CT Image Formation and Reconstruction Lecture PDF

CT: IMAGE FORMATION AND RECONSTRUCTION Dr. Anastasia Hadjiconstanti Acknowledgements: Dr. Constantinos Zervides LECTURE LOB’S 35. EXPLAIN CT IMAGE FORMATION PRINCIPLES. 36. EXPLAIN CT IMAGE RECONSTRUCTION. INTRODUCTION I Computed tomography (CT) is a volumetric imaging modality based on X-ray absorp...

CT: IMAGE FORMATION AND RECONSTRUCTION Dr. Anastasia Hadjiconstanti Acknowledgements: Dr. Constantinos Zervides LECTURE LOB’S 35. EXPLAIN CT IMAGE FORMATION PRINCIPLES. 36. EXPLAIN CT IMAGE RECONSTRUCTION. INTRODUCTION I Computed tomography (CT) is a volumetric imaging modality based on X-ray absorption. CT was introduced to medicine in the early 1970s. CT allows the reconstruction of a two or three-dimensional absorber map. CT vastly exceeds projection X-ray imaging in soft tissue contrast. However, the spatial resolution of a clinical CT scanner is significantly lower than that of plain X-ray imaging. CT was invented by Sir Godfrey Hounsfield who received the Nobel Prize in medicine in 1979. INTRODUCTION II INTRODUCTION III The first clinical CT scan on a patient took place on 1st October 1971 at Atkinson Morley's Hospital, in London, England. INTRODUCTION IV It is the first imaging modality where the computer is essential in the image reconstruction. Since the introduction of the first CT scanners, major progress has been made. Modern clinical CT scanners are very fast and can produce a 2D cross-sectional image in less than a second. Clinical CT scanners are expensive, ranging in the millions. This translates into a relatively high cost per CT scan. DATA ACQUISITION I In a projection image, such as a standard X-ray projection image, the exact location of an area of interest, cannot be determined. For this reason, radiologists often take two perpendicular projections (e.g., lateral and AP = anterior—posterior). DATA ACQUISITION II Data acquisition refers to the collection of X-ray transmission measurements through the patient. It requires an X-ray source which is collimated into the shape of a fan or cone. One possible geometry for CT scanner source and detectors: Both the source and arc-shaped detector array rotate in tandem, recording projections through a single plane within the body for many different angles. DATA ACQUISITION III How does a CT scan work https://youtu.be/l9swbAtRRbg DATA ACQUISITION IV When an X-ray beam passes through an object some of the photons are absorbed or scattered. The reduction of X-ray transmission (attenuation), depends on: the atomic composition of the crossed tissues, density of the crossed tissues, the energy of the photons. After passing through an object the partially attenuated X-rays are collected by X-ray detectors on the opposite side. DATA ACQUISITION V They are then converted from X-ray photons to electrical signals. These signals are then converted into digital data, after which the attenuation value is calculated. While the X-ray tube and detectors rotate around the patient, many projections are collected from consecutive angular orientations. DATA ACQUISITION VI Filtered back projection method DATA ACQUISITION VI Filtered back projection method IMAGE FORMATION I The aim of CT is to obtain a spatially resolved map of absorption coefficients in one slice of the patient’s body. Such a map, if sampled at a finite resolution, provides an image. To understand the mathematical foundations behind image reconstruction in CT consider the following image. IMAGE FORMATION II We can obtain four different projections and determine the overall attenuation (attenuated beams I1 ,I2, I4 ,I5). Since each projection follows Lambert Beer’s law, we obtain a linear equation system that we can solve for μ1, μ2, μ4, μ5. 𝐼1 = 𝐼0 𝑒𝑥𝑝(−𝜇1 𝑑−𝜇2 𝑑) 𝐼2 = 𝐼0 𝑒𝑥𝑝(−𝜇4 𝑑−𝜇5 𝑑) 𝐼4 = 𝐼0 𝑒𝑥𝑝(−𝜇1 𝑑−𝜇4 𝑑) 𝐼5 = 𝐼0 𝑒𝑥𝑝(−𝜇2 𝑑−𝜇5 𝑑) This simple equation system can only be solved when one of the absorption coefficients is known. IMAGE FORMATION III An arbitrary object, composed of n-by-n different materials requires n2 independent equations. To solve this more projections are taken at different angles. In fact, methods exist to solve a linear equation system of the type seen previously. IMAGE RECONSTRUCTION I The reconstruction of images from the X-ray measurements involves the steps shown. In today’s CT systems a convolution-back projection procedure is used. IMAGE RECONSTRUCTION II IMAGE RECONSTRUCTION III The selected ‘field of view’ is divided into small image elements, called pixels. The pixels that make up each cross-sectional image represent a small volume of tissue called a voxel (for volume element). For a tomographic axial image typically consisting of a matrix of 512 × 512 or 1024 × 1024 voxels, this means that over 260,000 or 1 million, respectively, grayscale values must be stored for each cross-sectional image. IMAGE RECONSTRUCTION IV Low- (left) and high- (right) resolution cross-sectional images of the brain. Individual pixels are evident on the older, low-resolution image, but less apparent in the more modern, higher-resolution image. IMAGE RECONSTRUCTION V The density value of each pixel depends on the composition of the tissue it represents and is expressed in Hounsfield units (HU). THE HOUNSFIELD UNITS ARE CALCULATED FROM THE ATTENUATION MEASUREMENTS RELATIVE TO THE ATTENUATION OF WATER. They range from –1024 to +3071 HU. IMAGE RECONSTRUCTION VI IMAGE RECONSTRUCTION VII IMAGE RECONSTRUCTION VIII https://youtu.be/D7m6T1pusbs SUMMARY I Computed tomography (CT) is a volumetric imaging modality based on X ray absorption. CT allows the reconstruction of a two or three-dimensional absorber map. CT was invented by Sir Godfrey Hounsfield at the laboratories of EMI Limited. Data acquisition refers to the collection of X-ray transmission measurements through the patient. It requires an X-ray source that produces an X-ray beam, which is collimated into the shape of a fan or cone. The aim of CT is to obtain a spatially resolved map of absorption coefficients in one slice of the patient’s body. SUMMARY II Such a map, if sampled at a finite resolution, provides an image. The reconstruction of images from the X-ray measurements involves various steps. The result is a two-dimensional matrix of preselected size and detail. REFERENCES Authors Title Edition Publisher Year ISBN E. Seeram Computed Tomography: Physical Principles, Clinical Applications, and Quality Control 4th Edition Saunders 2015 9780323312882 Medical Imaging and Radiation C. Martin, P. Dendy and Protection for Medical Students and R. Corbertt Clinical Staff 2nd Edition The British Institute 2014 of Radiology 9780905749549 M.A. Haidekker Medical Imaging Technology 1st Edition Springer 2013 9781461470724 A.B. Wolbarst, P. Capasso and A.R. Wyant Medical Imaging: Essentials for Physicians 1st Edition Wiley-Blackwell 2013 9780470505700 L.E. Romans Computed Tomography for Technologists: A Comprehensive Text Wollters Kluwer Health / Lippincott 2010 Williams & Wilkins 9780781777513 st 1 Edition