Radiologic Physics and X-ray Imaging Systems

Review of Basic Physics Fundamental Concepts

• Mass: Defined as the measure of an object's inertia, which is the resistance to acceleration. It is measured in kilograms ($kg$).

• Velocity: Refers to the constant speed of a body moving in a given direction. It is measured in meters per second ($m/s$).

• Acceleration: The rate of change of velocity over time. It is measured in meters per second squared ($m/s^2$).

• Electric Charge of Electrons ($e^-$) and Protons ($p^+$): The value is exactly $1.6 \times 10^{-19}$ coulombs ($C$).

• Electric Current: Measured in amperes ($A$). An Ampere represents the flow of electrons through a circuit. It is the amount of charge that flows divided by time ($1\,A = 1\,C/second$).

• Newton's Laws of Motion:

  • First Law (Law of Inertia): An object either remains at rest or continues to move at a constant velocity unless acted upon by an external force.

  • Second Law: Represented by the formula $F = ma$. The vector sum of the forces ($F$) on an object is equal to the mass ($m$) of that object multiplied by the acceleration vector ($a$) of the object.

  • Third Law: In every action, there is always an equal but opposite reaction.

Atom Structure and Historical Models

• Atom: The basic component and the smallest unit of matter.

• Parts of an Atom:

  1. Nucleus: The central core of an atom that contains nearly all of its mass. It contains nucleons.

     • Protons: Positively charged particles.

     • Neutrons: Neutral particles.

     • Nucleons: The collective term for protons and neutrons.

  2. Orbits or Shells: Composed of electrons orbiting the nucleus.

• Historical Models of the Atom:

  • John Dalton: Hook and eye model.

  • JJ Thomson: Plum pudding model.

  • Dmitri Mendeleev: Created the first table of elements.

  • Rutherford: Developed the nuclear model.

  • Neils Bohr: Miniature solar system model.

• Electron Binding Energy:

  • The energy possessed by an electron in its orbit.

  • The strength of attachment of an electron to its shell.

  • The specific magnitude of energy required to remove an electron from its shell.

Nuclear Arrangements

1. Isotopes: Atoms or elements that share the same number of Protons.

2. Isobars: Elements that share the same Atomic mass.

3. Isotones: Different elements that share the same number of Neutrons.

4. Isomers: Elements that share the same atomic mass and the same atomic number but differ in Energy levels.

Radioactivity and Radioactive Decay

• Becquerel ($Bq$): The SI unit of radioactivity.

  • $1\,Bq = 1\text{ disintegration per second (dis/s or dps)}$.

• Curie ($Ci$): The old unit of radioactivity.

  • $1\,Ci = 3.7 \times 10^{10}\,Bq$.

• Marie Curie: Coined the term radioactivity and discovered the elements polonium and radium.

• Radioactive Decay: The process where certain nuclides spontaneously emit radiation (in the form of alpha, beta, gamma rays, and other nuclear fragments) to reach a stable state.

• Physical Characteristics of Radioactive Atoms:

  1. Decay Disintegration / Transformation Constant ($\lambda$): The fraction or percentage of the original number of atoms decaying per unit of time.

  2. Half-life ($T_{1/2}$): The amount of time taken for a radioactive material (RAM) to decay to half of its original value; the time required for the activity of a sample to decay to one-half of its original value.

  3. Activity ($A$): The time rate of decay of radioactive material.

• Types of Half-Life:

  1. Biological.

  2. Physical.

  3. Effective.

Modes of Decay and Energy Units

• Alpha Decay: Occurs in heavy nuclides with high atomic numbers. It resembles the Helium ($He$) element. It has a relative charge of $2$ and a mass of $4$.

• Beta Decay: Includes negatron and positron decay. It has a relative charge of $-1$ and a mass of $0$.

• Isomeric Transition: This decay emits gamma ($\gamma$) rays and occurs only in elements in an excited state.

• Internal Conversion (K-Conversion): The removal of an electron within an atom by a $\gamma$-ray from the nucleus.

• Electron Capture (K-Capture): The nucleus captures an electron from an orbital shell of the atom.

• Auger Process: Defined as the removal of an electron by a characteristic x-ray within an atom.

• Electron Volt ($eV$): The energy acquired by an electron accelerated through a potential difference of $1\,volt$. The energy of x-rays is expressed in electron volts.

  • $1\,eV = 1.6 \times 10^{-19}\,J$.

  • $1\,J = 6.24 \times 10^{18}\,eV$.

Characteristics of Photons and Wave Equations

1. Photon Velocity: Equal to the speed of light.

2. Photon Amplitude: Refers to one-half the range from crest to valley over which the sine wave varies.

3. Photon Wavelength ($\lambda$): The distance from one crest to another.

4. Photon Frequency ($f$): The rate of rise and fall of a sine wave, measured in oscillations per second or cycles per second.

   • Unit: Hertz ($Hz$) or $1/s$.

   • $1\,Hz = 1\text{ cycle/second}$.

   • Cycle: One complete oscillation.

   • Period: The time required to complete a single cycle.

• Wave Equation: Describes the relationship between speed, wavelength, and frequency.

  • $c = f\lambda$

  • Where $c$ is the speed of light, $f$ is frequency, and $\lambda$ is wavelength.

  • Frequency ($f$) is directly proportional to velocity ($c$) and inversely proportional to wavelength ($\lambda$).

  • The velocity of electromagnetic radiation (EMR) or the speed of light is directly proportional to both $f$ and $\lambda$.

• Inverse Square Law: Describes the relationship between radiation intensity and distance.

  • Intensity of radiation is inversely proportional to the square of the distance between the source and the point of measurement.

  • Radiation intensity from the x-ray tube varies inversely with the square of the distance from the target.

Interaction of Radiation with Matter

• Sources of Radiation:

  1. Natural/Background.

  2. Man-made/Artificial.

• Fundamental Terms:

  • Range: The maximum distance traveled by the electron beam in the absorbing medium before completely losing all its energy.

  • Specific Ionization (SI): The number of ion pairs formed per unit path length for a given type of radiation.

  • Linear Energy Transfer (LET): The rate at which energy is transferred from ionizing radiation to soft tissue.

    • Expressed in kiloelectron volts per micrometer ($keV/\mu m$).

    • Diagnostic x-rays: approximately $3\,keV/\mu m$.

    • $5\,MeV$ Alpha particles: $100\,keV/\mu m$.

  • Bremsstrahlung: Known as "white" x-rays.

  • Characteristic X-rays: Produced from the filling of a vacancy in an orbital shell.

• Electron Interactions with Matter:

  1. Excitations.

  2. Ionization.

• Specific Radiation Interactions:

  1. Classical/Coherent/Thomson/Rayleigh Scattering:

     • Incident photon excites an atom, causing vibration.

     • Results in a change in direction without a change in wavelength ($\text{incident } \lambda = \text{scattered } \lambda$).

     • Occurs in low energy x-rays (<10\,keV).

     • Probability of occurrence is $5\text{--}10\%$.

     • Causes film fog; no useful radiographic effect.

     • No ionization occurs, only excitation.

  2. Compton Interaction/Scattering (Incoherent):

     • Incident photon of high energy ejects an outer-shell electron.

     • The photon is deflected and travels in a new direction as scattered or secondary radiation.

     • Produces enough energy to ionize other atoms.

     • Most hazardous to radiation workers due to scatter.

  3. Photoelectric Effect:

     • First observed by Heinrich Hertz (1887); explained by Albert Einstein.

     • Probability of occurrence is $75\%$.

     • Incident x-ray is totally absorbed while ionizing an inner-shell electron.

     • The incident photon disappears and the K-shell electron (photoelectron) is ejected.

  4. Pair Production:

     • Occurs with x-ray energies greater than $1.022\,MeV$.

     • Photon interacts with the nuclear force field, creating a negatron and a positron.

     • Each particle possesses $0.511\,MeV$.

     • Important in PET (Positron Emission Tomography); does not occur in diagnostic radiology.

  5. Photodisintegration:

     • High energy photon ($\ge 7\text{--}10\,MeV$) is absorbed by the nucleus.

     • A nuclear fragment is emitted.

Shielding Data: Half-Value Layer (HVL)

Electricity and Magnetism

• Units of Electric Charges:

  • Electrons: Smallest unit of electric charge; negatively charged.

    • $1\,e^- = 1.6 \times 10^{-19}\,C$.

    • $1\,C = 6.3 \times 10^{18}\,e^-$.

  • Protons: Positively charged particle.

• 4 Electric States of Matter:

  1. Conductors: Allow flow of electrons (e.g., copper, aluminum).

  2. Insulators: Inhibit electron flow (e.g., wood, glass, rubber).

  3. Semi-conductors: Behave as insulators or conductors (e.g., silicon, germanium).

  4. Superconductors: No resistance to electron flow (e.g., niobium, titanium).

• Ohm’s Law: Current passing through a conductor is directly proportional to potential difference and inversely proportional to resistance ($I = V/R$).

• Electric Power:

  • Rate at which energy is transferred; measured in watts ($W$).

  • $1\,watt = 1\,ampere \times 1\,volt \, (W = AV)$.

  • $P = IV$; also $P = I^2R$.

• Magnetic Field Strength:

  • SI unit: Tesla ($T$). Old unit: Gauss ($G$).

  • $1\,T = 10,000\,G$.

  • Earth's magnetic field: Approx $50\,\mu T$ at equator, $100\,\mu T$ at poles.

• Devices:

  • Electric Generator: Converts mechanical energy to electrical energy (Faraday’s Law).

  • Electric Motor: Transforms electrical energy into mechanical energy.

    • Rotor: Part of the motor inside the glass envelope.

    • Stator: Fixed electromagnets outside the glass envelope.

    • Commutator ring: Changes the polarity of the contact of the wire loop.

Transformers

• Function: Changes the intensity of alternating voltage and current by mutual induction. Does not convert energy types; only changes magnitude of AC voltage.

• Efficiency: Not $100\%$ efficient due to power losses:

  1. $I^2R$ Losses: Due to resistance in the wire.

  2. Hysteresis loss: Energy depleted during magnetization/demagnetization cycle of the core.

  3. Eddy Currents: Currents that oppose the magnetic field that induced them.

• Construction Types:

  1. Air core: Two insulated coils side by side.

  2. Open-core: Iron core inserted into a current-carrying coil.

  3. Closed-core: Continuous path for magnetic flux; reduces energy leakage.

  4. Shell-type: Most advanced and efficient; currently used as commercial power transformers.

  5. Autotransformer: Has only one winding; used to supply precise voltage to filament and high-voltage circuits.

• Capacitor: Stores charge temporarily; acts like a battery but does not conduct electricity.

X-ray Imaging System Components

• Bucky Tray: Discovered by Gustave Bucky and Hollis Potter (Potter-Bucky Tray, 1913/1921). Holds cassette and grid under the table.

• Bucky slot cover: Must have at least $0.25\,mm$ lead ($Pb$) equivalence to protect against radiation.

• Primary Components:

  1. X-ray Tube.

  2. Operating Console.

  3. High-Voltage Generator.

• Standard Operation Parameters:

  • Kilovoltage ($kVp$): $25$ to $150\,kVp$.

  • Tube Current ($mA$): $100$ to $1,200\,mA$.

• Line Compensator: Adjusts incoming voltage to precisely $220\,V$.

• Control of Milliamperage (mA):

  • Determined by filament temperature.

  • Filament operates at $3$ to $6\,A$.

  • Controlled by the filament circuit (uses a step-down transformer).

Exposure Timers and Radiation Detection

1. Mechanical Timers: Clockwork mechanism for exposures longer than $250\,ms$. Found in old dental units.

2. Synchronous Timers: Drives a shaft at $60\,rps$. Minimum exposure time is $1/60\,s$ ($17\,ms$).

3. Electronic Timers: Most sophisticated and accurate; controlled by microprocessors.

4. mAs Timers: Monitors product of $mA$ and time; terminates exposure when desired $mAs$ is reached. Anatomically Programmed Radiography (APR) uses these.

5. Phototimer: Measures radiation reaching the receptor to ensure correct film density.

6. Spinning Top: Mechanical device used to check timer accuracy.

7. Solid State Radiation Detectors: High-accuracy semiconductor materials (silicon/germanium) used to check exposure time.

High-Voltage Generator Components

• High-Voltage Transformer (Step-up): Turns ratio is between $500$ and $1000$. Converts incoming volts to kilovolts.

• Filament Transformer: Step-down transformer used to reduce current for the production of high-speed electrons.

• Rectifier (Diode): Converts AC to DC. Ensures electrons travel only from cathode to anode.

• Voltage Ripple:

  • Single-phase: $100\%$.

  • Three-phase, 6-pulse: $13\text{--}14\%$.

  • Three-phase, 12-pulse: $3\text{--}4\%$.

  • High-frequency: $1\%$.

  • Rule: Less voltage ripple results in higher radiation quantity and quality.

X-ray Tube Construction and Failure

• Protective Housing: Prevents x-ray leakage, provides cooling, and provides electrical isolation.

  • Leakage limit: Must not exceed $100\,mR/hr$ at $1\,meter$.

  • Insulating Oil: Mineral oil used as coolant.

  • Expansion Gasket: Rubber diaphragm that expands/contracts with oil heat; triggers a micro switch to stop exposure if too hot.

• Glass Envelope: Pyrex glass. Mammography uses a metallic beryllium window to prevent attenuation of lower energy photons.

• Cathode (Negative Electrode):

  • Filament: Thoriated tungsten (Tungsten + $1\text{--}2\%$ Thorium). Melting point: $3,410^\circ C$. Lasts longer than pure tungsten.

  • Focusing Cup: Made of molybdenum ($Mo$) or nickel ($Ni$). Negatively charged to repel/focus electrons.

  • Space Charge: Cloud of electrons accumulated during thermionic emission.

• Anode (Positive Electrode):

  • Rotating Target: Made of tungsten with $5\text{--}10\%$ rhenium.

  • Speed: $3,400\,RPM$ (standard) to $10,000\,RPM$ (high speed).

  • Target Angle: $8$ to $20$ degrees.

• Focal Spots:

  • Actual Focal Spot: Physical area bombarded by electrons.

  • Effective Focal Spot: Area projected toward the object; determined by the line-focus principle ($12^\circ$ angle most common).

  • Size uses: $0.3\,mm$ (magnification); $0.5\text{--}1.0\,mm$ (bony parts); $1.0\text{--}2.0\,mm$ (standard radiography).

• Anode Heel Effect: Radiation intensity is higher on the cathode side. Noticed more with small focal spots, short SID, and large fields.

• Causes of Tube Failure:

  1. Single Excessive Exposure: Causes pitting/cracking (never apply max factors to a cold anode; use warm-up: 3 exposures, 3 seconds apart, $200\,mA$, $1\,s$, $80\,kVp$).

  2. Long Exposure Times: Damages rotor bearings.

  3. Tungsten Vaporization: Most common cause; coats the envelope.

Cooling and Rating Charts

• Anode Cooling Chart: Calculation of time needed for anode to cool ($15\,minutes$ for complete cooling).

• Heat Units (HU): $HU = kVp \times mA \times time (s)$.

• Housing Cooling Chart: Capacity is approx $1$ to $1.5\,million\,HU$. Complete cooling takes $1$ to $2\,hours$.