Incompressible limit and well-posedness of PDE models of tissue growth

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. A coupled system of equations describes the cell density and the nutrient concentration and the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state.

Multi-scalar critical theories: first steps for a non perturbative functional renormalization group analysis

In this work the fundamental ideas to study properties of QFTs with the functional Renormalization Group are presented and some examples illustrated. First the Wetterich equation for the effective average action and its flow in the local potential approximation (LPA) for a single scalar field is derived. This case is considered to illustrate some techniques used to solve the RG fixed point equation and study the properties of the critical theories in D dimensions. In particular the shooting methods for the ODE equation for the fixed point potential as well as the approach which studies a polynomial truncation with a finite number of couplings, which is convenient to study the critical exponents. We then study novel cases related to multi field scalar theories, deriving the flow equations for the LPA truncation, both without assuming any global symmetry and also specialising to cases with a given symmetry, using truncations based on polynomials of the symmetry invariants. This is used to study possible non perturbative solutions of critical theories which are extensions of known perturbative results, obtained in the epsilon expansion below the upper critical dimension.

A Comparative Analysis of Dynamical Models for Tidal Dissipation in Natural Satellite Ephemerides

The study of the tides of a celestial bodies can unveil important information about their interior as well as their orbital evolution. The most important tidal parameter is the Love number, which defines the deformation of the gravity field due to an external perturbing body. Tidal dissipation is very important because it drives the secular orbital evolution of the natural satellites, which is even more important in the case of the the Jupiter system, where three of the Galilean moons, Io, Europa and Ganymede, are locked in an orbital resonance where the ratio of their mean motions is 4:2:1. This is called Laplace resonance. Tidal dissipation is described by the dissipation ratio k2/Q, where Q is the quality factor and it describes the dampening of a system. The goal of this thesis is to analyze and compare the two main tidal dynamical models, Mignard's model and gravity field variation model, to understand the differences between each model with a main focus on the single-moon case with Io, which can help also understanding better the differences between the two models without over complicating the dynamical model. In this work we have verified and validated both models, we have compared them and pinpointed the main differences and features that characterize each model. Mignard's model treats the tides directly as a force, while the gravity field variation model describes the tides with a change of the spherical harmonic coefficients. Finally, we have also briefly analyzed the difference between the single-moon case and the two-moon case, and we have confirmed that the governing equations that describe the change of semi-major axis and eccentricity are not good anymore when more moons are present.

Characterization Of Microsatellite Markers Developed From Prosopis Rubriflora And Prosopis Ruscifolia (leguminosae - Mimosoideae), Legume Species That Are Used As Models For Genetic Diversity Studies In Chaquenian Areas Under Anthropization In South America.

Prosopis rubriflora and Prosopis ruscifolia are important species in the Chaquenian regions of Brazil. Because of the restriction and frequency of their physiognomy, they are excellent models for conservation genetics studies. The use of microsatellite markers (Simple Sequence Repeats, SSRs) has become increasingly important in recent years and has proven to be a powerful tool for both ecological and molecular studies. In this study, we present the development and characterization of 10 new markers for P. rubriflora and 13 new markers for P. ruscifolia. The genotyping was performed using 40 P. rubriflora samples and 48 P. ruscifolia samples from the Chaquenian remnants in Brazil. The polymorphism information content (PIC) of the P. rubriflora markers ranged from 0.073 to 0.791, and no null alleles or deviation from Hardy-Weinberg equilibrium (HW) were detected. The PIC values for the P. ruscifolia markers ranged from 0.289 to 0.883, but a departure from HW and null alleles were detected for certain loci; however, this departure may have resulted from anthropic activities, such as the presence of livestock, which is very common in the remnant areas. In this study, we describe novel SSR polymorphic markers that may be helpful in future genetic studies of P. rubriflora and P. ruscifolia.

What Is The Best Indication For Single-incision Ophira Mini Sling? Insights From A 2-year Follow-up International Multicentric Study.

The Ophira Mini Sling System involves anchoring a midurethral, low-tension tape to the obturator internus muscles bilaterally at the level of the tendinous arc. Success rates in different subsets of patients are still to be defined. This work aims to identify which factors influence the 2-year outcomes of this treatment. Analysis was based on data from a multicenter study. Endpoints for analysis included objective measurements: 1-h pad-weight (PWT), and cough stress test (CST), and questionnaires: International Consultation on Incontinence Questionnaire-Short Form (ICIQ-SF) and Urinary Distress Inventory (UDI)-6. A logistic regression analysis evaluated possible risk factors for failure. In all, 124 female patients with stress urinary incontinence (SUI) underwent treatment with the Ophira procedure. All patients completed 1 year of follow-up, and 95 complied with the 2-year evaluation. Longitudinal analysis showed no significant differences between results at 1 and 2 years. The 2-year overall objective results were 81 (85.3%) patients dry, six (6.3%) improved, and eight (8.4%) incontinent. A multivariate analysis revealed that previous anti-incontinence surgery was the only factor that significantly influenced surgical outcomes. Two years after treatment, women with previous failed surgeries had an odds ratio (OR) for treatment failure (based on PWT) of 4.0 [95% confidence interval (CI) 1.02-15.57). The Ophira procedure is an effective option for SUI treatment, with durable good results. Previous surgeries were identified as the only significant risk factor, though previously operated patients showed an acceptable success rate.

Nebivolol Reduces Central Blood Pressure In Stage I Hypertensive Patients: Experimental Single Cohort Study.

Assessment of central blood pressure (BP) has grown substantially over recent years because evidence has shown that central BP is more relevant to cardiovascular outcomes than peripheral BP. Thus, different classes of antihypertensive drugs have different effects on central BP despite similar reductions in brachial BP. The aim of this study was to investigate the effect of nebivolol, a β-blocker with vasodilator properties, on the biochemical and hemodynamic parameters of hypertensive patients. Experimental single cohort study conducted in the outpatient clinic of a university hospital. Twenty-six patients were recruited. All of them underwent biochemical and hemodynamic evaluation (BP, heart rate (HR), central BP and augmentation index) before and after 3 months of using nebivolol. 88.5% of the patients were male; their mean age was 49.7 ± 9.3 years and most of them were overweight (29.6 ± 3.1 kg/m2) with large abdominal waist (102.1 ± 7.2 cm). There were significant decreases in peripheral systolic BP (P = 0.0020), diastolic BP (P = 0.0049), HR (P < 0.0001) and central BP (129.9 ± 12.3 versus 122.3 ± 10.3 mmHg; P = 0.0083) after treatment, in comparison with the baseline values. There was no statistical difference in the augmentation index or in the biochemical parameters, from before to after the treatment. Nebivolol use seems to be associated with significant reduction of central BP in stage I hypertensive patients, in addition to reductions in brachial systolic and diastolic BP.

Icatibant, An Inhibitor Of Bradykinin Receptor 2, For Hereditary Angioedema Attacks: Prospective Experimental Single-cohort Study.

Hereditary angioedema (HAE) with C1 inhibitor deficiency manifests as recurrent episodes of edema involving the skin, upper respiratory tract and gastrointestinal tract. It can be lethal due to asphyxia. The aim here was to evaluate the response to therapy for these attacks using icatibant, an inhibitor of the bradykinin receptor, which was recently introduced into Brazil. Prospective experimental single-cohort study on the efficacy and safety of icatibant for HAE patients. Patients with a confirmed HAE diagnosis were enrolled according to symptoms and regardless of the time since onset of the attack. Icatibant was administered in accordance with the protocol that has been approved in Brazil. Symptom severity was assessed continuously and adverse events were monitored. 24 attacks in 20 HAE patients were treated (female/male 19:1; 19-55 years; median 29 years of age). The symptoms were: subcutaneous edema (22/24); abdominal pain (15/24) and upper airway obstruction (10/24). The time taken until onset of relief was: 5-10 minutes (5/24; 20.8%); 10-20 (5/24; 20.8%); 20-30 (8/24; 33.4%); 30-60 (5/24; 20.8%); and 2 hours (1/24; 4.3%). The time taken for complete resolution of symptoms ranged from 4.3 to 33.4 hours. Adverse effects were only reported at injection sites. Mild to moderate erythema and/or feelings of burning were reported by 15/24 patients, itching by 3 and no adverse effects in 6. HAE type I patients who received icatibant responded promptly; most achieved improved symptom severity within 30 minutes. Local adverse events occurred in 75% of the patients.

Rapidly Switching Multidirectional Defibrillation: Reversal Of Ventricular Fibrillation With Lower Energy Shocks.

Cardiac arrest after open surgery has an incidence of approximately 3%, of which more than 50% of the cases are due to ventricular fibrillation. Electrical defibrillation is the most effective therapy for terminating cardiac arrhythmias associated with unstable hemodynamics. The excitation threshold of myocardial microstructures is lower when external electrical fields are applied in the longitudinal direction with respect to the major axis of cells. However, in the heart, cell bundles are disposed in several directions. Improved myocardial excitation and defibrillation have been achieved by applying shocks in multiple directions via intracardiac leads, but the results are controversial when the electrodes are not located within the cardiac chambers. This study was designed to test whether rapidly switching shock delivery in 3 directions could increase the efficiency of direct defibrillation. A multidirectional defibrillator and paddles bearing 3 electrodes each were developed and used in vivo for the reversal of electrically induced ventricular fibrillation in an anesthetized open-chest swine model. Direct defibrillation was performed by unidirectional and multidirectional shocks applied in an alternating fashion. Survival analysis was used to estimate the relationship between the probability of defibrillation and the shock energy. Compared with shock delivery in a single direction in the same animal population, the shock energy required for multidirectional defibrillation was 20% to 30% lower (P < .05) within a wide range of success probabilities. Rapidly switching multidirectional shock delivery required lower shock energy for ventricular fibrillation termination and may be a safer alternative for restoring cardiac sinus rhythm.

Censored Linear Regression Models For Irregularly Observed Longitudinal Data Using The Multivariate-t Distribution.

In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.

Compact Ag@fe3o4 Core-shell Nanoparticles By Means Of Single-step Thermal Decomposition Reaction.

A temperature pause introduced in a simple single-step thermal decomposition of iron, with the presence of silver seeds formed in the same reaction mixture, gives rise to novel compact heterostructures: brick-like Ag@Fe3O4 core-shell nanoparticles. This novel method is relatively easy to implement, and could contribute to overcome the challenge of obtaining a multifunctional heteroparticle in which a noble metal is surrounded by magnetite. Structural analyses of the samples show 4 nm silver nanoparticles wrapped within compact cubic external structures of Fe oxide, with curious rectangular shape. The magnetic properties indicate a near superparamagnetic like behavior with a weak hysteresis at room temperature. The value of the anisotropy involved makes these particles candidates to potential applications in nanomedicine.

On The Consistency Of Monte Carlo Track Structure Dna Damage Simulations.

Monte Carlo track structures (MCTS) simulations have been recognized as useful tools for radiobiological modeling. However, the authors noticed several issues regarding the consistency of reported data. Therefore, in this work, they analyze the impact of various user defined parameters on simulated direct DNA damage yields. In addition, they draw attention to discrepancies in published literature in DNA strand break (SB) yields and selected methodologies. The MCTS code Geant4-DNA was used to compare radial dose profiles in a nanometer-scale region of interest (ROI) for photon sources of varying sizes and energies. Then, electron tracks of 0.28 keV-220 keV were superimposed on a geometric DNA model composed of 2.7 × 10(6) nucleosomes, and SBs were simulated according to four definitions based on energy deposits or energy transfers in DNA strand targets compared to a threshold energy ETH. The SB frequencies and complexities in nucleosomes as a function of incident electron energies were obtained. SBs were classified into higher order clusters such as single and double strand breaks (SSBs and DSBs) based on inter-SB distances and on the number of affected strands. Comparisons of different nonuniform dose distributions lacking charged particle equilibrium may lead to erroneous conclusions regarding the effect of energy on relative biological effectiveness. The energy transfer-based SB definitions give similar SB yields as the one based on energy deposit when ETH ≈ 10.79 eV, but deviate significantly for higher ETH values. Between 30 and 40 nucleosomes/Gy show at least one SB in the ROI. The number of nucleosomes that present a complex damage pattern of more than 2 SBs and the degree of complexity of the damage in these nucleosomes diminish as the incident electron energy increases. DNA damage classification into SSB and DSB is highly dependent on the definitions of these higher order structures and their implementations. The authors' show that, for the four studied models, different yields are expected by up to 54% for SSBs and by up to 32% for DSBs, as a function of the incident electrons energy and of the models being compared. MCTS simulations allow to compare direct DNA damage types and complexities induced by ionizing radiation. However, simulation results depend to a large degree on user-defined parameters, definitions, and algorithms such as: DNA model, dose distribution, SB definition, and the DNA damage clustering algorithm. These interdependencies should be well controlled during the simulations and explicitly reported when comparing results to experiments or calculations.

Augmented Mixed Models For Clustered Proportion Data.

Often in biomedical research, we deal with continuous (clustered) proportion responses ranging between zero and one quantifying the disease status of the cluster units. Interestingly, the study population might also consist of relatively disease-free as well as highly diseased subjects, contributing to proportion values in the interval [0, 1]. Regression on a variety of parametric densities with support lying in (0, 1), such as beta regression, can assess important covariate effects. However, they are deemed inappropriate due to the presence of zeros and/or ones. To evade this, we introduce a class of general proportion density, and further augment the probabilities of zero and one to this general proportion density, controlling for the clustering. Our approach is Bayesian and presents a computationally convenient framework amenable to available freeware. Bayesian case-deletion influence diagnostics based on q-divergence measures are automatic from the Markov chain Monte Carlo output. The methodology is illustrated using both simulation studies and application to a real dataset from a clinical periodontology study.

Association Of Single Nucleotide Polymorphisms In The Gene Encoding Glut1 And Diabetic Nephropathy In Brazilian Patients With Type 1 Diabetes Mellitus.

Mesangial cells subject to high extracellular glucose concentrations, as occur in hyperglycaemic states, are unable to down regulate glucose influx, resulting in intracellular activation of deleterious biochemical pathways. A high expression of GLUT1 participates in the development of diabetic glomerulopathy. Variants in the gene encoding GLUT1 (SLC2A1) have been associated to this diabetic complication. The aim of this study was to test whether polymorphisms in SLC2A1 confer susceptibility to diabetic nephropathy (DN) in Brazilian type 1 diabetes patients. Four polymorphisms (rs3820589, rs1385129, rs841847 and rs841848) were genotyped in a Brazilian cohort comprised of 452 patients. A prospective analysis was performed in 155 patients. Mean duration of follow-up was 5.6±2.4years and the incidence of renal events was 18.0%. The rs3820589 presented an inverse association with the prevalence of incipient DN (OR: 0.36, 95% CI: 0.16 - 0.80, p=0.01) and with progression to renal events (HR: 0.20; 95% CI: 0.03 - 0.70; p=0.009). AGGT and AGAC haplotypes were associated with the prevalence of incipient DN and the AGAC haplotype was also associated with the prevalence of established/advanced DN. In conclusion, rs3820589 in the SLC2A1 gene modulates the risk to DN in Brazilian patients with inadequate type 1 diabetes control.

Biofilm And Saliva Affect The Biomechanical Behavior Of Dental Implants.

Friction coefficient (FC) was quantified between titanium-titanium (Ti-Ti) and titanium-zirconia (Ti-Zr), materials commonly used as abutment and implants, in the presence of a multispecies biofilm (Bf) or salivary pellicle (Pel). Furthermore, FC was used as a parameter to evaluate the biomechanical behavior of a single implant-supported restoration. Interface between Ti-Ti and Ti-Zr without Pel or Bf was used as control (Ctrl). FC was recorded using tribometer and analyzed by two-way Anova and Tukey test (p<0.05). Data were transposed to a finite element model of a dental implant-supported restoration. Models were obtained varying abutment material (Ti and Zr) and FCs recorded (Bf, Pel, and Ctrl). Maximum and shear stress were calculated for bone and equivalent von Misses for prosthetic components. Data were analyzed using two-way ANOVA (p<0.05) and percentage of contribution for each condition (material and FC) was calculated. FC significant differences were observed between Ti-Ti and Ti-Zr for Ctrl and Bf groups, with lower values for Ti-Zr (p<0.05). Within each material group, Ti-Ti differed between all treatments (p<0.05) and for Ti-Zr, only Pel showed higher values compared with Ctrl and Bf (p<0.05). FC contributed to 89.83% (p<0.05) of the stress in the screw, decreasing the stress when the FC was lower. FC resulted in an increase of 59.78% of maximum stress in cortical bone (p=0.05). It can be concluded that the shift of the FC due to the presence of Pel or Bf is able to jeopardize the biomechanical behavior of a single implant-supported restoration.

Combined External Pressure And Cu-substitution Studies On Bafe2as2 Single Crystals.

We report a combined study of external pressure and Cu-substitution on BaFe2As2 single crystals grown by the in-flux technique. At ambient pressure, the Cu-substitution is known to suppress the spin density wave (SDW) phase in pure BaFe2As2(TSDW ≈ 140 K) and to induce a superconducting (SC) dome with a maximum transition temperature [Formula: see text]. This [Formula: see text] is much lower than the Tc ∼ 15-28 K achieved in the case of Ru, Ni and Co substitutions. Such a lower Tc is attributed to a Cu(2+) magnetic pair-breaking effect. The latter is strongly suppressed by applied pressure, as shown herein, Tc can be significantly enhanced by applying high pressures. In this work, we investigated the pressure effects on Cu(2+) magnetic pair-breaking in the BaFe2-xCuxAs2 series. Around the optimal concentration (xopd = 0.11), all samples showed a substantial increase of Tc as a function of pressure. Yet for those samples with a slightly higher doping level (over-doped regime), Tc presented a dome-like shape with maximum Tc ≃ 8 K. Remarkably interesting, the under-doped samples, e.g. x = 0.02 display a maximum pressure induced Tc ≃ 30 K which is comparable to the maximum Tc's found for the pure compound under external pressures. Furthermore, the magnetoresistance effect as a function of pressure in the normal state of the x = 0.02 sample also presented an evolution consistent with the screening of the Cu(2+) local moments. These findings demonstrate that the Cu(2+) magnetic pair-breaking effect is completely suppressed by applying pressure in the low concentration regime of Cu(2+) substituted BaFe2As2.