An integral equation method for the inverse conductivity problem

We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced boundary potentials, as well as the boundary values of the electrical conductivity. We have used a priori information to find a regularized conductivity distribution by first solving a Fredholm integral equation of the second kind for the Laplacian of the potential, and then by solving a first order partial differential equation for the regularized conductivity itself. Many of the calculations involved in the method can be achieved analytically using the eigenfunctions of an integral operator defined in the paper.Comment: 15 pages, 8 figure

Proposed diagnostic criteria and nosology of acute transverse myelitis

Acute transverse myelitis (ATM) is a focal inflammatory disorder of the spinal cord, resulting in motor, sensory, and autonomic dysfunction. A set of uniform diagnostic criteria and nosology for ATM is proposed to avoid the confusion that inevitably results when investigators use differing criteria. This will ensure a common language of classification, reduce diagnostic confusion, and lay the groundwork necessary for multicenter clinical trials. In addition, a framework is suggested for evaluation of individuals presenting with signs and symptoms of ATM. Best treatment often depends on a timely and accurate diagnosis. Because acute transverse myelopathies are relatively rare, delayed and incomplete work-ups often occur. Rapid and precise diagnosis will ensure not only that compressive lesions are detected and treated but also that idiopathic ATM is distinguished from ATM secondary to a known underlying disease. Identification of etiologies may suggest medical treatment, whereas no clearly established medical treatment currently exists for idiopathic ATM. Establishment of a diagnostic algorithm will likely lead to improved care, although it is recognized that the entire evaluation may not be performed for each patient