Introduction to Biomedical Imaging

Transcription

1 Alejandro Frangi, PhD Computational Imaging Lab Department of Information & Communication Technology Pompeu Fabra University

2 X-ray Projection Imaging Computed Tomography Digital X-ray Imaging

3 The electromagnetic spectrum

4 Projection radiography Systems Chest X-rays, mammography Dental X-rays Fluoroscopy, angiography Properties High resolution Low dose Broad coverage Short exposure time

5 Projection radiography

6 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

7 Projection radiography Radiographic system

8 Projection radiography X-ray tube

9 Projection radiography X-ray tube Filament controls tube current (ma) Cathode and focusing cup Anode is switched to high potential kv Tungsten Bremsstrahlung is 1% Heat is 99% Spins at rpm Glass housing; vaccum

10 Projection radiography Cassette Light-tight tight and ensures screen contact with film Front surface - carbon fiber ID flash card area on back 1 or 2 Intensifying Screens Convert x-rays x to visible light Mounted on layers of compressed foam (produces force) Sheet of film Register the x-ray x distribution Chemically processed Storage and display

11 Projection radiography μ m (CS) μ m (PE) 26 kev 35 kev Most radiographic interactions produce scattered photons Scattered photons violation of the basic principle of projection imaging: mis- information reducing contrast

12 Projection radiography Scatter-to to-primary ratio (S/P) Area of collimated x-ray x field Object thickness kvp of x-ray x beam

13 Projection radiography Loss of contrast In the absence of scatter: C 0 = [A-B]/A In the presence of scatter: C = C 0 x [1 / (1 + S/P)] S/P contrast 1/(1+{S/P}): contrast reduction factor

14 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

15 Projection radiography

16 Image Formation from Projections

17 Projection-based image formation Image Formation from Projections The image formation process with external radiation sources: e.g. light for photography or X-ray for transmission imaging g( x) f ( α)

18 Image Formation from Projections Linear systems and impulse response: allows to give a general treatment to image formation { ( x) + ( x) } = { ( x) } + { ( x) } h ai bi ah I bh I General response function by superposition principle f ( x) + f ( x) = h( x; α, g ( α)) + h( x; α, g ( α)) If the system is linear the response does not depend on the intensity distribution f ( x) + f ( x) = h( x; α) g ( α) + h( x; α) g ( α) General response function for a linear system by summing over the extent of the energy source f ( x) h( x; α) g( α) dα Source f ( x) = h( x α) g( α) dα = h g = If furthermore the response is spatially invariant Source PSF

19 Image Formation from Projections Radon Transform: Line integral projection P(p,θ) of the twodimensional Radon transform Rotating the (x, y) coordinate system by θ we obtain the (x, y ) coordinate system

20 Image Formation from Projections Radon Transform: Line integral projection P(p,θ) of the two-dimensional Radon transform

21 Image Formation from Projections Sinogram: image formed by all line integral projections P(p,θ)

22 Image Formation from Projections The Fourier slice theorem The Fourier transform of the Radon transform is The Fourier transform of the 2D signal g (x) is G (u,v) = G (u) Transforming into polar coordinates we have

23 Image Formation from Projections Fourier Slice Theorem

24 Image Formation from Projections Fourier Slice Theorem

25 Image Formation from Projections Back projection Intuitive idea: invert the Radon Transform from a finite set of projections

26 Image Formation from Projections Back projection The inverse Fourier transform After some manipulation

27 Image Formation from Projections Filtered back projection By applying the Fourier Slice Theorem, the inverse Fourier transform can be written With a weighting function

28 Image Formation from Projections Filtered back projection Each pixel is formed by integrating along all projection angles

29 Projection Based Image Formation Implementing a filtered back projection algorithm

30 Projection Based Image Formation 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)

31 Projection Based Image Formation Reconstruction of the Shepp and Logan Head phantom Increased number of projections

32 X-ray Computed Tomography Digital X-ray

33 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).

34 X-ray Computed Tomography 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 monoenergetic source that in the actual polyenergetic source g d is the line integral of the attenuation coefficient at the effective energy Requires calibration measurement of Io

35 X-ray Computed Tomography 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 to aprox HU

36 X-ray Computed Tomography Hounsfield units and tissue contrast

37 X-ray Computed Tomography TUBE APERTURE With a weighting function DETECTORS

38 X-ray Computed Tomography

39 X-ray Computed Tomography

40 X-ray Computed Tomography

41 X-ray Computed Tomography

42 X-ray Computed Tomography X-ray emission in all directions X-ray tube Collimators Slice width Fan beam Detectors

43 X-ray Detectors There are two main types of detectors Ionization chambers the radiation liberates electrons from the gas atoms, creating positive charged ions Scintillation crystals make use of the property of certain chemical compounds to emit short light pulses after excitation by the passage of charged particles or by photons of high energy X-ray Computed Tomography Ionization chamber Photomultiplier tube

44 X-ray Computed Tomography

45 X-ray Computed Tomography Slip-ring technology Cine scanning (no table feed) CT fluoroscopy (several reconstruction per 360º) Spiral scanning (continuous table feed)

46 X-ray Computed Tomography

47 X-ray Computed Tomography

48 X-ray Computed Tomography

49 X-ray Computed Tomography

50 Digital X-ray Imaging Digital X-ray Imaging The imaged property is the attenuation coefficient μ but now only one projection Conventional systems had a very low efficiency which is nowadays improved with digital systems

51 Digital X-ray Imaging Digital X-ray Imaging The imaged property is the attenuation coefficient μ

52 Biplane & 3D Rotational Angiography Rotational angiography allows a 3D reconstruction based on dynamic X-raytype projection images