Dana Henry Brooks


Gilead Tadmor, Deniz Erdogmus, Robert S. MacLeod, John K. Triedman

Date of Award


Date Accepted


Degree Grantor

Northeastern University

Degree Level


Degree Name

Doctor of Philosophy

Department or Academic Unit

College of Engineering. Department of Electrical and Computer Engineering.


Differential Geometry, Dynamical Systems, Electrocardiography, Inverse Problems, Manifold Learning, Mathematical Optimization


Biomedical | Electrical and Computer Engineering


Bioelectric signals such as the electrocardiogram (ECG) and electroencephalogram (EEG) often contain important information about both the biophysics and the physiological state of the underlying organs. Thus understanding the physical and physiological reasons for changes in these signals is important in both science and medicine, and methods for the analysis and imaging of their dynamics are of significant ongoing interest. In this thesis we present algorithmic approaches that exploit the dynamical properties in the ECG signals, and to a lesser extent EEG as well. We leverage ideas from differential geometry and optimization theory to model the signals as lying on trajectories confined by their biophysical origins to a subset of the space in which the measured signals reside. These trajectories can be characterized by the spatio-temporal properties of the signals. First, characterizing these geometric subsets as smooth manifolds, we apply Laplacian eigenmaps—an established manifold learning method from the machine learning literature—to these data, along with several extensions which we have developed expressly to relate the learned low-dimensional dynamic structure to the underlying physiological behavior without specifying an explicit dynamical model. We concentrate primarily on ECG signals, but also present examples of the methods applied to EEG data containing frequent episodes of interictal epileptic spiking.

In the remainder of the thesis, we apply dynamic analysis to the inverse problem of electrocardiography—the problem of imaging parameters of cardiac electrical sources from electrical measurements on the body surface, given a model of the intervening torso volume conductor. This problem is ill-posed and requires regularization to achieve stable solutions. We present methods for each of the two most common formulations of this problem. The first method extends current approaches which estimate the potentials on the outer surfaces of the cardiac ventricles (the epicardium)—potential-based inverse ECG—to also estimate potentials on the inner surface (endocardium), which are more challenging to recover from the body surface but arguably of greater medical importance. We do so while using a less precise model of the subject's thorax geometry, compared to standard methods, constructed from a reduced set of acquired CT slices augmented by a coarse morphing of a single standardized anatomical model. The key innovation is a non-linear low-order temporal model of the signal trajectories. We present results from clinical measurements taken during a catheter-based endocardial pacing procedure and show that we can recover the pacing location with accuracy and stability comparable to recent reports for epicardial pacing with a full set of thoracic CT images. Addressing the second formulation, activation-based inverse ECG, in which cardiac electrical function during the QRS complex is parameterized by the activation times of equivalent electrical sources, we present a convex relaxation of the associated non-convex optimization problem and use it to study the uncertainty of solutions to the original problem, including those caused by violated model assumptions.

Document Type


Rights Information

copyright 2013

Rights Holder

Burak Erem

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