Lorraine Olson

Fusion of body surface potential and body surface Laplacian signals for electrocardiographic imaging

Various approaches to the solution to the inverse problem of electrocardiography have been proposed over the years. Recently, the use of inverse algorithms using measured body surface Laplacians has been proposed, and in various studies this technique has been shown to outperform the traditional use of body surface potentials in certain model problems. In this paper, we compare the use of body surface potentials and body surface Laplacians on two model problems with different assumed cardiac sources. For the spherical cap model problems with an anterior source, the epicardial estimates using body surface potentials had smaller average relative errors than when body surface Laplacians were used. For the spherical cap model problems with a posterior source, the epicardial estimates using body surface potential or body surface Laplacian sensors generally produced similar relative errors. For the radial dipole model, the epicardial estimates using body surface Laplacians had smaller errors than when body surface potentials were used. We introduce a fusion algorithm that combines the different types of signals and generally produces a good estimate for both model problems.

Optimization of wear-resistant coating architectures using finite element analysis

The goal of this work was to develop an approach for the design of multilayer coatings with enhanced toughness to fracture and improved adhesion for wear-resistant applications. Finite element analysis (FEA) was utilized to investigate the distribution of stress in single layer, bilayer and multilayer films under combined normal and tangential loads. Two-dimensional models were created for single layer CrN and Cr2N films and for a number of multilayer combinations of Cr, CrN and Cr2N layers. The FEA results were validated for uncoated solids through comparison with analytical solutions for Hertzian contacts, with and without frictional effects. A good fit was observed in all cases. Then the influence of film architecture and substrate material on the mechanical stress within the films was studied. It was determined that metallic layers had significantly lower σxx stress than ceramic layers, while both σyy and τxy stress within the layers was largely independent of the layer material. Simulation data was t...

The Steady Inverse Heat Conduction Problem: A Comparison of Methods With Parameter Selection

In the past we have developed the Generalized Eigensystem (GES L ) techniques for solving inverse boundary value problems in steady heat conduction, and found that these vector expansion methods often give superior results to those obtained with standard Tikhonov regularization methods. However, these earlier comparisons were based on the optimal results for each method, which required that we know the true solution to set the value of the regularization parameter (t) for Tikhonov regularization and the number of mode clusters (N clasters ) for GES L . In this paper we introduce a sensor sensitivity method for estimating appropriate values of N clusters for GES L . We compare those results with Tikhonov regularization using the Combined Residual and Smoothing Operator (CRESO) to estimate the appropriate values of t

A new method for incorporating weighted temporal and spatial smoothing in the inverse problem of electrocardiography

In this paper, we present a method for incorporating temporal smoothing (TS) into the estimate of epicardial potentials from body surface potential data. Our algorithm employs a different spatial smoothing parameter, chosen by the composite residual error and smoothing operator criteria, at each time step in the sequence. The total spatial smoothing term is then simply partitioned between temporal and spatial smoothing. The algorithm appears to be quite robust with regard to this partitioning. The new method was evaluated in the setting of additive Gaussian noise, but otherwise realistic conditions of body geometry and reference epicardial potentials. In examining the match between estimated and measured electrograms, or the match between estimated isopotential maps and measured isopotential maps, the estimates constructed using the new TS algorithm produced consistently smaller relative errors than those constructed using a quasi-static (QS) algorithm or those constructed by postprocessing the QS estimate with a moving average filter.

Numerical simulation of an inverse method for tumour size and location estimation

Manual breast exams are widely used for early detection of breast cancer. These exams rely heuristically on the significant stiffness (elastic modulus) difference between cancerous tissue and normal tissue. We wish to systematize this approach by developing an inverse technique which is capable of inferring the elastic modulus throughout the breast tissue based on the application of known surface forces. In this study, we proposed appropriate inverse computational algorithms and examined their performance on two-dimensional model problems. Finite element methods were used to model the tissue response for the forward problem–solving for the surface tissue displacements for a given forcing function. A variety of tumour locations were assumed, and ‘measured results’ were created with numerical noise added to simulate measurement errors. A genetic algorithm was then developed to solve the inverse problem–given the measured surface displacements, what is the distribution of tissue material properties within the breast? We developed an eigenvector expansion technique to create effective force test patterns for use in concert with the genetic algorithm. A series of test cases at various noise levels for a coarse and a fine mesh were examined. When a tumour was present, a tumour was always detected. When a tumour was absent, the algorithm always correctly reported no cancer.

Estimation of tool/chip interface temperatures for on-line tool monitoring: an inverse problem approach

We examine a steady inverse heat transfer problem that arises in online machine tool monitoring: identifying tool/chip interface temperatures from remote sensor measurements. The matrix equations relating the sensor temperatures and sensor fluxes to the prediction surface (tool/chip interface) temperatures are obtained by finite element methods. Truncated singular value decomposition, a standard inverse technique, is used as a baseline for comparing the inverse solutions. We also develop a new set of inverse approaches, vector projection inverse methods, specifically for this problem. Inverse solutions are computed with all methods for two temperature profiles and various noise levels. Because of the extreme ill-conditioning of the problem, only two coefficients can be obtained reliably for all of the inverse approaches examined. Truncated singular value decomposition does not perform well, but two of the new methods are robust and give reasonable accuracy. Combining data from temperature and flux sensors (data fusion) is far more effective than using temperature sensors alone, and with data fusion the inverse can be computed robustly with information from only four sensor locations.

Comments on "Fusion of body surface potential and body surface Laplacian signals for electrocardiographic imaging"

D.B. Geselowitz and J. Ferrara comment on a paper by R.D. Throne and L.G. Olson which was published in ibid., vol.47, p. 452-62 (2000). Throne and Olson reply to these comments. The discussion concerns the use of a spherical model and a body surface Laplacian in the solution of the electrocardiographic inverse problem and the influence of noise.

Improved Inverse Solutions for On-Line Machine Tool Monitoring

The identification of tool/chip interface temperatures from remote sensor measurements is a steady inverse heat transfer problem that arises in online machine tool monitoring. In a previous paper we developed a set of inverse approaches, vector projection inverse methods, specifically for this problem. These methods rely on two types of sensor measurements: temperatures and heat fluxes. However, because of the extreme ill-conditioning of the tool configuration we studied previously, only a very limited amount of information could be obtained using any of the inverse approaches examined. In an effort to understand the impact of physical parameters on the conditioning of the problem we examined two modifications to the simulated cutting tool: we increased the thermal conductivity of the tool insert, and we reduced the thickness of the tool insert. Inverse solutions were computed on both configurations with all methods for two temperature profiles and various noise levels. The estimated tool/chip interface temperature for the high conductivity tool showed no improvement compared to the original configuration, since the temperature profiles on the sensor surface were unchanged. However, for the thinner tool, the estimated temperatures were substantially more accurate than with the original configuration. With this thinner tool configuration, an optimal set of four sensors could be used to estimate these temperatures at the tool/chip interface to within a few degrees, even with noisy sensor data.

An Inverse Problem Approach to Stiffness Mapping for Early Detection of Breast Cancer

Early detection of breast cancer will continue to be crucial in improving patient survival rates. Our ultimate goal is to develop a system that automates, quantifies and enhances the resolution of the manual breast exam. In this study, we examine computational techniques which use breast surface force and deflection measurements to create detailed maps of the elastic modulus of the interior of the breast tissue. This approach is a reformulation of our earlier two-dimensional technique to make it more practical and we extend the approach to three dimensions. Finite element methods were used to model the tissue response (reaction force and surface displacements) to applied surface indentations. A variety of test cases with assumed tumour locations were defined, and ‘measured results’ were created. Numerical noise was added to these simulated measurements at two noise levels. A genetic algorithm was developed to identify the distribution of tissue material properties within the breast given the ‘measured’ reaction forces and surface displacements. For our two- and three-dimensional model problems, tumours as small as 1 cm could be detected reliably at a signal-to-noise ratio of 23 dB.

Estimates of Endocardial Potentials from Non-contact Intracavitary Probes

The EnSitetrade intracavitary probe system developed by Endocardial Solutions, Inc (St. Jude Medical, St. Paul, MN) was used to simultaneously record geometric information, probe potentials, and selected endocardial potentials within the right atria for four patients. Tikhonov regularization was then used to estimate endocardial potentials from probe measurements for each patient at each endocardial site. The correlation coefficients and relative errors between the estimated potentials and the measured endocardial potentials were then calculated. This inverse problem was quite ill-conditioned, and first-order Tikhonov regularization performed better than zero-order or second-order Tikhonov regularization in producing stable and accurate results. In choosing the regularization parameter mu, a constant value of mu=0.3 performed as well as CRESO and maximum curvature, which pick a different mu for each time instant