Forward Electrophysiological Modeling and Inverse Problem for Uterine Contractions during Pregnancy
Date of Award
Doctor of Philosophy (PhD)
Uterine contractile dysfunction during pregnancy is a significant healthcare challenge that imposes heavy medical and financial burdens on both human beings and society. In the U.S., about 12% of babies are born prematurely each year, which is a leading cause of neonatal mortality and increases the possibility of having subsequent health problems. Post-term birth, in which a baby is born after 42 weeks of gestation, can cause risks for both the newborn and the mother. Currently, there is a limited understanding of how the uterus transitions from quiescence to excitation, which hampers our ability to detect labor and treat major obstetric syndromes associated with contractile dysfunction. Therefore, it is critical to develop objective methods to investigate the underlying contractile mechanism using a non-invasive sensing technique. This dissertation focuses on the multiscale forward electromagnetic modeling of uterine contractile activities and the inverse estimation of underlying source currents from abdominal magnetic field measurements.
We develop a realistic multiscale forward electromagnetic model of uterine contractions in the pregnant uterus, taking into account current electrophysiological and anatomical knowledge of the uterus. Previous models focused on generating contractile forces at the organ level or on ionic concentration changes at the cellular level. Our approach is to characterize the electromagnetic fields of uterine contractions jointly at the cellular, tissue, and organ levels. At the cellular level, focusing on both plateau-type and bursting-type action potentials, we introduce a generalized version of the FitzHugh-Nagumo equations and analyze its response behavior based on bifurcation theory. To represent the anisotropy of the myometrium, we introduce a random conductivity tensor model for the fiber orientations at the tissue level. Specifically, we divide the uterus into contiguous regions, each of which is assigned a random fiber angle. We also derive analytical expressions for the spiking frequency and propagation velocity of the bursting potential. At the organ level, we propose a realistic four-compartment volume conductor, in which the uterus is modeled based on the magnetic resonance imaging scans of a near-term woman and the abdomen is curved to match the device used to take the magnetomyography measurements. To mimic the effect of the sensing direction, we incorporate a sensor array model on the surface of abdomen. We illustrate our approach using numerical examples and compute the magnetic field using the finite element method. Our results show that fiber orientation and initiation location are the key factors affecting the magnetic field pattern, and that our multiscale forward model flexibly characterizes the limited-propagation local contractions at term. These results are potentially important as a tool for interpreting the non-invasive measurements of uterine contractions.
We also consider the inverse problem of uterine contractions during pregnancy. Our aim is to estimate the myometrial source currents that generate the external magnetomyography measurements. Existing works approach this problem using synthetic electromyography data. Our approach instead proceeds in two stages: develop a linear approximation model and conduct the estimation. In the first stage, we derive a linear approximation model of the sensor-oriented magnetic field measurements with respect to source current dipoles in the myometrium, based on a lead-field matrix. In particular, this lead-field matrix is analytically computed from distributed current dipoles in the myometrium according to quasi-static Maxwell's equations, using the finite element method. In the second stage, we solve a constrained least-squares problem to estimate the source currents, from which we predict the intrauterine pressure. We demonstrate our approach through numerical examples with synthetic data that are generated using our multiscale forward model. In the simulations, we assume that the excitation is located at the fundus of the uterus. We also illustrate our approach using real data sets, one of which has simultaneous contractile pressure measurements. The results show that our method well captures the short-distance propagation of uterine contractile activities during pregnancy, the change of excitation area in subsequent contractions or even in a single contraction, and the timing of uterine contractions. These findings are helpful in understanding the physiological and functional properties of the uterus, potentially enabling the diagnosis of labor and the treatment of obstetric syndromes associated with contractile dysfunction such as preterm birth and post-term birth.
Mark A. Anastasio, R. Martin Arthur, Hari Eswaran, Lan Yang,
Permanent URL: https://doi.org/10.7936/cw1m-gb52