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Physics Principles for Nuclear Cardiology
E. LINDSEY TAUXE Med, FASNCDIVISION OF CARDIOVASCULAR DISEASEUNIVERSITY OF ALABAMA AT BIRMINGHAM
Disclosures to Report: Honoraria--Corscan
Atomic and Nuclear Emissions
Atomic and Nuclear Transitions
Atomic Structure / Emissions
Nuclear Structure / Emissions
Radioactive Decay
Interactions with Matter
Basic Atomic and Nuclear PhysicsQuantities and Units• Radioactive Decay Requires
Special Units of Mass and Energy– Mass Units
• Universal Mass Unit (u) *–1/12 mass of 12C–u = 1.66043 x 10-27Kg
• Atomic Mass Unit (amu) –based on average mass all O isotopes–u = 1.00083 amu
• * most commonly used
Basic Atomic and Nuclear PhysicsQuantities and Units• Mass and Energy Related by
– E = mc2
• c = Speed of Light (3 x 108 m/s)
– 1u =(1.66x10-27)(3 x 108 m/s)2
= 931.MeV
Basic Atomic and Nuclear PhysicsQuantities and Units• Electromagnetic Radiations are
Referred to as Photons– Wavelength and Energy Related by – c = λν
• c = speed of light (3 X 108 m/sec)• …... λ = wavelength (cm or nm)• …... ν = frequency
• E(keV) = 12.4/λ(nm)
Atomic and Nuclear Emissions
Atomic and Nuclear Transitions
Atomic Structure / Emissions
Nuclear Structure / Emissions
Radioactive Decay
Interactions with Matter
Basic Atomic and Nuclear PhysicsAtomic• Composition:
• Electrons: Negatively Charged Particles with Very Small Mass
• Protons: Positively Charged Particles with Very High Mass
• Neutrons : No Electric Charge with Very High Mass
–mass of proton ≅ mass of neutron–mass of electron ≅ 1/2000 mass of
proton–mass of atom ≅ 99+% P + N
Atomic and Nuclear Structure
Bohr Model of the Atom
Nucleus (Protons & Neutrons)
Orbiting Electrons
Electron shells or energylevels (K, L, M shown)
Outer Electron shell (N)is unoccupied
Atomic Energy Level DiagramAtomic Structure…Electron Orbitals
Ground state
BindingEnergy
Increases(eV or keV)
In shells closeto the nucleus
FreeElectron
NM
L
K
Low BE
High BE
Basic Atomic and Nuclear PhysicsAtomic Structure…Electron Energy• Binding Energy
– Amount of Energy Required to Remove an Electron from a Shell
– Specific to a Shell i.e. KB, LIB, LIIB, LIIIB
– Increases with Z Number (# of protons)– Energy Required to Move an Electron
from One Shell to Another = KB – LB
– Moving from L → K Results in Emission
Basic Atomic and Nuclear PhysicsAtomic Structure
• Atomic Emissions– Characteristic x-rays
occur when an inner shell electron is ejected, and it’s vacancy is filled by another electron
– 201Tl 69 – 80 KeV
K-shell vacancy
Characteristic x-ray
L-shell
• Atomic Emissions– Auger Effect is an
alternative to Characteristic X-rays
• occurs when the energy produced from filling vacancy is transferred to another electron
• called an Auger Electron
Auger Electron
Auger Effect
K L
K L
Basic Atomic and Nuclear PhysicsAtomic Structure
Atomic and Nuclear Emissions
Atomic and Nuclear Transitions
Atomic Structure / Emissions
Nuclear Structure / Emissions
Radioactive Decay
Interactions with Matter
Basic Atomic and Nuclear PhysicsNuclear Structure
Nucleus composed of protons + neutrons
Atomic Number (Z) = # of protons (determines element)
Atomic Mass (A) = # of protons and neutrons
Neutron Number (N) = A - Z
Element ‘X’ represented as , e.g.N
AZI 78
13153 I
Basic Atomic and Nuclear PhysicsNuclear Families - Definitions
Isotopes - nuclides composed of the same number of
protons (125I, 131I, 127I)
Isotones - nuclides with the same number of neutrons
(131I, 132Xe, 133Cs)
Isobars - nuclides with the same atomic mass A
(131I, 131Xe, 131Cs)
Isomers - nuclides in different excited / metastable
states (99mTc, 99mTc)
53 53 53
53 54 55
53 54 55
• comprised of protons and neutrons• called nucleons
– high density
Particle Charge Mass(u) Mass(MeV)
Proton +1 1.007277 938.211
Neutron 0 1.008665 939.505
Electron -1 0.000549 0.511
Basic Atomic and Nuclear PhysicsNuclear Structure
Basic Atomic and Nuclear PhysicsNuclear Structure
• Nuclear Forces– Nucleons are Subject to Coulombic forces
and Exchange Forces– When These Forces are Equal the Nuclide is
Called Stable or Ground State– When these Forces are not Balanced, then
• Exited State - very unstable and transient• Metastable State - unstable but longer lived
also called Isomeric States
Basic Atomic and Nuclear PhysicsNuclear Structure
• Nuclear Energy States– any transition in
which energy is carried off by a photon is a… γ ray
– if energy is imparted to an orbital electron, then particulate emission…internal conversion
• Characteristics of Stable Nuclei– Light Elements
• N = Z
– Heavy Elements• Z = 1.5N
• P:N ratio determines stability/instability
Line of Stability
Basic Atomic and Nuclear PhysicsNuclear Structure
Atomic and Nuclear Emissions
Atomic and Nuclear Transitions
Atomic Structure / Emissions
Nuclear Structure / Emissions
Radioactive Decay
Interactions with Matter
Basic Atomic and Nuclear PhysicsRadioactive Decay
• General Concepts– unstable nucleus is called the parent– the product, usually more stable,
daughter– radioactive decay is spontaneous
and therefore random– the energy released is called the
transition energy (Q)• carried off by particles, photons, and
nucleus
Nuclear Emissions
Decay by β-emission with / without γ-emission (β -, γ)
99Mo → 99mTc
Isomeric Transition (IT) or Internal Conversion (IC)
99mTc → 99Tc
Electron Capture and γ emission (EC, γ )
201Tl → 201Hg (characteristic x-rays)
Positron decay and γ emission (β +, γ)
Basic Atomic and Nuclear PhysicsRadioactive Decay
Basic Atomic and Nuclear PhysicsDecay Modes
• (β−,γ) Decay– If the β− results in an unstable daughter, the
daughter will likely decay by emitting a γ- ray• AX → A Y* → A Y
– Occurs in Neutron Rich NucleiiZ
β-
Z+1
γZ+1
Decay by β- Emission
β−
146 C
147 NIncreasing Atomic Number, Z
Basic Atomic and Nuclear PhysicsDecay Modes
99mTc
Basic Atomic and Nuclear PhysicsDecay Modes
• Isomeric Transition (IT) and Internal Conversion (IC)– if daughter is long lived a metastable state
occurs called Isomeric Transition• gamma ray emission occurs
– if nucleus transfers energy to an electron, then Internal Conversion occurs• conversion electron is emitted
Decay by Isomeric Transition
99mTc
99Tc
γ
Decay scheme for 99mTc
0.140 MeV
0 MeV
Decay by Internal Conversion
Internal ConversionTransition energy transferredto an orbiting electron (usuallyK-shell)
Conversion electron emittedwith energy equal to γ-rayenergy minus binding energyof K-shell.
Ee = Eγ - EK
Basic Atomic and Nuclear PhysicsDecay Modes
• Electron Capture– orbital electron captured by nucleus,
combines with proton to form a neutron• p+ + e- → n + ν + energy• AX → A Y
– Occurs in Proton Rich Nucleiiz Z-1
Basic Atomic and Nuclear PhysicsRadioactive Decay
Decay by Electron Capture
EC
12552 Te Decreasing Atomic Number, Z
12553 I
γ0.035 MeV
0 MeV
Decay by Electron Capture
e + p n + ν + energy (EC)e + p n + ν + γ + energy (EC,γ)
Characteristic x-ray
Basic Atomic and Nuclear PhysicsDecay Modes
201Tl → 201Hg
• Positron (β+) and (β+, γ) – a proton in the nucleus is transformed into
a neutron and a positively charged electron β+
• p+ → n + e+ ν + energy• AX → AY
– occurs in Proton Rich Nucleiiz Z-1
β+Positron Annihilation
Basic Atomic and Nuclear PhysicsDecay Modes
Decay by Positron(β+)Emission
p n + e (β+) + ν + energy
ν
β+
Annihilation ReactionPositron (β+) and an Electron (β-)
• Positron collides with an electron.
• Both are converted to energy
• Results in the emission – 2 gamma rays, each of
energy 511 keV– emitted in opposing
directions (~180o)
Decay by Positron(β+)Emission
188 O
Decreasing Atomic Number, Z
189 F
Eβmax = 0.633
MeV
Definition of Decay
A process by which an unstable nucleus transforms into a more stable one by emitting particles and / or photons and releasing energy.
Terminology
Parent nucleus = the unstable nucleusDaughter nucleus = the more stable productTransition energy Q = energy released
Radioactive DecayDefinitions
Radioactive DecayDefinitions
• Half-life– Sometimes called Physical Half-life.
– Time required for activity to decay to 50% of its initial value.
Radioactive DecayPhysical Half-Life
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Time - Hours
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Activ
ity
Decay curve withT1/2 = 4 hours
Radioactive DecayDefinitions…Activity
Curie (Ci) 1 Ci = 3.7 x 1010 disintegrations / sec1 mCi = 3.7 x 107 disintegrations / sec
Becquerel (Bq) 1 Bq = 1 disintegration / sec= 2.7 x 10-11 Ci
Conversion Factors1 mCi = 37 megaBecquerels (MBq)1 MBq = 27 µCi
Decay Constant (λ)
Fraction of the atoms undergoing radioactive decayper unit time (during a time period that is so short,only a small fraction decay during that interval)
For a sample of N radioactive atoms, the averagedecay rate dN/dt is given by
dN/dt = -λN
Radioactive DecayDefinitions…Decay Constant
Decay is an exponential function of time
Nt = No e (- λt)
where Nt = number of atoms at time tand No = number of atoms at time 0
λ = decay constant
Radioactive DecayDefinitions… Law of Decay
Decay Factor (e -λt)
Fraction of the atoms remaining after time t
For a sample of N radioactive atoms, the remaining atoms left after .25 hours is
e–(.1151)(.25hr) = .972N(15’) = N (0) e(- λt)
= 30 (.972)= 29.16
Radioactive DecayDefinitions…Decay Factor
Radioactive DecayDefinitions…Half-Life
The Physical Half-Life (T1/2 or T) is the time required for thenumber of atoms to decrease by half. The relationship
between the Decay Constant λ, and Half-Life T1/2is given below
At t = T1/2, Activity = 0.5 x Initial Activity
i.e. N / N0 = 0.5, or 0.5 = e- λ T1/2
∴ loge(0.5) = -λT1/2 , or -0.693 = - λT1/2
∴ λ = 0.693 / T1/2or T1/2 = 0.693 / λ
Time (t)Th
No
No/2
N(t) = No e -0.693t/Th
Th = Half-Life = ln 2/λ = 0.693/λNo = original number of atoms
dN(t)/N = - λtλ = decay constant
Radioactive DecayDefinitions…Half-Life
Atomic and Nuclear Emissions
Atomic and Nuclear Transitions
Atomic Structure / Emissions
Nuclear Structure / Emissions
Radioactive Decay
Interactions with Matter
Interactions of Radiation with Matter• Particulate
– Mass– Momentum– Kinetic Energy
• Photon– Pure Energy in Motion– No Mass– Frequency and Wavelength Determines
Energy
Charged Particles in MatterCollisions
• α and β particles loose energy through Collisions– Interactions with
charge fields…not mechanical
• Excitation• Ionization• Bremsstrahlung
Charged Particles in MatterInteractions
• Excitation occurs when the incident particle interacts with an outer shell electron– Energy carried off by molecular vibrations,
infrared, visible or UV radiation• Ionization occurs when an outer shell electron
is ejected– Secondary electron (δ ray) may cause
ionizations• Bremsstrahlung occurs when the particle
penetrates the electron cloud
• Particles with high mass, loose energy over a short path length and low mass over a longer path length
• The relative amount of energy loss as a function of path length is defined as, LINEAR ENERGY TRANSFER (LET)– α (• LET)– β (• LET)
Charged Particles in MatterLET
Photon Interactions with Matter
• 100% Energy Conversion
– EM to Kinetic Energy
• Spatially Discrete
• <100% Energy Conversion
– Energy Degraded Photon
• Altered Pathway
• High Energy– > 1.022 MeV
Photon Interactions with Matter
Photon Interactions with Matter
Photon Interactions with Matter
Photon Interactions with MatterMultiple Interactions
Photon Interactions with MatterSecondary Radiations
Photon Interactions with MatterProbability Distribution
Photon Interactions with MatterProbability Distribution
82Pb
99m Tc – 140 keV
Photon Interactions with MatterProbability Distribution
99m Tc – 140 keV
H20
201 Tl – 72 keV
Photon Interactions with MatterAttenuation
• Attenuation depends on the thickness and Z of the absorber– Greater thickness
leads to greater absorption
– Energy and Z relationship is more complicated
• Linear attenuation coefficient (µl)…cm-1
I(x) = I(0) e -µx
• Transmission through an absorber is described by:
• I(x) = I(0) e -µx
• HVT (aka HVL) is the thickness required to absorb 50% of the beam
• HVT = .693/µl
Photon Interactions with MatterHalf Value Thickness
Physics Principles for Nuclear CardiologySummary
• Relationship of atomic structure to– Mode of decay– Emissions
• Understand and explain radioactive decay
• Interactions of photons with matter– Tissue– Image quality
Basic Principles of Radiation Detection
Radiation DetectorsGas-filled Detectors
• Ionization chambers•Geiger-Mueller counters
Scintillation Detectors•Inorganic scintillators (NaI)•Organic liquid scintillators
Semiconductor Detectors• Ge(Li) and Si(Li) detectors• CZT detector
Gas-Filled Detectors
-+-+
-+
-+ -
+ -+
-+
-+Radiation
+ (Anode)
- (Cathode)
CurrentAmplifier
Effect of Voltage on Detector Performance
Voltage
Out
put
ProportionalCounterIon
Chamber
GMCounter
RecombinationZone
ContinuousDischargeZone
Ionization Plateau
GM Plateau
Gas-Filled Radiation Detectors
• Ion Chamber Used for dose calibrators, pocket dosimeters
• Geiger-Mueller CounterOutput independent of absorbed energyUsed for survey meters10 times more sensitive than ion chamber
Radiation Detectors
Gas-filled Detectors• Ionization chambers• Proportional counters• Geiger-Mueller counters
Scintillation Detectors•Inorganic scintillators (NaI)•Organic liquid scintillators
Semiconductor Detectors• Ge(Li) and Si(Li) detectors• CZT detector
Solid Scintillation Materials
• Sodium Iodide doped with Thallium (NaI)used extensively in Nuclear Medicine
• Bismuth Germanium Oxide (BGO)widely used in PET systems
• Barium Fluoride (BaF2) / Cesium Fluoride (CsF2)used in PET systems
• Luthetium Orthosilicate (LSO)used in hybrid PET/SPECT systems
• Plasticinexpensive bulk scintillator
Principle of γ-ray Detection
300 keV
200 keV
Radioactive sources
NaI (TI)crystal
Photomultiplier tube
Voltage output
Vo
ltag
e
T ime
Gamma rays Photons Voltage pulses of light
• BASIC PRINCIPLES OF PULSE HEIGHT ANALYSYS– Requires a proportional detector…
–
NaI PMTPreAmp AMP
HV
-+PHA
Examination of signal amplitudes to determine energy
Voltage (Energy) Discriminator
Voltage Pulse to γ-ray Energy
Energy Spectrum Components
50 60 70 80 90 100 110 120 130 140 150 1600
200
400
600
800
1000
1200
1400Photopeak+ComptonCompton 1st orderCompton 2nd orderCompton 3rd orderCompton 4th order
Energy (keV)
Act
ivity
(co
unts
)
Energy Spectrum Components
• Photopeak
• Compton Edge
• Backscatter Peak
•Lead x-ray Peaks
Energy Spectrum Components
PP
BP
CE C1
C2
Pb
NaI Detector
PP = Photopeak
BP = Backscatter Peak
CE = Compton Edge
C1 = 1st Order Compton
C2 = 2nd Order Compton
Pb = Lead X-ray
Lead
γ-ray Energy Spectrum
γ-ray Energy
Cou
nts
or N
o. o
f Eve
nts
Energy Windows
Energy Resolution
• FWHM – Full Width Half Maximum
• %FWHM– Expressed as a % of photopeak energy
Energy Resolution of NaI
Calculated : FWHM
Energy ResolutionMeasured FWHM
0 100 200 300Energy (keV)
5
10
15
20
FW
HM
(%
)
Pulse-Height Analysis
• What are the various peaksand valleys in the energy spectrum ?
• What parts of the spectrum containuseful information ?
• Where should we place the energywindow ?
• Why are the peaks so broad ?
Scintillation Detectors Summary
• Voltage pulse ∝ energy deposited in crystal• Measure voltage = measure energy• Low voltage gives error in energy measurement
Hence energy resolution ~ 1/√E
• Scatter in source ⇒range of detected energies• Energy window selects events / energies we want
• γ-ray detection efficiency depends on thickness of NaI crystal and energy of γ-ray.
Radiation Detectors
Gas-filled Detectors• Ionization chambers• Proportional counters• Geiger-Mueller counters
Scintillation Detectors•Inorganic scintillators (NaI)•Organic liquid scintillators
Semiconductor Detectors• Ge(Li) and Si(Li) detectors• CZT detector
Radiation Detectors
Semiconductor Detectors
• Ge(Li) and Si(Li) detectors
• CZT detector
Semiconductor PropertiesHow an Electrical Charge is Generated
Note: Someof the positive charge is lostdue to hole
charge carriertrapping losses.Leads to tailing
effects in energyspectrum !
Tc-99m Energy ResolutionSemiconductor vs Scintillation Technology
Tc-99m
CZTNaI