Diagnostic Radiology Physics Flashcards

Radiation Dosimetry and Measurement Principles

Introduction to Diagnostic Radiology Dosimetry Radiation measurement is critical for several key reasons:

Radiation Protection: Legal requirements to determine effective and equivalent doses (e.g., IRR17 to minimize risk and set dose limitations).
Controlled and Supervised Areas: Designation of physical spaces based on dose exposure.
Patient Risk Assessment: Guided by IRMER17, which governs Diagnostic Reference Levels (DRLs), optimization, and clinical trials.
Consistency and Performance: Monitoring equipment for performance changes and ensuring inter-unit consistency.

Radiation Measurement Foundations Measurement techniques focus on the biological or chemical response to radiation, including stochastic and deterministic effects. Direct quantification of biological effects is difficult, leading to the use of several physical and chemical indicators:

Heating: Energy deposition from X-rays is generally too low for an appreciable temperature increase in diagnostic ranges. For example, to heat a Pot Noodle (assumed specific heat capacity of $4.0\,kJ\,kg^{-1}\,K^{-1}$ ) from $15^{\circ}C$ to $100^{\circ}C$ ( $85\,K$ increase) would require approximately $300,000\,Gy$ , as $1\,Gy = 1\,J/kg$ .
Physical Effects: Thermoluminescence, fluorescence, or phosphoresence.
Chemical Changes: X-ray film darkening or the oxidation of ions (e.g., converting $Fe^{2+}$ to $Fe^{3+}$ ).
Biochemical/Biological Changes: Enzyme denaturation, cell death.
Ionization: Measurement of charge produced in a specific volume of material. Ionization in air is the preferred technique because it is precise, reproducible, and robust to energy changes.

Ionization in Air Air is a surrogate for biological tissue because its effective atomic number ( $effZ \approx 7.6$ ) is similar to soft tissue ( $effZ \approx 7.4$ ).

The energy required to produce one ion pair in air is approximately $34\,eV$ .
A $100\,keV$ photon will produce approximately $3000$ ion pairs.
Air density is easily controlled via temperature ( $T$ ) and pressure ( $P$ ) monitoring.

Radiation Quantities and Attenuation

Fluence and Energy Fluence

Fluence (\Phi): Defined as $\Phi = \frac{dN}{da}$ , where $dN$ is the number of photons crossing area $da$ . Units are $m^{-2}$ .
Energy Fluence (\Psi): Defined as $\Psi = \frac{dR}{da}$ , where $dR$ is the radiant energy ( $E \times dN$ ). Units are $J\,m^{-2}$ .

Attenuation Coefficients

Linear Attenuation Coefficient (\mu): The fraction of the incident beam absorbed or scattered per unit thickness ( $cm^{-1}$ ).
Mass Attenuation Coefficient (\mu / \rho): Normalized to density ( $cm^{2}/g$ ). The total mass attenuation ( $\mu_{tot} / \rho$ ) is the sum of all individual interaction processes.
Mass Energy Transfer Coefficient (\mu_{tr} / \rho): The product of $(\mu / \rho)$ and the energy fraction transferred to charged particles.

Radiation Exposure (X) Exposure is the sum of all electrical charges of one sign produced in air per mass of air ( $\Delta m$ ).

Formula: $X = \frac{\Delta Q}{\Delta m}$ .
Requirement: All associated ionizations produced by electrons liberated in the volume must occur within the mass. If a photoelectric effect occurs, all subsequent associations must happen in $\Delta m$ .
Units: $C\,kg^{-1}$ . Older texts use Roentgens ( $1\,R = 2.58 \times 10^{-4}\,C\,kg^{-1}$ ).

Kinetic Energy Released per unit Mass (KERMA) and Absorbed Dose

KERMA (K) KERMA describes the kinetic energy released when uncharged particles (photons) interact with the medium, transferring energy to charged particles (electrons).

Formula: $K = \frac{d\epsilon_{tr}}{dm}$ . Units are Gray ( $J\,kg^{-1}$ ).
Collision Kerma (K_{col}): Energy deposited via collisions.
Radiative Kerma (K_{rad}): Energy re-radiated as Bremsstrahlung.
Total K: $K = K_{col} + K_{rad}$ . In Diagnostic Radiology (DR), radiative losses are negligible, so $K \approx K_{col}$ .
$K_{col} = K(1 - g)$ , where $g$ is the fraction of initial kinetic energy re-radiated as Bremsstrahlung.

Energy Imparted (\epsilon) and Absorbed Dose (D)

Energy Imparted (\epsilon): The difference between radiant energy entering ( $R_{in}$ ) and leaving ( $R_{out}$ ) a volume, plus/minus changes in rest mass ( $m$ ) and energy ( $R$ ). In DR, specifically: $\epsilon = R_{in} - R_{out}$ .
Absorbed Dose (D): The mean energy imparted into a medium per unit mass.
Formula: $D = \frac{d\epsilon}{dm}$ . Units: Gray ( $Gy$ ).

Conceptual Comparison via Hypothetical Scenarios

Photon photoelectric interaction, electron exits volume: Energy is released by an uncharged particle (K > 0), but energy entering and leaving the mass is the same ( $D = 0$ ).
Photon photoelectric interaction, electron stops in volume: Contributes to both KERMA and Absorbed Dose.
Photon Compton scatters outside, electron enters and stops in volume: Energy was released outside ( $K = 0$ ), but energy was imparted to the volume (D > 0).

Charged Particle Equilibrium (CPE) In DR energies and low Z materials, KERMA and Absorbed Dose are effectively equal because charged particle ranges are short. CPE breaks down at interfaces (e.g., air-skin boundary) or where secondary particles entering/leaving aren't balanced.

Backscatter: Tissue produces free electrons that travel back toward the source, contributing to Absorbed Dose but not measured by a lead-backed KERMA detector. Backscatter can add an additional $30\% - 40\%$ to dose.

Ionization Chambers and Cavity Theories

Free-Air Ionization Chamber A primary measurement device where an X-ray beam is collimated into an air-filled chamber. High potential electric fields attract ionized particles to electrodes. Guard electrodes shape the field to define the collecting volume. Precision is typically within $1\%$ , but use is limited to primary institutions.

Cavity Theories Detectors (the "cavity") often differ from the medium of interest. These theories relate the dose measured in the detector to the dose in the medium.

Bragg-Gray Cavity Theory: Applicable when the detector is small compared to the range of secondary electrons. It assumes the cavity does not perturb the fluence or interact with uncharged particles. The ratio of dose in the medium to dose in the cavity equals the ratio of the stopping powers.
Large Cavity Theorem: Applicable in DR because electron ranges are small. The detector is large enough that secondary electrons from outside have negligible contribution compared to those created within.
Fano Theorem: States that in a medium with uniform primary radiation, the secondary radiation field is uniform and independent of density variations, relaxing requirements for cavity size.

Personnel and Patient Dosimetry

Personnel Monitoring Under IRR17, monitoring is required for Classified Workers.

Approved Dosimetry Services (ADS): Required for classified monitoring.
Thermoluminescent Detectors (TLDs): Incident photons trap electrons at impurity sites; heating releases them as detectable photons.
Optically Stimulated Detectors (OSL): Aluminum oxide crystal read by optical photons. Can be restimulated, though output reduces with each read.
Electronic Personal Dosimeters (EPDs): Utilize ion chambers or solid-state detectors for real-time display.

Patient Dose Quantification Absorbed dose is difficult to measure directly and varys based on radiation type/location.

Equivalent Dose (H_{T}): $H_{T} = w_{R} \times D_{T}$ . For photons, weighting factor $w_{R} = 1$ .
Effective Dose (E): $E = \sum w_{T} H_{T}$ . Weights exposure according to irradiated anatomy radiosensitivity ( $w_{T}$ ). Defined for populations, not individuals; sum of all $w_{T} = 1$ .
Population Dose (S_{E}): $S_{E} = \sum N_{i} E_{i}$ . Used for long-term trend analysis and new source risk assessment.

X-Ray Generation: Physics and Tube Components

Production Processes

Characteristic Radiation: Produced when an electron is knocked out of a shell (excitation/ionization). An outer shell electron fills the vacancy, releasing a photon equal to the binding energy difference ( $\Delta E$ ). Peaks are element-specific (e.g., Tungsten, Molybdenum).
Bremsstrahlung (Breaking Radiation): Charged particles (electrons) interact with the nucleus via Coulomb force. The energy of the resulting photon is equal to the change in the electron's kinetic energy. Probability of emission is proportional to $Z^{2}$ . Efficiency at $100\,keV$ is only about $1\%$ , with the rest converted to heat.

Tube Components

Housing: Lead-lined protective container. Protects against shock, radiation leakage, and heat. BSI standards specify leakage limits.
Envelope: Maintains a vacuum to increase efficiency, reduce electron deflection, and prevent arcing. Contains the thin "window."
Cathode: Contains filaments and focusing cups. The Tube Current is the measure of electrons traveling to the anode, distinct from the filament current.
Filament Current and Space Charge: Filaments are preheated to reduce stress. A "space charge" cloud forms around the filament. At low $kVp$ , this cloud limits further production (space charge limited). At high $kVp$ , it becomes emission limited based on the filament's physical saturation.
Anode Target Types: * Stationary: Used in dental or low-power units. Typically a Tungsten target ( $Z=74$ ) in a copper block. * Rotating: Uses Tungsten-Rhenium alloy (Rhenium adds structural strength for rotational stress). Mounted on Molybdenum (heat conductor) and Graphite (lightweight thermal storage). Supports use of higher fluence. * Mammography: Uses lower $Z$ targets like Molybdenum ( $Z=42$ ) or Rhodium ( $Z=45$ ) to favor characteristic radiation for soft tissue contrast.

Focal Spot and Geometry

Geometric Unsharpness (U_{g}): $U_{g} = \text{effective focal spot size} \times \frac{ODD}{FOD}$ , where $ODD$ is object-to-detector distance and $FOD$ is focus-to-object distance.
Line-Focus Principle: The Anode Angle determines the relationship between actual and effective focal spot. For a $12^{\circ}$ angle, a $1.2\,mm$ spot has an effective size of $\tan(12^{\circ}) \times 1.2 \approx 0.25\,mm$ .
Heel Effect: X-rays are attenuated as they escape the target. Flux is higher on the cathode side; the beam is "harder" on the anode side. A larger anode angle reduces the heel effect.

Generators and Waveforms

Generator Types Conversion of mains AC to DC for the tube.

Rectifiers: Block or flip AC half-waves.
High-frequency / 3-phase: Reduce Voltage Ripple, defined as the variation between peaks and troughs.
Capacitor Discharge: Used in mobile units; exhibits a kV overshoot followed by slow decay.

Heat Units (Q)

Formula: $Q = w \times kVp \times \text{Current} \times \text{Time}$ .
Waveform Factor (w): Converts peak potential to RMS. For single-phase, $w \approx 0.71$ . For 6-phase, $w \approx 0.96$ . In common practice, $1\,J = 1.4\,HU$ .

Filtration and the 15% Rule

Filtration: Removes low-energy X-rays to reduce skin dose without contributing to the image and helps make the beam more monochromatic.
15% Rule: A $15\%$ increase in $kVp$ is approximately equivalent to doubling the $mAs$ in terms of dose. This is most reliable around the center of the diagnostic range ( $\approx 80\,kVp$ ).

Photon Interactions and Imaging Chain

Interaction Dominance

Photoelectric Effect: $\sigma_{PE} \propto \frac{k Z^{n}}{E^{m}}$ . Values for $n$ range from $3.6$ to $5.3$ ; $m$ ranges from $2.5$ to $3.5$ . This effect is primarily responsible for contrast between materials (e.g., Bone $effZ \approx 14$ vs Fat $effZ \approx 6$ ).
Compton Scattering: $\sigma_{cs} \propto Z$ . Independent of energy and less dependent on $Z$ ; primarily produces noise and reduces contrast.

Beam Hardening As the beam passes through the patient, lower energy photons are preferentially absorbed.

Example: Before a patient, average energy is $\approx 51\,keV$ . After the patient, it shifts to $\approx 64\,keV$ , while Air Kerma drops from $\approx 199.5\,\mu Gy\,mAs^{-1}$ to $\approx 1.3\,\mu Gy\,mAs^{-1}$ .

Detector Technologies (CR and DR)

Computed Radiography (CR) Utilizes Photo-stimulable Phosphor (PSP) plates.

BaFX:Eu^{2+}: Barium fluorohalide doped with Europium. Europium creates electron traps.
Process: Incident X-rays create electron-hole pairs. Trapped electrons form a latent image. Stimulation with red light releases trapped electrons, which fluoresce.
Latency Decay: Trapped charges spontaneously decay (half-life $\approx 5\,hours$ ; $25\%$ decay every $2\,hours$ ).

Digital Radiography (DR)

Indirect Capture: Uses a scintillator (e.g., CsI:Tl) coupled to an amorphous silicon (a-Si) photodiode array. X-rays are converted to light, then to charge.
Direct Capture: Uses an amorphous selenium (a-Se) photoconductor and a bias electrode. X-rays are converted directly into electron-hole pairs.
Thin Film Transistors (TFT): An electronic array used to read out stored charge sequentially.

Signal Transfer Property (STP) Mathematical relationship between Raw Data and Pixel Value ( $Q$ ). Typically logarithmic to maximize contrast.

Agfa: $Q = 533 \times \ln(Kerma) + 1650$ .
Fuji: $Q = 138 \times \ln(Kerma) + 152$ .
Kodak: $Q = 422 \times \ln(Kerma) + 1180$ .
Konica: $Q = -451 \times \ln(Kerma) + 2840$ .

Image Correction and Indicators

Flat Field Correction: $Q = \frac{P - D}{F - D}$ , where $P$ is raw data, $D$ is dark field (no X-rays), and $F$ is uniformity image.
Dose Detector Index (DDI/EI): Based on the median kerma in the segmented detector region ( $K_{IND}$ ).
Deviation Index (DI): $DI = 10 \times \log_{10}\left(\frac{K_{IND}}{K_{TGT}}\right)$ . * $0$ : Perfect exposure. * $+1$ : $25\%$ overexposed. * $-1$ : $25\%$ underexposed.

Imaging Theory: Quality and Information

Resolution and Contrast

Point Spread Function (PSF): Describes the system's blurring of a 1:1 object-to-detector point.
Nyquist Frequency: Maximum frequency is $\frac{1}{2A}$ , where $A$ is pixel size. For a $200\,\mu m$ pixel, the limit is $2.5\,lp/mm$ .
Modulation Transfer Function (MTF): The ability of a system to transfer contrast as a function of spatial frequency.
Contrast Definitions: * Weber: $C = \frac{I_{a} - I_{b}}{I_{b}}$ . * Michelson: $C = \frac{I_{max} - I_{min}}{I_{max} + I_{min}}$ .

Broadly Quantified Parameters

Quantum Detective Efficiency (DQE): $DQE = \frac{SNR_{out}^{2}}{SNR_{in}^{2}}$ . Measures how much of the incident signal-to-noise ratio is preserved by the detector.
Noise Equivalent Quanta (NEQ): Effective number of photons to achieve a specific SNR in an ideal detector ( $NEQ = SNR_{out}^{2}$ ).
Signal-to-Noise Ratio (SNR): Poisson noise relates to $\sqrt{N}$ . Increasing photons ( $N$ ) increases SNR linearly as $\frac{N}{\sqrt{N}} = \sqrt{N}$ .

General Radiography and Dental Specifics

Scatter Control

Anti-scatter Grids: High Z material (lead strips) that attenuates oblique photons.
Grid Ratio: Defined as $H / D$ (Height of strips / Distance between strips).
Digital Grids: Software algorithms designed to simulate physical grid scatter removal.

Automatic Exposure Control (AEC)

Ionization Chambers: Positioned in front of the detector to terminate exposure at a target dose.
Safety Features: Backup timers and ceiling mAs limits prevent patient overexposure.

Dental Modalities

Intra-oral: Bitewing, Periapical, and Occlusal views. Typically uses fixed kV ( $60-70\,kV$ ).
Pan-oral (OPG): Tube rotates around the jaw. Features a dose boost when aligned with the spine.
Cephalometry: Skull radiography for facial structure (orthodontics).
Dental CBCT: Reconstructed using the Feldkamp, Davis, and Kress (FDK) algorithm. Images degrade as they move away from the center of rotation.

Computed Tomography (CT)

Technical Evolution and Design

Generations: Modern scanners are 3rd Generation (Rotate-Rotate). Electron Beam CT (EBCT) uses steered electrons but is less common.
Tube Requirements: High heat rating, long scan regions ( $30+s$ ), and high filtration ( $\approx 8\,mm\,Al.eq$ ) to reach a near-monochromatic spectrum.
Detectors: Modern systems use Scintillation Detectors (Ultra-fast ceramic scints) coupled to photodiodes. Historically used high-pressure Xenon gas ionization chambers.

Scan Parameters and Efficiency

Multi-Slice CT (MSCT): Detector rows can be Matrix (equal sizes) or Adaptive (varying sizes).
Helical Pitch: $\text{Pitch} = \frac{\text{Couch movement per rotation}}{\text{Physical X-ray beam width}}$ .
Geometric Efficiency (GE_{sw}): $GE_{sw} = \frac{Z_{FWHM}}{D_{FWHM}}$ , where $Z$ is imaged width and $D$ is irradiated width. Efficiency is lower if penumbra is not fully utilized.

Automatic Exposure Control (AEC) Modulates mAs based on attenuation. Types include:

Z-axis: Changes mAs per rotation slice-to-slice.
X-Y: Changes mAs as tube rotates around the patient (e.g., lower for AP, higher for lateral through shoulders).
Organ-based: Reduces mAs for sensitive organs (breast, eyes).

Reconstruction Principles

Filtered Back Projection (FBP): Smeared projections are corrected for radial blurring using a filter (kernel). Smooth kernels reduce noise but lower resolution; sharp kernels amplify high frequencies/edges but increase noise.
Iterative Reconstruction (IR): Guesses a distribution, simulates projections, compares to real data, and iterates. Reduces dose requirements while maintaining noise levels.
Hounsfield Units (HU): $HU = 1000 \times \frac{\mu_{med} - \mu_{water}}{\mu_{water}}$ . * Water = 0; Air = -1000. * Bone range: 300 - >1000. * Fat: $-30$ to $-70$ .

CT Artefacts

Partial Volume: Voxel averages data from two different materials.
Beam Hardening: Cupping effects or dark streaks between high-Z materials (bone/metal) due to increased mean energy of the beam.
Photon Starvation: Insufficient photons reaching the detector (e.g., through shoulders).
Ring Artefacts: Detector calibration or defect issues consistent across rotations.

Mammography and Breast Imaging

Anatomy and Contrast Glandular tissue and adipose tissue have very similar linear attenuation coefficients at standard energies.

Energy Requirement: Low energies ( $25 - 35\,kVp$ ) are used to maximize the photoelectric effect difference.
Target/Filter Materials: Common combinations include Mo/Mo, Mo/Rh, Rh/Rh, W/Rh, and W/Ag.

Dosimetry: Mean Glandular Dose (MGD) MGD cannot be measured directly. It is calculated using Entrance Surface Air Kerma ( $K$ ) and various factors.

Formula: $MGD = K \times g \times c \times s$ . * g: Conversion for $50\%$ glandularity based on HVL. * c: Correction for deviation from $50\%$ glandularity. * s: Spectrum correction factor (if not Mo/Mo).

Advanced Modes

Digital Breast Tomosynthesis (DBT): Pseudo-3D imaging using small-angle projections ( $15^{\circ} - 50^{\circ}$ ) to resolve overlapping structures.
Contrast Enhanced Mammography (CEM): Uses Iodine-based contrast agent and dual-energy imaging (high energy above iodine K-edge of $33.2\,keV$ ).

Fluoroscopy

Image Intensifiers (II) Older systems that use analogue signal amplification.

Process: Input Phosphor (X-ray to light) $ightarrow$ Photocathode (light to electron) $ightarrow$ Focusing electrodes (acceleration/minification) $ightarrow$ Output Phosphor (electron to light).
Minification Gain: $\frac{\text{Area}<em>{Input}}{\text{Area}</em>{Output}}$ . Summed with acceleration to provide total brightness gain.
Artefacts: Susceptible to magnetic fields (S-distortion) and pincushion distortion.

Flat Panel Detectors (FPD) Modern digital matrix detectors. Consist of a phosphor (columnar CsI) coupled to an a-Si array with TFTs. Fill-factor is the ratio of sensing area to total pixel area. FPDs are immune to magnetic field distortions.

Automatic Brightness/Dose Control (ABC/ADRC) A feedback loop to maintain input dose-rate or output brightness. Different "curves" govern the relationship between kV-mA-filtration:

Iodine/High-Contrast Curve: Keeps kVp near the iodine K-edge ( $\approx 50-60\,kVp$ ) as long as possible.
High-Dose Curve: Keeps kVp low for contrast, only increasing when generator limits are hit.

Quality Assurance (QA) Objects

TO10 / N3: Low contrast and noise detectability.
GS2: Grey scale steps and dynamic range check.
Geometry / Mesh: Checks for distortion and dead pixel lines.
Entrance Surface Dose-rate (ESD): Measured to monitor patient skin dose limits. Safety spacers must ensure at least $45\,cm$ from focal spot ( $30\,cm$ for mobile units).