Henning Haahr Andersen

Diabetic polyneuropathies: update on research definition, diagnostic criteria and estimation of severity

Prior to a joint meeting of the Neurodiab Association and International Symposium on Diabetic Neuropathy held in Toronto, Ontario, Canada, 13‐18 October 2009, Solomon Tesfaye, Sheffield, UK, convened a panel of neuromuscular experts to provide an update on polyneuropathies associated with diabetes (Toronto Consensus Panels on DPNs, 2009). Herein, we provide definitions of typical and atypical diabetic polyneuropathies (DPNs), diagnostic criteria, and approaches to diagnose sensorimotor polyneuropathy as well as to estimate severity. Diabetic sensorimotor polyneuropathy (DSPN), or typical DPN, usually develops on long‐standing hyperglycaemia, consequent metabolic derangements and microvessel alterations. It is frequently associated with microvessel retinal and kidney disease—but other causes must be excluded. By contrast, atypical DPNs are intercurrent painful and autonomic small‐fibre polyneuropathies. Recognizing that there is a need to detect and estimate severity of DSPN validly and reproducibly, we define subclinical DSPN using nerve conduction criteria and define possible, probable, and confirmed clinical levels of DSPN. For conduct of epidemiologic surveys and randomized controlled trials, it is necessary to pre‐specify which attributes of nerve conduction are to be used, the criterion for diagnosis, reference values, correction for applicable variables, and the specific criterion for DSPN. Herein, we provide the performance characteristics of several criteria for the diagnosis of sensorimotor polyneuropathy in healthy subject‐ and diabetic subject cohorts. Also outlined here are staged and continuous approaches to estimate severity of DSPN. Copyright

Isokinetic Muscle Strength in Long-Term IDDM Patients in Relation to Diabetic Complications

The isokinetic muscle strength in 56 IDDM patients with > 20 years of diabetes duration and in their individually sex-, age-, weight-, and height-matched control subjects was assessed. Peak torque of foot dorsal and plantar flexion and knee and wrist extension and flexion was measured. The neuropathic condition was assessed by a neurological disability score, a neuropathy symptom score, nerve conduction studies, and quantitative sensory examination. All results were summed to obtain a neuropathy rank-sum score for each patient. According to their renal albumin excretion, the patients were classified to have normo-, micro-, or macroalbuminuria. In addition, according to their retinal status, patients were classified as having no, simple, or proliferative retinopathy. The IDDM patients had a 21% reduction of muscle strength of both ankle dorsal (P < 1 × 10™4) and plantar flexors (P < 0.01), compared with control subjects. A 16% reduction of knee extensors (P < 0.005) and a 17% reduction of knee flexors (P < 0.01) was found. In contrast, muscle strength in wrist flexors and extensors was not significantly reduced (10 and 11%, respectively [NS]). In patients with the most severe weakness, muscle strength of the calf muscles was only 50% of the expected performance. Correlations were found between the neuropathy rank-sum score and the muscle strength of ankle dorsal (r = −0.66, P < 1 × 10™7) and plantar flexors (r = −0.51, P < 0.0005), knee extensors (r = −0.51, P < 0.0005) and flexors (r = −0.44, P < 0.005), and wrist flexors (r = −0.41, P < 0.005). No correlation was found for wrist extensors (r = 0). Neither were there any relationships between muscle strength at the ankle and knee and the degree of albuminuria or retinopathy. In conclusion, motor performance is substantially impaired in long-term IDDM patients, and the weakness is related to the presence of neuropathy but not to albuminuria or retinopathy per se.

Tensor products of quantized tilting modules

LetUk denote the quantized enveloping algebra corresponding to a finite dimensional simple complex Lie algebraL. Assume that the quantum parameter is a root of unity ink of order at least the Coxeter number forL. Also assume that this order is odd and not divisible by 3 if typeG2 occurs. We demonstrate how one can define a reduced tensor product on the familyF consisting of those finite dimensional simpleUk-modules which are deformations of simpleL and which have non-zero quantum dimension. This together with the work of Reshetikhin-Turaev and Turaev-Wenzl prove that (Uk,F) is a modular Hopf algebra and hence produces invariants of 3-manifolds. Also by recent work of Duurhus, Jakobsen and Nest it leads to a general topological quantum field theory. The method of proof explores quantized analogues of tilting modules for algebraic groups.

Fusion Categories Arising from Semisimple Lie Algebras

Using tilting modules we equip certain semisimple categories with a “reduced” tensor product structure. The fusion rules for this tensor product are determined via known character formulas for the involved modules.

Long-term therapy with high doses of subcutaneous immunoglobulin in multifocal motor neuropathy

Background: In multifocal motor neuropathy (MMN), high dose of IV immunoglobulin (IVIg) is the only established treatment. Subcutaneous self-infusion with immunoglobulin G (IgG) (SCIG) increases patient autonomy and treatment flexibility, and might be associated with fewer side effects due to lower peak IgG levels. In a recent study of 9 patients with MMN, we reported that SCIG preserves muscle strength for a few months of treatment. Five patients preferred to continue SCIG after the trial and another patient chose to apply SCIG. Methods: In this case series study of 6 IVIg-responsive patients with MMN on long-term SCIG maintenance therapy, a dose equivalent to their previous IVIg regimen was given for 2 years. Patients were evaluated before and after 3, 6, 9, 18, and 24 months of initiation of treatment using isokinetic strength examination of affected muscle groups, scores of neuropathy impairment and disability, and recording of side effects. The dosage of SCIG varied between 13 and 51 g per week, corresponding to a volume of 80 to 320 mL infused twice or thrice weekly. Results: No major side events were reported, local skin reactions being mild and transient. The impairment and disability scores remained unchanged. Isokinetic muscle strength was stable with a median (range) 3.7% (−8.8 to 14.5) increase at follow-up. Conclusion: Our study shows that long-term SCIG therapy is an alternative approach to IVIg that is desirable for some patients. Classification of evidence: This 2-year follow-up study provides Class IV evidence of tolerability and safety in a small (n = 6) case series of patients with MMN preferring SCIG to IVIg.

Schubert varieties and Demazure's character formula

In [3] M. Demazure constructed the so-called Bott-Samelson scheme (see also [6]) which gives desingularizations of the Schubert varieties in the flag manifold G/B. Here G denotes a semi-simple algebraic group over a field k and B is a Borel subgroup. He proved that this construction makes it easy to calculate the Chow ring of G/B and when k has characteristic zero he also used it to prove the following

An inversion formula for the Kazhdan-Lusztig polynomials for affine weyl groups

Let W be a Coxeter group. In [10] Kazhdan and Lusztig defined for each y, w e W certain polynomials Py,w over 7/. They conjectured that in the case where W is the Weyl group corresponding to a complex semi-simple Lie algebra (5 these polynomials determine the characters of the irreducible IS-modules. (This conjecture has now been proved; see [3, 4].) Later G. Lusztig [11] formulated a corresponding conjecture for the irreducible modules for a semi-simple algebraic group G defined over an algebraically closed field of prime characteristic p involving the same polynomials except that W is now the affine Weyl group corresponding to G. Elementary properties of the polynomials Py,w show that there exist polynomials Q .... x, z ~ W such that the inversion formula

Twisted Verma Modules

Using principal series Harish-Chandra modules, local cohomology with support in Schubert cells and twisting functors we construct certain modules parametrized by the Weyl group and a highest weight in the subcategory O of the category of representations of a complex semisimple Lie algebra. These are in a sense modules between a Verma module and its dual. We prove that the three different approaches lead to the same modules. Moreover, we demonstrate that they possess natural Jantzen type filtrations with corresponding sum formulae.

On the structure of the cohomology of line bundles on GB

One of the most intriguing problems in characteristic p representation theory for semisimple algebraic groups is the problem of finding the formal characters of the irreducible modules. An equivalent problem is to find the composition factors of Weyl modules. It is a (non-trivial) fact that the Weyl modules occur as the top cohomology groups of certain line bundles on homogeneous spaces. One could therfore more generally ask for the composition factors of all such cohomology groups. References [2] and [3] deal with aspects of this question. In the present paper we use a method primarily due to J. C. Jantzen [ 151 to extend the results in the abovementioned works. Our main results are (i) a translation principle (Theorem 2.5 below) generalizing Jantzen’s theorem in [ 15’1, (ii) a proof of the Carter-Lusztig conjecture (see [6, p. 2391, compare also [3, Theorem 4.11 and [ 71) on the existence of intertwining homomorphisms between Weyl modules (Theorem 3.3 below) together with some related results on higher Ext,-groups, and (iii) a rather general vanishing theorem for cohomology groups of line bundles on homogeneous spaces (Theorem 4.1 below). As will be apparent from a comparison with [ 151, many of Jantzen’s arguments in the proof of his translation principle can be directly carried over to our situation. However, the fact that we deal with all cohomology groups (not just the highest) allows us sometimes to shorten the proofs. In particular this is, the case for the proof of Proposition 2.3 (in which we give the effect of the translation functor on irreducible modules). In an earlier preprint [4], we showed that the vanishing theorem for dominant line bundles on homogeneous spaces can be proved (for p big) using “translation arguments.” Shortly after that preprint was written, the author 151 (and, independently, W. Haboush [ 111) found an even simpler way of proving that result. In order to describe the vanishing behaviour of the cohomology of non-ample line bundles the method is, however, still useful. This is demonstrated in the last section of this paper, where we 245 0021.8693/81,‘070245-14

Effects of resistance training and aerobic training on ambulation in chronic stroke.

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