A Variational Procedure for Time-Dependent Processes

A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed state cases, the Navier-Stokes equations of hydrodynamics, transport theory, etc. It recaptures the Least Dissipation Function condition of Rayleigh-Onsager {\bf and in practical applications is flexible}. The variational proposal is tested on a two level system interacting that is subject, in one instance, to an interaction with a single oscillator and, in another, that evolves in a dissipative mode.Comment: 25 pages, 4 figure

Evaluation of Spinal Toxicity and Long-term Spinal Reflex Function after Intrathecal Levobupivaciane in the Neonatal Rat

Neuraxial anesthesia is utilized in children of all ages. Local anesthetics produce dose-dependent toxicity in certain adult models, but the developing spinal cord may also be susceptible to drug-induced apoptosis. In postnatal rodents, we examined the effects of intrathecal levobupivacaine on neuropathology and long-term sensorimotor outcomes

On the stability of standing waves of Klein-Gordon equations in a semiclassical regime

We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.Comment: 9 page

Injectable alginate hydrogel loaded with GDNF promotes functional recovery in a hemisection model of spinal cord injury

We hypothesized that local delivery of GDNF in spinal cord lesion via an injectable alginate hydrogel gelifying in situ would support spinal cord plasticity and functional recovery. The GDNF release from the hydrogel was slowed by GDNF encapsulation in microspheres compared to non-formulated GDNF (free GDNF). When injected in a rat spinal cord hemisection model, more neurofilaments were observed in the lesion when the rats were treated with free GDNF-loaded hydrogels. More growing neurites were detected in the tissues surrounding the lesion when the animals were treated with GDNF microsphere-loaded hydrogels. Intense GFAP (astrocytes), low III tubulin (neural cells) and RECA-1 (endothelial cells) stainings were observed for non-treated lesions while GDNF-treated spinal cords presented less GFAP staining and more endothelial and nerve fiber infiltration in the lesion site. The animals treated with free GDNF-loaded hydrogel presented superior functional recovery compared with the animals treated with the GDNF microsphere-loaded hydrogels and non-treated animals

Effects of Combinatorial Treatment with Pituitary Adenylate Cyclase Activating Peptide and Human Mesenchymal Stem Cells on Spinal Cord Tissue Repair

The aim of this study is to understand if human mesenchymal stem cells (hMSCs) and neuropeptide pituitary adenylate cyclase-activating polypeptide (PACAP) have synergistic protective effect that promotes functional recovery in rats with severe spinal cord injury (SCI). To evaluate the effect of delayed combinatorial therapy of PACAP and hMSCs on spinal cord tissue repair, we used the immortalized hMSCs that retain their potential of neuronal differentiation under the stimulation of neurogenic factors and possess the properties for the production of several growth factors beneficial for neural cell survival. The results indicated that delayed treatment with PACAP and hMSCs at day 7 post SCI increased the remaining neuronal fibers in the injured spinal cord, leading to better locomotor functional recovery in SCI rats when compared to treatment only with PACAP or hMSCs. Western blotting also showed that the levels of antioxidant enzymes, Mn-superoxide dismutase (MnSOD) and peroxiredoxin-1/6 (Prx-1 and Prx-6), were increased at the lesion center 1 week after the delayed treatment with the combinatorial therapy when compared to that observed in the vehicle-treated control. Furthermore, in vitro studies showed that co-culture with hMSCs in the presence of PACAP not only increased a subpopulation of microglia expressing galectin-3, but also enhanced the ability of astrocytes to uptake extracellular glutamate. In summary, our in vivo and in vitro studies reveal that delayed transplantation of hMSCs combined with PACAP provides trophic molecules to promote neuronal cell survival, which also foster beneficial microenvironment for endogenous glia to increase their neuroprotective effect on the repair of injured spinal cord tissue

C3 Peptide Promotes Axonal Regeneration and Functional Motor Recovery after Peripheral Nerve Injury

Peripheral nerve injuries are frequently seen in trauma patients and due to delayed nerve repair, lifelong disabilities often follow this type of injury. Innovative therapies are needed to facilitate and expedite peripheral nerve regeneration. The purpose of this study was to determine the effects of a 1-time topical application of a 26-amino-acid fragment (C3156-181), derived from the Clostridium botulinum C3-exoenzyme, on peripheral nerve regeneration in 2 models of nerve injury and repair in adult rats. After sciatic nerve crush, different dosages of C3156-181 dissolved in buffer or reference solutions (nerve growth factor or C3bot-wild-type protein) or vehicle-only were injected through an epineurial opening into the lesion sites. After 10-mm nerve autotransplantation, either 8.0 nmol/kg C3156-181 or vehicle were injected into the proximal and distal suture sites. For a period of 3 to 10 postoperative weeks, C3156-181-treated animals showed a faster motor recovery than control animals. After crush injury, axonal outgrowth and elongation were activated and consequently resulted in faster motor recovery. The nerve autotransplantation model further elucidated that C3156-181 treatment accounts for better axonal elongation into motor targets and reduced axonal sprouting, which are followed by enhanced axonal maturation and better axonal functionality. The effects of C3156-181 are likely caused by a nonenzymatic down-regulation of active RhoA. Our results indicate the potential of C3156-181 as a therapeutic agent for the topical treatment of peripheral nerve repair sites

Treatment of Rat Spinal Cord Injury with the Neurotrophic Factor Albumin-Oleic Acid: Translational Application for Paralysis, Spasticity and Pain

Sensorimotor dysfunction following incomplete spinal cord injury (iSCI) is often characterized by the debilitating symptoms of paralysis, spasticity and pain, which require treatment with novel pleiotropic pharmacological agents. Previous in vitro studies suggest that Albumin (Alb) and Oleic Acid (OA) may play a role together as an endogenous neurotrophic factor. Although Alb can promote basic recovery of motor function after iSCI, the therapeutic effect of OA or Alb-OA on a known translational measure of SCI associated with symptoms of spasticity and change in nociception has not been studied. Following T9 spinal contusion injury in Wistar rats, intrathecal treatment with: i) Saline, ii) Alb (0.4 nanomoles), iii) OA (80 nanomoles), iv) Alb-Elaidic acid (0.4/80 nanomoles), or v) Alb-OA (0.4/80 nanomoles) were evaluated on basic motor function, temporal summation of noxious reflex activity, and with a new test of descending modulation of spinal activity below the SCI up to one month after injury. Albumin, OA and Alb-OA treatment inhibited nociceptive Tibialis Anterior (TA) reflex activity. Moreover Alb-OA synergistically promoted early recovery of locomotor activity to 50±10% of control and promoted de novo phasic descending inhibition of TA noxious reflex activity to 47±5% following non-invasive electrical conditioning stimulation applied above the iSCI. Spinal L4–L5 immunohistochemistry demonstrated a unique increase in serotonin fibre innervation up to 4.2±1.1 and 2.3±0.3 fold within the dorsal and ventral horn respectively with Alb-OA treatment when compared to uninjured tissue, in addition to a reduction in NR1 NMDA receptor phosphorylation and microglia reactivity. Early recovery of voluntary motor function accompanied with tonic and de novo phasic descending inhibition of nociceptive TA flexor reflex activity following Alb-OA treatment, mediated via known endogenous spinal mechanisms of action, suggests a clinical application of this novel neurotrophic factor for the treatment of paralysis, spasticity and pain

Derivations of the Born Rule

The Born rule, a cornerstone of quantum theory usually taken as a postulate, continues to attract numerous attempts for its derivation. A critical review of these derivations, from early attempts to very recent results, is presented. It is argued that the Born rule cannot be derived from the other postulates of quantum theory without some additional assumptions