Principles of medical imaging .pdf

Prescribed Text The prescribed text for students is: Bushong, S.C., Radiologic...

Prescribed Text The prescribed text for students is: Bushong, S.C., Radiologic Science for Technologists, 10th edition, RMI 213 Mosby/Elsevier; St Louis, 2012 Principles of medical imaging Lecture 1 Essential Concepts – 1 Slide 1 fchs.ac.ae Slide 2 fchs.ac.ae Learning Outcomes Matter At the conclusion of this lecture, associated tutorial and practical session (if relevant), you will be able to: Name given to the material of which ALL things are made 1. Describe matter and energy of. 2. List various forms of energy 3 physical states of matter are: 3. Define electromagnetic radiation a. Solids 4. Define what is meant by ionising radiation b. Liquids 5. Relate the discovery of x-rays by Rontgen c. gases 6. Review SI units and symbols 7. Review scientific notation and use of powers of 10 Slide 3 fchs.ac.ae Slide 4 fchs.ac.ae  Matter and Energy Energy Described as the ability to do work. Matter occupies space It exists in many form and can be converted from one form to another. Matter can be transformed and alter its state/shape Change of state does not alter the number of atoms, or mass Ex. Wind energy is converted into electric The Greek symbol “Delta”  indicates a change in the variable Relationship between energy and matter Energy is the ability to do work, W, as W = E Albert Einstien’s famous equation E=mc2 quantifies the E = Ef – Ei , relationship. with Ef = final energy, and Ei = initial energy. Slide 5 fchs.ac.ae Slide 6 fchs.ac.ae Worksheet Task Electromagnetic radiation 1. Forms of energy Form of energy that is produced by oscillating electric and 2. List the physical quantities and their units of magnetic disturbance, or by the movement of electrically measurements charged particles traveling through a vacuum or matter 3. Fundamental and derived quantities and units 4. Scales and scientific notations I lections Don't Slide 7 fchs.ac.ae Slide 8 fchs.ac.ae  Matter and Energy Electromagnetic (e/m) energy is that carried by e/m radiation, and this includes: lowenergy Radio waves him Microwaves any highene Infrared waves 9 Light increasing energy Shen y Ultraviolet waves X-rays niah Gamma rays, -rays Energy that travels through space is radiation Hence electromagnetic radiation Slide 9 fchs.ac.ae Slide 10 fchs.ac.ae Matter and Energy Electromagnetic spectrum Matter that intercepts radiation is said to be irradiated To be irradiated also means to be exposed The radiation imparts energy to the matter (patient) This is referred to as energy absorption Radiation is the transfer of energy Ionisation is the removal of an electron from an atom Ionising radiation can eject an electron from an atom This produces the electron plus an ion (charged atom) Slide 11 fchs.ac.ae Slide 12 fchs.ac.ae Ionisation Sources of Ionising Radiation Ionisation is the removal Many types of radiation (light, radio waves, sound waves) are of an atomic electron more or less harmless, but ionising radiation can severely The ejected electron and damage living tissue. the resultant positively- Ionising radiation comes from both natural sources and charged atom together Xray “man-made” sources are called an ion pair Irradiation gives rise to dose (absorbed energy) In addition to e/m radiation, energetic There are different forms of dose in humans particles – like - The derived SI unit of dose is the sievert, Sv (J/kg) particles, -particles, A more useful unit is the mSv (10-3 Sv) protons and neutrons – can ionise. Natural radiation gives humans a dose of about 3 mSv/year Bushong, Figure 1-2, page 7 Slide 13 fchs.ac.ae Slide 14 fchs.ac.ae Sources of Ionising Radiation Sources of Ionising Radiation Natural sources: Contribution of various Cosmic rays (from space) sources to the average Terrestrial (earth and rock) U.S. population Internally (potassium, K-40 is radioactive) radiation dose, 1990 and 2006. Gases (like radon, Rn, found in mines) (Note increase due to Man-made sources: medical use!) Radioactive sources, isotopes used in medicine, industry Go through calculation: Radiation from machines like x-ray tubes, synchrotrons Bushong, page 7. Bushong, Figure 1-3, page 7 Slide 15 fchs.ac.ae Slide 16 fchs.ac.ae Sources of Ionising Radiation – Calculation (Bushong p 7) Discovery of X-rays In 2006, what percentage of US radiation dose was attributable On 8 November 1895 by Wilhelm to medical imaging? Röntgen (sometimes spelt Roentgen) Medical imaging = 3.2 mSv x-ray image of the left hand of his Total dose = 6.3 mSV wife “x” because of the essentially Fraction = (3.2 mSv/6.3 mSv) unknown nature of the radiation at = 3.2/6.3 that time = 0.51 (keep just 2 significant figures – why?) This discovery rapidly (within 20 As a percentage, 0.51 = 51% years) led to the development of modern radiology Bushong, Figure 1-6, page 9 Slide 17 fchs.ac.ae Slide 18 fchs.ac.ae Some Important Words Development of Modern Radiology Radiography (includes mammography) Radiography – discipline of the production of medical images X-ray system (usually) above patient Radiographer – the person who produces the image Film, or solid state detectors Radiographic – things pertaining to radiography (as in CR, computed radiography and DR, digital radiography) Patient stationary and static 2-dimensional (2-D) image acquired Radiology – discipline of diagnosis from a medical image Fluoroscopy Radiologist – medically qualified diagnostician X-ray system below patient, solid state detectors Radiology – discipline of use of ionising radiation Patient stationary and moving 2-D image/video Radiologic – things pertaining to radiology Computed Tomography, CT x-ray system rotates around patient, solid state detectors Radiographer = Radiologic Technologist in some countries (US) Patient stationary and 3-D (x, y and z) image or 4-D (x, y, z and time) video acquired Slide 19 fchs.ac.ae Slide 20 fchs.ac.ae Development of Modern Radiology Development of Modern Radiology x-rays produced by a powered x-ray tube Development of diagnostic x-rays was made possible by: Characterised by: Transformer (increased voltage) Applied DC voltage, V, (in kVp; peak voltage in 1000 V) FilmI (as imaging R drd medium) fe imagereseptor.FR Tube current, I, (in milliamp, mA) Coolidge tube (evacuated glass envelope) Exposure time, t (in seconds, s) 1dm him Last two often run together as the product of current  time: Then came the inventions of the: Bucky (1913, grids to minimise imaging of x-ray scatter) So will see “kVp” and “mAs” as reported system parameters Light amplifier tube (1946, for fluoroscopy) X-rays will be: Computed tomography (1961, by Godfrey Hounsfield who Filtered – changes energy distribution within x-ray beam received a Nobel Prize in 1979) Collimated – to define the patient area to be exposed Solid state detectors (1960, LED) Slide 21 fchs.ac.ae Slide 22 fchs.ac.ae Reports of Radiation Injury Typical X-ray Room This is the other main topic of this course; Specifically, how to prevent them! A. x-ray tube Many early workers in this field died of radiation poisoning B. Table/couch Because of effective radiation protection practices, C. Lead curtain radiology/radiography is now considered a safe occupation D. Bucky (cover) You will learn about: E. Apron & gloves ALARA (dose will be “As Low As Reasonably Achievable”) Getting the ‘best’ x-ray image the first time (no repeats!) LF. Viewing window Use of lead aprons and gloves when necessary G. Imaging equipment Bushong, Figure 1-9, page 13 Minimise exposure, maximise distance and use shielding Slide 23 fchs.ac.ae Slide 24 fchs.ac.ae Summary Summary Check that you can satisfy the learning outcomes for this lecture Go over calculations/exercises undertaken during the lecture electromagnetic radiation Make sure that you can define the following terms: Electromagnetic spectrum matter ionising radiation energy and work electromagnetic radiation ionising radiation Check your understanding of *words “radiography”, “radiologic”, etc. Review SI units and symbols Review scientific notation and use of powers of 10 Slide 25 fchs.ac.ae Slide 26 fchs.ac.ae  Learning Outcomes At the conclusion of this lecture, associated tutorial and practical RMI 213 session (if relevant), you will be able to: Principles of medical imaging 1. List the basic concepts of radiation protection 2. Explain why different strategies to achieve protection are appropriate in different situations Lecture 2 3. List and define units of radiation and radioactivity Essential Concepts - 2 Slide 1 fchs.ac.ae Slide 2 fchs.ac.ae Basic Radiation Protection Basic Radiation Protection Protection of patients, and of the radiographer, is paramount: Use intensifying screens Practice the ALARA principle fdee ISs dT etIe __ Effectively amplifies Use protective apparel e the detected radiation Keeps radiation exposures As Low As Reasonably Achievable Radiographer wears apron and gloves if necessary Use Filtration Use gonadal shielding Absorbs low energy x-rays that contribute to dose but not to Protect groin area of patients of child-bearing age from image quality radiation, if not part of the required exposure region Use collimation Use protective barriers Protects adjacent tissue from irradiation Stand behind shield to reduce exposure Reduces scattered radiation Control from behind lead-glass viewing windows Slide 3 fchs.ac.ae Slide 4 fchs.ac.ae Basic Radiation Protection Read, and be sure to understand, the information in Box 1-2, Bushong page 14; “The Ten Commandments of Radiation Protection” You have a duty of care towards: The patient Any other person assisting Your own health and safety If in doubt, ASK. Slide 5 fchs.ac.ae Slide 6 fchs.ac.ae Units of Measurement Units of Measurement in Radiologic Physics Length –1 meter Radiographic Special Units International System Quantities (SI) Units Mass –1 kg Charge Roentgen (R) Time –1 s Exposure, X per unit mass, C/kg coulomb/kg of air (C/kg of air) Charge, Q , with units of coulomb, C Absorbed energy Dose Energy, E, with units of joule, J Dose, D per unit mass, J/kg Gray, Gy (or Gyt) (t for tissue) Effective dose, E Absorbed energy Sievert, Sv Equivalent dose, H per unit mass, J/kg Sievert, Sv Disintegration Radioactivity, A Becquerel, Bq per second, s-1 Slide 7 fchs.ac.ae Slide 8 fchs.ac.ae Measurement in Radiologic Physics Terminology for Radiologic Science Radiologic science is all about energy Some dose quantities relate to measurements in air Energy can be related to temperature Signified by subscript ‘a’, as in Gya – see opposite Some dose quantities relate to measurements in tissue Electromagnetic radiation energy can Signified by subscript ‘t’, as in Gyt also be related to frequency and wavelength through the expression E = hf = hc/ (we will review this later) Bushong, Figure 1-18, page 21 Slide 9 fchs.ac.ae Slide 10 fchs.ac.ae Terminology for Radiologic Science Terminology for Radiologic Science We have mentioned special units for exposure and dose: Radioactivity is not associated with x-ray tubes Air kerma: for expressing exposure (x-ray tube output) Radioactivity is used for quantifying radioactive output from Kerma = kinetic energy released in matter isotopes (radioactive substances) It is measured by the ionization of air (C/kg = Gya) Modern unit is the becquerel, Bq Starting point for determining dose in patients The old unit was the curie, Ci (the only SI unit ever named Instrument placed between the x-ray tube and the patient after a woman) For a given x-ray unit the exposure, X, is normally 1 Bq = 1 nuclear disintegration per second established for set values of kVp (voltage) and mAs (charge) 1 Ci = 3.7  1010 nuclear disintegrations per second Old unit of X was the röntgen, R 100 R = 1 C/kg = 1 Gya (subscript ‘a’ means in air) Slide 11 fchs.ac.ae Slide 12 fchs.ac.ae Terminology for Radiologic Science Summary Check that you can satisfy the learning outcomes for this lecture Go over calculations/exercises undertaken during the lecture Dose also has old units you may come Make sure you can define the following terms: across (particularly in texts from the USA) ALARA Old unit of effective dose was rem, charge (and its unit) 1 rem = 10 mSv Exposure (and its unit) dose (in its various forms, and the units) Old unit of absorbed dose was rad, Check your understanding of the words shown in the table of units 1 rad = 10 mGyt of measurement (subscript ‘t’ for tissue) Check information in Box 1-2, Bushong page 12; “The Ten Commandments of Radiation Protection” Bushong, Figure 1-20, page 23 Slide 13 fchs.ac.ae Slide 14 fchs.ac.ae  Learning Outcomes At the conclusion of this lecture, associated tutorial and practical RMI 213 session (if relevant), you will be able to: Principles of medical imaging 1. Relate the history – the evolution – of model of the atom 2. Describe the currently accepted structure of the atom 3. Describe electron shells, stability and instability within Lecture 3 atomic structure The Structure of Matter 4. Discuss radioactivity and describe the characteristics of alpha and beta particles 5. Explain the differences between the particulate form and the electromagnetic form of ionizing radiation Slide 1 fchs.ac.ae Slide 2 fchs.ac.ae Prescribed Text Atomic Species Bushong, S.C., Radiologic Science for Technologists, 10th edition, The atom is the basic ‘building block’ of matter Mosby/Elsevier; St Louis, 2012, pages 26-43. An atom is the smallest particle that has all the Notes: properties of an element The Greeks believed there were 4 elements; 1. Each lecture in this course will relate very closely to a specific represented in the diagram opposite set of pages in the above text. It is strongly recommended that We now know there are about 118 elements students read the pages indicated prior to coming to the 26 of these are artificially produced Bushong, Figure 2-2, page 28 lecture. 92 are naturally occurring 2. The students outcomes listed at the commencement of each Mendeleev arranged these elements in what, today, we know as the lecture are essentially those found in the prescribed text for Periodic Table (dates from the about 1860s) the relevant chapter. The Bohr atom is a reasonable approximation of a real atom Slide 3 fchs.ac.ae Slide 4 fchs.ac.ae The Periodic Table Closer Atoms harder forradiation tocomethrough http://chemicool.com/ Slide 5 fchs.ac.ae Slide 6 fchs.ac.ae Atomic Particles Bohr Model of the Atom Electron The Bohr model of the atom is a quantum model (1913) Charge: qe = –1.6  10-19 C Electrons exist in stable orbits with fixed energies Mass: me = 9.1  10-31 kg The electron extent defines the volume of the atom Electrons travel in defined circular orbits around the nucleus. Proton Electrons are negatively - charged Charge: qp = +1.6  10-19 C At the center is the positively-charged nucleus Mass: mp = 1.673  10-27 kg The nucleus provides the mass of the atom The nucleus comprises protons and neutrons Neutron Protons are positively + charged Charge: qn = 0 Neutrons are uncharged Mass: mn = 1.675  10-27 kg Bushong Figure 2-5, page 30 Slide 7 fchs.ac.ae Slide 8 fchs.ac.ae  Atomic Mass Protons and neutrons together are referred to as nucleons The atomic mass unit (amu) Atomic number z 1 amu = 1/12 mass of C-12 atom me = 0.000549 amu mp = 1.00728 amu mn = 1.00867 amu Atomic mass number A (an approximate mass) This is essentially the number of nucleons For the neutron and the proton, A = 1 For the electron, A = 0 Slide 9 fchs.ac.ae Slide 10 fchs.ac.ae Atomic Structure Atomic Structure The atom is virtually empty space Electrons exist in stable orbits, grouped in shells The atomic number Z is the number of protons; Np = Z Shells are labeled K, L, M, etc., from that closest to the nucleus for a neutral atom, Z is the number of electrons Electron binding energy, BEe , is the energy required to Z determines the chemistry of the atom ionize the atom – to remove an electron The number of neutrons is Nn = N K shell can contain a maximum of 2 electrons The number of nucleons is N + P L shell can contain a maximum of 8 electrons The atomic mass is normally given in amu M shell can contain a maximum of 18 electrons Isotopes are atomic species with same Z but different N N shell can contain a maximum of 32 electrons Item atoms Closed (filled) shells represent very stable (un-reactive) atoms Slide 11 fchs.ac.ae Slide 12 fchs.ac.ae Electron Shells Ionization Ionization is the removal of an Ionization of a carbon electron or the addition of an atom by an x-ray leaves electron to the neutral atom the atom with a net X-rays are able to ionize atoms, electric charge of +1 hence the term ionizing radiation BEes are around 5 eV and upwards The ionized atom and the released electron N is generally slightly greater than are called an ion pair Z, but there are exceptions Bushong Figure 2-6, page 31 Bushong Figure 2-7, page 32 Slide 13 fchs.ac.ae Slide 14 fchs.ac.ae Ask Dr Electron Orbit Atomic Nomenclature Electrons go around the nucleus in fixed orbits An alphabetic abbreviation is used for the chemical symbol Electrons are attracted to the positively charged nucleus This also defines Z Although accelerating, electrons exists in stable orbits Two systems are used – take the example of barium, Ba: 135Ba56 The subscript, Z = 56, is really redundant (why?) +Z The superscript is the atomic mass number, A = N + Z From this we see that N = 135 – 56 = 79 –1 The actual atomic mass of this element is 134.91 amu There are other isotopes of barium speed Monash University Department of Medical Imaging and Radiation Sciences An alternate notation is Ba-135 (easier to write) Slide 15 fchs.ac.ae Slide 16 fchs.ac.ae Atomic Nomenclature Some Elements A more complete notation can also be used: Some elements are important Atomic mass number Valence state in a study of radiologic science; N A +/– K-shell binding energies are Chemical symbol Z X# particularly important in determining x-ray energies. Atomic number Number of neutrons In the alternate notation X–n (e.g. Ba-135), n is the atomic mass number, X leads you to the atomic number, Z. Bushong Table 2-3, page 35 Slide 17 fchs.ac.ae Slide 18 fchs.ac.ae Nomenclature with A, Z and N Combinations of Atoms Isotopes are atomic nuclei with the same Z but different N A molecule is a collection of atoms with a fixed ratio of Example: I-130 and I-131 (I = iodine) elemental species in a fixed arrangement Isobars are atomic nuclei with the same A but different Z Na + Cl → NaCl Example: I-131 and Xe-131 (Xe = xenon) Here NaCl is a molecule (common salt in this example) Isotones are atomic nuclei with the same N but different A The structure depends on the type of bonding Example: I-130 and Xe-131 Types of bonds include Isomers are atomic nuclei with the same Z and same A Covalent (think of some examples) They have different nuclear energy states Ionic (think of some examples) H W Example: Tc-99 and Tc-99m (Tc = technetium, the ‘m’ Compounds denotes an ‘excited’ nuclear state) Are a quantity of matter of the one molecule Slide 19 fchs.ac.ae Slide 20 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: electron, proton, neutron atomic number, mass number, atomic mass unit electron arrangement in the atom arrangement of the Periodic Table radioactivity and half-life alpha-particle and beta-particles (two types) Slide 21 fchs.ac.ae timetook to lose half of energy  Learning Outcomes At the conclusion of this lecture, associated tutorial and practical RMI 213 session (if relevant), you will be able to: Principles of medical imaging 1. Identify the properties of photons 2. Explain the inverse square law 3. Describe the distinctions between wave theory and quantum Lecture 4 theory Electromagnetic Energy 4. Describe the electromagnetic spectrum and discuss the applications of each frequency region 5. Use the wave equation c = f  in simple calculations Slide 1 fchs.ac.ae Slide 2 fchs.ac.ae Prescribed Text Photons Bushong, S.C., Radiologic Science for Technologists, 10th edition, The electromagnetic (e/m) field surrounds us Mosby/Elsevier; St Louis, 2012, pages 44-59. This e/m energy exists in a continuum Notes: Only a very small energy region is visible as “light” 1. Each lecture in this course will relate very closely to a specific Photon: energy associated with a quantum of e/m energy set of pages in the above text. It is strongly recommended that Spectrum goes from: students read the pages indicated prior to coming to the very low energies – radio waves, to lecture. very high energies – gamma-rays (-rays) 2. The students outcomes listed at the commencement of each Includes microwaves, infra-red, light, ultraviolet, x-rays lecture are essentially those found in the prescribed text for e/m waves can be described classically as waves: f,  the relevant chapter. Can also be described by these energy quanta, photons Slide 3 fchs.ac.ae Slide 4 fchs.ac.ae Speed and Amplitude of Photons Frequency and Wavelength of Photons In a vacuum, the photon wave speed is c = 3.0  108m/s In time, the interval between adjacent crests is the period, T (s) In materials, speed will generally be a little lower than this In space, the interval between adjacent crests is the wavelength, E/m waves (classical) are sinusoidal  (m) T/  I variations of the electric field E and The wave frequency is the magnetic field H f = 1/T (units s–1 or Hz) The wave intensity, I, is related to The angular frequency is the amplitude, A, as I  A2 hi it 0  = 2f (units radian/s) The wave-number is k = 2/ (m–1) In this wave picture, the waves exist for all time and all space; e.g. as The wave speed is E = E0 sin(2[ft – x/]) 0 Bushong, Figure 3-1, page 46 c = f  = /T = /k (m.s–1) Bushong, Figure 3-1, page 46 Slide 5 fchs.ac.ae Slide 6 fchs.ac.ae Frequency and Wavelength – Example Calculation Electromagnetic Spectrum E/m waves cover a vast range of frequencies Yellow light has a wavelength of 580 nm. What is its frequency? This is the spectrum from around 102 Hz to 1024 Hz We are given  and asked to find f... Corresponds to wavelengths from 107 m to 10-16 m Use formula c = f  with c = 3.0 × 108 m/s Diagnostic medicine uses a few of the available ‘bands’: Radio-waves in Magnetic Resonance Imaging (MRI) Rearrange: f = c/ Light in the doctor’s visual examination of the patient With  = 580 nm = 580 × 10-9 m, x-rays in all forms of radiography and Computed Tomography (CT) then f = (3.0 × 108)/(580 × 10-9) -rays in Positron Emission Tomography (PET) and other related imaging schemes so f = 3.0/580 × 1017 = 0.00517 × 1017 Note: sound is used in medical ultrasound, as sonography, but sound Answer: f = 5.17 × 1014 Hz energy is not a form of electromagnetic energy Slide 7 fchs.ac.ae Slide 8 fchs.ac.ae The E/m Spectrum Visible Light Note the following: In a uniform medium, light rays travel in straight lines; Frequency range Different wavelengths are Wavelength range associated with different Energy range in eV colors; Light rays travel though Bands used in diagnostic imaging transparent media; http://en.wikipedia.org/wiki/Dispersion_relation Materials that absorb light totally are said to be opaque; The concept of the Travelling from one medium to another, waves are refracted photon is related directly to the energy (bent); of the wave. Light: from  = 400 nm to 700 nm (approximately). Bushong, Figure 3-6, page 50 Slide 9 fchs.ac.ae Slide 10 fchs.ac.ae Other E/m Bands near Light Ionising Radiation Infrared (IR) is the band slightly lower in energy than light; Ionising radiation – x-rays and -rays – will eject electrons and associated with heat energy, radiant heat. so ionise atoms; they are labelled by their photon energy, E RF is ususally characterised by its frequency, f Ultraviolet (UV) is the band slightly higher in energy than light; exposure to UV can result in molecular damage and IR, light, UV are usually characterised by their wavelength,  sunburn. x-rays and -rays differ only by their origin: Sunlight comprises IR, visible and UV radiation. x-rays result from changes in electron energy levels -rays result from changes in nuclear energy levels Radiofrequency (RF) is the radiation that radio and television As we shall see, photon energy is E = hf = hc/ use; usually defined by the frequency bands utilized; Here h is Planck’s constant: h = 6.63  10-34 Js (SI units) e.g. 63.7 MHz. You will sometimes see ħ = h/2; referred to as ‘h-bar’ Slide 11 fchs.ac.ae Slide 12 fchs.ac.ae Wave-Particle Duality Wave-Particle Duality E/m waves can be described by “Waves” waves – the classical picture energy bundles (quanta) This is the dual nature of e/m radiation. Changes in electron energy levels 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 Changes in nuclear energy levels “Particles / Photons” small ‘particles’ Bushong, Figures 3-8, 3-9 and 3-10, pages 50-51 Slide 13 fchs.ac.ae Slide 14 fchs.ac.ae Wave Model: Visible Light Interactions – Light Light is simplest to describe as a wave, Transmission possibilities: But light sometimes behaves as a stream of photons. Transparent Light interacts with matter and sets molecules vibrating; (low absorption and low The energy may continue unchanged – transmission – or scatter) The energy may be re-radiated in another direction – reflection or refraction (different forms of scatter); Translucent The energy may be removed – absorption by atoms (the analogy (medium absorption and with water waves is useful). scatter) Attenuation is the combination of scatter and absorption effects Opaque that removes photons from the initial incident beam direction. (high absorption) Bushong, Figure 3-13, page 54 Slide 15 fchs.ac.ae Slide 16 fchs.ac.ae µ ffsdgd Attenuation Interactions – x-rays Inverse Square Law Transmission possibilities: When radiation is emitted from a source, the intensity decreases with distance from the source Transparent: air Imagine a point source. At distance d from the point source, we (low absorption and low can imagine a sphere of radius d and surface area A = 4d2. scatter) The energy from the point source will be spread uniformly over this surface. Radiolucent: soft tissue From a point source, the radiation intensity follows the “inverse (medium absorption and square law” scatter) Id = I0 /(4d2) or Id  1/d2 Radiopaque: bone where Id is the intensity at distance d away from the source (high absorption) A more general expression is I1/I2 = d22/d12 Bushong, Figure 3-14, page 54 Slide 17 fchs.ac.ae Slide 18 fchs.ac.ae Inverse Square Law – Example Calculation Particle Model: Quantum Theory The intensity of a light is 100 mlm (milli-lumens) at distance 1 m X-rays and -rays are usually identified by the photon energy from the light source. What is the intensity 3 m from the source? 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, We are given I1 and d1 and d2 asked to find I2... 1 eV = 1.6  10-19 J Use formula I1/I2 = d22/d12 Range for x-rays and -rays is 10 eV to 50 MeV Wavelength range 10-10 m to 10-14 m Rearrange: I2 = I1 (d12/d22) Note: 10-10 m is about the size of a light atom Then I2 = 100 × (12/32) = 100/9 Note: 10-14 m is about the size of the atomic nucleus Answer: I2 = 11 mlm Photon energy is E = hf and c = f  so E = hc/ The photon is best considered as a ‘bundle’ of energy Slide 19 fchs.ac.ae Slide 20 fchs.ac.ae Photons – Example Calculation Waves and Photons What is the Energy, in J and in eV, of a photon of green light with A wave is best thought of as a continuous sine wave; a wavelength of 550 nm? It exists for many hundreds or thousands of wavelengths We are given  and asked to find E... It essentially has one frequency, f, and one wavelength,  Use formula E = hc/ with c = 3.0×108 m/s and h = 6.63×10-34 Js The e/m wave travels at c = 3  108 m/s Substitute: E = (6.63 × 10-34 Js) × (3.0 ×108 m/s)/(550×10-9 m) A photon is a wave of limited extent in so E = 0.0362 × 10-17 J = 3.62 × 10-19 J time and space; In eV, E = (0.0362 × 10-17 J)/(1.6  10-19 J/eV) A photon has a ‘start’ and an ‘end’ so E = 0.0226 × 102 eV = 2.26 eV The wave shape is not sinusoidal Answer: E = 3.62 × 10-19 J = 2.26 eV The photon travels at c = 3  108 m/s Bushong, Figure 3-16, page 57 Slide 21 fchs.ac.ae Slide 22 fchs.ac.ae Matter and Energy Matter and Energy – Example Calculation Classical physics embodies conservation laws of What is the energy equivalence of one electron mass? energy, E, Use me = 9.11 × 10-31 kg and c = 3 × 108 m/s mass, m, We are given me and c and asked to find E... charge, q, linear momentum, L = mv, and Use formula E = mc2 angular momentum, P Substitute: E = (9.11 × 10-31 kg) × (3 × 108 m/s)2 Quantum physics retains all these, apart from the conservation of mass so E = 82 × 10-15 J only these In eV, E = (82 × 10-15 J)/(1.6  10-19 J/eV) types Quantum physics considers mass to be a form of energy so E = 51.2  104 eV of This link is through Einstein’s famous equation E = mc2 Answer: E = 512 keV = 0.512 MeV Questions Slide 23 fchs.ac.ae Slide 24 fchs.ac.ae Mass and Energy Equivalence Summary Check that you can satisfy the learning outcomes for this lecture The figure opposite shows the Go over calculations/exercises undertaken during the lecture mass-energy equivalence for a range of energies, and includes Make sure you can define the following terms: the cases for electrons and speed, frequency and wavelength nucleons. period and wave number intensity and amplitude of a wave Nucleons are nuclear particles; transparent, translucent and opaque, radiolucent and radiopaque the neutron and the proton. photon and photon energy You should also be able to state and use the inverse square law and Einstein’s equation E = mc2 Bushong, Figure 3-17, page 58 Slide 25 fchs.ac.ae Slide 26 fchs.ac.ae  Learning Outcomes At the conclusion of this lecture, associated tutorial and practical RMI 213 session (if relevant), you will be able to: Principles of medical imaging 1. Define electrification and provide examples 2. State the laws of electrostatics Lecture 5 3. Identify units of electric current, electric potential, and Electricity and Magnetism infigns electric power 4. Identify the interactions between matter and magnetic fields. Slide 1 fchs.ac.ae Slide 2 fchs.ac.ae Prescribed Text Electrostatics Bushong, S.C., Radiologic Science for Technologists, 10th edition, Matter has mass, and an energy equivalence Mosby/Elsevier; St Louis, 2012, pages 60-74. Matter contains charged par;ticles (electrons and protons) Notes: Matter itself may be charged 1. Each lecture in this course will relate very closely to a specific Positive – fewer electrons (e) than protons (P) set of pages in the above text. It is strongly recommended that Negative – more electrons than protons students read the pages indicated prior to coming to the qe = –1.6  10-19 C (coulomb) lecture. qp = +1.6  10-19 C 2. The students outcomes listed at the commencement of each Any charge imbalance may be caused by contact, by friction, lecture are essentially those found in the prescribed text for or by induction the relevant chapter. Slide 3 fchs.ac.ae Slide 4 fchs.ac.ae Electrostatic Laws Electric Field Distribution Charges are associated with electric fields, E Electric field distributions for E is directed radially outwards from a positive charge; a number of simple cases are E is directed radially in towards a negative charge. shown; note E directions as Between two (or more) charged particles there is a force, F indicated by arrows. Like charges (same sign) repel; The repulsion/attraction is Unlike charges (opposite sign) attract. clearly seen in the E field distributions in diagrams C, D The direction of E for a charged object can be visualized as the and E. direction in which a positive charge would move. In case F, the diagram shows The force between two charges, Q1 and Q2 has magnitude that neutral particles such as F = k(Q1 Q2)/d2 (Coulomb’s law; note it is an inverse square law), the neutron (N) produce no where k is a constant and d is the distance between the two charges. electric field. Bushong, Figure 4-6, page 64 Slide 5 fchs.ac.ae Slide 6 fchs.ac.ae Electric Charge Distribution Electric Potential Electric charge distribution in To move one charge closer to another charge of the same sign (they repel, remember), you have to do work; matter is either uniform throughout, or located on the Doing work implies increasing the energy of the system (and lowering your total energy); material surface; Electric charges have potential energy, energy by virtue of their For a conductor, the electric charge position in the fields of other charged particles; is concentrated on the surfaces e.g. two positively charged bodies will, if released, accelerate with the highest curvature; away from each other (potential energy  kinetic energy). In most cases of interest here, it is The electric potential or voltage V is the potential energy per unit the free electrons that provide the charge; units joule per coulomb = volt; 1 V = 1 J/C moving charge in an electrical Don’t confuse V (voltage: italic) with unit V (volt: upright) conductor. Bushong, Figures 4-7, 4-8, page 65 In UAE, the mains supply is 220 V (AC, expressed as RMS) Slide 7 fchs.ac.ae Slide 8 fchs.ac.ae Electrodynamics VeryGood Superconductors Electrodynamics is the study of electric charges in motion, to make Superconductors have Concerned with electric current in electric conductors. Energy Fast zero resistance below A conductor allows easy flow of charge (electrons, usually); their An insulator is material where no current can be established; critical temperature TC A semiconductor is a material where, under certain conditions, the movement of charge may be controlled and Superconductors find behavior may vary significantly between conductor-type and use in magnetic insulator-type. resonance imaging, MRI At normal temperatures, all materials resist charge flow to some extent (insulators totally, conductors very little). Bushong, Figure 4-9, page 67 Slide 9 fchs.ac.ae Slide 10 fchs.ac.ae Material Examples Electric Circuits For much of this you are referred back to your common year physics course, GRU1123. Electric circuits are comprised of conducting wires (assumed to have zero resistance), circuit elements like resistors, capacitors, inductors, diodes, voltage sources: AC and DC (batteries), current sources. Parameters of relevance are the voltage, V , across elements, and the current, I , through elements. Generally in DC circuits, we use upper-case: V, I. In time-varying situations and AC circuits we use lower-case: v, i. Bushong, Table 4-1, page 67 Slide 11 fchs.ac.ae Slide 12 fchs.ac.ae Ohm’s Law Circuit Element / Component Symbols Ohm’s Law: V = IR (DC cases), or v = iR (AC cases) This table shows the The ratio of the voltage across the component to the current though symbols for common the component is a constant; the resistance, R circuit components. For certain circuits and components, Ohm’s Law holds Worked Example: Detector A DC voltage source Q2. A DC voltage of 5.0 V exists across a resistor R = 10 . In a closed circuit where a current can be established, determine the current. (a battery) is We are given voltage V and resistance R and asked to find the current I... Use Ohm’s Law V = I R ; rearrange: I = V / R An AC voltage source Substitute: I = 5.0 V / 10  is Answer: I = 0.5 A (DC) Bushong, Table 4-2, page 66 Slide 13 fchs.ac.ae Slide 14 fchs.ac.ae Series Circuits – Resistors Parallel Circuits – Resistors Here components are Here components are connected one after the other connected between the with wires, and connected to two power supply wires. the power supply. The total resistance, RT , The total resistance is the is expressed through sum of the individual 1 1 1 1 resistances,    ... etc. Bushong, Figure 4-11, page 67 RT R1 R2 R3 Bushong, Figure 4-12, page 68 RT = R1 + R2 + … etc. The currents through all components sum to the total current; The current through all components is identical, I1 = I2 = … etc. IT = I1 + I2 + … etc. The total voltage is the sum of the voltages, VT = V1 + V2 + etc. The voltage is the same across all components, and equal to The voltage across an individual resistor is VR = IR the supply voltage, VT = V1 = V2 = … etc. Slide 15 fchs.ac.ae Slide 16 fchs.ac.ae Simple Circuits – Example Calculations Current and Electron Flow Q3. What is the equivalent resistance of six 10  resistors connected in “Conventional current” – an historical definition – is the series? direction in which positive charges would flow. Use formula RT = R1 + R2 + … etc. The negatively charged electrons – the actual moving charges in Substitute: RT = 10  + 10  + 10  + 10  + 10  + 10  most cases – move in the opposite direction! Answer: RT = 60  In a DC circuit, we show the conventional current direction with Q4. What is the equivalent resistance of these six 10  resistors an arrow. connected in parallel? 1 1 1 1 Current is the rate at which (positive) charge moves, I = Q/t Use formula    ... etc. RT R1 R2 R3 So for electrons, I = –Qe/t (as Qe is negative) 1 1 1 1 1 1 1 6 Substitute:        If an electron goes this way , the current goes this way RT 10 10 10 10 10 10 10 In the AC case we have i = q t or, more generally, i = dq/dt Answer: RT = 10/6 = 1.7  Slide 17 fchs.ac.ae Slide 18 fchs.ac.ae DC and AC Electric Power In DC cases, Electric power, P, is measured in watts, W the charge flow is constant in time, 1 W = 1 J/s I = Q/t = constant; 1 W is the equivalent of a 1 A current flowing in a circuit the voltage V is also constant. established by a 1 V voltage across the circuit/component In AC cases, the current varies; In DC cases, this is simply calculated; with mains supply, the time variation for both current and voltage is sinusoidal: PDC = I V ( = I2R = V2/R ) v = v0 sin(2ft) in the UAE the mains frequency is f = 50 Hz. Bushong, Figures 4-13 & 4-14, pages 68, 69 Slide 19 fchs.ac.ae Slide 20 fchs.ac.ae Electric Power Electric Power – Example Calculation In AC cases, we first need the average voltage and current: Q5. If the cost of electric energy in the UAE is 1 Dhs per kW-hr, what will it cost to operate a 100 W light for an average of 5 hours per day For sinusoids which have positive and negative values, a for 30 days? simple average would yield zero, so We are given the power rating of the light, the times it is used and the Instead, we square each value, then calculate the mean of cost per energy unit (kW-hr)... all of the squares, then take the square root of that mean; Use formulae Energy used = Power × time, and the RMS (root-mean-square) value is square root of the Cost = (cost per energy unit) × (energy used) mean of the squared quantity. Substitute: Energy used = (100 W) × t = (100 W) × (5×30) In the UAE the mains voltage is 220 VRMS = 15000 W-hrs = 15 kW-hrs PDC = IV = I2R = V2/R 1 Dhs Substitute: Cost = kW. hr × 15 kW-hrs PAC = iRMSvRMS = iRMS2 R = vRMS2/R Answer: Cost = 15 Dhs Slide 21 fchs.ac.ae Slide 22 fchs.ac.ae Magnetism Moving Charged Particles In its simplest form, a magnetic A spinning charged particle will field is associated with a moving also produce a magnetic field; electric charge; This gives rise to the quantum Thus an electron in orbit around attribute of fundamental particles the nucleus in an atom produces called ‘spin’. a magnetic field. Strangely, neutrons also possess For an atom we define the this quantum attribute, even strength of the atomic magnetism though they are, overall, by the magnetic moment, m. electrically neutral particles. Bushong, Figures 4-15 & 4-16, page 71 Bushong, Figure 4-17, page 71 Slide 23 fchs.ac.ae Slide 24 fchs.ac.ae  Bar Magnets Electromagnets A bar magnet is a macroscopic piece of A current in a coil of wire (moving charges, remember) can material made up of N atoms, each act very much like a bar magnet. carrying a permanent magnetic moment, The current direction at each end of m, so M = Nm the coil defines the magnetic pole. The magnetic moment is a ‘dipole’ (a ‘bar I, current I, current magnet’ at the atomic or molecular level) Permanently aligned dipoles are referred to as ferromagnetic materials, and have a N and S pole. S N Bushong, Figure 4-20, page 72 Bushong, Figure 4-18, page 71 Slide 25 fchs.ac.ae Slide 26 fchs.ac.ae Magnetic Materials Electromagnetism Magnetic materials are classified by their interaction with an A moving charge constitutes a current external magnetic field, H. A current produces a magnetic field Diamagnetic – very weak (effectively zero) interaction with H A coil of wire is referred to as a solenoid Paramagnetic – weak interaction with H A solenoid with a DC current, I, produces a magnetic field, H, Ferromagnetic – strong interaction with H that is proportional to the current; H  I H is (approximately) constant within the solenoid, and (approximately) zero outside the solenoid The magnetic field H has units of amp/m, A.m-1 usedin with A solenoid with an AC sinusoidal current, i = i0 sin(2f t), Mri react m agnetic produces a magnetic field inside the solenoid; H = H0 sin(2f t) hing Bushong, Table 4-3, page 73 an fchs.ac.ae fchs.ac.ae takin Slide 27 Slide 28 Mri 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: electric charge, electric field and its distribution electrostatics law: force between charges Ohm’s law, voltage, current and resistance series and parallel circuits electric power and use of RMS in AC circuits relation between moving charge and magnetic moment magnetic poles for current carrying coils (solenoids) Slide 29 fchs.ac.ae  Learning Outcomes At the conclusion of this lecture, associated tutorial and practical RMI 213 session (if relevant), you will be able to: Principles of medical imaging List the magnetic parameters and explain their origin State the relation between B, H and M Define the constant 0 Lecture 6 Explain what is meant by magnetic susceptibility Electromagnetic Induction State Lenz’s law and use this in simple calculations Describe in general terms how an electric motor works Describe in general terms how an electric generator works Explain the operation of a transformer Slide 1 fchs.ac.ae Slide 2 fchs.ac.ae Prescribed Text Laws of Magnetism Bushong, S.C., Radiologic Science for Technologists, 10th edition, There is no ‘free’ pole (like a free charge) Mosby/Elsevier; St Louis, 2012, pages 75-83. All magnetic entities have both a N and S pole On-line movie clips of the workings of motors and generators at A magnetic arrangement of a N and a S separated by a small http://www.animations.physics.unsw.edu.au/jw/electricmotors.html distance is called a magnetic dipole (like a bar magnet) Notes: Otherwise, the laws of magnetism are similar to those for 1. Each lecture in this course will relate very closely to a specific set of electrostatics pages in the above text. It is strongly recommended that students Like poles (N-N, S-S) repel; read the pages indicated prior to coming to the lecture. Unlike poles (N-S) attract; 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 Slide 4 fchs.ac.ae Magnetic Force Straight Current-Carrying Wire A current-carrying conductor generates a magnetic field; A current produces a magnetic field, H A current-carrying conductor placed in a magnetic field experiences Lines of a magnetic field are always a force; think of this as two magnetic fields interacting. closed loop The magnitude of the force is F = IB sin() where The magnetic field strength is I is the electric current, H = I/(2R), units of Amp/m A.m-1  is the length of the conductor, The Right-Hand (RH) rule: B is the magnetic field of induction, and With your thumb in the  is the angle between the direction of current direction of the current, flow and B (maximum F when  = 90) your fingers will curl around The direction of the force is perpendicular to in the direction of H. both I and B http://commons.wikimedia.org/wiki/File:Right_hand_rule_cross_product.svg Bushong, Figure 4-29, page 76 and http://people.stfx.ca/jpowell/work/lab/rightframe.html Slide 5 fchs.ac.ae Slide 6 fchs.ac.ae Magnetic Susceptibility Magnetic Materials Magnetic permeability Magnetic materials are characterized by their value of r Ability of a material to attract the lines of magnetic field intensity, given by  r State r Material Non Magnetic 1 Air,wood,glass The magnetization, M, of a material is shape dependent Diamagnetic  1 – 10-3 Copper The susceptibility of a material to be magnetized when placed in a magnetic field H is given by Paramagnetic  1(but Gadolinium small) M = H ( = Greek letter “chi”) Ferromagnetic >> 1 (up Iron,Nickel,Cobalt where  = (r – 1) is called the magnetic susceptibility, to 1000) Degree to which a material can be magnetized Slide 7 fchs.ac.ae Slide 8 fchs.ac.ae  induction 5 91g Electromagnetism Electromagnetic Flux Any change in motion induces a Consider a loop of wire of area A placed in a B-field magnetic field H = nI Magnetic flux Φ through a surface is the component of the A coil of wire is called a solenoid, N S magnetic B field passing through that surface B  The solenoid acts like a bar magnet; Magnetic flux, , passing through this loop area is A http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html defined by In the solenoid, the direction of H is  = BA cos() B given by the right-hand (RH) rule: B – magnetic field with your thumb in the direction of A- Area A current at each point, your fingers - angle will point along H. http://simple.wikipedia.org/wiki/Magnetic_flux Slide 9 fchs.ac.ae Slide 10 fchs.ac.ae Electromagnet Electromagnet – Example Calculation An electromagnet is a current carrying coil of wire wrapped Q1. A coil has 1000 turns and is 50 cm long. With a DC current of around an iron core, which intensifies the induced magnetic 200 mA through the windings, what is the field inside the coil? field. We are given the number of turns, N , the length of the winding,  , H depends on the number of turns of wire per unit length, N/ H = (N/)I = nI , with n = N/ number orturns and the current I , and asked to determine the field strength H... Magnetic field of induction, B, is given by B = 0 r H Use formula H = (N/)I where 0 is the magnetic permeability of a vacuum, r is the relative permeability of the material placed in the field H Substitute: H = (1000 / 0.50 m) × 0.200 Magnetic permeability of a vacuum is 0 = 4  10-7 (SI units)