Linearized conductivity reconstructions and ecg imaging
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Authors
Wilcox, Christopher , Donald
Issue Date
2024-05
Type
Electronic thesis
Thesis
Thesis
Language
en_US
Keywords
Mathematics
Alternative Title
Abstract
During the cardiac cycle, cells in the heart undergo a process of depolarization and repolarization which cause the chambers in the heart to contract and relax pushing blood through the heart and out to the lungs to be oxygenated and pushing oxygenated blood from the lungs to the rest of the body. The change in polarization is described by a current density that results in an electric potential that we can measure on the body's surface. The problem of determining the heart's electrical activity using measurements made on the body's surface is the problem of Electrocardiography (ECG). The problem has largely been studied using fixed approximations to the conductivity distribution in a person's chest. Conductivity changes in time are often overlooked such as the change in conductivity due to blood flow and air movement. To measure these effects, we can use data taken from an Electrical Impedance Tomography (EIT) system. EIT is an imaging method by which electrical currents are applied on the body's surface using a set of electrodes and the resulting voltages are measured. The goal of EIT is to be able to image the conductivity in a region of the body to identify structures or derive some information about the physiological activity that is happening in a specific area. Up to now, the ability to use EIT and ECG data to solve the problem of electrocardiography has been limited due to the speed at which EIT systems are able to collect data as well as the need for two separate systems to collect each type of data. However, the development of the ACT5 system allows us to simultaneously measure EIT and ECG data at a speed of approximately 27 images per second and a sampling frequency of 864 Hz. A typical cardiac cycle lasts around 0.8 seconds which means we can use the reconstructed conductivity distribution from the EIT data at approximately 21 instances in time to help solve the ECG problem. This thesis describes both the forward and inverse problems of EIT and ECG. Because the inverse EIT problem is ill-posed, we want to determine the best current patterns that allow one to produce the most informative images. We begin by looking at the stability and resolution of the linearized conductivity reconstruction algorithm using two common current patterns, trigonometric and dipole, applied in a two-dimensional circular setting using the Complete Electrode Model. This study extends a previous study done by David Dobson and Fadil Santosa that showed that the trigonometric patterns were more stable and offered more resolution when using the point electrode model. Next we look at the forward and inverse problems of Electrocardiography and how choices in boundary conditions, conductivity, and source modelling affect the accuracy of our reconstructions using a set of simulations. Finally, by showing that the conductivity has a non-negligible effect on the reconstruction of the heart's current sources, we motivate the EIT and ECG problem and show how we can develop an algorithm that can be applied to human subjects.
The results obtained from the subject data show how boundary effects and conductivity influence the path of the total cardiac vector, or the total current produced by the heart, over a single cardiac cycle. When analyzing the path we see clusters of small magnitude vectors that correspond to atrial depolarization, a ring of large magnitude vectors that correspond to ventricular depolarization and a well-defined loop of moderate magnitude vectors that correspond to ventricular repolarization. We also look at using multiple dipole sources to describe the electrical activity of the heart and how using multiple dipole sources can improve our ability to reproduce a partial body surface map. To help interpret the results, this data is presented alongside an approximated lead II electrocardiogram and partial body surface map interpolated from the voltages measured by the ACT5 system.
Description
May2024
School of Science
School of Science
Full Citation
Publisher
Rensselaer Polytechnic Institute, Troy, NY