Physics of Imaging Systems Basic Principles of Computer ...

RUPRECHT-KARLSUNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad 10/30/2015 | Page 1

Master‘s Program in Medical Physics

Physics of Imaging Systems Basic Principles of Computer Tomography (CT) I Prof. Dr. Lothar Schad

Chair in Computer Assisted Clinical Medicine Faculty of Medicine Mannheim University of Heidelberg Theodor-Kutzer-Ufer 1-3 D-68167 Mannheim, Germany [email protected] www.ma.uni-heidelberg.de/inst/cbtm/ckm/


Literature I

Dance et al.: “Diagnostic Radiology Physics” Publisher: International Atomic Energy Agency http://www-pub.iaea.org/books/IAEABooks/8841/ Diagnostic-Radiology-Physics-A-Handbook-forTeachers-and-Students Free download !!!

Seite 1 1


Literature II

Kalender: “Computertomographie. Grundlagen, Gerätetechnologie, Bildqualität, Anwendungen”, 2006


Literature III

Dössel: “Bildgebende Verfahren in der Medizin”, Chapter 4, 2000

Seite 2 2


Computer Tomography Introduction

Computer Tomography Introduction


Literature

source: Kalender. Computertomographie, Publicis MCD Verlag 2000

Seite 3 3


Mean Effective Dose per Head in 1997

nuclear diagnostic

radon with derivates other radiation sources (nuclear wappons & fallout, Tschernobyl reactor accident, nuclear units, science, technic, household) food

X-ray diagnostic

terrestic radiation cosmic radiation at see level

Regulla et al. ZMP 2003


Radiodiagnostic Examinations in 1997 percentage of typical radiodiagnostic examinations to the collective effective dose and their frequency

collective effective dose

thorax skeletal esophagus uretic system Mammography angiography CT else

incidence

Regulla et al. ZMP 2003

Seite 4 4


Visionary Idea in 1896

„Und läßt man der Phantasie weiter die Zügel schießen, stellt man sich vor, daß es gelingen würde, die neue Methode des photographischen Prozesses mit Hilfe der Strahlen aus den Crookeschen Röhren so zu vervollkommnen, daß nur eine Partie der Weichteile des menschlichen Körpers durchsichtig bleibt, eine tiefer liegende Schicht aber auf der Platte fixiert werden kann, so wäre ein unschätzbarer Behelf für die Diagnose zahlloser anderer Krankheitsgruppen als die Knochen gewonnen.“

Frankfurter Zeitung, 7. Januar 1896



CT History

Seite 5 5


Computer Tomography 1973

original EMI CT head scanner 1973 (Mayo Clinic, Rochester, USA) and 80 x 80 matrix head CT image obtained with it source: Gray and Orton. Radiology 2000


Brain Image 1974, Matrix 80 x 80


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Historical Question …

in the early years of CT, an often-heard remark was „ Why would anyone want a new X-ray technique that when compared with traditional X-ray imaging: • yields

10 times more coarse spatial resolution

• is 1/100 as fast in collecting image data • costs 10 times more “

Hendee and Ritenour. Medical Imaging Physics, 4th ed. Wiley, 2002


… and Answer ! Ct volume data set, matrix 1024 × 1024


Seite 7 7


X-Ray and CT Contrast



Why Cross-Sections ?

1. no superposition → higher contrast 2. three-dimensional localization

Seite 8 8


CT Contrast

CT image

X-ray image

high local contrast of soft tissue structure

low soft tissue contrast due to superimposed bone



Computer Tomography Principle

Computer Tomography Principle

Seite 9 9


CT Measurement: Principle I

- gives system of equations for each projection - generate enough projections to solve system of equations


CT Measurement: Principle II

case 1: homogeneous object, monochromatic radiation

- intensity of X-ray radiation can be used to calculate the attenuation- or projection-value P which can lead to the absorption coefficient µ in a simple case (homogeneous object) - µ can not be calculated in inhomogeneous objects since µ is a function of (x, y) → tomographic method !

case 2: inhomogeneous object, monochromatic radiation

case 3: inhomogeneous object, polychromatic radiation


Seite 10 10


CT Measurement: Principle III

X-ray tube collimator detector with electronic collimator

intensity profile

attenuation profile = “projection”

in the simplest case object is scanned linearly by a needle beam at different angles to determine the attenuation profile source: Kalender. Computertomographie, Publicis MCD Verlag 2000


CT Measurement: Principle IV

algebraic reconstruction technique (ART)


Seite 11 11


CT Image Reconstruction and Convolution

X-ray tube

without convolution

back projection

with convolution

collimator collimator detector with electronic

attenuation profile (simplified)

- corresponds to high pass filter

profile cut source: Kalender. Computertomographie, Publicis MCD Verlag 2000


Hounsfield Values

definition CT-value: CT-values contain the linear absorption coefficients of the underlying tissue in every volume element with respect to the µ-value of water. Using this definition the CT-values of different organs are relatively stable and independent of the X-ray spectrum.

CT-value = (µ - µwater) / µwater x 1000 HU

Seite 12 12


Hounsfield Scale compact bone

CT-number [HU]

liver blood pancreas

spongy bone water

kidney

fat

lung

air

4096 values → 212 → 12 Bit source: Kalender. Computertomographie, Publicis MCD Verlag 2000


CT Windowing

CT-number [HU]

bone window

- windowing of Hounsfield values at different evaluations of CT images mediastinum window

- human eye can distinguish only 60-80 grey values !

lung window


Seite 13 13


Radon Transformation I

Θ = 0 - 180° s = smin - smax

source: Dössel. “Bildgebende Verfahren in der Medizin” 2000


Radon Transformation II

p(Θ,s)-diagram projection pΘ(s) = series of numbers of all line integrals of f(x,y) at constant angle Θ and variable distance s to the coordinate origin


Seite 14 14


Radon Transformation: Example

inside outside

radius of area



Fourier-Slice-Theorem I

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Fourier-Slice-Theorem II

- given is a function f(x,y) an its 2D Fourier transformation F(u,v) f(x,y)

2D-FT

F(u,v)

- given is also pΘ(s) defined as a projection of f(x,y) (i.e. a line of the Radon transformation with Θ = const.) and PΘ(w) its 1D Fourier transformation pΘ(s)

1D-FT

PΘ(w)

- then PΘ(w) describes the values of F(u,v) on a radial beam at angle Θ - how to get from the Radon transformation p(Θ,s) back to the function f(x,y) ? • evaluate from all projections pΘ(s) the 1D Fourier transformation PΘ(w) • take the values of the radial beam at Θ and put them into the function F(u,v) • find f(x,y) by doing the inverse 2D Fourier transformation


X-Ray Pencil Beam Through a Body

incoming X-ray intensity outgoing X-ray intensity X-ray absorption coefficient

Seite 16 16


CT Reconstruction Principle I - idea of backprojection: transform measured µ-values into “line thickness” for all projections and add up !

y

x

in the order of 1000 projections with 1000 channels are acquired per detector slice and rotation

y

courtesy: Kachelriess, Erlangen

x


CT Reconstruction Principle II

- wanted:

function µ(x,y) „X-ray absorption coefficient as a function of (x,y) in a body slice“

- measured:

all line integrals over µ(x,y) i.e. Radon transformation of the wanted function µ(x,y)

- generation of images: Fourier reconstruction • measurement of as many as possible projections with a large number of points (pΘ(s)) projections pΘ(s) are 1D Fourier transformed into (PΘ(w)) • transformed projections are recorded in a matrix F(u,v) problem: interpolation between known values on radial beams and required values on a cartesian grid (F(u,v) complex) • multiplication of F(u,v) with a filter function • inverse 2D Fourier transformation

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RUPRECHT-KARLSUNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad

CT Sinogram I

absorption µ

10/30/2015 | Page 35

x


CT Sinogram II

sinogram = sum of all projections

- sinogram: = sum of all projections = “Radon transformation” of µ(x,y) - absorption strength = brightness

scanning distance x

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CT: Back Projection

CT image

sinogram

reconstruction: back projection


CT: Filtering

sinogram

filtered sinogram

filtering

filter kernel

convolution kernel

unfiltered profile

= filtered profile

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RUPRECHT-KARLSUNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad

CT: Filtered Back Projection

10/30/2015 | Page 39

CT image

filtered sinogram

reconstruction: filtered back projection


Unfiltered and Filtered Projections

measurement

unfiltered back projection of one measurement

unfiltered back projection of all measurements

measurement

filtered back projection of one measurement

filtered back projection of all measurements


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CT: Projections and Filtered Projections

inverse Fourier transformation of

summing up all filtered projections source: Dössel. “Bildgebende Verfahren in der Medizin”, 2000


CT: Filtered Back Projection Principle

• filtering of all measured projections pΘ(s) with |w| gives ~ pΘ(s) • following all filtered projections ~ pΘ(s) with respect to Θ for the whole matrix and adding up all values of the filtered projections into the imaging matrix


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Filter Functions I - filter limiting:

- filter functions cernel from:

even, ≠ 0 odd

a = detector distance

filter functions H(w) source: Dössel. “Bildgebende Verfahren in der Medizin” 2000


Filter Functions II


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CT: Iterative Reconstruction

pencil beam j

- unknown: 512x512 = 262 144 pixel

- measured: 1000 projections with 800 detectors = 800 000 equations

part of area wij

→ can be algebraic solved !



CT: Iterative Reconstruction Solution • processing of 1. projection data value is distributed in equal shares to involved projection pixels • processing of 2. projection difference between “forward calculated data values” and really measured values is used for correction in equal shares to involved projection pixels • processing of all other projections in the same way about 1h calculation time for 512 x 512 ! source: Dössel. “Bildgebende Verfahren in der Medizin” 2000

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CT Scanner Generations 1-2

II.

I. CT scanner 1. generation pencil beam (1970)

CT scanner 2. generation partly fan beam (1975) 30 detectors, fan: 10°



CT Scanner Generation 1: EMI-Scanner

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CT Scanner Generation 2 multi-detector-translational-rotating system


CT Scanner Generation 3 CT scanner 3. generation fan beam (1976) 500 – 800 detectors fan: 40° - 60° (whole body) 1000 projections / sec but cable problems: 360° forward rotation stop 360° backward rotation stop …

rotating detector arch

III. rotation without translation

souirce: Kalender. Computertomographie, Publicis MCD Verlag 2000

Seite 25 25


CT 3. Generation: Collimation fan beam scanner

trajectory of X-ray tube

collimator lamellae


CT Scanner Generation 3: Principle tube 0°

tube beam at tube 180°

rotation

beam at tube 0°

detectors

III.

tube 180° beam at tube 180° and 0°

„jumping focus“


Seite 26 26


CT Scanner Generation 3: Jumping Focus

C cathode B

C

anode

cooling oil

straton tube courtesy: Kachelriess, Erlangen


III.

CT Scanner Generation 3-4

fancy beam unit

IV.

ring detector unit

rotation axis collimator lamellae

Xe-chamber

electrodes rotating detector arch (Xe high-pressure chamber)

fix detector arch (scintillators)

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CT Scanner Generation 4

fix detector ring

CT scanner 4. generation fan beam up to 5000 detectors problem: no collimation possible very high scatter radiation very expensive

IV.



CT Scanner Generation 3-4

“Mayo – Monster”

Seite 28 28


Typical CT Examination Room



Contact Ring Technique

X-ray tube

detector detector electronic

high voltage

projection data

schematic illustration of the contact ring technique for electric energy supply of the X-ray components and for signal transfer from the detectors to computer souirce: Kalender. Computertomographie, Publicis MCD Verlag 2000

Seite 29 29


Contact Ring Mounting and Testing



CT Components Geometry

X-ray tube form filter fix aperture adjustable aperture

gantry opening

field-of-view

rotation center

scatter radiation collimator

adjustable aperture

detector array

fix aperture


Seite 30 30


Subsecond CT

1 sec. rotation time

0.5 sec. rotation time

- mechanic forces: acceleration ~ 10-20 g, X-ray tube ~ 200 kg → 20-40 000 N ! - mechanic stability: 0.1 mm !

Seite 31 31

Physics of Imaging Systems Basic Principles of Computer ...

Physics of Imaging Systems Basic Principles of Computer ...

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