Effect of TENS on pain in relation to central sensitization in patients with osteoarthritis of the knee: study protocol of a randomized controlled trial

<p>Abstract</p> <p>Background</p> <p>Central sensitization has recently been documented in patients with knee osteoarthritis (OAk). So far, the presence of central sensitization has not been considered as a confounding factor in studies assessing the pain inhibitory effect of tens on osteoarthritis of the knee. The purpose of this study is to explore the pain inhibitory effect of burst tens in OAk patients and to explore the prognostic value of central sensitization on the pain inhibitory effect of tens in OAk patients.</p> <p>Methods</p> <p>Patients with knee pain due to OAk will be recruited through advertisements in local media. Temporal summation, before and after a heterotopic noxious conditioning stimulation, will be measured. In addition, pain on a numeric rating score, WOMAC subscores for pain and function and global perceived effect will be assessed. Patients will be randomly allocated to one of two treatment groups (tens, sham tens). Follow-up measurements will be scheduled after a period of 6 and 12 weeks.</p> <p>Discussion</p> <p>Tens influences pain through the electrical stimulation of low-threshold A-beta cutaneous fibers. The responsiveness of central pain-signaling neurons of centrally sensitized OAk patients may be augmented to the input of these electrical stimuli. This would encompass an adverse therapy effect of tens. To increase treatment effectiveness it might be interesting to identify a subgroup of symptomatic OAk patients, i.e., non-sensitized patients, who are likely to benefit from burst tens.</p> <p>Trial Registration</p> <p>ClinicalTrials.gov: <a href="http://www.clinicaltrials.gov/ct2/show/NCT01390285">NCT01390285</a></p

The concepts of general position and a second main theorem for non-linear divisors

The recent works of Evertse-Ferretti (Evertse and Ferretti, A generalization of the subspace theorem with polynomials of high degree, Dev. Math. (2008), pp.175-198) and Corvaja-Zannier (Corvaja and Zannier, On a general Theu's equation, Ann. Math. 160 (2004), pp. 705-726; Corvaja and Zannier, On integral points on surfaces, Amer. J. Math. 126 (2004), pp. 1033-1055) in diophantine approximations (Ru, A defect relation for holomorphic curves intersecting hypersurfaces, Amer. J. Math. 126 (2004), pp. 215-266; An, A defect relation for non-Archimedean analytic curves in arbitrary projective varieties, Proc. Amer. Math. Soc. 135 (2007), pp. 1255-1261) in complex and p-adic Nevanlinna theory extend the classical subspace theorem and the classical second main theorem to the case of non-linear divisors in general position. These had been long standing problems in diophantine approximation and Nevanlinna theory. However, their results when specialized to the case of hyperplanes are weaker than the classical results. In this article, we refine the concept of general position to the concepts of p-jet general position. These concepts of general position involve jets of order p and coincide with the usual concept of general position for hyperplanes, but are different for hypersurfaces of higher degrees. With the assumption that the hypersurfaces are in n-jet general position, a second main theorem, with ramification term, for non-linear divisors and d-non-degenerate map f:CgP n is obtained. The result when specialized to hyperplanes is precisely the classical result of Ahlfors (The theory of meromorphic curves, Acta Soc. Sci. Fenn. 3 (1941), pp. 1-31) (see also Cartan, Sur les zeros des combinations lineares de p fonctions holomorphes donees, Mathematica 7 (1933), pp. 5-31; Stoll, About the value distribution of holomorphic maps into the projective space, Acta Math. 123 (1969), pp. 83-114; Cowen and Griffiths, Holomorphic curves and metrics of nonnegative curvature, J. Anal. Math. 29 (1976), pp. 93-153; for small functions, see Yamanoi, The second main theorem for small functions and related problems, Acta Math. 192 (2004), pp. 225-294). In fact the proof is a modification of Ahlfors proof. There are a number of variations of Ahlfors proof, we choose the 'approximate negatively curved' approach used in Cowen and Griffiths (Holomorphic curves and metrics of non-negative curvature, J. Anal. Math. 29 (1976), pp. 93-153), Wong (Defect relation for meromorphic maps on parabolic manifolds and Kobayashi metrics on P n omitting hyperplanes, Ph.D. thesis, University of Notre Dame (1976)), Wong (Holomorphic curves in spaces of constant curvature, in Complex Geometry (Proceedings of the Osaka Conference, 1990), Lecture Notes in Pure and Applied Mathematics, Vol. 143, Marcel Dekker, New York, Basel, Hong Kong, 1993, pp. 201-223), Wong (On the second main theorem of Nevanlinna theory, Amer. J. of Math. 111 (1989), pp. 549-583) and Cowen (The Kobayashi metric on P n \ (2 n+1) hyperplanes, in Value Distribution Theory, Part A, R.O. Kujala and A.L. Vitter III, eds., Marcel Dekker, New York, 1974, pp. 205-223). © 2011 Taylor & Francis.link_to_subscribed_fulltex

A Second Main Theorem on ℙn for difference operator

The main result of this article is an extension of the Second Main Theorem, of Halburd and Korhonen, for meromorphic functions of finite order. Their result replaces the counting function of the ramification divisor Nramf(r) in the classical Second Main Theorem by the counting function of a finite difference divisor Npair(r). In this article, the Second Main Theorem of Halburd and Korhonen is extended to the case of holomorphic maps into ℙn of finite order. © 2009 Science in China Press and Springer Berlin Heidelberg.link_to_subscribed_fulltex

On polar ovals in abelian projective planes

A condition is introduced on the abelian difference set D of an abelian projective plane of odd order so that the oval 2D is the set of absolute points of a polarity, with the consequence that any such abelian projective plane is Desarguesian.published_or_final_versio