Leon Heller

Evaluation of boundary element methods for the EEG forward problem: effect of linear interpolation

The authors implement the approach for solving the boundary integral equation for the electroencephalography (EEG) forward problem proposed by de Munck (1992), in which the electric potential varies linearly across each plane triangle of the mesh. Previous solutions have assumed the potential is constant across an element. The authors calculate the electric potential and systematically investigate the effect of different mesh choices and dipole locations by using a three concentric sphere head model for which there is an analytic solution. Implementing the linear interpolation approximation results in errors that are approximately half those of the same mesh when the potential is assumed to be constant, and provides a reliable method for solving the problem.<<ETX>>

CHARACTERISTICS OF THE PROTON--PROTON INTERACTION DEDUCED FROM THE DATA BELOW 30 MeV.

Abstract A two-parameter description for each of the low energy 3P phase shifts is justified and used to perform the first comprehensive analysis of all of the proton-proton scattering data below 30 MeV. Particular attention is paid to magnetic moment, vaccuum polarization, and finite electromagnetic structure effects. Effective-range parameters for the 1S and 3P states are determined as well as possible, but distressing irregularities are noted in all of the data between 1 and 10 MeV. Nevertheless, some parameters are determined with precision, such as the singlet scattering length with a value of appE = − 7.822 ± 0.004 F. It is found that the central, tensor, and spin-orbit P-wave parameters reflect the uncertainties in the low energy data much more accurately than do the phase shifts themselves, and values of the parameters derived from experiment are given. The vacuum polarization interaction is shown to be present with a strength about equal to its theoretical value, but again with some irregularities. Finite electromagnetic structure effects deduced from the Hofstadter-Wilson dipole formula are found to be quite different from those found in previous calculations. The neutron-neutron scattering length, corrected for finite structure effects, is predicted to be ann = −17.06 F.

Modeling Direct Effects of Neural Current on MRI

We investigate the effect of the magnetic field generated by neural activity on the magnitude and phase of the MRI signal in terms of a phenomenological parameter with the dimensions of length; it involves the product of the strength and duration of these currents. We obtain an analytic approximation to the MRI signal when the neuromagnetically induced phase is small inside the MRI voxel. The phase shift is the average of the MRI phase over the voxel, and therefore first order in that phase; and the reduction in the signal magnitude is one half the square of the standard deviation of the MRI phase, which is second order. The analytic approximation is compared with numerical simulations. For weak currents the agreement is excellent, and the magnitude change is generally much smaller than the phase shift. Using MEG data as a weak constraint on the current strength we find that for a net dipole moment of 10 nAm, a typical value for an evoked response, the reduction in the magnitude of the MRI signal is two parts in 105, and the maximum value of the overall phase shift is

Computation of the return current in encephalography: the auto solid angle

\approx 4 \cdot 10^{-3}

The magnetic field inside special conducting geometries due to internal current

, obtained when the MRI voxel is displaced 2/3 the size of the neuronal activity. We also show signal changes over a large range of values of the net dipole moment. We compare these results with others in the literature. Our model overestimates the effect on the MRI signal. Hum Brain Mapp 2009.

Equilibrium Statistical Mechanics of Dissociating Diatomic Gases

Abstract not available.

Classical limit of demagnetization in a field gradient

In view of recent attempts to directly and noninvasively detect the neuromagnetic field, we derive an analytic formula for the magnetic field inside a homogeneous conducting sphere due to a point current dipole. It has a similar structure to a well-known formula for the field outside any spherically symmetric conductivity profile. For a radial dipole, the field on the inside has a very simple expression. A symmetry argument is given as to why the field of a radial dipole vanishes outside a spherical conductor. Illustrative plots of the magnetic field are presented for a radial and a tangential dipole; the slope of the tangential component of the magnetic field is discontinuous at the surface of the sphere. A spherical conductor having three concentric regions is discussed; and we also derive an analytic formula for the magnetic field inside a homogeneous infinite half space.

Electric and Magnetic Fields of the Brain

For the diatomic molecule AB in thermal and chemical equilibrium with its dissociated atoms, the pressure, density, specific entropy, and specific enthalpy are written as functions of the temperature and the fractional dissociation, with the approximations that the rotation is fully excited and there is no electronic excitation. These approximations are very good for many molecules over a large range of the variables. Atoms A and B can be either identical or distinct provided there is no excess of one atom over the other. For molecules composed of the isotopes of hydrogen, because of their large vibrational energies, it is possible to have considerable dissociation without vibration being important. If vibration is neglected, then the thermodynamic variables (written in dimensionless form) are related by equations which do not involve any properties of the species under consideration. Curves of constant pressure, density, specific entropy, and specific enthalpy are presented in the temperature‐dissociatio...

Relativistic description of directly interacting pions and nucleons

We calculate the rate of decrease of the expectation value of the transverse component of spin for spin-1/2 particles in a magnetic field with a spatial gradient, and determine the conditions under which a previous classical description is valid. A density matrix treatment is required for two reasons. The first arises because the particles initially are not in a pure state due to thermal motion. The second reason is that each particle interacts with the magnetic field and the other particles, with the latter taken to be via a two-body central force. The equations for the one-body Wigner distribution functions are written in a general manner, and the places where quantum mechanical effects can play a role are identified. One that may not have been considered previously concerns the momentum associated with the magnetic field gradient, which is proportional to the time integral of the gradient. Its relative magnitude compared with the important momenta in the problem is a significant parameter, and if their ratio is not small some nonclassical effects contribute to the solution. Assuming the field gradient is sufficiently small, and a number of other inequalities are satisfied involving the mean wavelength, range of the force, and the mean separation between particles, we solve the integro-partial differential equations for the Wigner functions to second order in the strength of the gradient. When the same reasoning is applied to a different problem with no field gradient, but having instead a gradient to the z component of the polarization, the connection with the diffusion coefficient is established, and we find agreement with the classical result for the rate of decrease of the transverse component of magnetization. The corresponding result for this rate in the absence of collisions is much greater. An approximate value for the

Variational Principles for the Return Current in Encephalography

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