Introduction au cours

Fund BioImag 20134-14: From x-ray to image Computed TomographyWhat factors influence contrast in x-ray imaging ? Beam hardeningSensitivity and resolution considerationsWhat is the fundamental basis for image reconstruction using x-ray absorption ?Radon TransformHow can x-ray images be reconstructed? Sinogram Backprojection vs. filtered backprojection Central Slice TheoremExamples

After this course youUnderstand the consequences of the Bremsstrahlung continuum on image contrastUnderstand how Compton scattering reduces image contrast and how its influence can be reduced Are familiar with the Radon transform Understand the principle of matrix reconstruction and backprojection Understand the major mechanisms leading to CT contrast Fund BioImag 20134-2Computed Tomographyinvented 1971

Physiology and Medicine engineerphysicist

Primitive pancreatic lesion (neoplastic) Godfrey Hounsfield Allan Cormack Nobel prize 1979

First clinical CT- 1972Fund BioImag 20134-3CT of animal models transgenic mice and cancer models

microCT (~50 m spatial resolution)

Mouse: blood vessels (red) micro-CT scannerheart and lungsabdomenrat spinekidneys with IV contrastfull body skeletonFund BioImag 20134-44-1. What does absorption in the real world imply ?Linear attenuation coefficient m : linear attenuation coefficient Unit: [cm-1]nn-dndxBut, =f(En,Z, r)

If is constant in x Two consequences:Beam hardeningDepth dependent contrastContrast is well-defined for monochromatic x-raysThe measurement that is wanted: m(x,y)What is measured: n(x)

(m for a homogeneous object of thickness x)Fund BioImag 20134-5What does the Energy Spectrum of an x-ray tube really look like ?filtered Bremsstrahlung and characteristic emission

Minimal energy is zero, but:Soft x-rays (low energy)are filtered by instrumenti(En): complex functionDefine effective photon energy EeffEeffEeff is increased by instrument (filtering of soft x-rays) Hard x-rays (high energy)Maximal x-ray energy is = kinetic energy of e- (eVcathode)Interaction with orbital electronsSoft x-rays (low energy)Bremsstrahlung continuumi(En)Fund BioImag 20134-6What is the consequence of energy-dependent absorption ?Beam Hardening - Effective energy depends on depthA similar consequence arises in tissue:

Ideal: Monochromatic x-rays (En(l) = d(l0))Reality: Polychromatic, multienergetic i(En)

Absorption is not uniform with EnContrast changes with large objects and depthExcessive radiation dose to superficial tissueSolution: Reduce i(En) for soft x-rays (e.g. 3mm Al eliminates 90% of 20keV photons)

Object (lesion)Fund BioImag 20134-7

How does x-ray scattering impact CNR ?Scattering increases with FOV (field-of-view) of irradiation Further reduction of image contrast

Solution: Anti-scatter grid (collimator)

With En : Compton scattering increased masking of object. Photoelectric effect: complete absorption of photons Object (lesion) easily detectedCollimation principle: establishes directionality of x-raysDetectorSlice selectionHigh Z, r: stop x-rays

Fund BioImag 20134-8How is CNR quantified ?

Signal: I(d) (no. photons detected) I0 (no. photons irradiated)

Contrast: DI(d) due to (d) differencesi(En), mC produces reduced contrastCompton scattering: Antiscatter gridCT intensity can be measured in absolute terms (CT-number)Soft tissue: Typically has weak contrast (small Hounsfield units)

HU : attenuation normalized to water (0)range from -1000 (air) to +3000 (bone and contrast agents) soft tissues: -300 to +100 Fund BioImag 20134-94-2. What is the basis of image reconstruction ? The Radon transformGiven a certain beam intensity (no. of photons) I at a given position y, I(y0), the beam intensity at y+Dy is

I(y)y0DyDy lim Dy0I0yxConsidering a two-dimensional objet:Recursive application to derive I(y0+2Dy)

I0: intensity of incident x-ray beamRadon transform g(x)Definition

Radon transform of a point-like homogeneous objectrectangular objectg(x)Fund BioImag 20134-10

Does each pixel have a unique trajectory ?SinogramDetector: is moved in circular motion around object (indicated by angular position f)Each point in space is uniquely represented by Amplitude R and phase f0 of sinusoidal trajectory in Sinogram (sic!): (x,y) (R,f0)f

Radon transform of a circular objectRadon transform = projection of objectTrajectory:Rsin(f+f0)Fund BioImag 20134-11Can a CT image be constructed by Matrix inversion ?

In principle such an n2 matrix can be inverted. Too complex, computationally intensive and unstable ln(I1/I0) = -m1Dx-m2 Dx ln(I2/I0) = -m3Dx-m4 Dx ln(I3/I0) = -m1Dy-m3 Dy ln(I4/I0) = -m2Dy-m4 Dy Decomposing an object into a 2x2 matrix requires a minimum of 4 measurements:

Setting Dx=Dy yields a linear 2x2 inversion problem linking mk to Ik

CT was introduced in 1970 simple reconstruction algorithm!Fund BioImag 20134-124-3. What algorithm is adapted to 1970s computing power ?Backprojection reconstructionBasic reconstruction principle: Along the measured projection direction fill in each pixel constant numbers corresponding to the Radon transform (projection intensity). Repeat for next orientation of the projection, sum the values in overlapping pixels. Illustration with gray shades (point-like object):11111111 1 1 1 1 1 122 Projections4 Projections8 Projections16 Projections

xy

180 backprojections: reconstruction is complete.the next 601st 60 ProjectionsFund BioImag 20134-13Why does simple Backprojection have poor spatial resolution ?

dxdy=dA=rsin(df)drrdfdrdrdfrrdfThe reconstruction falls off with 1/r(in analogy to the decrease of light intensity in 2D)Backprojection has poor spatial resolution:Reconstruction of a point-object falls of with 1/rWHY?Solution ?dfdA rNumber of rays (projections): constant with dfBut: pixel size = dxdy dA = const No. of rays 1/rFund BioImag 20134-14

How can good image resolution be maintained ? Filtered Backprojection

Example: Reconstruction of a slice from projections

Fund BioImag 20134-15How is Backprojection linked to Fourier transform ? Central Slice TheoremFTIFTk-space (Fourier space)kxkyMRI: Acquired DataImage spacexyFinal Image (CT: acquired data)

See also: Signals and Systems (SV)

FT of projection 1 line in k-space Reconstruction using FT :artifactskx=0Fund BioImag 20134-16

Bone (calcification) : bright (high absorption)Air is darkDifferent densities of tissue give inter-mediate results

Imaging of mummified bodiesDislodged arrow head

X-ray CT : Examples (Human)Fund BioImag 20134-17CT: Examples (mouse)

Pre-Post-contrast

3D CT scan of rodent spine treated with human mesenchymal stem cells (transduced with the human BMP-9 gene via an adenoviral vector) significant bone formation at the treatment sites (arrows)

13m micro CT of mouse placenta vasculature

Micro-CT of mouse femor boneFund BioImag 20134-18

CT: SummaryMain contrast is bone vs. soft tissue (or air) (calcium content i.e. e- density r)Contrast agents (increase Zeff) allow depiction of vessel architecture and lesions

Insect with iodine contrast agentSNR and CNR:Intensity can be increased by cathode currentHigh spatial resolution possible(limited only by radiation dose in humans)Fish larvae

18Fund BioImag 20134-19How have CT scanners evolved ?Generations of CT scannersFirst Generation Parallel beam designOne/two detectorsTranslation/rotation

2nd GenerationSmall fan beamTranslation/rotationLarger no. of detectors

3rd GenerationMultiple detectorsLarge fan beam

4th GenerationDetector ringLarge fan beam

EQ I0 = \I(0,,i(En)dEn)