Patient-specific finite element analysis of popliteal stenting

Nitinol self-expanding stents are used for the endovascular management of peripheral artery diseases of the popliteal artery, which is located behind the knee joint. Unfortunately, the complex kinematics of the artery during the leg flexion leads to severe loading conditions, favouring the mechanical failure of the stent, calling for a specific biomechanical analysis. For this reason, in the present study we reconstruct by medical image analysis the patient-specific popliteal kinematics during leg flexion, which is subsequently exploited to compute the mechanical response of a stent model, virtually implanted in the artery by structural finite element analysis (FEA). The medical image analysis indicates a non-uniform configuration change of the artery during the leg flexion, leading to an increase of the vessel curvature above the knee. The computed mechanical response of the stent reflects the non-uniform configuration change of the artery as after the flexion the average stress is higher in the part of the stent located above the knee. Although the proposed analysis is limited to a case-study, it shows the capability of patient-specific FEA simulations to compute the mechanical response of a stent model subjected to the complex and severe loading conditions of the popliteal artery during leg flexion.     

Hartogs Phenomena and Antisyzygies for Systems of Differential Equations

We introduce the notion of antisyzygies, which studies the inverse problem of finding a system of PDEs, given compatibility conditions. The system obtained possesses the property of removability of compact singularities. We write explicit computations in the cases of the Cauchy-Fueter system and Maxwell’s system for electromagnetism, and we conclude with a study of systems of non-maximal rank.      

Simultaneous determination of β2‐agonists in human urine by fast‐gas chromatography/mass spectrometry: method validation and clinical application

A fast screening protocol was developed and validated for the simultaneous determination of 15 β₂‐agonists in human urine (bambuterol, cimbuterol, clenbuterol, fenoterol, formoterol, isoproterenol, mapenterol, metaproterenol, procaterol, ractopamine, ritodrine, salbutamol, salmeterol, terbutaline, tulobuterol). The overall sample processing includes deconjugation with enzyme hydrolysis, liquid–liquid extraction, followed by derivatization of the extract and detection of β₂‐agonists trimethylsilyl‐derivatives by fast‐gas chromatography/electron impact–mass spectrometry (fast‐GC/EI‐MS). Sample extraction and derivatization were optimized with the purpose of improving recoveries and reaction yields for a variety of analytes with different structures simultaneously, while keeping the procedure simple and reliable. Validation parameters were determined for each analyte under investigation, including selectivity, linearity, intra‐ and inter‐assay precision, extraction recoveries and signal to noise ratio (S/N) at the lowest calibration level. Fast‐GC/MS sequences, based on the use of short columns, high carrier‐gas velocity and fast temperature ramping, allow considerable reduction of the analysis time (7 min), while maintaining adequate chromatographic resolution. The overall GC cycle time was less than 9 min, allowing a processing rate of 6 samples/h. High MS‐sampling rate, using a benchtop quadrupole mass analyzer, resulted in accurate peak shape definition under both scan and selected ion monitoring modes, and high sensitivity in the latter mode. The method was successfully tested on real samples arising from clinical treatments. Copyright © 2009 John Wiley & Sons, Ltd.     

A highly efficient stereocontrolled synthesis of (S)-2′,6′-dimethyltyrosine [(S)-DMT]

A new, practical and very convenient stereocontrolled synthesis of (S)-2′,6′-dimethyltyrosine [(S)-Dmt] 4 was accomplished in a good yield, starting from the chiral synthon 1,4-N,N-[(S)-phenylethyl]-piperazine-2,5-dione 1. The procedure, which is an extension of our original strategy and occurs with a high level of stereoselectivity (>98%), is simple and inexpensive allowing us to prepare the unnatural α-aminoacid (S)-Dmt also on a multi-gram scale.     

A novel hydroxy functionalized polyester obtained by ring opening copolymerization of L‐lactide with a pyrolysis product of cellulose

A hydroxylactone ((1R,5S)‐1‐hydroxy‐3,6‐dioxabicyclo [3.2.1] octan‐2‐one, abbreviated as LAC) obtained from catalytic pyrolysis of cellulose was investigated as a monomer in the synthesis of polyesters by ring‐opening polymerization (ROP) with L ‐lactide. Although stannous octoate resulted inactive, ROP initiated by zirconium (IV) acetylacetonate afforded novel copolyesters from LAC and lactide mixtures in the bulk at 110 °C. Copolymers were obtained with different LAC content (from 19 to 45%) with a random microstructure as established by detailed NMR analysis. FTIR spectrometry confirmed the presence in the polymer chain of the OH groups originally present in LAC, which do not react during polymerization due to steric hindrance and inter/intramolecular hydrogen bonding. Reaction with trichloroacetylisocyanide proved that OH groups of the polyesters can be readily derivatized. The application of LAC as a comonomer enables the insertion of the alcohol functionality in polylactide avoiding protection/deprotection steps and potentially expanding the realm of biomaterials affordable from carbohydrate feedstock. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 247–257, 2009     

Enantiopure N-Boc piperidine-2-ethanol for the synthesis of (+)- and (−)-dumetorine,and (+)- and (−)-epidihydropinidine

The convenient synthesis of both enantiomers of the piperidine alkaloids such as dumetorine and epidihydropinidine is described. Pure enantiomers of 2-(2-hydroxy-ethyl)-piperidine-1-carboxylic acid tert-butyl ester are used as a common starting material. The syntheses are based on a RCM reaction and on methylation of the piperidine ring according to Beak–Lee methodology, respectively.     

On the Multiplicity of Zeroes of Polynomials with Quaternionic Coefficients

Regular polynomials with quaternionic coefficients admit only isolated zeroes and spherical zeroes. In this paper we prove a factorization theorem for such polynomials. Specifically, we show that every regular polynomial can be written as a product of degree one binomials and special second degree polynomials with real coefficients. The degree one binomials are determined (but not uniquely) by the knowledge of the isolated zeroes of the original polynomial, while the second degree factors are uniquely determined by the spherical zeroes. We also show that the number of zeroes of a polynomial, counted with their multiplicity as defined in this paper, equals the degree of the polynomial. While some of these results are known in the general setting of an arbitrary division ring, our proofs are based on the theory of regular functions of a quaternionic variable, and as such they are elementary in nature and offer explicit constructions in the quaternionic setting. Partially supported by G.N.S.A.G.A.of the I.N.D.A.M. and by M.I.U.R.. Lecture held by G. Gentili in the Seminario Matematico e Fisico on February 12, 2007. Received: August 2008     

Computerized Developments in Design,Generation, Simulation of Meshing,and Stress Analysis of Gear Drives

The paper represents new computerized developments in design, generation, simulation of meshing, and stress analysis of gear drives. The main contents of the paper are: (i) application of a predesigned parabolic function of transmission errors for reduction of noise, (ii) computerized simulation of noise caused by transmission errors, (iii) modification of the basic algorithm of tooth contact analysis, and (iv) application of approaches developed for enhanced design and simulation of meshing of the following gear drives: (a) spiral bevel gear drives, (b) face-gear drives (including an approach for grinding), and (c) modified helical gear drives. The developed theory is illustrated with numerical examples.