Polygonally Meshed Dipole Model Simulation of the Electrical Field Produced by the Stomach and Intestines

Abstract

Cutaneous electrogastrography (EGG) is used in clinical and physiological fields to noninvasively measure the electrical activity of the stomach and intestines. Dipole models that mathematically express the electrical field characteristics generated by the stomach and intestines have been developed to investigate the relationship between the electrical control activity (ECA) (slow waves) shown in EGG and the internal gastric electrical activity. However, these models require a mathematical description of the movement of an annular band of dipoles, which limits the shape that can be modeled. In this study, we propose a novel polygonally meshed dipole model to conveniently reproduce ECA based on the movement of the annular band in complex shapes, such as the shape of the stomach and intestines, constructed in three-dimensional (3D) space. We show that the proposed model can reproduce ECA simulation results similar to those obtained using conventional models. Moreover, we show that the proposed model can reproduce the ECA produced by a complex geometrical shape, such as the shape of the intestines. The study results indicate that ECA simulations can be conducted based on structures that more closely resemble real organs than those used in conventional dipole models, with which, because of their intrinsic construction, it would be difficult to include realistic complex shapes, using the mathematical description of the movement of an annular band of dipoles. Our findings provide a powerful new approach for computer simulations based on the electric dipole model.

Figure 1

Schematic illustration of arbitrary point sampling on the centerline of the model. The black line represents the centerline of the model, and the surface of the model is red.

Figure 2

Constructing the model based on the centerline. (a) The grey line in the center of the figure is the centerline, and the yellow circle at the bottom of the figure is the vertex circle positioned at the starting point. From here, the vertex circle is determined at an arbitrary point on the centerline. (b) The vertex circle is rotated toward the x axis to face the same way as the adjacent point C _n+1 from an arbitrary point on the centerline C _n. (c) The vertex circle is rotated around the z axis to face the same way as the adjacent point C _n+1 from an arbitrary point on the centerline C _n. (d) The vertex circle is moved to the position of the arbitrary point on the centerline C _n.

Figure 3

Configuration of polygonally meshed dipole model. (a) The grey line in the center of the figure is the centerline, and the circle around the centerline is the vertex circle. (b) A surface is extended across the adjoining vertices. (c) The annular band microregion (yellow) is defined by the four adjacent vertices; the dipole band is positioned in the center of this region. (d) The annular band is defined by connecting the horizontal annular band microregions (yellow) facing the adjacent point C _n+1 from an arbitrary point on the centerline C _n.

Figure 4

Electrode coordinates (measurement points) E(x, y, z) and the distance vector ρ _m,n from the microregion to the measurement point.

Figure 5

Cylindrical model used in a polygonally meshed dipole model. (a) Centerline constructed using the equation for the conventional mathematical cylinder model. (b) Mathematical cylinder model constructed using the proposed method. (c) EGG simulation results for the conventional method and the proposed method obtained, in the latter case, by moving the annular band.

Figure 6

Conoidal dipole model used in a polygonally meshed dipole model. (a) Centerline constructed using the equation for the conventional conoidal dipole model. (b) Conoidal dipole model constructed using the proposed method. (c) EGG simulation results for the conventional method and the proposed method obtained by moving the annular band.

Figure 7

EGG simulation results acquired using sampling rates of 1 and 10 Hz and the conoidal dipole model.

Figure 8

Complex structure expressed using a polygonally meshed dipole model. (a) Centerline drawn by reference to the shape of the colon. (b) Pseudocolon model constructed using the proposed method. (c) EGG simulation results obtained by moving the annular band in the proposed method.