Physics Of Radiography - New York University

Physics of RadiographyYao WangPolytechnic University, Brooklyn, NY 11201Based on J. L. Prince and J. M. Links, Medical Imaging Signals andSystems, and lecture notes by Prince. Figures are from the textbook.

Lecture Outline Atomic structure and ionization Particulate Radiation– Focusing on energetic electron interaction EM Radiation–––––PhotoelectricCompton scatteringLikelihood of eachEM radiation measurementAttenuation of radiation Radiation Dosimetry– Exposure, doseEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn2

Atomic Structure An atom {a nucleus,electrons} nucleons {protons; neutrons} mass number A # nucleons atomic number Z # protons # electrons– Define an element with aparticular symbol: H, C, etc.– An element is denoted by its Aand Z– Ex:126C or C - 12EL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn3

Stable vs. Unstable States Stable nuclides:– # neutrons # protons (A 2Z) Unstable nuclides (radionuclides, radioactive atoms)– Likely to undergo radioactive decay, which gives off energy andresults in a more stable nucleusEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn4

Orbits of ElectronsGround state: electrons are in the lowest orbital shells and within the lowestenergy quantum states within each shellEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn5

Electron Binding Energy A free electron has higher energy than when it is bounded to annuclei in an atom Binding energy total energy with free electrons – total energy inground state– Depends on the element to which the electron is bound and the shellwithin which it resides in ground state– Sufficient to consider “average” binding energy of a given atom One electron volt (eV) kinetic energy gained by an electron whenaccelerated across one volt potential– 1 eV 1.6 x 10 {-19} Joule Binding energies of typical elements:––––hydrogen 13.6 eV, Smallest among all lighter atomsAir: 29 eVLead: 1 KeVTungsten: 4 KeVEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn6

Ionization and Excitation Ionization is “knocking” an electron out of an atom– Creates a free electron ion (an atom with 1 charge)– Occurs when radiated with energy above the electron bindingenergy Excitation is “knocking” an electron to a higher orbit– When the radiation energy is lower than the binding energy After either ionization or excitation, an atom has higherenergyEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn7

Characteristic Radiation What happens to ionized or excited atom?– Return to ground state by rearrangement of electrons– Causes atom to give off energy– Energy given off as characteristic radiation infrared light x-raysEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn8

Example Consider an electron accelerated through an X-ray tube where the anode ifmade of tungsten. If the anode is held at 120 KV, what is the maximumnumber of tungsten atoms that can be ionized?Solution:– The electron will have 120 KeV kinetic energy when reaching the anode, bydefinition of eV– The average binding energy of tungsten 4 KeV– # ionized atoms 120/4 20EL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn9

Ionizing RadiationEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn10

Two Types of Ionizing Radiation Particulate Electro-magnetic (EM)EL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn11

Particulate Radiation Radiation by any particle (proton, neutron or electron) if itpossesses enough kinetic energy to ionize an atomKinetic Energy the energy gained due to motionMass of a moving particle : m m01 v2c2Energy vs. mass : E mc 2Kinetic Energy : KE E E0 (m m0 )c 2When v c, KE EL582 Radiation Physics1 2mv2Yao Wang, Polytechnic U., Brooklyn12

Particulate Radiation by EnergeticElectrons We are only concerned with the electron accelerated in a X-raytube here– An electron accelerated across a tube with 100 KV potentialpossesses 100 KeV kinetic energyEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn13

Energetic Electron Interactions Two primary interactions– Collisional transfer Most common Produces heat– Radiative transfer Produces x-ray Characteristic radiation– Collide with K-shell Bremsstrahlung radiation– Collide with nucleus– More common thancharacteristic radiationEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn14

Collisional Transfer The energetic electron collides with an atom in the targetTypically, a small fraction of the kinetic energy of the electron is transferredto another electron in the atom– As the affected atom returns to its original state, infrared radiation (heat) isgenerated Occasionally, a large fraction of the incident energy is transferred to anotherelectron, the newly freed electron may form a delta rayThe incident electron’s path may be redirected, and many other subsequentinteractions may occur, until the kinetic energy of the incident electron isexhaustedEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn15

Characteristic X-Ray The incident electron collides with a K-shell electron,exciting or ionizing the atom, leaving a hole in that shell.– As the atom returns to its ground state, the k-shell hole is filledby a higher shell electron– The loss of energy creates an EM photon, known asCharacteristic x-ray– The energy of the x-ray photon difference between the bindingenergy of the two shells (element dependent)EL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn16

Bremsstrahlung Ray As the incident electron approaches the nucleus of an atom, thepositive charge of the nucleus causes the incident electron to bendaround the nucleus and decelerates– The loss of energy leads to the Bremsstrahlung x-ray (energy vary overa continuous range, depending on the speed loss) Occasionally when the incident electron collides with the nucleus,the electron is annihilated, emitting a photon with an energy equal tothe kinetic energy of the incident electron (highest possible energy) Primary source of x-rays from an x-ray tubeEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn17

Spectrum of X-RayDifferent curvesare generatedwhen differentvoltagepotentialsapplied in a x-raytubeGenerated when K-shellelectrons are replaced bydifferent outer shellsWhen theincidentelectroncollides witha nucleusEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn18

EM Radiation EM radiation comprises an electric wave and a magneticwave traveling at right angles to each other Typical EM waves:– Non ionizing: radio, microwaves, infrared, visible light, ultraviolet– Ionizing: X-rays, gamma rays Energy of a photon of an EM wave with frequency v:EL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn19

EM Waves for Medical Imaging X-rays and Gamma rays:– Have energy in the KeVs to MeVs - Ionizing Radiation– used in X-ray/CT and nuclear medicine respectively– X-rays are created in the electron cloud of atoms due to ionizingradiation– Gamma rays are created in the nuclei of atoms due toradioactive decay or characteristic radiation Radio waves– Used to stimulate nuclei in MRI to generate EM radiation Visible light– Used in radiography to improve the efficiency of photographicfilm to detect X-rays See Table 4.2 for more detailsEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn20

EM Radiation Interactions Two main interactions– Photoelectric effect The incoming photon is completely absorbed and ejecting K-shell orL-shell electrons, producing characteristic x-ray– Compton scattering The incoming photon changes its directionEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn21

Photoelectric Effect An incoming photon interacts with the nucleus of an atom, causingejection of a K-shell or L-shell electron (photoelectron)– Atom completely absorbs incident photon and all energy is transferred– The photoelectron propagates away with energyE hv EeB– The affected atom produces characteristic x-ray, while outer electrons fillthe K-shell.– Sometimes the characteristic x-ray transfers its energy to an outerelectron (called Auger electron) Both photo electron and Auger electron are energetic electrons thatcan interact with the matter as discussed beforeEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn22

Photoelectric EffectEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn23

Compton Scattering An incoming photon ejects an outer shell electron,yielding a Compton electron The incident photon loses its energy and changes itsdirection The scattered photon is called Compton photonEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn24

The energy of the scattered photon depends on thescatter angle– The maximum energy loss occurs when the photon is deflectedbackward (\theta 180 o)– When E is higher, more photons scatter forward– The kinetic energy of the Compton photon E-E’EL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn25

Which interaction is better? Photoelectric effect helps to differentiate different humantissues/organs Compton scattering causes incident photons to deviatefrom straight path, and causes unnecessary exposure ofx-ray to untargeted areas In medical imaging, we want to increase the likelihood ofphotoelectric events, while minimizing ComptonscatteringEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn26

Probability of Photoelectric Effect Recall that photoelectric event happens when incident photonsinteract with the coulomb field of the nucleus of an atom More likely when colliding with an atom with more photons (higher Znumber) Less likely when incident photons have higher energy (higherfrequency)– The probability increases abruptly when the photon energy rises abovethe binding energy of L-shell or K-shell electrons (so as to eject theelectrons), then begins to diminish– Rationale behind the use of “contrast agent”EL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn27

Probability of Compton Scattering Recall that Compton scattering occurs when an incident photoncollides with outer shell electrons Likelihood proportional to the number of electrons per kilogram ofthe material (the electron density or ED) Relatively independent of incident photon energy in the biologicalmaterialED N AZWmN A : Avogadro's number (atoms/mole)Z : atomic number (electrons/atom)Wm : molecular weight (grams/mole ED is approximately constant for various biological material, 3E26, except for Hydrogen (6E26)EL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn28

Relative Likelihood Compton scattering is equally likely in various materialsand invariant of incident energy Photoelectric effect is more likely in high Z material andless likely with high incident energy Overall, Compton scattering is more dominant withhigher incident energy in the same material But the percent of energy deposited due to photoelectricevent is larger because all incident energy is absorbed.EL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn29

Measures of X-ray Beam: Photon CountEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn30

Measures of X-ray Beam: Energy FlowEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn31

Spectrum of X-Ray The x-ray beam produced by an x-ray tube (mainlyBremsstrahlung) is polyenergetic (consisting photonswith different energies or frequencies) X-ray spectrum S(E):– The number of photons with energy E per unit area per unit timeEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn32

Spectrum of X-RayDifferent curvesare generatedwhen differentvoltagepotentialsapplied in a x-raytubeGenerated when K-shellelectrons are replaced bydifferent outer shellsWhen theincidentelectroncollides witha nucleusEL582 Radiation PhysicsYao Wang, Polytechnic U., Brooklyn33