(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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In particular, the reconstruction of one lobe of the thyroid \ gland is considered. The output sought, besides the visualization of the \ organ in space, is the approximation of the functional and morphological \ volume of the organ; this value is also taken as the approximation of the \ vascularization volume. \ \>", "Abstract"], Cell["\<\ Blood vessels in the human body have complex branching structures \ and recent studies indicate that they are likely to have a fractal element in \ their aggregation. In this work, we initiate a study of the possibility for \ recreating the geometry of the thyroid arteries. By employing an angiographic \ image, showing the entire profile of one thyroid lobe, we analyze the \ feasibility of identifying its arterial reticule. An image analysis approach \ is followed for studying the fractal nature of the thyroid arterial tree \ geometry. The aim is to understand whether it is practicable to model the \ lobe vascular framework, in such a way that it represents the correct \ anatomical network, on which to design an organ that maintains the \ morphological and physiological features of the thyroid gland. \ \>", \ "Abstract"], Cell[TextData[{ "We will discuss the features of ", StyleBox["Mathematica", FontSlant->"Italic"], " that are useful in modeling each phase of the problem considered: image \ data acquisition, analysis and visualization. ", StyleBox["Mathematica ", FontSlant->"Italic"], "represents an ideal framework for the creation of prototypal procedures \ and the development of new algorithms, as it is now fast enough for 2D and 3D \ image analysis. The symbolic and numeric capabilities of ", StyleBox["Mathematica", FontSlant->"Italic"], " are exploited, together with its facilities for importing and rendering \ image data of various origin, as well as for data approximation. Image \ processing and graphical tools are also employed, for the shape analysis and \ reconstruction." }], "Abstract"], Cell[TextData[{ StyleBox["Keywords:", FontWeight->"Bold"], " ", StyleBox["edge detection; data approximation; volume estimation; \ vascularization volume; fractal branching model.", FontSlant->"Italic"] }], "Text"], Cell[CellGroupData[{ Cell["1. Introduction", "Section"], Cell[TextData[{ "A single echographic, scintigraphic or angiographic image of one lobe of \ the thyroid gland is considered. The focus is on patients affected by a \ particular pathology of the thyroid, namely the ", StyleBox["Plummer's nodule. ", FontSlant->"Italic"], "The ideas that will be pursued in this work, in the tridimensional \ treatment of the lobe, can be applied to other human glands and organs, as \ long as their morphology is similar to that of the thyroid. " }], "Text"], Cell["\<\ Currently the volume of a thyroid is estimated as half the volume \ of a parallelepiped, using the measures of its three axes as provided by the \ echographer. Aside from the tridimensional visualization of the thyroid \ lobe, the scope is to provide a numerical approximation to the lobe volume \ that is more accurate than the current way of estimating it \ [Spaletta:2004].\ \>", "Text"], Cell["\<\ Through the tridimensional information obtained, the aim is to \ perform both a functional and morphological analysis of lobes affected by the \ Plummer's nodule, to establish such a pathology with the least invasive and \ expensive examination.\ \>", "Text"], Cell["\<\ There exists a relation between the occurrence of the Plummer's \ pathology and the vascularization of one lobe. It is thus important to \ identify its arterial reticule and to design a model for the thyroid arterial \ tree geometry. Our study, currently at an initial state, follows a fractal \ branching approach, to reproduce the lobe vascular framework. In doing so, \ the aim is to preserve the morphological and physiological features of the \ thyroid gland.\ \>", "Text"], Cell["\<\ This paper is organized as follows. The medical problem is \ explained in \[Section] 2, in which details of the morphology and functions \ of the thyroid gland are given. The numerical model and solution method are \ described in \[Section] 3, containing an outline of the procedures for the \ data collection and approximation, as well as the volume evaluation and the \ tridimensional visualization techniques [Gray:1998], [Gonzalez:2002]; a \ numerical example is given in \[Section] 4. A variation of the proposed \ method, in the case of two input images, is outlined in \[Section] 5. The \ current research, on the fractal branching modelling of the thyroid arterial \ system, is briefly illustrated in \[Section] 6. Some conclusions are drawn in \ \[Section] 7.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["2. Thyroidal Morphology and Function", "Section"], Cell["\<\ The thyroid is the biggest gland in the neck, situated in the \ anterior neck, below the skin and muscle layers. 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