MCM 1998 Problem A2011

# MCM 1998 Problem A2011 - A Scanner Problem MCM 1998 PROBLEM...

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2/8/2011 1 A Scanner Problem MCM 1998 PROBLEM A MRI MACHINE

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2/8/2011 2 MRI IMAGES INTRODUCTION ´ Industrial and medical diagnostic machines known as Magnetic Resonance Imagers (MRI) scan a three-dimensional object, such as a brain, and deliver their results in the form of a three-dimensional array of pixels. ´ Each pixel consists of one number, indicating a color or a shade of gray that encodes a measure of water concentration in a small region of the scanned object.
2/8/2011 3 PIXEL INTENSITY LEVELS ´ For instance, 0 can picture high water concentration in black (ventricles, blood vessels) ´ 128 can picture a medium water concentration in gray (brain nuclei and gray matter) 255 can pict re a lo ater densit ´ 255 can picture a low water density in white SLICES AVAILABLE ´ Such MRI scanners also include facilities to picture on a screen any horizontal or vertical slice through the three-dimensional array (slices are parallel to any of the three Cartesian coordinate axes). ´ Animation travels from head to toe in 135 transverse sections (X-Y).

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2/8/2011 4 OBLIQUE PLANES ´ Algorithms for picturing slices through oblique planes, however, are proprietary. Reiter syndrome. MRI with spin echo sequence in an oblique plane parallel to the aorta shows mild ectasia in the aortic arch and a normal descending aorta. Sagittal, oblique, T1-weighted MRI through the right orbit shows the hyperintense subretinal fluid ( arrow ).
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