Human Fallopian Tube Mesenchymal Stromal Cells Enhance Bone Regeneration in a Xenotransplanted Model

We have recently reported that human fallopian tubes, which are discarded during surgical procedures of women submitted to sterilization or hysterectomies, are a rich source of human fallopian tube mesenchymal stromal cells (htMSCs). It has been previously shown that human mesenchymal stromal cells may be useful in enhancing the speed of bone regeneration. This prompted us to investigate whether htMSCs might be useful for the treatment of osteoporosis or other bone diseases, since they present a pronounced capacity for osteogenic differentiation in vitro. Based on this prior knowledge, our aim was to evaluate, in vivo, the osteogenic capacity of htMSCs to regenerate bone through an already described xenotransplantation model: nonimmunosuppressed (NIS) rats with cranial defects. htMSCs were obtained from five 30-50 years old healthy women and characterized by flow cytometry and for their multipotenciality in vitro capacity (osteogenic, chondrogenic and adipogenic differentiations). Two symmetric full-thickness cranial defects on each parietal region of seven NIS rats were performed. The left side (LS) of six animals was covered with CellCeram (Scaffdex)-a bioabsorbable ceramic composite scaffold that contains 60% hydroxyapatite and 40% beta-tricalciumphosphate-only, and the right side (RS) with the CellCeram and htMSCs (10(6) cells/scaffold). The animals were euthanized at 30, 60 and 90 days postoperatively and cranial tissue samples were taken for histological analysis. After 90 days we observed neobone formation in both sides. However, in animals euthanized 30 and 60 days after the procedure, a mature bone was observed only on the side with htMSCs. PCR and immunofluorescence analysis confirmed the presence of human DNA and thus that human cells were not rejected, which further supports the imunomodulatory property of htMSCs. In conclusion, htMSCs can be used successfully to enhance bone regeneration in vivo, opening a new field for future treatments of osteoporosis and bone reconstruction.

Amitriptyline prolongs the antihyperalgesic effect of 2- or 100-Hz electro-acupuncture in a rat model of post-incision pain

The mechanisms through which electro-acupuncture (EA) and tricyclic antidepressants produce analgesia seem to be complementary: EA inhibits the transmission of noxious messages by activating supraspinal serotonergic and noradrenergic neurons that project to the spinal cord, whereas tricyclic antidepressants affect pain transmission by inhibiting the reuptake of norepinephrine and serotonin at the spinal level. This study utilized the tail-flick test and a model of post-incision pain to compare the antihyperalgesic effects of EA at frequencies of 2 or 100 Hz in rats treated with intraperitoneal or intrathecal amitriptyline (a tricyclic antidepressant). A gradual increase in the tail-flick latency (TFL) occurred during a 20-min period of EA. A strong and long-lasting reduction in post-incision hyperalgesia was observed after stimulation; the effect after 2 Hz lasting longer than after 100-Hz EA. Intraperitoneal or intrathecal amitriptyline potentiated the increase in TFL in the early moments of 2- or 100-Hz EA, and the intensity of the antihyperalgesic effect of 100-Hz EA in both the incised and non-incised paw. In contrast, it did not significantly change the intensity of the antihyperalgesic effect of 2-Hz EA. The EA-induced antihyperalgesic effects lasted longer after intraperitoneal or intrathecal amitriptyline than after saline, with this effect of amitriptyline being more evident after 100-than after 2-Hz EA. The synergetic effect of amitriptyline and EA against post-incision pain shown here may therefore represent an alternative for prolonging the efficacy of EA in the management of post-surgical clinical pain.

Treatment with probiotics in experimental oral colonization by Candida albicans in murine model (DBA/2)

The aim of this study is to evaluate the oral colonization by Candida albicans in experimental murine immunosuppressed DBA/2 and treatment with probiotic bacteria. To achieve these objectives, 152 DBA/2-immunosuppressed mice were orally inoculated with a suspension of C. albicans containing 10(8) viable yeast cells, the animals were treated with nystatin or with the probiotics (Lactobacillus acidophilus and Lactobacillus rhamnosus). Evaluations were performed by Candida count from oral mucosa swabbing. The oral mucosa colonization by C. albicans started at day 1 after inoculation, remained maximal from day 3 until day 7, and then decreased significantly. Probiotics reduced the C. albicans colonization significantly on the oral mucosa in comparison with the untreated animal group. In the group treated with L. rhamnosus, the reduction in yeast colonization was significantly higher compared with that of the group receiving nystatin. Immunosuppressed animal model DBA/2 is a relevant model for experimental Candida oral colonization, and the treatment with probiotics in this model may be an effective alternative to prevent it. Oral Diseases (2012) 18, 260-264

STOCHASTIC MODEL FOR SIMULATING MAIZE YIELD

Maize is one of the most important crops in the world. The products generated from this crop are largely used in the starch industry, the animal and human nutrition sector, and biomass energy production and refineries. For these reasons, there is much interest in figuring the potential grain yield of maize genotypes in relation to the environment in which they will be grown, as the productivity directly affects agribusiness or farm profitability. Questions like these can be investigated with ecophysiological crop models, which can be organized according to different philosophies and structures. The main objective of this work is to conceptualize a stochastic model for predicting maize grain yield and productivity under different conditions of water supply while considering the uncertainties of daily climate data. Therefore, one focus is to explain the model construction in detail, and the other is to present some results in light of the philosophy adopted. A deterministic model was built as the basis for the stochastic model. The former performed well in terms of the curve shape of the above-ground dry matter over time as well as the grain yield under full and moderate water deficit conditions. Through the use of a triangular distribution for the harvest index and a bivariate normal distribution of the averaged daily solar radiation and air temperature, the stochastic model satisfactorily simulated grain productivity, i.e., it was found that 10,604 kg ha(-1) is the most likely grain productivity, very similar to the productivity simulated by the deterministic model and for the real conditions based on a field experiment.

Exogenous Administration of 15d-PGJ(2)-Loaded Nanocapsules Inhibits Bone Resorption in a Mouse Periodontitis Model

The 15-deoxy-(Delta 12,14)-PG J(2) (15d-PGJ(2)) has demonstrated excellent anti-inflammatory results in different experimental models. It can be used with a polymeric nanostructure system for modified drug release, which can change the therapeutic properties of the active principle, leading to increased stability and slower/prolonged release. The aim of the current study was to test a nano-technological formulation as a carrier for 15d-PGJ(2), and to investigate the immunomodulatory effects of this formulation in a mouse periodontitis model. Poly (D, L-lactide-coglycolide) nanocapsules (NC) were used to encapsulate 15d-PGJ(2). BALB/c mice were infected on days 0, 2, and 4 with Aggregatibacter actinomycetemcomitans and divided into groups (n = 5) that were treated daily during 15 d with 1, 3, or 10 mu g/kg 15d-PGJ(2)-NC. The animals were sacrificed, the submandibular lymph nodes were removed for FACS analysis, and the jaws were analyzed for bone resorption by morphometry. Immunoinflammatory markers in the gingival tissue were analyzed by reverse transcriptase-quantitative PCR, Western blotting, or ELISA. Infected animals treated with the 15d-PGJ(2)-NC presented lower bone resorption than infected animals without treatment (p < 0.05). Furthermore, infected animals treated with 10 mu g/kg 15d-PGJ(2)-NC had a reduction of CD4(+)CD25(+)FOXP3(+) cells and CD4/CD8 ratio in the submandibular lymph node (p < 0.05). Moreover, CD55 was upregulated, whereas RANKL was downregulated in the gingival tissue of the 10 mu g/kg treated group (p < 0.05). Several proinflammatory cytokines were decreased in the group treated with 10 mu g/kg 15d-PGJ(2)-NC, and high amounts of 15d-PGJ(2) were observed in the gingiva. In conclusion, the 15d-PGJ(2)-NC formulation presented immunomodulatory effects, decreasing bone resorption and inflammatory responses in a periodontitis mouse model. The Journal of Immunology, 2012, 189: 1043-1052.

Magnetic moments of the low-lying J(P)=1/2(-), 3/2(-) Lambda resonances within the framework of the chiral quark model

The magnetic moments of the low-lying spin-parity J(P) = 1/2(-), 3/2(-) Lambda resonances, like, for example, Lambda(1405) 1/2(-), Lambda(1520) 3/2(-), as well as their transition magnetic moments, are calculated using the chiral quark model. The results found are compared with those obtained from the nonrelativistic quark model and those of unitary chiral theories, where some of these states are generated through the dynamics of two hadron coupled channels and their unitarization.

Fractionation of lemon essential oil by solvent extraction: Phase equilibrium for model systems at T=298.2 K

The fractioning of lemon essential oil can be performed by liquid-liquid extraction using hydrous ethanol as a solvent. A quaternary mixture composed of limonene, gamma-terpinene, beta-pinene, and citral was used to simulate lemon essential oil. In this paper, we present (liquid + liquid) equilibrium data that were experimentally determined for systems containing essential oil compounds, ethanol, and water at T = 298.2 K. The experimental data were correlated using the NRTL and UNIQUAC models, and the mean deviations between calculated and experimental data were less than 0.0053 in all systems, indicating the accuracy of these molecular models in describing our systems. The results show that as the water content in the solvent phase increased, the values of the distribution coefficients decreased, regardless of the type of compound studied. However, the oxygenated compound always showed the highest distribution coefficient among the components of the essential oil, thus making deterpenation of the lemon essential oil a feasible process. (C) 2012 Elsevier Ltd. All rights reserved.

BEM modeling of saturated porous media susceptible to damage

This paper deals with the numerical analysis of saturated porous media, taking into account the damage phenomena on the solid skeleton. The porous media is taken into poro-elastic framework, in full-saturated condition, based on Biot's Theory. A scalar damage model is assumed for this analysis. An implicit boundary element method (BEM) formulation, based on time-independent fundamental solutions, is developed and implemented to couple the fluid flow and two-dimensional elastostatic problems. The integration over boundary elements is evaluated using a numerical Gauss procedure. A semi-analytical scheme for the case of triangular domain cells is followed to carry out the relevant domain integrals. The non-linear problem is solved by a Newton-Raphson procedure. Numerical examples are presented, in order to validate the implemented formulation and to illustrate its efficacy. (C) 2011 Elsevier Ltd. All rights reserved.

Cannabidiol, a non-psychotropic plant-derived cannabinoid, decreases inflammation in a murine model of acute lung injury: Role for the adenosine A(2A) receptor

Acute lung injury is an inflammatory condition for which treatment is mainly supportive because effective therapies have not been developed. Cannabidiol, a non-psychotropic cannabinoid component of marijuana (Cannabis sativa), has potent immunosuppressive and anti-inflammatory properties. Therefore, we investigated the possible anti-inflammatory effect of cannabidiol in a murine model of acute lung injury. Analysis of total inflammatory cells and differential in bronchoalveolar lavage fluid was used to characterize leukocyte migration into the lungs; myeloperoxidase activity of lung tissue and albumin concentration in the bronchoalveolar lavage fluid were analyzed by colorimetric assays; cytokine/chemokine production in the bronchoalveolar lavage fluid was also analyzed by Cytometric Bead Arrays and Enzyme-Linked Immunosorbent Assay (ELISA). A single dose of cannabidiol (20 mg/kg) administered prior to the induction of LPS (lipopolysaccharide)-induced acute lung injury decreases leukocyte (specifically neutrophil) migration into the lungs, albumin concentration in the bronchoalveolar lavage fluid, myeloperoxidase activity in the lung tissue, and production of pro-inflammatory cytokines (TNF and IL-6) and chemokines (MCP-1 and MIP-2) 1, 2, and 4 days after the induction of LPS-induced acute lung injury. Additionally, adenosine A(2A) receptor is involved in the anti-inflammatory effects of cannabidiol on LPS-induced acute lung injury because ZM241385 (4-(2[7-Amino-2-(2-furyl)[1,2,4] triazolo[2,3-a][1,3,5]triazin-5-ylamino]ethyl) phenol) (a highly selective antagonist of adenosine A(2A) receptor) abrogated all of the anti-inflammatory effects of cannabidiol previously described. Thus, we show that cannabidiol has anti-inflammatory effects in a murine model of acute lung injury and that this effect is most likely associated with an increase in the extracellular adenosine offer and signaling through adenosine A(2A) receptor. (C) 2012 Elsevier B. V. All rights reserved.

Atorvastatin Prevents the Downregulation of Aquaporin-2 Receptor After Bilateral Ureteral Obstruction and Protects Renal Function in a Rat Model

OBJECTIVE To assess the effects of atorvastatin (ATORV) on renal function after bilateral ureteral obstruction (BUO), measuring inulin clearance and its effect on renal hemodynamic, filtration, and inflammatory response, as well as the expression of Aquaporin-2 (AQP2) in response to BUO and after the release of BUO. METHODS Adult Munich-Wistar male rats were subjected to BUO for 24 hours and monitored during the following 48 hours. Rats were divided into 5 groups: sham operated (n = 6); sham + ATORV (n = 6); BUO (n = 6); BUO + ATORV (10 mg/kg in drinking water started 2 days before BUO [n = 5]; and BUO + ATORV (10 mg/kg in drinking water started on the day of the release of BUO [n = 5]). We measured blood pressure (BP, mm Hg); inulin clearance (glomerular filtration rate [GFR]; mL/min/100 g); and renal blood flow (RBF, mL/min, by transient-time flowmeter). Inflammatory response was evaluated by histologic analysis of the interstitial area. AQP2 expression was evaluated by electrophoresis and immunoblotting. RESULTS Renal function was preserved by ATORV treatment, even if initiated on the day of obstruction release, as expressed by GFR, measured by inulin clearance. Relative interstitial area was decreased in both BUO + ATORV groups. Urine osmolality was improved in the ATORV-treated groups. AQP2 protein expression decreased in BUO animals and was reverted by ATORV treatment. CONCLUSION ATORV administration significantly prevented and restored impairment in GFR and renal vascular resistance. Furthermore, ATORV also improved urinary concentration by reversing the BUO-induced downregulation of AQP2. These findings have significant clinical implication in treating obstructive nephropathy. UROLOGY 80: 485.e15-485.e20, 2012. (c) 2012 Elsevier Inc.

"Evaluating the model of classification and valuation of disabilities used in Brazil and defining the elaboration and adoption of a unique model for all the country": Brazilian Interministerial Workgroup Task

The President of Brazil established an Interministerial Work Group in order to “evaluate the model of classification and valuation of disabilities used in Brazil and to define the elaboration and adoption of a unique model for all the country”. Eight Ministries and/or Secretaries participated in the discussion over a period of 10 months, concluding that a proposed model should be based on the United Nations Convention on the Rights of Person with Disabilities, the International Classification of Functioning, Disability and Health, and the ‘support theory’, and organizing a list of recommendations and necessary actions for a Classification, Evaluation and Certification Network with national coverage.

Small volume of hypertonic saline as the initial fluid replacement in experimental hypodynamic sepsis

Abstract Introduction We conducted the present study to examine the effects of hypertonic saline solution (7.5%) on cardiovascular function and splanchnic perfusion in experimental sepsis. Methods Anesthetized and mechanically ventilated mongrel dogs received an intravenous infusion of live Escherichia coli over 30 minutes. After 30 minutes, they were randomized to receive lactated Ringer's solution 32 ml/kg (LR; n = 7) over 30 minutes or 7.5% hypertonic saline solution 4 ml/kg (HS; n = 8) over 5 minutes. They were observed without additional interventions for 120 minutes. Cardiac output (CO), mean arterial pressure (MAP), portal and renal blood flow (PBF and RBF, respectively), gastric partial pressure of CO2 (pCO2; gas tonometry), blood gases and lactate levels were assessed. Results E. coli infusion promoted significant reductions in CO, MAP, PBF and RBF (approximately 45%, 12%, 45% and 25%, respectively) accompanied by an increase in lactate levels and systemic and mesenteric oxygen extraction (sO2ER and mO2ER). Widening of venous-arterial (approximately 15 mmHg), portal-arterial (approximately 18 mmHg) and gastric mucosal-arterial (approximately 55 mmHg) pCO2 gradients were also observed. LR and HS infusion transiently improved systemic and regional blood flow. However, HS infusion was associated with a significant and sustained reduction of systemic (18 ± 2.6 versus 38 ± 5.9%) and mesenteric oxygen extraction (18.5 ± 1.9 versus 36.5 ± 5.4%), without worsening other perfusional markers. Conclusion A large volume of LR or a small volume of HS promoted similar transient hemodynamic benefits in this sepsis model. However, a single bolus of HS did promote sustained reduction of systemic and mesenteric oxygen extraction, suggesting that hypertonic saline solution could be used as a salutary intervention during fluid resuscitation in septic patients.

Antimicrobial activity of triantibiotic paste, 2% chlorhexidine gel, and calcium hydroxide on an intraoral-infected dentin biofilm model

Introduction: The purpose of this study was to evaluate the antimicrobial activity of calcium hydroxide, 2% chlorhexidine gel, and triantibiotic paste (ie, metronidazole, minocycline, and ciprofloxacin) by using an intraorally infected dentin biofilm model. Methods: Forty bovine dentin specimens were infected intraorally using a removable orthodontic device in order to induce the biofilm colonization of the dentin. Then, the samples were treated with the medications for 7 days. Saline solution was used as the control. Two evaluations were performed: immediately after the elimination of the medication and after incubation in brain-heart infusion medium for 24 hours. The Live/Dead technique (Invitrogen, Eugene, OR) and a confocal microscope were used to obtain the percentage of live cells. Nonparametric statistical tests were performed to show differences in the percentage of live cells among the groups (P < .05). Results: Calcium hydroxide and 2% chlorhexidine gel did not show statistical differences in the immediate evaluation. However, after application of the brain-heart infusion medium for 24 hours, 2% gel chlorhexidine showed a statistically lesser percentage of live cells in comparison with calcium hydroxide. The triantibiotic paste significantly showed a lower percentage of live cells in comparison with the 2% chlorhexidine gel and calcium hydroxide groups in the immediate and secondary (after 24 hours) evaluations. Conclusions: The triantibiotic paste was most effective at killing the bacteria in the biofilms on the intraorally infected dentin model in comparison with 2% chlorhexidine gel and calcium hydroxide

Periodontal treatment downregulates protease-activated receptor 2 in human gingival crevicular fluid cells

Protease-activated receptor 2 (PAR2) is implicated in the pathogenesis of chronic inflammatory diseases, including periodontitis; it can be activated by gingipain and produced by Porphyromonas gingivalis and by neutrophil protease 3 (P3). PAR2 activation plays a relevant role in inflammatory processes by inducing the release of important inflammatory mediators associated with periodontal breakdown. The effects of periodontal treatment on PAR2 expression and its association with levels of proinflammatory mediators and activating proteases were investigated in chronic periodontitis patients. Positive staining for PAR2 was observed in gingival crevicular fluid cells and was reflective of tissue destruction. Overexpression of PAR2 was positively associated with inflammatory clinical parameters and with the levels of interleukin-6 (IL-6), IL-8, tumor necrosis factor alpha, matrix metalloprotease 2 (MMP-2), MMP-8, hepatocyte growth factor, and vascular endothelial growth factor. Elevated levels of gingipain and P3 and decreased levels of dentilisin and the protease inhibitors secretory leukocyte protease inhibitor and elafin were also associated with PAR2 overexpression. Healthy periodontal sites from individuals with chronic periodontitis showed diminished expression of PAR2 mRNA and the PAR2 protein (P < 0.05). Furthermore, periodontal treatment resulted in decreased PAR2 expression and correlated with decreased expression of inflammatory mediators and activating proteases. We concluded that periodontal treatment resulted in decreased levels of proteases and that proinflammatory mediators are associated with decreased PAR2 expression, suggesting that PAR2 expression is influenced by the presence of periodontal infection and is not a constitutive characteristic favoring periodontal inflammation.

Statistical properties of Radio Halos and the re-acceleration model

Galaxy clusters occupy a special position in the cosmic hierarchy as they are the largest bound structures in the Universe. There is now general agreement on a hierarchical picture for the formation of cosmic structures, in which galaxy clusters are supposed to form by accretion of matter and merging between smaller units. During merger events, shocks are driven by the gravity of the dark matter in the diffuse barionic component, which is heated up to the observed temperature. Radio and hard-X ray observations have discovered non-thermal components mixed with the thermal Intra Cluster Medium (ICM) and this is of great importance as it calls for a “revision” of the physics of the ICM. The bulk of present information comes from the radio observations which discovered an increasing number of Mpcsized emissions from the ICM, Radio Halos (at the cluster center) and Radio Relics (at the cluster periphery). These sources are due to synchrotron emission from ultra relativistic electrons diffusing through µG turbulent magnetic fields. Radio Halos are the most spectacular evidence of non-thermal components in the ICM and understanding the origin and evolution of these sources represents one of the most challenging goal of the theory of the ICM. Cluster mergers are the most energetic events in the Universe and a fraction of the energy dissipated during these mergers could be channelled into the amplification of the magnetic fields and into the acceleration of high energy particles via shocks and turbulence driven by these mergers. Present observations of Radio Halos (and possibly of hard X-rays) can be best interpreted in terms of the reacceleration scenario in which MHD turbulence injected during these cluster mergers re-accelerates high energy particles in the ICM. The physics involved in this scenario is very complex and model details are difficult to test, however this model clearly predicts some simple properties of Radio Halos (and resulting IC emission in the hard X-ray band) which are almost independent of the details of the adopted physics. In particular in the re-acceleration scenario MHD turbulence is injected and dissipated during cluster mergers and thus Radio Halos (and also the resulting hard X-ray IC emission) should be transient phenomena (with a typical lifetime <» 1 Gyr) associated with dynamically disturbed clusters. The physics of the re-acceleration scenario should produce an unavoidable cut-off in the spectrum of the re-accelerated electrons, which is due to the balance between turbulent acceleration and radiative losses. The energy at which this cut-off occurs, and thus the maximum frequency at which synchrotron radiation is produced, depends essentially on the efficiency of the acceleration mechanism so that observations at high frequencies are expected to catch only the most efficient phenomena while, in principle, low frequency radio surveys may found these phenomena much common in the Universe. These basic properties should leave an important imprint in the statistical properties of Radio Halos (and of non-thermal phenomena in general) which, however, have not been addressed yet by present modellings. The main focus of this PhD thesis is to calculate, for the first time, the expected statistics of Radio Halos in the context of the re-acceleration scenario. In particular, we shall address the following main questions: • Is it possible to model “self-consistently” the evolution of these sources together with that of the parent clusters? • How the occurrence of Radio Halos is expected to change with cluster mass and to evolve with redshift? How the efficiency to catch Radio Halos in galaxy clusters changes with the observing radio frequency? • How many Radio Halos are expected to form in the Universe? At which redshift is expected the bulk of these sources? • Is it possible to reproduce in the re-acceleration scenario the observed occurrence and number of Radio Halos in the Universe and the observed correlations between thermal and non-thermal properties of galaxy clusters? • Is it possible to constrain the magnetic field intensity and profile in galaxy clusters and the energetic of turbulence in the ICM from the comparison between model expectations and observations? Several astrophysical ingredients are necessary to model the evolution and statistical properties of Radio Halos in the context of re-acceleration model and to address the points given above. For these reason we deserve some space in this PhD thesis to review the important aspects of the physics of the ICM which are of interest to catch our goals. In Chapt. 1 we discuss the physics of galaxy clusters, and in particular, the clusters formation process; in Chapt. 2 we review the main observational properties of non-thermal components in the ICM; and in Chapt. 3 we focus on the physics of magnetic field and of particle acceleration in galaxy clusters. As a relevant application, the theory of Alfv´enic particle acceleration is applied in Chapt. 4 where we report the most important results from calculations we have done in the framework of the re-acceleration scenario. In this Chapter we show that a fraction of the energy of fluid turbulence driven in the ICM by the cluster mergers can be channelled into the injection of Alfv´en waves at small scales and that these waves can efficiently re-accelerate particles and trigger Radio Halos and hard X-ray emission. The main part of this PhD work, the calculation of the statistical properties of Radio Halos and non-thermal phenomena as expected in the context of the re-acceleration model and their comparison with observations, is presented in Chapts.5, 6, 7 and 8. In Chapt.5 we present a first approach to semi-analytical calculations of statistical properties of giant Radio Halos. The main goal of this Chapter is to model cluster formation, the injection of turbulence in the ICM and the resulting particle acceleration process. We adopt the semi–analytic extended Press & Schechter (PS) theory to follow the formation of a large synthetic population of galaxy clusters and assume that during a merger a fraction of the PdV work done by the infalling subclusters in passing through the most massive one is injected in the form of magnetosonic waves. Then the processes of stochastic acceleration of the relativistic electrons by these waves and the properties of the ensuing synchrotron (Radio Halos) and inverse Compton (IC, hard X-ray) emission of merging clusters are computed under the assumption of a constant rms average magnetic field strength in emitting volume. The main finding of these calculations is that giant Radio Halos are naturally expected only in the more massive clusters, and that the expected fraction of clusters with Radio Halos is consistent with the observed one. In Chapt. 6 we extend the previous calculations by including a scaling of the magnetic field strength with cluster mass. The inclusion of this scaling allows us to derive the expected correlations between the synchrotron radio power of Radio Halos and the X-ray properties (T, LX) and mass of the hosting clusters. For the first time, we show that these correlations, calculated in the context of the re-acceleration model, are consistent with the observed ones for typical µG strengths of the average B intensity in massive clusters. The calculations presented in this Chapter allow us to derive the evolution of the probability to form Radio Halos as a function of the cluster mass and redshift. The most relevant finding presented in this Chapter is that the luminosity functions of giant Radio Halos at 1.4 GHz are expected to peak around a radio power » 1024 W/Hz and to flatten (or cut-off) at lower radio powers because of the decrease of the electron re-acceleration efficiency in smaller galaxy clusters. In Chapt. 6 we also derive the expected number counts of Radio Halos and compare them with available observations: we claim that » 100 Radio Halos in the Universe can be observed at 1.4 GHz with deep surveys, while more than 1000 Radio Halos are expected to be discovered in the next future by LOFAR at 150 MHz. This is the first (and so far unique) model expectation for the number counts of Radio Halos at lower frequency and allows to design future radio surveys. Based on the results of Chapt. 6, in Chapt.7 we present a work in progress on a “revision” of the occurrence of Radio Halos. We combine past results from the NVSS radio survey (z » 0.05 − 0.2) with our ongoing GMRT Radio Halos Pointed Observations of 50 X-ray luminous galaxy clusters (at z » 0.2−0.4) and discuss the possibility to test our model expectations with the number counts of Radio Halos at z » 0.05 − 0.4. The most relevant limitation in the calculations presented in Chapt. 5 and 6 is the assumption of an “averaged” size of Radio Halos independently of their radio luminosity and of the mass of the parent clusters. This assumption cannot be released in the context of the PS formalism used to describe the formation process of clusters, while a more detailed analysis of the physics of cluster mergers and of the injection process of turbulence in the ICM would require an approach based on numerical (possible MHD) simulations of a very large volume of the Universe which is however well beyond the aim of this PhD thesis. On the other hand, in Chapt.8 we report our discovery of novel correlations between the size (RH) of Radio Halos and their radio power and between RH and the cluster mass within the Radio Halo region, MH. In particular this last “geometrical” MH − RH correlation allows us to “observationally” overcome the limitation of the “average” size of Radio Halos. Thus in this Chapter, by making use of this “geometrical” correlation and of a simplified form of the re-acceleration model based on the results of Chapt. 5 and 6 we are able to discuss expected correlations between the synchrotron power and the thermal cluster quantities relative to the radio emitting region. This is a new powerful tool of investigation and we show that all the observed correlations (PR − RH, PR − MH, PR − T, PR − LX, . . . ) now become well understood in the context of the re-acceleration model. In addition, we find that observationally the size of Radio Halos scales non-linearly with the virial radius of the parent cluster, and this immediately means that the fraction of the cluster volume which is radio emitting increases with cluster mass and thus that the non-thermal component in clusters is not self-similar.