diseases 22 with our MCVM-VCH method.
Taken together, by using Monte Carlo Modeling method for 3D voxelized media and VCH head dataset, we obtained reliable light °uence distribution at di®erent illumination parameters combinations.We surprisingly found that 810 nm light enabled maximum penetration depth (> 5 cm) penetration depth when beam size is smaller than 2 cm, no matter what type of beam pro¯le.It means that light stimulation at such illumination set allowed light crossing through gray matter into white matter, which supports the therapeutic e®ect of low-level therapy for brain function de¯cit or dysfunction.Additionally, the quantitative evaluation of light penetration depth at commonly used illumination parameter range is very helpful for researchers and clinicians guiding and optimizing the light stimulation and parameters, precision or personal medicine, and safety control.This study advantageously offered us reliable and quantitative evaluation of photon penetration depth for light stimulation and treatment ¯eld of biomedical optics.Plus, it showed us an innovative, fast, low cost, nonanimal-test way to achieve light penetration depth at actually used illumination properties for research and clinics.

Fig. 1 .
Fig. 1.VCH head model.(a) Digital color photograph of one typical slice in the VCH head dataset; (b) Segmentation of the slice in (a) and identi¯cation of di®erent types of tissues.

Fig. 2 .
Fig. 2. Percentage of light °uence distribution in each type of tissue in VCH head model under normal condition.Data are shown in average statistics among di®erent emitting positions on the forehead.

Fig. 3 .
Fig. 3. Light °uence distribution with the background of head geometry and 3D structure.The result in the slice numbered 269 are shown.(a) The LLLT °uence distribution respective to Gaussian and Top-hat beams at di®erent wavelengths (660, 810 and 980 nm); (b) The LLLT °uence distribution respective to Gaussian and Top-hat beams of di®erent diameters (2, 4 and 6 cm).

Fig. 4 .
Fig. 4. The °uence decline following with the penetrated depth from the beam center into head tissue at normal light incidence direction.G and T denote to Gaussian and Top-hat beams respectively.Wavelengths 660, 810 and 980 nm are included.

Fig. 5 .
Fig. 5.The °uence decline following with the penetrated depth from the beam center into head tissue at normal light incidence direction.G and T denote to Gaussian and Top-hat beams, respectively.

Fig. 6 .
Fig. 6.(a) Mean number of light penetrated voxels within cerebral tissue respective to Gaussian and Top-hat beams at di®erent wavelengths; (b) Mean number of penetrated voxels within brain tissue respective to Gaussian and Top-hat beams of di®erent diameters.

Table 1 .
Optical properties of head tissues for 660, 810 and 980 nm light.The units of both absorption coe±cient (u a ) and scattering coe±cient (u s ) are cm À1 .

Table 3 .
The penetration depth value extracted from Fig.5.G means Gaussian beam; T means Top-hat beam.