From Lagrangian to Quantum Mechanics with Symmetries

We present an old and regretfully forgotten method by Jacobi which allows one to find many Lagrangians of simple classical models and also of nonconservative systems. We underline that the knowledge of Lie symmetries generates Jacobi last multipliers and each of the latter yields a Lagrangian. Then it is shown that Noether's theorem can identify among those Lagrangians the physical Lagrangian(s) that will successfully lead to quantization. The preservation of the Noether symmetries as Lie symmetries of the corresponding Schr\"odinger equation is the key that takes classical mechanics into quantum mechanics. Some examples are presented.Comment: To appear in: Proceedings of Symmetries in Science XV, Journal of Physics: Conference Series, (2012

A direct approach to the construction of standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients

We present a direct approach to the construction of Lagrangians for a large class of one-dimensional dynamical systems with a simple dependence (monomial or polynomial) on the velocity. We rederive and generalize some recent results and find Lagrangian formulations which seem to be new. Some of the considered systems (e.g., motions with the friction proportional to the velocity and to the square of the velocity) admit infinite families of different Lagrangian formulations.Comment: 17 page

Quantification of 3α-hydroxytibolone in human plasma by high performance liquid chromatography coupled to electrospray ionization tandem mass spectrometry (HPLC-ESI-MS/MS): Application in a bioequivalence study in healthy postmenopausal volunteers

Abstract A sensitive, specific and fast method to quantify 3α-hydroxytibolone in human plasma using deuterated 3α-hydroxytibolone (d5) as internal standard is described. The analyte and the internal standard were extracted from plasma (900 μL) by liquid-liquid extraction using ethyl ether/hexane (50/50, v/v) and ammonium hydroxide (50%). The extracts were analyzed by high performance liquid chromatography coupled to electrospray ionization tandem mass spectrometry without derivatization. Chromatography was performed isocratically on a Gemini-NX™ C18 5 μm (150 × 4.6 mm i. d.) column. The method had a chromatographic run time of 3.75 min and a linear calibration curve over the range 1–100 ng/mL. The limit of quantification validated was 1 ng/mL. This method was used to assess the bioequivalence between two different tibolone oral formulations: Livolon (1.25 mg tablet) provided by Biolab Sanus Farmaceutica (Brazil), as the test formulation, and Libiam™ (1.25 mg tablet) produced by Libbs Farmaceutica (Brazil), as the reference formulation. A single 3.75 mg dose of each formulation was administered to 46 postmenopausal female healthy volunteers. The study was conducted in an open, randomized, two-period crossover balanced design with a 2 week washout interval between the doses. The 90% confidence interval for Cmax, AUC(0-last) and AUC(0-inf) individual test/reference ratios were 97.48–111.51, 95.35–103.20 and 96.42–103.86, respectively. It is concluded that Livolon (1.25 mg tablet) is bioequivalent to Libiam™ (1.25 mg tablet), with regards to both rate and extent of absorption

CB1R, CB2R and TRPV1 expression and modulation in in vivo, animal glaucoma models: A systematic review

Background: The endocannabinoid system (ECS) is a complex biological regulatory system. Its expression and functionality have been widely investigated in ocular tissues. Recent data have reported its modulation to be valid in determining an ocular hypotensive and a neuroprotective effect in preclinical animal models of glaucoma. Aim: This study aimed to explore the available literature on cannabinoid receptor 1 (CB1R), cannabinoid receptor 2 (CB2R), and transient receptor potential vanilloid 1 (TRPV1) expression in the trabecular meshwork (TM), ciliary body (CB), and retina as well as their ocular hypotensive and neuroprotective effects in preclinical, in vivo, animal glaucoma models. Materials and methods: The study adhered to both PRISMA and SYRCLE guidelines. Sixty-nine full-length articles were included in the final analysis. Results: Preclinical studies indicated a widespread distribution of CB1R, CB2R, and TRPV1 in the TM, CB, and retina, although receptor-, age-, and species-dependent differences were observed. CB1R and CB2R modulation have been shown to exert ocular hypotensive effects in preclinical models via the regulation of inflow and outflow pathways. Retinal cell neuroprotection has been achieved in several experimental models, mediated by agonists and antagonists of CB1R, CB2R, and TRPV1. Discussion: Despite the growing body of preclinical data regarding the expression and modulation of ECS in ocular tissues, the mechanisms responsible for the hypotensive and neuroprotective efficacy exerted by this system remain largely elusive. Research on this topic is advocated to further substantiate the hypothesis that the ECS is a new potential therapeutic target in the context of glaucoma

Decade-long profile of imaging biomarker use in ophthalmic clinical trials

PURPOSE. The purpose of this study was to investigate the use of imaging biomarkers in published clinical trials (CTs) in ophthalmology and its eventual changes during the past 10 years. METHODS. We sampled from published CTs in the fields of cornea, retina, and glaucoma between 2005\u20132006 and 2015\u20132016. Data collected included year of publication, phase, subspecialty, location, compliance with Consolidated Standards for Reporting Trials, impact factor, presence and use of imaging biomarkers (diagnostic, prognostic and predictive; primary and secondary surrogate endpoints), and use of centralized reading centers. RESULTS. We included 652 articles for analysis, equally distributed in three timeframes (2005\u2013 2006, 2010\u20132011, and 2015\u20132016), mainly reporting phase IV CTs and trials on procedures (42.2% and 35.4%, respectively). Imaging biomarkers were included in 46.3% of the analyzed CTs and their use significantly increased over time (P < 0.05). Optical coherence tomography was the most frequently used device (27.7%), whereas diagnostic biomarkers and secondary surrogate endpoints were the most frequent biomarker types (19.5% and 22.5%, respectively). Early-phase CTs showed an increase in the use of biomarkers for patient selection and stratification over time (P < 0.05), but not in the use of imaging surrogate endpoints (P = 0.90). Only 3 of 59 (5.1%) of phase III CTs included primary surrogate imaging endpoints, whereas secondary surrogate imaging endpoints were present in 50.8% of these trials (P < 0.001). Retinal CTs had the highest prevalence for each type of imaging biomarker (P < 0.001). Reading centers were used in 52 of 302 CTs (17.2%), with no significant time-related increase. CONCLUSIONS. Imaging biomarkers are increasingly used in published CTs in ophthalmology. Additional efforts, including centralized reading centers, are needed to improve their validation and use, allowing a wider use of these tools as primary surrogate endpoints in phase III CTs

Combined use of coenzyme Q10 and citicoline: A new possibility for patients with glaucoma

Glaucoma is the leading cause of irreversible blindness worldwide. Several risk factors have been involved in the pathogenesis of the disease. By now, the main treatable risk factor is elevated intraocular pressure. Nevertheless, some patients, whose intraocular pressure is considered in the target level, still experience a progression of the disease. Glaucoma is a form of multifactorial ocular neurodegeneration with complex etiology, pathogenesis, and pathology. New evidence strongly suggests brain involvement in all aspects of this disease. This hypothesis and the need to prevent glaucomatous progression led to a growing interest in the pharmacological research of new neuroprotective, non-IOP-lowering, agents. The aim of this paper is to report evidence of the usefulness of Coenzyme Q10 and Citicoline, eventually combined, in the prevention of glaucomatous neurodegeneration

The Effect of Intact Protein from Foods and Phenylalanine Free Medical Foods on Large Neutral Amino Acids in Patients with Phenylketonuria.

Objective: The primary aim of this retrospective cohort study was to determine the association between the source of dietary protein intake and the sum of plasma concentration of large neutral amino acids (LNAA) in patients with Phenylketonuria (PKU). A secondary aim of the study was to examine the effect of dietary compliance on plasma concentration of LNAA. Methods: The analysis included combined participant data from two previous studies conducted at the Emory University School of Medicine. Subjects are males (n=34) and females (n=43) with PKU ages 4-50 years. A Student t-test was used to compare total combined plasma LNAA (excluding tryptophan and phenylalanine) by dietary compliance status (alpha=0.05). Correlation statistics were used to determine the association between the ratio of reported intact food protein to medical food protein on plasma levels of LNAA. Multiple regression analysis was used to examine the contribution of intact protein to medical food protein ratio and other variables to plasma LNAA. Results: The median ratio of intact protein to medical food protein reported was 0.354 (IQR: 0.188, 0.914). Median percent of PHE intake over the PHE intake recommendation was 31.64 (Interquartile range [IQR]; 7.44, 104.98). Plasma concentration of LNAA did not differ significantly between those with plasma PHE levels within the therapeutic range μmol/L (compliant; 611.7 μmol/L [n=19]) vs levels above the therapeutic range (non-compliant; 595.3 μmol/L [n=47]); p=0.613). There was an inverse marginal correlation between the ratio of intact protein to medical food protein and plasma concentration of LNAA for those who were compliant (r = -0.436, r = 0.1) although the association was not statistically significant (p=0.08). No correlation was found for patients who were non-compliant. Regression analysis revealed that plasma concentration of LNAA was not significantly affected by the ratio of intact protein to medical food protein ratio, age, or gender. Conclusions: Although not statistically significant, a negative trend was observed between plasma LNAA concentration and the intact protein to medical food protein ratio in patients compliant with the PHE prescription. This suggests that the ratio of intact dietary protein to protein coming from medical food, as reported by patient diet records, may promote increased plasma LNAA levels in the effective treatment of PKU. The majority of the sample (74%) were non-compliant with diet based on plasma PHE levels. Future studies are needed to determine the consequences of non-compliance by decreased intake of medical food protein or increased intake of intact protein on plasma LNAA concentration and downstream health effects

Fibrodysplasia Ossificans Progressiva: Case Report.

Fibrodysplasia ossificans progressiva is a rare genetic disease characterized by widespread soft tissue ossification and congenital stigmata of the extremities. We report on a male child followed for ten years since the age of 3 years and 9 months, when the diagnosis was made. He was born with bilateral hypoplasic hallux valgus and ventricular septal defect, corrected by trans-sternal approach when 32 months old. Restriction of neck mobility followed and foci of ectopic ossification appeared. Four crises of disease exacerbation were treated with oral prednisone and/or other antiinflammatory drugs. Sodium etidronate 5 to 10 mg/kg/day was prescribed intermittently during about six years but was discontinued due to osteopenia. The disease course has been relentless, with severe movement restriction including the chest wall. A review showed few similar case reports in the Brazilian literature. We revisit the criteria for diagnosis and the essentials of management and treatment.58342-