Su alcune applicazioni del teorema di Stokes

Nel lavoro si dimostrano il Teorema della Divergenza e il Teorema di Stokes e le sue generalizzazioni a una curva chiusa di ordine k e a una varietà M, n-dimensionale, orientata con bordo. Successivamente si espongono due applicazioni alla fisica: l'elettromagnetismo e la formula del rotore. Nel primo caso si mostra come applicando il Teorema alle leggi di Biot-Savarat e di Faraday si ottengono le equazioni di Maxwell; nel secondo invece si osserva come il rotore rappresenti la densità superficiale di circuitazione.

The effect of high-energy extracorporeal shock waves on hyaline cartilage of adult rats in vivo

The aim of this study was to determine if extracorporeal shock wave therapy (ESWT) in vivo affects the structural integrity of articular cartilage. A single bout of ESWT (1500 shock waves of 0.5 mJ/mm(2)) was applied to femoral heads of 18 adult Sprague-Dawley rats. Two sham-treated animals served as controls. Cartilage of each femoral head was harvested at 1, 4, or 10 weeks after ESWT (n = 6 per treatment group) and scored on safranin-O-stained sections. Expression of tenascin-C and chitinase 3-like protein 1 (Chi3L1) was analyzed by immunohistochemistry. Quantitative real-time polymerase chain reaction (PCR) was used to examine collagen (II)alpha(1) (COL2A1) expression and chondrocyte morphology was investigated by transmission electron microscopy no changes in Mankin scores were observed after ESWT. Positive immunostaining for tenascin-C and Chi3L1 was found up to 10 weeks after ESWT in experimental but not in control cartilage. COL2A1 mRNA was increased in samples 1 and 4 weeks after ESWT. Alterations found on the ultrastructural level showed expansion of the rough-surfaced endoplasmatic reticulum, detachment of the cell membrane and necrotic chondrocytes. Extracorporeal shock waves caused alterations of hyaline cartilage on a molecular and ultrastructural level that were distinctly different from control. Similar changes were described before in the very early phase of osteoarthritis (OA). High-energy ESWT might therefore cause degenerative changes in hyaline cartilage as they are found in initial OA.

Calcium waves driven by "sensitization" wave-fronts

OBJECTIVE: Cellular Ca(2+) waves are understood as reaction-diffusion systems sustained by Ca(2+)-induced Ca(2+) release (CICR) from Ca(2+) stores. Given the recently discovered sensitization of Ca(2+) release channels (ryanodine receptors; RyRs) of the sarcoplasmic reticulum (SR) by luminal SR Ca(2+), waves could also be driven by RyR sensitization, mediated by SR overloading via Ca(2+) pump (SERCA), acting in tandem with CICR. METHODS: Confocal imaging of the Ca(2+) indicator fluo-3 was combined with UV-flash photolysis of caged compounds and the whole-cell configuration of the patch clamp technique to carry out these experiments in isolated guinea pig ventricular cardiomyocytes. RESULTS: Upon sudden slowing of the SERCA in cardiomyocytes with a photoreleased inhibitor, waves indeed decelerated immediately. No secondary changes of Ca(2+) signaling or SR Ca(2+) content due to SERCA inhibition were observed in the short time-frame of these experiments. CONCLUSIONS: Our findings are consistent with Ca(2+) loading resulting in a zone of RyR 'sensitization' traveling within the SR, but inconsistent with CICR as the predominant mechanism driving the Ca(2+) waves. This alternative mode of RyR activation is essential to fully conceptualize cardiac arrhythmias triggered by spontaneous Ca(2+) release.

Use of pressure waves to confirm the correct placement of epidural needles in dogs

An epidural puncture was performed using the lumbosacral approach in 18 dogs, and the lack of resistance to an injection of saline was used to determine that the needle was positioned correctly. The dogs' arterial blood pressure and epidural pressure were recorded. They were randomly assigned to two groups: in one group an injection of a mixture of local anaesthetic agents was made slowly over 90 seconds and in the other it was made over 30 seconds. After 10 minutes contrast radiography was used to confirm the correct placement of the needle. The mean (sd) initial pressure in the epidural space was 0.1 (0.7) kPa. After the injection the mean maximum epidural pressure in the group injected slowly was 5.5 (2.1) kPa and in the group injected more quickly it was 6.0 (1.9) kPa. At the end of the period of measurement, the epidural pressure in the slow group was 0.8 (0.5) kPa and in the rapid group it was 0.7 (0.5) kPa. Waves synchronous with the arterial pulse wave were observed in 15 of the dogs before the epidural injection, and in all the dogs after the epidural injection.

Limitations of the use of pressure waves to verify correct epidural needle position in dogs

The use of pressure waves to confirm the correct position of the epidural needle has been described in several domestic species and proposed as a valid alternative to standard methods, namely, control radiographic exam and fluoroscopy. The object of this retrospective clinical study was to evaluate the sensitivity of the epidural pressure waves as a test to verify the correct needle placement in the epidural space in dogs, in order to determine whether this technique could be useful not only in the clinical setting but also when certain knowledge of needle's tip position is required, for instance when performing clinical research focusing on epidural anaesthesia. Of the 54 client-owned dogs undergoing elective surgeries and enrolled in this retrospective study, only 45% showed epidural pressure waves before and after epidural injection. Twenty-six percent of the animals showed epidural pressure waves only after the injection, whereas 29% of the dogs showed epidural pressure waves neither before nor after injection and were defined as false negatives. Our results show that the epidural pressure wave technique to verify epidural needle position lacks sensitivity, resulting in many false negatives. As a consequence, the applicability of this technique is limited to situations in which precise, exact knowledge of the needle's tip position is not mandatory.