💡Biophotonics Unit 2 – Optics and Light-Tissue Interactions Basics

Light Basics

• Light is a form of electromagnetic radiation that travels in waves and consists of photons
• Photons are massless particles that carry energy and momentum and exhibit both wave and particle properties (wave-particle duality)
• The wavelength of light determines its color, with shorter wavelengths corresponding to higher energy (blue) and longer wavelengths corresponding to lower energy (red)
• The visible light spectrum ranges from approximately 380 nm (violet) to 700 nm (red)
• Light can interact with matter through processes such as absorption, scattering, reflection, and refraction
• The speed of light in a vacuum is a constant, denoted as c, and is approximately 299,792,458 meters per second
• In different media, light travels at a slower speed, determined by the medium's refractive index (n)
  • The refractive index is the ratio of the speed of light in a vacuum to the speed of light in a given medium

Optical Properties of Tissues

• Tissues have unique optical properties that depend on their composition, structure, and physiological state
• The main optical properties of tissues are absorption, scattering, refraction, and reflection
• Absorption occurs when light energy is converted into other forms of energy (heat) by molecules in the tissue
  • The primary absorbers in tissues are water, hemoglobin, and melanin
• Scattering occurs when light changes direction due to interaction with tissue components (cells, organelles, and extracellular matrix)
  • Scattering can be classified as Rayleigh scattering (particles much smaller than the wavelength) or Mie scattering (particles comparable to or larger than the wavelength)
• The scattering coefficient (μs) and the absorption coefficient (μa) quantify the amount of scattering and absorption per unit length in a tissue
• The reduced scattering coefficient (μs') accounts for the anisotropy of scattering and is defined as: $μ_s' = μ_s(1 - g)$, where g is the anisotropy factor
• The penetration depth of light in tissue depends on the wavelength and the tissue's optical properties, with longer wavelengths generally penetrating deeper than shorter wavelengths

Absorption and Scattering

• Absorption and scattering are the two main processes by which light interacts with tissues
• Absorption occurs when photons are absorbed by molecules, leading to a transfer of energy from the photon to the molecule
  • This energy can cause electronic transitions, vibrational transitions, or rotational transitions in the molecule
• The absorption coefficient (μa) quantifies the probability of absorption per unit length and depends on the concentration and extinction coefficient of the absorbing molecules
• Beer-Lambert law describes the attenuation of light due to absorption: $I = I_0 e^{-μ_a d}$, where I is the transmitted intensity, I0 is the incident intensity, and d is the path length
• Scattering occurs when photons change direction due to interaction with tissue components
  • Scattering can be elastic (no energy loss) or inelastic (energy loss, e.g., Raman scattering)
• The scattering coefficient (μs) quantifies the probability of scattering per unit length and depends on the size, shape, and refractive index of the scattering particles
• The anisotropy factor (g) describes the directionality of scattering, ranging from -1 (complete backscattering) to 1 (complete forward scattering)
  • Most biological tissues have g values between 0.7 and 0.9, indicating predominantly forward scattering

Refraction and Reflection

• Refraction occurs when light changes direction as it passes from one medium to another with a different refractive index
  • The refractive index (n) is the ratio of the speed of light in a vacuum to the speed of light in the medium
• Snell's law describes the relationship between the angles of incidence and refraction: $n_1 \sin θ_1 = n_2 \sin θ_2$, where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively
• Total internal reflection occurs when light traveling from a higher refractive index medium to a lower refractive index medium reaches a critical angle (θc), causing all light to be reflected back into the higher index medium
  • The critical angle is given by: $θ_c = \arcsin(n_2 / n_1)$
• Reflection occurs when light bounces off a surface, changing direction without entering the medium
  • Specular reflection occurs when light reflects off a smooth surface at the same angle as the incident light
  • Diffuse reflection occurs when light reflects off a rough surface in multiple directions
• Fresnel equations describe the amount of light reflected and transmitted at an interface between two media, depending on the refractive indices, angle of incidence, and polarization of the light

Fluorescence and Phosphorescence

• Fluorescence and phosphorescence are processes by which molecules emit light after absorbing photons
• In fluorescence, a molecule absorbs a photon, exciting an electron to a higher energy state, and then emits a photon as the electron relaxes back to the ground state
  • The emitted photon typically has a longer wavelength (lower energy) than the absorbed photon, a phenomenon known as the Stokes shift
• The fluorescence lifetime is the average time a molecule spends in the excited state before emitting a photon, typically on the order of nanoseconds
• Quantum yield is the ratio of the number of photons emitted to the number of photons absorbed, indicating the efficiency of the fluorescence process
• Phosphorescence is similar to fluorescence but involves a transition to a triplet excited state, resulting in longer emission lifetimes (microseconds to seconds)
  • The longer lifetime is due to the forbidden nature of the triplet-to-singlet transition, which requires a spin flip
• Fluorescence and phosphorescence are used in various applications, such as fluorescence microscopy, flow cytometry, and fluorescence-guided surgery, to visualize and study biological processes and structures

Photon Transport in Tissues

• Photon transport in tissues is governed by the combined effects of absorption and scattering
• The radiative transfer equation (RTE) is a mathematical model that describes the propagation of light in tissues, considering absorption, scattering, and emission
  • The RTE is a complex integro-differential equation that is difficult to solve analytically in most cases
• The diffusion approximation is a simplified model of photon transport that assumes scattering dominates over absorption and that the light distribution is nearly isotropic
  • The diffusion equation is a partial differential equation that can be solved analytically or numerically for simple geometries and boundary conditions
• Monte Carlo simulations are a numerical method for modeling photon transport in tissues, where photons are treated as individual particles that undergo random absorption and scattering events based on probability distributions
  • Monte Carlo simulations can accurately model complex tissue geometries and heterogeneities but are computationally intensive
• The mean free path (MFP) is the average distance a photon travels between successive scattering events and is given by: $MFP = 1 / μ_s$
• The transport mean free path (TMFP) is the average distance a photon travels before its direction becomes randomized and is given by: $TMFP = 1 / μ_s'$
• The optical penetration depth (δ) is the depth at which the light intensity decreases to 1/e (about 37%) of its initial value and is given by: $δ = 1 / \sqrt{3μ_a(μ_a + μ_s')}$

Optical Imaging Techniques

• Optical imaging techniques use light to visualize and study biological structures and processes
• Microscopy techniques:
  • Brightfield microscopy: Samples are illuminated with white light, and contrast is generated by absorption and scattering
  • Fluorescence microscopy: Samples are labeled with fluorescent dyes or proteins, and contrast is generated by the emission of light from the fluorophores
  • Confocal microscopy: Uses a pinhole to reject out-of-focus light, improving resolution and contrast in thick samples
  • Two-photon microscopy: Uses pulsed infrared light to excite fluorophores via two-photon absorption, allowing deeper tissue penetration and reduced photobleaching
• Macroscopic imaging techniques:
  • Optical coherence tomography (OCT): Uses low-coherence interferometry to generate high-resolution, cross-sectional images of tissues based on backscattered light
  • Diffuse optical tomography (DOT): Uses near-infrared light to image the absorption and scattering properties of tissues, enabling functional imaging of hemodynamics and metabolism
  • Photoacoustic imaging: Uses pulsed laser light to generate ultrasonic waves in tissues, which are detected to form images based on the optical absorption properties of the tissue
• Spectroscopic techniques:
  • Raman spectroscopy: Measures the inelastic scattering of light by molecules, providing information about the chemical composition and molecular structure of tissues
  • Fluorescence spectroscopy: Measures the emission spectra of fluorophores in tissues, providing information about the concentration and environment of the fluorophores

Applications in Biomedicine

• Optical techniques have numerous applications in biomedicine, enabling the study, diagnosis, and treatment of various diseases and conditions
• Diagnostic applications:
  • Early detection and monitoring of cancer: Optical techniques can detect changes in tissue morphology, vasculature, and metabolism associated with cancer development
  • Imaging of retinal diseases: OCT and fundus photography are used to diagnose and monitor conditions such as age-related macular degeneration, diabetic retinopathy, and glaucoma
  • Monitoring of brain function: Near-infrared spectroscopy (NIRS) and functional OCT can measure changes in cerebral blood flow and oxygenation related to brain activity
• Therapeutic applications:
  • Photodynamic therapy (PDT): Uses light-activated drugs (photosensitizers) to generate reactive oxygen species that selectively kill cancer cells or pathogenic microorganisms
  • Laser surgery: Uses focused laser light to precisely cut, ablate, or coagulate tissues, minimizing damage to surrounding healthy tissue
  • Low-level laser therapy (LLLT): Uses low-power lasers to stimulate cellular processes, promote wound healing, and reduce pain and inflammation
• Research applications:
  • Studying cellular processes: Fluorescence microscopy and biosensors enable the visualization and quantification of various cellular processes, such as gene expression, protein interactions, and signaling pathways
  • Investigating tissue biomechanics: Optical elastography techniques, such as OCT elastography and Brillouin microscopy, can measure the mechanical properties of tissues, providing insights into disease progression and tissue engineering
  • Monitoring drug delivery and nanoparticle distribution: Fluorescence and photoacoustic imaging can track the distribution and fate of drugs and nanoparticles in tissues, aiding in the development of targeted therapies