Multiscale forward electromagnetic model of uterine contractions during pregnancy

Abstract

Background: Analyzing and monitoring uterine contractions during pregnancy is relevant to the field of reproductive health assessment. Its clinical importance is grounded in the need to reliably predict the onset of labor at term and pre-term. Preterm births can cause health problems or even be fatal for the fetus. Currently, there are no objective methods for consistently predicting the onset of labor based on sensing of the mechanical or electrophysiological aspects of uterine contractions. Therefore, modeling uterine contractions could help to better interpret such measurements and to develop more accurate methods for predicting labor. In this work, we develop a multiscale forward electromagnetic model of myometrial contractions during pregnancy. In particular, we introduce a model of myometrial current source densities and compute its magnetic field and action potential at the abdominal surface, using Maxwell's equations and a four-compartment volume conductor geometry. To model the current source density at the myometrium we use a bidomain approach. We consider a modified version of the Fitzhugh-Nagumo (FHN) equation for modeling ionic currents in each myocyte, assuming a plateau-type transmembrane potential, and we incorporate the anisotropic nature of the uterus by designing conductivity-tensor fields.

Results: We illustrate our modeling approach considering a spherical uterus and one pacemaker located in the fundus. We obtained a travelling transmembrane potential depolarizing from -56 mV to -16 mV and an average potential in the plateau area of -25 mV with a duration, before hyperpolarization, of 35 s, which is a good approximation with respect to the average recorded transmembrane potentials at term reported in the technical literature. Similarly, the percentage of myometrial cells contracting as a function of time had the same symmetric properties and duration as the intrauterine pressure waveforms of a pregnant human myometrium at term.

Conclusions: We introduced a multiscale modeling approach of uterine contractions which allows for incorporating electrophysiological and anatomical knowledge of the myometrium jointly. 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 using magnetomyography (MMG) and electromyography (EMG).

Figure 1

Diagram of microanatomy of pregnant human myometrium [4]. Red lines represent current flows.

Figure 2

Illustration of the proposed modeling approach.

Figure 3

Representation of the four-compartment volume conductor geometry and the forward electromagnetic problem of uterine contractions.

Figure 4

Illustration of the bidomain modeling approach.

Figure 5

Simplified illustrations ofa₃(r)with respect to the local coordinates axis given by$\{\hat{\mathit{n}}\left(r\right),{\hat{\mathit{t}}}_{\mathbf{1}}\left(r\right)$,${\hat{\mathit{t}}}_{\mathbf{2}}\left(r\right)\}$. The blue plane contains the vectors $\hat{\mathit{n}}\left(\mathit{r}\right)$, $\hat{\mathit{k}}\left(\mathit{r}\right)$, and ${\hat{\mathit{t}}}_1\left(\mathit{r}\right)$, and it is perpendicular to the gray plane formed by vectors ${\hat{\mathit{t}}}_1\left(\mathit{r}\right)$, ${\hat{\mathit{t}}}_1\left(\mathit{r}\right)$ and a₃(r). The orange plane is the cross section of the uterus perpendicular to the vector ${\left(\frac{d{\mathit{r}}_C\left(t\right)}{\mathit{\text{dt}}}\right|}_{t_0}$. The gray curve is the curve of symmetry r_C(t)with r_C(t₁)and r_C(t₂)extreme points of the curve.

Figure 6

Four-compartment volume conductor geometry used in the numerical examples. (a) View of z-x plane, and (b) z-y plane. Each compartment is assigned a different color. The myometrium has a non-uniform color to denote that its conductivity is anisotropic.

Figure 7

Geometry and fiber orientation in spherical myometrium given byα=45°.

Figure 8

FEM solution at time instants t=10 [s], 36 [s], 55 [s] for one pacemaker on the fundus of a spherical myometrium, assuming anisotropy. (a)-(c) transmembrane potential and source current density distribution at the myometrium, (d)-(f) electrical potential at the abdominal surface, and (g)-(i) magnetic field density at the abdominal surface.

Figure 9

(a) Temporal response of the FEM solutions for transmembrane potential at different elevations; (b) Percentage of contracting myometrial volume as a function of time.