Computational modeling aspects of photon transport equations in biological media

This paper presents an overview of modeling light propagation through biological media by solving the photon transport equation. Different variants of the photon transport equation (PTE) are discussed. Several methods for modeling static distributions and the transient response are presented. A discussion on how to mix and match electromagnetic problems with the PTE is also provided.

Generalized coupled photon transport equations for handling correlated photon streams with distinct frequencies

A generalized form of coupled photon transport equations that can handle correlated light beams with distinct frequencies is introduced. The derivation is based on the principle of energy conservation. For a single frequency, the current formulation reduces to a standard photon transport equation, and for fluorescence and phosphorescence, the diffusion models derived from the proposed photon transport model match for homogenous media. The generalized photon transport model is extended to handle wideband inputs in the frequency domain. © 2012 Optical Society of America.

A fresh look at the validity of diffusion equations for modelling phosphorescence imaging of biological tissue

Phosphorescence lifetime imaging has become a widely used technique for tomographic oxygen imaging. The conventional model used to characterize photon transport in phosphorescence imaging is two coupled diffusion equations. On the premise that the total energy of excitation and phosphorescence photon flows must be conserved, we derive the diffusion equations in phosphorescence imaging and show that there must be an additional term to account for the transport of phosphorescent photons. This additional term accounts for the transport of phosphorescence photon energy density due to its gradients. The significance of this term in modelling phosphorescence in biological tissue is assessed.

An approximate numerical technique for characterizing optical pulse propagation in inhomogeneous biological tissue

An approximate numerical technique for modeling optical pulse propagation through weakly scattering biological tissue is developed by solving the photon transport equation in biological tissue that includes varying refractive index and varying scattering/absorption coefficients. The proposed technique involves first tracing the ray paths defined by the refractive index profile of the medium by solving the eikonal equation using a Runge-Kutta integration algorithm. The photon transport equation is solved only along these ray paths, minimizing the overall computational burden of the resulting algorithm. The main advantage of the current algorithm is that it enables to discretise the pulse propagation space adaptively by taking optical depth into account. Therefore, computational efficiency can be increased without compromising the accuracy of the algorithm.

A fresh look at the validity of the diffusion approximation for modeling fluorescence spectroscopy in biological tissue

Fluorescence has become a widely used technique for applications in noninvasive diagnostic tissue spectroscopy. The standard model used for characterizing fluorescence photon transport in biological tissue is based on the diffusion approximation. On the premise that the total energy of excitation and fluorescent photon flows must be conserved, we derive the widely used diffusion equations in fluorescence spectroscopy and show that there must be an additional term to account for the transport of fluorescent photons. The significance of this additional term in modeling fluorescence spectroscopy in biological tissue is assessed.

Aggregation, ageing and transport properties of surface modified fumed silica dispersions

We have investigated the aggregation, ageing and transport properties of surface modified silica dispersions in DMSO by photon correlation spectroscopy and conductivity measurements. The surface modification introduces Li+-ions that dissociate in the dispersion creating a single Li+-ion conducting electrolyte. We show that the surface modification changes the aggregation and ageing properties of the material. There is a pronounced ageing observed for the modified silica dispersions. At high concentrations of fumed silica a gel state is found, which in the case of the surface modified silica is a very weak gel that can be rejuvenated by ultrasonic treatment. The key parameter controlling the aggregation in this system is hydrogen bonding and the surface modification results in a very low number of sites for hydrogen bonding. In addition there is a contribution from repulsive electrostatic interactions in the surface modified silica dispersions due to the highly charged surfaces of these particles. Furthermore, the Li+-ion diffusion, at low silica concentration, is three orders of magnitude faster than that of the silica particles and in the gel state the silica particles are immobile. We also find that the Li+-ion diffusion is virtually independent of the silica concentration in the dispersions.

Plasmon-enhanced two-photon-induced isomerization for highly-localized light-based actuation of inorganic/organic interfaces

Two-photon initiated photo-isomerization of an azobenzene moiety adsorbed on silver nanoparticles (Ag NPs) is demonstrated. The azobenzene is linked to a materials-binding peptide that brings it into intimate contact with the Ag NP surface, producing a dramatic enhancement of its two-photon absorbance. An integrated modeling approach, combining advanced conformational sampling with Quantum Mechanics/Capacitance Molecular Mechanics and response theory, shows that charge transfer and image charges in the Ag NP generate local fields that enhance two-photon absorption of the cis isomer, but not the trans isomer, of adsorbed molecules. Moreover, dramatic local field enhancement is expected near the localized surface plasmon resonance (LSPR) wavelength, and the LSPR band of the Ag NPs overlaps the azobenzene absorbance that triggers cis to trans switching. As a result, the Ag NPs enable two-photon initiated cis to trans isomerization, but not trans to cis isomerization. Confocal anti-Stokes fluorescence imaging shows that this effect is not due to local heating, while the quadratic dependence of switching rate on laser intensity is consistent with a two-photon process. Highly localized two-photon initiated switching could allow local manipulation near the focal point of a laser within a 3D nanoparticle assembly, which cannot be achieved using linear optical processes.