Psychobiophysics of transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a technique that stimulates the brain using a magnetic coil placed on the scalp. Since it is applicable to humans non-invasively, directly interfering with neural electrical activity, it is potentially a good tool to study the direct relationship between perceptual experience and neural activity. However, it has been difficult to produce a clear perceptible phenomenon with TMS of sensory areas, especially using a single magnetic pulse. Also, the biophysical mechanisms of magnetic stimulation of single neurons have been poorly understood.

In the psychophysical part of this thesis, perceptual phenomena induced by TMS of the human visual cortex are demonstrated as results of the interactions with visual inputs. We first introduce a method to create a hole, or a scotoma, in a flashed, large-field visual pattern using single-pulse TMS. Spatial aspects of the interactions are explored using the distortion effect of the scotoma depending on the visual pattern, which can be luminance-defined or illusory. Its similarity to the distortion of afterimages is also discussed. Temporal interactions are demonstrated in the filling-in of the scotoma with temporally adjacent visual features, as well as in the effective suppression of transient visual features. Also, paired-pulse TMS is shown to lead to different brightness modulations in transient and sustained visual stimuli.

In the biophysical part, we first develop a biophysical theory to simulate the effect of magnetic stimulation on arbitrary neuronal structure. Computer simulations are performed on cortical neuron models with realistic structure and channels, combined with the current injection that simulates magnetic stimulation. The simulation results account for general and basic characteristics of the macroscopic effects of TMS including our psychophysical findings, such as a long inhibitory effect, dependence on the background activity, and dependence on the direction of the induced electric field.

The perceptual effects and the cortical neuron model presented here provide foundations for the study of the relationship between perception and neural activity. Further insights would be obtained from extension of our model to neuronal networks and psychophysical studies based on predictions of the biophysical model.

Energy inequalities and error estimates for axisymmetric torsion of thin elastic shells of revolution

The problem motivating this investigation is that of pure axisymmetric torsion of an elastic shell of revolution. The analysis is carried out within the framework of the three-dimensional linear theory of elastic equilibrium for homogeneous, isotropic solids. The objective is the rigorous estimation of errors involved in the use of approximations based on thin shell theory.

The underlying boundary value problem is one of Neumann type for a second order elliptic operator. A systematic procedure for constructing pointwise estimates for the solution and its first derivatives is given for a general class of second-order elliptic boundary-value problems which includes the torsion problem as a special case.

The method used here rests on the construction of “energy inequalities” and on the subsequent deduction of pointwise estimates from the energy inequalities. This method removes certain drawbacks characteristic of pointwise estimates derived in some investigations of related areas.

Special interest is directed towards thin shells of constant thickness. The method enables us to estimate the error involved in a stress analysis in which the exact solution is replaced by an approximate one, and thus provides us with a means of assessing the quality of approximate solutions for axisymmetric torsion of thin shells.

Finally, the results of the present study are applied to the stress analysis of a circular cylindrical shell, and the quality of stress estimates derived here and those from a previous related publication are discussed.