Computed Tomography (CT):Physics and Technology

Clinical Applications

Computed Tomography (CT):Physics and Technology

Clinical Applications

Ontario Cancer InstitutePrincess Margaret HospitalUniversity Health Network

Medical BiophysicsMedical ImagingIBBME

JH Siewerdsen PhD

Dept. of Medical Biophysics, University of TorontoOntario Cancer Institute, Princess Margaret Hospital

jeff.siewerdsen@uhn.on.ca

JH Siewerdsen PhD

Dept. of Medical Biophysics, University of TorontoOntario Cancer Institute, Princess Margaret Hospital

jeff.siewerdsen@uhn.on.ca

M O’Malley MD

Dept. of Medical Imaging, University of TorontoDept. of Medical Imaging, University Health Network / Mt. Sinai Hospital

martin.o’malley@uhn.on.ca

M O’Malley MD

Dept. of Medical Imaging, University of TorontoDept. of Medical Imaging, University Health Network / Mt. Sinai Hospital

martin.o’malley@uhn.on.ca

• Computed Tomography (CT)- Basic principles of CT

Natural history of scanner technologies (“generations”)

- CT reconstructionFourier slice theoremFiltered backprojectionOther techniques

- Image quality / artifactsPhysical factorsPerformance metrics

- Radiation doseMagnitude and risk (in context)

- ApplicationsDiagnostic imaging… IG interventions… Radiation therapy

OverviewOverview

Circa 1895

Projection radiography I0

I

I = Io e-∫µ(x,y)dy0

d

Computed Tomography

P = ln(Io/I) = ∫µ(x,y)dySir Godfrey Hounsfield

Nobel Prize, 1979

γ source

9-day acquisition 2.5-hr recon

Detector

Turntableand linear track

Hounsfield’s CT Scanner

First Generation CT

xScan and Rotate:Linear scan of source and detector

Line integral measuredat each position: P(x)

Rotate source-detector ∆θ

Repeat linear scan…

Projection data: P(x;θ)

x x x x x x x

P(x)

CT “Generations”

WA Kalender, Computed Tomography, 2nd Edition (2005)

1st Generation (1970)

Pencil BeamTranslation / Rotation

2nd Generation (1972)

Fan BeamTranslation / Rotation

CT “Generations”3rd Generation (1976)

Fan BeamContinuous Rotation

4th Generation (1978)

Fan BeamContinuous Tube Rotation

Stationary Detector

The Fourier Transform of a projection of an object at a given angleyields a slice of the Fourier Transform of the objectat the corresponding angle in the Fourier domain.

Fourier Slice Theorem

f(x,y)

y

x

v

u

FT

F(u,v)

CT Image ReconstructionFourier Slice Theorem

v

u

f(x,y)

ξ

θ

y

x

p(ξ,θ)

X-rays

θ

F(u,v)

F [p(ξ,θ)]

CT Image Reconstruction

y

x

v

u

f(x,y) p(ξ,θ) F(u,v)

F -1[F(u,v)]

BackprojectionSimple Backprojection:

Trace projection data P(x;θ)through the reconstruction matrixfrom the detector (x) to the source

Simple backprojection yieldsradial density (1/r)

Therefore, a point-object isreconstructed as (1/r)

Solution: “Filter” the projection databy a “ramp filter” |r|

P(x;θ)

X-ray source

Sinogram p(x,θ)

Sinogram:Line integral projection: p(x)

measured at each angle (θ)

Projection data (sinogram): p(x;θ)

x

θ

p(x;θ)

“Sinogram”

p(x) = ln(Io/I) = ∫µ(x,y)dy

SinogramFiltered Sinogram

CT Image ReconstructionFiltered Back-Projection

Object

Projection p(θ,ξ)

Back-P

rojec

t

CT Image ReconstructionFiltered Back-Projection

Filtered SinogramObject Space

Back

-Pro

ject

CT Image ReconstructionFiltered Back-Projection

Filtered SinogramObject Space

ReconstructedImage

Filtered Backprojection: Implementation

Projection at angle θp(ξ,θ)

Filtered Projectiong(ξ,θ)

Backproject g(ξ,θ).Add to image µ(x,y)

µ(x,y)

Loop

ove

r all

view

s (al

l θ)

Helical CT

WA Kalender, Computed Tomography, 2nd Edition (2005)

Slip ring gantryContinuous gantry rotationContinuous couch translation

Pitch =Table increment / rotation (mm)

Beam collimation width (mm)

Pitch <1 :OverlapHigher z-resolutionHigher patient dose

Pitch >1:Non-overlapLower z-resolutionLower patient dose

Recent Advances: Dual-Source CT

Two complete x-ray and data acquisition systems on one gantry.330 ms rotation time

(effective 83 ms scan time)

Siemens Medical Solutions – Somatom Definition

Recent Advances: Multi-Detector CT

• Multiple slices acquired in each revolution

• Higher speed• Reduced slice thickness

(Improved axial resolution)

GE Light Speed multi-row CT detector

4x1.25 mm

4x2.5 mm

4x3.75 mm

4x5.0 mm

From “Fan” to “Cone”

Recent Advances: Multi-Detector CT

Fast (whole-body) scansat high resolution (thin slices) Dynamic (4D) imaging

Recent Advances: Cone-Beam CTFully 3-D Volumetric CT

Conventional CT:Fan-Beam

1-D Detector RowsSlice Reconstruction

Multiple Rotations

Cone-Beam CT:Cone-Beam CollimationLarge-Area Detector3-D Volume ImagesSingle Rotation

Cone-Beam CT

Projection data (2D)200 – 2000 projections

over 180o – 360o

Volume reconstruction~1 mm spatial resolution

+ soft tissue visibility

CT Detectors

K. Kanal, University of Wisconsin

Gas (Xenon)

Conventional (old)Single-slice CT only

Scintillator / Semiconductor

State of the artWell-suited to MDCT

Single-Slice CT vs Multi-Detector CT

K. Kanal, University of Wisconsin

Cone-Beam Filtered Backprojection

Weight Filter 2D Interpolation

Geometry

# of voxels# of projectionsRepeat ×

Reconstruction Volume

CT Image Reconstructions

1975

Liver

GB

Spine

Spleen

AO

Pancreas

2000

282

237

Contrast

Contrast =I1 – I2

(I1 + I2)/2

CT Radiograph

6325 25

252524182219251920 40

20214022 17 3019

Why CCT >> Crad?

CCT =63–25

(63+25)/2=86%

Crad =282–237

(282+237)/2=17%

CT Number (Pixel Value)

Hounsfield Units (HU)

The CT image pixel values have units ofthe attenuation coefficient, µ (cm-1 or mm-1)

Commonly converted to a convenient scale: Hounsfield Units (HU)

HU’ = µ’ - µwaterµwater

1000 (+1000)(sometimes)

Brain (8)

Fat (-100)

Liver (+85)

Breast (-50)

Water (0)

Polyeth (-60)

NoiseNoise:Standard deviation in voxelvalues in an otherwise uniform region of interest

(4.6 ± 3.2)(5.6 ± 2.4) (-1.3 ± 6.2)

(3.8 ± 4.2)

(4.4 ± 4.2)

∫∝cf

winTTdf0

2interp

2

Bandwidth Integral

xyK

zxyo

Evox aaD

k3

2

ησ = xyK

(Fourier domain integral over the low-pass ‘smoothing’ filters)

Minimum resolvableline-pair group

Spatial ResolutionFactors affecting spatial resolution:Focal spot sizeDetector pixel sizeSlice thicknessPitchNumber of projectionsReconstruction filter (kernel)Field of viewPatient motion

Metrics of spatial resolution:Minimum resolvable line-pairPoint-spread function (psf)Modulation transfer function (MTF)

www.impactscan.org

“Smooth” “Sharp”

Reconstruction Filter

Reduced Spatial ResolutionLower Noise

Improved SNRImproved Soft-Tissue Visibility

Improved Spatial ResolutionHigher NoiseReduced SNR

Reduced Soft-Tissue Visibility

Artifacts

Rings Shading

Lag

Motion

Metal

Streaks

“Cone-Beam”Truncation

Dosimetrics

Measure Common Units SI UnitsActivity Ci Bq (disintegrations / sec)

Exposure R C/kg (ionization in air)

Absorbed Dose rad Gy (1 Gy = 1 J/kg = 1 Rad)

Effective Dose rem Sv (1 Sv = 100 rem)

Some forms of radiation more efficient than others at transferring energy to the cell.To level the playing field, multiply dose (Gy) by a quality factor (Q).

Q compares biological damage to that associated with the same dose of X rays (photons). The resulting unit is the Sv (seivert). Thus, Sv = Gy x Q.

1 Sv is the amount of (any type of) radiation which would cause the same amount of biological damage as would result from 1 Gy of X rays.

CT Dose Measurement (CTDI)

Kanal, University of Wisconsin

Dose estimate from a single scan:CT Dose Index (CTDI)

CTDI = f XT

L

f = exposure-to-dose factor (mGy/R)X = exposure (R)L = length of ion chamber (100 mm)T = slice thickness (mm)

Standard (Cylindrical) Phantoms:Head (16 cm diameter acrylic)Body (32 cm diameter acrylic)

Radiation Dose

Bushberg, The Essential Physics of Medical Imaging, 2nd Ed.

CTDIw =

Surface dose > Central doseHead: (Dsurf / Dcenter) ~1Body: (Dsurf / Dcenter) ~2

CTDIw combines:

Peripheral dose: CTDIperiphCentral dose: CTDIcenter

(2/3 CTDIperiph ++1/3 CTDIcenter)

Electrometer (mGy / C)

Ion Chamber

16 or 32 cm DiameterAcrylic Cylinder

center

periphery

Factors Affecting Radiation Dose

Typical Skin Dose:Head ~ 20 mGyBody ~ 40 mGy

(induction of erythema: ~2 Gy)

kVp

mAs

Kanal, University of Wisconsin

Doseα~(kVp)2

Dose α mAs

Effective Dose

Region FactorHead 0.0023Neck 0.0054Chest 0.017Abdomen 0.015Pelvis 0.019

(mSv/mGy.cm)

30 mGy x 30 cm = 900 mGy.cm

EffectiveDose

(mSv)2-8

10-2010-20

20 mGy x 50 cm = 1000 mGy.cm

Effective Dose

ExamSkullChest (PA)AbdomenPelvisBa swallowBa enema

HeadChestAbdomenPelvis

EffectiveDose (mSv)

0.070.021.00.71.57

28

10-2010-20

Equivalent# CXR

3.51503575350

100400500500

Approx. PeriodBackroundRadiation

-3 days

6 months4 months

--

3.6 yrs4.5 yrs4.5 yrs

(typical background= 3 mSv / yr)

Rad

iogra

phy

CT

• Key to numerous areas of medical imaging- Screening

E.g., low-dose CT screening of early-stage lung cancer

- DiagnosisE.g., almost everything…

- Staging and prognosisE.g., PET-CT

- Treatment planningE.g., Dose calculation in radiation therapy

- Image guidanceE.g., CT-guided biopsy, interventions, surgery, and RT

- Response assessmentE.g., Tumor regression; perfusion changes

- Pre-clinical imagingE.g., Micro-CT of mice (drug development, etc.)

Computed TomographyComputed Tomography

• Remaining Challenges- Reduced imaging dose

E.g., pediatrics… mA modulation… Low-dose protocols

- Imaging speedCardiac imaging… 4D… CT-fluoroscopy

- Image qualityE.g., Improved SNR… Artifact management

Computed TomographyComputed Tomography

• Ongoing Developments- Multi-detector CT (“The Slice Wars”)

Single-slice → 8 → 16 → 64 → 256 slice → Volume CT

- Alternative source configurations (“The Source Wars)Dual-source… Multiple-source… → No moving parts

- CT imaging functionality and applications