Doctor of Philosophy, The Ohio State University, 2021, Biomedical Engineering

Lung cancer is leading cause of cancer-related deaths in the United States with 5-year survival rate of 18.6%. This is due to late detection of lung cancer and problems in screening for lung cancer. Indeterminate pulmonary nodules (IPNs) are pulmonary nodules size between 7-20mm diameter solid nodules. 90% of IPNs are incidentally found and they are hard to diagnosis due to their small size and current diagnosis methods such as CT, PET scans and biopsy involve high exposure to radiation or invasive and could lead to complications. The majority of lung cancer patients have non-small cell lung cancer (NSCLC) and 64% of these patients exhibit driver mutations such as epithelial growth factor receptor (EGFR), anaplastic lymphoma kinase (ALK) and Ras mutations. These patients have shown to have improved survival rate if they are treated with targeted therapies directed against the driver mutations. Although these patients initially show strong response to targeted therapies, most patients develop resistance to these targeted treatments through secondary point mutation and epithelial to mesenchymal transition (EMT). The lung is a dynamic organ where alveolar epithelial cells are normally exposed to significant mechanical forces (i.e. ~8% cyclic strain, transmural pressure and shear stress) while primary lung tumor cells experience a 40-fold decrease in these mechanical forces/strain. Although biomechanical factors in the tumor microenvironment have been shown to be a significant driver of cancer progression, there is limited information about how biophysical forces alters drug sensitivity in lung adenocarcinoma cells. Based on the known importance of mechanical forces/strain on lung injury and repair and the significant difference in cyclic strain applied to normal and cancer cells in the lung, we hypothesized that cyclic mechanical strain would activate important oncogenic pathways and alter drug sensitivity. Although local mechanical properties of the lung tumor may (open full item for complete abstract)

MS, University of Cincinnati, 2017, Engineering and Applied Science: Mechanical Engineering

This study develops a polygonal finite element solver for 2-D crack propagation simulation along with a meshing algorithm which creates necessary polygonal mesh. The work starts with a brief literature review of historical development of computational fracture mechanics. After reviewing multiple methods employed for modeling fracture problems, Wachspress formulation is selected for constructing the polygonal finite element solver. Polygonal interpolants are developed using Wachspress' framework and validated using published results. A polygonal meshing algorithm is also developed since conventional finite element meshers do not support domain meshing using higher order polygons. The meshing algorithm is then used to create the mesh and input files for the polygonal finite element solver. The polygonal solver is validated using conventional patch tests. The accuracy and convergence of the method is assessed using classical solid mechanics problems with known analytical solutions. Next, ability to include cracks geometrically is added to the meshing algorithm. The polygonal solver is updated with crack tracking and remeshing capability. A fracture problem is solved using the developed subroutines.

Doctor of Engineering, Cleveland State University, 2014, Washkewicz College of Engineering

The cornea is the outermost layer of the human eye where the tissue meets with the external environment. It provides the majority of the eye's refractive power and is the most important ocular determinant of visual image formation. The refractive power of the cornea derives from its shape, and this shape is a function of the ocular biomechanical properties and loading forces such as the intraocular pressure (IOP). With having the majority of refractive power in the eye, the cornea is the primary tissue of interest for refractive intervention. Globally, the predominant mode of surgical treatment of refractive disorders is photoablation. However, optical power regression over time and under/over correction due to neglected corneal biomechanical properties were still observed following refractive procedures including LASIK, PRK, Astigmatic Keratotomy etc especially at high degree corrections. Also, some evolving procedures such as corneal collagen crosslinking (CXL), a collagen stiffening procedure most commonly performed through UVA photoactivation of riboflavin in the corneal stroma, currently lack surgical guidance for optimizing visual outcomes. Thus, there is a need for methods that explore the patient specific treatment planning strategies for refractive procedures. This work will have a potential impact in translating mechanical principles into corneal surgical planning in order to provide a better guidance and predictive environment to the corneal surgeons. The goals of this thesis are three fold: 1) To develop patient specific models from clinical LASIK cases and to compare the outcomes of these models with clinical outcomes in a patient population. 2) To simulate investigational procedures that utilize CXL. 3) To advance a potential approach to characterize corneal mechanical properties in vivo.

PhD, University of Cincinnati, 0, Engineering and Applied Science: Mechanical Engineering

Accurate prediction of structural responses under combined, extreme environments often involves a wide range of spatial and temporal scales. In the traditional analysis of structural response problems, time dependent problems are generally solved using a semi-discrete finite element method. These methods have difficulty simulating high frequency ranges, long time durations, and capturing sharp gradients and discontinuities. Some limitations include time step constraints or a lack of convergence. The space-time finite element method based on time-discontinuous formulation extends the discretization into the temporal domain and is able to address some of these concerns. The constraints on the time-step are relaxed and the method has had some success in accurately capturing sharp gradients and discontinuities. For applications featured by multiscale responses in both space and time, the regular space-time finite element method is unable to capture the full spectrum of the response. An enriched space-time finite element method is proposed based on a coupled space-time approximation. Enrichment is introduced into the space-time framework based on the extended finite element method (XFEM). The effects of continuous enrichment functions are explored for high frequency wave propagation. Previous works are based primarily on enrichment in time. Numerical solvers are developed and benchmarked for the space-time system on high-performance platform. The method's robustness is demonstrated by convergence studies using energy error norms. Improvements are observed in terms of the convergence properties of the enriched space-time finite element method over the traditional space-time finite element method for problems with fine scale features. As a result, enrichment may be considered an alternative to mesh refinement. The numerical instability associated with the high condition number of the enriched space-time analogous stiffness matrices is studied. The factors affecting the (open full item for complete abstract)

MS, University of Cincinnati, 2012, Engineering and Applied Science: Mechanical Engineering

Space-time finite element method provides a robust and accurate alternative to the traditional FEM based on semi-discrete schemes due to its extended capability in establishing approximations in both space and time. The extended capability, however, requires the simultaneous discretization of spatial and temporal domains. This subsequently results in a system of equations that is considerably larger in size than those obtained in the standard finite element formulation. In general, solving equations generated based on the space-time formulation requires substantially more computing time. In some cases, it becomes a bottle neck for practical implementation due to the large number of degrees of freedom. There is thus a need to explore ways to accelerate the procedure for finding a solution to the system of equations in the space-time method. With the recent developments in the use of Graphics Processing Units (GPUs) for general purpose parallel computations (GPGPU), an effort is made in this thesis to explore the possibility of developing a GPU based solver for the space-time finite element method to accelerate the computation. A two-step approach is taken: In the first step, the GPU version of the direct solver based on LAPACK and a preconditioned conjugate gradient method are tested for systems of linear equations involving both dense and sparse matrices. Both methods are shown to significantly accelerate the process of finding the solution. Subsequently, the developed GPU-based algorithms are implemented on the system of linear equations obtained from space-time FEM and enriched space-time FEM. It is reported that GPU-based implementation yields significant speed up. Based on these implementations, it is concluded that the GPU-based system could serve as an effective platform for the space-time method.

PhD, University of Cincinnati, 2011, Engineering and Applied Science: Mechanical Engineering

Multiscale methods based on coupled atomistic-continuum representations have received significant attention in recent years due to their unique approach in balancing accuracy with efficiency for a wide spectrum of problems in solid mechanics. Examples include dislocation-originated plasticity, fracture, shear band localization and many others. Motivated by these advances, a concurrent simulation approach employing the space-time finite element method and molecular dynamics (MD) is developed in this dissertation with a focus on lattice dynamics and fracture. A space-time version of MD is initially proposed based on the time discontinuous Galerkin space-time finite element method. In the multiscale simulations, MD is coupled with coarse scale space-time finite element simulation based on a coarse grained material model. For the numerical approximation, standard space-time shape functions are augmented with enrichment function(s) based on the problem physics by exploiting the partition of unity concept. With the appropriate enrichment function(s), fine scale physics such as phonons and fractures can be represented in the coarse scale simulation in spatial and temporal scales. The two simulations can employ different time steps; the unconditional stability of the method makes selection of a large time step possible. Coupling between the simulations is achieved with the introduction of a projection operator and bridging scale treatment. The proposed approach is first employed to solve lattice dynamics with a focus on wave propagation. It is shown that a reflectionless interface at the atomistic-continuum simulation interface is achieved. The enriched continuum simulation retains all the atomistic level details and is able to transmit this information to another distinct atomistic region within the domain resulting in an energy conserving simulation method. The method is applied to systems with both linear and nonlinear potentials. An important feature of this approach (open full item for complete abstract)

Doctor of Philosophy, The Ohio State University, 2007, Electrical Engineering

This dissertation presents a domain decomposition method as an effective and efficient preconditioner for frequency domain FEM solution of geometrically complex and electrically large electromagnetic problems. The method reduces memory requirements by decomposing the original problem domain into several non-overlapping and possibly repeatable sub-domains. At the heart of this research are the Robin-to-Robin map, the “cement” finite element coupling of non-conforming grids and the concept of duality paring. The Robin's transmission condition is employed on interfaces between adjacent sub-domains to enforce continuity of electromagnetic fields and to ensure the sub-domain problems are well-posed. Through the introduction of cement variables, the meshes at the interface could be non-conformal which significantly relaxes the meshing procedures. By following the spirit of duality paring a symmetric system is obtained to better reflect physical nature of the problem. These concepts in conjunction with the so-called finite element tearing and interconnecting algorithm form the basic modules of the present domain decomposition method. To enhance the convergence of DDM solver, the Krylov solvers instead of classical stationary solvers are employed and studied. In order to account the radiation condition exactly thus eliminating spurious reflection, a boundary element formulation is hybridized with the present DD method, also through the aforementioned novel concepts. One of the special cases of present hybridization is the well known hybrid finite element and boundary element method. It will be shown that the proposed hybrid offers simultaneously: (1) symmetry, (2) modularity, (3) non-conformity between FEM and BEM domains, (4) free of internal resonance, and (5) natural and effective preconditioning scheme that guarantees spectral radius less or equal to one. Lastly this dissertation presents a DDM solution scheme for analyzing electromagnetic problems involving multiple se (open full item for complete abstract)

Master of Science (MS), Ohio University, 1999, Mechanical Engineering (Engineering)

Formulation of steady-state and transient potential problems using boundary elements

Master of Science, The Ohio State University, 2007, Graduate School

Master of Science, The Ohio State University, 2007, Graduate School

Master of Science, The Ohio State University, 2008, Graduate School

Master of Science, The Ohio State University, 2005, Graduate School

Master of Science, The Ohio State University, 2005, Graduate School

Master of Science, The Ohio State University, 2008, Graduate School

Master of Science, The Ohio State University, 2007, Graduate School

Master of Science, The Ohio State University, 2005, Graduate School

Master of Science, The Ohio State University, 2006, Graduate School

Master of Science, The Ohio State University, 2005, Graduate School

Master of Science, The Ohio State University, 2005, Graduate School

Master of Arts (MA), Bowling Green State University, 2024, Mathematics/Scientific Computation

This thesis investigates one-dimensional elliptic and parabolic interface problems characterized by both nonlinear and linear jump conditions. We develop weak formulations for these equations and employ computational methods, including the Galerkin Finite Element Method and the $s-$ method for approximation. Our analysis addresses the uniqueness and existence of solutions for elliptic problems with linear interface jump conditions, as well as the well-posedness and convergence of parabolic equations with both linear and nonlinear interface jump conditions. Additionally, we explore the steady-state solutions achievable for the parabolic problem. Numerical solutions are presented to demonstrate the accuracy and effectiveness of our approach.