Search

A study is presented of the significant issues encountered in the modeling and characterization of uncertainties in the parameters of hysteretic nonlinear systems that are subjected to deterministic excitations. A single-degree-of-freedom system, with bilinear hysteretic characteristics, is employed to investigate the propagation of uncertainties in the dominant parameters that control the idealized restoring force associated with such a system. Random variations are introduced in the nominal value of each of the dominant parameters. Monte Carlo simulation approaches are used to generate a large, statistically significant, ensemble of time history records that are subsequently used to determine the distribution of the corresponding transient response and establish the probabilistic bounds on the response time history. The restoring force method is used to determine the power-series coefficients that define an approximating surface that characterizes the system behavior. The statistics of the identified coefficients are determined and shown to provide a powerful tool for quantifying the level and features of the uncertainty in the nonlinear system. Furthermore, it is shown that the general methodology presented allows the estimation through analytical procedures of the uncertain system's response bounds when it is excited by a different dynamic load than the one used to identify it.

A novel modular multiplatform software tool was developed for display, registration and fusion of cardiac electrophysiology (EP) voltage data with PET/SPECT cardiac images and their polar maps. The EP voltage measurements were acquired at discrete locations on the endocardial surface by a catheter-based electroanatomic mapping system as part of left ventricular tachycardia ablation procedures. These data were output as a list of voltages and 3-D mapping system coordinates. PET/SPECT data were 3-D short axis perfusion or viability images and derived polar maps. CardioViewer allows GUI menu-driven data input and display of EP and PET/SPECT data as well as their fusion in orthogonal slice, point cloud and polar map views. The software development environment was C++ using Qt Creator IDE, Open GL, ITK, freeglut and dicomlib. The modular program architecture facilitated addition of new functionalities and CardioViewer has been successfully run on Linux, Windows and Apple operating systems. Initial registration of EP and PET/SPECT datasets was achieved with user-input control points, after which the six degrees of freedom registration parameters could be interactively adjusted. EP voltage and PET/SPECT values can be output at matched polar map locations, which avoids regional averaging of tissue properties. CardioViewer is being used to investigate local prediction of EP tissue categories from PET/SPECT images. An example ROC analysis using Tl-201 SPECT data is provided.

A study is presented to develop and assess the utility of some data analysis and representation tools that are useful for dealing with complex nonlinear systems that simultaneously involve aleatory (intrinsic) and epistemic (modeling) uncertainties. A representative uncertain nonlinear system is employed to quantify the interaction effects between model-parameter uncertainty and modeling errors in hysteretic nonlinear systems under random excitation. A single-degree-of-freedom system with bilinear hysteretic characteristics is used to investigate the propagation of uncertainties in the dominant parameters that control the idealized restoring force associated with such a system: the yield level, the stiffness in the ‘elastic range’, and the stiffness in the ‘yielded range’. Monte Carlo simulation approaches are used to generate a large, statistically significant, ensemble of time history records that are subsequently used to determine the distribution of the corresponding transient response, and establish the probabilistic bounds on the response time history. The Restoring Force Method is used to determine the power-series coefficients that define an equivalent, approximating surface that characterizes the system behavior. The statistics of the identified coefficients are determined and shown to provide a powerful tool for quantifying the level of uncertainty in the nonlinear system, as well as providing a means for interpreting the significant features of the underlying complex nonlinear behavior. It is shown that the general methodology presented for representing and propagating the effects of uncertainties in complex nonlinear systems through the use of model-free representation, allows the estimation through analytical procedures of the uncertainty bounds on the transient response of the uncertain system when excited by a different dynamic load than the one used to identify it. Copyright © 2009 John Wiley & Sons, Ltd.

One of the main purposes in computational anatomy is the measurement and statistical study of anatomical variations in organs, notably in the brain or the heart. Over the last decade, our group has progressively developed several approaches for this problem, all related to the Riemannian geometry of groups of diffeomorphisms and the shape spaces on which these groups act. Several important shape evolution equations that are now used routinely in applications have emerged over time. Our goal in this paper is to provide an overview of these equations, placing them in their theoretical context, and giving examples of applications in which they can be used. We introduce the required theoretical background before discussing several classes of equations of increasingly complexity. These equations include energy minimizing evolutions deriving from Riemannian gradient descent, geodesics, parallel transport and Jacobi fields.