Author's School

School of Engineering & Applied Science

Author's Department/Program

Electrical and Systems Engineering

Language

English (en)

Date of Award

5-24-2010

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Chair and Committee

Arye Nehorai

Abstract

In this dissertation, we develop a novel mathematical framework for modeling and analyzing uterine contractions using biomagnetic measurements. The study of myometrium contractility during pregnancy is relevant to the field of reproductive assessment. Its clinical importance is grounded in the need for a better understanding of the bioreproduction mechanisms. For example, in the last decade the number of preterm labors has increased significantly. Preterm birth can cause health problems or even be fatal for the fetus if it happens too early, and, at the same time, it imposes significant financial burdens on health care systems. Therefore, it is critical to develop models and statistical tools that help to monitor non-invasively the uterine activities during pregnancy. We derive a forward electromagnetic model of uterine contractions during pregnancy. Existing models of myometrial contractions approach the problem either at an organ level or lately at a cellular level. At the organ level, the models focus on generating contractile forces that closely resemble clinical measurements of normal intrauterine pressure during contractions in labor. At the cellular level, the models focus on predicting the changes of ionic concentrations in a uterine myocyte during a contraction, and, as a consequence, on modeling the transmembrane potential evolution as a function of time. In this work, we propose an electromagnetic modeling approach taking into account electrophysiological and anatomical knowledge jointly at the cellular, tissue, and organ levels. Our model aims to characterize myometrial contractions using magnetomyography: MMG) and electromyography: EMG) at different stages of pregnancy. In particular, we introduce a four-compartment volume conductor geometry, and we use a bidomain approach to model the propagation of the myometrium transmembrane potential on the human uterus. The bidomain approach is given by a set of reaction-diffusion equations. The diffusion part of the equations governs the spatial evolution of the transmembrane potential, and the reaction part is given by the local ionic current cell dynamics. Here we introduce a modified version of the Fitzhugh-Nagumo: FHN) equation for modeling ionic currents in each myocyte, assuming a plateau-type transmembrane potential. We incorporate the anisotropic nature of the uterus by considering conductivity tensors in our model. In particular, we propose a general approach to design the conductivity-tensor orientation and to estimate the conductivity-tensor values in the extracellular and intracellular domains for any uterine shape. We use finite element methods: FEM) to solve our model, and we illustrate our approach by presenting a numerical example to model a uterine contraction at term. Our results are in good agreement with the values reported in the experimental technical literature, and these are potentially important as a tool for helping in the characterization of contractions and for predicting labor. We propose an automatic, robust, single-channel statistical detector of uterine MMG contractions. One common restriction of previous techniques is that algorithm parameters, such as the detection threshold and the window length of analysis need to be calibrated experimentally, based on a particular data set. Therefore, the detection performance might change from patient to patient, for example, because of differences in the pregnancy stage and tissue conductivities. In contrast, the proposed algorithm does not require the use of a sliding window of analysis, and the detection threshold is determined analytically; thus, it does not need to be calibrated. Our detection algorithm consists of two stages: In the first stage, we segment the measurements using a multiple change-point estimation algorithm and assuming a piecewise constant time-varying autoregressive model of the measurements; In the second stage, we apply the non-supervised K-means cluster algorithm to classify each time segment, using the RMS and FOZC as candidate features. As a result a discrete-time binary decision signal is generated indicating the presence of a contraction. Moreover, since each single channel detector provides local information regarding the presence of a contraction, we propose a spatio-temporal estimator of the magnetic activity generated by uterine contractions. The algorithm, when evaluated with real MMG measurements, detects uterine activity much earlier than the patient begins to sense it. It also enables visualizing the relative location of the origin of uterine contraction and quantifying the amount of energy delivered during a contraction. These results are important in obstetrics, e.g., as a tool for helping to characterize contractions and to predict labor. For the aforementioned problem of multiple change-point estimation, a class of one-dimensional segmentation, we also compute fundamental mathematical results for minimal bounds on mean-square error estimation. Indeed, if an estimator is available, the evaluation of its performance depends on knowing whether it is optimal or if further improvement is still possible. In our segmentation problem the parameters are discrete therefore the conventional Cramer-Rao bound does not apply. Hence, we derive Barankin-type lower bounds, the greatest lower bound on the covariance of any unbiased estimator, which are applicable to discrete parameters. The computation of the bound is challenging, as it requires finding the supremum on a finite set of symmetric matrices with respect to the Loewner ordering, which is not a lattice order. Therefore, we discuss the existence of the supremum, propose a minimal upper-bound by using tools from convex geometry, and compute closed-form solutions for the Barankin information matrix for several distributions. The results have broad biomedical applications, such as DNA sequence segmentation, MEG and EEG segmentation, and uterine contraction MMG detection, and they also have applications for signal segmentation in general, such as speech segmentation and astronomical data analysis.

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Permanent URL: http://dx.doi.org/10.7936/K7V122V4

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