Department of Physics

Glioblastoma multiforme (GBM) is an aggressive and highly resistant brain tumour, necessitating advanced treatment approaches to improve patient outcomes. This thesis provides a comprehensive review of recent advancements in GBM treatment, including innovations in treatment planning, radiation therapy, and their impacts on patient survival. The study also involves a detailed analysis of five GBM patients, examining critical dosimetric and radiobiological parameters, including Dose Volume Histogram, CT and MRI Images, T1, T2, T3 and T4 images. These parameters are analyzed using key radiobiological models, such as the linear-quadratic model, and factors like α/β, dose per fraction, and survival fractions. Through this data analysis, the study aims to evaluate the effectiveness of the treatment protocols and their impact on tumour control probability (TCP) and normal tissue complication probability (NTCP). The results will contribute to the understanding of GBM radiotherapy outcomes and provide insights for optimizing future treatment strategies.

We propose an approach to the quantization of the interior of a Schwarzschild black hole, represented by a Kantowski-Sachs (KS) framework, by requiring its covariance under a notion of residual diffeomorphisms. We solve for the family of Hamiltonian constraint operators satisfying the associated covariance condition, in addition to parity covariance, preservation of the Bohr Hilbert space of Loop Quantum KS and a correct (naïve) classical limit. We further explore imposing minimality of the number of terms, and compare the solution with other Hamiltonian constraints proposed for Loop Quantum KS in the literature, with special attention to a most recent case. In addition, we discuss a lapse commonly chosen to decouple the evolution of the two degrees of freedom of the model, yielding exact solubility of the model, and we show that such choice can indeed be quantized as an operator densely defined on the Bohr Hilbert space, but must include an infinite number of shift operators. Also, we show the reasons why we call the classical limit “naïve”, and point this out as a reason for one limitation of some present prescriptions.

This study presents two significant investigations in the field of proton therapy, leveraging advanced Monte Carlo simulations to improve our understanding and modeling of proton beam characteristics and secondary particle dynamics. The first investigation centers on the development and validation of a Monte Carlo model tailored for the single-room Varian ProBeam pencil beam scanning system. The study begins with an in-depth simulation analysis to justify the selection of the "g4h-phy_QGSP_FTFP_BERT" physics list configuration for our TOPASSFPTI model, developed using the TOPAS 3.9 tool with a Geant4 base, version 10.07.p03. Comprehensive verification against clinical measurements in a water phantom demonstrated the accuracy of the model. A comparative analysis between the TOPASSFPTI model and a previously published TOPAS model for the Varian ProBeam system at Emory Proton Therapy Center (TOPASEmory) revealed distinct differences in the beam characteristics. Notably, the TOPASSFPTI model exhibited a closer alignment with the specific beam characterization at SFPTI, showing a strong consistency in beam energy spread (σE) and integrated depth dose distributions (IDDs), with a 98-100% agreement under 2%/2 mm γ-index criteria. Differences in lateral spot sizes were observed, with the TOPASSFPTI model showing slightly larger spot sizes compared to TOPASEmory, which aligns more closely with SFPTI’s clinical setup. Additionally, the calibration of absolute dose values indicated significant differences in the number of protons per monitor unit (MU) between the TOPASSFPTI and the clinical treatment planning system (TPS) data, with the TOPASSFPTI model consistently showing higher values.

Dynamical systems play a pivotal role across various scientific domains, encompassing disciplines from physics to biology and engineering. The long-term behavior of these systems hinges on the structure of their attractors, with many exhibiting multistability characterized by multiple minimal attractors. Understanding the structure of these attractors and their corresponding basins is a central theme in dynamical systems theory.
In recent years, machine learning algorithms have emerged as potent tools for clustering, prediction, and modeling complex data. By harnessing the capabilities of neural networks along with techniques from topological data analysis, in particular persistence homology, we can construct surrogate models of system asymptotics. This approach also allows for the decomposition of phase space into polygonal regions and the identification of plausible attracting neighborhoods, facilitating homological Conley index computation at reduced computational expense compared to current methods. Through various illustrative examples, we demonstrate that sufficiently low training loss yields constructed neighborhoods whose homological Conley indices aligns with a priori knowledge of the dynamics.

In the current world of fast-paced data production, statistics and machine learning tools are essential for interpreting and utilizing the full potential of this data. This dissertation comprises three studies employing statistical analysis and Convolutional Neural Network models. First, the research investigates the genetic evolution of the SARS-CoV-2 RNA molecule, emphasizing the role of epistasis in the RNA virus’s ability to adapt and survive. Through statistical tests, this study validates the significant impacts of genetic interactions and mutations on the virus’s structural changes over time, offering insights into its evolutionary dynamics. Secondly, the dissertation explores medical diagnosis by implementing Convolutional Neural Networks to differentiate between lung CT-scans of COVID-19 and non-COVID patients. This portion of the research demonstrates the capability of deep learning to enhance diagnostic processes, thereby reducing time and increasing accuracy in clinical settings. Lastly, we delve into gravitational wave detection, an area of astrophysics requiring precise data analysis to identify signals from cosmic events such as black hole mergers. Our goal is to utilize Convolutional Neural Network models in hopes of improving the sensitivity and accuracy of detecting these difficult to catch signals, pushing the boundaries of what we can observe in the universe. The findings of this dissertation underscore the utility of combining statistical methods and machine learning models to solve problems that are not only varied but also highly impactful in their respective fields.

Quantum tetrahedron is a key building block in the theory of Loop Quantum Gravity (LQG) and plays a crucial role in the boundary states of the spinfoam amplitude of LQG. In LQG with vanishing cosmological constant, the physical Hilbert space of the quantum at tetrahedron is the 4-valent SU(2) intertwiner space labeled by irreducible representation, each assigned to a face of the quantum at tetrahedron. Furthermore, the space is the solution space of the quantum at closure condition. The area spectrum of each face of the quantum at tetrahedron is discrete and is characterized by a spin label. Classically, the correspondence between a set of solutions of at closure condition and at tetrahedron is guaranteed by the Minkowski theorem. This theorem has been generalized to the curved case, where a curved closure condition applies. The curved Minkowski theorem allows us to reconstruct homogeneously curved tetrahedra (spherical or hyperbolic tetrahedra) from a family of four SU(2) holonomies that satisfy the curved closure condition Although the quantization of the closure condition for a at tetrahedron has been extensively studied in LQG, the quantization of the curved closure condition and curved tetrahedron has not been explored yet. The homogeneously curved tetrahedron has played an important role in the recent construction of the spinfoam model with cosmological constant in 3+1 dimensional LQG. It is anticipated that the quantization of a curved tetrahedron should deFIne the building block for the boundary Hilbert space of the spinfoam model.

Though general relativity (GR) is proven to be a successful theory in describing the macroscopical nature of our universe, it still has several problems to be resolved. One of them is known as the time problem of GR. GR is a pure constraint theory, and the time evolution of the system is a gauge transformation, without carrying any physical information. One potential resolution to this issue is the relational formalism, which considers the dynamics of a material frame by coupling it to gravity. This approach allows for constructing gauge invariant observables and subsequent quantization.
One realization of the relational formalism is the Brown-Kuchaˇr formalism. In this formalism, the gravity couples Brown-Kuchaˇr dust fields, and the Brown-Kuchaˇr dust fields play the roles as a family of observers. Then, one can introduce a gauge fixing scheme to the system and construct gauge invariant observables (Dirac observables) in the reduced phase Space. The probe time of the dust plays the role as the physical time of each point of the spacetime. In this thesis, we consider the Brown-Kuchaˇr formalism in an asymptotically flat background. A set of boundary conditions for the asymptotic flatness are formulated for Dirac observables on the reduced phase space. We compute the boundary term of the physical Hamiltonian, which is identical to the ADM mass. We construct a set of the symmetry charges on the reduced phase space, which encompass both the bulk terms and the boundary terms are conserved by the physical Hamiltonian evolution. The symmetry charges generate transformations preserving the asymptotically flat boundary conditions. Under the reduced-phase space Poisson bracket, the symmetry charges form an infinite dimensional Lie algebra AG after adding a central charge. A suitable quotient of AG is analogous to the BMS algebra at spatial infinity by Henneaux and Troessaert.

Dose uniformity in the Planning Target Volume (PTV) can induce a higher-than-expected dose distribution in the nearby critical organs. The goal of this study is to evaluate the influence of the Planning Target volume dose uniformity on the surrounding critical organs (OAR).
Ten cases of anonymized patients’ data were selected for our study including: Breast cancer, Brain cancer, Head and Neck cancer, Lung and Prostate calculations of Conformity indices, Biological Effective Doses (BED), Tumor Control Probability (TCP) and Normal Tissue Complication Probability (NTCP) were used to calculate the dose distribution in PTV as well as the dose delivered to the surrounding critical organs of each PTV. We assume that the tumors PTVs have homogeneous density as well as the surrounding normal tissue.
Conformity indices (CI) for Breast (PTV) are between 1.8 – 1.9, for Brain (PTV) are between 1.6 – 2.0, for Lungs are 1.5 – 1.6, for Prostate are between 0.4 – 0.5, for Head and Neck are 0.3 – 0.4. Dose uniformity in all the PTVs is 1.089 which is a good indication of the quality of treatment delivered to the tumor. TCP is averaging of value of 87.94 and NTCP is 3.4445.

Acute pH sensitivity of many neural mechanisms highlights the vulnerability of neurotransmission to the pH of the extracellular milieu. The dogma is that the synaptic cleft will acidify upon neurotransmission because the synaptic vesicles corelease neurotransmitters and protons to the cleft, and the direct data from sensory ribbon-type synapses support the acidification of the cleft. However, ribbon synapses have a much higher release probability than conventional synapses, and it’s not established whether conventional synapses acidify as well. To test the acidification of the cleft in the conventional synapse, we used genetically encoded fluorescent pH reporters targeted to the synaptic cleft of Drosophila larvae. We observed alkalinization rather than acidification during activity, and this alkalinization was dependent on the exchange of protons for calcium at the postsynaptic membrane.
A reaction-diffusion computational model of the pH dynamics at the Drosophila larval neuromuscular junction was developed to leverage the experimental data. The model incorporates the release of glutamate, ATP, and protons from synaptic vesicles into the cleft, PMCA activity, bicarbonate, and phosphate buffering systems. By means of numerical simulations, we reveal a highly dynamic pH landscape within the synaptic cleft, harboring deep but exceedingly rapid acid transients that give way to a prolonged period of alkalinization.

Intensity modulated proton beam scanning therapy allows for highly conformal dose distribution and better sparing of organ-at-risk compared to conventional photon radiotherapy, thanks to the characteristic dose deposition at depth, the Bragg Peak (BP), of protons as a function of depth and energy. However, proton range uncertainties lead to extended clinical margins, at the expense of treatment quality. Prompt Gamma (PG) rays emitted during non- elastic interactions of proton with the matter have been proposed for in-vivo proton range tracking. Nevertheless, poor PG statistics downgrade the potential of the clinical implementation of the proposed techniques. We study the insertion of the nonradioactive elements 19F, 17O, 127I in a tumor area to enhance the PG production of 4.44 MeV (P1) and 6.15 MeV (P2) PG rays emitted during proton irradiation, both correlated with the distal fall-off of the BP. We developed a novel Monte Carlo (MC) model using the TOPAS MC package. With this model, we simulated incident proton beams with energies of 75 MeV, 100 MeV and 200 MeV in co-centric cylindrical phantoms. The outer cylinder (scorer) was filled with water and the inner cylinder (simulating a tumor region inside water-equivalent body) was filled with water containing 0.1%–20% weight fractions of each of the tested elements.