The bioelectric fields produced in the human thorax can be mathematically
described by Maxwell's equations. For electrostatic problems in dielectric
volume conductors, an electric field, 
, can be described in
terms of the gradient of a scalar potential field 
[18]
In the frequency range
of the electrocardiographic signals (0-100 Hz [19]), the volume
conductor can be considered purely resistive so that a quasi-static
approximation is justified [20].
Thus the current density associated with the electric field is given by
Ohm's law,
where 
is the current density and 
is the electrical
conductivity of the tissue, represented mathematically as a 3 x 3
symmetric tensor. If active current sources are also present, this
equation becomes
Under quasi-static conditions, the net current flow is solenoidal such that
the divergence of equation (3) is zero. Therefore,
Substituting equation (1) into equation (5),
we obtain
or
where
which is a form of Poisson's equation.
For this study, Isv = 0, because we bound the volume of interest by
the epicardial and body surfaces so that all sources are outside the
bounded volume domain. As such, equation (7) simplifies to a
general form of Laplace's equation. By applying the Dirichlet and Neumann
boundary conditions, we can formulate an electrocardiographic forward
problem in terms of epicardial sources as
with
where
