RMI 213 Principles of Medical Imaging Lecture 4 PDF

RMI 213 Principles of medical imaging Lecture 4 Electromagnetic Energy Slide 1 fchs.ac.ae Learning Outcomes At the conclusion of this lecture, associated tutorial and practical session (if relevant), you will be able to: 1. Identify the properties of...

RMI 213 Principles of medical imaging Lecture 4 Electromagnetic Energy Slide 1 fchs.ac.ae Learning Outcomes At the conclusion of this lecture, associated tutorial and practical session (if relevant), you will be able to: 1. Identify the properties of photons 2. Explain the inverse square law 3. Describe the distinctions between wave theory and quantum theory 4. Describe the electromagnetic spectrum and discuss the applications of each frequency region 5. Use the wave equation c = f  in simple calculations Slide 2 fchs.ac.ae Prescribed Text Bushong, S.C., Radiologic Science for Technologists, 10th edition, Mosby/Elsevier; St Louis, 2012, pages 44-59. Notes: 1. Each lecture in this course will relate very closely to a specific set of pages in the above text. It is strongly recommended that students read the pages indicated prior to coming to the lecture. 2. The students outcomes listed at the commencement of each lecture are essentially those found in the prescribed text for the relevant chapter. Slide 3 fchs.ac.ae Photons The electromagnetic (e/m) field surrounds us This e/m energy exists in a continuum Only a very small energy region is visible as “light” Photon: energy associated with a quantum of e/m energy Spectrum goes from: Very low energies – radio waves, to Very high energies – gamma-rays (-rays) Includes microwaves, infra-red, light, ultraviolet, x-rays e/m waves can be described classically as waves: f,  Can also be described by these energy quanta, photons Slide 4 fchs.ac.ae Speed and Amplitude of Photons In a vacuum, the photon wave speed is c = 3.0  108 m/s In materials, speed will generally be a little lower than this E/m waves (classical) are sinusoidal variations of the electric field E and the magnetic field H The wave intensity, I, is related to the amplitude, A, as I  A2 In this wave picture, the waves exist for all time and all space; e.g. as E = E0 sin(2[ft – x/]) Bushong, Figure 3-1, page 46 Slide 5 fchs.ac.ae Frequency and Wavelength of Photons In time, the interval between adjacent crests is the period, T (s) In space, the interval between adjacent crests is the wavelength,  (m) T/  The wave frequency is f = 1/T (units s–1 or Hz) The angular frequency is  = 2f (units radian/s) The wave-number is k = 2/ (m–1) The wave speed is c = f  = /T = /k (m.s–1) Bushong, Figure 3-1, page 46 Slide 6 fchs.ac.ae Frequency and Wavelength – Example Calculation Yellow light has a wavelength of 580 nm. What is its frequency? We are given  and asked to find f... Use formula c=f with c = 3.0 × 108 m/s Rearrange: f = c/ With  = 580 nm = 580 × 10-9 m, then f = (3.0 × 108)/(580 × 10-9) so f = 3.0/580 × 1017 = 0.00517 × 1017 Answer: f = 5.17 × 1014 Hz Slide 7 fchs.ac.ae Electromagnetic Spectrum E/m waves cover a vast range of frequencies This is the spectrum from around 102 Hz to 1024 Hz Corresponds to wavelengths from 107 m to 10-16 m Diagnostic medicine uses a few of the available ‘bands’: Radio-waves in Magnetic Resonance Imaging (MRI) Light in the doctor’s visual examination of the patient x-rays in all forms of radiography and Computed Tomography (CT) -rays in Positron Emission Tomography (PET) and other related imaging schemes. Note: sound is used in medical ultrasound, as sonography, but sound energy is not a form of electromagnetic energy Slide 8 fchs.ac.ae The E/m Spectrum Note the following: Frequency range Wavelength range Energy range in eV Bands used in diagnostic imaging The concept of the photon is related directly to the energy of the wave. Bushong, Figure 3-6, page 50 Slide 9 fchs.ac.ae Visible Light File:Prism rainbow schema.png In a uniform medium, light rays travel in straight lines; Different wavelengths are associated with different colors; Light rays travel though transparent media; http://en.wikipedia.org/wiki/Dispersion_relation Materials that absorb light totally are said to be opaque; Travelling from one medium to another, waves are refracted (bent); Light: from  = 400 nm to 700 nm (approximately). Slide 10 fchs.ac.ae Other E/m Bands near Light Infrared (IR) is the band slightly lower in energy than light; associated with heat energy, radiant heat. Ultraviolet (UV) is the band slightly higher in energy than light; exposure to UV can result in molecular damage and sunburn. Sunlight comprises IR, visible and UV radiation. Radiofrequency (RF) is the radiation that radio and television use; usually defined by the frequency bands utilized; e.g. 63.7 MHz. Slide 11 fchs.ac.ae Slide 12 fchs.ac.ae Ionising Radiation Ionising radiation – x-rays and -rays – will eject electrons and so ionise atoms; they are labelled by their photon energy, E RF is usually characterized by its frequency, f IR, light, UV are usually characterised by their wavelength,  x-rays and -rays differ only by their origin: x-rays result from changes in electron energy levels -rays result from changes in nuclear energy levels As we shall see, photon energy is E = hf = hc/ Here h is Planck’s constant: h = 6.63  10-34 Js (SI units) Slide 13 fchs.ac.ae Wave-Particle Duality E/m waves can be described by: waves – the classical picture energy bundles (quanta, Photon) This is the dual nature of e/m radiation. Low energy e/m waves tend to behave more like waves High energy e/m waves tend to behave more like a stream of little bundles of energy; these are the photons, E = hf Photons interact most readily when matter has distances (atom separations) comparable to the photon wavelength Photons – little bundles of energy – can be pictured as very small ‘particles’ Slide 14 fchs.ac.ae Wave-Particle Duality “Waves” Changes in electron energy levels “Particles / Photons” Changes in nuclear energy levels Bushong, Figures 3-8, 3-9 and 3-10, pages 50-51 Slide 15 fchs.ac.ae Wave Model: Visible Light Light is simplest to describe as a wave, But light sometimes behaves as a stream of photons. Light interacts with matter and sets molecules vibrating; The energy may continue unchanged – transmission – or The energy may be re-radiated in another direction – reflection or refraction (different forms of scatter); The energy may be removed – absorption by atoms (the analogy with water waves is useful). Attenuation is the combination of scatter and absorption effects that removes photons from the initial incident beam direction. Slide 16 fchs.ac.ae Interactions – Light Transmission possibilities: Transparent (low absorption and low scatter) Translucent (medium absorption and scatter) Opaque (high absorption) Bushong, Figure 3-13, page 54 Slide 17 fchs.ac.ae Interactions – x-rays Transmission possibilities: Transparent: air (low absorption and low scatter) Radiolucent: soft tissue (medium absorption and scatter) Radiopaque: bone (high absorption) Bushong, Figure 3-14, page 54 Slide 18 fchs.ac.ae Inverse Square Law When radiation is emitted from a source, the intensity decreases with distance from the source Imagine a point source. At distance d from the point source, we can imagine a sphere of radius d and surface area A = 4d2. The energy from the point source will be spread uniformly over this surface. From a point source, the radiation intensity follows the “inverse square law” Id = I0 /(4d2) or Id  1/d2 where Id is the intensity at distance d away from the source A more general expression is I1/I2 = d22/d12 Slide 19 fchs.ac.ae Inverse Square Law – Example Calculation The intensity of a light is 100 mlm (milli-lumens) at distance 1 m from the light source. What is the intensity 3 m from the source? We are given I1 and d1 and d2 asked to find I2... Use formula I1/I2 = d22/d12 Rearrange: I2 = I1 (d12/d22) Then I2 = 100 × (12/32) = 100/9 Answer: I2 = 11 mlm Slide 20 fchs.ac.ae Particle Model: Quantum Theory X-rays and -rays are usually identified by the photon energy The unit of energy used is almost always the electron-volt (eV), the energy gained by an electron accelerated across a potential difference of 1 volt, 1 eV = 1.6  10-19 J Range for x-rays and -rays is 10 eV to 50 MeV Wavelength range 10-10 m to 10-14 m Note: 10-10 m is about the size of a light atom Note: 10-14 m is about the size of the atomic nucleus Photon energy is E = hf and c = f  so E = hc/ The photon is best considered as a ‘bundle’ of energy Slide 21 fchs.ac.ae Photons – Example Calculation What is the Energy, in J and in eV, of a photon of green light with a wavelength of 550 nm? We are given  and asked to find E... Use formula E = hc/ with c = 3.0×108 m/s and h = 6.63×10-34 Js Substitute: E = (6.63 × 10-34 Js) × (3.0 ×108 m/s)/(550×10-9 m) so E = 0.0362 × 10-17 J = 3.62 × 10-19 J In eV, E = (0.0362 × 10-17 J)/(1.6  10-19 J/eV) so E = 0.0226 × 102 eV = 2.26 eV Answer: E = 3.62 × 10-19 J = 2.26 eVSlide 22 fchs.ac.ae Waves and Photons A wave is best thought of as a continuous sine wave; It exists for many hundreds or thousands of wavelengths It essentially has one frequency, f, and one wavelength,  The e/m wave travels at c = 3  108 m/s A photon is a wave of limited extent in time and space; A photon has a ‘start’ and an ‘end’ The wave shape is not sinusoidal The photon travels at c = 3  108 m/s Bushong, Figure 3-16, page 57 Slide 23 fchs.ac.ae Matter and Energy Classical physics embodies conservation laws of energy, E, mass, m, charge, q, linear momentum, L = mv, and angular momentum, P Quantum physics retains all these, apart from the conservation of mass Quantum physics considers mass to be a form of energy This link is through Einstein’s famous equation E = mc2 Slide 24 fchs.ac.ae Matter and Energy – Example Calculation What is the energy equivalence of one electron mass? Use me = 9.11 × 10-31 kg and c = 3 × 108 m/s We are given me and c and asked to find E... Use formula E = mc2 Substitute: E = (9.11 × 10-31 kg) × (3 × 108 m/s)2 so E = 82 × 10-15 J In eV, E = (82 × 10-15 J)/(1.6  10-19 J/eV) so E = 51.2  104 eV Answer: E = 512 keV = 0.512 MeV Slide 25 fchs.ac.ae Mass and Energy Equivalence The figure opposite shows the mass-energy equivalence for a range of energies, and includes the cases for electrons and nucleons. Nucleons are nuclear particles; the neutron and the proton. Bushong, Figure 3-17, page 58 Slide 26 fchs.ac.ae Summary Check that you can satisfy the learning outcomes for this lecture Go over calculations/exercises undertaken during the lecture Make sure you can define the following terms: speed, frequency and wavelength period and wave number intensity and amplitude of a wave transparent, translucent and opaque, radiolucent and radiopaque photon and photon energy You should also be able to state and use the inverse square law and Einstein’s equation E = mc2 Slide 27 fchs.ac.ae