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Single Particle Tracking (SPT) plays an important role in the study of physical and dynamic properties of biomolecules moving in their native environment. To date, many algorithms have been developed for localization and parameter estimation in SPT. Though the performance of these methods is good when the signal level is high and the motion model simple, they begin to fail as the signal level decreases or model complexity increases. In addition, the inputs to the SPT algorithms are sequences of images that are cropped from a large data set and that focus on a single particle. This motivates us to seek machine learning tools to deal with that initial step of extracting data from larger images containing multiple particles. This thesis makes contributions to both data extraction question and to the problem of state and parameter estimation. First, we build upon the Expectation Maximization (EM) algorithm to create a generic framework for joint localization refinement and parameter estimation in SPT. Under the EM-based scheme, two representative methods are considered for generating the filtered and smoothed distributions needed by EM: Sequential Monte Carlo - Expectation Maximization (SMC-EM), and Unscented - Expectation Maximization (U-EM). The selection of filtering and smoothing algorithms is very flexible so long as they provide the necessary distributions for EM. The versatility and reliability of EM based framework have been validated via data-intensive modeling and simulation where we considered a variety of influential factors, such as a wide range of {\color{red}Signal-to-background ratios (SBRs)}, diffusion speeds, motion blur, camera types, image length, etc. Meanwhile, under the EM-based scheme, we make an effort to improve the overall computational efficiency by simplifying the mathematical expression of models, replacing filtering/smoothing algorithms with more efficient ones {\color{purple} (trading some accuracy for reduced computation time)}, and using parallel computation and other computing techniques. In terms of localization refinement and parameter estimation in SPT, we also conduct an overall quantitative comparison among EM based methods and standard two-step methods. Regarding the U-EM, we conduct transformation methods to make it adapted to the nonlinearities and complexities of measurement model. We also extended the application of U-EM to more complicated SPT scenarios, including time-varying parameters and additional observation models that are relevant to the biophysical setting. The second area of contribution is in the particle detection and extraction problem to create data to feed into the EM-based approaches. Here we build Particle Identification Networks (PINs) covering three different network architectures. The first, \PINCNN{}, is based on a standard Convolutional Neural Network (CNN) structure that has previously been successfully applied in particle detection and localization. The second, \PINRES, uses a Residual Neural Network (ResNet) architecture that is significantly deeper than the CNN while the third, \PINFPN{}, is based on a more advanced Feature Pyramid Network (FPN) that can take advantage of multi-scale information in an image. All networks are trained using the same collection of simulated data created with a range of SBRs and fluorescence emitter densities, as well as with three different Point Spread Functions (PSFs): a standard Born-Wolf model, a model for astigmatic imaging to allow localization in three dimensions, and a model of the Double-Helix engineered PSF. All PINs are evaluated and compared through data-intensive simulation and experiments under a variety of settings. In the final contribution, we link all above together to create an algorithm that takes in raw camera data and produces trajectories and parameter estimates for multiple particles in an image sequence.

<p> Advances in robotics and information technology are leading to the development of virtual reality-based surgical simulators as an alternative to the conventional means of medical training. Modeling and simulation of medical procedures also have numerous applications in pre-operative and intra-operative surgical planning as well as robotic (semi)-autonomous execution of surgical tasks. </p> <p> Surgical simulation requires modeling of human soft-tissue organs. Soft-tissues exhibit geometrical and material nonlinearities that should be taken into account for realistic modeling of the deformations and interaction forces between the surgical tool and tissues during medical procedures. However, most existing work in the literature, particularly for modeling of cutting, use linear deformation models. In this thesis, modeling of two common surgical tasks, i.e. palpation and cutting, using nonlinear modeling techniques has been studied. The complicated mechanical behavior of soft-tissue deformation is modeled by considering both geometrical and material nonlinearities. Large deformations are modeled by employing a nonlinear strain measure, the Green-Lagrange strain tensor, and a nonlinear stress-strain curve is employed by using an Ogden-based hyperelastic constitutive equation. The incompressible property of soft-tissue material during the deformation is enforced by modifying the strain energy function to include a term that penalizes changes in the object's area/volume. The problem of simulating the tool-tissue interactions using nonlinear dynamic analysis is formulated within a total Lagrangian framework. The finite element method is utilized to discretize the deformable object model in space and an explicit time integration is employed to solve for the resulting deformations. </p> <p> In this thesis, the nonlinear finite element analysis with the Ogden-based constitutive equation has also been applied to the modeling of soft-tissue cutting. Element separation and node snapping are used to create a cut in the mesh that is close to the tool trajectory. The external force applied on the object along the tool direction is used as a physical cutting criterion. The possibility of producing degenerated elements by node snapping that can cause numerical instability in the simulation is eliminated by remeshing the local elements when badly shaped elements are generated. The remeshing process involves retriangulation of the local elements using the Delaunay function and/ or moving a node depending on what is needed in order to generate elements with the required quality. </p> <p> Extensive simulations have been carried out in order to evaluate and demonstrate the effectiveness of the proposed modeling techniques and the results are reported in the thesis. A two-dimensional object with a concentrated external force has been considered in the simulations. </p> / Thesis / Master of Applied Science (MASc)

The heart rate variability (HRV) signal has been employed as a measure of sympathovagal balance in the human autonomic nervous system (ANS). It is known that aging affects the functional characteristics of the ANS. It has been suggested that complexity as measured by nonlinear dynamical indices, decays with age. We developed several algorithms and test protocols to characterize nonlinear dynamics in the HRV signal and to test the hypothesis that aging reduces the complexity within the HRV signal. Continuous HRV signal was obtained from 93 healthy subjects (41 males and 52 females) ranging in age between 5 and 78 years under controlled laboratory conditions in supine state. Subjects were from pediatric (PED, 5-12 years, n=15, 9 male, 6 female), adolescent (ADO, 13-17 years, n=16, 6 male, 10 female), adult (ADL, 18-30 years, n=22, 12 male, 10 female), middle aged (MDA, 31-60 years, n=21, 8 male, 13 female) and elderly (ELD, 61+ years, n=19, 6 male, 13 female) age groups. The length of data was 1000 or more R-R intervals for adequate computation. Stationary Holter HRV data from these controls were also used for the present study. Our results are as follows: There is a continuous systematic decay in the power-law scaling (beta), which decreases from -1.162 ± 0.388 for the PED group to -1.95 ± 0.6 for the ELD group (F = 6.649, p < 0.001; R = 0.475, p < 0.001. Approximate entropy (ApEn) decreases with age from 1.456 ± 0.093 for the PED group to 1.272 ± 0.135 for the ELD group (F = 7.82, p < 0.001; R = 0.519, p < 0.001. The detrended fluctuation analysis (DFA) of short-term data yielded an increase in short-range DFA scaling exponent (alpha)1 from 0.774 ± 0.204 for the PED group to 1.138 ± 0.289 for the ELD group (F = 7.535, p < 0.001), and in long-range DFA scaling exponent (alpha)2 increased from 0.667 ± 0.082 for the PED group to 0.86 ± 0.172 for the ELD group (F= 4.841,p < 0.001). The detrended fluctuation analysis (DFA) of long-term data yielded an increase in short-range DFA scaling exponent (alpha)1 from 1.052 ± 0.218 for the PED group to 1.204 ± 0.205 for the ELD group (F = 1.922), and in long-range DFA scaling exponent (alpha)2 increased from 0.961 ± 0.081 for the PED group to 1.076 ± 0.102 for the ELD group (F = 4.06, p < 0.01). Surrogate data analysis demonstrated that the hypothesis that the HRV signal is generated by a linear stochastic process is not always rejected. In summary, the HRV signal lends itself to an analysis using nonlinear dynamical methods and studies in patients may yield useful clinical information in the future. / Thesis / Master of Engineering (ME)

Nonlinear optics is a field with new applications being regularly discovered, which leads to a growing interest in computing these properties. In this work, we attempt to determine new methods of computationally determining the properties of biologically relevant systems. We do so through testing a novel finite-field method to compute these properties. To facilitate the computation of molecular energies required for finite-field calculations, we tested a hypergeometric resummation scheme. Together, these projects form a strong step into being able to compute the nonlinear optical properties for larger systems of biological relevance. / Thesis / Master of Science (MSc)