Structure of Biological Materials

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1 ELEC ENG 3BA3: Structure of Biological Materials Notes for Lecture #19 Monday, November 22, 2010

2 6.5 Nuclear medicine imaging Nuclear imaging produces images of the distribution of radiopharmaceuticals in patients through the measurement of: gamma rays, x-rays, or annihilation photons, that result from radionuclide decay. 2

3 Gamma rays can be emitted as a result of: beta-minus (negatron) decay, or isomeric transition. X-rays are emitted as a result of: electron capture decay. Annihilation photons are emitted as a result of: beta-plus decay (positron emission). 3

4 Annihilation radiation following positron emission: 4

5 Radionuclide decay equation: In addition to the type of decay that a radionuclide undergoes and the spectrum of photonic energy that is emitted, the timecourse of decay is different for different radionuclides. The number of radionuclides N at any time t is: where N o is the initial number of nuclides and λ is the decay rate. 5

6 Physical half-life: The time for half of the sample of radionuclides to decay is: (Bushberg et al., 2001) 6

7 X-rays, gamma rays and annihilation photons are converted to visible or ultraviolet light via scintillators: 7

8 Planar nuclear medicine imaging via a scintillation camera: 8

9 Scintillation camera detector: 9

10 Single-photon emission tomography (SPECT) system: 10

11 Positron emission tomography (PET) system: 11

12 Annihilation coincidence detection in PET: 12

13 True, scatter and accidental coincidence in PET: 13

14 6.6 Ultrasound Ultrasound consists of sound waves of frequencies exceeding the range of human hearing (15 Hz to 20 khz). Medical diagnostic ultrasound makes use of frequencies in the range of 2 to 10 MHz. Images are formed based on the echoed response of tissues to a pulsed ultrasound emission from a transducer pulse echo technique. 14

15 Medical diagnostic ultrasound system: 15

16 Ultrasound image formation: The depth of an echo-producing structure is determined by the time between the pulse emission and the echo return. Note: To compute the depth from the echo time, the speed of sound is assumed to be 1540 m s -1 in human tissues. The amplitude of the echo is encoded as a gray-scale value. Note: The amplitude of the echo depends on the reflection properties of tissue interfaces. 16

17 Speed of sound in different materials: Recall from Lecture #10 that: 17

18 Sound pressure and intensity: Sound intensity I is defined as the sound power per unit area. Consequently: where p is the acoustic pressure (force/area) and v is the acoustic particle velocity (displacement/time). For a plane travelling wave: where Z is the acoustic impedance of the material in which the wave is propagating. 18

19 Sound pressure and intensity (cont.): Therefore, for a plane wave: The SI units of intensity are consequently W/m 2. Because of the relationship between sound intensity and pressure, on a decibel scale: 19

20 Acoustic impedance of different materials: in units of kg m -2 s -1 1 SI-rayls 0.1 cgs-rayls 20

21 Reflection and refraction at tissue boundaries: 21

22 Reflection coefficients: The pressure reflection coefficient is defined as: where P r is the reflected pressure and P i is the incident pressure. 22

23 Reflection coefficients (cont.): The intensity reflection coefficient is defined as: where I r is the reflected intensity and I i is the incident intensity. Because of conservation of energy: where I t is the transmitted intensity. 23

24 Ultrasound interactions with boundaries and particles at small wavelengths: 24

25 Attenuation of ultrasound in different tissues: where I o is the source intensity, μ is the attenuation coefficient and d is the tissue thickness. 25

26 Single-element ultrasound transducer: 26

27 Multi-element transducer arrays: 27

28 Doppler ultrasound: The velocity of blood flow can be estimated using Doppler ultrasound. The frequency f r of ultrasound reflected from the blood is: where f o is the frequency of the impinging sound beam (Hz) and f is the Doppler shift (Hz). 28

29 Doppler shift: The Doppler shift is: where v is the velocity of blood flow (m s -1 ), f o is the frequency of the impinging sound beam (Hz), c is the speed of sound in the tissue medium (m s -1 ), and θ is the angle between the sound beam axis and the blood flow velocity vector. 29

30 Example of Doppler ultrasound: 30

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(INCLUDING THIS FRONT PAGE) I'IFIITIIBIFI UNIVERSITY OF SCIEI'ICE RITD TECHNOLOGY FACULTY OF HEALTH AND APPLIED SCIENCES DEPARTMENT OF NATURAL AND APPLIED SCIENCES QUALIFICATION: BACHELOR OF SCIENCE (MAJOR AND MINOR) QUALIFICATION