Piecewise linear perturbations of a linear center

This paper is mainly devoted to the study of the limit cycles that can bifurcate from a linear center using a piecewise linear perturbation in two zones. We consider the case when the two zones are separated by a straight line Σ and the singular point of the unperturbed system is in Σ. It is proved that the maximum number of limit cycles that can appear up to a seventh order perturbation is three. Moreover this upper bound is reached. This result confirms that these systems have more limit cycles than it was expected. Finally, center and isochronicity problems are also studied in systems which include a first order perturbation. For the latter systems it is also proved that, when the period function, defined in the period annulus of the center, is not monotone, then it has at most one critical period. Moreover this upper bound is also reached.

Embriologia e desenvolvimento pós-seminal de espécies de Poaceae (Poales)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Determinação da idade e crescimento da piramutaba Brachyplatystoma vaillantii (Valenciennes, 1840) (Siluriformes : Pimelodidae) capturada no estuário amazônico

Neste trabalho foram analisados exemplares de piramutaba (Brachyplalystoma vaillantii) provenientes de pescarias experimentais no estuário amazônico. Para o estudo de determinação da idade foram analisados acúleos das nadadeiras peitorais e dorsal, opérculos, otólitos (lapillus) e vértebras. Da análise destas estruturas rígidas foi concluído que a vértebra é a estrutura mais adequada para determinar a idade da piramutaba, pois esta estrutura apresentou 59% de anéis nítidos e uma boa correlação entre o seu raio e o comprimento furcal do peixe (r² = 0,9889 e p<0,05). Os anéis etários das vértebras foram validados pelo método da distribuição de freqüências por classes de comprimento. A piramutaba forma dois anéis etários por ano em suas vértebras. A relação entre o peso total e o comprimento furcal da piramutaba descreve seu crescimento como alométrico e a equação que descreve este crescimento é Wt = 6,1 * 10^-6 * Lf^3,1129. A proporção sexual de piramutaba verificada não foi de 1:1, onde o número de fêmeas foi superior ao de machos. Foi observado um número máximo de dez anéis nítidos nas vértebras de piramutaba. O modelo de crescimento utilizado neste trabalho foi o de von Bertalanffy para as estimativas das equações de crescimento em comprimento e em peso. Os parâmetros de crescimento (k, t₀ e L∞) foram estimados através de quatro diferentes métodos: contagem de anéis nas vértebras, retrocálculo, decomposição dos raios e distribuição de freqüências por classes de comprimento. Os parâmetros de crescimento foram: k = 0,138 ano^-1, t₀ = -0,239 e L∞ = 110,5 cm (contagem de anéis); k = 0,119 ano^-1, t₀ = -0,202 e L∞ = 110,5 cm (retrocálculo); k = 0,096 ano^-1, t₀ = -0,146 e L∞ = 110,5 cm (decomposição dos raios) e k = 0,127 ano^-1, t₀ = -0,236 e L∞ = 110,5 cm (distribuição de freqüências).

Respostas eletromagnéticas dos arranjos coplanar e coaxial em poço

Foi estudado a viabilidade de aplicação do arranjo coplanar de bobinas nas sondas de perfilagem em poço por indução eletromagnética. Paralelamente foram geradas as respostas do convencional arranjo coaxial, que é o amplamente utilizado nas sondas comerciais, com o propósito de elaborar uma análise comparativa. Através da solução analítica (meios homogêneos) e semi-analítica (meios heterogêneos) foram geradas inicialmente as respostas para modelos mais simples, tais como os do (1) meio homogêneo, isotrópico e ilimitado; (2) uma casca cilíndrica simulando a frente de invasão; (3) duas cascas cilíndricas para simular o efeito annulus; (4) uma interface plana e dois semi-espaços simulando o contato entre duas camadas espessas e (5) uma camada plano-horizontal e dois semi-espaços iguais. Apesar da simplicidade destes modelos, eles permitem uma análise detalhada dos efeitos que alguns parâmetros geoelétricos têm sobre as respostas. Aí então, aplicando ainda as condições de contorno nas fronteiras (Sommerfeld Boundary Value Problem), obtivemos as soluções semi-analíticas que nos permitiram simular as respostas em modelos relativamente mais complexos, tais como (1) zonas de transição gradacional nas frentes de invasão; (2) seqüências de camadas plano-paralelas horizontais e inclinadas; (3) seqüências laminadas que permitem simular meios anisotrópicos e (4) passagem gradacional entre duas camadas espessas. Concluimos que o arranjo coplanar de bobinas pode ser uma ferramenta auxiliar na (1) demarcação das interfaces de camadas espessas; (2) posicionamento dos reservatórios de pequenas espessuras; (3) avaliação de perfis de invasão e (4) localizar variações de condutividade azimutalmente.

The role of B-mode ultrasonography in the musculoskeletal anatomical evaluation of the cervical region of the dog spine

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Limit cycles of cubic polynomial differential systems with rational first integrals of degree 2

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A new species of ischnocnema parva species series (Anura, Brachycephalidae) from northern state of Rio de Janeiro, Brazil

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

TRANSITIVITY AND ROTATION SETS WITH NONEMPTY INTERIOR FOR HOMEOMORPHISMS OF THE 2-TORUS

We show that if f is a homeomorphism of the 2-torus isotopic to the identity and its lift (f) over tilde is transitive, or even if it is transitive outside the lift of the elliptic islands, then (0,0) is in the interior of the rotation set of (f) over tilde. This proves a particular case of Boyland's conjecture.

Utilzzo dei parametri ecocardiografici tradizionali ed a Doppler tissutale nella valutazione della disfunzione atrio-ventricolare in cani affetti da malattia mitralica cronica

In questo lavoro ci siamo posti come obiettivo lo studio della disfunzione atrio-ventricolare mediante tecniche ecocardiografiche avanzate (come il Tissue Doppler Imaging - TDI) in cani affetti da malattia mitralica cronica (MVD). Una prima parte è volta alla valutazione della funzionalità diastolica del ventricolo destro. Ci siamo proposti di analizzare la funzione del ventricolo destro in cani affetti da malattia del cuore sinistro per comprendere se quest’ultima possa condizionare direttamente la performance del settore cardiaco controlaterale. I risultati più importanti che abbiamo riscontrato sono: l’assenza di differenze significative nella disfunzione sisto-diastolica del ventricolo destro in cani con MVD a diverso stadio; la diretta correlazione tra le variabili TDI di funzionalità del ventricolo destro con il grado di disfunzione del ventricolo sinistro, come indicatori di interdipendenza ventricolare; ed infine il riscontro di una maggior tendenza ad alterazioni diastoliche del ventricolo sinistro in cani con ipertensione polmonare. A quest’ultimo proposito, per quanto riguarda le variabili TDI, il rapporto E/e’ dell’anulus mitralico laterale e settale è risultato avere una differenza significativa tra i cani con ipertensione polmonare e quelli privi di ipertensione polmonare (P<0,01). Nel secondo studio abbiamo applicato il TDI per l’analisi della funzione sisto-diastolica dell’atrio sinistro. Il lavoro è stato articolato in una parte di validazione della metodica su cani normali ed una su animali affetti da MDV. I risultati ottenuti mostrano che la valutazione ecocardiografica delle proprietà di deformazione dell’atrio sinistro basata sul TDI è attuabile e riproducibile nel cane. Abbiamo fornito dei valori di normalità per questa specie e confrontato questi dati con quelli ricavati in cani portatori di MVD. Le differenza tra le varie classi di malattia, nei diversi gradi di dilatazione atriale, sono risultate limitate, ma abbiamo individuato delle correlazioni tra i parametri TDI ed alcune variabili di funzionalità atriale.

Structured antibody surfaces for bio-recognition and a label-free detection of bacteria

Antibody microarrays are of great research interest because of their potential application as biosensors for high-throughput protein and pathogen screening technologies. In this active area, there is still a need for novel structures and assemblies providing insight in binding interactions such as spherical and annulus-shaped protein structures, e.g. for the utilization of curved surfaces for the enhanced protein-protein interactions and detection of antigens. Therefore, the goal of the presented work was to establish a new technique for the label-free detection of bio-molecules and bacteria on topographically structured surfaces, suitable for antibody binding.rnIn the first part of the presented thesis, the fabrication of monolayers of inverse opals with 10 μm diameter and the immobilization of antibodies on their interior surface is described. For this purpose, several established methods for the linking of antibodies to glass, including Schiff bases, EDC/S-NHS chemistry and the biotin-streptavidin affinity system, were tested. The employed methods included immunofluorescence and image analysis by phase contrast microscopy. It could be shown that these methods were not successful in terms of antibody immobilization and adjacent bacteria binding. Hence, a method based on the application of an active-ester-silane was introduced. It showed promising results but also the need for further analysis. Especially the search for alternative antibodies addressing other antigens on the exterior of bacteria will be sought-after in the future.rnAs a consequence of the ability to control antibody-functionalized surfaces, a new technique employing colloidal templating to yield large scale (~cm2) 2D arrays of antibodies against E. coli K12, eGFP and human integrin αvβ3 on a versatile useful glass surface is presented. The antibodies were swept to reside around the templating microspheres during solution drying, and physisorbed on the glass. After removing the microspheres, the formation of annuli-shaped antibody structures was observed. The preserved antibody structure and functionality is shown by binding the specific antigens and secondary antibodies. The improved detection of specific bacteria from a crude solution compared to conventional “flat” antibody surfaces and the setting up of an integrin-binding platform for targeted recognition and surface interactions of eukaryotic cells is demonstrated. The structures were investigated by atomic force, confocal and fluorescence microscopy. Operational parameters like drying time, temperature, humidity and surfactants were optimized to obtain a stable antibody structure.

Parametric T2 and T2* mapping techniques to visualize intervertebral disc degeneration in patients with low back pain: initial results on the clinical use of 3.0 Tesla MRI

To assess, compare and correlate quantitative T2 and T2* relaxation time measurements of intervertebral discs (IVDs) in patients suffering from low back pain, with respect to the IVD degeneration as assessed by the morphological Pfirrmann Score. Special focus was on the spatial variation of T2 and T2* between the annulus fibrosus (AF) and the nucleus pulposus (NP).

Preparation of intact bovine tail intervertebral discs for organ culture

The intervertebral disc (IVD) is the joint of the spine connecting vertebra to vertebra. It functions to transmit loading of the spine and give flexibility to the spine. It composes of three compartments: the innermost nucleus pulposus (NP) encompassing by the annulus fibrosus (AF), and two cartilaginous endplates connecting the NP and AF to the vertebral body on both sides. Discogenic pain possibly caused by degenerative intervertebral disc disease (DDD) and disc herniations has been identified as a major problem in our modern society. To study possible mechanisms of IVD degeneration, in vitro organ culture systems with live disc cells are highly appealing. The in vitro culture of intact bovine coccygeal IVDs has advanced to a relevant model system, which allows the study of mechano-biological aspects in a well-controlled physiological and mechanical environment. Bovine tail IVDs can be obtained relatively easy in higher numbers and are very similar to the human lumbar IVDs with respect to cell density, cell population and dimensions. However, previous bovine caudal IVD harvesting techniques retaining cartilaginous endplates and bony endplates failed after 1-2 days of culture since the nutrition pathways were obviously blocked by clotted blood. IVDs are the biggest avascular organs, thus, the nutrients to the cells in the NP are solely dependent on diffusion via the capillary buds from the adjacent vertebral body. Presence of bone debris and clotted blood on the endplate surfaces can hinder nutrient diffusion into the center of the disc and compromise cell viability. Our group established a relatively quick protocol to "crack"-out the IVDs from the tail with a low risk for contamination. We are able to permeabilize the freshly-cut bony endplate surfaces by using a surgical jet lavage system, which removes the blood clots and cutting debris and very efficiently reopens the nutrition diffusion pathway to the center of the IVD. The presence of growth plates on both sides of the vertebral bone has to be avoided and to be removed prior to culture. In this video, we outline the crucial steps during preparation and demonstrate the key to a successful organ culture maintaining high cell viability for 14 days under free swelling culture. The culture time could be extended when appropriate mechanical environment can be maintained by using mechanical loading bioreactor. The technique demonstrated here can be extended to other animal species such as porcine, ovine and leporine caudal and lumbar IVD isolation.

Hydrogels for nucleus replacement—Facing the biomechanical challenge

Hydrogels are considered promising for disc regeneration strategies. However, it is currently unknown whether the destruction of the natural interface between nucleus and surrounding structures caused by nucleotomy and an inadequate annulus closure diminishes the mechanical competence of the disc. This in vitro study aimed to clarify these mechanisms and to evaluate whether hydrogels are able to restore the biomechanical behaviour of the disc. Nucleus pressure in an ovine intervertebral disc was measured in vivo during day and night and adapted to an in vitro axial compressive diurnal (15min) and night (30min) load. Effects of different defects on disc height and nucleus pressure were subsequently measured in vitro using 30 ovine motion segments. Following cases were considered: intact; annulus incision repaired by suture and glue; annulus incision with removal and re-implantation of nucleus tissue; and two different hydrogels repaired by suture and glue. The intradiscal pressure in vivo was 0.75MPa during day and 0.5MPa during night corresponding to an in vitro axial compressive force of 130 and 58N, respectively. The compression test showed that neither the implantation of hydrogels nor the re-implantation of the natural nucleus, assumed as being the ideal implant, was able to restore the mechanical functionality of an intact disc. Results indicate the importance of the natural anchorage of the nucleus with its surrounding structures and the relevance of an appropriate annulus closure. Therefore, hydrogels that are able to mimic the mechanical behaviour of the native nucleus may fail in restoring the mechanical behaviour of the disc.

Biomaterials for Intervertebral Disc Regeneration

The intervertebral disc (IVD) is a complex avascular organ of viscoelastic properties. The current research focus is to regenerate and to partially restore a degenerated IVD by ‘smart’ biomaterials in combination of cell therapy and/or growth factors. For the two tissues of the IVD, that is, the nucleus pulposus (NP) and the annulus fibrosus (AF), biomaterials of different mechanical properties are needed. The ideal biomaterial to restore the water-rich NP and the tensile-force resistant AF has not been identified yet. The lack of blood vessels and the relative scarcity of specially adapted cells of the IVD organ demand novel concepts of tissue-engineered biological approaches to regenerate or replace the IVD. Injectable biodegradable hydrogels with swelling properties are in focus for NP replacement, whereas electrospun biphasic composites and silk, among other biodegradable polymers, are discussed for AF reinforcement.

Intervertebral disc regeneration or repair with biomaterials and stem cell therapy--feasible or fiction?

The "gold standard" for treatment of intervertebral disc herniations and degenerated discs is still spinal fusion, corresponding to the saying "no disc - no pain". Mechanical prostheses, which are currently implanted, do only have medium outcome success and have relatively high re-operation rates. Here, we discuss some of the biological intervertebral disc replacement approaches, which can be subdivided into at least two classes in accordance to the two different tissue types, the nucleus pulposus (NP) and the annulus fibrosus (AF). On the side of NP replacement hydrogels have been extensively tested in vitro and in vivo. However, these gels are usually a trade-off between cell biocompatibility and load-bearing capacity, hydrogels which fulfill both are still lacking. On the side of AF repair much less is known and the question of the anchoring of implants is still to be addressed. New hope for cell therapy comes from developmental biology investigations on the existence of intervertebral disc progenitor cells, which would be an ideal cell source for cell therapy. Also notochordal cells (remnants of the embryonic notochord) have been recently pushed back into focus since these cells have regenerative potential and can activate disc cells. Growth factor treatment and molecular therapies could be less problematic. The biological solutions for NP and AF replacement are still more fiction than fact. However, tissue engineering just scratched the tip of the iceberg, more satisfying solutions are yet to be added to the biomedical pipeline.