Light Propagation in Biological Tissue for PPG: Optical Properties and Photon Transport

The PPG signal is fundamentally determined by how photons travel through the complex multilayered structure of biological tissue, a process governed by the wavelength-dependent absorption and scattering properties of skin, blood, and subcutaneous structures. Understanding photon transport in tissue is essential for interpreting PPG measurements, designing optimal sensor geometries, selecting appropriate wavelengths, and predicting how patient-specific factors like skin pigmentation and tissue thickness affect signal quality. This article provides a technical review of tissue optical properties relevant to PPG and the computational methods used to model light propagation.

For an introduction to how PPG technology works at the system level, see our PPG technology overview. For guidance on wavelength selection based on tissue optics, see our wavelength comparison guide.

Tissue Layer Structure Relevant to PPG

The optical path of PPG photons traverses several distinct tissue layers, each with different optical properties. Understanding this layered structure is prerequisite to modeling light propagation.

Epidermis

The epidermis is the outermost skin layer, typically 50-150 micrometers thick depending on body site. The stratum corneum (10-20 micrometers of dead keratinized cells) has relatively low absorption but moderate scattering. The viable epidermis contains melanocytes that produce melanin, the dominant chromophore in this layer.

Melanin absorbs light across the entire visible and near-infrared spectrum, with absorption decreasing approximately as a power law with increasing wavelength. Jacques (2013; DOI: 10.1088/0031-9155/58/11/R37) compiled melanin absorption data and reported that the absorption coefficient of the epidermis varies from approximately 50 cm^-1 in lightly pigmented skin to over 500 cm^-1 in darkly pigmented skin at 500nm. At 940nm, these values drop to approximately 5-50 cm^-1, a 10-fold reduction. This wavelength dependence explains why infrared PPG is less sensitive to skin color than green PPG.

The epidermis contains no blood vessels. It is a purely attenuating layer that reduces the optical budget for detecting blood-related signals in deeper layers without contributing to the pulsatile PPG signal.

Dermis

The dermis (1-4 mm thick depending on body site) is the primary tissue layer interrogated by PPG. It is subdivided into the papillary dermis (upper 200-400 micrometers) containing the superficial capillary plexus, and the reticular dermis containing the deep vascular plexus with arterioles, venules, and arteriovenous anastomoses.

The dominant chromophore in the dermis is hemoglobin in blood, with absorption properties that depend critically on oxygenation state. At 525nm (green), the absorption coefficient of the dermis with normal blood content is approximately 2-5 cm^-1. At 660nm (red), it drops to 0.3-1 cm^-1. At 940nm (infrared), it is approximately 0.5-1.5 cm^-1, with the increase relative to red reflecting the higher absorption of oxyhemoglobin at infrared wavelengths.

Scattering in the dermis is dominated by collagen fibers (which constitute 70-80% of the dermis dry weight) and is well-described by Mie scattering theory. The reduced scattering coefficient of the dermis is approximately 15-25 cm^-1 at 525nm, decreasing to 8-15 cm^-1 at 940nm following an approximate power law: mu_s' = A * lambda^(-b), where b is typically 0.7-1.5 (Jacques, 2013).

Subcutaneous Tissue

Subcutaneous tissue (hypodermis) lies below the dermis and consists primarily of adipose (fat) tissue with larger blood vessels. The optical properties of adipose tissue differ markedly from the dermis: lipid absorption dominates over hemoglobin absorption at near-infrared wavelengths, and scattering is lower due to the more homogeneous cellular structure.

For reflectance-mode PPG with typical source-detector separations of 2-5 mm, the majority of detected photons do not reach the subcutaneous layer when using green LEDs. However, with infrared wavelengths and larger source-detector separations, a significant fraction of photons probe the subcutaneous tissue, potentially sampling deeper vascular structures. This depth dependence has implications for what the PPG signal actually represents at different wavelengths and sensor configurations.

Fundamental Optical Properties

Four optical parameters govern photon transport in tissue: the absorption coefficient (mu_a), the scattering coefficient (mu_s), the anisotropy factor (g), and the refractive index (n). Together, these determine the path length, sampling volume, and signal characteristics of PPG measurements.

Absorption Coefficient (mu_a)

The absorption coefficient describes the probability of photon absorption per unit path length, with units of cm^-1. In tissue, mu_a is the sum of contributions from all chromophores present:

mu_a = epsilon_HbO2 * C_HbO2 + epsilon_Hb * C_Hb + epsilon_melanin * C_melanin + epsilon_water * C_water + epsilon_lipid * C_lipid

Where epsilon represents the specific absorption coefficient and C the concentration of each chromophore. For PPG, the most important chromophores are hemoglobin species (HbO2 and Hb), whose concentrations change with the cardiac pulse. This pulsatile change in mu_a is what generates the AC component of the PPG signal.

Prahl (1999) compiled definitive hemoglobin absorption spectra that remain the standard reference for PPG and pulse oximetry calculations. At 660nm, the molar extinction coefficients are: epsilon_Hb = 3.35 cm^-1/(mmol/L) and epsilon_HbO2 = 0.81 cm^-1/(mmol/L). At 940nm: epsilon_Hb = 0.69 cm^-1/(mmol/L) and epsilon_HbO2 = 1.21 cm^-1/(mmol/L). These values underpin the modified Beer-Lambert law calculations used in pulse oximetry.

Scattering Coefficient and Anisotropy

The scattering coefficient (mu_s) describes the probability of photon scattering per unit path length. In tissue, mu_s is very high (100-500 cm^-1 at visible wavelengths), meaning photons scatter every 20-100 micrometers on average. However, scattering in tissue is highly forward-directed, with the anisotropy factor g (average cosine of scattering angle) typically 0.8-0.95. This means that most scattering events deflect the photon by only a small angle.

For modeling purposes, the transport or reduced scattering coefficient mu_s' = mu_s * (1-g) is often used, which describes the effective scattering after accounting for forward scattering. Typical values of mu_s' for skin are 15-25 cm^-1 at green wavelengths and 8-15 cm^-1 in the near-infrared (Bashkatov et al., 2011; DOI: 10.1117/1.3484498).

The ratio of scattering to absorption (the albedo, a = mu_s' / (mu_s' + mu_a)) determines the character of light transport. In most skin tissue at PPG wavelengths, the albedo exceeds 0.9, indicating highly scattering-dominated transport. This means that photons undergo many scattering events before being absorbed, creating diffuse light distributions rather than sharp beams, and enabling the reflectance-mode PPG geometry where the detector collects multiply-scattered photons that have explored the tissue volume.

Refractive Index

The refractive index of tissue (n approximately 1.38-1.45 for skin, compared to n = 1.0 for air) creates Fresnel reflections at the tissue-air interface and internal reflections at boundaries between tissue layers with different refractive indices. The refractive index mismatch at the skin surface causes approximately 4-6% specular reflection of incident light, which does not carry physiological information and constitutes a background signal that reduces PPG contrast.

Internal refractive index variations at cell membranes (n approximately 1.46 vs cytoplasm n approximately 1.37) contribute to microscopic scattering. Barer and Joseph (1954) established these fundamental refractive index values that underpin tissue optics models used today.

Photon Transport Models

Predicting the PPG signal from tissue optical properties requires solving the photon transport problem: given the optical properties and geometry, what is the light distribution and detected signal intensity?

The Radiative Transport Equation

The rigorous description of photon transport in tissue is the radiative transport equation (RTE), a Boltzmann-type integro-differential equation that describes the radiance (photon flux per unit area per unit solid angle) at every point in the tissue as a function of position, direction, and wavelength. The RTE accounts for absorption, scattering (with angular dependence described by the phase function), and source terms.

Analytical solutions to the RTE exist only for very simple geometries (infinite homogeneous media, semi-infinite half-spaces with plane wave illumination). Real tissue with its layered structure, curved surfaces, and spatially varying optical properties requires either numerical solutions or approximate methods.

Diffusion Approximation

The diffusion approximation simplifies the RTE by assuming that the light field is nearly isotropic at positions far from sources and boundaries. Under this assumption, the radiance can be expanded in spherical harmonics and truncated after the first-order (P1) term, yielding a simpler diffusion equation characterized by the effective attenuation coefficient mu_eff = sqrt(3 * mu_a * (mu_a + mu_s')).

The diffusion approximation works well in the bulk of highly scattering tissue (where mu_s' >> mu_a) but breaks down near sources, boundaries, and in regions where absorption is comparable to scattering. For PPG, the diffusion approximation is useful for estimating penetration depth and source-detector sensitivity profiles but may not accurately predict the absolute detected signal intensity, particularly for small source-detector separations (<3 mm) where the diffusion conditions are not fully met.

Schmitt (1991; DOI: 10.1117/12.44117) applied the diffusion approximation to analyze the sensitivity of reflectance PPG to changes in blood volume at different tissue depths and showed that the interrogation depth increases approximately linearly with source-detector separation distance.

Monte Carlo Simulation

Monte Carlo (MC) simulation is the gold standard for modeling photon transport in tissue for PPG applications. The method tracks individual photon packets through the tissue, with each photon undergoing a random walk of absorption and scattering events governed by the tissue's optical properties.

Each photon begins at the LED source position, enters the tissue, and is tracked step by step. At each step: the step length is drawn from an exponential distribution with mean 1/mu_t (where mu_t = mu_a + mu_s is the total attenuation coefficient). At each interaction site, a fraction mu_a/mu_t of the photon's weight is absorbed, and the photon is scattered in a new direction sampled from the phase function (typically Henyey-Greenstein with parameter g). The photon continues until its weight drops below a threshold (and Russian roulette is applied) or it exits the tissue. Photons exiting through the surface within the detector area and acceptance angle are counted as detected.

Wang et al. (1995; DOI: 10.1016/0169-2607(95)01640-F) developed the MCML (Monte Carlo Multi-Layered) code that became the standard tool for tissue optics simulation. For PPG modeling, MCML and its derivatives allow researchers to predict signal intensity, interrogation depth, and sensitivity to pulsatile blood volume changes as functions of wavelength, source-detector geometry, and tissue layer thicknesses and optical properties.

Chatterjee and Bhattacharya (2021; DOI: 10.1016/j.bspc.2020.102355) used Monte Carlo simulation to investigate the effect of melanin concentration on PPG signal characteristics across six Fitzpatrick skin types and found that the DC signal dropped by 65% from Type I to Type VI at 525nm, while the AC modulation depth decreased by 40%. At 940nm, the DC reduction was only 15% and AC modulation depth decreased by 12%, quantitatively confirming the advantage of infrared wavelengths for equitable PPG performance.

Interrogation Volume and Depth Sensitivity

A critical question for PPG design and interpretation is: what volume of tissue actually contributes to the detected signal? The answer depends on wavelength, source-detector geometry, and tissue optical properties.

Banana-Shaped Sensitivity Region

In reflectance-mode PPG, photons traveling from source to detector follow curved paths through the tissue, creating a banana-shaped sensitivity region. The depth of this region increases with source-detector separation. For a separation of 3 mm with green light, the maximum interrogation depth is approximately 1.5 mm. For a separation of 5 mm with infrared light, it extends to approximately 3-4 mm.

Cui et al. (1991; DOI: 10.1088/0031-9155/36/4/001) mapped the sensitivity profiles of reflectance optical measurements using Monte Carlo simulation and demonstrated the banana-shaped geometry. They showed that shallow source-detector separations (1-2 mm) are predominantly sensitive to the superficial dermis, while wider separations (5-10 mm) sample deeper tissue layers including the deep vascular plexus and potentially subcutaneous structures.

Wavelength-Dependent Penetration

The effective penetration depth, defined as the depth at which light intensity falls to 1/e (37%) of the surface value, varies substantially with wavelength. At 525nm (green): approximately 0.7-1.5 mm due to high hemoglobin absorption. At 660nm (red): approximately 2-4 mm as hemoglobin absorption decreases. At 940nm (near-infrared): approximately 3-7 mm, limited mainly by water absorption at longer wavelengths.

These penetration depths have direct implications for what the PPG signal represents. Green PPG primarily samples the superficial capillary plexus, providing a signal dominated by capillary-level blood volume changes. Infrared PPG samples deeper, including arterioles and venules in the reticular dermis, potentially providing information about larger vessel hemodynamics but also introducing more venous pulsation contamination.

Implications for Sensor Design

Understanding the interrogation volume informs PPG sensor design decisions. For heart rate monitoring, where the goal is maximizing the pulsatile signal-to-noise ratio, a short source-detector separation (2-3 mm) with green light concentrates the measurement in the superficial capillary bed where pulsatile amplitude is highest. For SpO2 measurement, which requires red and infrared wavelengths, the source-detector geometry must be optimized for each wavelength's different penetration characteristics to ensure both wavelengths sample comparable tissue volumes.

Multi-distance PPG, using multiple detectors at different separations from a single source, can provide depth-resolved information. Liu et al. (2017; DOI: 10.1364/BOE.8.005441) demonstrated that dual-distance reflectance PPG can separate superficial from deep pulsatile signals, potentially enabling simultaneous measurement of capillary and arteriolar hemodynamics. This approach also offers a path to mitigating motion artifacts, as superficial and deep tissue layers respond differently to mechanical perturbation.

Tissue Optical Property Variations

Inter-individual and intra-individual variations in tissue optical properties create significant variability in PPG signal characteristics, which must be accounted for in device design and algorithm development.

Skin Pigmentation

As discussed, melanin concentration varies dramatically across individuals and body sites, producing up to 10-fold variation in epidermal absorption at visible wavelengths. This variation directly affects PPG signal amplitude and SNR, with implications for device accuracy across diverse populations. Fallow et al. (2013; DOI: 10.1088/0967-3334/34/7/879) measured PPG signal quality across five skin pigmentation groups and found that SNR at 525nm decreased from approximately 42 dB in the lightest group to approximately 28 dB in the darkest group.

Age-Related Changes

Aging produces several changes in skin optical properties relevant to PPG. Epidermal thinning (approximately 6.4% per decade after age 20) reduces the attenuating effect of the epidermis. Dermal collagen cross-linking increases scattering slightly. Reduced capillary density in the papillary dermis decreases the available pulsatile blood volume. Arterial stiffening changes the shape and amplitude of the pulsatile waveform. These combined effects can reduce PPG AC amplitude by 30-50% in elderly compared to young adults, as documented by Allen (2007; DOI: 10.1088/0967-3334/28/3/R01) in a comprehensive review.

Body Site Variation

Tissue thickness, vascular density, and subcutaneous fat thickness vary greatly across body sites, producing site-dependent PPG characteristics. The fingertip has thin skin, high vascular density, and arteriovenous anastomoses that produce strong pulsatile signals. The wrist has thicker skin, lower vascular density, and a reflectance geometry that produces weaker signals. The forehead has thin skin and relatively high perfusion but is subject to venous congestion when supine. The ear lobe, commonly used for transmittance pulse oximetry, has thin tissue and consistent optical properties but limited contact area.

Understanding these site-specific tissue optical properties is essential for calibrating PPG algorithms across different measurement locations, a growing concern as wearable PPG sensors appear on wrists, fingers, ears, and even ring form factors.

Conclusion

The physics of light propagation through biological tissue fundamentally determines what the PPG signal measures, how deeply it probes, and how it varies across wavelengths, individuals, and body sites. Tissue optical properties, particularly the interplay of hemoglobin absorption, melanin attenuation, and collagen scattering, set the performance envelope within which PPG technology operates. Monte Carlo simulation provides the computational framework for predicting and optimizing PPG signal characteristics, enabling evidence-based sensor design rather than empirical trial and error. As PPG applications expand beyond simple heart rate monitoring into blood pressure, glucose, and hydration sensing, rigorous understanding of tissue optics becomes not merely academic but engineering-critical.

For deeper exploration of how tissue optics underpins specific PPG measurements, see our algorithms reference and PPG learning center.