Introduction to Biomedical Imaging

Alejandro Frangi, PhDComputational Imaging Lab

Department of Information & Communication TechnologyPompeu Fabra University

www.cilab.upf.edu

Introduction to Biomedical Imaging

X-ray Projection ImagingComputed TomographyDigital X-ray Imaging

Introduction to Biomedical Imaging

The electromagnetic spectrum

Introduction to Biomedical Imaging

Projection radiography

SystemsChest X-rays, mammographyDental X-raysFluoroscopy, angiography

PropertiesHigh resolutionLow doseBroad coverageShort exposure time

Introduction to Biomedical Imaging

Projection radiography

Introduction to Biomedical Imaging

Projection radiography

Projection imaging is the acquisition of a 2D image of a patient’s 3D anatomy Projection radiography is a transmission imaging procedure The optical density at any location on the film corresponds to the attenuation characteristics (e-mx) of the patient at that location

Introduction to Biomedical Imaging

Projection radiography

Radiographic system

Introduction to Biomedical Imaging

Projection radiography

X-ray tube

Introduction to Biomedical Imaging

Projection radiography

X-ray tube

Filament controls tube current (mA)Cathode and focusing cupAnode is switched to high potential

30-150 kVTungstenBremsstrahlung is 1%Heat is 99%Spins at 3200-3600 rpm

Glass housing; vaccum

Introduction to Biomedical Imaging

Projection radiography

Cassette Cassette LightLight--tight and ensures screen tight and ensures screen contact with film contact with film Front surface Front surface -- carbon fiber carbon fiber

ID flash card area on back ID flash card area on back 1 or 2 Intensifying Screens 1 or 2 Intensifying Screens Convert xConvert x--rays to visible light rays to visible light

Mounted on layers of Mounted on layers of compressed foam (produces compressed foam (produces force) force)

Sheet of film Sheet of film Register the xRegister the x--ray distribution ray distribution Chemically processed Chemically processed Storage and displayStorage and display

Introduction to Biomedical Imaging

Projection radiography

μμmm(CS(CS) ) ≈≈ μμmm(PE(PE) ) Tissue @ 26 Tissue @ 26 keVkeVBone @ 35 Bone @ 35 keVkeV

Most radiographic Most radiographic interactions produce interactions produce scattered photons scattered photons Scattered photons Scattered photons →→violation of the basic principle violation of the basic principle of projection imaging: of projection imaging: mismis--information reducing contrastinformation reducing contrast

Introduction to Biomedical Imaging

Projection radiography

ScatterScatter--toto--Primary ratio (S/P) Primary ratio (S/P) Area of collimated xArea of collimated x--ray field ray field Object thickness Object thickness kVpkVp of xof x--ray beamray beam

Introduction to Biomedical Imaging

Projection radiography

Loss of contrast In the absence of scatter:

C0 = [A-B]/A In the presence of scatter: C = C0 x [1 / (1 + S/P)]S/P ↑ → contrast ↓1/(1+{S/P}): contrast reduction factor

Introduction to Biomedical Imaging

Projection radiography

Antiscatter grid

Between object and detector Uses geometry to ↓ scatter

Thin lead septa separated by aluminum or carbon fiber Grid ratio (GR) = H/W = septa height/interspace width 8:1, 10:1 and 12:1 common, 5:1 for mammography

↑ GR → ↓ S/P ↑ GR → ↑ dose

Introduction to Biomedical Imaging

Projection radiography

Introduction to Biomedical Imaging

Image Formation from Projections

Introduction to Biomedical Imaging

Projection-based image formation

The image formation process with external radiation sources: e.g. light for photography or X-ray for transmission imaging

( )f α( )g x

Image Formation from Projections

Introduction to Biomedical Imaging

Linear systems and impulse response: allows to give a general treatment to image formation

{ } { } { }1 2 1 2( ) ( ) ( ) ( )h aI bI ah I bh I+ = +x x x x

General response function by superposition principle

1 2 1 2( ) ( ) ( ; , ( )) ( ; , ( ))f f h g h g+ = +x x x α α x α αIf the system is linear the response does not depend on the intensity distribution

General response function for a linear system by summing over the extent of the energy source

1 2 1 2( ) ( ) ( ; ) ( ) ( ; ) ( )f f h g h g+ = +x x x α α x α α

( ) ( ; ) ( )Source

f h g d= ∫∫∫x x α α α( ) ( ) ( )

Source

f h g d h g= − = ∗∫∫∫x x α α α

If furthermore the response is spatially invariant

PSF

Image Formation from Projections

Introduction to Biomedical Imaging

Radon Transform: Line integral projection P(p,θ) of the two-dimensional Radon transform

Rotating the (x, y) coordinate system by θ we obtain the (x’, y’) coordinate system

Image Formation from Projections

Introduction to Biomedical Imaging

Radon Transform: Line integral projection P(p,θ) of the two-dimensional Radon transform

Image Formation from Projections

Introduction to Biomedical Imaging

Sinogram: image formed by all line integral projections P(p,θ)

Image Formation from Projections

Introduction to Biomedical Imaging

The Fourier slice theorem

Transforming into polar coordinates we have

The Fourier transform of the Radon transform is

The Fourier transform of the 2D signal g (x) is G (u,v) = G (u)

Image Formation from Projections

Introduction to Biomedical Imaging

Fourier Slice Theorem

Image Formation from Projections

Introduction to Biomedical Imaging

Fourier Slice Theorem

Image Formation from Projections

Introduction to Biomedical Imaging

Back projection

Intuitive idea: invert the Radon Transform from a finite set of projections

Image Formation from Projections

Introduction to Biomedical Imaging

After some manipulation

Back projection

The inverse Fourier transform

Image Formation from Projections

Introduction to Biomedical Imaging

With a weighting function

Filtered back projection

By applying the Fourier Slice Theorem, the inverse Fourier transform can be written

Image Formation from Projections

Introduction to Biomedical Imaging

Filtered back projection

Each pixel is formed by integrating along all projection angles

Image Formation from Projections

Introduction to Biomedical Imaging

Implementing a filtered back projection algorithm

Projection Based Image Formation

Introduction to Biomedical Imaging

Shepp and Logan Head phantom

Consists of 10 ellipses

Based on the linearity of the Radon Transform there is an analytical form of the P(r,θ)

Projection Based Image Formation

Introduction to Biomedical Imaging

Reconstruction of the Shepp and Logan Head phantom

Increased number of projections

Projection Based Image Formation

Introduction to Biomedical Imaging

X-ray Computed TomographyDigital X-ray

Introduction to Biomedical Imaging

X-ray Computed Tomography

Scanning geometry

Currently most X-ray CT scanners have an X-ray source with a fan beam geometry an a 360º ring of X-ray Detectors (~1000).

Introduction to Biomedical Imaging

CT Measurement Model

Monoenergetic model

Where E is the effective energy or the energy that in a given material will produce the same measured intensity in a monoenergeticsource that in the actual polyenergetic source

• gd is the line integral of theattenuation coefficient at the effective energy

• Requires calibration measurement of Io

X-ray Computed Tomography

Introduction to Biomedical Imaging

Hounsfield units and tissue contrast

Consistency across CT scanners desired

CT number (Hounsfield units) is defined as:

h has Hounsfield Units (HU)

Usually rounded or truncated to nearest integer

Range from -1000 to aprox + 3000 HU

X-ray Computed Tomography

Introduction to Biomedical Imaging

Hounsfield units and tissue contrast

X-ray Computed Tomography

Introduction to Biomedical Imaging

TUBE

DETECTORSAPERTUREWith a weighting function

X-ray Computed Tomography