Fractional Telegrapher's Equation under Resetting: Non-Equilibrium Stationary States and First-Passage Times.

We consider two different time fractional telegrapher's equations under stochastic resetting. Using the integral decomposition method, we found the probability density functions and the mean squared displacements. In the long-time limit, the system approaches non-equilibrium stationary states, while the mean squared displacement saturates due to the resetting mechanism. We also obtain the fractional telegraph process as a subordinated telegraph process by introducing operational time such that the physical time is considered as a Lévy stable process whose characteristic function is the Lévy stable distribution. We also analyzed the survival probability for the first-passage time problem and found the optimal resetting rate for which the corresponding mean first-passage time is minimal.

Entropy Production in Reaction-Diffusion Systems Confined in Narrow Channels.

This work analyzes the effect of wall geometry when a reaction-diffusion system is confined to a narrow channel. In particular, we study the entropy production density in the reversible Gray-Scott system. Using an effective diffusion equation that considers modifications by the channel characteristics, we find that the entropy density changes its value but not its qualitative behavior, which helps explore the structure-formation space.

Surface diffusion in narrow channels on curved domains.

We study the transport properties of diffusing particles restricted to confined regions on curved surfaces. We relate particle mobility to the curvature of the surface where they diffuse and the constraint due to confinement. Applying the Fick-Jacobs procedure to diffusion in curved manifolds shows that the local diffusion coefficient is related to average geometric quantities such as constriction and tortuosity. Macroscopic experiments can record such quantities through an average surface diffusion coefficient. We test the accuracy of our theoretical predictions of the effective diffusion coefficient through finite-element numerical solutions of the Laplace-Beltrami diffusion equation. We discuss how this work contributes to understanding the link between particle trajectories and the mean-square displacement.

COVID-19 Secondary Infections in ICU Patients and Prevention Control Measures: A Preliminary Prospective Multicenter Study.

The incidence of secondary infections in critically ill coronavirus disease 2019 (COVID-19) patients is worrisome. We investigated whether selective digestive decontamination (SDD) added to infection control measures during an intensive care unit (ICU) stay modified these infection rates. Methods: A retrospective observational cohort study was carried out in four ICUs in Spain. All consecutive ventilated patients with a SARS-CoV-2 infection engaged in national infection control programs between 1 March and 10 December 2020 were investigated. Patients were grouped into two cohorts according to the site of ICU admission. Secondary relevant infections were included. Infection densities corresponding to ventilator-associated pneumonia (VAP), catheter bacteremia, secondary bacteremia, and multi-resistant germs were obtained as the number of events per 1000 days of exposure and were compared between SDD and non-SDD groups using Poisson regression. Factors that had an independent association with mortality were identified using multidimensional logistic analysis. Results: There were 108 patients in the SDD cohort and 157 in the non-SDD cohort. Patients in the SDD cohort showed significantly lower rates (p < 0.001) of VAP (1.9 vs. 9.3 events per 1000 ventilation days) and MDR infections (0.57 vs. 2.28 events per 1000 ICU days) and a non-significant reduction in secondary bacteremia (0.6 vs. 1.41 events per 1000 ICU days) compared with those in the non-SDD cohort. Infections caused by MDR pathogens occurred in 5 patients in the SDD cohort and 21 patients in the non-SDD cohort (p = 0.006). Differences in mortality according to SDD were not found. Conclusion: The implementation of SDD in infection control programs significantly reduced the incidence of VAP and MDR infections in critically ill SARS-CoV-2 infected patients.

Differences between the first and the second wave of critically ill COVID-19 patients admitted to the intensive care units.

Background: To compare the demographic characteristics and prognosis of patients admitted to the intensive care unit (ICU) for coronavirus disease 2019 (COVID-19) pneumonia during the first wave (March-July) versus those admitted during the second wave (August-December). Methods: Prospective, observational, descriptive cohort-study including patients admitted to the ICU for COVID-19 pneumonia during the first wave (March-July 2020) or the second wave (August-December). The demographic characteristics, comorbidities, treatments, complications, and mortality in both pandemic waves were studied. Results: A total of 72 patients were included: Twenty-six admitted during the first wave and 46 during the second wave. Men were predominant in both waves: 61.5% versus 73.9%. The most frequently associated comorbidities in both periods were: arterial hypertension 65.4% versus 65.2%, diabetes mellitus 46.2% versus 34.8% and overweight, measured as (body mass index), 29.13 ± 3.38 versus 28.98 ± 4.25. More patients received noninvasive mechanical ventilation prior to invasive ventilation during the second wave (P < 0.01); the incidence of atelectasis and bronchial obstruction were lower during the second wave (P < 0.01 and P = 0.055 respectively); no further differences were observed in the occurrence of other complications. Conclusions: No significant differences were observed between the first and the second wave in the demographic characteristics or comorbidities of admitted patients. Blood hypertension, diabetes and overweight were remarkable risk factors. Improving our knowledge of the complications, these patients tend to develop was essential to reduce some of them, such as endotracheal tube obstruction or atelectasis, and to promote the use of noninvasive ventilation therapies.

Polymer-dendrimer Hybrids as Carriers of Anticancer Agents.

In recent years, polymeric materials with the ability to self-assemble into micelles have been increasingly investigated for application in various fields, mainly in biomedicine. Micellar morphology is important and interesting in the field of drug transport and delivery since micelles can encapsulate hydrophobic molecules in their nucleus, improve the solubility of drugs, have active molecules in their outer layer, and, due to their nanometric size, they can take advantage of the EPR effect, prolong circulation time and avoid renal clearance. Furthermore, bioactive molecules (could be joined covalently or by host-host interaction), such as drugs, bioimaging molecules, proteins, targeting ligands, "cross-linkable" molecules, or linkages sensitive to internal or external stimuli, can be incorporated into them. The confined multivalent cooperativity and the ability to modify the dendritic structure provide versatility to create and improve the amphiphiles used in the micellar supramolecular field. As discussed in this review, the most studied structures are hybrid copolymers, which are formed by the combination of linear polymers and dendrons. Amphiphilic dendrimer micelles have achieved efficient and promising results in both in vitro and in vivo tests, and this encourages research for their future application in nanotherapies.

C-terminal Motifs of HIV-1 gp41 as Possible Determinants of Viral Pathogenesis / Motivos C-terminales de gp41 del VIH-1 como posibles determinantes de la patogénesis viral / Motivos C-terminais do HIV-1 gp41 como Possíveis Determinantes da Patogénese Viral

Abstract: human immunodeficiency virus type 1 (HIV-1) is the etiological agent of acquired immunodeficiency syndrome (AIDS), a pandemic with high economic and social costs. The envelope glycoprotein (ENV) of the virus mediates the infectious process by binding to and entering the host cell, one of the main target components of studies since its discovery. Its endodomain or C-terminal tail (CTT) participates in late replicative cycle processes, such as intracellular trafficking, activation, and cell death, which occurs because it interacts with multiple cellular factors through motifs or signal sequences present throughout its structure. Although these interactions have not been fully understood at specific levels, studies over more than three decades leave no doubtthatthis domain plays a fundamental role in the biology of the virus and probably the development of the disease. This review describes the studies carried out to date that demonstrate the importance of the CTT, focusing on the motifs responsible for its interactions and its possible roles in the pathogenicity of the infection.

Resumen: el virus de la inmunodeficiencia humana tipo 1 (VIH-1) es el agente etiológico del síndrome de inmunodeficiencia adguirida (SIDA), una pandemia con altos costos económicos y sociales. La glicoproteína de la envoltura (ENV) del virus media el proceso infeccioso al unirse a la célula huésped y entrar en ella, uno de los principales componentes objetivo de los estudios desde su descubrimiento. Su endodominio o cola C-terminal (CTT) participa en procesos tardíos del ciclo replicativo, como tráfico intracelular, activación y muerte celular, lo que ocurre porque interactúa con múltiples factores celulares a través de motivos o secuencias señal presentes en toda su estructura. Aunque estas interacciones no se han entendido completamente a niveles específicos, los estudios durante más de tres décadas no dejan dudas de que este campo juega un papel fundamental en la biología del virus y probablemente en el desarrollo de la enfermedad. Esta revisión describe los estudios realizados hasta la fecha que demuestran la importancia de la CTT, centrándose en los motivos responsables de sus interacciones y sus posibles roles en la patogenicidad de la infección.

Resumo: o vírus da imunodeficiência humana tipo 1 (HIV-1) é o agente etiológico da síndrome da imunodeficiência adquirida (AUXILIA), urna pandemia com elevados custos económicos e sociais. A glicoproteína do envelope (ENV) do vírus media o processo infeccioso ligando-se e entrando na célula hospedeira, um dos principais componentes alvo dos estudos desde sua descoberta. Seu endo domínio ou cauda C-terminal (CTT) participa de processos do ciclo replicativo tardio, como tráfego intracelular, ativação e morte celular, que ocorre porque interage com múltiplos fatores celulares por meio de motivos ou sequências-sinal presentes em toda a sua estrutura. Embora essas interações não tenham sido totalmente compreendidas em níveis específicos, estudos ao longo de mais de três décadas não deixam dúvidas de que esse domínio desempenha um papel fundamental na biologia do vírus e provavelmente no desenvolvimento da doença. Esta revisão descreve os estudos realizados até o momento que demonstram a importância da CTT, com foco nos motivos responsáveis por suas interações e seus possíveis papéis na patogenicidade da infecção.

Nanomedical Applications of Amphiphilic Dendrimeric Micelles.

In recent years, polymeric materials with the ability to self-assemble into micelles have been increasingly investigated for application in various fields, mainly in biomedicine. Micellar morphology is interesting in the field of drug transport and delivery since micelles can encapsulate hydrophobic molecules in their nucleus, have active molecules in their outer layer, and due to their nanometric size, can take advantage of the enhanced permeability and retention (EPR) effect, prolong the time in circulation and avoid renal clearance. In addition, nanobioactive molecules (joined in covalent form or by host-host interaction), such as drugs, bioimaging molecules, targeting ligands, "crosslinkable" molecules or bonds, sensitive to internal or external stimuli, can be incorporated into them and showed better activity as anticancer agents, siRNA delivery agents as well as antiviral and antiparasitic compounds. The present work is a review of the information published, which is the most important about the synthesis and biological importance of the confined multivalent cooperation and the ability to modify the dendritic structure, provide the versatility to create and improve the amphiphiles used in the micellar supramolecular field. The most studied structures are the hybrid copolymers formed by the combination of linear polymers and dendrons. However, small dendritic molecules that do not involve linear polymers have also been developed, such as Janus dendrimers, facial dendrons, and dendritic amphiphiles with only one dendron. Amphiphilic dendrimer micelles have achieved efficient and promising results, both in in vitro and in vivo tests, which encourage their research for future application in nanotherapies.

Effect of Savings on a Gas-Like Model Economy with Credit and Debt.

In kinetic exchange models, agents make transactions based on well-established microscopic rules that give rise to macroscopic variables in analogy to statistical physics. These models have been applied to study processes such as income and wealth distribution, economic inequality sources, economic growth, etc., recovering well-known concepts in the economic literature. In this work, we apply ensemble formalism to a geometric agents model to study the effect of saving propensity in a system with money, credit, and debt. We calculate the partition function to obtain the total money of the system, with which we give an interpretation of the economic temperature in terms of the different payment methods available to the agents. We observe an interplay between the fraction of money that agents can save and their maximum debt. The system's entropy increases as a function of the saved proportion, and increases even more when there is debt.

Evaluation of a loop-mediated isothermal amplification method for rapid detection of human respiratory syncytial virus in children with acute respiratory infection / Evaluación de un método de amplificación isotérmica medida por bucle para la detección rápida del virus sincitial respiratorio en niños con infección respiratoria aguda

Introduction: Human respiratory syncytial virus (hRSV) is the most frequent cause of acute respiratory infection of the lower respiratory tract in children under the age of five. The development of molecular techniques able to identify hRSV is one of the current challenges in the field of clinical research. Objective: To evaluate the ability of an isothermal amplification method to rapidly detect hRSV in children with acute respiratory infection. Materials and methods: We collected 304 nasopharyngeal swab samples from children with symptoms of acute respiratory infection who attended the emergency unit at Hospital de la Universidad del Norte in Barranquilla from April, 2016, to July, 2017. After extracting viral RNA from the samples, we evaluated the ability of the reverse transcriptase-loop-mediated isothermal amplification (RT-LAMP) M assay to rapidly detect hRSVA and hRSVB compared to other molecular techniques: quantitative PCR (qPCR), reverse transcriptase-LAMP L assay, and as a standard, the multiplex nested reverse transcriptase polymerase chain reaction (nested RT-PCR). Results: The RT-LAMP M assay had a sensitivity of 93.59% and a specificity of 92.92%, and a concordance of 0.83 ± 0.036 as compared with the nested RT-PCR test. While the Kappa index of the RT-LAMP M assay was higher than the values for the RT-LAMP L assay and the qPCR, the values of the latter two methods were in agreement (0.75 ± 0.043 and 0.71 ± 0.045, respectively). Conclusion: Due to the shorter running times, lower costs and better performance of the RT-LAMP M assay, it can be considered as a useful clinical tool for the detection of RSVA.

Introducción. El virus sincicial respiratorio humano (hRSV) es la causa más frecuente de infección respiratoria aguda de las vías respiratorias inferiores en niños menores de cinco años. El desarrollo de técnicas moleculares para identificarlo es uno de los retos actuales en el campo de la investigación clínica. Objetivo. Evaluar un método de amplificación isotérmica para la detección rápida del hRSV en niños con infección respiratoria aguda. Materiales y métodos. Se extrajo el ARN viral de 304 muestras de hisopado nasal en niños con síntomas de infección respiratoria aguda atendidos en el servicio de urgencias del Hospital de la Universidad del Norte en Barranquilla entre abril del 2016 y julio del 2017. Se evaluó la prueba de amplificación isotérmica mediada por bucle mediante transcriptasa inversa de la proteína de la matriz (M) (Reverse Transcription Loop-Mediated Isothermal Amplification, RT-LAMP) comparada con técnicas moleculares como la reacción en cadena de la polimerasa mediante transcriptasa inversa múltiple anidada (Reverse Transcription-Polymerase Chain Reaction, RT-PCR), la cual se empleó como la prueba estándar, la PCR en tiempo real (quantitative PCR, qPCR) y la RT-LAMP de la proteína L (L) para la detección rápida del virus sincicial respiratorio (VSR), subtipo A y subtipo B. Resultados. La prueba de RT-LAMP (M) tuvo una sensibilidad de 93,59 %, una especificidad de 92,92 % y una concordancia de 0,83 ± 0,036 comparada con la prueba de RT-PCR anidada. El índice kappa del RT-LAMP (M) fue superior, y los valores del RTLAMP (L) y la qPCR concordaron (0,75 ± 0,043 y 0,71 ± 0,045, respectivamente).

Evaluación de un método de amplificación isotérmica mediado por bucle para la detección rápida del virus sincicial respiratorio en niños con infección respiratoria aguda / Evaluation of a loop-mediated isothermal amplification method for the rapid detection of human respiratory syncytial virus in children with acute respiratory infection

Resumen Introducción. El virus sincicial respiratorio humano (hRSV) es la causa más frecuente de infección respiratoria aguda de las vías respiratorias inferiores en niños menores de cinco años. El desarrollo de técnicas moleculares para identificarlo es uno de los retos actuales en el campo de la investigación clínica. Objetivo. Evaluar un método de amplificación isotérmica para la detección rápida del hRSV en niños con infección respiratoria aguda. Materiales y métodos. Se extrajo el ARN viral de 304 muestras de hisopado nasal en niños con síntomas de infección respiratoria aguda atendidos en el servicio de urgencias del Hospital de la Universidad del Norte en Barranquilla entre abril del 2016 y julio del 2017. Se evaluó la prueba de amplificación isotérmica mediada por bucle mediante transcriptasa inversa de la proteína de la matriz (M) (Reverse Transcription Loop-Mediated Isothermal Amplification, RT-LAMP) comparada con técnicas moleculares como la reacción en cadena de la polimerasa mediante transcriptasa inversa múltiple anidada (Reverse Transcription- Polymerase Chain Reaction, RT-PCR), la cual se empleó como la prueba estándar, la PCR en tiempo real (quantitative PCR, qPCR) y la RT-LAMP de la proteína L (L) para la detección rápida del virus sincicial respiratorio (VSR), subtipo A y subtipo B. Resultados. La prueba de RT-LAMP (M) tuvo una sensibilidad de 93,59 %, una especificidad de 92,92 % y una concordancia de 0,83 ± 0,036 comparada con la prueba de RT-PCR anidada. El índice kappa del RT-LAMP (M) fue superior, y los valores del RT-LAMP (L) y la qPCR concordaron (0,75 ± 0,043 y 0,71 ± 0,045, respectivamente). Conclusiones. Estos resultados indican que la prueba RT-LAMP (M) puede considerarse como una herramienta de utilidad clínica para detectar el hSRVA, dado que el tiempo requerido para la obtención de resultados, así como los costos, es menor, y su desempeño es mejor que el de las otras pruebas moleculares evaluadas.

Abstract Introduction: Human respiratory syncytial virus (hRSV) is the most frequent cause of acute respiratory infection of the lower respiratory tract in children under the age of five. The development of molecular techniques able to identify hRSV is one of the current challenges in the field of clinical research. Objective: To evaluate the ability of an isothermal amplification method to rapidly detect hRSV in children with acute respiratory infection. Materials and methods: We collected 304 nasopharyngeal swab samples from children with symptoms of acute respiratory infection who attended the emergency unit at Hospital de la Universidad del Norte in Barranquilla from April, 2016, to July, 2017. After extracting viral RNA from the samples, we evaluated the ability of the reverse transcriptase-loop-mediated isothermal amplification (RT-LAMP) M assay to rapidly detect hRSVA and hRSVB compared to other molecular techniques: quantitative PCR (qPCR), reverse transcriptase-LAMP L assay, and as a standard, the multiplex nested reverse transcriptase polymerase chain reaction (nested RT-PCR). Results: The RT-LAMP M assay had a sensitivity of 93.59% and a specificity of 92.92%, and a concordance of 0.83 ± 0.036 as compared with the nested RT-PCR test. While the Kappa index of the RT-LAMP M assay was higher than the values for the RT-LAMP L assay and the qPCR, the values of the latter two methods were in agreement (0.75 ± 0.043 and 0.71 ± 0.045, respectively). Conclusion: Due to the shorter running times, lower costs and better performance of the RT-LAMP M assay, it can be considered as a useful clinical tool for the detection of RSVA.

Stability Analysis of Anthocyanins Using Alcoholic Extracts from Black Carrot (Daucus Carota ssp. Sativus Var. Atrorubens Alef.).

Anthocyanins are used for food coloring due their low toxicity and health benefits. They are extracted from different sources, but black carrot has higher anthocyanin content compared with common fruits and vegetables. Here, we study alcoholic anthocyanin extracts from black carrot to enhance their stability. The objective of our research is to determine if microencapsulation with tetraethyl orthosilicate (TEOS) is a feasible option for preventing black carrot anthocyanin degradation. Extraction solvents were solutions of (1) ethanol/acetic acid and (2) ethanol/citric acid. Samples were purified through a resin column and microencapsulated using TEOS. Fourier Transformed Infrared Spectroscopy (FTIR) spectra of samples were obtained, and degradation studies were performed under different conditions of UV radiation, pH and temperature. Antioxidant activity was evaluated with radical 2,2-diphenyl-1-picrylhydrazyl (DPPH) scavenging and electrochemical cupric reducing antioxidant capacity (CUPRAC). Color evaluation on food models were performed with CIE Lab at the beginning of experiments and after 25 days of storage. Results indicate that the more stable extracts against pH media changes are samples obtained with ethanol/acetic acid solution as extraction solvent. Extract purification through resin and TEOS microencapsulation had no significant effect on extract stability. In conclusion, although TEOS microencapsulation has proven to be effective for some dried materials from natural extracts in our previous research, we do not recommend its use for black carrot extracts considering our results in this particular case.

Unbiased diffusion of Brownian particles in a helical tube.

A theoretical framework based on using the Frenet-Serret moving frame as the coordinate system to study the diffusion of bounded Brownian point-like particles has been recently developed [L. Dagdug et al., J. Chem. Phys. 145, 074105 (2016)]. Here, this formalism is extended to a variable cross section tube with a helix with constant torsion and curvature as a mid-curve. For the sake of clarity, we will divide this study into two parts: one for a helical tube with a constant cross section and another for a helical tube with a variable cross section. For helical tubes with a constant cross section, two regimes need to be considered for systematic calculations. On the one hand, in the limit when the curvature is smaller than the inverse of the helical tube radius R, the resulting coefficient is that obtained by Ogawa. On the other hand, we also considered the limit when torsion is small compared to R, and to the best of our knowledge, the expression thus obtained has not been previously reported in the literature. In the more general case of helical tubes with a variable cross section, we also had to limit ourselves to small variations of R. In this case, we obtained one of the main contributions of this work, which is an expression for the diffusivity dependent on R', torsion, and curvature that consistently reduces to the well-known expressions within the corresponding limits.

Patients' perspective on sedation during upper gastrointestinal endoscopy. Systematic use of sedation or systematic prior information?

Although sedation in endoscopy is increasingly used and contributes to the quality of procedures, its role in upper gastrointestinal endoscopy (UGE) is not as well defined as in other procedures. For this reason, we conducted a prospective pilot study where the patient, once informed of the different options, decided whether or not to undergo sedation for UGE. Remarkably, almost 60% preferred not to undergo sedation, with a high degree of satisfaction and no adverse effects in any of the groups (Ferrer Rosique JA, et al. XXXIX Congreso SEED, Toledo 2017).

Perspectiva del paciente sobre la sedación en endoscopia alta. ¿Uso sistemático de sedación o la sistemática información previa? / Patients' perspective on sedation during upper gastrointestinal endoscopy. Systematic use of sedation or systematic prior information?

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A Lachnospiraceae-dominated bacterial signature in the fecal microbiota of HIV-infected individuals from Colombia, South America.

HIV infection has a tremendous impact on the immune system's proper functioning. The mucosa-associated lymphoid tissue (MALT) is significantly disarrayed during HIV infection. Compositional changes in the gut microbiota might contribute to the mucosal barrier disruption, and consequently to microbial translocation. We performed an observational, cross-sectional study aimed at evaluating changes in the fecal microbiota of HIV-infected individuals from Colombia. We analyzed the fecal microbiota of 37 individuals via 16S rRNA gene sequencing; 25 HIV-infected patients and 12 control (non-infected) individuals, which were similar in body mass index, age, gender balance and socioeconomic status. To the best of our knowledge, no such studies have been conducted in Latin American countries. Given its compositional nature, microbiota data were normalized and transformed using Aitchison's Centered Log-Ratio. Overall, a change in the network structure in HIV-infected patients was revealed by using the SPIEC-EASI MB tool. Genera such as Blautia, Dorea, Yersinia, Escherichia-Shigella complex, Staphylococcus, and Bacteroides were highly relevant in HIV-infected individuals. Differential abundance analysis by both sparse Partial Least Square-Discriminant Analysis and Random Forest identified a greater abundance of Lachnospiraceae-OTU69, Blautia, Dorea, Roseburia, and Erysipelotrichaceae in HIV-infected individuals. We show here, for the first time, a predominantly Lachnospiraceae-based signature in HIV-infected individuals.

Effects of curved midline and varying width on the description of the effective diffusivity of Brownian particles.

Axial diffusion in channels and tubes of smoothly-varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with a position-dependent effective diffusion coefficient, by means of the modified Fick-Jacobs equation. In this work, we derive analytical expressions for the position-dependent effective diffusivity for two-dimensional asymmetric varying-width channels, and for three-dimensional curved midline tubes, formed by straight walls. To this end, we use a recently developed theoretical framework using the Frenet-Serret moving frame as the coordinate system (2016 J. Chem. Phys. 145 074105). For narrow tubes and channels, an effective one-dimensional description reducing the diffusion equation to a Fick-Jacobs-like equation in general coordinates is used. From this last equation, one can calculate the effective diffusion coefficient applying Neumann boundary conditions.

On the description of Brownian particles in confinement on a non-Cartesian coordinates basis.

We developed a theoretical framework to study the diffusion of Brownian point-like particles in bounded geometries in two and three dimensions. We use the Frenet-Serret moving frame as the coordinate system. For narrow tubes and channels, we use an effective one-dimensional description reducing the diffusion equation to a Fick-Jacobs-like equation. From this last equation, we can calculate the effective diffusion coefficient applying Neumann boundary conditions. On one hand, for channels with a straight axis our theoretical approximation for the effective coefficient does coincide with the reported in the literature [D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001) and P. Kalinay and J. K. Percus, ibid. 74, 041203 (2006)]. On the other hand, for tubes with a straight axis and circular cross-section our analytical expression does not coincide with the reported by Rubí and Reguera and by Kalinay and Percus, although it is practically identical.