7 & 8 Computed Tomography

# X-Ray CT vs Projection X-Ray

# Introduction

CAT: Computed Axial Tomography, same as a CT

# Scanner Generations

First generation CT scanner

One detector

Pencil-like x-ray beam

Translate/rotate movements

Usually lasted 25-30min

Second generation CT scanner

2-30 detectors

Fan-shaped x-ray beam

Translate/rotate movements

Lasted less than 90 seconds

Third generation CT scanner

288 sometimes over 1k scanners

Fan-shaped x-ray beam

Rotate-rotate movement

Lasted only 5 seconds

Fourth generation CT scanner

More than 2k scanners

Fan-shaped x-ray beam

Rotate-fixed

Lasted only a few seconds

Spiral CT

Spiral x-ray rube and detector around the patient

Uses slip ring technology, brushes along the fixed part of the machine so that cables wouldn’t get wound up in the CT

# Data Measurement

The projection function sums the attenuation of the X-ray beam along line t in the s-direction

(perpendicular to the axis t).The one-dimensional Fourier Transform of the projection function at an angle θ , ( ) P t θ , can be

written asIf we take these projections at many angles, then we can get the 2D Fourier transform of the projections at many such lines inclined at various angles. If the number of angles is large enough, we will get many lines of 2D Fourier transforms of the object.

The most commonly used algorithm for actually reconstructing a medical image from projection data is the filtered backprojection algorithm

the magnitude of the filter increases with frequency (compensates for lack of data)

More projections yields an increase in the accurately of the reconstructed image (but it can increase radiation delivered to the patient)

The conventional way to image a 3D object is to use a 2D reconstruction algorithm on successive

planes, and stacking the planes. A more efficient method is to illuminate the object from a point

source, and the X-ray flux is measured on a plane.Cone Beam reconstruction: illuminate the object from a point source, and the X-ray flux is measured on a plane to create a 3D image

Measure signal intensity and convert to attenuation

Line integram: integral of mu as a function of time (negative natural log of I over I0)

## Sinogram

Forward projection: Generate the singogram from all line integrals stacked as a attenuation vs projection angel

The sinogram is a x’-Φplot of the projection data PΦ (X’)

0 to 180 degrees

Depicts how object(s) appear when viewed from different angles

Shows the shadows an object makes on the detector at an angle Φ

Shows the attenuation profile of the object at angle Φ

Shows the line integral at angle Φ

Can be used to estimate internal object structure (location, size, etc.)

# CT Image Reconstruction

Filters are used (convolution kernels) to smooth the attentuation profiile

More angles means more clear determining of objects in an image

The image produced is an array of density values

2D image is a 2D density matrix

3D image is a 3D density matrix

Matrix is numbers in Hounsfield units

Hounsfield units: Values calculated to represent the attenuation of differed substance of a diagnostic image

HU = 1000 x (initial mu - mu of water all divided by mu of water)

The HU of water is zero

CT number is proportional to physical density, which produces contrast between different tissue types

# 7 & 8 Computed Tomography

# X-Ray CT vs Projection X-Ray

# Introduction

CAT: Computed Axial Tomography, same as a CT

# Scanner Generations

First generation CT scanner

One detector

Pencil-like x-ray beam

Translate/rotate movements

Usually lasted 25-30min

Second generation CT scanner

2-30 detectors

Fan-shaped x-ray beam

Translate/rotate movements

Lasted less than 90 seconds

Third generation CT scanner

288 sometimes over 1k scanners

Fan-shaped x-ray beam

Rotate-rotate movement

Lasted only 5 seconds

Fourth generation CT scanner

More than 2k scanners

Fan-shaped x-ray beam

Rotate-fixed

Lasted only a few seconds

Spiral CT

Spiral x-ray rube and detector around the patient

Uses slip ring technology, brushes along the fixed part of the machine so that cables wouldn’t get wound up in the CT

# Data Measurement

The projection function sums the attenuation of the X-ray beam along line t in the s-direction

(perpendicular to the axis t).The one-dimensional Fourier Transform of the projection function at an angle θ , ( ) P t θ , can be

written asIf we take these projections at many angles, then we can get the 2D Fourier transform of the projections at many such lines inclined at various angles. If the number of angles is large enough, we will get many lines of 2D Fourier transforms of the object.

The most commonly used algorithm for actually reconstructing a medical image from projection data is the filtered backprojection algorithm

the magnitude of the filter increases with frequency (compensates for lack of data)

More projections yields an increase in the accurately of the reconstructed image (but it can increase radiation delivered to the patient)

The conventional way to image a 3D object is to use a 2D reconstruction algorithm on successive

planes, and stacking the planes. A more efficient method is to illuminate the object from a point

source, and the X-ray flux is measured on a plane.Cone Beam reconstruction: illuminate the object from a point source, and the X-ray flux is measured on a plane to create a 3D image

Measure signal intensity and convert to attenuation

Line integram: integral of mu as a function of time (negative natural log of I over I0)

## Sinogram

Forward projection: Generate the singogram from all line integrals stacked as a attenuation vs projection angel

The sinogram is a x’-Φplot of the projection data PΦ (X’)

0 to 180 degrees

Depicts how object(s) appear when viewed from different angles

Shows the shadows an object makes on the detector at an angle Φ

Shows the attenuation profile of the object at angle Φ

Shows the line integral at angle Φ

Can be used to estimate internal object structure (location, size, etc.)

# CT Image Reconstruction

Filters are used (convolution kernels) to smooth the attentuation profiile

More angles means more clear determining of objects in an image

The image produced is an array of density values

2D image is a 2D density matrix

3D image is a 3D density matrix

Matrix is numbers in Hounsfield units

Hounsfield units: Values calculated to represent the attenuation of differed substance of a diagnostic image

HU = 1000 x (initial mu - mu of water all divided by mu of water)

The HU of water is zero

CT number is proportional to physical density, which produces contrast between different tissue types