The essentials of Computed Tomography and its application in cardiac imaging

Term Paper, 2011

15 Pages, Grade: 1,3




1. Introduction

2. Computed Tomography
2.1. X-rays (Roentgen rays)
2.2. Inverse Problem

3. Image Processing
3.1. Radon Transform
3.2. Fourier Transform
3.3. Filtered backprojection

4. Cardiac CT
4.1. ECG Triggering
4.2. Coronary CT Angiography


List of Figures


This paper introduces into the essentials of computed tomography and gives a brief lead-in to Cardiac CT, which is the clinical application of computed tomography in cardiac imaging. At first, the usage of X-rays is explained and the resulting main task of a CT scanner: The reconstruction of a three-dimensional image from the X-ray shadows, that are captured by the digital radiation detector unit. This reconstruction problem is known as the inverse problem in mathematics, which was initially solved by Johann Radon. Transferred to the field of computed tomography, the inverse problem means the definition of a volume dataset by reconstruction algorithms like for instance the Fourier Transform, which is shortly introduced, as well as the filtered backprojec- tion. The main issue of Cardiac CT is the steady movement of the heart and chest of an examined patient. To ensure high image quality the scanner is triggered by a concurrently recorded ECG. ECG Triggering can ensure that the scanner only captues images during the phases of the heartbeat, where movement is minimal. One major application of Cardiac CT is non-invasive coronary angiography, which possibly could substitute invasive diagnostic surgeries like cardiac catheterization of non-emergency patients.

1 Introduction

In 1895, Wilhelm Conrad Röntgen invented a new type of radiation, which enabled physicians to visualize the inner structure of the human body. Starting with this first approach to produce diagnostic images in medicine, scientists have been steadily working on the improvement of imaging technologies based on the so called X-rays. A computer tomograph produces X-ray images, from every position around the patient’s body. These recorded overlaying shadows, or projections from different angles have to be transformed into a slice, to get an image, that is interpretable by human beings.

In mathematics, this kind of reconstruction process is known as the inverse problem, which was primarily solved by Johann Radon in 1917. By capturing and computing many of these slices, a three dimensional model of the underlying body can be created, which provides a detailed view into the inside of the scanned tissue. “The invention of the [first] CT scanner in the late 1960s”[BS06, P. 1] is credited to Godfrey Hounsfield, which used a reconstruction algorithm based on “the mathematical fundaments pub- lished by Johann Radon”[OFB+06, P. 1], as also modern computer tomographs do today. The first working tomograph, “that could image the brain”[OFB+06, P. 1] was constructed by Hounsfield in 1971. One crucial difference between computed to- mography by former scanners and modern ones is the time that the scanner needs to provide an 3D image of certain parts of the body. In the early ages of computed tomography, namely “during the 1960s and 1970s”[Buz08, P. 1], scanning one single slice took several minutes, what also resulted in a very huge amount of radiation, the patient was exposed to. Nowadays, one of the main goals is, to keep the radiation exposure as low as possible, which can be achieved by a scan time around millisec- onds. Besides the general technical improvement of CT scanners, further applications of computed tomography have evolved. For instance the “introduction of the electron beam technology concept”[Sch04, P. 3], which was invented by Douglas Boyd in 1980 “moved CT into the realm of cardiac imaging.”[Sch04, P. 3]

In the past computed tomography was the first and only “method to non-invasively acquire images of the inside of the human body.”[Buz08, P. 1] Today it has become the main diagnostic technology in modern shock rooms, where it is used to get a fast overview of all injuries, an emergency trauma patient has suffered. But not only in case of emergency, computer tomographs are the first choice, also in cases where magnetic resonance imaging is not applicable, because for example the “object to be examined is dehydrated.”[Buz08, P. 2]

2 Computed Tomography

2.1. X-rays (Roentgen rays)

Computer tomographs work with X-rays, that are produced by an X-ray generator, or X-ray tube. In this generator, electrons are accelerated from a cathode by high voltage. The electrons travel through a vacuum and are decelerated very fast by hitting a rotating anode disc, whereby different kinds of radioation are emitted, including X- rays. Through a small opening, the radiation is sent out directed towards the patient. After crossing the body, the X-rays encounter a detector, which is located at the opposite side.

illustration not visible in this excerpt

Figure 2.1.: Schematic drawing of an X-ray tube. [Buz08, Fig. 2.1.]

One crucial reason “for the wide exploitation of Röntgen’s radiation”[Buz08, P. 15] was, that the generation as well as the detection of X-rays is very easy and can be achieved by quite “simple equipment.”[Buz08, P. 15]

2.2. Inverse Problem

The tissues, which the X-rays go through, attenuate a certain amount of radiation, depending on their physical density. Bone structure for instance has a high density, so it appears in white or light grey, because the radiation is absorbed for the most part and only a marginal amount obtains the detector. Contrary to lungs that are full of air, which is visualized in dark grey or black. The amount of attenuation is measured in Hounsfield units (HU) typically at a range from -1000 to 5000. Consequently, to every type of tissue, a certain HU value can be determined, as listed in the Hounsfield Scala that is shown in figure 2.2.

illustration not visible in this excerpt

Figure 2.2.: Typical attenuation values of body structures and other objects, measured in Hounsfield units (HUs). [OFB+06, Fig. 1.4.]

illustration not visible in this excerpt

Figure 2.3.: Schematic illustration of computed tomography. [Buz08, Fig. 1.1.]

The CT scanner rotates around the patient to capture attenuation profiles from every perspective, or angle. Due to the f act that X-rays that cross a human body will of course successively cross many different types of tissue, the projection captured from one single perspective shows the summation of all the HU values of these tis- sues. The image, that is captured after one complete rotation shows the aggregated overlaying shadows of the scanned body, which leads to the “fundamental problem of computed tomography [. . . ]: [The] Reconstruct[ion of] an object from its shadows or, more precisely, from its projections”[Buz08, P. 2], which is formally known as the inverse problem in mathematics.

In the domain of CT this means, to reproduce the three dimensional slice of the body from the overlaying two dimensional X-ray shadows, like illustrated in figure 2.4. Contrary to conventional X-ray examination, in computed tomography the ra- diation is not captured on a photosensitive film, which is developed afterwards, but rather converted into electrical impulses by a digital detector unit. These impulses are collected and translated into a slice image by a computer. After each complete rotation the patient table is moved ahead, so that the scanner is able to take the next slice. The aggregate of all recorded slices is then computed into a volume dataset, which finally can be visualized three-dimensionally. In modern, so called spiral CTs, this table movement is continuous, so that the scanner does not capture single slices but one proceeding helical image, from which the three-dimensional volume dataset is calculated directly.

illustration not visible in this excerpt

Figure 2.4.: Schematic illustration of the inverse problem. [Buz08, Fig. 1.2.]


Excerpt out of 15 pages


The essentials of Computed Tomography and its application in cardiac imaging
University of Applied Sciences Ulm  (Informatik)
Medizinische Bildverarbeitung
Catalog Number
ISBN (eBook)
ISBN (Book)
File size
1681 KB
computertomographie, computed tomography, x-ray, ct, cardiac ct, ecg triggering, radon transform, radontransformation, fourier transform, fouriertransformation
Quote paper
B.Sc. Christian Brugger (Author), 2011, The essentials of Computed Tomography and its application in cardiac imaging, Munich, GRIN Verlag,


  • No comments yet.
Read the ebook
Title: The essentials of Computed Tomography and its application in cardiac imaging

Upload papers

Your term paper / thesis:

- Publication as eBook and book
- High royalties for the sales
- Completely free - with ISBN
- It only takes five minutes
- Every paper finds readers

Publish now - it's free