Light propagation from fluorescent probes in biological tissues by coupled time-dependent parabolic simplified spherical harmonics equations

We introduce a system of coupled time-dependent parabolic simplified spherical harmonic equations to model the propagation of both excitation and fluorescence light in biological tissues. We resort to a finite element approach to obtain the time-dependent profile of the excitation and the fluorescence light fields in the medium. We present results for cases involving two geometries in three-dimensions: a homogeneous cylinder with an embedded fluorescent inclusion and a realistically-shaped rodent with an embedded inclusion alike an organ filled with a fluorescent probe. For the cylindrical geometry, we show the differences in the time-dependent fluorescence response for a point-like, a spherical, and a spherically Gaussian distributed fluorescent inclusion. From our results, we conclude that the model is able to describe the time-dependent excitation and fluorescent light transfer in small geometries with high absorption coefficients and in nondiffusive domains, as may be found in small animal diffuse optical tomography (DOT) and fluorescence DOT imaging

Three-Dimensional Quantitative Cerenkov Luminescence Imaging

Cerenkov luminescence imaging (CLI) is an up-and-coming optical technique for in vivo imaging of beta-emitting radioisotopes. CLI relies on measurements of the Cerenkov radiation emitted when high-energy beta-particles travel through tissue. Compared to the well-established methods for radionuclide imaging, SPECT and PET, CLI has a potentially higher throughput for superficial measurements. The detection device used for CLI, usually a CCD, is in general cheaper and more flexible than the gamma cameras required for SPECT and PET. As the Cerenkov radiation is emitted in the UV-NIR range the imaging capabilities of CLI is however very depth limited. In this work a forward model for the emission and propagation of Cerenkov radiation induced by beta-particles originating from radioactive decay is presented. From the forward model an inverse model for the reconstruction of the radioisotope’s distribution is formulated. The models has been tested with both simulated data and measurements from in vitro phantom studies. Good results has been observed for the forward model as well as reconstructions based on simulated data. Reconstruction from the experimental measurements has however proven difficult

Formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium

Background: The bioluminescent enzyme firefly luciferase (Luc) or variants of green fluorescent protein (GFP) in transformed cells can be effectively used to reveal molecular and cellular features of neoplasia in vivo. Tumor cell growth and regression in response to various therapies can be evaluated by using bioluminescent imaging. In bioluminescent imaging, light propagates in highly scattering tissue, and the diffusion approximation is sufficiently accurate to predict the imaging signal around the biological tissue. The numerical solutions to the diffusion equation take large amounts of computational time, and the studies for its analytic solutions have attracted more attention in biomedical engineering applications. Methods: Biological tissue is a turbid medium that both scatters and absorbs photons. An accurate model for the propagation of photons through tissue can be adopted from transport theory, and its diffusion approximation is applied to predict the imaging signal around the biological tissue. The solution to the diffusion equation is formulated by the convolution between its Green's function and source term. The formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium can be obtained to accelerate the forward simulation of bioluminescent phenomena. Results: The closed form solutions have been derived for the time-dependent diffusion equation and the steady-state diffusion equation with solid and hollow spherical sources in a homogeneous medium, respectively. Meanwhile, the relationship between solutions with a solid sphere source and ones with a surface sphere source is obtained. Conclusion: We have formulated solutions for the diffusion equation with solid and hollow spherical sources in an infinite homogeneous medium. These solutions have been verified by Monte Carlo simulation for use in biomedical optical imaging studies. The closed form solution is highly accurate and more computationally efficient in biomedical engineering applications. By using our analytic solutions for spherical sources, we can better predict bioluminescent signals and better understand both the potential for, and the limitations of, bioluminescent tomography in an idealized case. The formulas are particularly valuable for furthering the development of bioluminescent tomography

Modelling Light Transport Through Biological Tissue Using the Simplified Spherical Harmonics Approximation

Optical Tomography is a medical imaging modality that can be used to non- invasively image functional changes within the body. As near-infrared light is highly scattered by biological tissue, the process of image reconstruction is ill-posed and, in general is also under-determined. As such, model based iterative image reconstruction methods are used. These methods require an accurate model of light propagation through tissue, also known as the forward model. The diffusion approximation (DA) to the radiative transport equation is one of the most widely used forward models. It is based on the assumption that scattering events dominate over absorption events resulting in a diffuse light distribution. This is valid in cases with low absorption coefficients or large geometries (greater than a few scattering lengths). In many cases, however, such as in small animal imaging where the source-detector separation is small, this assumption is not valid and so a higher-ordered approximation is required. In this thesis, a three-dimensional frequency domain forward model based on the simplified spherical harmonics (SPN) approximation to the radiative transport equation is introduced. By comparison with a Monte- Carlo model, the SPN approximation is shown to be more accurate than the DA, especially in regions near to the sources and detectors and the increase in accuracy is greater in cases with stronger absorption. This is particularly important for bioluminescent imaging of small animals which involve both small geometries and strong absorption. Due to the asymptotic nature of the 3 SPN approximation, the highest ordered model was not necessarily the most accurate, but all models with N>1 were more accurate than the DA. The SPN based forward model has also been implemented into an image reconstruction algorithm. Despite the fact that the SPN approximation does not combine the scattering coefficient and anisotropy factor into a single variable, as is the case in the DA, it was found that it is not possible to reconstruct them uniquely. The SPN based models were shown to be able to reconstruct optical maps with greater accuracy than the DA. However, due to the increased number of unknowns to be recovered, the SP7 based reconstructed images contained significant artefact and cross-talk. Finally, a SPN-Diffusion hybrid model was developed in which the SPN model was used in the regions near to the source and the DA elsewhere. This model provides the increase of accuracy of the SPN models in the regions where the DA is insufficient, whilst retaining the computational efficiency of the DA. It was shown that the hybrid model leads to increased accuracy not only in the regions solved using the SPN model, but also in the DA based regions where as in a pure DA model, the errors near the source were propagated throughout the domain. It is also shown that the hybrid model can be solved in half the time of the full SPN model

Reconstruction methods for single-shot diffractive imaging of free nanostructures with ultrashort x-ray and XUV laser pulses

With x-ray and XUV single-shot diffractive imaging on free nanoparticles it is possible to investigate structure and shape of the particles. The scattering image of the nanoparticle only contains the intensity distribution but not the phase of the scattered light. Thus, numerical methods are required to infer information from experimental data. In the thesis, different reconstruction methods are implemented, advanced and applied to different scattering scenarios to characterize diffraction patterns for different laser parameters, reconstruct optical properties and 3d shapes of nanotargets.Mit Einzelschussmessungen an freien Nanoteilchen mit Hilfe von Röntgenstrahlung ist es möglich, die Teilchenstruktur zu untersuchen. Damit die Information aus Experimenten gewonnen werden kann, sind numerische Methoden notwendig, da das Streubild der Nanoteilchen nur die Inensitätsverteilung des gestreuten Lichtes, aber nicht die Phase bereitstellt. Es werden verschiedene Rekonstruktionsmethoden implementiert, weiterentwickelt und auf verschiedene Streuszenarien angewandt, um Streubilder für verschiedene Laserparameter zu charakterisieren, optische Eigenschaften und 3D-Formen zu rekonstruieren

Model for quantitative tip-enhanced spectroscopy and the extraction of nanoscale-resolved optical constants

Near-field infrared spectroscopy by elastic scattering of light from a probe tip resolves optical contrasts in materials at dramatically sub-wavelength scales across a broad energy range, with the demonstrated capacity for chemical identification at the nanoscale. However, current models of probe-sample near-field interactions still cannot provide a sufficiently quantitatively interpretation of measured near-field contrasts, especially in the case of materials supporting strong surface phonons. We present a model of near-field spectroscopy derived from basic principles and verified by finite-element simulations, demonstrating superb predictive agreement both with tunable quantum cascade laser near-field spectroscopy of SiO$_2$ thin films and with newly presented nanoscale Fourier transform infrared (nanoFTIR) spectroscopy of crystalline SiC. We discuss the role of probe geometry, field retardation, and surface mode dispersion in shaping the measured near-field response. This treatment enables a route to quantitatively determine nano-resolved optical constants, as we demonstrate by inverting newly presented nanoFTIR spectra of an SiO$_2$ thin film into the frequency dependent dielectric function of its mid-infrared optical phonon. Our formalism further enables tip-enhanced spectroscopy as a potent diagnostic tool for quantitative nano-scale spectroscopy.Comment: 19 pages, 9 figure

Photoacoustic imaging in biomedicine

Photoacoustic imaging (also called optoacoustic or thermoacoustic imaging) has the potential to image animal or human organs, such as the breast and the brain, with simultaneous high contrast and high spatial resolution. This article provides an overview of the rapidly expanding field of photoacoustic imaging for biomedical applications. Imaging techniques, including depth profiling in layered media, scanning tomography with focused ultrasonic transducers, image forming with an acoustic lens, and computed tomography with unfocused transducers, are introduced. Special emphasis is placed on computed tomography, including reconstruction algorithms, spatial resolution, and related recent experiments. Promising biomedical applications are discussed throughout the text, including (1) tomographic imaging of the skin and other superficial organs by laser-induced photoacoustic microscopy, which offers the critical advantages, over current high-resolution optical imaging modalities, of deeper imaging depth and higher absorptioncontrasts, (2) breast cancerdetection by near-infrared light or radio-frequency–wave-induced photoacoustic imaging, which has important potential for early detection, and (3) small animal imaging by laser-induced photoacoustic imaging, which measures unique optical absorptioncontrasts related to important biochemical information and provides better resolution in deep tissues than optical imaging