A stochastic representation for the solution of approximated mean curvature flow

The evolution by horizontal mean curvature flow (HMCF) is a partial differential equation in a sub-Riemannian setting with applications in IT and neurogeometry . Unfortunately this equation is difficult to study,since the horizontal normal is not always well defined. To overcome this problem the Riemannian approximation was introduced. In this article we obtain a stochastic representation of the solution of the approximated Riemannian mean curvature using the Riemannian approximation and we will prove that it is a solution in the viscosity sense of the approximated mean curvature ow, generalizing the result of Dirr,Dragoni, von Renesse, 2010

Endovascular repair for acute traumatic transection of the descending thoracic aorta: experience of a single centre with a 12-years follow up

Background: Most blunt aortic injuries occur in the proximal proximal descending aorta causing acute transection of this vessel. Generally, surgical repair of the ruptured segment of aorta is associated with high rates of morbidity and mortality and in this view endovascular treatment seems to be a valid and safer alternative. Aim of this article is to review our experience with endovascular approach for the treatment of acute traumatic rupture of descending thoracic aorta. Methods: From April 2002 to November 2014, 11 patients (9 males and 2 females) were referred to our Department with a diagnosis of acute transection of thoracic aorta. Following preoperative Computed Tomography (CT) evaluation, thoracic endovascular aortic repair (TEVAR) with left subclavian artery coverage was performed. Follow-up consisted clinical and instrumental (CT, Duplex ultrasound) controls at discharge, 1, 3 and 6 months and yearly thereafter. Results: At 12-year follow up, the overall survival for the entire patients cohort was 100 %, no major or minor neurological complications and no episode of left arm claudication occurred. Cardiovascular, respiratory and bleeding complications, in the early period, was represented by minor, non fatal events. No stent graft failure, collapse, leak or distal migration were detected at CT scan during the entire follow up period. Conclusions: According to our experience, despite the small number of patient population, TEVAR procedure with with left subclavian artery coverage, performed in emergency settings, seems to provide excellent long term results. Trials registration: The protocol was registered at a public trials registry, www.clinicaltrials.gov (trial identifier NCT02376998)

Horizontal mean curvature flow and nonlinear PDEs in sub-Riemannian spaces

The horizontal mean curvature flow is an evolution of a hypersurface, which is interesting not only in a theoretical framework but also in applied science, for example in neurogeometry and computer science (e.g. [13, 14, 15]). The associated equation, roughly speaking, describes the motion of a hypersurface embedded in a sub-Riemannian geometry (e.g. the Heisenberg group or a Carnot group, see [4, 43]) in relation to its horizontal mean curvature

The impact of endodontic anatomy on clinical practice: a micro-CT study and tribute to Prof. Francesco Riitano

Aim: To evaluate the quality of root canal preparation using two different mechanical NiTi systems. Methodology: 40 maxillary and mandibular molars were selected. Specimens were randomly assigned to two groups and were scanned using a micro-computed tomography scanner before and after root canal preparation that was performed using ProFile instrument sequence and Reciproc single file technique. Each system was used to obtain an optimal apical size for each specimen, following common clinical guidelines. 3D models were reconstructed and evaluated for volume, areas and root canal axis. The total volume of dentine removed and the volume of the coronal, middle and apical thirds of each root canal were calculated, as well as the average deviation of the root canal axis at different levels and the values compared. Student t-test was used to determine the difference between the two experimental groups (P < 0.05). A qualitative evaluation of root canal preparation was also performed. Results: No statistically significant differences were noted between the groups in the volume of dentine removed after root canal preparation, except for the volume of the coronal third (P < 0.05) and the volume of the apical third (P < 0.05) of the disto-buccal canal of maxillary molars and in the mesial canals of mandibular molars, where ProFile instruments produced significantly less enlarged canal volume in the apical third and more enlarged canal volume in the coronal third (P < 0.05). No statistically significant differences were found in the root canal axis deviation. Conclusions: Under the conditions of this study, both the systems analyzed were able to prepare molar teeth with similar amount of dentine removal and a relatively low risk of procedural errors

Precision medicine and precision nursing. The era of biomarkers and precision health

Precision health, by means of the support of precision medicine and precision nursing, is able to support clinical decision making in order to tailor optimal health-care decisions, around the individual characteristics of patients. The operational arm of precision health is represented by the use of biomarkers that can give useful information about disease susceptibility, exposure, evolution and response to treatment. Omics, imaging and clinical biomarkers are actually studied for their ability to positively impact health-care management. In this article, we try to address the role of biomarkers in the context of modern medicine and nursing with the view of improving patients care