Fractional-order nonlinear hereditariness of tendons and ligaments of the human knee.

In this paper the authors introduce a nonlinear model of fractional-order hereditariness used to capture experimental data obtained on human tendons of the knee. Creep and relaxation data on fibrous tissues have been obtained and fitted with logarithmic relations that correspond to power-laws with nonlinear dependence of the coefficients. The use of a proper nonlinear transform allows one to use Boltzmann superposition in the transformed variables yielding a fractional-order model for the nonlinear material hereditariness. The fundamental relations among the nonlinear creep and relaxation functions have been established, and the results from the equivalence relations have been contrasted with measures obtained from the experimental data. Numerical experiments introducing polynomial and harmonic stress and strain histories have been reported to assess the provided equivalence relations. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.

Fractional hereditariness of lipid membranes: Instabilities and linearized evolution.

In this work lipid ordering phase changes arising in planar membrane bilayers is investigated both accounting for elasticity alone and for effective viscoelastic response of such assemblies. The mechanical response of such membranes is studied by minimizing the Gibbs free energy which penalizes perturbations of the changes of areal stretch and their gradients only (Deseri and Zurlo, 2013). As material instabilities arise whenever areal stretches characterizing homogeneous configurations lie inside the spinoidal zone of the free energy density, bifurcations from such configurations are shown to occur as oscillatory perturbations of the in-plane displacement. Experimental observations (Espinosa et al., 2011) show a power-law in-plane viscous behavior of lipid structures allowing for an effective viscoelastic behavior of lipid membranes, which falls in the framework of Fractional Hereditariness. A suitable generalization of the variational principle invoked for the elasticity is applied in this case, and the corresponding Euler-Lagrange equation is found together with a set of boundary and initial conditions. Separation of variables allows for showing how Fractional Hereditariness owes bifurcated modes with a larger number of spatial oscillations than the corresponding elastic analog. Indeed, the available range of areal stresses for material instabilities is found to increase with respect to the purely elastic case. Nevertheless, the time evolution of the perturbations solving the Euler-Lagrange equation above exhibits time-decay and the large number of spatial oscillation slowly relaxes, thereby keeping the features of a long-tail type time-response.

A frequency-based hypothesis for mechanically targeting and selectively attacking cancer cells.

Experimental studies recently performed on single cancer and healthy cells have demonstrated that the former are about 70% softer than the latter, regardless of the cell lines and the measurement technique used for determining the mechanical properties. At least in principle, the difference in cell stiffness might thus be exploited to create mechanical-based targeting strategies for discriminating neoplastic transformations within human cell populations and for designing innovative complementary tools to cell-specific molecular tumour markers, leading to possible applications in the diagnosis and treatment of cancer diseases. With the aim of characterizing and gaining insight into the overall frequency response of single-cell systems to mechanical stimuli (typically low-intensity therapeutic ultrasound), a generalized viscoelastic paradigm, combining classical and spring-pot-based models, is introduced for modelling this problem by neglecting the cascade of mechanobiological events involving the cell nucleus, cytoskeleton, elastic membrane and cytosol. Theoretical results show that differences in stiffness, experimentally observed ex vivo and in vitro, allow healthy and cancer cells to be discriminated, by highlighting frequencies (from tens to hundreds of kilohertz) associated with resonance-like phenomena­prevailing on thermal fluctuations­that could be helpful in targeting and selectively attacking tumour cells.

Adverse interactions of rofecoxib with lisinopril in spontaneously hypertensive rats.

BACKGROUND: Hypertension and arthritis are frequent comorbidities. Nonsteroidal anti-inflammatory drugs (NSAIDs) are well known to produce hypertension or attenuate the effects of antihypertensive agents in a few patients. The influence of selective NSAIDs on blood pressure and the cardiovascular and renal effects of coxibs have still to be investigated. The purpose of this study was to test the hypothesis that rofecoxib interferes with antihypertensive activity and cardiorenal protective effects of lisinopril in spontaneously hypertensive rats (SHRs). METHODS: Twenty-one unanaesthetised, male spontaneously hypertensive rats (SHRs), 16 weeks old, were randomized to receive lisinopril (LS) 15 mg/kg/d or rofecoxib (RF) 20 mg/kg/d or combination of lisinopril (LS) and rofecoxib (RF) for 2 weeks. The arterial blood pressure changes were recorded each week. The Sodium Hydrogen Exchange (NHE) activity of erythrocytes was determined 2 weeks after the study. The surviving animals were sacrificed 24 h after the last dose, and the sections of their hearts and kidneys were assessed histologically for injury by a pathologist masked to the treatment. RESULTS: RF completely prevented the hypotensive effects of LS during the first week of treatment but the antihypertensive efficacy of LS was restored during the second week of treatment. The NHE in erythrocytes of 18-week-old SHRs was found to be significantly lower than the age-matched Wistar rats (P < 0.05), and LS treatment reversed these values to Wistar control in SHRs. RF was devoid of any effect on NHE of erythrocytes. The histological examination revealed that the myocardial and renal protection induced by LS was attenuated by concomitant RF therapy. CONCLUSIONS: These results indicate that COX-2 inhibitors should be used judiciously in patients with history of hypertension, ischemic heart disease, or chronic renal failure.