Light can be considered either as a stream of particles (photons) or an electromagnetic wave, that oscillates at a given frequency defining its color. Both theories are interrelated by the formula E = hv (E, photon energy; h, Planck´s constant, v: frequency of the wave, related to its wavelength (λ) by the speed of light, v = c/λ), which shows how the photon energy is inversely proportional to its wavelength. However, to understand the dynamics of the light propagation, the wave theory is more useful. The electrical component, orthogonal to the magnetic one, is responsible of its tissue interactions. Propagating light, with a given direction, inside of a given tissue, can transfer some of its energy to a given atom, specifically to its more external electrons. This energy can either be absorbed or not. When it is absorbed it can drive chemical reactions, be-remitted as light or converted into heat. If it is not absorbed, it can be reflected, refracted or scattered. The behavior of light propagating through a given material depends on the features of the incident light and the optical properties of the medium. The main light parameters include its: wavelength, power, spot size, spatio-temporal-spectral profile (including its spot size and duration) and polarization state. The spatio-temporal-spectral profile address how the irradiance varies across the beam, during the pulse and as a function of the wavelength. The optical properties of the medium (normally wavelength dependent, but also might be dependent on temperature, pressure, and polarization) include the absorption
17 coefficient (µa), the scattering coefficient (µs), the scattering anisotropy (g) and the refractive index. The first refers to the probability of a photon of being absorbed by the medium per unit of the path length. The rest define how the path traced by the photons is. The scattering coefficient defines the probability of light scattering in a medium per unit of the path length.
Scattering anisotropy is the mean of the cosine of the scattering angle, and describes the variation in direction in which the scattered light is propagated (Periyasamy and Pramanik, 2017; Welch and van Gemert, 2011). The definition of the refractive index is a bit more complex and it is further developed as following.
In a very simplistic way, we could imagine charged particles within a material as masses attached to the surrounding by a spring, which has a natural resonant frequency. If the frequency of the propagating wave is equal to this frequency, the energy is absorbed. If it is different, the transfer of energy to the material is poor (Welch and van Gemert, 2011). For most interactions, the energy received is not enough to trigger a fluorescence (re-emit that energy with a lower energy) or ionizing (removal of the electron, which can be trigger by heat) event, but it causes the oscillation of that electron. The energy associated with that oscillation is released in the form of another light wave. This newly generated light wave, also called wavelet, propagates in all directions, as an expanding spherical wave. Furthermore, the electron cloud-light wave interaction very briefly stops the progression of the wave, causing a phase delay (in the range of a femtosecond, 10-15s, for visible light). The sum of several of this
“slowing down” events, after consecutive interactions with several molecules within the material, causes an important reduction in the velocity of the light as it propagates and is what we call the refractive index. Thus, the refractive index is defined as the ratio between the speed of light in vacuum and in the medium (Richardson and Lichtman, 2015). Although the mismatch of the refractive index at the interface between two different media is commonly known as scattering, it would be more accurate to define scattering as the inhomogeneous distribution of the amount of scattering between different regions in the material.
Homogenous materials (e.g. air, water, glass) have a high density of scatterers of dimensions much smaller than any wavelength of light, that are very close to each other (3 nm in the air, 10 nm in the water). If we imagine light travelling as a plane, when it enters in any of this example medium, it sets all the molecules in that plane into a brief excited state that when relaxed generate densely packed spherical waves. Given that this event occurs simultaneously in a single plane, a nearly complete destructive interference is generated, avoiding the propagation of light in the lateral directions. In the forward direction, the wavelet propagates with a phase delay. The scatterers that are in the following plane experience the same phenomenon. Thus, all the phase-delayed forward-moving wavelets constructively sum their amplitudes, allowing the light propagation. In biological tissues, the inhomogeneity in the
18 scatterers present in the different components (e.g. in the intracellular space, in the membrane and in the extracellular matrix) would cause that the destructive interference will not happen totally and light will propagate also in the perpendicular direction. The tissue, then, will behave as if it would contain many small light sources propagating light of all wavelength in all directions, causing the characteristic whitish translucency of tissues (Richardson and Lichtman, 2015).
The inhomogeneity of scatterers can happen at different spatial scales. If it happens at scales much smaller than the wavelength of the travelling wave, short wavelengths have a greater probability of being scattered (e.g. Membranes, cells sub compartments, collagen fibrils). This is due to the fact the fractional intensity of the scattered light is inversely proportional to the forth power of the wavelength of incident light. This type of scattering, known as Rayleigh scattering, is more prominent for short wavelength light. This is the foundation, for example, of two-photon microscopy, that achieves deep fluorescence imaging in the tissue, or the reason why the sky is blue (the blue component of the white light is scattered more efficiently than red component by the molecules in the air). If it happens for particle larger than the wavelength of the propagating light, like big protein complexes or organelles, the scattering is mostly in the forward direction, the wavelength dependence of scattering is not significant and it follows the so-called Mie scattering. One example is why the clouds are white (when the concentration of water in the atmosphere is high enough, water droplets form and scatter all the wavelengths equally). To summarize, propagating light through a tissue can be scattered isotropically (Rayleigh) or dominantly forward (Mie) if the incident wavelength is smaller or bigger than the dimensions of the scatterers, respectively. Since the scattered light has the same wavelength as the incident one, both types of scattering are termed elastic, and both can affect the light propagation in tissue. Inelastic scattering, also known as Raman scattering, in which the scattered wavelength is different, is generally too weak in tissue and can be neglected (Richardson and Lichtman, 2015; Vo-Dinh, 2003; Welch and van Gemert, 2011).
Since we consider light as substitute of electric pulses in order to achieve a more spatially confined stimulation of the spiral ganglion, estimating how the tissue-light interaction alters the available light is crucial for the design and choice of suitable light sources in optical CIs.
Although there are many alternatives to obtain an approximation of the light distribution both in 2D and 3D, we considered Monte Carlo simulation to be the most suitable method to study light propagation from our intracochlear light sources in combination with realistic reconstructions of the cochlear tissues.
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