Observed supersymmetry in baryon and meson spectra with IBFM, the interacting Boson-fermion model

Supersymmetry is already observed in (i) nuclear physics where the same empirical formula based on a graded Lie group described even-even and odd-even nuclear spectra and (ii) in Nambu-BCS theory where there is a simple relationship between the energy gap of the basic fermion and the bosonic collective modes. We now suggest similar relationships between the large number of mesonic and baryonic excitations based on the SU(3) substructure in the U(15/30) graded Lie group.

One dimensional extended Hubbard model: two-particle bound states and resonances.

In questo lavoro di tesi è stato svolto uno studio analitico sul modello di Hubbard esteso unidimensionale al fine di osservare la presenza di eventuali risonanze che possano dare origine alla formazione di stati legati di due particelle. L'esistenza di uno stato legato stabile ha suscitato grande interesse negli ultimi anni, sia in ambito teorico che sperimentale, poichè è alla base di molti fenomeni che vengono osservati nei sistemi a molti corpi a basse temperature, come il BCS-BEC crossover. Pertanto si è ritenuto utile studiare il problema a due corpi nel modello di Hubbard esteso, che in generale non è integrabile. Il modello considerato contiene interazioni a primi e secondi vicini, in aggiunta all'interazione di contatto presente nel modello di Hubbard. Il problema è stato indagato analiticamente attraverso il Bethe ansatz, che consente di trovare tutti gli autovalori e le autofunzioni dell'Hamiltoniana. L'ansatz di Bethe sulla funzione d'onda è stato generalizzato per poter tener conto dei termini di interazione a più lungo raggio rispetto all'interazione di contatto. Si trova che, in questo modello, nel limite termodinamico, possono avvenire delle risonanze (o quasi-risonanze) in cui la lunghezza di scattering diverge, contrariamente a quanto avviene nel modello di Hubbard. Tale fenomeno si verifica quando il livello energetico discreto degli stati legati “tocca” la banda di scattering. Inoltre, con l'aggiunta di nuovi termini di interazione emergono nuovi stati legati. Nel caso in esame, si osservano due famiglie di stati legati, se lo spin totale delle due particelle è 1, e tre famiglie di stati legati, se lo spin totale è 0.

Einfluss von Hilfsstoffen auf die Bioverfügbarkeit von Substanzen der BCS Klasse III

In dieser Arbeit wurde der Effekt verschiedener Hilfsstoffe auf die Permeabilität von Substanzen der BCS Klasse III untersucht. Drei pharmazeutische Hilfsstoffe wurden hinsichtlich der Möglichkeit ihres Einsatzes als Permeationsverbesserer in Arzneistoffformulierungen untersucht. Außerdem wurde die Beteiligung von Gallensalzen an der Nahrungsmittel-Interaktion von Trospium untersucht.rnEs wurden Komplexe aus Trospium und λ-Carrageen hergestellt. Eine verbesserte Permeation, die höchstwahrscheinlich durch Mukoadhäsion zustande kam, war im Ussing-Kammer-Modell sehr gut reproduzierbar. In vivo war der Effekt nur bei einigen Tieren zu sehen und es kam zu hohen Standardabweichungen.rnTrospium bildet Ionenpaare mit Gallensalzen, welche zu einer besseren Permeabilität des Wirkstoffes führten. In Gegenwart von Nahrungsfetten blieb dieser Effekt aus. Eine Beteiligung der Interaktion von Trospium und Gallensalzen am Food-Effekt kann auf Basis dieser Ergebnisse als wahrscheinlich gelten.rnIm Caco-2-Modell konnte bereits eine Verbesserung der Permeabilität von Trospium durch Zusatz von Eudragit E gezeigt werden. Nun konnte gezeigt werden, dass durch den Hilfsstoff auch in vivo in Ratten eine verbesserte Permeation erreicht werden kann.rnDie Permeationsverbesserung von Aciclovir durch Zusatz von Chitosan-HCl sollte untersucht werden. Im Caco-2-Modell kam es zu einer signifikanten Permeationsverbesserung. Im Ussing-Kammer-Modell wurde die Permeation nicht verbessert. In Loop-Studien konnte nur bei hohen Hilfsstoff-Konzentrationen eine Tendenz zur Permeationsverbesserung erkannt werden.rn

FaSSIF-C, a Cholesterol containing biorelevant intestinal model medium for development and test of oral drug formulations

Biorelevante Medien sind entwickelt worden, um die Bedingungen im Magen-Darm-Trakt vor und nach der Mahlzeit zu imitieren. Mit FaSSIF und FeSSIF wurden Medien eingeführt, die nicht nur die pH- und Puffer-Kapazität des Dünndarms widerspiegeln, sondern auch Lipid und physiologische Tensid-Arten enthalten. Diese Medien (FaSSIF-V2 und FaSSlFmod6.5) wurden für Bioverfügbarkeitstudien in der Medikamentenentwicklung im Laufe der Jahre kontinuierlich weiterentwickelt. Dennoch sind die auf dem Markt verfügbaren Medien immer noch nicht in der Lage, die realen physiologischen Bedingungen zu simulieren. In der jetzigen Zusammensetzung sind nicht alle Kompetenten enthalten, welche natürlicher Weise im Duodenum vorkommen. Darüber hinaus wird nur eine 1:5 Verdünnung von FeSSIF zu FaSSIF angenommen, die individuelle Wasserzufuhr bei Medikamentengabe wird hierdurch jedoch nur eingeschränkt simuliert, obwohl diese von Patient zu Patient schwanken kann. rnZiel dieser Dissertation war die Verbesserung der Vorhersage der Auflösung und Absorption lipophiler Arzneistoffe durch Simulation der Bedingungen im zweiten Teil des Zwölffingerdarms mit neuen biorelevanten Medien, sowie unter Einwirkung zusätzlicher Detergention als Wirkstoffträger. rnUm den Effekt der Verdünnungsrate und Zeit im Dünndarm zu untersuchen, wurde die Entwicklung der Nanopartikel in der Magen-Darm-Flüssigkeit FaSSIFmod6.5 zu verschiedenen Zeitpunkten und Wassergehalten untersucht. Dafür wurden kinetische Studien an verschieden konzentrierten Modellmedien nach Verdünnungssprung untersucht. Das Modell entspricht der Vermischung der Gallenflüssigkeit mit dem Darminhalt bei variablem Volumen. Die Ergebnisse zeigen, dass Art und Größe der Nanopartikel stark von Verdünnung und Einirkungszeit abhängen. rnrnDie menschliche Darmflüssigkeit enthält Cholesterin, welches in allen früheren Modellmedien fehlt. Daher wurden biokompatible und physiologische Modellflüssigkeiten, FaSSIF-C, entwickelt. Der Cholesteringehalt von FaSSIF - 7C entspricht der Gallenflüssigkeit einer gesunden Frau, FaSSIF - 10C der einer gesunden männlichen Person und FaSSIF - 13C der in einigen Krankheitszuständen. Die intestinale Teilchen-Struktur-Untersuchung mit dynamische Lichtstreuung (DLS) und Neutronen-Kleinwinkelstreuung (SANS) ergab, dass die Korngröße von Vesikeln mit zunehmender Cholesterin-Konzentration abnahm. Zu hohe Cholesterin-Konzentration bewirkte zusätzlich sehr große Partikel, welche vermutlich aus Cholesterin-reichen “Disks“ bestehen. Die Löslichkeiten einiger BCS Klasse II Wirkstoffe (Fenofibrat, Griseofulvin, Carbamazepin, Danazol) in diesen neuen Medien zeigten, dass die Löslichkeit in unterschiedlicher Weise mit der Cholesteringehalt zusammen hing und dieser Effekt selektiv für die Droge war. rnDarüber hinaus wurde die Wirkung von einigen Tensiden auf die kolloidale Struktur und Löslichkeit von Fenofibrat in FaSSIFmod6.5 und FaSSIF -7C untersucht. Struktur und Löslichkeit waren Tensid- und Konzentrations-abhängig. Im Falle von FaSSIFmod6.5 zeigten die Ergebnisse eine dreifache Verzweigung der Lösungswege. Im Bereich mittlerer Tensidkonzentration wurde eine Löslichkeitslücke der Droge zwischen der Zerstörung der Galle-Liposomen und der Bildung von Tensid-reichen Mizellen beobachtet. In FaSSIF - 7C, zerstörten Tenside in höherer Konzentration die Liposomenstruktur trotz der allgemeinen Stabilisierung der Membranen durch Cholesterin. rnDie in dieser Arbeit vorgestellten Ergebnisse ergeben, dass die Anwesenheit von Cholesterin als eine fehlende Komponente der menschlichen Darmflüssigkeit in biorelevanten Medien wichtig ist und dazu beitragen kann, das in vivo Verhalten schwerlöslicher Arzneistoffe im Körper besser vorhersagen zu können. Der Verdünnungsgrad hat einen Einfluss auf die Nanopartikel-Struktur und Tenside beeinflussen die Löslichkeit von Medikamenten in biorelevanten Medien: Dieser Effekt ist sowohl von der Konzentration das Tensids abhängig, als auch dessen Typ.rnrn

AUGMENTATION OF RECONSTITUTION OF GUT ASSOCIATED LYMPHOID TISSUE IN THE SYNGENEIC MURINE BONE MARROW TRANSPLANTATION MODEL

Gut was studied as a prototypical mucosal membrane in the murine BDF-1 syngeneic bone marrow transplant model. Measures of jejunal intraepithelial lymphocytes (IELs) and crypt cells were obtained by standard techniques and a method of quantifying gut lamina propria plasma cells (PCs) was developed. The degree of ablation of gut PCs and IELs after 900 rads total body irradiation with ('60)Co, and their repopulation effected by transplantation with 2.0 x 10('5) or 1.0 x 10('6) bone marrow cells demonstrated a prolonged period of profound depression in population levels of these cells which was not reflected by the extent of damage sustained to the epithelium. Differences in the depopulation and recovery of gut PCs and IELs revealed a tendency towards initial differentiation of effector cells. A positive dose response to high bone marrow cell innocula was obtained. Subsequent studies determined that gut IEL and PC repopulation was potentiated by the addition of IELs or buffy coat cells (BCs) to the bone marrow transplant. A method of isolating 1.4 - 4.0 x 10('7) viable IELs per gram of murine small bowel was devised employing intralumenal hyaluronidase digestion of the epithelial layer and centrifugation of the resulting suspension through discontinuous Percoll gradients. Irradiated mice received 2.0 x 10('5) bone marrow cells along with an equal number of IELs or BCs. The extent and duration of depression of numbers of IELs and PCs was markedly reduced by the addition of the IEL isolate to the transplantation innocula, and to a lesser degree by the addition of BCs. The augmentation of repopuation far exceeded that expected by simple lodging of cells suggesting that the additionally transplanted cells contained a subpopulation of mucosal membrane lymphoid stem cells or helper cells. Correlation analysis of PC versus IEL levels suggests a possible feedback mechanism governing the relative size of their populations. Normal ratios of IgA, IgM, and IgG bearing PCs was maintained post transplantation with all of the regimens. ^

Integrated Proteomics Identified Up-regulated Focal Adhesion-mediated Proteins In Human Squamous Cell Carcinoma In An Orthotopic Murine Model.

Understanding the molecular mechanisms of oral carcinogenesis will yield important advances in diagnostics, prognostics, effective treatment, and outcome of oral cancer. Hence, in this study we have investigated the proteomic and peptidomic profiles by combining an orthotopic murine model of oral squamous cell carcinoma (OSCC), mass spectrometry-based proteomics and biological network analysis. Our results indicated the up-regulation of proteins involved in actin cytoskeleton organization and cell-cell junction assembly events and their expression was validated in human OSCC tissues. In addition, the functional relevance of talin-1 in OSCC adhesion, migration and invasion was demonstrated. Taken together, this study identified specific processes deregulated in oral cancer and provided novel refined OSCC-targeting molecules.

Electronic And Structural Study Of Pt-modified Au Vicinal Surfaces: A Model System For Pt-au Catalysts.

Two single crystalline surfaces of Au vicinal to the (111) plane were modified with Pt and studied using scanning tunneling microscopy (STM) and X-ray photoemission spectroscopy (XPS) in ultra-high vacuum environment. The vicinal surfaces studied are Au(332) and Au(887) and different Pt coverage (θPt) were deposited on each surface. From STM images we determine that Pt deposits on both surfaces as nanoislands with heights ranging from 1 ML to 3 ML depending on θPt. On both surfaces the early growth of Pt ad-islands occurs at the lower part of the step edge, with Pt ad-atoms being incorporated into the steps in some cases. XPS results indicate that partial alloying of Pt occurs at the interface at room temperature and at all coverage, as suggested by the negative chemical shift of Pt 4f core line, indicating an upward shift of the d-band center of the alloyed Pt. Also, the existence of a segregated Pt phase especially at higher coverage is detected by XPS. Sample annealing indicates that the temperature rise promotes a further incorporation of Pt atoms into the Au substrate as supported by STM and XPS results. Additionally, the catalytic activity of different PtAu systems reported in the literature for some electrochemical reactions is discussed considering our findings.

The Soluble Guanylyl Cyclase Activator Bay 60-2770 Potently Relaxes The Pulmonary Artery On Congenital Diaphragmatic Hernia Rabbit Model.

Congenital diaphragmatic hernia (CDH) is associated with pulmonary hypertension which is often difficult to manage, and a significant cause of morbidity and mortality. In this study, we have used a rabbit model of CDH to evaluate the effects of BAY 60-2770 on the in vitro reactivity of left pulmonary artery. CDH was performed in New Zealand rabbit fetuses (n = 10 per group) and compared to controls. Measurements of body, total and left lung weights (BW, TLW, LLW) were done. Pulmonary artery rings were pre-contracted with phenylephrine (10 μM), after which cumulative concentration-response curves to glyceryl trinitrate (GTN; NO donor), tadalafil (PDE5 inhibitor) and BAY 60-2770 (sGC activator) were obtained as well as the levels of NO (NO3/NO2). LLW, TLW and LBR were decreased in CDH (p < 0.05). In left pulmonary artery, the potency (pEC50) for GTN was markedly lower in CDH (8.25 ± 0.02 versus 9.27 ± 0.03; p < 0.01). In contrast, the potency for BAY 60-2770 was markedly greater in CDH (11.7 ± 0.03 versus 10.5 ± 0.06; p < 0.01). The NO2/NO3 levels were 62 % higher in CDH (p < 0.05). BAY 60-2770 exhibits a greater potency to relax the pulmonary artery in CDH, indicating a potential use for pulmonary hypertension in this disease.

Bay 41-2272, A Soluble Guanylate Cyclase Stimulator, Relaxes Isolated Human Ureter In A Standardized In Vitro Model.

To characterize the relaxation induced by BAY 41-2272 in human ureteral segments. Ureter specimens (n = 17) from multiple organ human deceased donors (mean age 40 ± 3.2 years, male/female ratio 2:1) were used to characterize the relaxing response of BAY 41-2272. Immunohistochemical analysis for endothelial and neuronal nitric oxide synthase, guanylate cyclase stimulator (sGC) and type 5 phosphodiesterase was also performed. The potency values were determined as the negative log of the molar to produce 50% of the maximal relaxation in potassium chloride-precontracted specimens. The unpaired Student t test was used for the comparisons. Immunohistochemistry revealed the presence of endothelial nitric oxide synthase in vessel endothelia and neuronal nitric oxide synthase in urothelium and nerve structures. sGC was expressed in the smooth muscle and urothelium layer, and type 5 phosphodiesterase was present in the smooth muscle only. BAY 41-2272 (0.001-100 μM) relaxed the isolated ureter in a concentration dependent manner, with a potency and maximal relaxation value of 5.82 ± 0.14 and 84% ± 5%, respectively. The addition of nitric oxide synthase and sGC inhibitors reduced the maximal relaxation values by 21% and 45%, respectively. However, the presence of sildenafil (100 nM) significantly potentiated (6.47 ± 0.10, P <.05) this response. Neither glibenclamide or tetraethylammonium nor ureteral urothelium removal influenced the relaxation response by BAY 41-2272. BAY 41-2272 relaxes the human isolated ureter in a concentration-dependent manner, mainly by activating the sGC enzyme in smooth muscle cells rather than in the urothelium, although a cyclic guanosine monophosphate-independent mechanism might have a role. The potassium channels do not seem to be involved.

Atomic Charge Transfer-counter Polarization Effects Determine Infrared Ch Intensities Of Hydrocarbons: A Quantum Theory Of Atoms In Molecules Model.

Atomic charge transfer-counter polarization effects determine most of the infrared fundamental CH intensities of simple hydrocarbons, methane, ethylene, ethane, propyne, cyclopropane and allene. The quantum theory of atoms in molecules/charge-charge flux-dipole flux model predicted the values of 30 CH intensities ranging from 0 to 123 km mol(-1) with a root mean square (rms) error of only 4.2 km mol(-1) without including a specific equilibrium atomic charge term. Sums of the contributions from terms involving charge flux and/or dipole flux averaged 20.3 km mol(-1), about ten times larger than the average charge contribution of 2.0 km mol(-1). The only notable exceptions are the CH stretching and bending intensities of acetylene and two of the propyne vibrations for hydrogens bound to sp hybridized carbon atoms. Calculations were carried out at four quantum levels, MP2/6-311++G(3d,3p), MP2/cc-pVTZ, QCISD/6-311++G(3d,3p) and QCISD/cc-pVTZ. The results calculated at the QCISD level are the most accurate among the four with root mean square errors of 4.7 and 5.0 km mol(-1) for the 6-311++G(3d,3p) and cc-pVTZ basis sets. These values are close to the estimated aggregate experimental error of the hydrocarbon intensities, 4.0 km mol(-1). The atomic charge transfer-counter polarization effect is much larger than the charge effect for the results of all four quantum levels. Charge transfer-counter polarization effects are expected to also be important in vibrations of more polar molecules for which equilibrium charge contributions can be large.

Mesenchymal Stromal Cells From Adipose Tissue Attached To Suture Material Enhance The Closure Of Enterocutaneous Fistulas In A Rat Model.

Surgical treatment for enterocutaneous fistulas (EF) frequently fails. Cell therapy may represent a new approach to treatment. Mesenchymal stromal cells (MSCs) have high proliferative and differentiation capacity. This study aimed to investigate whether MSCs could adhere to suture filament (SF), promoting better EF healing. MSCs, 1 × 10(6), from adipose tissue (ATMSCs) were adhered to a Polyvicryl SF by adding a specific fibrin glue formulation. Adhesion was confirmed by confocal and scanning electron microscopy (SEM). A cecal fistula was created in 22 Wistar rats by incising the cecum and suturing the opening to the surgical wound subcutaneously with four separate stitches. The animals were randomly allocated to three groups: control (CG)-five animals, EF performed; injection (IG)-eight animals 1 × 10(6) ATMSCs injected around EF borders; and suture filament (SG): nine animals, sutured with 1 × 10(6) ATMSCs attached to the filaments with fibrin glue. Fistulas were photographed on the operation day and every 3 days until the 21st day and analyzed by two observers using ImageJ Software. Confocal and SEM results demonstrated ATMSCs adhered to SF (ATMSCs-SF). The average reduction size of the fistula area at 21st day was greater for the SG group (90.34%, P < 0.05) than the IG (71.80%) and CG (46.54%) groups. ATMSCs adhered to SF maintain viability and proliferative capacity. EF submitted to ATMSCs-SF procedure showed greater recovery and healing. This approach might be a new and effective tool for EF treatment.

Changes In Motor Behavior During Pregnancy In Rats: The Basis For A Possible Animal Model Of Restless Legs Syndrome.

Pregnant women have a 2-3 fold higher probability of developing restless legs syndrome (RLS - sleep-related movement disorders) than general population. This study aims to evaluate the behavior and locomotion of rats during pregnancy in order to verify if part of these animals exhibit some RLS-like features. We used 14 female 80-day-old Wistar rats that weighed between 200 and 250 g. The rats were distributed into control (CTRL) and pregnant (PN) groups. After a baseline evaluation of their behavior and locomotor activity in an open-field environment, the PN group was inducted into pregnancy, and their behavior and locomotor activity were evaluated on days 3, 10 and 19 of pregnancy and in the post-lactation period in parallel with the CTRL group. The serum iron and transferrin levels in the CTRL and PN groups were analyzed in blood collected after euthanasia by decapitation. There were no significant differences in the total ambulation, grooming events, fecal boli or urine pools between the CTRL and PN groups. However, the PN group exhibited fewer rearing events, increased grooming time and reduced immobilization time than the CTRL group (ANOVA, p<0.05). These results suggest that pregnant rats show behavioral and locomotor alterations similar to those observed in animal models of RLS, demonstrating to be a possible animal model of this sleep disorder.

Urothelial Carcinogen Resistance Driven By Stronger Toll-like Receptor 2 (tlr2) And Uroplakin Iii (up Iii) Defense Mechanisms: A New Model.

The objective of the study was to illustrate the applicability and significance of the novel Lewis urothelial cancer model compared to the classic Fisher 344. Fischer 344 and Lewis females rats, 7 weeks old, were intravesical instilled N-methyl-N-nitrosourea 1.5 mg/kg every other week for a total of four doses. After 15 weeks, animals were sacrificed and bladders analyzed: histopathology (tumor grade and stage), immunohistochemistry (apoptotic and proliferative indices) and blotting (Toll-like receptor 2-TLR2, Uroplakin III-UP III and C-Myc). Control groups received placebo. There were macroscopic neoplastic lesions in 20 % of Lewis strain and 70 % of Fischer 344 strain. Lewis showed hyperplasia in 50 % of animals, normal bladders in 50 %. All Fischer 344 had lesions, 20 % papillary hyperplasia, 30 % dysplasia, 40 % neoplasia and 10 % squamous metaplasia. Proliferative and apoptotic indices were significantly lower in the Lewis strain (p < 0.01). The TLR2 and UP III protein levels were significantly higher in Lewis compared to Fischer 344 strain (70.8 and 46.5 % vs. 49.5 and 16.9 %, respectively). In contrast, C-Myc protein levels were significantly higher in Fischer 344 (22.5 %) compared to Lewis strain (13.7 %). The innovative Lewis carcinogen resistance urothelial model represents a new strategy for translational research. Preservation of TLR2 and UP III defense mechanisms might drive diverse urothelial phenotypes during carcinogenesis in differently susceptible individuals.

Prostatic Angiogenic Responses In Late Life: Antiangiogenic Therapy Influences And Relation With The Glandular Microenvironment In The Transgenic Adenocarcinoma Of Mouse Prostate (tramp) Model.

Aging is considered one of the main predisposing factors for the development of prostate malignancies. Angiogenesis is fundamental for tumor growth and its inhibition represents a promising therapeutic approach in cancer treatment. Thus, we sought to determine angiogenic responses and the effects of antiangiogenic therapy in the mouse prostate during late life, comparing these findings with the prostatic microenvironment in the Transgenic Adenocarcinoma of Mouse Prostate (TRAMP) model. Male mice (52 week-old FVB) were submitted to treatments with SU5416 (6 mg/kg; i.p.) and/or TNP-470 (15 mg/kg; s.c.). Finasteride was administered (20 mg/kg; s.c.), alone or in association to both inhibitors. The dorsolateral prostate was collected for VEGF, HIF-1α, FGF-2 and endostatin immunohistochemical and Western Blotting analyses and for microvessel density (MVD) count. Senescence led to increased MVD and VEGF, HIF-1α and FGF-2 protein levels in the prostatic microenvironment, similarly to what was observed in TRAMP mice prostate. The angiogenic process was impaired in all the treated groups, demonstrating significantly decreased MVD. Antiangiogenic and/or finasteride treatments resulted in decreased VEGF and HIF-1α levels, especially following TNP-470 administration, either alone or associated to SU5416. The combination of these agents resulted in increased endostatin levels, regardless of the presence of finasteride. Prostatic angiogenesis stimulation during senescence favored the development of neoplastic lesions, considering the pro-angiogenic microenvironment as a common aspect also observed during cancer progression in TRAMP mice. The combined antiangiogenic therapy was more efficient, leading to enhanced imbalance towards angiogenic inhibition in the organ. Finally, finasteride administration might secondarily upregulate the expression of pro-angiogenic factors, pointing to the harmful effects of this therapy. Prostate 75: 484-499, 2015. © 2014 Wiley Periodicals, Inc.

Application Of A Semi-empirical Model For The Evaluation Of Transmission Properties Of Barite Mortar.

The aim of this study was to estimate barite mortar attenuation curves using X-ray spectra weighted by a workload distribution. A semi-empirical model was used for the evaluation of transmission properties of this material. Since ambient dose equivalent, H(⁎)(10), is the radiation quantity adopted by IAEA for dose assessment, the variation of the H(⁎)(10) as a function of barite mortar thickness was calculated using primary experimental spectra. A CdTe detector was used for the measurement of these spectra. The resulting spectra were adopted for estimating the optimized thickness of protective barrier needed for shielding an area in an X-ray imaging facility.