PowerPoint - Basics of CT - IFIC

Siemens 2⋅2⋅32=128-slice dual source cone-beam spiral CT (2005)

Basics of Clinical X-Ray Computed Tomography

EMI parallel beam scanner (1972)

y

Marc Kachelrieß x

z

Institute of Medical Physics University of Erlangen-Nürnberg Germany

1536 views per rotation in 0.33 s 2⋅32×(672+352) 2-byte channels per view 600 MB/s data transfer rate 180 views per rotation in 300 s

www.imp.uni-erlangen.de

GE LightSpeed

5 GB data size typical

2×160 positions per view

Toshiba Aquilion

What does CT Measure? • Polychromatic Radon transform p( L ) = − ln dE w( E ) e Siemens Somatom Definition

µ (r , E )

− dL µ ( r , E )

with normalized detected spectrum: 1 = dE w( E )

Philips Brilliance

• Widely used monochromatic approximation: p ( L ) ≈ dL µ ( r , Eeff )

with the effective energy being around 70 keV Dual Source

CT-Performance (Best-of Values)

CT Basics From Single-Slice to Cone-Beam Spiral CT

Trot

• Technology

1972 300 s×42

– Basic parameters – Detector concepts, tube technology – Scan trajectories, scan modes – – – –

Spiral CT

• Algorithms 2D filtered backprojection Spiral z-interpolation ASSR and EPBP (cone-beam recon.) Phase-correlated CT (e.g. cardiac CT)

• Image quality and dose – – – –

Spatial resolution (PSF, SSP, MTF) Relation of noise, dose and resolution Dose values (CTDI, patient dose) Dose reduction techniques

collimation

typ. 30 cm scan1

slices/s

2×13 mm

---

0.007/42

1980

2s

2 mm

20 mm, 30 s

0.5

1990

1s

1 mm

10 mm, 30 s

13

1995

0.75 s

1 mm

8 mm, 30 s

1.33

1998

0.5 s

4×1 mm

4×1 mm, 30 s

124

2002

0.4 s

16×0.75 mm 16×0.75 mm, 12 s

604

2004

0.33 s

64×0.5 mm

2404

2010

0.2 s

512×0.5 mm 512×0.5 mm, 0.2 s

1 2 3 4

64×0.5 mm, 3 s

2500

assuming a breath-hold limit of 30 s factor 4 converts from head FOM to full body FOM assuming p = 1, otherwise Seff is increased assuming p = 1.5 since IQ is independent of pitch for MSCT

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1

Fan-Beam Geometry (transaxial / in-plane / x-y-plane)

p.a. →

x-ray tube

y

180°

Acquisition lateral →

x

Reconstruction field of measurement (FOM) and object Object, Image detector (typ. 1000 channels) y

a.p. → Sinogram, Rawdata x

(illustration without quarter detector offset)

Data Completeness

y

y

x

x

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

y

Each object point must be viewed by an angular interval of 180°or more. Otherwise image reconstruction is not possible.

y

x

x

(illustration without quarter detector offset)

Basic Parameters

Demands on the Mechanical Design

(best-of values typical for modern scanners) • • • • • • • • • • •

In-plane resolution: 0.4 … 0.7 mm Nominal slice thickness: S = 0.5 … 1.5 mm Effective slice thickness: Seff = 0.5 … 10 mm Tube (max. values): 100 kW, 140 kV, 800 mA Effective tube current: mAseff = 10 mAs … 1000 mAs Rotation time: Trot = 0.33 … 0.5 s Simultaneously acquired slices: M = 4 … 64 Table increment per rotation: d = 2 … 50 mm Pitch value: p = 0.3 … 1.5 Scan speed: up to 16 cm/s Temporal resolution: 50 … 250 ms

• Continuous data acquisition in spiral scanning mode • Able to withstand very fast rotation – Centrifugal force at 550 mm with 0.5 s: F = 9 g – with 0.4 s: F = 14 g – with 0.3 s: F = 25 g

• • • • •

Mechanical accuracy better than 0.1 mm Compact and robust design Short installation times Long service intervals Low cost

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Tube Technology

Demands on X-Ray Sources

conventional tube

high performance tube

(rotating anode, helical wire emitter)

(rotating cathode, anode + envelope, flat emitter)

cooling oil

cooling oil

cathode

cathode anode

Photo courtesy of GE

∂z ∂RF

• Available as multi-row arrays • Very fast sampling (typ. 300 µs) • Favourable temporal characteristics (decay time < 10 µs) • High absorption efficiency • High geometrical efficiency • High count rate (up to 108 cps*) • Adequate dynamic range (at least 20 bit)

2∂z

cooling oil

2∂RF B

2∂RF

anode

C

Photo courtesy of Siemens

Demands on CT Detector Technology

C cathode

B

C

C

anode

tan φ =

cathode

anode

High instantaneous power levels (typ. 50-100 kW) Increasing with rotation speed High continuous power levels (typ. >5 kW) High cooling rates (typ. >1 MHU/minute) High tube current variation (low inertia) Compact and robust design

anode

• • • • • •

* in the order of 105 counts per reading and 103 readings per second Straton Tube

Multirow Detectors for Multi-Slice CT 2006

z

Adaptive Array Technology

40 mm GE 64 / 0.37 s / 3.8°

64 × 0.625 mm

40 mm

β

Philips 64 / 0.4 s / 3.8°

64 × 0.625 mm

19 mm

16 channels (of 103) shown

Siemens 2⋅64 / 0.33 s / 1.9°

2⋅2⋅32 × 0.6 mm 24 × 1.2 mm

32 mm 64 × 0.5 mm

Toshiba M = 64 / 0.4 s / 3.2° z Data courtesy of Siemens Medical Solutions, Forchheim, Germany

Number of simultaneously acquired slices M / Rotation time trot / Cone-angle Γ

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Scan Trajectories

Rows vs. Slices z

z

z

FOM

z

4 Rows 4 Slices

6 Rows 4 Slices

1 Rows 4 Slices

4 Rows 8 Slices

M = 1⋅ 4

M = 1⋅ 4

M = 4 ⋅1

M = 2⋅4

p=

d ≤ 1.5 M ⋅S

Spiral

p=

d ≤ 0.9 M ⋅S

Sequence

p=

1 N rot

Circle

CT Basics From Single-Slice to Cone-Beam Spiral CT

• Technology – Basic parameters – Detector concepts, tube technology – Scan trajectories, scan modes

• Algorithms – – – –

2D filtered backprojection Spiral z-interpolation ASSR and EPBP (cone-beam recon) Phase-correlated CT (e.g. cardiac CT)

• Image quality and dose – – – –

Animation by Udo Buhl, Aachen

Spatial resolution (PSF, SSP, MTF) Relation of noise, dose and resolution Dose values (CTDI, patient dose) Dose reduction techniques

Emission vs. Transmission Emission tomography • Infinitely many sources • No source trajectory • Detector trajectory may be an issue • 3D reconstruction relatively simple

2D: In-Plane Geometry

Transmission tomography • A single source • Source trajectory is the major issue • Detector trajectory is an important issue • 3D reconstruction extremely difficult

• • • •

Decouples from longitudinal geometry Useful for many imaging tasks Easy to understand 2D reconstruction – Rebinning = resampling, resorting – Filtered backprojection

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Fan-beam geometry

Parallel-beam geometry

transaxial rebinning

(β ,α )

(ξ ,ϑ )

Fan-beam geometry

Parallel-beam geometry

In-Plane Parallel Beam Geometry β RF

y

α

y

ϑ

x

ξ

(β ,α )

y

ϑ

x

ξ

x

Measurement: p(ϑ , ξ ) = Rf (ϑ , ξ ) = dx dy f ( x, y ) δ (x cos ϑ + y sin ϑ − ξ )

(ξ ,ϑ )

FBP (Filtered Backprojection)

2D Backprojection (Discrete Version of the Transpose Radon Transform)

Measurement: 1D FT:

p(ϑ , ξ ) = dx dy f ( x, y ) δ (x cos ϑ + y sin ϑ − ξ )

dξ p (ϑ , ξ ) e

− 2π iξu

Central slice theorem: π

Inversion:

= dx dy f ( x, y ) e

P2 (ϑ , u ) = F (u cos ϑ , u sin ϑ ) ∞

f ( x, y ) = dϑ du u P2 (ϑ , u ) e 0

− 2π iu ( x cosϑ + y sin ϑ )

2π iu ( x cos ϑ + y sin ϑ ) p(ϑ , ξ )

−∞

π

= dϑ p(ϑ , ξ ) ∗ k (ξ ) 0

ξ = x cos ϑ + y sin ϑ

Add ray value to each pixel in the “vicinity“ of the ray.

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Spiral CT Scanning Principle Filtered Backprojection (FBP)

Scan trajectory

Start of spiral scan

1. Filter projection data with the reconstruction kernel. 2. Backproject the filtered data into the image:

Direction of continuous patient transport

Reconstruction kernels balance between spatial resolution and image noise.

1996:

1998:

2002:

1× 5 mm, 0.75 s

4× 1 mm, 0.5 s

16× 0.75 mm, 0.42 s

0

z

0

t

2004:

2⋅⋅32×0.6 mm, 0.33 s Kalender et al., Radiology 173(P):414 (1989) and 176:181-183 (1990)

Spiral z-Interpolation for Single-Slice CT M=1

without z-interpolation

with z-interpolation

d p= ≤2 M ⋅S

z

z = zR Spiral z-interpolation is typically a linear interpolation between points adjacent to the reconstruction position to obtain circular scan data.

Spiral z-Filtering for Multi-Slice CT M=2, …, 6 d p=

M ⋅S

CT Angiography: Axillo-femoral bypass

≤ 1.5

M=4 z

120 cm in 40 s 0.5 s per rotation 4× ×2.5 mm collimation pitch 1.5

z = zR Spiral z-filtering is collecting data points weighted with a triangular or trapezoidal distance weight to obtain circular scan data.

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The Cone-Beam Problem

Animation by Siemens

1×5 mm 0.75 s

4×1 mm 16×0.75 mm 2⋅⋅32×0.6 mm 0.5 s 0.375 s 0.375 s

256×0.5 mm