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.

Transthyretin cardiac amyloidosis: a review of the nuclear imaging findings with emphasis on the radiotracers mechanisms.

Cardiac amyloidosis is a protein deposition disease characterized by the infiltration of the myocardium and coronary arteries resulting in a progressive thickening of both ventricles, interatrial septum and atrioventricular valves, eventually leading to organ failure. It is a disease hard to diagnose, due to the lack of diagnostic investigations. However, development of new and more accurate examinations is undergoing. Endomyocardial biopsy is the gold standard investigation for this disease, but it has its limitations (invasive and not widely available). Other investigations may be able to detect the presence of cardiac amyloidosis but cannot specify the type involved. To that end, nuclear medicine through bone scanning offers a simple, non-invasive solution to detect, differentiate and diagnose transthyretin cardiac amyloidosis (ATTR) from other types of cardiac amyloidosis. In order to demonstrate the importance of bone scanning we will present a few methods of image processing based on literature and a personalized method, followed by a few important examples of positive cases. The aim of this review was to present the current methods of ATTR detection with emphasis on nuclear medicine bone scanning and its important place in the decision algorithm of the cardiologist for a personalized approach to this pathology.

Fine Tuning of Traumatic Brain Injury Management in Neurointensive Care-Indicative Observations and Future Perspectives.

Neurointensive care (NIC) has contributed to great improvements in clinical outcomes for patients with severe traumatic brain injury (TBI) by preventing, detecting, and treating secondary insults and thereby reducing secondary brain injury. Traditional NIC management has mainly focused on generally applicable escalated treatment protocols to avoid high intracranial pressure (ICP) and to keep the cerebral perfusion pressure (CPP) at sufficiently high levels. However, TBI is a very heterogeneous disease regarding the type of injury, age, comorbidity, secondary injury mechanisms, etc. In recent years, the introduction of multimodality monitoring, including, e.g., pressure autoregulation, brain tissue oxygenation, and cerebral energy metabolism, in addition to ICP and CPP, has increased the understanding of the complex pathophysiology and the physiological effects of treatments in this condition. In this article, we will present some potential future approaches for more individualized patient management and fine-tuning of NIC, taking advantage of multimodal monitoring to further improve outcome after severe TBI.

Systemic Hyperthermia in Traumatic Brain Injury-Relation to Intracranial Pressure Dynamics, Cerebral Energy Metabolism, and Clinical Outcome.

BACKGROUND: Systemic hyperthermia is common after traumatic brain injury (TBI) and may induce secondary brain injury, although the pathophysiology is not fully understood. In this study, our aim was to determine the incidence and temporal course of hyperthermia after TBI and its relation to intracranial pressure dynamics, cerebral metabolism, and clinical outcomes. MATERIALS AND METHODS: This retrospective study included 115 TBI patients. Data from systemic physiology (body temperature, blood pressure, and arterial glucose), intracranial pressure dynamics (intracranial pressure, cerebral perfusion pressure, compliance, and pressure reactivity), and cerebral microdialysis (glucose, pyruvate, lactate, glycerol, glutamate, and urea) were analyzed during the first 10 days after injury. RESULTS: Overall, 6% of patients did not have hyperthermia (T>38°C) during the first 10 days after injury, whereas 20% had hyperthermia for >50% of the time. Hyperthermia increased from 21% (±27%) of monitoring time on day 1 to 36% (±29%) on days 6 to 10 after injury. In univariate analyses, higher body temperature was not associated with higher intracranial pressure nor lower cerebral perfusion pressure, but was associated with lower cerebral glucose concentration (P=0.001) and higher percentage of lactate-pyruvate ratio>25 (P=0.02) on days 6 to 10 after injury. Higher body temperature and lower arterial glucose concentration were associated with lower cerebral glucose in a multiple linear regression analysis (P=0.02 for both). There was no association between hyperthermia and worse clinical outcomes. CONCLUSION: Hyperthermia was most common between days 6 and 10 following TBI, and associated with disturbances in cerebral energy metabolism but not worse clinical outcome.

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'.

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.

A model of the viscoelastic behavior of flowable resin composites prior to setting.

OBJECTIVE: The aim of this study is to develop fractional derivative models for the assessment of viscoelastic properties related to handling characteristics of dental resin composites belonging to two classes: flowable (Revolution Formula 2 and Filtek Ultimate) and posterior "bulk-fill" flowable base (Smart Dentin Replace). METHODS: Rheological measurements on all materials tested in this study were performed using dynamic oscillatory rheometer at temperature of 23°C. A parallel plates module with a diameter of 20mm was used to measure the properties of the resin composites tested. We developed two models to describe the obtained data: the generalized Newton model and the generalized Zener model (the so-called three parameter model). Both models contain fractional derivatives of Riemann-Liouville type. By determining the parameters of the model we were able to fit experimental data with high accuracy. RESULTS: Our results show that flowable "bulk-fill" resin-composite material (SDR) has distinct properties as compared to other two flowable resin composite materials (Revolution Formula 2 and Filtek Ultimate). Thus, previously found SDR properties as "bulk-fill" flowable base results in the fact that it is described by generalized Zener model (i.e., it has properties of solid like viscoelastic material). SIGNIFICANCE: Our model may be used to predict behavior of tested composites in different flow conditions. The SDR has initially small almost constant complex viscosity showing that it has good self-leveling property.

A biomechanical model for a new incremental technique for tooth restoration.

The objective of this study is to introduce a modified incremental technique that leads to improved marginal adaptation and to develop a mathematical model that explains the results obtained. The technique proposed is a two-step incremental technique that reduces volume of a resin that is polymerized at each step and eliminates the central point in resin, so that the stresses are additionally reduced. In the first step, the resin is placed in the cylindrical cavity with a conical dental instrument embedded in the middle of restoration. After polymerization, the conical dental instrument is removed and the conical hole is filled with the second layer of composite and polymerized. This technique is a variant of a method where singular stress point is eliminated. We modified the previous technique by introducing a conical dental instrument into the centre of the cavity. The procedure proposed was compared with the bulk and horizontal layer incremental technique. This study confirmed that the incremental type placement technique used here has better marginal adaptation than bulk technique and horizontal two-layer incremental technique although it has larger C-factor in the first step than the two-layer incremental technique. Thus, the elimination of the central point of restoration leads to better marginal adaptation. Conical shape of the cavity that is filled in the second step makes this technique easy to apply in clinical conditions. A mathematical model describing stresses in the restoration shows stress reduction as a consequence of applying the procedure proposed.

A nonlinear two compartmental fractional derivative model.

This study presents a new nonlinear two compartmental model and its application to the evaluation of valproic acid (VPA) pharmacokinetics in human volunteers after oral administration. We have used literature VPA concentrations. In the model, the integer order derivatives are replaced by derivatives of real order often called fractional order derivatives. Physically that means that the history (memory) of a biological process, realized as a transfer from one compartment to another, is taken into account with the mass balance conservation observed. Our contribution is the analysis of a specific nonlinear two compartmental model with the application in evaluation of VPA pharmacokinetics. The agreement of the values predicted by the proposed model with the values obtained through experiments is shown to be good. Thus, pharmacokinetics of VPA after oral application can be described well by a nonlinear two compartmental model with fractional derivatives of the same order proposed here. Parameters in the model are determined by the least-squares method and the particle swarm optimization (PSO) numerical procedure is used. The results show that the nonlinear fractional order two compartmental model for VPA pharmacokinetics is superior in comparison to the classical (integer order) linear two compartmental model and to the linear fractional order two compartmental model.

A method of improving marginal adaptation by elimination of singular stress point in composite restorations during resin photo-polymerization.

OBJECTIVES: To reduce the effect of stresses due to volumetric shrinkage the authors propose an incremental technique for placing composite restorations. METHODS: The goal of the method is to reduce the volume of the resin that is polymerized and eliminate a stress singular point in the resin that is positioned at the geometric center of the cavity. This is achieved by a two step type incremental technique. In the first step the resin is placed in the cylindrical cavity with a metal pin embedded in the middle of the composite restoration. After polymerization, the metal pin is removed and the cylindrical hole is filled with the second layer of composite. Finally, the second layer in the center of the composite restoration is polymerized. RESULTS: This study confirmed that the proposed incremental type placement technique reduces marginal debonding. SIGNIFICANCE: The main hypothesis is that the elimination of a stress singular point at the center of the restoration results in the reduction of stresses at tooth-composite interface and therefore improve the marginal adaptation (reduces length of the contraction gap at tooth-composite interface).

A new approach to the compartmental analysis in pharmacokinetics: fractional time evolution of diclofenac.

This study presents a new two compartmental model and its application to the evaluation of diclofenac pharmacokinetics in a small number of healthy adults, during a bioequivalence trial. In the model the integer order derivatives are replaced by derivatives of real order often called fractional order derivatives. Physically that means that a history (memory) of a biological process, realized as a transfer from one compartment to another one with the mass balance conservation, is taken into account. This kind of investigations in pharmacokinetics is founded by Dokoumetzidis and Macheras through the one compartmental models while our contribution is the analysis of multi-dimensional compartmental models with the applications of the two compartmental model in evaluation of diclofenac pharmacokinetics. Two experiments were preformed with 12 healthy volunteers with two slow release 100 mg diclofenac tablet formulations. The agreement of the values predicted by the proposed model with the values obtained through experiments is shown to be good. Thus, pharmacokinetics of slow release diclofenac can be described well by a specific two compartmental model with fractional derivatives of the same order. Parameters in the model are determined by the least-squares method and the Particle Swarm Optimization (PSO) numerical procedure is used. The results show that the fractional order two compartmental model for diclofenac is superior in comparison to the classical two compartmental model. Actually this is true in general case since the classical one is a special case of the fractional one.

A model for shrinkage strain in photo polymerization of dental composites.

OBJECTIVES: We formulate a new model for the shrinkage strain developed during photo polymerization in dental composites. The model is based on the diffusion type fractional order equation, since it has been proved that polymerization reaction is diffusion controlled (Atai M, Watts DC. A new kinetic model for the photo polymerization shrinkage-strain of dental composites and resin-monomers. Dent Mater 2006;22:785-91). Our model strongly confirms the observation by Atai and Watts (see reference details above) and their experimental results. The shrinkage strain is modeled by a nonlinear differential equation in (see reference details above) and that equation must be solved numerically. In our approach, we use the linear fractional order differential equation to describe the strain rate due to photo polymerization. This equation is solved exactly. RESULTS: As shrinkage is a consequence of the polymerization reaction and polymerization reaction is diffusion controlled, we postulate that shrinkage strain rate is described by a diffusion type equation. We find explicit form of solution to this equation and determine the strain in the resin monomers. Also by using equations of linear viscoelasticity, we determine stresses in the polymer due to the shrinkage. The time evolution of stresses implies that the maximal stresses are developed at the very beginning of the polymerization process. SIGNIFICANCE: The stress in a dental composite that is light treated has the largest value short time after the treatment starts. The strain settles at the constant value in the time of about 100s (for the cases treated in Atai and Watts). From the model developed here, the shrinkage strain of dental composites and resin monomers is analytically determined. The maximal value of stresses is important, since this value must be smaller than the adhesive bond strength at cavo-restoration interface. The maximum stress determined here depends on the diffusivity coefficient. Since diffusivity coefficient increases as polymerization proceeds, it follows that the periods of light treatments should be shorter at the beginning of the treatment and longer at the end of the treatment, with dark interval between the initial low intensity and following high intensity curing. This is because at the end of polymerization the stress relaxation cannot take place.

On a mathematical model of a human root dentin.

OBJECTIVE: On the basis of recent experimental data, a new mathematical model that predicts creep in human root dentin has been developed. METHOD: The chosen constitutive model comprises fractional derivatives of stress and strain and the restrictions on the coefficients that follow from the Clausius-Duhem inequality. RESULTS: The four constants describing mechanical properties of the human dentin at constant temperature are calculated from a highly non-linear system involving Mittag-Leffler-type functions. Special attention is paid to thermodynamical restrictions that should be observed in determining parameters of the model from experimental results. SIGNIFICANCE: The proposed model allows us to predict behavior of a human dentin in different load situations. Also it could be used for describing mechanical properties of dentin that are important in the development of 'dentin-like' restorative materials.

Serodiagnosis of extrapulmonary tuberculosis by enzyme-linked immunosorbent assay (ELISA).

Antibodies against Mycobacterium tuberculosis antigenic glycolipids were determined by enzyme-linked immunosorbent assay (ELISA). The 720 sera were collected from adult patients under investigation, suspected with extrapulmonary tuberculosis. The test performance was estimated according to definitive diagnosis in terms of specificity, sensitivity, positive predictive value and negative predictive value. These parameters calculated on 142 sera from patients with extrapulmonary tuberculosis and on 578 sera from patients with different nontuberculosis diseases were 92%, 81.6%, 70.9% and 95.1%, respectively. The specificity decreased to 85% when tuberculosis was associated with cancer or hepatic cirrhosis. In reactivated tuberculosis the sensitivity and the positive predictive value were 86.9% and 83.3%, respectively. Our results showed that ELISA was conclusive for patients with active tuberculosis, before the initiation of the treatment. The sensitivity decreased to 30% in inactive forms. It was demonstrated that ELISA was positive in cases with negative microscopy genitourinary tuberculosis. ELISA could be used as a supporting test in the laboratory diagnosis of active extrapulmonary tuberculosis in adults, disregarding the site involved.