No / We propose an efficient alternative to commonly used parametric surfaces such as NURBS surfaces for definition of complex geometry in shared virtual spaces. Our mathematical model allows to define objects by only providing coordinates of the section curves in 3-space. The resulting parametric functions allow fast calculation of the coordinates of the points on the surface of the objects. We devise an algorithm which evaluates the coefficients of these functions in real time. Given the small size of the resulting formulas and interactive rates for their calculation, we are able to efficiently use such PDE-based models for making virtual objects in shared virtual spaces. We describe the modeling framework and illustrate the proposed theoretical concepts with our function-based extension of VRML and X3D.

Pharmaceutical tablets have been the most dominant form for drug delivery and they need to be strong enough to withstand external stresses due to packaging and loading conditions before use. The strength of the produced tablets, which is characterised by their compressibility and compactibility, is usually deter-mined through a physical prototype. This process is sometimes quite expensive and time consuming. Therefore, simulating this process before hand can over-come this problem. A technique for shape modelling of pharmaceutical tablets based on the use of Partial Differential Equations is presented in this thesis. The volume and the sur-face area of the generated parametric tablet in various shapes have been es-timated numerically. This work also presents an extended formulation of the PDE method to a higher dimensional space by increasing the number of pa-rameters responsible for describing the surface in order to generate a solid tab-let. The shape and size of the generated solid tablets can be changed by ex-ploiting the analytic expressions relating the coefficients associated with the PDE method. The solution of the axisymmetric boundary value problem for a finite cylinder subject to a uniform axial load has been utilised in order to model a displace-ment component of a compressed PDE-based representation of a flat-faced round tablet. The simulation results, which are analysed using the Heckel model, show that the developed model is capable of predicting the compressibility of pharmaceutical powders since it fits the experimental data accurately. The opti-mal design of pharmaceutical tablets with particular volume and maximum strength has been obtained using an automatic design optimisation which is performed by combining the PDE method and a standard method for numerical optimisation.

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Thesis advisor: Charles Hoffman / The second messenger cyclic 3’-5’ adenosine monophosphate (cAMP) signaling pathway plays an important physiological role in many organisms. Cyclic nucleotide phosphodiesterases (PDEs) regulate signal transduction by catalyzing the hydrolysis of cAMP and cGMP allowing for the downregulation of cyclic nucleotide levels. Human PDEs are encoded by 21 genes grouped into 11 families. The biological role of the most recently discovered PDE family (PDE11) remains poorly understood partly due to the lack of selective inhibitors. Mutations in the PDE11A gene have been linked to a wide range of diseases, such as Cushing Syndrome, which is a result of inactivating mutations expressed in adrenocortical tumors. Meanwhile, PDE11 levels are seen to increase in the ventral hippocampus as a function of aging, and is associated with a loss of social memory. Thus, the development of a selective PDE11 inhibitor could provide a potential therapeutic benefit to patients receiving long-term corticosteroid treatment by stimulating cortisol production by the adrenal gland, as well as to aging adults to maintain social memory. To address these needs, candidate PDE11 inhibitors related to a compound discovered by the Hoffman lab in a high throughput screen for PDE11 inhibitors are being synthesized by the Rotella laboratory. I have been evaluating these compounds using two fission yeast-based growth assays in complement with in vitro enzyme assays carried out by Dr. Jeremy Eberhard. Here I describe my role in the project, leading to the identification of a compound, SMQ2-57, which is a selective inhibitor of the PDE11 enzyme whose potency has been confirmed through both yeast-based assays and in vitro enzyme assays. In addition, I have taken both a forward and reverse genetic approach to identify PDE11A4 mutant alleles that confer resistance to inhibitor compounds as such knowledge could guide a rational drug design approach to produce more effective PDE11 inhibitors. Based on our results, SMQ2-57 could serve as a useful tool in understanding the biological role of PDE11. Meanwhile, data from my study of compound resistant mutant PDE11 alleles should allow for the characterization of the physical interaction between PDE11 and its inhibitors in an effort to guide a medicinal chemistry program to develop a more potent and drug-like PDE11 inhibitor. / Thesis (BS) — Boston College, 2023. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: Scholar of the College. / Discipline: Biology.

In this two-part study, I investigated whether the cyclic-adenosine monophosphate response element-binding (CREB) protein has the potential to be clinically modulated as a therapeutic target for the treatment of neurodegenerative diseases. Part one consisted of a systematic review that was conducted on select articles gathered through a stepwise method to explore (1) the relationship between diseased, neurodegenerative brains and levels of active, phosphorylated CREB (pCREB), (2) increased activation of CREB as a treatment for neurodegenerative symptoms, and (3) a potential therapeutic drug for neurodegenerative diseases that can target CREB signaling. The results of the systematic review showed evidence that suggested excitotoxic concentrations of N-methyl-D-aspartate (NMDA) results in decreased pCREB levels, while decreased pCREB levels were associated with impaired cognition and behavior, increased cell death, as well as decreased CRE-gene transcription and long-term potentiation (LTP). Part two consisted of a systematic review and meta-analysis on clinical trials that used the phosphodiesterase type IV inhibitor, roflumilast, on healthy and schizophrenic patients. It was found that 100 µM roflumilast was able to improve verbal learning in healthy and schizophrenic subjects (ES = 64). Initial evidence indicates that future research on neurodegenerative diseases should further investigate CREB’s potential to be clinically modulated and research investigating PDE4 inhibitor drug therapy for the treatment of neurodegeneration should be expanded upon further in subsequent studies.

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Turbulent flows occur in various fields and are a central, yet an extremely complex, topic in fluid dynamics. Understanding the behaviour of fluids is vital for multiple research areas including, but not limited to: biological models, weather prediction, and engineering design models for automobiles and aircraft. In this thesis, we study a number of fundamental problems that arise in 2D turbulent flows, using the 2D Navier-Stokes system. Introducing optimization techniques for systems described by partial differential equations (PDE), we frame these problems such that they can be solved using computational methods. We utilize adjoint calculus to build the computational framework to be implemented in an iterative gradient flow procedure, using the "optimize-then-discretize" approach. Pseudospectral methods are employed for solving PDEs in a numerically efficient manner. The use of optimization methods together with computational mathematics in this work provides an illuminating perspective on fluid mechanics. We first apply these techniques to better understand enstrophy dissipation in 2D Navier-Stokes flows, in the limit of vanishing viscosity. By defining an optimization problem to determine optimal initial conditions, multiple branches of local maximizers were obtained each corresponding to a different mechanism producing maximum enstrophy dissipation. Viewing this quantity as a function of viscosity revealed quantitative agreement with an analytic bound, demonstrating the sharpness of this bound. We also introduce an extension of this problem, where enstrophy dissipation is maximized in the context of kinetic theory using the Boltzmann equation. Secondly, these PDE-constrained optimization techniques were used to probe the fundamental limitations on the performance of the Leith eddy-viscosity closure model for 2D Large-Eddy Simulations of the Navier-Stokes system. Obtained by solving an optimization problem with a non-standard structure, the results demonstrate the optimal eddy viscosities do not converge to a well-defined limit as regularization and discretization parameters are refined, hence the problem of determining an optimal eddy viscosity is ill-posed. Further extending the problem of finding optimal eddy-viscosity closures, we consider imposing an additional nonlinear constraint on the control variable in the problem, in the form of requiring the time-averaged enstrophy be preserved. To address this problem in a novel way, we employ adjoint calculus to characterize a subspace tangent to the constraint manifold, which allows one to approximately enforce the constraint. Not only do we demonstrate that this produces better results when compared to the case without constraints, but this also provides a flexible computational framework for approximate enforcement of general nonlinear constraints. Lastly in this thesis, we introduce an optimization problem to study the Kolmogorov-Richardson energy cascade, where a pathway towards solutions is outlined. / Thesis / Doctor of Philosophy (PhD)

No / Pharmaceutical tablets have been the most dominant form for drug delivery and most of them are used in the oral administration of drugs. These tablets need to be strong enough so that they can tolerate external stresses. Hence, during the design process, it is important to produce tablets with maximum mechanical strength while conserving the properties of powder form components. The mechanical properties of these tablets are assessed by measuring the tensile strength, which is commonly measured using diametrical or axial compression tests. This work describes the parametric design and optimisation of solid pharmaceutical tablets in cylindrical and spherical shapes, which are obtained using a formulation based on the use of Partial Differential Equations (PDEs) for shape design. The PDE-based formulation is capable of parameterised complex shapes using the information from some boundary curves that describe the shape. It is shown that the optimal design of pharmaceutical tablets with a particular volume and maximum strength can be obtained using an automatic design optimisation which is performed by combining the PDE method and a standard method for numerical optimisation.