Bradley J. Roth

Optimal focal transcranial magnetic activation of the human motor cortex: effects of coil orientation, shape of the induced current pulse, and stimulus intensity.

We studied the effects of coil orientation, stimulus intensity, and shape of the induced current pulse on the amplitudes of motor evoked potentials in the left abductor pollicis brevis of 10 normal adults who had transcranial magnetic stimulation. The optimal direction of currents induced in the brain is approximately perpendicular to the central sulcus, flowing diagonally from back to front. The most effective coil orientation depends on the shape of the induced current pulse and. when the first and second phases of the pulse are of similar size, also on the intensity of stimulation. Optimal mapping of the human motor cortex with magnetic stimulation requires knowledge of the influences of all these factors.

Current injection into a two-dimensional anisotropic bidomain

A two-dimensional sheet of anisotropic cardiac tissue is represented with the bidomain model, and the finite element method is used to solve the bidomain equations. When the anisotropy ratios of the intracellular and extracellular spaces are not equal, the injection of current into the tissue induces a transmembrane potential that has a complicated spatial dependence, including adjacent regions of depolarized and hyperpolarized tissue. This behavior may have important implications for the electrical stimulation of cardiac tissue and for defibrillation.

A model of the stimulation of a nerve fiber by electromagnetic induction

A model is presented to explain the physics of nerve stimulations by electromagnetic induction. Maxwells equations predict the induced electric field distribution that is produced when a capacitor is discharged through a stimulating coil. A nonlinear Hodgkin-Huxley cable model describes the response of the nerve fiber to this induced electric field. Once the coils position, orientation, and shape are given and the resistance, capacitance, and initial voltage of the stimulating circuit are specified, this model predicts the resulting transmembrane potential of the fiber as a function of distance and time. It is shown that the nerve fiber is stimulated by the gradient of the component of the induced electric field that is parallel to the fiber, which hyperpolarizes or depolarizes the membrane and may stimulate an action potential. The model predicts complicated dynamics such as action potential annihilation and dispersion.<<ETX>>

Using a magnetometer to image a two‐dimensional current distribution

We describe a mathematical algorithm to obtain an image of a two‐dimensional current distribution from measurements of its magnetic field. The spatial resolution of this image is determined by the signal‐to‐noise ratio of the magnetometer data and the distance between the magnetometer and the plane of the current distribution. In many cases, the quality of the image can be improved more by decreasing the current‐to‐magnetometer distance than by decreasing the noise in the magnetometer.

A theoretical calculation of the electric field induced in the cortex during magnetic stimulation

We present a mathematical model for calculating the electric field induced in the head during magnetic stimulation of the cortex. The electric field arises from 2 sources: (1) the changing magnetic field creates an electric field in the tissue by electromagnetic induction, and (2) a charge distribution arises on the surface of the head and produces its own electrostatic field. A 3-sphere model is used to represent the brain, skull and scalp. The electric field as a function of the coil position, shape and orientation is computed numerically. The charge distribution partially shields the brain from the stimulus. The electric field is insensitive to the skull conductivity, in contrast with electrical stimulation using surface electrodes. Different coil shapes and orientations are considered, and a figure-of-eight coil is shown to deliver the largest and most focal stimulus.

Electrical conductivity values used with the bidomain model of cardiac tissue

Electrical conductivities in the bidomain model of cardiac tissue are expressed as functions of four parameters. These expressions allow simulations to be performed using nominal, equal, and reciprocal anisotropy without introducing undesired effects, such as length constant variations. Relative values of the bidomain conductivities are estimated to be: /spl sigma//sub iL/=1, /spl sigma//sub iT/=0.1, /spl sigma//sub eL/=1, and /spl sigma//sub eT/=0.4.

Virtual Electrodes and Deexcitation: New Insights into Fibrillation Induction and Defibrillation

Deexcitation During Fibrillation Induction and Defibrillation. Previous models of fibrillation induction and defibrillation stressed the contribution of depolarization during the response of the heart to a shock. This article reviews recent evidence suggesting that comprehending the role of negative polarization (hyperpolarization) also is crucial for understanding the response to a shock. Negative polarization can “deexcite” cardiac cells, creating regions of excitable tissue through which wavefronts can propagate. These wavefronts can result in new reentrant circuits, inducing fibrillation or causing defibrillation to fail. In addition, deexcitation can lead to rapid propagation through newly excitable regions, resulting in the elimination of excitable gaps soon after the shock and causing defibrillation to succeed.

Action potential propagation in a thick strand of cardiac muscle.

A theoretical model of action potential propagation in a thick strand of cardiac muscle is presented. The calculation takes into account the anisotropic and syncytial properties of the tissue, the presence of the interstitial space, the effect of the surrounding tissue bath, and the variation of the potential both along the strand length and across the strand cross section. The bidomain model is used to represent the electrical properties of the tissue, and the Ebihara-Johnson model is used to represent the properties of the active sodium channels. The calculated wave front is curved, with the action potential at the surface of the strand leading that at the center. The rate of rise of the action potential and the time constant of the action potential foot vary with depth into the tissue. The velocity of the wave front is nearly independent of strand radius for radii greater than 0.5 mm. The conduction velocity decreases as the volume fraction of the interstitial space decreases. In the limit of tightly packed cells, an action potential propagates quickly over the surface of the strand; the bulk of the tissue is then excited by a slow inward wave front initiated on the surface. This model does not predict an increase in conduction velocity when cells are tightly packed, a hypothesis that has been proposed previously to explain the fast conduction velocity in Purkinje fibers of some species.

The response of a spherical heart to a uniform electric field: a bidomain analysis of cardiac stimulation

A mathematical model describing electrical stimulation of the heart is developed, in which a uniform electric field is applied to a spherical shell of cardiac tissue. The electrical properties of the tissue are characterized using the bidomain model. Analytical expressions for the induced transmembrane potential are derived for the cases of equal anisotropy ratios in the intracellular and interstitial (extracellular) spaces, and no transverse coupling between fibers. Numerical calculations of the transmembrane potential are also performed using realistic electrical conductivities. The model illustrates several mechanisms for polarization of the cell membrane, which can be divided into two categories, depending on if they polarize fibers at the heart surface only or if they polarize fibers both at the surface and within the bulk of the tissue. The latter mechanisms can be classified further according to whether they originate from continuous or discrete properties of cardiac tissue.<<ETX>>

Quatrefoil reentry in myocardium: an optical imaging study of the induction mechanism.

Quatrefoil Reentry in Myocardium. Introduction: The “critical point hypothesis” for induction of ventricular fibrillation has previously been extended to infer the coexistence of four critical points, and hence four simultaneous spiral reentries or a quatrefoil reentry, resulting from only one premature stimulus delivered to the same location as the pacing stimulus. An optical imaging technique was used to explore its existence and to study the induction mechanism of this peculiar reentry pattern.