On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Corpus callosum index and long-term disability in multiple sclerosis patients

Prediction of long-term disability in patients with multiple sclerosis (MS) is essential. Magnetic resonance imaging (MRI) measurement of brain volume may be of predictive value but sophisticated MRI techniques are often inaccessible in clinical practice. The corpus callosum index (CCI) is a normalized measurement that reflects changes of brain volume. We investigated medical records and 533 MRI scans at diagnosis and during clinical follow-up of 169 MS patients (mean age 42 +/- 11 years, 86% relapsing-remitting MS, time since first relapse 11 +/- 9 years). CCI at diagnosis was 0.345 +/- 0.04 and correlated with duration of disease (p = 0.002; r = -0.234) and expanded disability status scale (EDSS) score at diagnosis (r = -0.428; p < 0.001). Linear regression analyses identified age, duration of disease, relapse rate and EDSS at diagnosis as independent predictors for disability after mean of 7.1 years (Nagelkerkes' R:0.56). Annual CCI decrease was 0.01 +/- 0.02 (annual tissue loss: 1.3%). In secondary progressive MS patients, CCI decrease was double compared to that in relapsing-remitting MS patients (p = 0.04). There was a trend of greater CCI decrease in untreated patients compared to those who received disease modifying drugs (p = 0.2). CCI is an easy to use MRI marker for estimating brain atrophy in patients with MS. Brain atrophy as measured with CCI was associated with disability progression but it was not an independent predictor of long-term disability.

Reproducibility of retinal thickness measurements in patients with age-related macular degeneration using 3D Fourier-domain optical coherence tomography (OCT) (Topcon 3D-OCT 1000)

Conventional time-domain optical coherence tomography (OCT) has become an important tool for following dry or exudative age-related macular degeneration (AMD). Fourier-domain three-dimensional (3D) OCT was recently introduced. This study tested the reproducibility of 3D-OCT retinal thickness measurements in patients with dry and exudative AMD.

Ocular involvement in paediatric haemolytic uraemic syndrome

The aim of this study was to estimate the frequency and severity of ocular involvement in paediatric patients with haemolytic uraemic syndrome (HUS).

Ophthalmological findings in Joubert syndrome

Joubert syndrome (JS) is an autosomal-recessive inherited complex malformation of the midbrain-hindbrain. It has been associated with ocular and oculomotor abnormalities. The aim of our study was to extend the ophthalmic knowledge in JS and to add new findings.

[Diagnosis and treatment of oculomotor deficits in Möbius sequence]

This article reviews the spectrum of possible motility disorders and ocular misalignment in patients with Möbius sequence. The various options for strabismus surgery are discussed and a stepwise algorithm is presented.

[Non-oculomotor eye involvement in Moebius sequence]

Moebius sequence is a congenital disorder that not only affects the oculomotor system but also the eyes themselves. Ocular involvement might be sight-threatening and needs regular follow-up by an ophthalmologist.

Longterm follow-up of children with traumatic optic nerve avulsion

We report the longterm follow-up of children with optic nerve avulsion (ONA) caused by traumatic events. The remarkable differences in courses and outcomes may elucidate the spectrum of ONA-associated symptoms and injuries.