Methodology

Building upon our previous work on a vascular finger phantom with interchangeable skin-tone layers,12 an advanced version of the phantom was designed and developed to enhance the overall perfusion and physiological realism of the model. The initial phantom demonstrated that limited perfusion within the vascular channel restricted the PPG signal’s formation, resulting in poor signal quality or the absence of green-light PPG in medium and dark skin tones, and no transmittance mode signals were observed. In addition to the restricted perfusion, other factors such as the relatively thick skin layer, the deep positioning of the vessel (∼2.5 mm from the surface), and the high scattering of the adipose layer further attenuated the optical signal and limited light penetration, particularly at shorter wavelengths. To overcome these challenges, the vascular network of the phantom was redesigned with a channel-based perfusion network that aimed to enhance fluid distribution throughout the fingertip and promote more uniform pulsatile flow. This new configuration improves light–tissue interaction, enabling the acquisition of both reflectance and transmittance PPG signals across all skin tones and relevant wavelengths.

Finger Phantom

Finger phantom design

The advanced finger phantom preserved the multilayer architecture of the previous version, consisting of a subcutaneous adipose matrix, an interchangeable skin layer, and a vascularization-simulating channel network. Together, these components replicate the anatomical, optical, and mechanical features of the human index finger, with particular emphasis on enhancing fluid perfusion.

The vascular network design was guided by the arterial anatomy of the fingertip. In the human finger, two proper palmar digital arteries converge distally to form the superficial arcade, giving rise to longitudinal branches that create the proximal and distal subungual arcades.18–20 To approximate this behavior within fabrication constraints, a simplified single-inlet, single-outlet network was implemented that bifurcated into multiple channels, simulating the superficial and subungual arcades. Although the model did not replicate venous drainage, the branching pattern provided physiologically relevant fluid dynamics suitable for dynamic PPG signal generation.

The vascular geometry consisted of three interconnected channel layers (Fig. 1). The two outer layers, representing superficial perfusion near the dermal surface, comprised parallel oval-shaped channels with a radius of 0.7 mm, a spacing of 0.6 mm, and a layer thickness of 1 mm, arranged to follow the curved fingertip contour. The inner layer simulated deeper perfusion within the fingertip core and consisted of a 1 mm thick honeycomb structure formed by 0.9 mm hexagonal cells separated by 0.7 mm spacing. Oblique perforator channels connected the outer and inner layers, enabling volumetric fluid exchange between peripheral and central regions and allowing distributed pulsatile flow across multiple depths.

Fig. 1: (a) Schematic of the arterial anatomy of the human fingertip, highlighting the superficial and subungual arcades (adapted from Jasionyte et al.20). (b) Simplified three-layer vascular channel geometry implemented in the finger phantom, representing superficial and deep perfusion pathways within fabrication constrains.

Figure 2 illustrates the schematic design and dimensions of the advanced finger phantom. Only the distal and middle phalanges of the index finger were replicated, corresponding to a total length of 50 mm, a width of 18.6 mm, and a thickness of 14.6 mm, consistent with anatomical averages reported in the literature.21 The model consisted of three layers: (1) an outer skin layer representing the epidermis, with a thickness of 0.3 mm; (2) a subcutaneous adipose layer forming the bulk matrix; and (3) an embedded three-layer vascular channel network. The skin layer was designed to match reported ranges for human volar epidermal fingertip thickness (0.1 to 0.5 mm),22–26 ensuring optical and mechanical realism. The vascular network occupied approximately the distal 14 mm of the phantom and was positioned with its most superficial channels ∼0.8 mm below the skin surface, enabling sensitivity to both reflectance and transmittance PPG illumination geometries.

Fig. 2: Schematic design and dimensions of the advanced finger (a) Top view showing the multilayer structure and embedded vascular network within the adipose matrix. (b) Longitudinal cross-section illustrating skin thickness, subcutaneous tissue, and depth of the vascular channels. (c) Perspective view of the phantom highlighting overall geometry.

Optical and mechanical characterization

To ensure optical realism, the optical properties of the phantom layers were tailored to replicate the absorption and scattering characteristics of human skin and subcutaneous tissue across 500 to 1000 nm wavelength range. All formulations were based on Platsil Gel-00 silicone (Polytek Development Corp., Easton, Pennsylvania, United States), selected for its refractive index (n=1.4) comparable to that of human soft tissue. Optical properties were tuned by adjusting the concentrations of titanium dioxide (TiO2; Kronos Worldwide Inc., Dallas, Texas, United States) as the scattering agent and a combination of Bismarck Brown (BDH Chemicals Ltd., London, England), India Ink (Jackson’s Art Supplies, London, United Kingdom), and Epolight 5532 dye (Epolin Inc., Newark, New Jersey, United States) as absorbers.

Three skin tone layers representing pale, medium, and dark pigmentation were fabricated, corresponding approximately to Fitzpatrick I to II, III to IV, and V to VI categories. The optical properties were adjusted by varying absorber concentrations while maintaining constant scattering concentration. The formulations for both adipose and skin layers (Table 1) were iteratively refined to match the absorption (μa) and reduced scattering (μs′) coefficients reported in the literature for human adipose tissue27–31 and skin across different pigmentation levels.30,32,33 Absorbers and the scatterer were first mixed with Part A silicone and the curing retarder, followed by the addition of Part B at an equal ratio. The mixture was then thoroughly stirred and degassed under vacuum to eliminate air bubbles.

Layer | Bismarck Brown stock solution (25 mg/L in isopropanol) [μL/g] | Epolight dye stock solution (1 mg/mL in acetone) [μL/g] | India ink (1% v/v) [μL/g] | Titanium dioxide [mg/g]
Adipose | 7.74 | 0 | 0 | 0.5
Pale skin tone | 20 | 70 | 10 | 1
Medium skin tone | 40 | 100 | 20 | 1
Dark skin tone | 130 | 400 | 30 | 1

Optical characterization was performed using a Lambda 1050 dual-beam spectrophotometer (Perkin Elmer Corp., Waltham, Massachusetts, United States) equipped with a 100 mm integrating sphere and PMT/InGaAs detector. Total reflectance and transmittance were measured over the 500 to 1000 nm range using 10 mm path-length cuvettes. The μa and μs′ were then extracted using the Inverse Adding-Doubling (IAD) algorithm,34 assuming a refractive index of 1.4 and anisotropy factor (g) of 0.9. These measured optical parameters were used as inputs for the subsequent Monte Carlo light-transport simulations (Table 2).

Tissue layer / Component | μa (mm−1) | μs′ (mm−1) | μs (mm−1) | g
Wavelength | 530 nm | 665 nm | 940 nm | 530 nm | 665 nm | 940 nm | 530 nm | 665 nm | 940 nm | 
Pale skin | 0.183 | 0.053 | 0.022 | 1.612 | 2.249 | 1.427 | 16.120 | 22.490 | 14.270 | 0.900
Medium skin | 0.248 | 0.092 | 0.034 | 1.296 | 2.050 | 1.402 | 12.964 | 20.497 | 14.020 | 0.900
Dark skin | 0.290 | 0.134 | 0.067 | 1.018 | 1.603 | 1.291 | 10.180 | 16.030 | 12.910 | 0.900
Adipose | 0.037 | 0.013 | 0.004 | 1.565 | 1.246 | 0.607 | 15.649 | 12.455 | 6.066 | 0.900
Blood | 0.162 | 0.119 | 0.071 | 0.254 | 0.161 | 0.036 | 2.535 | 1.611 | 0.364 | 0.900

The measured μa and μs′ spectra for the adipose and the three skin tones are shown in Fig. 3. The absorption coefficients have a strong dependence on pigmentation in the visible range, with higher μa values at 530 nm for darker tones due to higher melanin concentration. The reduced scattering shows a non-monotonic trend across wavelengths, decreasing from 500 to 530 nm, increasing toward 665 nm, and decreasing again at longer wavelengths, consistent with a general decrease toward the infrared.

Fig. 3: Measured absorption (μa) and reduced scattering (μs′) coefficients of the adipose and skin-tone layers compared with literature data. Panels (a)–(b) show the adipose phantom versus reported values from Refs. 27–31. Panels (c)–(d) show pale, medium, and dark skin phantoms versus literature data from Refs. 30, 32, 33 within 500 to 1000 nm wavelength range.

In addition to optical characterization, the mechanical properties of the phantom materials were assessed to ensure physiologically relevant tissue compliance. Platsil Gel-00 silicone was selected due to its ease of handling, optical stability, and ability to reproduce human soft tissue. Target hardness values were guided by reported human fingertip measurements (25 to 35 Shore OO).35,36 Hardness was measured using a Shore OO durometer following ASTM D2240-15, with values reported as the mean of multiple measurements. The resulting hardness was 31.2±1.9 (Shore OO), falling within the physiological range.

Finger phantom fabrication

The vascular channel network was fabricated and integrated into the finger phantom through a casting process (Fig. 4). The vascular network was 3D printed using a Bambu Lab X1 Carbon Series printer (Bambu Lab, Hong Kong, China) with polyvinyl alcohol (PVA) filament, allowing it to act as a water-soluble sacrificial template material [Fig. 4(a)]. After printing, the PVA structure was cleaned to remove supports and residual filament using fine tools. To prevent damage to the delicate structure, any remaining filaments were softened in warm water (approximately 40°C) and carefully detached [Fig. 4(b)].

The external finger geometry was formed using a custom two-part mold representing the distal and middle phalanges of an adult male index finger [Fig. 4(c)]. Before embedding the PVA network, a uniform 0.5 mm adipose silicone coating was fabricated using a secondary mold scaled down 0.5 mm on all sides [Fig. 4(d)], ensuring a consistent positioning of the vascular network ∼0.5 mm below the surface of the adipose region, corresponding to the depth of the superficial vascular plexus in vivo [Fig. 4(e)]. The PVA network was then placed within the mold cavity [Fig. 4(f)], after which the mold halves were assembled and sealed. The remaining adipose silicone mix was poured through the dedicated 4 mm inlet [Fig. 4(g)] and allowed to cure. One cured, the mold was removed [Fig. 4(h)], and the PVA template was dissolved in warm water, leaving a fully enclosed internal channel network.

Fig. 4: Fabrication of the finger phantom. (a) 3D-printed PVA sacrificial template. (b) Cleaned PVA structure, (c) Two-part finger mold. (d) Secondary mold for casting a 0.5 mm adipose silicone layer. (f) Placement of the PVA network within the mold. (g) Mold assembly and silicone casting. (h) Final phantom after curing and dissolution of the PVA.

In vitro experimental setting and protocol

The fabricated vascular finger phantom was evaluated using the in vitro cardiovascular system previously described.12 The system reproduces physiological pulsatile flow and pressure conditions throughout a closed-loop circuit driven by a programmable pulsatile pump (BDC Labs, Colorado, United States), connected to the phantom via compliant tubing that mimics the peripheral arterial tree (Fig. 5). During the experiments, the system was operated at a heart rate of 60 bpm with a flow rate of 8 L/min, generating an overall system pressure of ∼90 mmHg. A blood mimicking fluid composed of 0.1% w/v Nigrosine dye (Thermo Fisher Scientific, Loughborough, United Kingdom) diluted in deionized water was circulated through the vascular network to simulate the broadband optical absorption of blood across 500 to 1000 nm wavelength range.

Fig. 5: Schematic of the in vitro cardiovascular flow loop used to evaluate the vascular finger phantom. The programmable pulsatile pump generates physiological pulsatile flow that circulates through the ascending aorta, brachial artery, radial artery, and the finger phantom before returning through the venous pathway (radial vein, brachial vein, and vena cava) in a closed-loop circuit. The system was operated at a heart rate of 60 bpm, with a flow rate of 8 L/min, producing an overall system pressure of ∼90mmHg.

Both reflectance and transmittance PPG configurations were implemented to assess the influence of the three pigmented skin layers on optical performance. A custom-made PPG finger clip probe operating in reflectance and transmittance mode was used. In the reflectance mode, the light source and the reflectance photodetector were positioned on the same side of the fingertip with a source-detector separation of 4 mm. In the transmittance mode, the LEDs were positioned directly opposite the transmittance photodetector, enabling light to pass through the fingertip. The PPG finger clip probe was interfaced with a PPG acquisition system developed by the Research Centre for Biomedical Engineering (RCBE),37 at a sampling rate of 2 kHz. The probe incorporated an integrated multiwavelength LED chip (SFH 7016, OSRAM), with all LEDs driven at a constant current of 40 mA. The manufacturer’s datasheet reports a total radiant flux values of 14, 14, and 11 mW at 20 mA, for the green, red, and infrared LEDs respectively, at 20 mA38 drive current, indicating comparable optical output across wavelengths at equivalent drive conditions. As all three LEDs were subject to the same drive current in the present study, the relative comparability of optical output across wavelengths is expected to be preserved.

PPG signals were recorded for five minutes per skin tone phantom under pulsatile conditions. Signal processing was performed in MATLAB (R2024a) using a fourth-order Butterworth band-pass filter (0.4 to 10 Hz) to extract the AC component and a low-pass filter (<0.3 Hz) for the DC component. The AC/DC ratio, signal-to-noise ratio (SNR), and amplitude were computed to quantify the impact of skin pigmentation on PPG signal quality.

In this study, the AC/DC ratio is used as a measure of relative pulsatile signal strength and signal quality, rather than within the conventional ratio-of-ratios formulation used in pulse oximetry. AC amplitude and AC/DC were calculated using peak-to-peak measurements of the pulsatile PPG waveform, while SNR was computed from 5-s analysis windows as the ratio of signal power within the physiological frequency band (0.5 to 10 Hz) to high-frequency power (>10 Hz), estimated using a high-pass filter. The calculation was implemented using MATLAB’s built-in snr function.

Monte Carlo Modelling of Photon-Tissue Interaction

Monte Carlo simulations were performed to model photon propagation through the multilayer structure of the vascular finger phantom and to quantify how skin pigmentation influences light transport and signal detection. This computational approach complements the in vitro experiments by isolating the contribution of tissue absorption and scattering to the measured PPG amplitudes.

Model geometry and optical properties

The Monte Carlo model was constructed based on the multi-layered tissue framework described by Wang and Jacques,39 representing the same geometry and layer arrangement used in the fabricated finger phantom. As shown in Fig. 6, the tissue volume consisted of three primary optical regions: skin, adipose tissue, and blood, arranged into multiple sublayers to replicate the spatial distribution of the vascular channels. The total tissue thickness was 14.6 mm. From top to bottom, the layers were defined as: top skin (0.3 mm), top adipose (0.5 mm), upper blood (1.0 mm), upper adipose (5.0 mm), middle blood (1.0 mm), lower adipose (5.0 mm), lower blood (1.0 mm), bottom adipose (0.5 mm), and bottom skin (0.3 mm). The three vascular layers were included to represent the depth distribution of the vascular network within the phantom. A schematic of the model geometry and source-detector configuration is shown in Fig. 6.

Fig. 6: Geometry of the multilayer Monte Carlo model replicating the vascular finger phantom. (a) 3D schematic of the layered tissue geometry showing the top and bottom skin layers, adipose regions, and embedded blood channels. (b) Source–detector configuration used in reflectance and transmittance simulations, matching the in vitro PPG setup.

The optical properties assigned to each layer were derived directly from the experimental optical characterization (μa and μs′) of the phantom described in Sec. 2.1.2, ensuring consistency between the in vitro phantom and the Monte Carlo model. A refractive index of 1.37 was assumed for all tissue layers, with the surrounding medium set to air (n=1). The resulting optical coefficients used for each wavelength are summarized in Table 2.

Simulation parameters

The photon-transport simulations were implemented in MATLAB (R2024a) using a custom Monte Carlo photon-tracing algorithm based on the statistical approach of Wang and Jacques.39 The model allowed for full control over layer geometry, optical properties, and detectors configuration.

A total of 1×107 photons were launched per wavelength (530, 665, and 940 nm). Light source was modeled as a normally incident Gaussian beam 1/e2 radius of 1 mm, representative of the LED emission profile. Each photon was assigned an initial statistical weight of 1 and propagated throughout the multilayered medium. Photon step sizes were randomly sampled from an exponential distribution governed by the total interaction coefficient: where the scattering coefficient was derived from the reduced scattering coefficient using,

μt=μa+μs,

μs=μs′1−g.

Photon scattering directions were determined using the Henyey-Greenstein phase function. Absorption was modeled by decrementing photon weight proportionally to μa/μt and reflections at tissue interfaces were handled using Fresnel equations. Photons crossing into a new layer were assigned its corresponding optical parameters. Photons with a weight below 10−4 underwent Russian roulette termination to preserve energy balance.

Two detector configurations were simulated to replicate the experimental setup. Reflectance mode, where photons exiting the top surface within a 3 mm radius circular detector offset 4 mm laterally from the light source were recorded; and transmittance mode, where photons exiting the bottom surface within a 3 mm radius circular detector centered on the illumination axis were detected.

Simulations were performed for the three skin pigmentation layers (pale, medium, and dark) by varying the absorption and scattering coefficients of the skin layers according to the experimentally measured optical properties. All other layers, such as adipose tissue and blood, remained constant across simulations.

Diffuse reflectance (R), transmittance (T), and absorption (A) were computed as the ratio of the total detected photon weight to the number of photons launched, excluding the specular reflection component. Spatial energy deposition was recorded in a fluence density matrix (200×200 bins), from which fluence maps were generated to visualize photon confinement and propagation across wavelengths and skin tones.

Optical path length (OPL) was calculated as the cumulative distance travelled within the tissue by each reflected photon, weighted by its exited energy, representing the effective photon migration distance contributing to the detected signal. Layer-specific absorption fractions were computed to quantify the contribution of each tissue-simulating layer to total absorption. A skin contribution index (SCI) was defined as the sum of the absorption in the top and bottom skin layers, expressed as a percentage of total absorbed energy. Penetration depth was quantified using fluence-based metrics, defined as the depth at which 50% of the cumulative absorbed energy occurred.

Correlation Analysis

To compare Monte Carlo simulations with experimental measurements, the simulated skin layer absorption fraction quantified using the SCI was correlated with experimentally measured PPG AC/DC ratios. In addition, simulated diffuse reflectance and transmittance values were correlated with the corresponding in vitro PPG peak-to-peak amplitudes across wavelengths and skin tones. Pearson’s correlation coefficient was used to assess the agreement between simulated optical metrics and experimental PPG signal features.