1. I2 Medical imaging

2. X-rays
X-rays pass through human (or dog) flesh very easy, but do not pass through bone as easily.

3. Absorption
Light passing through a solid is absorbed if the photon energy is enough to increase the energy of an electron so it can jump from a low energy level to a higher one.

4. Absorption
Since light photons have an energy about the same as an electron transition (1 eV approx) most are absorbed.

5. X-ray photons X-ray photons have much more energy (>120 eV)
They can knock electrons out of the atom in 2 ways

6. 1. Photoelectric effect
X-ray photon is completely absorbed – giving all of its energy to the KE of the electron (minus the work function of course)

7. 2. Compton scattering
The photon gives some of its energy to the electron and continues with less energy and so longer wavelength (E = hf = hc/λ)

8. 2. Compton Scattering

9. Attenuation

10. Attenuation Reduction in X-ray intensity with thickness 100
# interaction is proportional to the # photons, so the curve is exponential decay
Number of photons x 1015 50 3
Thickness/cm 6 3

11. Attenuation coefficient
I = I0e-μx
where I0 = the original intensity
x = distance through absorber
μ = attenuation coefficient

12. Half-value thickness x½
Thickness required to reduce the intensity to half its original intensity
I = I0/2 = I0e-μx½
Taking logs
x½ = ln2/μ = 0.693/μ
Half value thickness depends on the energy of the X-rays and the substance

13. Example
A parallel beam of X-rays of intensity 0.2 kW.m-2 is passed through 5 mm of a material of half-value thickness 2 mm. Calculate the intensity of the beam.
HL Physics, C. Hamper, Pearson 2009

14. Example First calculate the attenuation coefficient μ
A parallel beam of X-rays of intensity 0.2 kW.m-2 is passed through 5 mm of a material of half-value thickness 2 mm. Calculate the intensity of the beam.
First calculate the attenuation coefficient μ
μ = 0.693/x½ = 0.693/2 = 0.35 mm-1
I = I0e-μx = 0.2e-0.35x5 = kW.m-2
HL Physics, C. Hamper, Pearson 2009

15. Taking an X-ray picture

16. Taking an X-ray picture
Have to choose X-rays of the right intensity/energy
X-rays are dangerous (ionising) – need to keep exposure time and intensity to a minimum
Simplest way is to place broken part on photographic film (which is enclosed in a light proof box

17. Black areas are where lots of photons hit the photographic film and “exposed” it
Few X-ray photons travelled through and hit paper

18. Intensifying screen
A screen of fluorescent material which gives out visible light when X-rays hit it is put on either side of the photographic film. This means X-rays of lower intensity can be used.

19. Barium Meal
To help see soft-tissue such as the gut, it can be filled with a material with is opaque to X-rays like barium sulphate. Drinking a “barium meal”

20. Digital images
A array of photosensitive diodes works in a similar way to a CCD. They gain charge when exposed to X-rays. This produces a p.d. which can be converted to a digital signal.

21. Digital images
The digital image can be enhanced and coloured electronically – as in airport security.

22. Tomography
For parts deep in the body a “slicing” technique called tomography can be used

23. Tomography

24. Computer Tomography (CT scan)

25. Computer Tomography (CT scan)
X-ray source and a circular array of sensors are rotated around the patient

26. Computer Tomography (CT scan)
By moving along the length of the body and using computers to analyse the digital signals a complete 3-D image can be built.

27. Let’s try a worksheet

28. Ultrasound

29. Ultrasound
Higher frequency than a healthy human can hear (>20 kHz).
Ultrasounds are reflected off different layers in the body and a picture is built up.

30. Piezoelectric effect
When a quartz crystal is stretched, a p.d. is produced (due to polarisation of the molecules in the crystal)
If a p.d. is applied, the same happens, the quartz is deformed.

31. Piezoelectric effect

32. Piezoelectric effect

33. Piezoelectric effect

34. Piezoelectric effect

36. Ultrasound production
An alternating p.d. of frequency >20 kHz is applied to a quartz crystal causing it to vibrate

37. Ultrasound detection
A sound wave causes a crystal to vibrate, producing an alternating p.d.

38. Reflections
Because the reflections are analysed, the transmitter and receiver are in the same place. The same crystal can be used as transmitter and receiver if pulsed signals are used that are short enough so the reflected wave returns before a new pulse is produced.

39. Example
If the pulse length is 10-6 s and the speed of sound in body tissue is 1500 m.s-1 then the minimum distance the wave can travel before the pulse has finished transmitting is 1500 x 10-6 = 1.5 mm. So it could be reflected off something at a depth of 0.75 mm. This is fine!

40. Frequency?
Need to use a short wavelength to avoid the wave spreading out from diffraction. Smallest object a doctor might be interested in is around a few mm, so wavelength needs to be a bit less. If λ = 1mm and velocity = 1500 m.s-1 then f = 1500/10-3 = 1.5 MHz.

41. Frequency
Higher frequencies would give higher resolution but are absorbed easier (higher attenuation). Operator adjusts frequency and pulse length to get the best image for organs of different depth and size.

42. Acoustic impedance
When ultrasound is incident on a boundary between two media (materials), part of the wavefront is reflected and part refracted.

43. Acoustic impedance - Z
The percentage reflected depends upon the relative acoustic impedance of the two media.
Acoustic impedance (Z) = ρc
where ρ = density of medium
c = the velocity of the ultrasound
Unit of Z = kg.m-2.s-1

44. Acoustic impedance
The greater the difference in acoustic impedance, the greater the % reflection.

45. Acoustic impedance
The greater the difference in acoustic impedance, the greater the % reflection. The difference between air and skin is great. To prevent all of the ultrasound being reflected by the skin, gel is used to fill the gap between the transmitter and the skin.

46. A - scans A plot of strength of reflected beam against time
Signal strength
Time

47. A - scans
organ
probe
The depth and thickness of the organ can be deduced from the times of the reflected pulse
tissue
gel

48. A - scans Notice the 2nd pulse is smaller due to attenuation organ
probe
Notice the 2nd pulse is smaller due to attenuation
tissue
gel

49. A - scans
organ
probe
The last pulse is large as most of the ultrasound is reflected by the last boundary
tissue
gel

50. A - scans
organ
probe
To gain more information the probe can be moved up and down to reveal the size, shape and changes in thickness of the organ.
tissue
gel

51. A - scans
organ
probe
To gain more information the probe can be moved up and down to reveal the size, shape and changes in thickness of the organ.
tissue
gel

52. B - scans
An A scan gives information but not an image. B – scans converts the signal into a dot whose brightness corresponds to the strength of the signal. By sweeping the probe across the organ an image can be produced.

53. 3-D ultrasound
An array of probes moved around the patient can be used to construct a 3D image using a computer.

54. Questions!