Functional differential equations of advanced type with piecewise constant argument deviations are studied. They are closely related to impulse, loaded and, especially, to difference equations, and have the structure of continuous dynamical systems within intervals of unit length

ObjectiveTo determine clinical manifestations, immunotherapy responsiveness and outcomes of glutamic acid decarboxylase-65 (GAD65) neurological autoimmunity.MethodsWe identified 323 Mayo Clinic patients with high-titre (>20 nmol/L in serum) GAD65 antibodies out of 380 514 submitted anti-GAD65 samples (2003–2018). Patients classified as having GAD65 neurological autoimmunity after chart review were analysed to determine disease manifestations, immunotherapy responsiveness and predictors of poor outcome (modified Rankin score >2).ResultsOn review, 108 patients were classified as not having GAD65 neurological autoimmunity and 3 patients had no more likely alternative diagnoses but atypical presentations (hyperkinetic movement disorders). Of remaining 212 patients with GAD65 neurological autoimmunity, median age at symptom onset was 46 years (range: 5–83 years); 163/212 (77%) were female. Stiff-person spectrum disorders (SPSD) (N=71), cerebellar ataxia (N=55), epilepsy (N=35) and limbic encephalitis (N=7) could occur either in isolation or as part of an overlap syndrome (N=44), and were designated core manifestations. Cognitive impairment (N=38), myelopathy (N=23) and brainstem dysfunction (N=22) were only reported as co-occurring phenomena, and were designated secondary manifestations. Sustained response to immunotherapy ranged from 5/20 (25%) in epilepsy to 32/44 (73%) in SPSD (p=0.002). Complete immunotherapy response occurred in 2/142 (1%). Cerebellar ataxia and serum GAD65 antibody titre >500 nmol/L predicted poor outcome.InterpretationHigh-titre GAD65 antibodies were suggestive of, but not pathognomonic for GAD65 neurological autoimmunity, which has discrete core and secondary manifestations. SPSD was most likely to respond to immunotherapy, while epilepsy was least immunotherapy responsive. Complete immunotherapy response was rare. Serum GAD65 antibody titre >500 nmol/L and cerebellar ataxia predicted poor outcome.

Background: Optic neuritis (ON) is often the presenting symptom in inflammatory central nervous system demyelinating disorders. Objective: To compare the frequency and pattern of optic chiasm involvement in patients with aquaporin-4-immunoglobulin G (AQP4-IgG)-associated ON to patients with myelin oligodendrocyte glycoprotein-immunoglobulin G (MOG-IgG)-associated ON. Methods: Retrospective review of all patients evaluated at Mayo Clinic, Stanford University and Ramathibodi Hospital who were found to have: (1) ON, (2) either MOG-IgG or AQP4-IgG by cell-based assay, and (3) magnetic resonance imaging (MRI) at the time of ON. MRI was reviewed for contrast enhancement of the optic chiasm and the pattern of involvement. Results: One hundred and fifty-four patients (74 AQP4-IgG and 80 MOG-IgG) were included. Among patients with AQP4-IgG-ON, 20% had chiasmal involvement, compared with 16% of patients with MOG-IgG-ON ( p = 0.66). In patients with chiasmal involvement, longitudinally extensive optic nerve enhancement (from orbit extending to chiasm) was identified in 54% of MOG-IgG-ON patients, compared with 7% of AQP4-IgG-ON patients ( p = 0.01). Conclusion: Chiasmal involvement of MOG-IgG-ON and AQP4-IgG-ON occur at more similar frequencies than previously reported. Furthermore, MOG-IgG-ON chiasmal involvement is more likely to be part of a longitudinally extensive optic nerve lesion.

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