Radiative transfer equation modeling by streamline diffusion modified continuous Galerkin method

Modeling photoacoustic pressure generation in colloidal suspensions at different volume fractions based on a multi-scale approach

Further development of quantitative photoacoustic tomography requires understanding the photoacoustic pressure generation by modeling the generation process. This study modeled the initial photoacoustic pressure in colloidal suspensions, used as tissue phantoms, at different volume fractions on a multi-scale approach. We modeled the thermodynamic and light scattering properties on a microscopic scale with/without treating the hard-sphere interaction between colloidal particles. Meanwhile, we did the light energy density on a macroscopic scale. We showed that the hard-sphere interaction significantly influences the initial pressure and related quantities at a high volume fraction except for the thermodynamic properties. We also showed the initial pressure at the absorber inside the medium logarithmically decreases with increasing the volume fractions. This result is mainly due to the decay of the light energy density with light scattering. Our numerical results suggest that modeling light scattering and propagation is crucial over modeling thermal expansion.

Model equations of light scattering properties and a characteristic time of light propagation for polydisperse colloidal suspensions at different volume fractions

We developed model equations of light scattering properties and a characteristic time of light propagation for polydisperse colloidal suspensions at different volume fractions. By the model equations, we examined numerical results using the first-order (dependent) scattering theory (FST) and radiative transfer theory in 600-980 nm wavelength. The model equations efficiently treat the interference of electric fields scattered from colloidal particles by a single effective coefficient, providing fast computation. Meanwhile, the FST provides accurate but complicated treatment. We found the interference effects on the scattering properties and characteristic time depend linearly on wavelength. Dimensionless analysis showed a simple mechanism of the interference effects, independently of wavelength and source-detector distance.

Numerical Study of Near-Infrared Light Propagation in Aqueous Alumina Suspensions Using the Steady-State Radiative Transfer Equation and Dependent Scattering Theory

Understanding light propagation in liquid phantoms, such as colloidal suspensions, involves fundamental research of near-infrared optical imaging and spectroscopy for biological tissues. Our objective is to numerically investigate light propagation in the alumina colloidal suspensions with the mean alumina particle diameter of 55 nm at the volume fraction range 1–20%. We calculated the light scattering properties using the dependent scattering theory (DST) on a length scale comparable to the optical wavelength. We calculated the steady-state radiative transfer and photon diffusion equations (RTE and PDE) using the DST results based on the finite difference method in a length scale of the mean free path. The DST calculations showed that the scattering and reduced scattering coefficients become more prominent at a higher volume fraction. The anisotropy factor is almost zero at all the volume fractions, meaning the scattering is isotropic. The comparative study of the RTE with the PDE showed that the diffusion approximation holds at the internal region with all the volume fractions and the boundary region with the volume fraction higher than 1%. Our findings suggest the usefulness of the PDE as a light propagation model for the alumina suspensions rather than the RTE, which provides accurate but complicated computation.

A homogenized cerebrospinal fluid model for diffuse optical tomography in the neonatal head

Diffuse optical tomography is a non-invasive and non-irradiating medical imaging technique that is particularly suitable for cerebral monitoring of newborns since it can be used at the bedside of the patient. Here, a new model for optical tomography in the neonatal brain is presented that takes into account the presence of arachnoid trabeculae in the cerebrospinal fluid (CSF). It is known that the classical diffusion approximation (DA) for light propagation is at the limit of validity in the CSF layer due to the low values of the absorption and scattering coefficients. The new model is obtained by the DA of the homogenized radiative transfer equation and is rigorously justified. Numerical results in two and three dimensions attest for the improved sensitivity of the new model to the presence of perturbations in the brain layer.

Solutions for single-scattered radiance in the semi-infinite medium based on radiative transport theory

In this paper, some explicit analytical solutions for single-scattered radiance in a half-space medium under consideration of a reflecting boundary are derived. We consider both a unidirectional beam source as well as an isotropic point source. In addition to direct applications within optical tomography and computer graphics, the obtained solutions are also needed when solving the radiative transport equation after the separation of the unscattered and single-scattered contribution. Comparisons between the derived analytical solutions and the Monte Carlo method display excellent agreement.

Photon transport model for dense polydisperse colloidal suspensions using the radiative transfer equation combined with the dependent scattering theory

In near-infrared imaging and spectroscopy, high-fidelity modeling of photon transport for dense polydisperse colloidal suspensions is crucial. We developed photon transport models using the radiative transfer equation (RTE) with the dependent scattering theory (DST) at volume fractions up to 20%. The polydispersity and interference effects strongly influence results of the scattering properties and the RTE in cases of small mean diameter and large variance of the particle size distribution. We compared the RTE-results for the Henyey-Greenstein (conventional) function with those for the phase function using the DST. The RTE-results differ between both functions at low volume fractions for forward scattering media, suggesting the limitation of the conventional function.

Single-cell computational analysis of light harvesting in a flat-panel photo-bioreactor

BACKGROUND

Flat-panel photo-bioreactors (PBRs) are customarily applied for investigating growth of microalgae. Optimal design and operation of such reactors is still a challenge due to complex non-linear combinations of various impact factors, particularly hydrodynamics, light irradiation, and cell metabolism. A detailed analysis of single-cell light reception can lead to novel insights into the complex interactions of light exposure and algae movement in the reactor.

RESULTS

The combined impacts of hydrodynamics and light irradiation on algae cultivation in a flat-panel PBR were studied by tracing the light exposure of individual cells over time. Hydrodynamics and turbulent mixing in this air-sparged bioreactor were simulated using the Eulerian approach for the liquid phase and a slip model for the gas phase velocity profiles. The liquid velocity was then used for tracing single cells and their light exposure, using light intensity profiles obtained from solving the radiative transfer equation at different wavelengths. The residence times of algae cells in defined dark and light zones of the PBR were statistically analyzed for different algal concentrations and sparging rates. The results indicate poor mixing caused by the reactor design which can be only partially improved by increased sparging rates.

CONCLUSIONS

The results provide important information for optimizing algal biomass productivity by improving bioreactor design and operation and can further be utilized for an in-depth analysis of algal growth by using advanced models of cell metabolism.

Filtered maximum likelihood expectation maximization based global reconstruction for bioluminescence tomography

The reconstruction of bioluminescence tomography (BLT) is severely ill-posed due to the insufficient measurements and diffuses nature of the light propagation. Predefined permissible source region (PSR) combined with regularization terms is one common strategy to reduce such ill-posedness. However, the region of PSR is usually hard to determine and can be easily affected by subjective consciousness. Hence, we theoretically developed a filtered maximum likelihood expectation maximization (fMLEM) method for BLT. Our method can avoid predefining the PSR and provide a robust and accurate result for global reconstruction. In the method, the simplified spherical harmonics approximation (SP_N) was applied to characterize diffuse light propagation in medium, and the statistical estimation-based MLEM algorithm combined with a filter function was used to solve the inverse problem. We systematically demonstrated the performance of our method by the regular geometry- and digital mouse-based simulations and a liver cancer-based in vivo experiment. Graphical abstract The filtered MLEM-based global reconstruction method for BLT.