Fractional Euler-Lagrange differential equations via Caputo derivatives

We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in pres

Fractional variational calculus of variable order

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.Comment: Submitted 26-Sept-2011; accepted 18-Oct-2011; withdrawn by the authors 21-Dec-2011; resubmitted 27-Dec-2011; revised 20-March-2012; accepted 13-April-2012; to 'Advances in Harmonic Analysis and Operator Theory', The Stefan Samko Anniversary Volume (Eds: A. Almeida, L. Castro, F.-O. Speck), Operator Theory: Advances and Applications, Birkh\"auser Verlag (http://www.springer.com/series/4850

RISK OF DEATH AFTER PACLITAXEL EXPOSURE DURING FEMOROPOPLITEAL ARTERY ANGIOPLASTY – NARRATIVE REVIEW

Paclitaxel molecule has been on the market since 1991 and is indicated for the treatment of multiple neoplasms. Since 2012 has been used in endovascular devices for the treatment of peripheral artery disease and have become a mainstay in the treatment of symptomatic femoro-popliteal lesions, in particular for preventing arterial restenosis. They have a proven benefit in patency and freedom-from re-intervention up to 5 years. A recent meta-analysis of RCT showed an increased late-mortality rate, however, real-life cohorts analyses presents contradictory results. RCT meta-analysis is comprised mainly by claudicants, and CLTI patients are underrepresented. Further studies are needed to clarify this matter, in particular with a higher percentage of CLTI presentation. For now, patients should be advised about risks and benefits of paclitaxel exposure and a shared decision-making process should be followed

DIBMA nanodiscs keep α-synuclein folded

α-Synuclein (αsyn) is a cytosolic intrinsically disordered protein (IDP) known to fold into an α-helical structure when binding to membrane lipids, decreasing protein aggregation. Model membrane enable elucidation of factors critically affecting protein folding/aggregation, mostly using either small unilamellar vesicles (SUVs) or nanodiscs surrounded by membrane scaffold proteins (MSPs). Yet SUVs are mechanically strained, while MSP nanodiscs are expensive. To test the impact of lipid particle size on α-syn structuring, while overcoming the limitations associated with the lipid particles used so far, we compared the effects of large unilamellar vesicles (LUVs) and lipid-bilayer nanodiscs encapsulated by diisobutylene/maleic acid copolymer (DIBMA) on αsyn secondary-structure formation, using human-, elephant- and whale -αsyn. Our results confirm that negatively charged lipids induce αsyn folding in h-αsyn and e-αsyn but not in w-αsyn. When a mixture of zwitterionic and negatively charged lipids was used, no increase in the secondary structure was detected at 45 °C. Further, our results show that DIBMA/lipid particles (DIBMALPs) are highly suitable nanoscale membrane mimics for studying αsyn secondary-structure formation and aggregation, as folding was essentially independent of the lipid/protein ratio, in contrast with what we observed for LUVs having the same lipid compositions. This study reveals a new and promising application of polymer-encapsulated lipid-bilayer nanodiscs, due to their excellent efficiency in structuring disordered proteins such as αsyn into nontoxic α-helical structures. This will contribute to the unravelling and modelling aspects concerning protein-lipid interactions and α-helix formation by αsyn, paramount to the proposal of new methods to avoid protein aggregation and disease.info:eu-repo/semantics/publishedVersio

Universality in Systems with Power-Law Memory and Fractional Dynamics

There are a few different ways to extend regular nonlinear dynamical systems by introducing power-law memory or considering fractional differential/difference equations instead of integer ones. This extension allows the introduction of families of nonlinear dynamical systems converging to regular systems in the case of an integer power-law memory or an integer order of derivatives/differences. The examples considered in this review include the logistic family of maps (converging in the case of the first order difference to the regular logistic map), the universal family of maps, and the standard family of maps (the latter two converging, in the case of the second difference, to the regular universal and standard maps). Correspondingly, the phenomenon of transition to chaos through a period doubling cascade of bifurcations in regular nonlinear systems, known as "universality", can be extended to fractional maps, which are maps with power-/asymptotically power-law memory. The new features of universality, including cascades of bifurcations on single trajectories, which appear in fractional (with memory) nonlinear dynamical systems are the main subject of this review.Comment: 23 pages 7 Figures, to appear Oct 28 201

Circulating biomarkers of cardiovascular disease are related to aneurysm volume in abdominal aortic aneurysm

Background: Surveillance programs in abdominal aortic aneurysms (AAA) are mainly based on imaging and leave room for improvement to timely identify patients at risk for AAA growth. Many biomarkers are dysregulated in patients with AAA, which fuels interest in biomarkers as indicators of disease progression. We examined associations of 92 cardiovascular disease (CVD)-related circulating biomarkers with AAA and sac volume. Methods: In a cross-sectional analysis, we separately investigated (1) 110 watchful waiting (WW) patients (undergoing periodic surveillance imaging without planned intervention) and (2) 203 patients after endovascular aneurysm repair (EVAR). The Cardiovascular Panel III (Olink Proteomics AB, Sweden) was used to measure 92 CVD-related circulating biomarkers. We used cluster analyses to investigate protein-based subphenotypes, and linear regression to examine associations of biomarkers with AAA and sac volume on CT scans. Results: Cluster analyses revealed two biomarker-based subgroups in both WW and EVAR patients, with higher levels of 76 and 74 proteins, respectively, in one subgroup versus the other. In WW patients, uPA showed a borderline significant association with AAA volume. Adjusting for clinical characteristics, there was a difference of −0.092 (−0.148, −0.036) loge mL in AAA volume per SD uPA. In EVAR patients, after multivariable adjustment, four biomarkers remained significantly associated with sac volume. The mean effects on sac volume per SD difference were: LDLR: −0.128 (−0.212, −0.044), TFPI: 0.139 (0.049, 0.229), TIMP4: 0.110 (0.023, 0.197), IGFBP-2: 0.103 (0.012, 0.194). Conclusion: LDLR, TFPI, TIMP4, and IGFBP-2 were independently associated with sac volume after EVAR. Subgroups of patients with high levels of the majority of CVD-related biomarkers emphasize the intertwined relationship between AAA and CVD. ClinicalTrials.gov Identifier: NCT03703947.</p

MORPHOLOGIC CHANGES AND CLINICAL CONSEQUENCES OF WIDE AAA NECKS TREATED WITH 34-36MM PROXIMAL DIAMETER EVAR DEVICES

Introduction: Endovascular aneurysm repair (EVAR) became the preferred modality for infrarenal aneurysm (AAA) repair. Several available endografts have main body proximal diameters up to 36mm, allowing for treatment of proximal AAA necks up to 32 mm. However, large neck represents a predictor of proximal complications after EVAR. The purpose of this study is to evaluate mid-term outcomes of patients requiring 34-36mm main body devices. Methods: Retrospective review of a prospectively maintained database including all patients undergoing elective EVAR for degenerative AAA in a single tertiary referral hospital in The Netherlands were eligible. All measurements were performed on center-lumen line reconstructions obtained on dedicated software. Patients were classified as large diameter (LD) if the implanted device was >32mm wide. The remaining patients were classified as normal diameter (ND). Primary endpoint was neck-related events (a composite of “endoleak” (EL) 1A, neck-related secondary intervention or migration >5mm). Neck morphology changes and survival were also assessed. Differences in groups were adjusted by multivariable analysis. Results: The study included 502 patients (90 in the LD group; 412 in the ND group). Median follow-up was 3.5 years (1.5–6.2) and 4.5 years (2.1–7.3) for the LD and ND groups, respectively (P = .008). Regarding baseline characteristics, hypertension (83% vs 69.7%, P=.012) and smoking (86% vs 74.1%, P=.018) were more frequent in the LD group. Patients in the LD group had wider (Proximal neck Ø > 28 mm: 75% vs 3.3%, P45º: 21% vs 9%, P=.002), more conical (39.8% vs 20.3%, P25%: 42% vs 32.3%, P 5mm occurred similarly in both groups (7.8% vs 5.1%, P=.32). Neck-related secondary interventions were also more common among LD patients (13.3% vs 8.7%; P = .027). On multivariable regression analysis, LD group was an independent risk factor for neck-related adverse events (Hazard Ratio [HR]: 2.29; 95% confidence interval [CI], 1.37–3.83, P=0.002). Neck dilatation was greater among LD patients (median, 3 mm [IQR, 0–6] vs 2mm [IQR, 0–4]; P =.034) On multivariable analysis, LD was an independent predictor for neck dilatation > 10 % (HR: 1.61 CI 95% 1.08–2.39, P=.020). Survival at 5-years was 66.1% for LD and 71.2% for SD groups, P=.14. Conclusion: Standard EVAR in patients with large infrarenal necks requiring a 34- to 36-mm proximal endograft is independently associated to increased rate of neck related events and more neck dilatation. This subgroup of patients could be considered for more proximal seal strategies with fenestrated or branched devices, if unfit for open repair. Tighter surveillance following EVAR in these patients in the long term is also advised

ENDOVASCULAR ANEURYSM REPAIR IN WIDE INFRARENAL NECKS - INCREASED RISK OF COMPLICATIONS?

EVAR has become the predominant repair technique for abdominal aortic aneurysm. Long-term clinical success relies greatly upon a long-lasting proximal seal. EVAR has achieved good outcomes on the short-term in patients with hostile neck features such as large proximal necks. However, the long-term outcomes in these patients is greatly unknown. In this article, the authors perform a literature review in order to assess the clinical impact of wide proximal neck on mid to long-term outcomes following EVAR