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J. Eur. Opt. Society-Rapid Publ. 22, 48( 2026)
Table S1, Section A: Magnetic Resonance Imaging – Derived Cadaveric Head Anatomy). Skin pore geometries were explicitly represented using truncated semi – elliptical structures [ 26, 27 ] embedded within the top surface of the scalp layer, defined by a fixed diameter – to – depth ratio of 10:1. This semi-ellipsoidal approximation was selected as the optimal first-order geometric model to isolate the influence of surface curvature and aperture-driven diffraction on incident light, as it accurately captures the high aspect ratios and characteristic morphology observed in standard dermatological histology [ 28 ]. Furthermore, this geometry accounts for the critical refractive index mismatch at the air – tissue interface, which dictates the initial phase-space distribution of ballistic photons before they enter the diffusive regime [ 5 ]. Multiple pore diameters were evaluated across separate simulation runs, with pore diameters of 500, 250, 125, 62.5, 31.25, and 15.625 lm selected to span a physiologically realistic and literature – reported range [ 29, 30 ] and to assess scale – dependent ray interactions. To approximate realistic surface irregularities, pore boundary roughness was introduced by perturbing the idealized geometry using Gaussian noise. This was implemented in COMSOL Multiphysics via a stochastic function with normal distribution( mean 0, standard deviation 0.1 lm) and a fixed random seed, which was applied to the parametric representation of the truncated semi – elliptical boundaries. The computational domain was discretized using a free triangular mesh, with minimum and maximum element sizes of 2 lm and 1 mm, respectively. A maximum element growth rate of 1.1, a curvature factor of 0.2, and a narrow – region resolution of 1 were employed to ensure accurate ray – interface interactions while maintaining computational efficiency. Within the geometric optics interface, the intensity computation setting was configured to compute intensity and power in graded media, to correctly account for continuous refractive index variations in heterogeneous tissue [ 25 ]. The same wavelength – dependent optical properties used in the MC simulations( Table 1) were also assigned to the scalp tissue layers in the COMSOL Multiphysics model to ensure methodological consistency since the geometric optics interface requires specification of a complex refractive index, the real part n was directly assigned from Table 1, while the imaginary part j was computed from the absorption coefficient l a according to,
j ¼ l ak 4p; ð5Þ
where k denotes the operating wavelength 735 nm. A release boundary condition was assigned to the right vertical edge of a5 5 mm square source domain to emulate an unpolarized optical source with an irradiance of 1 W / m, emitting rays in the positive x – direction with the central emission axis aligned horizontally. A 70 ° half-angle was specified to replicate the divergence characteristics of commonly used NIR optical tissue imaging systems [ 32 ]. Thesourcewasoriented perpendicular to the scalp layer, vertically( radially) centered, andplacedindirectcontactwithitssurface. Ray directions were defined using the conical emission option, with the number of rays per release and the number of rays in wave vector space set to 50 and 100, respectively, resulting in an effective emission of 5000 primary rays per simulation. Unlike stochastic MC methods, geometric optics ray tracing is deterministic; therefore, simulations employing 10 3 – 10 4 rays provide robust solutions, consistent with COMSOL Multiphysics Ray Optics Module guidelines [ 25 ]. A wall boundary conditions configured with the disappear option were assigned to the outer perimeters of the computational domain to ensure elimination of rays exiting the model, thereby reducing the number of rays tracked during propagation and improving computational efficiency without influencing internal ray – tissue interactions. Simulations were repeated across 6 distinct skin – pore diameters( 500, 250, 125, 62.5, 31.25, and 15.625 lm). A time – dependent ray tracing study was conducted over a 0 – 500 ps interval with a time step of 10 ps. To evaluate positional sensitivity, a parametric sweep was applied to the vertical location of the skin pore geometry, spanning �1 to0mm in increments of 0.1 mm, where 0 mm corresponds to the vertical centerline of the optical source. Simulations for positive vertical positions were not performed, as the computational domain is vertically symmetric about the source centerline; thus, such configurations would yield mirrored photon trajectories and redundant results. For qualitative assessment, 2D ray trajectory maps were generated using a rainbow color scale to visualize ray propagation paths and interface interactions. Simulations were performed on a high performance workstation, with each run requiring approximately 4.36 s. In total, 66 simulation runs were executed, corresponding to 11 vertical pore positions, and 6 pore diameters. Upon completion of the ballistic photon propagation simulations, photon positions, directions, and weights were recorded at the point of exit from the skin pore and exported as. txt files. To transition from the 2D ballistic photon propagation simulations to the 3-dimensional( 3D) diffusive photon transport simulations, the 2D photon positions and directions were revolved around the x- axis, effectively distributing photons uniformly around the axis, x 3D ¼ y 2D cos h; ð6Þ y 3D ¼ y 2D sin h;
z 3D ¼ x 2D; ð7Þ
ð8Þ
where h is the rotation angle around the 2D x-axis and is sampled uniformly from [ 0, 2p) to distribute photons evenly around the axis, avoiding duplication at h = 0 and h = 2p. This procedure generates fully 3D photon states, which were subsequently used as input for MC-based diffusive photon transport simulations.
2.3 Diffusive photon transport simulations
Diffusive photon transport in the eight individual cadaveric head models, as well as in the corresponding mean head model, was simulated using Monte Carlo eXtreme( MCX, v2025.10, Northeastern University, Boston, MA, USA),