Relationship between pain and anxiety in rats

Clinically, it is well known that neuropathic pain often induces comorbid symptoms such as anxiety. In turn, also anxiety has been associated with a heightened experience of pain. Although, the link between pain and anxiety is well recognized in humans, the neurobiological basis of this relationship remains unclear. Therefore, the aim of the current study was to investigate the influence of neuropathic pain on anxiety and vice versa in rats by assessing not only pain-related behaviour but also by discovering possible key substrates which are responsible for the interrelation of pain and anxiety.rnIn rats with a chronic constriction of the sciatic nerve (CCI model) anxiety-like behaviour was observed. Since anxiety behaviour could be completely abolished after the treatment of the pure analgesic drugs gabapentin and morphine, we concluded that anxiety was caused by the strong persistent pain. Furthermore, we found that the neuropeptides oxytocin and vasopressin were upregulated in the amygdala of CCI rats, and the intra-amygdala treatment of an oxytocin antagonist but not the vasopressin antagonist could reduce anxiety-like behaviour in these animals, while no effect on mechanical hypersensitivity was observed. These data indicate that oxytocin is implicated in the underlying neuronal processes of pain-induced anxiety and helps to elucidate the pathophysiological mechanisms of neuropathic pain. rnTo assess the influence of trait anxiety on pain sensation in rats, we determined mechanical hypersensitivity after sciatic nerve lesion (CCI) in animals selectively bred for high anxiety or low anxiety behaviour. The paw withdrawal thresholds were significantly decreased in high anxiety animals in comparison to low anxiety animals 2 and 3 weeks after surgery. In a second model state anxiety was induced by the sub-chronic injection of the anxiogenic drug pentylentetrazol in naive rats. Pain response to mechanical stimuli was increased after pharmacologically-induced anxiety. These results provided evidence for the influence of both trait and state anxiety on pain sensation. rnThe studies contribute to the elucidation of the relationship between pain and anxiety. We investigated that the neuropathic pain model displays sensory as well as emotional factors of peripheral neuropathy. Changes in expression levels of neuropeptides in the central nervous system due to neuropathic pain may contribute to the pathophysiology of neuropathic pain and its related symptoms in animals which might also be relevant for human scenarios. The results of the current study also confirm that anxiety plays an important role in the perception of pain. rnA better understanding of pain behaviour in animals might improve the preclinical profiling of analgesic drugs during development. The study highlights the potential use of the rat model as a new preclinical tool to further investigate the link between pain and anxiety by determining not only the sensory reflexes after painful stimuli but also the more complex pain-related behaviour such as anxiety.rn

Mathematical aspects of Feynman integrals

In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals.rnrnThe integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph.rnrnStarting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative step to an abstract combinatorial problem, known as Hironaka's polyhedra game. We present a publicly available implementation of the improved algorithm. Furthermore we explain the relationship of the sector decomposition method with the resolution of singularities of a variety, given by a sequence of blow-ups, in algebraic geometry.rnrnMotivated by the connection between Feynman integrals and topics of algebraic geometry we consider the set of periods as defined by Kontsevich and Zagier. This special set of numbers contains the set of multiple zeta values and certain values of polylogarithms, which in turn are known to be present in results for Laurent coefficients of certain dimensionally regularized Feynman integrals. By use of the extended sector decomposition algorithm we prove a theorem which implies, that the Laurent coefficients of an arbitrary Feynman integral are periods if the masses and kinematical invariants take values in the Euclidean momentum region. The statement is formulated for an even more general class of integrals, allowing for an arbitrary number of polynomials in the integrand.