Bragg-Gray Cavity Theory

Study Notes

Cavity theory relates the absorbed dose in an irradiated material to the ionization produced in a gas-filled cavity within the material

Applies to small cavities where the presence of the cavity does not significantly perturb the charged particle fluence
The cavity size is small compared to the range of charged particles crossing it
The energy deposited in the cavity is due to charged particles that have been produced in the surrounding medium
The absorbed dose in the cavity is proportional to the ionization produced in the gas
The Bragg-Gray equation states that the absorbed dose in the material, $D_{med}$, is equal to the product of the absorbed dose in the gas, $D_{gas}$, and the ratio of the mass stopping powers of the material and the gas: $D_{med} = D_{gas} * (S_{med}/S_{gas})$
$S_{med}$ and $S_{gas}$ are the mass stopping powers of the medium and gas, respectively, for the charged particles crossing the cavity
The mass stopping power is defined as the energy loss per unit path length divided by the density of the material
The absorbed dose in the gas can be determined from the ionization produced in the gas, using the relationship $D_{gas} = J * W/e$, where $J$ is the ionization charge produced per unit mass, $W$ is the average energy required to produce an ion pair in the gas, and $e$ is the electronic charge

An intermediate case between the Bragg-Gray and large cavity theories
Accounts for the energy deposited in the cavity by electrons that originate in the cavity
It introduces the concept of a restricted stopping power, $L_{\Delta}$, which considers only energy losses less than a certain value, $\Delta$
The Spencer-Attix equation is given by: $D_{med} = D_{gas} * (L_{med}/L_{gas})$
$L_{med}$ and $L_{gas}$ are the restricted mass collision stopping powers of the medium and the gas, respectively
The restricted stopping power considers only the energy deposited locally, excluding energy losses due to delta rays that escape the cavity
The value of $\Delta$ chosen should be such that the range of an electron with energy $\Delta$ is approximately equal to the cavity dimensions
The Spencer-Attix theory is more accurate than the Bragg-Gray theory for larger cavities, where the electron fluence may be significantly perturbed by the cavity itself

Applies when the cavity is large compared to the range of the charged particles
The charged particle fluence within the cavity is primarily due to interactions within the cavity gas itself
The absorbed dose in the cavity is determined by the energy absorbed from the primary radiation beam directly interacting with the gas
The dose in the medium is related to the energy fluence of the primary radiation and the mass energy absorption coefficient of the medium
The Burlin cavity theory is a more general theory that interpolates between the Bragg-Gray and large cavity theories, using a weighting factor to account for the relative contributions of the energy deposited by charged particles originating in the medium and those originating in the gas
The weighting factor depends on the cavity size and the energy spectrum of the radiation beam

Cavity theory is used to relate the detector reading to the absorbed dose in a reference material
A calibrated ionization chamber is often used as a reference detector
The calibration factor is determined by comparing the detector reading to the absorbed dose in the reference material, as determined by cavity theory

Cavity theory is used to determine the absorbed dose in a patient undergoing radiotherapy
The dose is calculated based on the ionization produced in a detector placed in the radiation beam
Corrections are made for the size and composition of the detector cavity

Cavity theory assumes that the radiation field is uniform across the cavity
The theory may not be accurate for very small or very large cavities
The accuracy of the theory depends on the accuracy of the stopping power data used

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