Skip to main content

View full-text article in PMC

. 2016 Mar 28;11(3):e0152421. doi: 10.1371/journal.pone.0152421

Table 1. Equations of uterine model in [14].

Magnetic field

\nabla \times B (r, t) = μ_{0} (J_{s} (r, t) - G (r) \nabla ϕ (r, t))

(1)

Electrical potential

\nabla \cdot G_{A} (r) \nabla ϕ (r, t) = 0, i n A

(2)

\nabla \cdot G_{U} (r) \nabla ϕ (r, t) = 0, i n U

(3)

\nabla \cdot G_{e}^{'} \nabla ϕ_{e} (r, t) = - \nabla \cdot \frac{ζ}{ζ + 1} G_{e}^{'} \nabla v_{m} (r, t), i n ℳ

(4)

Source current density

J_{s} (r, t) = - ζ G_{e}^{^{'}} \nabla v_{m} (r, t), i n M

(5)

Transmembrane potential model

\nabla \cdot \frac{ζ}{ζ + 1} G_{e}^{^{'}} \nabla v_{m} (r, t) = a_{m} (c_{m} \frac{\partial v_{m} (r, t)}{\partial t} + J_{ion} (r, t) - J_{stim} (r, t)), i n M

(6)

Pacemaker activity model

J_{stim} (r, t) = \frac{1}{ε_{1}} \sum_{i = 1}^{N_{p}} ν_{i} h_{i} (r, t)

(7)

Boundary conditions

ϕ_{e} (r, t) = ϕ_{A} (r, t), i n \partial ℳ

(8)

{\hat{n}}_{ℳ} \cdot (G_{i}^{'} \nabla ϕ_{i} (r, t) + G_{e}^{'} \nabla ϕ_{e} (r, t)) = {\hat{n}}_{ℳ} \cdot G_{A} \nabla ϕ_{A} (r, t), i n \partial ℳ

(9)

{\hat{n}}_{ℳ} \cdot G_{i}^{'} \nabla v_{m} (r, t) = 0, i n \partial ℳ

(10)

ϕ_{e} (r, t) = ϕ_{U} (r, t), i n \partial U

(11)

{\hat{n}}_{U} \cdot (G_{i}^{'} \nabla ϕ_{i} (r, t) + G_{e}^{'} \nabla ϕ_{e} (r, t)) = {\hat{n}}_{U} \cdot G_{U} \nabla ϕ_{U} (r, t), i n \partial U

(12)

{\hat{n}}_{U} \cdot G_{i}^{'} \nabla v_{m} (r, t) = 0, i n \partial U

(13)

{\hat{n}}_{A} \cdot G_{A} \nabla ϕ_{A} (r, t) = 0, i n \partial A

(14)

{\hat{n}}_{ℱ} \cdot G_{U} \nabla ϕ_{U} (r, t) = λ ({\hat{n}}_{ℱ} \cdot G_{ℱ} \nabla ϕ_{ℱ} (r, t)), i n \partial ℱ

(15)