Simulation of Photoplethysmography Signal in Reflection Mode Using Three-layer Skin Optical Modeling

Abstract

Background:

Photoplethysmography (PPG) is an optical, noninvasive method widely applied to detect changes in blood volume within the skin. Accurate modeling of light-tissue interaction is essential for improving PPG sensor design and signal interpretation.

Methods:

In this study, the three main layers of human skin were simulated using the nonsequential mode of Zemax optical software. Each layer was assigned specific optical properties to accurately represent physiological conditions. A light source with a wavelength of 600 nm was directed onto the modeled skin, and the propagation of light through the tissue to the photodetector was simulated. The direct current (DC) component of the PPG signal was first modeled, representing the baseline optical response. Then, the alternating current (AC) component (pulsatile component linked to cardiac blood-volume changes) was added by simulating periodic changes in blood volume within the dermal vessels during cardiac cycles.

Results:

The light transport from the source through the skin tissue was successfully simulated, modeling the interaction of photons within the three skin layers. Subsequently, the resulting signal reaching the photodetector was simulated, capturing both DC and AC components of the PPG waveform. Two of the model’s output PPG signals were compared with experimental data, showing good agreement in waveforms.

Conclusion:

Using a three-layer skin tissue model combined with the Henyey–Greenstein scattering model to calculate light’s angular distribution, along with accurate optical properties of skin layers and blood volume changes during each cardiac cycle, the PPG signal was successfully simulated. This simulation marks a significant step toward developing PPG sensors for the physiological measurement of blood components on the skin.

Introduction

Photoplethysmography (PPG) is a straightforward, noninvasive optical method used to measure the physiological signals on the skin’s surface. In each PPG device, light from the source is shone onto the skin surface and the intensity of the transmitted or reflected light is measured by the detector.[1] There are two working modes: (1) transmission mode in which the skin tissue is situated between the source and the photodetector and (2) reflection mode in which the light source and photodetector are located side-by-side. The absorption and transmission of light at a given wavelength depends on the distance the light travels, the composition and volume percentage of blood, and the optical properties of skin tissue.[2,3,4]

Accurate skin modeling is vital for realistic PPG signal simulation because each skin layer, epidermis; dermis; and subcutaneous tissue, has distinct optical properties affecting light absorption, scattering, and propagation. The epidermis mainly influences absorption due to melanin, the dermis plays a key role in scattering and signal modulation, and the subcutaneous layer contributes differently due to its depth and composition. These variations impact how light propagates, scatters, and is absorbed, thereby shaping the fidelity of the simulated PPG waveform.

Light interacts with skin tissue through complex optical phenomena such as absorption, scattering, reflection, and transmission.[4,5] Absorption reduces the intensity of light. In the visible region, there are two substances that have the greatest effect on light absorption: hemoglobin and melanin.[5] Scattering refers to the alteration of light’s direction and polarization, often characterized as either a surface phenomenon or an interaction occurring within a small region that has different optical properties compared to its surroundings.[5] The radiative transfer equation effectively characterizes the overall movement of light within scattering materials, although obtaining an analytical solution for light propagation in media with complex structures remains challenging.[6,7] To address this challenge, numerous Monte Carlo-based light propagation analyses have been developed and are now widely employed as a fundamental technique in biological optics. These methods provide a standard and reliable approach for simulating photon transport within biological tissues.[7,8,9,10,11] In 2014, Hideki et al. performed a simulation study of spectral reflectance in human skin tissue by utilizing ray-tracing software in combination with a Monte Carlo method accelerated by graphics processing units (GPUs). This approach allowed for detailed modeling of the complex skin structure, including surface grooves and layer interfaces, while significantly enhancing computational efficiency through GPU-based processing Simulation of a three-layer skin tissue model was performed using five parameters studied in their laboratory.[6]

Compared to simpler single-layer models, this three-layer approach provides enhanced differentiation of light interaction mechanisms within each skin region, leading to improved accuracy in reproducing both alternating current (AC) and direct current (DC) components of PPG signals. Concurrently, it balances physical realism with computational feasibility better than highly detailed multilayer models, making it particularly suitable for simulation platforms such as Zemax.

The typical waveform of a PPG signal consists of an AC component with a frequency of about 1 Hz, superimposed on a quasi-DC (slow baseline component of the PPG signal) component.[12,13,14] The DC component changes slightly under the influence of factors such as respiration, thermoregulation, and sympathetic nervous system activity.[3,15] The AC component arises from the change in absorption caused by the change in arterial blood volume during each cardiac cycle. The DC component is related to absorption by nonpulsatile arterial blood and other nonblood skin tissues.[1]

Multiple recent investigations have focused on examining the features of the PPG signal. For example, Chatterjee et al.[16] examined how key optical properties, such as absorbance, reflectance, and penetration depth, change with different wavelengths and source-detector separations. Later, in 2022, Lapitan et al.[17] investigated how the distance between the light source and detector affects the shape of the PPG waveform. Building on this work, their 2024 study[18] used simulations to explore how changes in blood volume and the behavior of red blood cells within the skin might influence the signal. Across all of these investigations, the Monte Carlo method played a central role in modeling light-tissue interactions and the resulting PPG waveform. In this work, a PPG signal is simulated in standard conditions in reflection mode by modeling the skin and tracing the light ray at a wavelength of 600 nm using the Zemax optical software and by programming in the Python environment. The importance of simulation is that through sensitivity tests, the effect of various biological factors on the DC and AC components of the signal can be studied.

The structure of this paper is organized in the following manner. Section 2 describes the materials, simulation methods, and data used. Section 3 analyzes the model outputs and then validates some results by comparing them with available experimental data. Section 4 discusses the advantages and disadvantages of this simulation and provides suggestions for further research. The last section provides the conclusion.

Methods

This study employs a combination of theoretical and computational approaches to investigate the interaction of light with the multilayered structure of human skin. The primary objective is to model the PPG signal by analyzing the processes of light transmission, absorption, and scattering within skin tissues. The detailed methodology is presented in the following subsections.

Propagation of light in biotissues

Biological tissues are optically scattering media with a mean refractive index greater than that of air at visible and infrared wavelengths. The variation in refractive index leads to partial reflection of light at the boundary between tissue and air, with the rest of the light entering the tissue.[19] Approximately 4%–7% of visible light is reflected from the skin surface, a value that remains consistent regardless of wavelength, skin pigmentation, or structure.[5,20] The way light interacts with the skin, which consists of multiple layers and various components, is highly complex.[16] In classical physics, the propagation of light through matter, characterized by simultaneous absorption and scattering, is fundamentally described by Maxwell’s equations. However, solving these equations exactly in complex media such as skin tissue is challenging. Therefore, the commonly employed approximation is the radiative transfer theory, which models the emission and diffusion of light in various directions. This approach considers key parameters such as the mean free path M (average photon step length), absorption coefficient μ_a, and scattering coefficient μ_s to describe the light transport in tissue.[5] As a photon travels a distance x, the probability of a scattering event occurring is given by an exponential:

So far, several bulk scattering models have been proposed for the angular distribution of light in materials. Here, we use the Henyey–Greenstein scattering model,[22] which has been widely employed to approximate the scattering profile of a biotissue.[23,24] In this model, the angular distribution of scattered light is given by phase function p(θ):

Where g is the average cosine of the scattering angle θ and is usually called the scattering anisotropy parameter.

The value of g changes in the range 0–1: g = 0 corresponds to isotropic scattering and g = 1 to total forward scattering.[16]

Given the assumption of a random distribution of scatters in the tissue, we must have:

Skin optical modeling

The human skin consists of three primary layers: the outer epidermis, the middle dermis, and the innermost subcutaneous tissue.[6] Some researchers have considered two or more sublayers for the epidermis and dermis to simulate skin.[11,25,26] In this study, we focus exclusively on the three primary skin layers and show that using these layers provides accurate simulation results for the PPG signal. Each layer, defined by its thickness d, is described by four optical properties: refractive index n, absorption coefficient μ_a, scattering coefficient, and scattering μ_s, anisotropy g.[6]

Skin modeling was performed using the non-sequential mode of Zemax OpticStudio (Ansys Zemax LLC, Canonsburg, PA, USA). Zemax is a software used for the design and simulation of optical systems. It is widely used in the field of optics and photonics for ray tracing in materials and the design and analysis of the performance of optical systems. With this software, the behavior of light in the interaction with various optical components can be modeled and optical designs can be optimized for optimal performance. In the nonsequential component editor of Zemax, three objects corresponding to the epidermis, dermis, and subcutaneous tissue layers are defined, whose types and geometric properties are detailed in the following subsection. The input parameters of the Henyey–Greenstein scattering model used in this work for each skin layer are: mean free path M, transmission fraction T (nonabsorptive interaction fraction; sets scattering versus absorption), and anisotropy parameter g. The relationship between the mean free path M and the transmission fraction T with the absorption and scattering coefficients is as follows:

Absorption coefficients μ_a and scattering coefficient μ_s at a wavelength of 600 nm and thickness d for each layer reported by Funamizue et al.[6] are used in this work, as shown in Table 1.

Table 1.

Absorption coefficients μ_a and scattering coefficient μ_a of three-layer skin at a wavelength of 600 nm[6]

Layer	μa (mm−1)	μs (mm−1)	D (mm)
Epidermis	0.774	21.040	0.075
Dermis	0.135	56.827	1.000
Subcutaneous	4.72	134.419	6.000

Setting input variables and updating optical parameters

Blood in the human skin tissue plays a key role in forming the PPG signal, and light is absorbed or scattered more strongly by blood than surrounding tissue. The blood volume fraction in the cutaneous blood content is about 2%–5%.[27,28,29] The epidermis contains very few blood vessels, and the cells in its deepest region receive nourishment primarily through oxygen absorbed directly from the environment.[30] The blood volume fractions in the papillary dermis and reticular dermis are approximately 2.5% and 1.4%, respectively.[31] Therefore, in this work, we have considered average values of 2% and 3% for the base blood content in the dermis and subcutaneous tissue.

In Zemax, we model the three layers of skin using three Rectangular Volume objects. We also use three Rectangular Detector objects to observe the results. Two of these detectors, which are equal in size to the skin layers and oriented to face the source and the skin, respectively, measure the incident and backscattered light. The third detector, also facing the skin, functions as a typical photodetector. Table 2 lists the parameters of these objects and shows their configuration relative to the source. Each column header indicates specific attributes of the model elements:

Table 2.

Optical model components and parameters in Zemax

Object type	Reference object	X position	Z position	Tilt X	Material	X half width	Y half width	Z length
Source file	0	0	−1	0	-	12	12	-
Rectangular volume	0	0	0	0	1.340	12	12	0.075
Rectangular volume	2	0	0.075	0	1.394	12	12	1
Rectangular volume	3	3	1	0	1.430	12	12	6
Detector rectangular	0	3	0.0008	180°	-	2	2	-
Detector rectangular	0	0	−0.001	180°	Absorb	12	12	-
Detector rectangular	0	0	−0.001	0	-	12	12	-

All length units are in millimeters (mm)

• Obj. Type (Object Type): Specifies the type of the component or object in the model, such as Source File, Rectangular Volume, or Detector Rectangular

• Ref. Obj. (Reference Object): Indicates the reference object relative to which the position and orientation of the current element are defined. A value of zero means the coordinates and position are referenced to the global coordinate system (Global Coordinate System) rather than any specific object within the model

• X Pos. and Z Pos. (X and Z Position): Represent the position coordinates of the component along the X and Z axes relative to the defined reference

• Tilt X: The tilt or rotation angle of the component about the X-axis

• Mat. (Material): Specifies the material property or coefficient associated with the element. This could be a numerical value such as a refractive index or a descriptor like ABSORB indicating absorption

• X Half W., Y Half W., Z Len. (X Half Width, Y Half Width, and Z Length): These columns show the geometric dimensions of the component, with half widths given for X and Y directions and full length for the Z direction.

The pixel density of the detectors was considered to be 10 pixels per millimeter along both the X and Y directions. The light source used in this work is a diode with a power of 1 watt and a central wavelength of 600 nanometers. The emission spectrum of this diode has a Full Width at Half Maximum of 20 nanometers, indicating a relatively narrow spectral bandwidth suitable for precise optical simulations. To control noise and ensure statistical reliability in the results, one million rays were used for ray tracing in the model. Using fewer rays tends to increase the noise level in the output, leading to less accurate and less stable simulation results. Employing a high number of rays improves the signal-to-noise ratio, resulting in smoother and more reliable optical performance predictions.

According to the explanations provided, the input optical parameters for the model include the refractive index, mean free path, transmission coefficient, and scattering anisotropy parameter. These parameters are entered into the model in Zemax as follows:

• The refractive index is assigned in the Material column of the Nonsequential Component Editor, specifying the optical material properties of each skin layer.

• The other three parameters, mean free path, transmission coefficient, and scattering anisotropy, are set within the scattering model configuration found under the Volume Physics tab for each rectangular volume object representing the epidermis, dermis, and subcutaneous tissue layers.

The values of these parameters, along with the blood volume fraction, are presented in Table 3.

Table 3.

Layer-wise input parameters for reflection-mode photoplethysmography simulations at λ ≈ 600 nm (full width at half maximum ≈ 20 nm)

Layer	n	Mean (mm)	t	g	Cb (%)
Epidermis	1.340	0.046	0.964	0.790	0
Dermis	1.394	0.017	0.997	0.870	2
Subcutaneous	1.440	0.007	0.996	0.682	3

Columns: n – Refractive index (sets interface reflection/refraction); Mean – Mean free path (average photon step length in the layer); t – Nonabsorptive interaction fraction (controls scattering vs. absorption split); g – Scattering anisotropy (average scattering angle/forwardness); b – Dermal blood-volume fraction

As the heart contracts during systole, blood is pumped into the body’s vessels, increasing blood volume, which can reach 1.3–2 times the basal volume during diastole. During diastole, as the heart relaxes, blood volume in the skin vessels decreases to a minimum basal value. The relative changes in blood content in the vessels of the skin layers cause changes in the optical parameters of the skin during the cardiac cycle. Therefore, at each moment of the cycle, considering changes in blood volume, the optical parameters of the skin, i.e. refractive index, absorption coefficient, scattering coefficient, and scattering anisotropy parameter, must be updated. Here we have assumed that blood volume increases by two times in one cardiac cycle and have used the following relationships to update the optical properties of the dermis and subcutaneous layers of the skin with changing blood volume fraction:

In the above equations, the subscript “b” refers to the optical properties of blood, whereas the subscript “skin” corresponds to the tissue without blood. The following values were used for the optical properties of blood:[32]

Note that the optical properties of the skin are calculated according to the above relationships, Table 1, and the column corresponding to the blood volume fraction in Table 3.

The slope of blood volume increase in arteries during ventricular systole is generally steeper than the slope of volume decrease during diastole. This asymmetry arises because systolic ejection is a rapid, high-pressure process, while diastolic runoff is a slower, gradual phase. Although exact quantitative values differ depending on physiological conditions, some studies indicate the rate of blood volume increase can be approximately 2–4 times greater than the rate of decrease.[33,34] In this study, we approximated the increase and decrease of blood volume in the vessels as nearly linear, assuming that the slope of the volume increase during systole is approximately 2–3 times greater than that during diastole.

Calculations related to updating optical parameters due to the changes in blood volume in skin vessels are performed by programming in the Python environment and connecting it to Zemax.

Normalization and quantitative comparison of photoplethysmography signals

Normalizing the data ensures that the comparison between the model and experimental signals focuses on their intrinsic features rather than extrinsic factors like amplitude magnitude or baseline shifts. Without normalization, differences in sensor gain or noise levels can dominate similarity metrics, masking the true correspondence or deviation between the signals. By scaling both signals to a standardized range (commonly from −1 to 1), all values become dimensionless and comparable. This process enhances the reliability of subsequent statistical analyses and improves the interpretability of similarity and error metrics. In this study, the min-max normalization method was used, which is the most common approach for normalizing PPG signals in the range of −1 to 1. The formula used is:

Where x is the original signal value, and and are the minimum and maximum values found in the signal, respectively. This formula first scales the signal data to the range, then linearly transforms it to (−1, 1). After normalization, signals from different sources have comparable amplitude ranges, facilitating more accurate analysis.

Once normalized, signals can be compared quantitatively by computing similarity and error metrics:

• Pearson correlation coefficient (PCC): This coefficient ranges from −1 to 1. A value close to +1 indicates a strong positive linear relationship, meaning the two signals are highly similar in shape and timing. Values near 0 imply no linear correlation, while values close to −1 indicate a strong negative correlation (inverse relationship). Higher positive correlation values represent greater similarity

• Mean absolute error (MAE): MAE quantifies the average absolute difference between the model and experimental signals. Its values range from 0 upward. A smaller MAE means the signals are closer in amplitude on average, indicating less error

• Root mean square error (RMSE): RSME provides a measure of the average magnitude of errors by giving greater weight to larger deviations. Lower RMSE values indicate fewer or smaller large errors and better agreement between signals.

Results

Photoplethysmography modeling and validation

Light transport in the three-layer skin model is shown in Figure 1. As light passes through the different layers of the skin, the photons of light interact with skin components, and some photons are absorbed and some are scattered. A small fraction of the scattered light reaches the detector. The less light absorption in the skin tissue, the more photons reach the detector and the greater the signal power on the detector, and vice versa. Most of the unabsorbed photons of light are scattered and reflected before reaching the subcutaneous layer and almost no photons at this wavelength pass through this layer.

Figure 1.

Photon absorption and light transmission in the skin layers. Only some photons reach the detector, and less absorption results in a stronger signal. Most photons are scattered before reaching the subcutaneous layer

Variations in pressure inside the heart drive blood flow through its chambers and throughout the body. During systole, the ventricles generate increased pressure to pump blood into the systemic circulation, reaching levels sufficient to overcome the hemodynamic resistance in the aorta.[35] As the heart contracts during systole and pumps blood into the vessels, the relative blood volume within the skin layers can increase up to twice its baseline level. This rise occurs due to the augmented blood flow and pressure transmitted through the arterial system, leading to enhanced perfusion in the skin’s microvasculature.[36] On the other hand, the amount of light absorbed increases/decreases in approximately the same proportion as the volume of blood in the vessels increases/decreases. However, as more light is absorbed by the skin, the signal intensity on the detector decreases further [Figure 2]. Thus, the pulsation of the blood causes an opposite phase shift in the signal on the detector. Here, we first ignore the pulsation of blood caused by changes in intracardiac pressure. Therefore, the blood volume in the skin vessels is a constant value over time [Figure 3a]. The relative content of blood in this case is equal to one, that is, one times the baseline blood content. Note that this quantity has no units. The signals obtained from light absorption and scattering within the stationary skin structure represent the DC component of the PPG signal [Figure 3b and c]. As Figure 3c shows, the detector signal power variations for the DC component are relatively small, around 0.00001 watts. The diagram of the number of rays reaching the detector [Figure 3b] and the signal power [Figure 3c] are very similar because these two quantities are proportional to each other.

Figure 2.

The relationship between the change in light intensity received by the detector and the change in blood volume in the skin tissue. As blood volume increases, light absorption increases, so the intensity of reflected light of the skin decreases

Figure 3.

Diagrams related to the direct current (DC) component of the photoplethysmography (PPG) signal. (a) Relative content of blood in the skin vessels over time. (b) Number of rays reaching the detector versus time. (c) DC component of PPG power signal. The horizontal axis represents time (seconds), and the vertical axes show: top-relative content (unitless), middle-number of rays (counts, dimensionless), bottom-power (watts)

The model is then extended to include the pulsatile movement of blood in the skin’s vessels, which results from the heart’s cyclical contraction and relaxation. The absorption and scattering of light from this variable blood flow forms the AC component of the PPG signal. First, we assume that the AC component of the blood flow increases linearly during the systolic phase, followed by a decrease with a slightly gentler slope. In addition, a small notch is introduced at the end of the systole phase. The pulse duration is set to 0.67 s, corresponding to a heart rate (HR) of 90 beats per minute (bpm), which is typical for adolescents aged 10–15 years. For the model simulation, each pulse is divided into 4 time steps during systole and 6 time steps during diastole, with each time step lasting 67 ms [Figure 4a]. It is important to note that the graph begins with the diastole phase. Figure 4b and c show the number of rays reaching the detector and the PPG output power signal, respectively, after incorporating the pulsatile blood flow into the DC component. Figure 5 presents a comparison between the vertically inverted model output [Figure 4c] and the measured signal of an 11-year-old boy from the Mendeley dataset. The openly available Mendeley dataset contains PPG signals from 35 healthy individuals, with an average age of 28.4 years, and includes 50–60 PPG recordings per person.[37] As explained in the previous paragraph, based on physiological principles, during the systolic phase of the heart when blood volume in the vessels increases, the PPG power signal exhibits a decreasing trend, and during the diastolic phase, it shows an increasing trend. This is because light absorption is higher during systole and lower during diastole. However, in many signal acquisition and processing systems, the raw photodiode output is inverted to align the peaks and troughs of the PPG signal with other physiological signals such as the electrocardiogram or arterial pressure waveforms. This inversion is also observed in the Mendeley dataset signals; contrary to expectations, the signal shows an upward trend during systole and a downward trend during diastole. Therefore, for an accurate comparison between the model’s power output signal and the experimental signals from the Mendeley dataset, we first invert all the model output signals before performing the comparison. In addition, both signals have been normalized between −1 and 1, as described in the previous section. As shown in Figure 6, a typical PPG waveform consists of two peaks, the systolic and diastolic peaks, with a slight dip or notch between them called the dicrotic notch (small dip on the descending limb related to aortic valve closure and wave reflections).[35] The systolic peak represents the phase of systole, during which the heart contracts and propels blood into the arteries. The diastolic peak corresponds to the diastole phase when the heart refills with blood. Dicrotic notch occurs due to closure of the aortic valve and represents a temporary interruption of blood flow as the valve prevents backflow during diastole. As Figure 5 shows, the characteristics of the simulated signal are in relatively good agreement with the measured signal, and systolic and diastolic peaks and a slight dip between them are visible. For a quantitative comparison, we calculated parameters including the PCC, MAE, and RMSE. Table 4 shows that the PCC for the 11-year-old boy is 0.8211, indicating strong similarity between the model output and the measured signal. The MAE and RMSE values of 0.304 and 0.370, respectively, further confirm the good agreement between the simulated and experimental signals. These results support the visual similarities illustrated in Figure 5. For a quantitative comparison, we calculated PCC, MAE, and RMSE. Table 4 shows that the PCC for the 11-year-old boy is 0.8211, indicating strong similarity between the model output and the measured signal. The MAE and RMSE values of 0.304 and 0.370, respectively, further confirm the good agreement between the simulated and experimental signals. These results support the visual similarities illustrated in Figure 5.

Figure 4.

Pulsatile blood flow simulation and resulting photoplethysmography (PPG) Signal components at adolescent heart rate. (a) Relative content of blood in the skin vessels over time. (b) Number of rays reaching the detector versus time. (c) The PPG power signal. The horizontal axis represents time (seconds), and the vertical axes show: top-relative content (unitless), middle-number of rays (counts, dimensionless), bottom-power (watts)

Figure 5.

Model–data comparison in an 11-year-old: model (dashed) and experimental (solid) signals are min–max normalized to (−1, 1). The model signal is inverted for comparison because the raw experimental photoplethysmography in some datasets (e.g., Mendeley) is stored/displayed in the opposite direction (to show upward systolic peaks and match electrocardiogram/arterial pressure). Axes: horizontal: time in seconds; vertical: normalized amplitude

Figure 6.

Characteristic parameters of a typical photoplethysmography wave

Table 4.

Comparison of statistical metrics for simulated and measured photoplethysmography signals across different ages

Age (years)	PCC	MAE	RMSE
11	0.8211	0.303959	0.369841
22	0.7168	0.2625	0.4063
31	0.7524	0.2692	0.3945
75	0.6622	0.2498	0.4998

PCC – Pearson correlation coefficient; MAE – Mean absolute error; RMSE – Root mean square error

Figures 7 and 8 present a comparison between the model output signals and the measured signals from two young men aged 22 and 31, respectively. Based on the measurement duration and the number of cardiac cycles recorded, the HRs (BPM) for these individuals were determined to be 100 for the 22-year-old and 80 for the 31 years old. Accordingly, the model simulation assumed a cycle duration of 0.6 s for the 22 years old and 0.75 s for the 31 years old. The number of discrete time steps per cycle was set to 10 and 12 for the 22- and 31-year-old patients, respectively. The increase in blood volume during the systolic phase was modeled as a strictly linear rise, while during the diastolic phase, both before and after the dicrotic notch, blood volume changes were approximately linear but with slightly varying slopes. On average, the slope of the blood volume change during diastole was considered to be about one-third of that during systole. For the 22- and 31-year-old individuals, the quantitative similarity between the model output and the measured PPG signals is demonstrated by the PCC, MAE, and RMSE values presented in Table 4. These parameters indicate a relatively strong positive correlation, with PCC values of 0.7168 for the 22-year-old and 0.7524 for the 31-year-old, suggesting that the model captures the overall signal patterns well for both ages. The MAE and RMSE values further support this relatively good agreement. As shown in Figures 7 and 8, which correspond to the 22- and 31-year-old individuals respectively, the waveforms of the simulated and measured signals are relatively similar. The timing of peaks and troughs aligns closely, and the dicrotic notch appears at nearly the same point in the diastolic phase. The signals exhibit simultaneous rises and falls in amplitude, confirming their relative resemblance. Together, these quantitative and qualitative observations show that the model effectively replicates the key characteristics of PPG signals for young adults aged 22 and 31 years.

Figure 7.

Comparison between model and experimental data (22-year-old; ≈ 100 bpm, cycle = 0.60 s). Model (dashed) and experimental (solid) signals are min–max normalized to (−1, 1); the model signal is inverted for comparison. Metrics: Pearson correlation coefficient = 0.7168, mean absolute error = 0.2625, root mean square error = 0.4063. Axes: horizontal: time in seconds; vertical: normalized amplitude

Figure 8.

Comparison between model and experimental data (31 years old; ≈ 80 bpm, cycle = 0.75 s). Model (dashed) and experimental (solid) signals are min–max normalized to (−1, 1); the model signal is inverted for comparison. Metrics: Pearson correlation coefficient = 0.7524, mean absolute error = 0.2692, root mean square error = 0.3945. Axes: horizontal: time in seconds; vertical: normalized amplitude. PPG: Photoplethysmography

It should be noted that in quantitative comparisons of PPG signals, physiological variations and environmental conditions during data acquisition play a crucial role and can lead to significant differences in statistical results. For example, Figure 9 shows a comparison between two signals measured from the same 31-year-old individual at different times, alongside the simulated model signal. Although these signals exhibit high qualitative similarity, statistical comparisons between the two experimental signals reveal a very low PCC (0.024) and relatively high values of MSE (0.541), MAE (0.578), and RMSE (0.735), indicating considerable differences in the timing of cardiac cycles. This temporal discrepancy is likely due to HR changes caused by activity, excitement, or other physiological variations at different measurement times. The comparisons between the model and each experimental signal also show low correlation (~0.10) and similar error magnitudes. These findings emphasize that HR variability and physiological changes significantly affect the precise temporal alignment of PPG signals and therefore must be considered as the key parameters in quantitative analyses and model evaluation.

Figure 9.

Temporal variability within the same 31-year-old participant. Top panel: Model signal (red, solid), vertically inverted and min–max normalized to (−1, 1). Bottom panel: Two overlaid experimental signals – Experimental-1 (blue, solid) and Experimental-2 (green, solid) – each min–max normalized to (−1, 1). Despite similar morphology, alignment between the two experimental segments differs (Pearson correlation coefficient ≈ 0.024). Axes: horizontal: time in seconds; vertical: normalized amplitude. PPG: Photoplethysmography

Figure 10 compares the model output with the PPG signal of a 75-year-old individual with an approximate HR of 78 beats per minute, obtained from the Mendeley dataset. Based on this HR, the duration of one cardiac cycle was set to 0.76 s, and the model was simulated with 12 time steps, including 5 steps in the systolic phase and 7 steps in the diastolic phase. Since the dicrotic notch typically diminishes or disappears in elderly individuals,[32] no notch was introduced in the blood volume change signal. The blood volume changes were modeled as strictly linear during both the systolic and diastolic phases, with a slightly lower slope during diastole. Qualitatively, the model signal and the experimental signal of the 75-year-old individual show a relatively good similarity; the two signals vary in phase, meaning that when the model signal reaches its maximum, the experimental signal also peaks at the same time, and the same applies to the troughs. This indicates a successful reproduction of the main patterns of the PPG signal by the model. Quantitatively, based on the statistical parameters presented, the model demonstrates acceptable performance; the PCC for the 75 years old is 0.6622, indicating a moderate positive correlation between the two signals. The MAE and RMSE are 0.2498 and 0.4998, respectively, which, although slightly higher than in younger age groups, still show that the model can relatively predict the experimental signal in this age range.

Figure 10.

Comparison between model and experimental data (75-year-old). Experimental (dotted) and model (solid) signals are min–max normalized; the model signal is inverted for comparison. Metrics: Pearson correlation coefficient = 0.6622, mean absolute error = 0.2498, root mean square error = 0.4998. Axes: horizontal: time in seconds; vertical: normalized amplitude

Sensitivity to blood absorption coefficient and dermal thicknesses

Sensitivity analyses were conducted using the 22-year-old configuration (HR ≈ 100 bpm; 0.6 s cycle) with the same optical setup. Figure 11 overlays the detected power waveforms (0–6 s) for four blood absorption coefficients (μ = 3, 4, 5, 6 mm^⁻1). Increasing μ_a produces a clear, monotonic attenuation of the signal: both the baseline (DC) level and the pulsatile excursions (AC) shift downward while the temporal morphology remains qualitatively similar. This pattern is consistent with higher absorption shortening photon paths and lowering the flux at the detector, thereby compressing the dynamic range available for pulse-related variability.

Figure 11.

Overlaid detected‐power waveforms (0–6 s) for four blood absorption coefficients (μ = 3, 4, 5, 6 mm⁻¹). Increasing μa lowers the baseline and peak amplitudes while preserving overall time-domain shape. Axes: time (s) and power (W)

To quantify this trend, Figure 12 summarizes the mean detected power over the full window for each μ_a. Mean power declines from 0.0006067 W at μ_a = 3 to 0.0002594 W at μ_a = 6, a net reduction of 57.3%. Stepwise decreases are 32.5% (μ_a: 3 → 4), 27.7% (μ_a: 4 → 5), and 12.4% (μ_a: 5 → 6), indicating a diminishing rate of change at higher μ (sub-linear sensitivity). The temporal dispersion also narrows as μ_a increases, suggesting that stronger absorption not only lowers the DC level but also damps higher-frequency fluctuations, yielding a visually “stiffer” waveform. Together, Figures 11 and 12 show that the detected power in reflection-mode PPG is highly sensitive to the blood absorption coefficient, with practical implications for wavelength selection and source power.

Figure 12.

Mean detected power versus blood absorption coefficient (μa=3–6 mm⁻¹). Bars show the mean over 0–6 s; error bars indicate temporal standard deviation (SD). The monotonic decrease confirms higher μ yields lower detected power. Axes: absorption coefficient and mean power (W)

Figure 13 overlays the PPG waveforms for five dermal thicknesses (t = 0.7, 1.0, 1.3, 1.7, and 2.0 mm). The epidermal and subcutaneous layer thicknesses were held constant; we varied dermal thickness only because the dermis contains the microvascular bed that dominantly drives pulsatile absorption/backscatter in reflection-mode PPG at these wavelengths. This control isolates the dermal path-length effect and avoids confounding from superficial scattering changes (epidermis) or deep attenuation (subcutis). Across this range, the time-domain morphology is essentially preserved: baseline level and pulsatile excursions remain stable, deviations near peaks are subtle and nonsystematic, and no consistent phase shift is observed, indicating no first-order change in either DC level or AC pulsatile component with dermal thickness. Figure 14 summarizes mean detected power versus thickness with ± standard error of the mean (SEM) error bars (SEM defined as standard deviation/√n). The mean values are effectively invariant across conditions, and the small undulations lie within the SEM, indicating that the apparent fluctuations are attributable to measurement variability rather than a thickness-driven effect. Taken together, Figures 13 and 14 show that, within the examined thickness interval, dermal thickness is not a first-order determinant of reflected PPG amplitude or pulsatility. This contrasts with the strong dependence on blood absorption reported earlier [Figures 11 and 12] and suggests that system design and calibration should prioritize optical absorption (e.g. wavelength selection and source power) over modest variations in skin thickness.

Figure 13.

Overlaid photoplethysmography (PPG) waveforms for five dermal thicknesses (t = 0.7, 1.0, 1.3, 1.7, 2.0 mm). Epidermal and subcutaneous layer thicknesses were held constant; only dermis thickness was varied to isolate the layer that contains the microvascular bed driving pulse-related absorption/backscatter. Across this range, the baseline level and beat-to-beat alternating current excursions remain essentially unchanged. Axes: time(s) and PPG amplitude. PPG: Photoplethysmography

Figure 14.

Mean detected power versus dermal thickness with ± standard error of the mean (SEM) error bars. SEM = SD/√n, where SD is the temporal standard deviation over the 0–6 s window and n is the number of time samples per condition (n = 110). The small variations fall within SEM, indicating no systematic dependence on thickness in this interval. Axes: dermal thickness (mm) and mean power (W)

Discussion

Scientific implications and capacity for extension

This framework can be used to improve the accuracy of wearable sensors in the real-world scenarios, for example, when facing variations in skin properties and perfusion patterns. In the present study, we implemented and validated a co-simulation of device optics and tissue by coupling Nonsequential Zemax ray tracing to a multilayer skin model driven by time-varying blood volume, enabling reconstruction of the detector-level reflection-mode signal. Comparing the model output with representative measurements shows that the approach is useful for interpreting the origins of features in the pulse waveform and for assessing model-data agreement, thereby providing a conceptual basis for posing sensor-design questions without testing geometric or hardware variations in this version. Accordingly, the main contribution of the present work is to establish a dependable framework for device tissue co-simulation and to demonstrate that detector-level signals can be predicted under the study’s defined configuration. Consistent with the sensitivity analysis [Figures 11-14], the detector-level signal in our configuration is strongly influenced by the blood absorption coefficient, whereas varying dermal thickness within 0.7–2.0 mm produced no first-order change in mean power or time-domain waveform morphology. In practice, this prioritizes wavelength selection and source power over modest thickness differences for preserving signal strength and pulse-related AC amplitude.

On this basis, the same framework can be extended to physiological measurements on skin, for example, indices linked to blood and tissue composition (e.g., Hb/HbO₂ and Hct in dermal microvasculature, epidermal melanin, and water/lipids in subcutaneous tissue) or metrics that reflect changes in perfusion. Realizing this extension requires reliable layer-specific optical data and a clear mapping between absorption/scattering/anisotropy and the relevant biological constituents, as well as the incorporation of wavelength dependence and temporal dynamics so that each factor’s influence on the amplitude and morphology of the reflected waveform can be evaluated separately.

Model development and sensitivity analysis (concise implementation roadmap)

To make practical use of the above capacity, we propose a staged development plan:

• (1) Data-driven parameterization: assemble and harmonize reliable layer-wise values of μ_a, μ_s, and g, and map them to the relevant biological constituents (Hb/HbO₂, Hct, melanin, water, and lipids) over the study’s wavelength range

• (2) Targeted sensitivity analysis: run controlled scenarios to quantify the effect of each factor on the detector-level signal using simple, reproducible indices (e.g., signal strength and waveform morphology) and identify the dominant contributors. Given our results, μ_a-driven factors (e.g., wavelength/spectrum and blood-related absorbers) should be prioritized before exploring geometric variations in dermal thickness

• (3) Refinement with matched measurements: narrow the influential parameter ranges and increase simulation fidelity in line with available measurements

• (4) Purposeful spectral extension: add complementary wavelengths only when required by a specific design or assessment question, updating the source spectrum, detector response, and layer optics accordingly.

Conflicts of interest

There are no conflicts of interest.

Funding Statement

Nil.