Creep, Relaxation and Viscosity Properties for Basic Fractional Models in Rheology

The purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyze the basic fractional models as far as their creep, relaxation and viscosity properties are considered. The basic models are those that generalize via derivatives of fractional order the classical mechanical models characterized by two, three and four parameters, that we refer to as Kelvin-Voigt, Maxwell, Zener, anti-Zener and Burgers. For each fractional model we provide plots of the creep compliance, relaxation modulus and effective viscosity in non dimensional form in terms of a suitable time scale for different values of the order of fractional derivative. We also discuss the role of the order of fractional derivative in modifying the properties of the classical models.Comment: 41 pages, 8 figure

Antioxidant properties of agri-food byproducts and specific boosting effects of hydrolytic treatments

Largely produced agri\u2010food byproducts represent a sustainable and easily available source of phenolic compounds, such as lignins and tannins, endowed with potent antioxidant properties. We report herein the characterization of the antioxidant properties of nine plant\u2010derived byproducts. 2,2\u2010Diphenyl\u20101\u2010picrylhydrazyl (DPPH) and ferric reducing/antioxidant power (FRAP) assays indicated the superior activity of pomegranate peels and seeds, grape pomace and pecan nut shell. An increase in the antioxidant potency was observed for most of the waste materials following a hydrolytic treatment, with the exception of the condensed tannin\u2010rich pecan nut shell and grape pomace. UV\u2010Vis and HPLC investigation of the soluble fractions coupled with the results from IR analysis and chemical degradation approaches on the whole materials allowed to conclude that the improvement of the antioxidant properties was due not only to removal of non\u2010active components (mainly carbohydrates), but also to structural modifications of the phenolic compounds. Parallel experiments run on natural and bioinspired model phenolic polymers suggested that these structural modifications positively impacted on the antioxidant properties of lignins and hydrolyzable tannins, whereas significant degradation of condensed tannin moieties occurred, likely responsible for the lowering of the reducing power observed for grape pomace and pecan nut shell. These results open new perspectives toward the exploitation and manipulation of agri\u2010food byproducts for application as antioxidant additives in functional

Determination of free 25(OH)D concentrations and their relationships to total 25(OH)D in multiple clinical populations

Context : The optimal measure of vitamin D(D) status is unknown. Objective : Directly measure circulating free 25(OH)D concentrations and relationships to total 25(OH)D in a clinically diverse sample of humans. Design : Cross-sectional analysis Setting : Seven academic sites Patients : 1661 adults: (healthy(n=211), pre-diabetic(n=479), outpatients(n=783), cirrhotic(n=90), pregnant(n=20), nursing home(n=79)) Interventions : Merge research data on circulating free 25(OH)D (directly measured immunoassay), total 25(OH)D (LC/MS/MS), D binding protein (DBP by radial (polyclonal) immunodiffusion assay)), albumin, creatinine, iPTH and DBP haplotype Main outcome measures : Distribution of free 25(OH)D (ANOVA with Bonferroni correction for post hoc comparisons) and relationships between free and total 25(OH)D (mixed effects modeling incorporating clinical condition, DBP haplotype with sex, race, eGFR, BMI and other covariates). Results : Free 25(OH)D was 4.7±1.8 pg/mL (mean ±SD) in healthy and 4.3 ±1.9 pg/mL in outpatients with 0.5-8.1 pg/mL and 0.9-8.1 pg/mL encompassing 95% of healthy and outpatients, respectively. Free 25(OH)D was higher in cirrhotics (7.1 ±3.0 pg/mL, pnursing home>prediabetic > outpatient > pregnant), and BMI (lesser effect) as covariates affecting relationships but not eGFR, sex, race or DBP haplotype. Conclusions : Total 25(OH)D, health condition, race and DBP haplotype affected free 25(OH)D, but only health conditions and BMI affected relationships between total and free 25(OH) D. Clinical importance of free 25(OH)D needs to be established in studies assessing outcomes

The use of a physiologically based pharmacokinetic model to evaluate deconvolution measurements of systemic absorption

BACKGROUND: An unknown input function can be determined by deconvolution using the systemic bolus input function (r) determined using an experimental input of duration ranging from a few seconds to many minutes. The quantitative relation between the duration of the input and the accuracy of r is unknown. Although a large number of deconvolution procedures have been described, these routines are not available in a convenient software package. METHODS: Four deconvolution methods are implemented in a new, user-friendly software program (PKQuest, ). Three of these methods are characterized by input parameters that are adjusted by the user to provide the "best" fit. A new approach is used to determine these parameters, based on the assumption that the input can be approximated by a gamma distribution. Deconvolution methodologies are evaluated using data generated from a physiologically based pharmacokinetic model (PBPK). RESULTS AND CONCLUSIONS: The 11-compartment PBPK model is accurately described by either a 2 or 3-exponential function, depending on whether or not there is significant tissue binding. For an accurate estimate of r the first venous sample should be at or before the end of the constant infusion and a long (10 minute) constant infusion is preferable to a bolus injection. For noisy data, a gamma distribution deconvolution provides the best result if the input has the form of a gamma distribution. For other input functions, good results are obtained using deconvolution methods based on modeling the input with either a B-spline or uniform dense set of time points

Fractional dynamics pharmacokinetics–pharmacodynamic models

While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics

Physiologically based pharmacokinetic modeling of arterial – antecubital vein concentration difference

BACKGROUND: Modeling of pharmacokinetic parameters and pharmacodynamic actions requires knowledge of the arterial blood concentration. In most cases, experimental measurements are only available for a peripheral vein (usually antecubital) whose concentration may differ significantly from both arterial and central vein concentration. METHODS: A physiologically based pharmacokinetic (PBPK) model for the tissues drained by the antecubital vein (referred to as "arm") is developed. It is assumed that the "arm" is composed of tissues with identical properties (partition coefficient, blood flow/gm) as the whole body tissues plus a new "tissue" representing skin arteriovenous shunts. The antecubital vein concentration depends on the following parameters: the fraction of "arm" blood flow contributed by muscle, skin, adipose, connective tissue and arteriovenous shunts, and the flow per gram of the arteriovenous shunt. The value of these parameters was investigated using simultaneous experimental measurements of arterial and antecubital concentrations for eight solutes: ethanol, thiopental, (99)Tc(m)-diethylene triamine pentaacetate (DTPA), ketamine, D(2)O, acetone, methylene chloride and toluene. A new procedure is described that can be used to determine the arterial concentration for an arbitrary solute by deconvolution of the antecubital concentration. These procedures are implemented in PKQuest, a general PBPK program that is freely distributed . RESULTS: One set of "standard arm" parameters provides an adequate description of the arterial/antecubital vein concentration for ethanol, DTPA, thiopental and ketamine. A significantly different set of "arm" parameters was required to describe the data for D(2)O, acetone, methylene chloride and toluene – probably because the "arm" is in a different physiological state. CONCLUSIONS: Using the set of "standard arm" parameters, the antecubital vein concentration can be used to determine the whole body PBPK model parameters for an arbitrary solute without any additional adjustable parameters. Also, the antecubital vein concentration can be used to estimate the arterial concentration for an arbitrary input for solutes for which no arterial concentration data is available

Ellagitannins of the fruit rind of pomegranate (Punica granatum) antagonize in vitro the host inflammatory response mechanisms involved in the onset of malaria

<p>Abstract</p> <p>Background</p> <p>The sun-dried rind of the immature fruit of pomegranate (<it>Punica granatum</it>) is presently used as a herbal formulation (OMARIA, Orissa Malaria Research Indigenous Attempt) in Orissa, India, for the therapy and prophylaxis of malaria. The pathogenesis of cerebral malaria, a complication of the infection by <it>Plasmodium falciparum</it>, is an inflammatory cytokine-driven disease associated to an up-regulation and activity of metalloproteinase-9 and to the increase of TNF production. The <it>in vitro </it>anti-plasmodial activity of <it>Punica granatum (Pg) </it>was recently described. The aim of the present study was to explore whether the anti-malarial effect of OMARIA could also be sustained via other mechanisms among those associated to the host immune response.</p> <p>Methods</p> <p>From the methanolic extract of the fruit rind, a fraction enriched in tannins (<it>Pg</it>-FET) was prepared. MMP-9 secretion and expression were evaluated in THP-1 cells stimulated with haemozoin or TNF. The assays were conducted in the presence of the <it>Pg</it>-FET and its chemical constituents ellagic acid and punicalagin. The effect of urolithins, the ellagitannin metabolites formed by human intestinal microflora, was also investigated.</p> <p>Results</p> <p><it>Pg</it>-FET and its constituents inhibited the secretion of MMP-9 induced by haemozoin or TNF. The effect occurred at transcriptional level since MMP-9 mRNA levels were lower in the presence of the tested compounds. Urolithins as well inhibited MMP-9 secretion and expression. <it>Pg</it>-FET and pure compounds also inhibited MMP-9 promoter activity and NF-kB-driven transcription.</p> <p>Conclusions</p> <p>The beneficial effect of the fruit rind of <it>Punica granatum </it>for the treatment of malarial disease may be attributed to the anti-parasitic activity and the inhibition of the pro-inflammatory mechanisms involved in the onset of cerebral malaria.</p

Quantification system for the viral dynamics of a highly pathogenic simian/human immunodeficiency virus based on an in vitro experiment and a mathematical model

<p>Abstract</p> <p>Background</p> <p>Developing a quantitative understanding of viral kinetics is useful for determining the pathogenesis and transmissibility of the virus, predicting the course of disease, and evaluating the effects of antiviral therapy. The availability of data in clinical, animal, and cell culture studies, however, has been quite limited. Many studies of virus infection kinetics have been based solely on measures of total or infectious virus count. Here, we introduce a new mathematical model which tracks both infectious and total viral load, as well as the fraction of infected and uninfected cells within a cell culture, and apply it to analyze time-course data of an SHIV infection <it>in vitro</it>.</p> <p>Results</p> <p>We infected HSC-F cells with SHIV-KS661 and measured the concentration of Nef<it>-</it>negative (target) and Nef<it>-</it>positive (infected) HSC-F cells, the total viral load, and the infectious viral load daily for nine days. The experiments were repeated at four different MOIs, and the model was fitted to the full dataset simultaneously. Our analysis allowed us to extract an infected cell half-life of 14.1 h, a half-life of SHIV-KS661 infectiousness of 17.9 h, a virus burst size of 22.1 thousand RNA copies or 0.19 TCID₅₀, and a basic reproductive number of 62.8. Furthermore, we calculated that SHIV-KS661 virus-infected cells produce at least 1 infectious virion for every 350 virions produced.</p> <p>Conclusions</p> <p>Our method, combining <it>in vitro </it>experiments and a mathematical model, provides detailed quantitative insights into the kinetics of the SHIV infection which could be used to significantly improve the understanding of SHIV and HIV-1 pathogenesis. The method could also be applied to other viral infections and used to improve the <it>in vitro </it>determination of the effect and efficacy of antiviral compounds.</p