Contents. X-ray and Computed Tomography. Characterization of X-rays. Production of X-rays

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J. E. Wilhjelm Ørsted• D TU T echnical Univ er sit y of Denmark, Bldg. 34 8, DK-2800 Kon gens Lyngb y, Denmark.

X-ray and Computed

Tomography

Ted Meyer: Structural Abnormalities (1992).Oil on canvas, 3' by 4'.

Contents

History and characterization of X-rays

Conventional (projection) X-ray

Attenuation, contrast and resolution

(Fluoroscopy and examples)

CT scanning

Principle

Image reconstruction

Image presentation techniques

Examples of images from the VH project

Key points of history of X-ray

1895 Wilhelm Conrad Röntgen discovered X-ray

1896 After being public, X-rays were all over the world within weeks 1896 GE and Siemens begins selling X-ray equipment

1896 Fluoroscopy appears

1904 Hazards of radiation is described 1924 Introduction of "tolerance dose"

1925 The meeting where they could not eat meat 1956 First reconstruction algorithm

1958 First model CT scanner without computer 1968 Hounsfield's method for CT patented

1972 Hounsfield's method for CT demonstrated in the US 1989 First spiral CT scanner enters the market

The effect of ignoring what can't be seen

Mihran K. Kassbian (1870-1910) and his X-ray dermatitis hands. Courtesy of the American College of Radiology.

Characterization of X-rays

Electromagnetic radiation (photons)

10 pm <

λ

< 10 nm

c

0

= 300 000 km/s

ν

=

c

0/

λ

[Hz]

Ionizing

The energy of the individual photon:

E

=

h

ν

[J],

where

Planck's number, h

= 6.62

⋅

10

-34

Js

Production of X-rays

e

-M

eta

l

Photon

0 20 40 60 80 100 Re la tiv e i nte ns ity

Photon energy (keV) Bremsstrahlung Bremsestråling Characteristic radiation

High kinetic

energy

_Electron's energy loss Electrons moving from one shell to another

(2)

Electron volts

1 eV is the energy increase that an

electron experiences, when accelerated

over a potential difference of 1 V.

1 eV =

q

e

Δ

V = 1.6

⋅

10

-19

J

In medical imaging:

20 keV <

E

< 150 keV

μ

- problem

Calculate the frequency and energy for

monochromatic x-rays with

λ

= 1 nm

Answer:

ν =

E

=

Contents

Conventional (projection) X-ray

Fluoroscopy and examples

CT scanning

Principle

X-ray tube with rotating anode

Cathode Anode Anode

(20 - 150 kV)

Stator

Fokus Vacuum

Al-filter (removes low energy radiation) Secondary radiation (Compton scattering) Object Screens (skærme) Film Protective shield of lead Collimator (Primærblænde) Grid (sekundærblænde) X-ray tube (røntgenrør)

Principle of X-ray system

Primary radiation (fotoelectric absorption) Exposure: milliseconds to a few seconds 20 - 150 kV

Lambert-Beer's law

for monocromatic radiation

I = I

0

exp(-

μ

l

l)

I

0

I

l

μ

l

μ

l

= linear attenuation coefficient (

μ

l

=

μ

l

(

ν

))

(3)

Attenuating material with inhomogeniety

(μ

- problem)

I

0

I

0

I

0

l

1

l

3

l

2

μ

2

μ

1

I

2

=

I

1

=

I

3

=

Film

Now write

I

1

relative to

I

2

and

I

3

I

1

/ I

2

=

exp((

μ

2

-

μ

1

)

l

2

)

I

1

/ I

3

=

exp(

μ

1

l

3

)

Define contrast as

K =

(

I

1

- I

2

)

/

(

I

1

+ I

2

)

Example:

K >

0.03

gives

I

1

/

I

2

> 1.06

Using the same argument for

I

1

and

I

3

gives that

l

Δμ

1

> 0.06 or

μ

1

Δ

l

> 0.06

must be fulfilled to see a difference on the film.

0 0.5

1 K

0,5 1 2 4 lp/mm

Modulation transfer function

X-ray tube P b "r as ter "

Contents

Conventional (projection) X-ray

Fluoroscopy and examples

CT scanning

Principle

Invention of Computed Tomograhpy

abbreviated CT or CAT

1972: G.N. Hounsfield, scientist in Middlesex, England

Announced computed axial transverse scanning

Presented cross-sectional images of the head showing tissues inside the brain as separate structures of gray matter, white matter, CSF, and bone

Pathologic processes such as blood clots, tumors, and infarcts could be easily seen

Dr. Hounsfield's discovery completely revolutionized the practice of medicine: Structures inside the human body that had never been imaged before, could now be visualized.

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Development of computed tomograhpy

Acquisition speed:

In the early 70's: Several minutes to acquire a single slice through the brain.

Today: The newest scanners can image the entire body in 1 to 2 minutes.

Basic principle of computed tomograhpy

(algebraic reconstruction)

μ

11

μ

12

μ

21

μ

22

I

0

I

0

I

0

I

0

I

r1

= I

0

exp(

-

μ

11

l -

μ

12

l

)

I

r2

= I

0

exp(

-

μ

21

l -

μ

22

l

)

I

c1

= I

0

exp(

-

μ

11

l -

μ

21

l

)

I

c2

= I

0

exp(

-

μ

12

l -

μ

22

l

)

Recording scheme for CT scanning

R

D

Atten

uatio

n

Note: We actually record intensity, so curve should be inverse

Recording scheme for CT scanning

R D A ttenu at ion

R

D

Attenua tion

μ μ

(5)

(assuming 128 lines)

Either

128 equations with 128 unknowns

1. Problems with noise 2. Huge calculation times

or

Linear superposition of filtered back projections (LSFBP)

Imaging a point target

R

D

μ

Imaging a point target

R

D

μ

Back projection - point target

μ

The resulting image

Distance

Explaining the process

in terms of a transfer function

H

(6)

f r g r

*

Pre-filtering

(before back projection)

Show Matlab demo

Measured signal

"Inverse impulse response"

Some questions to Matlab demo

What do we see on the thorax image?

What is the orientation of this image?

R R

X-ray source and

detectors rotate

X-ray source rotate, but

detectors are stationary

Different implementations

CT Spiral Scanner

CT Images based on

The Visible Human Project

(Show movie)

What can be seen on the CT images?

(7)

Anatomical photograph

CT image

What can be seen on the CT images?

Anatomical photograph

CT image

Advantages - disadvantages

(Tomography)

Advantages:

Can image the entire body

Disadvantages:

Ionizing radiation Equipment is expensive

Expensive in acquisition and use Not good in distinguishing soft tissues