Physics Principles for Nuclear Cardiology - CadmiumCDmeetingproceedings.us/2011/asnc-bp-sept/contents/papers/1c1.pdf · Physics Principles for Nuclear Cardiology E. LINDSEY TAUXE

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)





Radioactive Decay


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





Radioactive Decay


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



• 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


• 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






Radioactive Decay


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 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


99mTc


• 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


• 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


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


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


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





Radioactive Decay


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 MatterMultiple Interactions

Photon Interactions with MatterSecondary Radiations

Photon Interactions with MatterProbability Distribution


82Pb

99m Tc – 140 keV


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



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

)


• Photopeak

• Compton Edge

• Backscatter Peak

•Lead x-ray Peaks


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



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

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Physics Principles for Nuclear Cardiology - CadmiumCDmeetingproceedings.us/2011/asnc-bp-sept/contents/papers/1c1.pdf · Physics Principles for Nuclear Cardiology E. LINDSEY TAUXE