Sodium (23Na) plays a critical role in all organisms – it is crucial in cellular homeostasis, pH regulation and action potential propagation in muscle and neuronal fibres. Healthy cells have a low intracellular 23Na and high extracellular concentration, with the sodium-potassium pump maintaining this sodium gradient. In the human brain approximately 50% of its total energy consumption is occupied by maintenance of this gradient, demonstrating the pump’s importance in health. A failure of the sodium-potassium pump leads to cellular apoptosis and ultimately necrosis, with potentially disastrous results for neurological function. Magnetic resonance imaging (MRI) of 23Na is of great interest because of the ubiquity of sodium in cellular processes. However, it is hampered by many technical challenges. Among these are a low gyromagnetic ratio, short T2∗ relaxation times, and low concentrations all of which lead to long acquisitions in order to account for the poor inherent signal. In addition, 23Na MRI requires specialized hardware, non-standard pulse sequences and reconstruction methods in order to create images. These have all contributed to render clinical applications for 23Na MRI virtually non-existent, despite research indicating sodium’s role in various neurological disorders, including multiple sclerosis, Alzheimer’s, stroke, cancer, and traumatic brain injury. This work is motivated by a desire to use 23Na MRI in clinical settings. To that end, hardware and software methods were initially developed to process sodium images. In order to quantify the imaging system the point-spread function (PSF) and the related modulation transfer function (MTF) were calculated with the aid of a 3D-printed resolution phantom with different 23Na concentrations in gelatin. Two pulse sequences, density-adapted projection reconstruction (DA-3DPR) and Fermat looped orthogonally encoded trajectories (FLORET), with similar acquisition times were tested. Reconstructions were performed with the non-uniform fast Fourier transform. Results indicated a full-width, half-maximum (FWHM) value of 1.8 for DA-3DPR and 2.3 for FLORET. In a follow-up study, simulation experiments were added to various sodium phantom concentrations in 3% agar. The simulations indicated high potential variability in the MTF calculations depending on the methodology, while the phantom experiments found a FWHMs of 2.0 (DA-3DPR), and 2.5 (FLORET). Diffusion tensor imaging (DTI) is an MRI technique with wide adoption for the assessment of a variety of neurological disorders. Combining DTI with 23Na MRI could provide novel insight into brain pathology; however, a study with a healthy population is warranted before examinations with other populations. Fifteen subjects were scanned with DTI and sodium MRI, and the latter was used to derive voxel-wise tissue sodium concentration (TSC). Regional grey and white matter (WM) TSC was analyzed and compared to fractional anisotropy (FA) and cerebrospinal fluid (CSF) proximity. Results indicated that WM voxels proximal to CSF regions (i.e. corpus callosum) could have lower than expected FA values and higher measured TSC, with an inverse correlation between TSC and distance to CSF. This is likely the result of the broad PSF of 23Na MRI, as regions distal to CSF did not exhibit this phenomenon. This potentially represents a confounding effect when interpreting sodium concentrations, especially in regions proximal to the high 23Na content in CSF. / Thesis / Doctor of Philosophy (PhD)

In the past two decades, Fluorescence microscopy has imparted tremendous impact in Biology and Imaging. Several super-resolution Fluorescence imaging techniques (e.g. PALM, STED, STORM, 4Pi and structured illumination) have enabled diff raction-unlimited imaging. But high resolution is limited to a depth of few tens of microns. Thus, deep tissue imaging and simultaneous volume imaging have become a highly sought after feature in Fluorescence microscopy. The research work in this thesis address these issues by using spatial filtering techniques to tailor the point spread function (PSF) which uniquely characterizes the optical sys-tem. The advantage of this approach lies in the fact that intricate details about the focal region can be computed and designed with the help of well established theory and experimentation. In particular, this technique was applied to both spherical and cylindrical lenses. The former was used to generate Bessel-like, non-diffracting beams which demonstrated the ability to penetrate deep inside tissue-like media and thereby yielded an imaging depth of nearly 650μm as compared to about 200μm for a state-of-the-art confocal microscope. The latter gave rise to light-sheet and it's extended version that is ideal for planar imaging at large penetration depths. Another development is the generation of multiple light-sheet illumination pattern that can simultaneously illuminate several planes of the specimen. The proposed multiple light-sheet illumination microscopy (MLSIM) technique may enable volume imaging in Fluorescence microscopy. The first two chapters of this thesis are introductory in nature and provides a general overview of the principles of Fluorescence microscopy and three state-of-the-art Fluorescence imaging techniques; namely confocal, multi-photon and light-sheet based microscopy. Confocal microscopes are widely considered as a standard tool for biologists and this discussion shows that even though they have made signi ficant contributions in the fields of biophysics, biophotonics and nanoscale imaging, their inability to achieve better penetration depth has prevented their use in thick, scattering samples such as biological tissue. The system PSF of a confocal microscope broadens as it goes deeper in-side a scattering sample resulting in poor-resolution thereby destroying the very concept of high resolution, noise-free imaging. Additionally, confocal microscopy suffers from in-creased photo-bleaching due to o -layer (above and below the focal plane) excitation and low temporal resolution since it requires point-by-point scanning mechanism. On the other hand, multi-photon microscopy offers several advantages over confocal microscopy such as reduced photo-bleaching and inherent optical sectioning ability, however, it still lacks in providing high temporal resolution. Light-sheet based microscopy have gained popularity in recent years and promises to deliver high spatio-temporal resolution with minimized photo-bleaching. Recently, a considerable amount of research has been dedicated to further develop this promising technique for a variety of applications. The ability to look deeper inside a biological specimen has profound implications. How-ever, at depths of hundreds of microns, several effects (such as scattering, PSF distortion and noise) deteriorates the image quality and prohibits detailed study of key biological phenomenon. Chapter 3 of this thesis describes the original research work which experimentally addresses to this issue. Here, Bessel-like beam is employed in conjugation with an orthogonal detection scheme to achieve imaging at large penetration depth. Bessel beams are penetrative, non-di ffracting and have self-reconstruction properties making them a natural choice for imaging scattering prone specimens which are otherwise inaccessible by other microscopy imaging techniques such as, Widefield, CLSM, 4PI, Structural illumination microscopy and others. In this case such a Bessel-like beam is generated by masking the back-aperture of the excitation objective with a ring-like spatial filter. The proposed excitation scheme allow continuous scanning by simply translating the detection optics. Additionally, only a pencil-like region of the specimen can be illuminated at a given instance thereby reducing premature photobleaching of neighboring regions. This illumination scheme coupled with orthogonal detection shows the ability of selective imaging from a desired plane deep inside the specimen. In such a configuration, the lateral resolution of the illumination arm determines the axial resolution of the overall imaging system. Such an imaging system is a boon for obtaining depth information from any desired specimen layer that includes nano-particle tracking in thick tissue. Experiments performed by imaging the Fluorescent polymer tagged-CaCO3 particles and yeast cell in a tissue-like gel-matrix demonstrates penetration depth that extends up to 650 m. This will advance the field of fluorescence imaging microscopy and imaging. Similar to the ability to observe deep inside a sample, simultaneous 3D monitoring of whole specimens play a vital role in understanding many developmental process in Biology. At present, light-sheet based microscopy is the prime candidate amongst the various microscopy techniques, that is capable of providing high signal-to-background-ratio as far as planar imaging is concerned. Since spatial filtering technique was found to successfully give rise to novel features (such as large penetration depth) in a fluorescence microscope setup, a logical extension would be to implement a similar approach with a light-sheet based microscope setup. These implementations are discussed in Chapter 4 of this thesis where spatial filtering is employed with cylindrical lenses. For facilitating computational and experimental studies, a vectorial formalism was derived to give an explicit computable integral solution of the electric field generated at the focal region of a cylindrical lens. This representation is based on vectorial diffraction theory and further enables the computation of the point spread function of a cylindrical lens. Commonly used assumptions are made in the derivation such as no back-scattering and negligible contribution from evanescent fields. Stationary phase approximation along with the Fresnel transmission coefficients are employed for evaluating the polarization dependent electric field components. Computational studies were carried out to determine the polarization effects and calculate the system resolution. Experimental comparison of light-sheet intensity pro les show good agreement with the theoretical calculations and hence validate the model. This formalism was derived as a first step since it gives the essential understanding of tightly focused E-fields of a high N.A. cylindrical lens systems and thereby helps in further understanding the effect of spatial filtering. As the next step, generation of extended light-sheet for fluorescence microscopy is pro-posed by introducing a specially designed double-window spatial filter at the back-aperture of a cylindrical lens. The filter allows the light to pass through the periphery and center of a cylindrical lens. When illuminated with a plane wave, the proposed filter results in an extended depth-of-focus along with side-lobes which are due to other interferences in the transverse focal plane. Computational studies show a maximum extension of light-sheet by 3:38 times for single photon excitation, and 3:68 times for multi-photon excitation as compared to state-of-art single plane illumination microscopy (SPIM) system and essentially implies a larger field of view. Finally, generation of multiple light-sheet pattern is proposed and demonstrated using a different spatial filter placed at the back aperture of a cylindrical lens. A complete imaging setup consisting of multiple light-sheets for illumination and an orthogonal detection arm, is implemented for volume imaging in fluorescence microscopy. This proposed scheme is a single shot technique that enables whole volume imaging by simultaneously exciting multiple specimen layers. Experimental results confirm the generation of multiple light-sheets of thickness 6:6 m with an inter-sheet spacing of 13:4 m. Imaging of 3 5 m sized fluorescently coated Yeast cells (encaged in Agarose gel-matrix) is per-formed and conclusively demonstrates the usefulness and potential of multiple light-sheet illumination microscopy (MLSIM) for volume imaging. As part of the future scope of the research work presented in this thesis, the Bessel-beam based improved depth microscopy technique may attract applications in particle tracking deep inside tissues and optical injection apart from fluorescence imaging applications. The vectorial formalism derived for cylindrical lens can be used to predict other, complex optical setups involving cylindrical lenses. Extended light-sheet generation proposed in this work by using appropriate spatial filtering with a cylindrical lens, complements the existing and popular selective plane illumination microscopy technique and may facilitate the study of large biological specimens (such as, full-grown Zebra sh and tissue) with high spatial resolution and reduced photobleaching. Finally, the MLSIM technique presented in this thesis may accelerate the field of developmental biology, cell biology, fluorescence imaging and 3D optical data storage.

Tato diplomová práce se zabývá modelováním bodové rozptylové funkce (point spread function, PSF) u skenovacího transmisního elektronového mikroskopu (STEM). Nejprve je provedena teoretická rešerše, kde jsou popsány všechny důležitě aspekty, potřebné k následnému modelování. Je tedy proveden základní popis konstrukce přístroje a určeny jeho klíčové komponenty, které mají hlavní vliv na tvar výsledné PSF. Následně jsou popsány hlavní zobrazovací vady, které ovlivňují výslednou PSF. Ty jsou popsány z hlediska vlnové optiky. Na základě toho je pak navržen a zrealizován poměrně přesný model PSF u mikroskopu STEM. Poté je vytvořeno GUI, které umožňuje plné využití daného vytvořeného modelu. Na závěr je získaný model otestován na modelových a reálných datech, pomocí metody Lucy-Richardson.