Diffusion with random distribution of static traps

The random walk problem is studied in two and three dimensions in the presence of a random distribution of static traps. An efficient Monte Carlo method, based on a mapping onto a polymer model, is used to measure the survival probability P(c,t) as a function of the trap concentration c and the time t. Theoretical arguments are presented, based on earlier work of Donsker and Varadhan and of Rosenstock, why in two dimensions one expects a data collapse if -ln[P(c,t)]/ln(t) is plotted as a function of (lambda t)^{1/2}/ln(t) (with lambda=-ln(1-c)), whereas in three dimensions one expects a data collapse if -t^{-1/3}ln[P(c,t)] is plotted as a function of t^{2/3}lambda. These arguments are supported by the Monte Carlo results. Both data collapses show a clear crossover from the early-time Rosenstock behavior to Donsker-Varadhan behavior at long times.Comment: 4 pages, 6 figure

Detection of early age-related macular degeneration using novel functional parameters of the focal cone electroretinogram

The focal cone electroretinogram is a sensitive marker for macular disease, but have we unlocked its full potential? Typically assessment of waveform parameters is subjective and focuses on a small number of locations (e.g. the a-wave). This study evaluated the discriminatory and diagnostic potential of 4 conventional and 15 novel, objectively determined, parameters in patients with early Age-related Macular Degeneration. Focal cone electroretinograms were recorded in 54 participants with early Age-related Macular Degeneration (72.9±8.2 years) and 54 healthy controls (69±7.7 years). Conventional a and b wave amplitudes and implicit times were measured and compared to novel parameters derived from both the 1st and 2nd derivatives and the frequency-domain power spectrum of the electroretinogram.Statistically significant differences between groups were shown for all conventional parameters, the majority of 1st and 2nd derivative parameters and the power spectrum at 25 and 30 Hz. Receiver operating characteristics showed that both conventional and 1st and 2nd derivative implicit times had provided the best diagnostic potential. A regression model showed a small improvement over any individual parameter investigated. The non-conventional parameters enhanced the objective evaluation of the focal electroretinogram, especially when the amplitude was low. Furthermore, the novel parameters described here allow the implicit time of the electroretinogram to be probed at points other than the peaks of the a and b waves. Consequently these novel analysis techniques could prove valuable in future electrophysiological investigation, detection and monitoring of Age-related Macular Degeneration

Real-world clinical experience with Idebenone in the treatment of Leber hereditary optic neuropathy

Background: Leber hereditary optic neuropathy (LHON) leads to bilateral central vision loss. In a clinical trial setting, idebenone has been shown to be safe and to provide a trend toward improved visual acuity, but long-term evidence of effectiveness in real-world clinical practice is sparse. Methods: Open-label, multicenter, retrospective, noncontrolled analysis of long-term visual acuity and safety in 111 LHON patients treated with idebenone (900 mg/day) in an expanded access program. Eligible patients had a confirmed mitochondrial DNA mutation and had experienced the onset of symptoms (most recent eye) within 1 year before enrollment. Data on visual acuity and adverse events were collected as per normal clinical practice. Efficacy was assessed as the proportion of patients with either a clinically relevant recovery (CRR) or a clinically relevant stabilization (CRS) of visual acuity. In the case of CRR, time to and magnitude of recovery over the course of time were also assessed. Results: At time of analysis, 87 patients had provided longitudinal efficacy data. Average treatment duration was 25.6 months. CRR was observed in 46.0% of patients. Analysis of treatment effect by duration showed that the proportion of patients with recovery and the magnitude of recovery increased with treatment duration. Average gain in best-corrected visual acuity for responders was 0.72 logarithm of the minimal angle of resolution (logMAR), equivalent to more than 7 lines on the Early Treatment Diabetic Retinopathy Study (ETDRS) chart. Furthermore, 50% of patients who had a visual acuity below 1.0 logMAR in at least one eye at initiation of treatment successfully maintained their vision below this threshold by last observation. Idebenone was well tolerated, with most adverse events classified as minor. Conclusions: These data demonstrate the benefit of idebenone treatment in recovering lost vision and maintaining good residual vision in a real-world setting. Together, these findings indicate that idebenone treatment should be initiated early and be maintained more than 24 months to maximize efficacy. Safety results were consistent with the known safety profile of idebenone

Full field electroretinogram in autism spectrum disorder

Purpose To explore early findings that individuals with autism spectrum disorder (ASD) have reduced scotopic ERG b-wave amplitudes. Methods Dark adapted (DA) ERGs were acquired to a range of flash strengths, (-4.0 to 2.3 log phot cd.s.m-2), including and extending the ISCEV standard, from two subject groups: (ASD) N=11 and (Control) N=15 for DA and N=14 for light adapted (LA) ERGs who were matched for mean age and range. Naka-Rushton curves were fitted to DA b-wave amplitude growth over the first limb (-4.0 to -1.0 log phot cd.s.m-2). The derived parameters (Vmax, Km and n) were compared between groups. Scotopic 15 Hz flicker ERGs (14.93Hz) were recorded to 10 flash strengths presented in ascending order from -3.0 to 0.5 log Td.s to assess the slow and fast rod pathways respectively. LA ERGs were acquired to a range of flash strengths, (-0.5 to 1.0 log phot cd.s.m-2). Photopic 30 Hz, flicker ERGs, oscillatory potentials (OPs) and the responses to prolonged 120 ms ON- OFF stimuli were also recorded. Results For some individuals the DA b-wave amplitudes fell below the control 5th centile of the controls with up to four ASD participants (36%) at the 1.5 log phot cd.s.m-2 flash strength and two (18%) ASD participants at the lower -2 log phot cd.s.m-2 flash strength. However, across the thirteen flash strengths there were no significant group differences for b-wave amplitude’s growth (repeated measures ANOVA p=0.83). Nor were there any significant differences between the groups for the Naka-Rushton parameters (p>0.09). No group differences were observed in the 15Hz scotopic flicker phase or amplitude (p>0.1), DA ERG a- wave amplitude or time to peak (p>26). The DA b-wave time to peak at 0.5 log phot cd.s.m-2 were longer in the ASD group (corrected p=0.04). The single ISCEV LA 0.5 log phot cd.s.m-2 (p0.08) to the single flash stimuli although there was a significant interaction between group and flash strength for the b-wave amplitude (corrected p=0.006). The prolonged 120 ms ON-responses were smaller in the ASD group (corrected p=0.003), but the OFF response amplitude (p>0.6) and ON and OFF times to peaks (p>0.4) were similar between groups. The LA OPs showed an earlier bifurcation of OP2 in the younger ASD participants, however no other differences were apparent in the OPs or 30Hz flicker waveforms. Conclusion Some ASD individuals show subnormal DA ERG b-wave amplitudes. Under LA conditions the b-wave is reduced across the ASD group along with the ON response of the ERG. These exploratory findings, suggest there is altered cone-ON bipolar signalling in ASD

Income-Tested College Financial Aid and Labor Disincentives

Working has become commonplace among college students; however, this activity can have unexpected financial consequences. Federal formulas implicitly tax the amount of financial aid students are eligible to receive by as much as 50 cents for each marginal dollar of income. This tax creates an incentive for college students to reduce income, though abstruse formulas and the timing of financial aid receipt are likely to limit responses. Using data from a national sample of financially independent college students in the United States, I do not find that students bunch below earnings protection thresholds in a manner that would indicate attempts to avoid reductions in financial aid in total or grants specifically. Moreover, I do not find evidence that implicit income taxes predict lower earnings in a manner that suggests that students meaningfully reduce earnings in response to the tax. Therefore, while economically efficient, the reduction in aid has the potential to burden low-income students who need to both work and receive financial aid in order to afford college expenses

Time course of the flash response of dark- and light-adapted human rod photoreceptors derived from the electroretinogram

The a-wave of the electroretinogram was recorded from human subjects with normal vision, using a corneal electrode and ganzfeld stimulation. We applied the paired-flash technique, in which an intense ‘probe’ flash was delivered at different times after a ‘test’ flash. The amplitude of the probe-flash response provided a measure of the circulating current remaining at the appropriate time after the test flash.We extended previous methods by measuring not at a fixed time, but at a range of times after the probe flash, and then calculating the ratio of the ‘test-plus-probe’ response to the ‘probe-alone’ response, as a function of time.Under dark-adapted conditions the rod response derived by the paired-flash technique (in response to a relatively dim test flash) peaked at ca 120 ms, with a fractional sensitivity at the peak of ca 0.1 Td−1 s−1.As reported previously, background illumination reduced the maximal response, reflecting a reduction in rod circulating current. In addition, it shortened the time to peak (to ca 70 ms at an intensity of 170 Td), and reduced the flash sensitivity measured at the peak. The flash sensitivity declined approximately according to Weber's Law, with a 10-fold reduction occurring at an intensity of 100-200 Td. We could not reliably measure responses at significantly higher background intensities because the circulating current became so small.In order to investigate the phototransduction process after correction for response compression, we expressed the derived response as a fraction of the maximal response that could be elicited in the presence of the background. The earliest rising phase of this ‘fractional response per unit intensity’ was little affected by background illumination, suggesting that the amplification constant of transduction was unaltered by light adaptation

Light responses in the mouse retina are prolonged upon targeted deletion of the HCN1 channel gene

Hyperpolarization-activated and cyclic nucleotide-gated (HCN) channels contribute to pacemaker activity, and co-determine the integrative behaviour of neurons and shape their response to synaptic stimulation. Four channel isoforms, HCN1-4, have been described in mammals. Recent studies showed particularly strong expression of HCN1 channels in rods and cones of the rat retina, suggesting that HCN1 channels are involved in the shaping of light responses in both types of photoreceptors. Therefore, the loss of HCN1 channels should lead to pronounced changes in light-induced electrical responses under both scotopic and photopic conditions. This was tested using a mouse transgenic approach. We used immunohistochemistry and patch-clamp recording to study the distribution of HCN1 channels in the mouse retina. HCN1 channels were strongly expressed in rod and cone photoreceptors, as well as in some bipolar, amacrine and ganglion cell types. In electroretinograms (ERGs) from animals in which the HCN1 channel gene had been knocked out, the b-wave amplitudes were unaltered (scotopic conditions) or somewhat reduced (photopic conditions), whereas the duration of both scotopic and photopic ERG responses was strikingly prolonged. Our data suggest that in visual information processing, shortening and shaping of light responses by activation of HCN1 at the level of the photoreceptors is an important step in both scotopic and photopic pathways