Nous considérons deux modèles d’arbres aléatoires continus, à savoir les arbres de Lévy et les arbres inhomogènes. Les arbres de Lévy, introduits par Le Gall et Le Jan (1998) comme extension de l’arbre brownien d’Aldous (1991), décrivent les structures généalogiques des processus de branchement. Nous donnons une description de la loi d’un arbre de Lévy conditionné par son diamètre, ainsi qu’une décomposition de l’arbre le long de ce diamètre, qui est décrite à l’aide d’une mesure ponctuelle de Poisson. Dans le cas particulier d’un mécanisme de branchement stable, nous caractérisons la loi jointe du diamètre et de la hauteur d’un arbre de Lévy conditionné par sa masse totale. Dans le cas brownien nous obtenons une formule explicite de cette loi jointe, ce qui permet de retrouver par un calcul direct sur l’excursion brownienne, un résultat de Szekeres (1983) et Aldous (1991) concernant la loi du diamètre. Dans les cas stables, nous obtenons également des développements asymptotiques pour les lois de la hauteur et du diamètre. Les arbres inhomogènes sont introduits par Aldous et Pitman (2000), Camarri et Pitman (2000). Ce sont des généralisations de l’arbre brownien d’Aldous. Pour un arbre inhomogène, nous étudions une fragmentation de cet arbre qui généralise celle introduite par Aldous et Pitman pour l’arbre brownien. Nous construisons un arbre généalogique de cette fragmentation. En utilisant des arguments de convergence, nous montrons qu’il y a une dualité́ en loi entre l’arbre initial et l’arbre généalogique de fragmentation. Pour l’arbre brownien, nous trouvons aussi une façon de reconstruire l’arbre initial à partir de l’arbre généalogique. / We consider two models of random continuous trees: Lévy trees and inhomogeneous continuum random trees. Lévy trees are scaling limits of Galton-Watson trees. They describe the genealogical structures of continuous-state branching processes. The class of Lévy trees is introduced by Le Gall and Le Jan (1998) as an extension of Aldous’ notion of Brownian Continuum Random Tree (1991). For a Lévy tree, we give a description of its law conditioned to have a fixed diameter that is expressed in terms of a Poisson point measure. In the special case of a stable branching mechanism, we characterize the joint law of the diameter and the height of a Lévy tree conditioned on its total mass. From this, we deduce explicit distributions for the diameter in the Brownian case, as well as tail estimates in the general case.Inhomogeneous continuum random trees are introduced by Aldous and Pitman (2000), Camarri and Pitman (2000). They are also generalizations of Aldous’ Brownian Continuum Random Tree (and of Lévy trees). For an inhomogeneous continuum random tree, we consider a fragmentation which generalizes the one introduced by Aldous and Pitman on the Brownian tree. We construct a genealogical tree for this fragmentation. With weak limit arguments, we show that there is a duality in distribution between the initial tree and the genealogical tree. For the Brownian tree, we also present a way to reconstruct the initial tree from the genealogical tree.

Kärlsjukdomar är en av de vanligaste sjukdomarna som förekommer bland befolkningen. Två artärer som huvudsakligen försörjer kroppens armar med blod heter arteria subclavia och arteria brachialis. I dagsläget finns det inga referensvärden för arteria subclavia och arteria brachialis. Detta faktum gör det svårare att undersöka dessa kärl och besvara frågeställningar som rör dem. Ultraljud är en lämplig metod för att följa upp sjukdomstillstånd i dessa kärl, eftersom ultraljud både är non-invasivt, kostnadseffektivt och ger inte patienten några obehag eller utsätter dem för strålning. Syftet med studien var att samla in ett referensmaterial för olika värden i arteria subclavia och arteria brachialis som kan användas i kliniken. För att utarbeta referensvärden av diameter, volymflöde och blodflödeshastighet utfördes en ultraljudsundersökning på 25 friska deltagare, 8 män och 17 kvinnor. Referensvärden för vänster respektive höger diameter av arteria brachialis låg mellan 3,1-3,5 mm och 3,2-3,6 mm. Volymflödet i vänster respektive höger arteria brachialis låg mellan 0,029-0,042 L/min och 0,035-0,049 L/min. Blodflödeshastigheten i vänster respektive höger arteria brachialis låg mellan 0,818-0,968 m/s och 0,881-0,946 m/s. Diametern av vänster respektive höger arteria subclavia låg mellan 4,7-5,4 mm och 4,8-5,5 mm. Volymflödet i vänster respektive höger arteria subclavia låg mellan 0,087-0,124 L/min och 0,096-0,119 L/min. Blodflödeshastigheten i vänster respektive höger arteria subclavia låg mellan 0,948-1,106 m/s och 0,909-1,118 m/s. Parametrar som hade signifikant samband med ålder i denna studie var blodflödeshastighet och volymflöde i höger arteria brachialis och diametern i vänster och höger arteria subclavia. Utifrån denna studie kan inga tydliga slutsatser dras gällande vilka referensvärden som bör användas i kliniken. Detta på grund av låga antalet deltagare och liten åldersspridning. / Vascular disease is one of the most common diseases that occurs among the population. Two of the arteries, which mainly supply the arms with blood, is called subclavian artery and brachial artery. Today, there are no reference values for the subclavian artery and the brachial artery. This makes it more difficult to examine these vessels and answer questions that concern them. Ultrasound is a suitable method in order to observe conditions in these vessels, since the ultrasound is both non-invasive and cost-effective and the method do not give the patient any discomfort or expose them to radiation. The purpose of this study was to obtain reference values for subclavian artery and brachial artery plexus, which can be used in different vessel examinations at the department. In order to develop the reference values of the diameter, the volume flow rate and the blood flow velocity of subclavian artery and brachial artery, an ultrasound scan was carried out in 25 healthy participants, 8 males and 17 females. Reference values for the left and right diameters of the brachial artery were between 3.1-3.5 mm and 3.2-3.6 mm. The volume flow in the left and right brachial artery was between 0.029-0.042 L/min and 0.035-0.049 L/min. The blood flow velocity in the left and right brachial artery was between 0.818-0.968 m/s and 0.881-0.946 m/s. The diameter in the left and right subclavian was between 4.7-5.4 mm and 4.8-5.5 mm. The volume flow in the left and right subclavian, was between 0.087-0.124 L/min and 0.096-0.119 L/min. The blood flow velocity in the left and right subclavian was between 0.948-1.106 m/s and 0.909-1.118 m/s. Parameters that had significant correlation with age in this study were blood flow velocity and volume flow in the right brachial artery and the diameter of the left and right subclavian artery. Based on this study, no clear conclusions can be drawn as to which reference values should be used in the clinical practice. This is due to a low number of participants and low age distribution.

The work of the Cal Poly Tissue Engineering Lab is primarily focused on the fabrication, characterization, and improvement of “Blood Vessel Mimics” (BVMs), tissue engineered constructs used to evaluate cellular response to vascular medical devices. Currently, cells are grown onto fibrous, porous tubes made using an in-house electrospinning process from PLGA, a biocompatible co-polymer. The adhesion and proliferation of cells in a BVM is reliant on the micro-scale structure of the PLGA scaffold, and as such it is of great importance for the electrospinning process to consistently produce scaffolds of similar morphologies. Additionally, it has been shown that cell proliferation increases with scaffolds of smaller fibers and pores than the current electrospinning protocol can produce. Finally, the Tissue Engineering Lab has interest in testing devices in more tortuous BVM bioreactor designs, however the use of relatively rigid PLGA scaffolds has severely limited the ability to construct more complicated vessel geometries. The overall goal of this thesis was to improve fabrication and characterization of electrospun polymer scaffolds for BVM use. The specific aims of this thesis were to: 1) Improve scaffold characterization by comparing two techniques for fiber diameter measurement and implementing a technique for pore area measurement. 2) Reduce scaffold fiber diameter and pore area by investigating humidity and solvent composition electrospinning parameters. 3) Reduce process variability by developing a more specific electrospinning protocol. 4) Improve scaffold consistency and use by understanding and reducing PLGA scaffold shrinkage. 5) Identify and evaluate more flexible polymers as potential alternatives for electrospun BVM scaffolds. In order to accomplish these aims, first, several BVM and outside literature images were taken and evaluated with current and prospective fiber diameter techniques, and with 2 prospective pore area techniques to characterize accuracy and consistency of each method. It was found that the prospective fiber diameter measurement technique was not superior to the current method. The techniques developed for pore area measurement were found to produce results that differed significantly from each other and from the published value for a given image. Next, changes to environmental and solution composition parameters were made with the hopes of reducing fiber diameter and pore area of electrospun PLGA scaffolds. Changes in relative humidity did not appear to significantly affect scaffold fiber diameter while changes to solvent composition, specifically the use of acetone, resulted in fibers significantly smaller than those regularly achieved in the BVM lab. Next, several sources of variability in the electrospinning protocol were identified and subsequently altered to improve consistency and usability. Specifically, this included redefining the precision with which PLGA mass was measured, repositioning electrical equipment to reduce the effect of stray electrostatic forces on the polymer solution jet, attempting to control the temperature and humidity inside the electrospinning enclosure, and improving the ease with which scaffolds are removed from their mandrels through alternative mandrel surface treatments. In addition to overall process variability, the issue of scaffold shrinkage during BVM use was investigated and two possible treatments, exposure to either ethanol or elevated temperatures, were proposed based on previous electrospinning literature results. Each was tested for their effectiveness in mitigating shrinkage through exposure to BVM setup-mimicking conditions. It was found that both treatments reduced scaffold shrinkage compared to control samples when exposed to BVM setup-mimicking conditions. Finally, 3 flexible polymers were selected and electrospun to compare against typical PLGA results and to conduct a kink radius test as a metric for measuring flexibility as it pertains to the proposed BVM lab application. It was concluded that two types of thermoplastic polyurethane (tPU) were not acceptable electrospinning materials for use in the BVM lab. Additionally, while polycaprolactone (PCL) could be successfully electrospun it could not undergo the amount bending required for more tortuous BVM bioreactor designs without kinking. Overall, the work in this thesis provided insight into multiple scaffold characterization techniques, reduced overall electrospinning variability in the fabrication and use of PLGA scaffolds, and defined processing parameters that have been shown to yield scaffolds with smaller morphological features than all prior Tissue Engineering Lab work. By creating better, more effective scaffolds, researchers in the Tissue Engineering Lab can more accurately mimic the structure and properties of native blood vessels; this, in turn, will result in BVM cell responses that more closely resemble that of native tissue. Creating consistent and appropriate BVMs will then lead to impactful contributions to the existing body of tissue engineering research and to better preclinical device testing.

This work is focused on extruded fiber diameter measurement problem. For this purpose a procedure has been proposed. This procedure makes use of numerical methods for image processing, which are described in theoretical part of work. The proposed procedure has been processed into single-purpose software and in the final part is assessed its repeatability and reproducibility.

The content of this work is the analysis of retinal vessels pulsation of video sequences acquired by experimental fundus camera based on measuring the brightness profile of the vessel. The first level of analysis in this work is the segmentation of blood vessels and diameter measurement of blood vessels during the sequence. The work contains research methods dealing with the diameter measurement and evaluation of pulsation and analysis segmentation methods using for analysing the vasculature of the retina. From these methods, a vessel tracking method was selected. In segmented video sequences is on the ground of intensity profiles analysed vessel pulsation. Analysis is also made on original dataset and results are discussed considering the frequency characteristic.

In this thesis was presented Nové Heřminovy dam with basic parameters. Requirements on bottom outlets and intake objects are presented as well. Analysis of used valves on all dams in Czech Republic was done as an underlay for suggestions of bottom outlets in this thesis. The main task was to suggest three variations of bottom outlets. Differences are in number of outlets, dimensions, placing and valves. Then variation of intake objects. Each of variation was verbally described and filled with calculations.

Three-dimensional fibrillar networks reconstituted from collagen I are widely used as biomimetic scaffolds for in vitro and in vivo cell studies. Various physicochemical parameters of buffer conditions for in vitro fibril formation are well known, including pH-value, ion concentrations and temperature. However, there is a lack of a detailed understanding of reconstituting well-defined 3D network topologies, which is required to mimic specific properties of the native extracellular matrix. We screened a wide range of relevant physicochemical buffer conditions and characterized the topology of the reconstituted 3D networks in terms of mean pore size and fibril diameter. A congruent analysis of fibril formation kinetics by turbidimetry revealed the adjustment of the lateral growth phase of fibrils by buffer conditions to be key in the determination of pore size and fibril diameter of the networks. Although the kinetics of nucleation and linear growth phase were affected by buffer conditions as well, network topology was independent of those two growth phases. Overall, the results of our study provide necessary insights into how to engineer 3D collagen matrices with an independent control over topology parameters, in order to mimic in vivo tissues in in vitro experiments and tissue engineering applications.

No description available.

A graph $$G$$G is diameter 2-critical if its diameter is two and the deletion of any edge increases the diameter. Murty and Simon conjectured that the number of edges in a diameter-2-critical graph G of order n is at most ⌊n2/4⌋ and that the extremal graphs are the complete bipartite graphs K⌊n/2⌋,⌈n/2⌉. We survey the progress made to date on this conjecture, concentrating mainly on recent results developed from associating the conjecture to an equivalent one involving total domination.

A graph G is diameter 2-critical if its diameter is two and the deletion of any edge increases the diameter. Murty and Simon conjectured that the number of edges in a diameter 2-critical graph of order n is at most n2/4 and that the extremal graphs are complete bipartite graphs with equal size partite sets. We use an important association with total domination to prove the conjecture for the graphs whose complements have vertex connectivity k for k∈1,2,3.