Time-varying magnetic fields used both in nerve stimulation and in magnetic resonance imaging induce electric fields and currents in conducting tissues. Knowledge of the spatial distributions of these induced electric fields and currents in the tissues is very limited because of the complex geometry and inhomogeneous, anisotropic conductivities of the tissues, as well as the spatial nonuniformity of the applied magnetic fields. In this paper, we present a finite element solution method that can be used to compute the induced electric field and current density distributions in tissues when the time rate of change of the applied magnetic field is low enough that the propagation time and magnetic diffusion time in the conductive tissues are negligible, and when the conduction current in the tissues is substantially larger than the displacement current. This finite element implementation is tested for some simple conductive models with both spatially uniform and nonuniform magnetic fields. Our solutions for a homogeneous isotropic conductive slab and a homogeneous anisotropic conductive slab exposed to a uniform magnetic field are in good agreement with analytical results. The finite element approach enables us to include conductive inhomogeneity and anisotropy. I allows us to closely model the complex geometry of the tissues. Therefore, it is well suited for realistic models of the conductive anatomy of biological tissues. >

A three-dimensional finite element method for computing magnetically induced currents in tissues

The paper gives a bibliographical review of the finite element modelling and simulations in cardiovascular mechanics and cardiology from the theoretical as well as practical points of views The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1993 and 2004 At the end of this paper, more than 890 references are given dealing with subjects as: Cardiovascular soft tissue modelling; material properties; mechanisms of cardiovascular components; blood flow; artificial components; cardiac diseases examination; surgery; and other topics

Finite element modelling and simulations in cardiovascular mechanics and cardiology: a bibliography 1993-2004.

Defibrillation is thought to occur because of changes in the transmembrane potential that are caused by current flow through the heart tissue. Impedance to electric countershock is an important parameter because it is determined by the magnitude and distribution of the current that flows for a specific shock voltage. The impedance is comprised of resistive contributions from: (1) extra-tissue sources, which include the defibrillator, leads, and electrodes; (2) tissue sources, which include intracardiac and extra-cardiac tissue; and (3) the interface between electrode and tissue. Tissue sources dominate the impedance and probably contribute to the wide range of impedance values presented to the defibrillation pulse. Because impedance is not constant within or between subjects, defibrillators must be designed to accommodate these differences without compromising patient safety or therapeutic efficacy. Experimental investigations in animals and humans suggest that impedance changes at several different time scales ranging from milliseconds to years. These alterations are believed to be a result of both electrochemical and physiological mechanisms. It is commonly thought that impedance is optimized when it has been decreased to a minimum, since this allows the most current flow for a given voltage shock. However, if the impedance is lowered by changing the location or size of the electrodes in such a way that current flow is decreased in part of the heart even though current flow is increased elsewhere, then the total voltage, current, and energy needed for defibrillation may increase, not decrease, even though impedance is decreased. A simple boundary element computer model suggests that the most even distribution of current flow through the heart is achieved for those electrode locations in which the impedance across the heart is at or near the maximum cardiac impedance for any location of these particular electrodes. Thus, the optimum shock impedance is achieved when impedance is minimized for extra-tissue and extra-cardiac tissue sources and is at or near a maximum for intracardiac tissue sources.

Impedance to defibrillation countershock: does an optimal impedance exist?

This thesis presents a mathematical model of the electric field from implantable
defibrillators, together with the numerical implementation, validation
and examples of application of the model.
The model was based on Laplace's equation for potential and was implemented
using the boundary element method with constant quadrilateral
elements and realistic torso structures. An efficient out-of-core solver was developed,
allowing any size problem to be solved, subject only to computer
speed and time available. A method was also developed that allowed matrices
calculated in one problem to be used in other, similar problems, often reducing
calculation times by an order of magnitude. Model validation included comparison of myocardial potentials from the
model to those from a finite element model (r.e..2.8%) and from measurements
in a sheep (c.c.=0.464, r.e..23.6%). Validation was also done against
resistance and voltage at defibrillation threshold from 29 patients implanted
with a transvenous system and 8 patients with the transvenous system and an
additional subcutaneous patch. Without the patch, the relative error between
the average of the clinical results and the model result was 9.4% (voltage)
and 0.8% (resistance). The average of the relative errors between each clinical
result and the model result was 23.4% (voltage) and 11.6% (resistance). With
the patch, the equivalent relative errors were 33.9%, 19.4%, 44.0% and 22.5%.
Transvenous, epicardial and subcutaneous electrode configurations were
modelled in a series of investigations. The best transvenous configuration was
with a right ventricular cathode and an anode in the inferior vena cava, where
defibrillation voltage and energy were reduced by 35% and 55%, respectively,
compared to a standard configuration with the anode in the superior vena
cava. Configurations with a right ventricular cathode and large epicardial
patch performed best, though, and reduced voltage and energy by up to 59%
and 79%, respectively. The optimal length of the right /ventricular transvenous
electrode was approximately 60mm. An infarcted heart was also modelled.
For future work, anisotropy may be added to the heart and skeletal muscle
of the model. Anisotropic regions may be represented by many small boundary
element regions or by finite elements. Automated construction of the torso
mesh and an algorithm for automatically optimising electrode position may
be developed. Individual patients may be modelled and predicted values of
defibrillation voltage, energy and resistance compared to values measured at
the time of implantation.
In conclusion, the boundary element model was successful in modelling the
electric field in the torso and in predicting implantable defibrillator performance.
The model has potential to be used in research and development and
in clinical settings.

Modelling the electric field from implantable defibrillators

A realistic three-dimensional (3D) finite element model (FEM) of the conductive anatomy of a human thorax has been constructed to quantitatively assess the current density distribution produced in the heart and thorax during transthoracic defibrillation. The model is based on a series of cross-sectional CT scans and incorporates isotropic conductivities for 8 tissues and an approximation of the anisotropic conductivity of skeletal muscle. Current density distributions were determined for 4 paddle pairings and 2 paddle sizes. Our results show fairly uniform myocardial current density distributions for all paddle pairs and sizes examined. Maximum current density values < 4 times the minimum current density (Jlh) necessary to inactivate a myocyte suggest that common clinically used defibrillation paddle positions have a safety factor of at least 2.5.

Paddle position and size effects in human transthoracic defibrillation- a three-dimensional finite element model

http://ieeexplore.ieee.org/iel5/7705/21095/00978858.pdf

M.A. Camacho

Papers

Paddle position and size effects in human transthoracic defibrillation- a three-dimensional finite element model

The effects of epicardial patch electrodes on transthoracic defibrillation: a three-dimensional finite element study