Two compartmental fractional derivative model with general fractional derivative.

This study presents a new two compartmental model with, recently defined General fractional derivative. We review that concept of General fractional derivative and use the kernel function that generalizes the classical Caputo derivative in a mathematically consistent way. Next we use this model to study the release of antibiotic gentamicin in poly (vinyl alcohol)/gentamicin(PVA/Gent) hydrogel aimed for wound dressing in medical treatment of deep chronical wounds. The PVA/Gent hydrogel was prepared by physical cross linking of poly (vinyl alcohol) dispersion using freezing-thawing method, and then was swollen in gentamicin solution at 37 °C during 48 h. The concentration of released gentamicin was determined using a high-performance liquid chromatography coupled with mass spectrometer. The advantage of this model is the existence of new parameters in the definition of fractional derivative, as compared with classical fractional compartmental models. The model proposed here in the special case reduces to the classical (integer order) linear two compartmental model as well as classical fractional order two compartmental model since it has more parameters that are determined from the experimental results.

On the thermodynamical restrictions in isothermal deformations of fractional Burgers model.

We investigate, in the distributional setting, the restrictions on the constitutive equation for a fractional Burgers model of viscoelastic fluid that follow from the weak form of the entropy inequality under isothermal conditions. The results are generalized, from the Burgers model, to an arbitrary class of linear constitutive equations with fractional derivatives. Our results show that the restrictions obtained here on the coefficients of constitutive equations are weaker when compared with the restrictions obtained by Bagley-Torvik method. We show the precise relation between restrictions derived here and those derived by Bagley-Torvik. We deal with the creep test, for the case when Bagley-Torvik conditions are violated, and new conditions obtained in this work are satisfied. The results show a qualitative difference in the form of creep function. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.

Semiautomatic Epicardial Fat Segmentation Based on Fuzzy c-Means Clustering and Geometric Ellipse Fitting.

Automatic segmentation of particular heart parts plays an important role in recognition tasks, which is utilized for diagnosis and treatment. One particularly important application is segmentation of epicardial fat (surrounds the heart), which is shown by various studies to indicate risk level for developing various cardiovascular diseases as well as to predict progression of certain diseases. Quantification of epicardial fat from CT images requires advance image segmentation methods. The problem of the state-of-the-art methods for epicardial fat segmentation is their high dependency on user interaction, resulting in low reproducibility of studies and time-consuming analysis. We propose in this paper a novel semiautomatic approach for segmentation and quantification of epicardial fat from 3D CT images. Our method is a semisupervised slice-by-slice segmentation approach based on local adaptive morphology and fuzzy c-means clustering. Additionally, we use a geometric ellipse prior to filter out undesired parts of the target cluster. The validation of the proposed methodology shows good correspondence between the segmentation results and the manual segmentation performed by physicians.

Viscoelastic properties of uncured resin composites: Dynamic oscillatory shear test and fractional derivative model.

OBJECTIVE: In this study we analyze viscoelastic properties of three flowable (Wave, Wave MV, Wave HV) and one universal hybrid resin (Ice) composites, prior to setting. We developed a mathematical model containing fractional derivatives in order to describe their properties. METHODS: Isothermal experimental study was conducted on a rheometer with parallel plates. In dynamic oscillatory shear test, storage and loss modulus, as well as the complex viscosity where determined. We assumed four different fractional viscoelastic models, each belonging to one particular class, derivable from distributed-order fractional constitutive equation. The restrictions following from the Second law of thermodynamics are imposed on each model. The optimal parameters corresponding to each model are obtained by minimizing the error function that takes into account storage and loss modulus, thus obtaining the best fit to the experimental data. RESULTS: In the frequency range considered, we obtained that for Wave HV and Wave MV there exist a critical frequency for which loss and storage modulus curves intersect, defining a boundary between two different types of behavior: one in which storage modulus is larger than loss modulus and the other in which the situation is opposite. Loss and storage modulus curves for Ice and Wave do not show this type of behavior, having either elastic, or viscous effects dominating in entire frequency range considered. SIGNIFICANCE: The developed models may be used to predict behavior of four tested composites in different flow conditions (different deformation speed), thus helping to estimate optimal handling characteristics for specific clinical applications.