Teichm\"uller's problem in space

Quasiconformal homeomorphisms of the whole space Rn, onto itself normalized at one or two points are studied. In particular, the stability theory, the case when the maximal dilatation tends to 1, is in the focus. Our main result provides a spatial analogue of a classical result due to Teichm\"uller. Unlike Teichm\"uller's result, our bounds are explicit. Explicit bounds are based on two sharp well-known distortion results: the quasiconformal Schwarz lemma and the bound for linear dilatation. Moreover, Bernoulli type inequalities and asymptotically sharp bounds for special functions involving complete elliptic integrals are applied to simplify the computations. Finally, we discuss the behavior of the quasihyperbolic metric under quasiconformal maps and prove a sharp result for quasiconformal maps of R^n \ {0} onto itself.Comment: 25 pages, 2 figure

Alleviation of migraine symptoms by application of repetitive peripheral magnetic stimulation to myofascial trigger points of neck and shoulder muscles - A randomized trial

Migraine is a burdensome disease with an especially high prevalence in women between the age of 15 and 49 years. Non-pharmacological, non-invasive therapeutic methods to control symptoms are increasingly in demand to complement a multimodal intervention approach in migraine. Thirty-seven subjects (age: 25.0 +/- 4.1 years;36 females) diagnosed with high-frequency episodic migraine who presented at least one active myofascial trigger point (mTrP) in the trapezius muscles and at least one latent mTrP in the deltoid muscles bilaterally prospectively underwent six sessions of repetitive peripheral magnetic stimulation (rPMS) over two weeks. Patients were randomly assigned to receive rPMS applied to the mTrPs of the trapezius (n = 19) or deltoid muscles (n = 18). Whereas the trapezius muscle is supposed to be part of the trigemino-cervical complex (TCC) and, thus, involved in the pathophysiology of migraine, the deltoid muscle was not expected to interfere with the TCC and was therefore chosen as a control stimulation site. The headache calendar of the German Migraine and Headache Society (DMKG) as well as the Migraine Disability Assessment (MIDAS) questionnaire were used to evaluate stimulation-related effects. Frequency of headache days decreased significantly in both the trapezius and the deltoid group after six sessions of rPMS (trapezius group: p = 0.005;deltoid group: p = 0.003). The MIDAS score decreased significantly from 29 to 13 points (p = 0.0004) in the trapezius and from 31 to 15 points (p = 0.002) in the deltoid group. Thus, rPMS applied to mTrPs of neck and shoulder muscles offers a promising approach to alleviate headache frequency and symptom burden. Future clinical trials are needed to examine more profoundly these effects, preferably using a sham-controlled setting

[Childhood stroke : What are the special features of childhood stroke?]

Childhood arterial ischemic stroke differs in essential aspects from adult stroke. It is rare, often relatively unknown among laypersons and physicians and the wide variety of age-specific differential diagnoses (stroke mimics) as well as less established care structures often lead to a considerable delay in the diagnosis of stroke. The possible treatment options in childhood are mostly off-label. Experiences in well-established acute treatment modalities in adult stroke, such as thrombolysis and mechanical thrombectomy are therefore limited in children and only based on case reports and case series. The etiological clarification is time-consuming due to the multitude of risk factors which must be considered. Identifying each child's individual risk profile is mandatory for acute treatment and secondary prevention strategies and has an influence on the individual outcome. In addition to the clinical neurological outcome the residual neurological effects of stroke on cognition and behavior are decisive for the integration of the child into its educational, later professional and social environment

Qualitative and quantitative muscle ultrasound in patients with Duchenne muscular dystrophy: Where do sonographic changes begin?

Objective: The number of studies investigating and understanding the disease mechanisms of Duchenne muscular dystrophy (DMD) in human clinical trials have increased substantially over the last decade. Suitable clinical instruments for the measurement of disease progress and drug efficiency are mandatory, but currently not available, especially in the youngest patients. The aim of this study was to detect a reproducible pattern of muscle involvement in early stages potentially preceding evidence of motor regression. Material and methods: A cohort of 25 DMD patients aged 1-6 years at the first presentation were examined at multiple timepoints and compared with age-matched healthy controls. Muscle ultrasound was quantified using computer-analyzed gray scale levels (GSL) and blinded visual rating, using a modified Heckmatt scale. Results: Changes in muscle echogenicity in DMD patients occurred very early, clearly preceding motor regression and in some cases, even before the motor plateau phase was reached. Visual rating and GSL identified the earliest changes in the proximal adductor magnus muscle. Conclusion: Muscle ultrasound can be used as an additional method to assess the disease progression and for decision-making in paucisymptomatic DMD patients. Sonographic changes in the ad-ductor magnus muscle seem to be the first detectable changes with a recognisable pattern. (c) 2020 European Paediatric Neurology Society. Published by Elsevier Ltd. All rights reserved

Psychometric Properties of the German Version of the Rivermead Post-Concussion Symptoms Questionnaire in Adolescents after Traumatic Brain Injury and Their Proxies

The Rivermead Post-Concussion Symptoms Questionnaire (RPQ) assesses post-concussion symptoms (PCS) after traumatic brain injury (TBI). The current study examines the applicability of self-report and proxy versions of the German RPQ in adolescents (13–17 years) after TBI. We investigated reliability and validity on the total and scale score level. Construct validity was investigated by correlations with the Post-Concussion Symptoms Inventory (PCSI-SR13), Generalized Anxiety Disorder Scale 7 (GAD-7), and Patient Health Questionnaire 9 (PHQ-9) and by hypothesis testing regarding individuals’ characteristics. Intraclass correlation coefficients (ICC) assessed adolescent–proxy agreement. In total, 148 adolescents after TBI and 147 proxies completed the RPQ. Cronbach’s α (0.81–0.91) and McDonald’s ω (0.84–0.95) indicated good internal consistency. The three-factor structure outperformed the unidimensional model. The RPQ was strongly correlated with the PCSI-SR13 (self-report: r = 0.80; proxy: r = 0.75) and moderately–strongly with GAD-7 and PHQ-9 (self-report: r = 0.36, r = 0.35; proxy: r = 0.53, r = 0.62). Adolescent–proxy agreement was fair (ICC [2,1] = 0.44, CI95% [0.41, 0.47]). Overall, both self-report and proxy assessment forms of the German RPQ are suitable for application in adolescents after TBI. As proxy ratings tend to underestimate PCS, self-reports are preferable for evaluations. Only if a patient is unable to answer, a proxy should be used as a surrogate

Instrumented Balance Error Scoring System in Children and Adolescents—A Cross Sectional Study

Background: The Balance Error Scoring System (BESS) is a commonly used method for clinically evaluating balance after traumatic brain injury. The utilization of force plates, characterized by their cost-effectiveness and portability, facilitates the integration of instrumentation into the BESS protocol. Despite the enhanced precision associated with instrumented measures, there remains a need to determine the clinical significance and feasibility of such measures within pediatric cohorts. Objective: To report a comprehensive set of posturographic measures obtained during instrumented BESS and to examine the concurrent validity, reliability, and feasibility of instrumented BESS in the pediatric point of care setting. Methods: Thirty-seven participants (18 female; aged 13.32 ± 3.31 years) performed BESS while standing on a force plate to simultaneously compute stabilometric measures (instrumented BESS). Ellipse area (EA), path length (PL), and sway velocity (VM) were obtained for each of the six BESS positions and compared with the respective BESS scores. Additionally, the effects of sex and age were explored. A second BESS repetition was performed to evaluate the test–retest reliability. Feedback questionnaires were handed out after testing to evaluate the feasibility of the proposed protocol. Results: The BESS total score was 20.81 ± 6.28. While there was no statistically significant age or sex dependency in the BESS results, instrumented posturography demonstrated an age dependency in EA, VM, and PL. The one-leg stance on a soft surface resulted in the highest BESS score (8.38 ± 1.76), EA (218.78 cm2 ± 168.65), PL (4386.91 mm ± 1859.00), and VM (21.93 mm/s ± 9.29). The Spearman’s coefficient displayed moderate to high correlations between the EA (rs = 0.429–0.770, p = 0.001–0.009), PL (rs = 0.451–0.809, p = 0.001–0.006), and VM (rs = 0.451–0.809, p = 0.001–0.006) when compared with the BESS scores for all testing positions, except for the one-leg stance on a soft surface. The BESS total score significantly correlated during the first and second repetition (rs = 0.734, p ≤ 0.001), as did errors during the different testing positions (rs = 0.489–0.799, p ≤ 0.001–0.002), except during the two-legged stance on a soft surface. VM and PL correlated significantly in all testing positions (rs = 0.465–0.675, p ≤ 0.001–0.004; (rs = 0.465–0.675, p ≤ 0.001–0.004), as did EA for all positions except for the two-legged stance on a soft surface (rs = 0.392–0.581, p ≤ 0.001–0.016). A total of 92% of participants stated that the instructions for the testing procedure were very well-explained, while 78% of participants enjoyed the balance testing, and 61% of participants could not decide whether the testing was easy or hard to perform. Conclusions: Instrumented posturography may complement clinical assessment in investigating postural control in children and adolescents. While the BESS score only allows for the consideration of a total score approximating postural control, instrumented posturography offers several parameters representing the responsiveness and magnitude of body sway as well as a more differentiated analysis of movement trajectory. Concise instrumented posturography protocols should be developed to augment neuropediatric assessments in cases where a deficiency in postural control is suspected, potentially stemming from disruptions in the processing of visual, proprioceptive, and/or vestibular information

Neurological soft signs are associated with reduced medial-lateral postural control in adolescent athletes

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