Dietary aspects of cow's milk allergy in young children

Cow s milk allergy (CMA) affects about 2-6% of infants and young children. Environmental factors during early life are suggested to play a role in the development of allergic diseases. One of these factors is likely to be maternal diet during pregnancy and lactation. The association between maternal diet and development of CMA in offspring is not well known, but diet could contain factors that facilitate development of tolerance. After an established food allergy, another issue is gaining tolerance towards an antigen that causes symptoms. The strictness of the elimination depends on the individual level of tolerance. This study aimed at validating a questionnaire used to inquire about food allergies in children, at researching associations between maternal diet during pregnancy and lactation and subsequent development of cow s milk allergy in the offspring, and at evaluating the degree of adherence to a therapeutic elimination diet of children with CMA and factors associated with the adherence and age of recovery. These research questions were addressed in a prospective birth cohort born between 1997 and 2004 at the Tampere and Oulu University Hospitals. Altogether 6753 children of the Diabetes Prediction and Prevention (DIPP) Nutrition cohort were investigated. Questionnaires regarding allergic diseases are often used in studies without validation. High-quality valid tools are therefore needed. Two validation studies were conducted here: one by comparing parentally reported food allergies with information gathered from patient records of 1122 children, and the other one by comparing parentally reported CMA with information in the reimbursement records of special infant formulae in the registers of the Social Insurance Institution for 6753 children. Both of these studies showed that the questionnaire works well and is a valid tool for measuring food allergies in children. In the first validation study, Cohen s kappa values were within 0.71-0.88 for CMA, 0.74-0.82 for cereal allergy, and 0.66-0.86 for any reported food allergy. In the second validation study, the kappa value was 0.79, sensitivity 0.958, and specificity 0.965 for reported and diagnosed CMA. To investigate the associations between maternal diet during pregnancy and lactation and CMA in offspring, 6288 children were studied. Maternal diet during pregnancy (8th month) and lactation (3rd month) was assessed by a validated, 181-item semi-quantitative food frequency questionnaire (FFQ), and as an endpoint register-based information on diagnosed CMA was obtained from the Social Insurance Institution and complemented with parental reports of CMA in their children. The associations between maternal food consumption and CMA in offspring were analyzed by logistic regression comparing the highest and lowest quarters with two middle quarters of consumption and adjusted for several potential confounding factors. High maternal intake of milk products (OR 0.56, 95% CI 0.37-0.86 p = 0.002) was associated with a lower risk of CMA in offspring. When stratified according to maternal allergic rhinitis or asthma, a protective association of high use of milk products with CMA was seen in children of allergy-free mothers (OR 0.30, 95% CI 0.13 - 0.69, p < 0.001), but not in children of allergic mothers. Moreover, low maternal consumption of fish during pregnancy was associated with a higher risk of CMA in children of mothers with allergic rhinitis or asthma (OR 1.47, 95% CI 0.96 - 2.27 for the lowest quarter, p = 0.043). In children of nonallergic mothers, this association was not seen. Maternal diet during lactation was not associated with CMA in offspring, apart from an inverse association between citrus and kiwi fruit consumption and CMA. These results imply that maternal diet during pregnancy may contain factors protective against CMA in offspring, more so than maternal diet during lactation. These results need to be confirmed in other studies before giving recommendations to the public. To evaluate the degree of adherence to a therapeutic elimination diet in children with diagnosed CMA, food records of 267 children were studied. Subsequent food records were examined to assess the age at reintroduction of milk products to the child s diet. Nine of ten families adhered to the elimination diet of the child with extreme accuracy. Older and monosensitized children had more often small amounts of cow s milk protein in their diet (p < 0.001 for both). Adherence to the diet was not related to any other sociodemographic factor studied or to the age at reintroduction of milk products to the diet. Low intakes of vitamin D, calcium, and riboflavin are of concern in children following a cow s milk-free diet. In summary, we found that the questionnaires used in the DIPP study are valid in investigating CMA in young children; that there are associations between maternal diet during pregnancy and lactation and the development of CMA in offspring; and that the therapeutic elimination diet in children with diagnosed CMA is rigorously adhered to.

Photo-activated cytotoxicity of a pyrenyl-terpyridine copper(II) complex in HeLa cells

Terpyridine copper(II) complexes Cu(L)(2)](NO3)(2) where L is (4'-phenyl)-2 2' 6' 2 `'-terpyridine (ph-tpy in 1) and 4-(1 pyrenyl)]-2 2' 6' 2'-terpyridine (py-tpy in 2) are prepared characterized and their photocytotoxic activity studied The crystal structure of complex 1 shows distorted octahedral CuN6 coordination geometry The 1 2 electrolytic and one-electron paramagnetic complexes show a visible band near 650 nm in DMF-H2O The complexes show emission band at 352 nm for 1 and 425 nm for 2 when excited at 283 and 346 nm respectively The Cu(II)-Cu(I) redox couple is observed near -0 2 V versus SCE in DMF-0 1 m TBAP The complexes are avid partial-intercalative binders to calf thymus DNA giving binding constant (K-b) values of similar to 10(6) M-1 Complex 2 with its photoactive pyrenyl moiety exhibits significant photocleavage of pUC19 DNA in red light via singlet oxygen pathway Complex 2 also exhibits significant photo-activated cytotoxicity in HeLa cancer cells in visible light giving IC50 value of 11 9 mu M while being non-toxic in dark with an IC50 value of 130 5 mu M (C) 2010 Elsevier Ltd All rights reserved

Uncoupling Protein 2 and 3 Gene Polymorphisms and Their Association with Type 2 Diabetes in Asian Indians

Background: This study examined the association of -866G/A, Ala55Val, 45bpI/D, and -55C/T polymorphisms at the uncoupling protein (UCP) 3-2 loci with type 2 diabetes in Asian Indians. Methods: A case-control study was performed among 1,406 unrelated subjects (487 with type 2 diabetes and 919 normal glucose-tolerant NGT]), chosen from the Chennai Urban Rural Epidemiology Study, an ongoing population-based study in Southern India. The polymorphisms were genotyped using polymerase chain reaction-restriction fragment length polymorphism and direct sequencing. Haplotype frequencies were estimated using an expectation-maximization algorithm. Linkage disequilibrium was estimated from the estimates of haplotypic frequencies. Results: The genotype (P = 0.00006) and the allele (P = 0.00007) frequencies of Ala55Val of the UCP2 gene showed a significant protective effect against the development of type 2 diabetes. The odds ratios (adjusted for age, sex, and body mass index) for diabetes for individuals carrying Ala/Val was 0.72, and that for individuals carrying Val/Val was 0.37. Homeostasis insulin resistance model assessment and 2-h plasma glucose were significantly lower among Val-allele carriers compared to the Ala/Ala genotype within the NGT group. The genotype (P = 0.02) and the allele (P = 0.002) frequencies of -55C/T of the UCP3 gene showed a significant protective effect against the development of diabetes. The odds ratio for diabetes for individuals carrying CT was 0.79, and that for individuals carrying TT was 0.61. The haplotype analyses further confirmed the association of Ala55Val with diabetes, where the haplotypes carrying the Ala allele were significantly higher in the cases compared to controls. Conclusions: Ala55Val and -55C/T polymorphisms at the UCP3-2 loci are associated with a significantly reduced risk of developing type 2 diabetes in Asian Indians.

Lipeäkäsitellyn vehnän vaikutus lypsylehmien syöntiin ja tuotokseen vapaalla seosrehuruokinnalla

Lipeä on vahva emäs, jonka on havaittu lisäävän hemiselluloosan ja ligniinin hydrolyysiä pötsissä. Näin ollen lipeäkäsittelyllä on mahdollista korvata viljan mekaaninen litistys ja jauhatus. Seosrehuruokinnalla, jonka osana on lipeäkäsitelty vilja, on mahdollista vähentää liiallisesta tärkkelyksestä aiheutuvia metabolisia ongelmia pötsissä. Tämän tutkielman tarkoituksena oli selvittää lipeäkäsitellyn vehnän vaikutusta lypsylehmien syöntiin ja tuotokseen ad libitum seosrehuruokinnoilla. Ruokinnoissa korvattiin kuivaa murskattua vehnää asteittain kokonaisella lipeäkäsitellyllä vehnällä. Kontrollina oli perinteisesti käytetty kuiva, murskattu ohra-kaura seos. Koe tehtiin Ruotsin maatalousyliopiston (SLU) maataloustieteiden laitoksella Uumajassa. Koe alkoi syyskuussa ja päättyi joulukuussa 2010. Kokeessa oli 17 useamman kerran poikinutta lehmää ja 6 ensikkoa (Ruotsin punainen -rotu). Lehmät olivat lämpimässä pihattonavetassa, jossa seosrehun syöntiä mitattiin vaakakuppien avulla. Koekäsittelyt olivat murskattu ohra-kaura seos (1:1), murskattu kuiva vehnä (1:0), murskatun kuivan vehnän ja kokonaisen lipeävehnän seos (1:1) ja kokonainen lipeävehnä (1:0). Ruokintojen kuiva-ainepitoisuudeksi asetettiin 370 g/kg ja raakavalkuaispitoisuudeksi 180 g/kg kuiva-ainetta. Näennäinen ravintoaineen sulavuus määritettiin happoon liukenemattoman tuhkan avulla. Typen hyväksikäyttöä arvioitiin laskennallisen typpitaseen avulla. Koe toteutettiin 4x4 latinalaisen neliön koemallin mukaisesti ja käsittelyjen väliset tilastolliset erot testattiin kontrastien avulla. Kuiva-aineen (PQ=0,02) ja orgaanisen aineen (PQ=0,02) syönnit lisääntyivät, samalla kun niiden sulavuudet paranivat korvattaessa puolet kuivasta vehnästä lipeävehnällä. Ruokintojen välillä ei ollut tilastollisesti merkitsevää eroa maitotuotoksessa eikä energiakorjatussa maitotuotoksessa. Maidon rasvatuotos lisääntyi vähän (PQ=0,04) ja rasvapitoisuus selvästi (PQ=0,004), kun kuivasta vehnästä korvattiin puolet lipeävehnällä. Kun kaikki kuiva vehnä korvattiin lipeävehnällä, maidon valkuaispitoisuus väheni (PL<0,001). Samoin kävi maidon ureapitoisuudelle (PL=0,002). Lipeäkäsittely ei tuottanut tässä kokeessa taloudellisesti kannattavaa tulosta, sillä maidon valkuaispitoisuus väheni ja syönti lisääntyi maitotuotoksen pysyessä samana. Vehnäruokinnoista paras tuotosvaste saatiin kuivan vehnän ja lipeävehnän seoksella.

Diaphragm-type sputtered platinum thin film strain gauge pressure transducer

A diaphragm-type pressure transducer with a sputtered platinum film strain gauge (sensing film) has been designed and fabricated. The various steps followed to prepare thin film strain gauges on the diaphragm are described. M-bond 450 adhesive (Measurements Group, USA) has been employed as the insulating layer. A detailed procedure to cure this layer is given. A d.c. sputtering method is employed to prepare the platinum films. This paper also includes details of the strain gauge pattern and its location on the diaphragm. A description of the output characteristics and overall behaviour of the platinum thin film pressure transducer is reported.

Magnetoresistance of FexNi80-xCr20 (50

The authors have measured longitudinal and transverse magnetoresistance (MR) of crystalline pseudo-binary alloys FexNi80-xCr20 (50

Fatigue life prediction of adhesively bonded single lap joints

Better fatigue performance of adhesively bonded joints makes them suitable for most structural applications. However, predicting the service life of bonded joints accurately remains a challenge. In this present study, nonlinear computational simulations have been performed on adhesively bonded single lap ASTM-D1002 shear joint considering both geometrical and material nonlinearities to predict the fatigue life by judiciously applying the modified Coffin-Manson equation for adhesive joints. Elasto-plastic material models have been employed for both the adhesive and the adherends. The predicted life has close agreement in the high cycle fatigue (HCF) regime with empirical observations reported in the literature. (C) 2010 Elsevier Ltd. All rights reserved.

Heraproteiinivalmisteen vaikutus laihdutukseen ja laihdutustuloksen pysyvyyteen ylipainoisilla aikuisilla

Johdanto: Lihavuus on maailmalaajuisesti merkittävä kansanterveydellinen ja –taloudellinen ongelma. Lihavuuden ehkäisemiseksi ja epidemian leviämisen hillitsemiseksi on tärkeää tuntea lihavuuteen vaikuttavat tekijät. Yksittäisistä ruoka-aineista maidon käytön on havaittu monissa epidemiologisissa ja kokeellisissa tutkimuksissa olevan yhteydessä alhaisempaan painoon, ehkäisevän lihomista ja edistävän laihtumista. Maidon sisältämistä yhdisteistä kalsiumin vaikutuksia on tutkittu eniten. Myös heraproteiinin on esitetty olevan yksi mahdollinen painoon vaikuttava komponentti, ja näyttöä tästä on saatu eläinkokeista. Tavoitteet: Tutkimuksessa tavoitteena oli selvittää, vaikuttaako päivittäin nautittu heraproteiinia sisältävä välipalajuoma laihtumiseen tai saavutetun laihdutustuloksen pysyvyyteen ylipainoisilla aikuisilla. Aineisto ja menetelmät: Tutkimus toteutettiin osana Valio Oy:n OMPPU2-tutkimusta, joka oli satunnaistettu, lumekontrolloitu ja kaksoissokkoutettu kahden rinnakkaisen ryhmän tutkimus. Tutkimus alkoi rekrytoinneilla alkuvuodesta 2010, joissa tutkimukseen valittiin 105 ylipainoista (BMI 27–35), tervettä, 20–50-vuotiasta naista ja miestä. Tutkimushenkilöt satunnaistettiin tutkimus- ja verrokkiryhmiin, ja molemmat ryhmät nauttivat tutkimusvalmisteensa päivittäin hedelmätäysmehuun sekoitettuna (tutkimusryhmä heraproteiinijauheen ja verrokkiryhmä maltodekstriinijauheen). Tutkimus koostui kahdesta jaksosta: viiden kuukauden laihdutusjaksosta ja tätä seuranneesta kolmen kuukauden painonhallintajaksosta. Tutkimuskäynneillä tutkimuksen alussa, laihdutusjakson lopussa ja painonhallintajakson lopussa mitattiin tutkimushenkilöiden paino ja vyötärönympärys sekä määritettiin kehonkoostumus bioimpedanssilaitteella. Tutkimushenkilöiden ruoankäyttö ja ravinnonsaanti laskettiin samoissa aikapisteissä kerättyjen kolmen päivän ruokapäiväkirjojen perusteella. Tutkimushenkilöitä, joilla tutkimusvalmisteen käyttö oli alle 50 %, ei otettu huomioon tilastoanalyyseissä. Tilastollinen analyysi tehtiin käyttäen kahden riippumattoman otoksen t-testiä ja kaksisuuntaista parittaista t-testiä normaalijakautuneilla muuttujilla, ja Mann-Whitneyn U-testiä ja Wilcoxonin ttestiä ei-normaalijakautuneilla muuttujilla. Tutkimusvalmisteen ja painonmuutosten välinen korrelaatio laskettiin käyttäen Pearsonin korrelaatiokertoimia. Tulokset on ilmaistu keskiarvoina (keskihajonta). Tulokset: Molemmat ryhmät laihtuivat laihdutusjakson aikana. Heraproteiiniryhmässä painonpudotus oli 2,4 (3,8) kg (p=0,002) ja verrokkiryhmässä 3,4 (4,1) kg (p<0,001). Ryhmien välinen ero ei ollut merkitsevä. Rasvamassa väheni verrokkiryhmässä 2,4 (3,8) kg (p<0,001), mikä oli viiteellisesti enemmän (p=0,054) kuin heraproteiiniryhmässä 1,1 (3,1) kg (p=0,129). Rasvaprosentti ja viskeraalirasvan määrä pienenivät verrokkiryhmässä heraproteiiniryhmää enemmän (p<0,025). Vyötärönympärys pieneni heraproteiiniryhmässä 1,9 (3,0) cm (p=0,001) ja verrokkiryhmässä 3,8 (3,8) cm (p<0,001) ryhmien välisen eron ollessa merkitsevä (p=0,017). Maltodekstriinin käyttö korreloi käänteisesti painonmuutosten kanssa laihdutusjaksolla (r=-0,389, p=0,013). Painonhallintajaksolla painossa ei tapahtunut merkitseviä muutoksia kummassakaan ryhmässä. Heraproteiinin käytön ja painonmuutosten välisestä negatiivisesta korrelaatiosta oli viitteitä tällä jaksolla (r=-0,344, p=0,063). Kun tarkasteltiin koko tutkimuksen aikana tapahtuneita muutoksia (laihdutusjakson alusta painonhallintajakson loppuun), ei ryhmien välillä ollut merkitseviä eroja painon tai kehonkoostumuksen muutoksissa. Energiansaanti väheni molemmissa ryhmissä merkitsevästi laihdutusjakson aikana (p<0,01), mutta muutos ei eronnut ryhmien välillä. Ravintoaineista rasvan saanti väheni (p<0,001) ja C-vitamiinin saanti lisääntyi (p<0,001) molemmissa ryhmissä laihdutusjaksolla. Alkoholin saanti väheni verrokkiryhmässä (p=0,017). Proteiinin saanti lisääntyi heraproteiiniryhmässä merkitsevästi enemmän kuin verrokkiryhmässä (p=0,002). Painonhallintajaksolla energiansaanti ei muuttunut kummassakaan ryhmässä laihdutusjakson loppuun verrattuna. Fyysisessä aktiivisuudessa tutkimuksen aikana ei ollut eroa ryhmien välillä. Johtopäätökset: Heraproteiinin ei havaittu tehostavan laihdutusta maltodekstriiniin verrattuna tässä tutkimuksessa. Sen sijaan maltodekstriiniä nauttineessa ryhmässä rasvaprosentti ja erityisesti vatsan alueen rasva pienenivät heraproteiiniryhmää enemmän laihdutusjaksolla. Tulos oli lähes täysin vastakkainen tutkimushypoteesin kanssa, eikä vaikuttaisi selittyvän eroilla energiansaannissa tai fyysisessä aktiivisuudessa. Tämä tutkimus ei siis tue olettamusta, että heraproteiini osana laihdutusruokavaliota auttaisi laihdutuksessa. Painonhallintajaksolla heraproteiinin ja painonmuutosten välinen lähes merkitsevä käänteinen korrelaatio saattaa viitata heraproteiinin merkitykseen painonhallinnassa. Vapaasti elävien ihmisten kohdalla sekoittavia tekijöitä on kuitenkin vaikea vakioida, mikä vaikeuttaa johtopäätösten tekemistä.

Multilayer Bi1.5Zn1.0Nb1.5O7/Ba0.6Sr0.4TiO3/Bi1.5Zn1.0Nb1.5O7 thin films for tunable microwave applications

Bi1.5Zn1.0Nb1.5O7/Ba0.6Sr0.4TiO3/Bi1.5Zn1.0Nb1.5O7 tunable multilayer thin film has been fabricated by pulsed laser ablation and characterized. Phase composition and microstructure of multilayer films were characterized by X-ray diffraction, scanning electron microscopy (SEM) and atomic force microscopy (AFM). The film has very smooth surface with RMS roughness of 1.5-2nm and grain size of 100-150 nm. Total film thickness has been measure to be 375 nm. The BZN thin films at 300 K, on Pt(1 1 1)/SiO2/Si substrate showed zero-field dielectric constant of 105 and dielectric loss tangent of 0.002 at frequency of 0.1 MHz. Thin films annealed at 700 degrees C shows the dielectric tunability of 18% with biasing field 500 kV/cm at 0.1 MHz. The multilayer thin film shows nonferroelectric behavior at room temperature. The good physical and electrical properties of multilayer thin films make them promising candidate for tunable microwave device applications. (C) 2010 Elsevier B.V. All rights reserved.

Solvent effect on the spectroscopic properties of 6MAMC and 7MAMC

The absorption and emission spectra of two dyes namely 6MAMC and 7MAMC have been recorded at room temperature in solvents of different polarities. The ground-state dipole moments (mu(g)) of these two were determined experimentally by Guggenheim method and were compared with theoretical values obtained using quantum chemical method. The exited state (mu(e))dipole moments were estimated from Lippert's, Bakhshiev's and Chamma-Viallet's equations by using the variation of the Stokes shift with the solvent dielectric constant and refractive index. The ground and excited-state dipole moments were calculated by means of the solvatochromic shift method and also the excited-state dipole moments are determined in combination with ground-state dipole moments. It was observed that dipole moments of excited state were higher than those of the ground state, indicating a substantial redistribution of the pi-electron densities in a more polar excited state for these two dyes. (C) 2010 Elsevier B.V. All rights reserved.

Fatigue crack propagation model and size effect in concrete using dimensional analysis

It is well known that fatigue in concrete causes excessive deformations and cracking leading to structural failures. Due to quasi-brittle nature of concrete and formation of a fracture process zone, the rate of fatigue crack growth depends on a number of parameters, such as, the tensile strength, fracture toughness, loading ratio and most importantly the structural size. In this work, an analytical model is proposed for estimating the fatigue crack growth in concrete by using the concepts of dimensional analysis and including the above parameters. Knowing the governed and the governing parameters of the physical problem and by using the concepts of self-similarity, a relationship is obtained between different parameters involved. It is shown that the proposed fatigue law is able to capture the size effect in plain concrete and agrees well with different experimental results. Through a sensitivity analysis, it is shown that the structural size plays a dominant role followed by loading ratio and the initial crack length in fatigue crack propagation. (C) 2010 Elsevier Ltd. All rights reserved.

Structural and electrical properties of radio frequency magnetron sputtered tantalum oxide films: Influence of post-deposition annealing

The as-deposited and annealed radio frequency reactive magnetron sputtered tantalum oxide (Ta2O5) films were characterized by studying the chemical binding configuration, structural and electrical properties. X-ray photoelectron spectroscopy and X-ray diffraction analysis of the films elucidate that the film annealed at 673 K was stoichiometric with orthorhombic beta-phase Ta2O5. The dielectric constant values of the tantalum oxide capacitors with the sandwich structure of Al/Ta2O5/Si were in the range from 14 to 26 depending on the post-deposition annealing temperature. The leakage current density was < 20 nA cm(-2) at the gate bias voltage of 0.04 MV/cm for the annealed films. The electrical conduction mechanism observed in the films was Poole-Frenkel. (C) 2010 Elsevier Ltd. All rights reserved.

A Ten-microRNA Expression Signature Predicts Survival in Glioblastoma

Glioblastoma (GBM) is the most common and aggressive primary brain tumor with very poor patient median survival. To identify a microRNA (miRNA) expression signature that can predict GBM patient survival, we analyzed the miRNA expression data of GBM patients (n = 222) derived from The Cancer Genome Atlas (TCGA) dataset. We divided the patients randomly into training and testing sets with equal number in each group. We identified 10 significant miRNAs using Cox regression analysis on the training set and formulated a risk score based on the expression signature of these miRNAs that segregated the patients into high and low risk groups with significantly different survival times (hazard ratio HR] = 2.4; 95% CI = 1.4-3.8; p < 0.0001). Of these 10 miRNAs, 7 were found to be risky miRNAs and 3 were found to be protective. This signature was independently validated in the testing set (HR = 1.7; 95% CI = 1.1-2.8; p = 0.002). GBM patients with high risk scores had overall poor survival compared to the patients with low risk scores. Overall survival among the entire patient set was 35.0% at 2 years, 21.5% at 3 years, 18.5% at 4 years and 11.8% at 5 years in the low risk group, versus 11.0%, 5.5%, 0.0 and 0.0% respectively in the high risk group (HR = 2.0; 95% CI = 1.4-2.8; p < 0.0001). Cox multivariate analysis with patient age as a covariate on the entire patient set identified risk score based on the 10 miRNA expression signature to be an independent predictor of patient survival (HR = 1.120; 95% CI = 1.04-1.20; p = 0.003). Thus we have identified a miRNA expression signature that can predict GBM patient survival. These findings may have implications in the understanding of gliomagenesis, development of targeted therapy and selection of high risk cancer patients for adjuvant therapy.

Prediction of nonlocal scaling parameter for armchair and zigzag single-walled carbon nanotubes based on molecular structural mechanics, nonlocal elasticity and wave propagation

Atomic vibration in the Carbon Nanotubes (CNTs) gives rise to non-local interactions. In this paper, an expression for the non-local scaling parameter is derived as a function of the geometric and electronic properties of the rolled graphene sheet in single-walled CNTs. A self-consistent method is developed for the linearization of the problem of ultrasonic wave propagation in CNTs. We show that (i) the general three-dimensional elastic problem leads to a single non-local scaling parameter (e(0)), (ii) e(0) is almost constant irrespective of chirality of CNT in the case of longitudinal wave propagation, (iii) e(0) is a linear function of diameter of CNT for the case of torsional mode of wave propagation, (iv) e(0) in the case of coupled longitudinal-torsional modes of wave propagation, is a function which exponentially converges to that of axial mode at large diameters and to torsional mode at smaller diameters. These results are valid in the long-wavelength limit. (C) 2011 Elsevier Ltd. All rights reserved.