2.4 Radiation Measurement Quantities, Units & Dosimeters

Radiation Measurement Quantities, Units & Dosimeters

Quick Reference: Accurate clinical radiation therapy requires precise physical measurement quantities and calibrated dosimetric instrumentation. Dosimetric units bridge physical ionization in air (Exposure, Kerma) to energy absorbed in tissue (Absorbed Dose) and biological risk (Equivalent and Effective Dose).

Dosimetric Quantities, Units & Conversions

Quantifying ionizing radiation requires distinguishing between radiation in air, kinetic energy transferred, energy absorbed by tissue, and biological risk.

Exposure ($X$), Kerma ($K$), and Absorbed Dose ($D$)

1. Exposure ($X$): The total electrical charge ($dQ$) of ions of one sign produced in air when all electrons liberated by photons per unit mass ($dm$) of dry air are completely stopped.

   • SI Unit: Coulomb per kilogram ($C/kg$).
   • Traditional Unit: Roentgen ($R$). $1\text{ R} = 2.58 \times 10^{-4}\text{ C/kg}$.
   • Restriction: Exposure is defined only for photons (x-rays and gamma rays) interacting in air at energies strictly below $3\text{ MeV}$ (above $3\text{ MeV}$, charged particle equilibrium cannot be maintained in standard air chambers).

2. Kerma ($K$ - Kinetic Energy Released per unit Mass): The sum of initial kinetic energies of all charged ionizing particles liberated by uncharged radiation per unit mass of medium ($K = \frac{dE_{\text{tr}}}{dm}$).

   • SI Unit: Gray ($Gy$), where $1\text{ Gy} = 1\text{ Joule/kg}$.
   • Components: Total Kerma is divided into Collisional Kerma ($K_{\text{col}}$, energy transferred to electrons that undergo ionization/excitation) and Radiative Kerma ($K_{\text{rad}}$, energy converted to Bremsstrahlung).
   • Relationship to Dose: Under conditions of Charged Particle Equilibrium (CPE), absorbed dose equals collisional kerma ($D = K_{\text{col}}$).

3. Absorbed Dose ($D$): The mean energy ($dE_{\text{dep}}$) imparted by ionizing radiation to matter per unit mass ($dm$) of tissue ($D = \frac{dE_{\text{dep}}}{dm}$).

   • SI Unit: Gray ($Gy$). $1\text{ Gy} = 1\text{ J/kg} = 100\text{ cGy}$.
   • Traditional Unit: Rad ($rad$). $1\text{ Gy} = 100\text{ rad}$; $1\text{ cGy} = 1\text{ rad}$.
   • Roentgen-to-Rad Conversion ($f$-factor): $D_{\text{medium}} = f_{\text{medium}} \times X$. In soft tissue, $f_{\text{medium}} \approx 0.96\text{ cGy/R}$.

Equivalent Dose ($H$) and Effective Dose ($E$)

• Equivalent Dose ($H_T$): Quantifies biological harm to a specific organ or tissue by weighting absorbed dose ($D_T$) by the Radiation Weighting Factor ($w_R$): $H_T = D_T \times w_R$

  • SI Unit: Sievert ($Sv$). Traditional Unit: Rem ($rem$). $1\text{ Sv} = 100\text{ rem}$.
  • Radiation Weighting Factors ($w_R$): Photons & Electrons = $1$; Protons = $2$; Alpha Particles = $20$; Neutrons = $5-20$ (energy dependent).

• Effective Dose ($E$): Measures overall risk of stochastic effects (carcinogenesis) to the entire body by multiplying Equivalent Dose by Tissue Weighting Factors ($w_T$): $E = \sum (H_T \times w_T)$

  • Tissue Weighting Factors ($w_T$): Gonads = $0.08$; Red Bone Marrow, Colon, Lung, Stomach = $0.12$; Bladder, Breast, Liver, Thyroid = $0.04$; Skin, Bone Surface = $0.01$.

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Ionization Chambers & Cavity Theory Protocols

Gas-filled ionization chambers are the primary reference instruments for absolute radiation beam calibration in medical physics.

Thimble Chambers & Farmer Chamber Architecture

A Farmer-type thimble chamber consists of a cylindrical cavity (typically $0.6\text{ cc}$ active volume) with a thin graphite or PMMA wall (outer electrode) and a central aluminum or graphite collector electrode. A polarizing high-voltage potential (typically $+300\text{ V}$) is applied across the electrodes.

• Function: As photons ionize air within the cavity, free electrons are collected, generating an electrical current measured by a high-precision electrometer.
• Parallel-Plate Chambers: Feature two flat parallel disc electrodes separated by a narrow gap ($1-2\text{ mm}$). Used for measuring surface doses, depth dose build-up regions, and electron beam calibrations below $10\text{ MeV}$.

Bragg-Gray Cavity Theory & Temperature-Pressure Corrections

Bragg-Gray Cavity Theory relates the ionization measured in a small gas cavity inside a phantom to the absorbed dose in the surrounding medium: $D_{\text{medium}} = D_{\text{gas}} \cdot \left(\frac{\bar{S}}{\rho}\right)_{\text{gas}}^{\text{medium}}$

Because open-air ionization chambers are unsealed, the mass of air in the cavity fluctuates with ambient room temperature ($T$) and barometric pressure ($P$). Dosimetrists must multiply raw electrometer readings by the Temperature-Pressure Correction Factor ($P_{\text{TP}}$): $P_{\text{TP}} = \frac{273.15 + T(^\circ\text{C})}{273.15 + 22} \times \frac{760}{P(\text{mmHg})}$ Reference calibration conditions are defined at $22^\circ\text{C}$ ($295.15\text{ K}$) and $760\text{ mmHg}$ ($101.325\text{ kPa}$).

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Survey Instruments & Personnel Monitoring Devices

Radiation safety programs deploy specialized survey instruments and personal monitoring badges.

TLD vs. OSL Personnel Monitors

• Thermoluminescent Dosimeters (TLD): Utilize Lithium Fluoride ($ ext{LiF:Mg,Ti}$). When exposed, electrons are trapped in lattice impurities. During readout, the crystal is heated to $\sim 400^\circ\text{C}$, releasing light measured by a photomultiplier tube. Reading the TLD clears the signal completely, preventing re-analysis.
• Optically Stimulated Luminescence (OSL): Utilize Carbon-doped Aluminum Oxide ($\text{Al}_2\text{O}_3:\text{C}$). Readout uses green laser light to stimulate electron release, emitting blue light proportional to dose. OSL badges can be re-read multiple times because laser stimulation leaves residual trapped electrons intact for archival verification. Minimum reporting threshold is $0.01\text{ mSv}$ ($1\text{ mrem}$).

Neutron detectors

High-energy linacs (>10 MV) produce neutron contamination via photodisintegration. Neutron detectors (for example, boron-lined or moderated proportional counters and activation foils used in surveys) complement ionization chambers, Geiger-Müller detectors, TLD/OSL, and diodes when characterizing vault/door neutron fields and verifying shielding performance after high-energy treatments.