# Dosimetry Basics

## Units

Becquerel (Bq): A measure of source activity defined as 1 disintegration per second.

Curie (Ci):  A historical measure of activity defined as approximately the activity of 1 gram of Radium-226.

Exposure rate constant : exposure per hour (R/h) at 1cm distance from a 1mCi point source. Units:

mg-Radium Equivalent: a historical unit used to allow convenient conversion from Ra-226 source strength and the strength of a radionuclide.

Air Kerma Strength (SK): As defined in TG-43U1: "Air-Kerma Strength (SK) is the air-kerma rate $$\dot{K}_{\delta}(d)$$, in vacuo, due to photons of energy greater than δ at a distance d, multiplied by the square of this distance, d2." Units: U. 1U = 1$$\frac{\mu Gy \ m^2}{hr}$$ = 1$$\frac{cGy \ cm^2}{hr}$$

• $$\dot{K}_{\delta}(d)$$ denotes the air kerma rate at point d for photons with energy greater than δ.
• Measured in vacuo, meaning corrected for all photon attenuation and scattering due to air as well as surrounding objects
• δ is typically taken to be 5keV
• d denotes the the point of measurement

mg-hour: Milligram hours was used as a measure of total exposure/dose when using Radium-226 seeds. It is defined as the product mass of Radium-226 and irradiation time.

Total Reference Air Kerma (TRAK): an analogous quantity to mg-hours defines as the product of Air-kerma strength and time.

$$TRAK = \sum{t \cdot S_{k}}$$

NuclideHalf-lifePhoton Energy
(MeV)
HVL
Exposure Rate Constant
(R-cm2/mCi-hr)
192Ir73.8 days0.38 average2.54.69
226Ra1,600 years0.83 average12.08.25
222Rn3.83 days0.83 average12.010.15
60Co5.26 years1.17, 1.3311.013.07
137Cs30.0 years0.6625.53.26
198Au2.7 days0.4122.52.38
125I59.4 days0.028 average0.0251.46
103Pd17.0 days0.021 average0.0081.48

## NIST Photon Source Calibration

The Wide Angle Free-Air Chamber (WAFAC) is the current NIST standard instrument for the characterization of brachytherapy sources. The WAFAC is a cylindrical chamber with circular symmetry about the beam axis.

#### WAFAC Components

• Beam enters the dosimeter through a 8cm circular aperture located 30cm from the source.
• An aluminum filter is placed between the source and the dosimeter eliminate Ti K-shell X-rays arising from source encapsulation.
• Varying the active volume of the dosimeter allows for correction of measurement induced effects such as those induced by the aluminized-PET electrodes.

#### NIST Beta Source Calibration

NIST uses an extrapolation chamber to determine the zero gap measure (dose at window surface).

• Dose is specified to water.
• For intravascular sources, dose is specified to a depth of 2mm.
• For ophtalmic sources (sources for ocular therapy), dose id specified to surface.
WAFAC measurement setup. Source: AAPM TG-43U1.

# Source Dosimetry (AAPM TG-43)

## Overview

AAPM TG-43: Dosimetry of Interstitial Brachytherapy Sources was published in 1995 to standardize brachytherapy source strength and dose rate calculations. The report also gave consensus data for several sources, discussed uncertainty, and provided information on the relationship between TG-43 quantities on other formalisms.

TG-43 was updated in 2004 with the publication of Update of AAPM Task Group No. 43 Report: A revised AAPM protocol for brachytherapy dose calculations which is typically referred to as AAPM TG-43U1. TG-43U1 updated some definitions (outlined below), corrected minor inconsistencies, and provided additional consensus data sets.

In 2007 Supplement to the 2004 update of the AAPM Task Group No. 43 Report was released. This supplement provided additional consensus source data sets.

### Changes between TG-43 and TG-43U1

• Revised definition of air-kerma strength
• Included cutoff energy and specified in vacuo measurement
• Elimination of apparent activity for specification of source strength
• Replaces anisotropy constant with the distance-dependent 1D anisotropy function.
• Provides guidance on extrapolating TG-43 parameters to longer and shorter distances
• Corrects some errors and omissions

## 2D Formalism

The general 2 dimensional equation for dose rate (D˙) is given below:

• denotes the distance in centimeters from the center of the source
• θ denotes the polar angle between the point of interest and the longitudinal axis of the source
• The subscript “0” (as in r0 or θ0denotes measurements to the reference point which is specified at 1cm from the center of the course at an angle of 90 degrees relative to the source’s longitudinal axis
• The subscript “L” (as in GL or gL) denotes that the quantities are for a line source.
Coordinate system used for TG-43 brachytherapy dose calculations.

### Air-Kerma Strength

As defined in TG-43U1: "Air-Kerma Strength (SK) is the air-kerma rate $$\dot{K}_{\delta}(d)$$, in vacuo, due to photons of energy greater than δ at a distance d, multiplied by the square of this distance, d2."

• Sis the Air-Kerma Strength
• A typical value to a 10Ci Ir-192 HDR source is about 40,000U.
• $$\dot{K}_{\delta}(d)$$ denotes the air kerma rate at point d for photons with energy greater than δ.
• Measured in vacuo, meaning corrected for all photon attenuation and scattering due to air as well as surrounding objects.
• δ is typically taken to be 5keV.
• d denotes the the point of measurement
• Units: $$\frac{\mu Gy \ m^2}{h}$$, $$\frac{cGy \ cm^2}{h}$$
• The unit "U" is defined as 1U = 1$$\frac{\mu Gy \ m^2}{h}$$ = 1$$\frac{cGy \ cm^2}{h}$$

#### Determining Air-Kerma Strength from Apparent Activity (Aapp)

• Aapp is apparent activity in (mCi).
• W/e = 33.97 (J/C) = 0.876 (cGy/R) for dry air.
• Γ𝛿 is the exposure rate constant. Nominally 4.69 (R cm2 / mCi hr) for Ir-192.

#### Differences in Air-Kerma Strength between TG-43 and TG-43U1

• The cutoff energy, δ, was not included in either the original TG-32 nor the TG-43 definition of Air-Kerma Strength. However, it was included in TG-43U1 because inclusion of low energy photons greatly increased measurement uncertainty while invaliding some theoretical underpinnings of dosimetry models.
• Prevailing conditions (i.e. in vacuo) are explicitly stated in TG-43U1

### Dose Rate Constant

The dose-rate constant, Λ, is the ratio of dose rate at the reference point, $$\dot{D}(r_0, \theta_0)$$, to the air-kerma strength, SK, as in the below equation:

• Λ is defined influenced both by radionuclide and the design of the source model.
• Sometimes denoted "ΛnnD,PqqS" (I.e. Λ97D,N99S)
• D denotes reference dose rate
• nn denotes the year that the reference dose rate was published
• P denotes the provider of the source strength standard (N for NIST, T for Theragenic Corporation)
• qq denotes the year the source strength standard was implemented
• S denotes the word "standard"
• Units: $$\frac{cGy}{h \ U} = cm^{-1}$$
• Common source values:
• VariSource (Ir-192): Λ = 1.044 $$\frac{cGy}{h \ U}$$
• MicroSelectron (Ir-192): Λ = 1.115 $$\frac{cGy}{h \ U}$$
• Flexitron (Ir-192): Λ = 1.112 $$\frac{cGy}{h \ U}$$

### Geometry Function

The geometry function, G, exists to interpolate between data tabulated at discrete points. Geometry functions for point and line sources, denoted with the P or subscript respectively, are given in the below equations:

• Accounts only for inverse square law, neglecting scatter and attenuation
• β is the angle, in radians, subtended by the line source at the calculation point P(r, θ)
• TG-43 and TG-43U1 recommend using the line source approximation, GL, for all 2D dose calculations.
• 1D dose calculations may use either point or line source approximations. Use of the line source approximation is preferred but most planning systems use the point source approximation.

### Effective Length

For sources containing multiple, uniformly spaced radioactive components effective length, the below equation should be used.

• is the number of discrete radioactive pellets.
• ΔS is the nominal center-to-center spacing of the radioactive pellets.
• Lcap is the physical length of the source capsule. (Not defined in TG-43, used here for brevity.)
• Pdist is the distal aspect of the source. (Not defined in TG-43, used here for brevity.)
• Pprox is the proximal aspect of the source. (Not defined in TG-43, used here for brevity.)

Accounts for dose fall off in the transverse plane due to photon scattering and attenuation. If does not include inverse square fall off which is handled by the Geometry Function.

• X (as in gXLX,and GX) is a placeholder for point source, P, or line source, L.
• gis provided in tabular form fitting a 5th order polynomial to within 2%
• $$g_x(r) = a_0 + a_1 r + a_2 r^2 + a_3 r^3 + a_4 r^4 + a_5 r^5$$
• g(1cm) = 1 by definition
• For an Ir-192 HDR source, g(r) increases to a maximum value of about 1.005 at a depth of approximately 3cm. After that point g(r) decreases to around 0.7 at 20cm.

#### 2D Anisotropy Function

The 2D Anisotropy Function expresses the variation in dose with polar angle relative to the transverse plane.

F(r, θ) decreases as

• r decreases
• θ approaches 0° or 180° (minimum values may be as low as 0.65 to 0.45 for an HDR source)
• Encapsulation thickness increases
• Photon energy decreases

## 1D Formalism

Although it is only an approximation of the 2D procedure, the 1D dose rate formalism, below, simplifies source localization procedures because information about source orientation is not needed.

• It is recommended that the line source approximation be used for the geometry function GX.

### 1D Anisotropy Function

The 1D anisotropy function, φan, is the ratio  of dose rate at a distance r, averaged with respect to solid angle, to dose rate on the transverse axis at the same distance.

• Typically φan < 1.
• The 1D anisotropy function may be appropriate for LDR setups with many seeds of unknown orientations. (E.g. LDR prostate brachytherapy).

#### Anisotropy Constant (eliminated in TG-43U1)

In TG-43, an anisotropy constant $$\bar{\phi}_{an}$$ was allowed rather than a distance dependent function. However, this constant was eliminated in TG-43U1.

# Brachytherapy Quality Assurance

Brachytherapy requires a high degree of manual labor which, owing to steep dose gradients and variable source strength, must be performed to high standards of precision. The majority of brachytherapy medical errors are preventable with an appropriate quality assurance program.

AAPM TG-40 provides general guidance on brachytherapy quality control. This report states that a precision of +/-15% is realistic for brachytherapy dosimetry and may be lower for complex multiplane interstitial implants. Regulatory requirement for radiation safety are found in NRC 10 CFR.

Data from IAEA Report No 17

Cause of AccidentIncidence Rate
Incorrect Source Strength22%
Dose Calculation Error19%
Equipment Failure13%
Error in Quantities or Units6%
Other41%
Total Accidents32

## Important QA Points

• A vendor supplied source calibration may be accepted but must be verified to +/- 3% (batch) and +/-5% (individual deviation from mean)
• At least 10% of a batch of sources should be assayed.
• Source inventories must be maintained
• List source type and radionuclide
• Total number of sources, their strength, and location.
• Log use of sources and track their movement into and out of safe storage.
• Patient name
• Attending physician
• Source disposal
• Treatment Planning Software
• Source models and dosimetry as per TG-43
• Correctly assigns source location and dwell time, especially for HDR afterloader based planning.
• Film verification or imaging (CT) may be helpful here.
• Radiation surveys should be performed before, during, and after procedures.

## Required QA Equimpent

### QA Equipment

• Well-type ionization chamber
• Electrometer
• Wipe test equipment
• Thermometer
• Barometer
• Records management system
• Length test ruler
• Film

### Tools and Safety Equipment

• Hand detector (Gieger Counter, etc)
• Source retrieval equipment
• Pliers
• Wire cutter
• Shielded “pig”
Well type ionization chambers used for source activity verification.
(a) Ruler with channel used for length test may be visualized either using in room camera or (b) marked gafchromic film.
Shielded “pig” on cart.

Key Point: Well chambers typically exhibit a strong energy dependence in the brachytherapy energy range. Therefore, it is important to calibrate the well chamber using the correct source nuclide and source model as source construction impacts attenuation and energy spectrum.

## Quality Assurance for High Dose Rate Afterloaders

### 10 CFR Part 35 - Afterloader QA

Key Point: While the AAPM TG-40 provides guidelines for quality assurance of remote afterloaders, most states require the quality assurance mandated in 10 CFR Part 35.

#### Full Calibration (10 CFR 35.633)

Full calibration is required prior to first afterloader use, after source replacement, after significant repair, and at least quarterly.

Required QA

• Output +/-5%
• Position accuracy +/-1mm
• Emergency source retraction under power failure
• Verify source transfer tube lengths
• Timer accuracy and linearity
• Verify applicator length
• Verify function of transfer tubes, applicators, and all interfaces.

#### Daily/Periodic Checks (10 CFR 35.643)

Spot checks are required prior to first treatment in a given day.

Required QA

• Verify vault entrance interlock
• Verify source exposure indicator light at control console, on the afterloader, and at the vault door
• Verify audio visual system function
• Verify presence of emergency response equipment
• Verify function of radiation monitor equipment
• Verify timer accuracy
• Verify computer clock, date and time
• Verify source strength is accurately presented in the computer

### AAPM TG-40 - Afterloader QA Recommendations

Daily Checks

• Interlock function
• Audiovisual system
• Catheter function and locking
• Presence of emergency tools

Weekly Checks

• Source and dummy positioning: +/-1%

Annual Checks

• Dose calculation algorith: 3% and 1mm
• Simulate emergency conditions
• Source Inventory Audit

Source Change Checks

• Calibration of source: +/- 3%
• Verify timing accuracy: +/- 1%
• Verify source positioning: +/- 1%

### Source Change Quality Assurance

Source change is performed by a qualified field service engineer. Appropriate afterloader preventative maintenance will also be performed during a source change. Quality assurance focuses on assuring source strength and positional accuracy of the afterloader.

1. A source chance is typically performed every 3-4 months corresponding to a drop of activity by 60-70% (3-4Ci assuming an initial activity of 10Ci).
2. Source will arrive in shielded shipping container and prior to source change and must be stored in secure room until.
• Source packaging must be inspected for damage and surveyed via wipe test upon receipt.
3. On the day of source exchange, the service engineer will safely remove the old source and insert the new source.
4. Physicist performs quality assurance after source change.
• Verify appropriate source received compared with documentation.
• Verify source activity using calibrated well-type ionization chamber.
• Verify source length and positioning.
• Update treatment planning system with source activity (around 10Ci).
An Ir-192 source arrives in a shielded bucket.

### AAPM TG-41 - Afterloader and Applicator Acceptance Testing

The following tests are recommended by AAPM TG-41 for the acceptance testing of a remote afterloader unit.

1. All console functions and indicators are operational
2. Source retracts appropriately when:
• End of preset time
• An interrupt is engaged
• Loss of power
• A blockage is encountered
3. The battery is adequate to power source retraction
4. Timer accuracy
5. Accuracy of source decay calculation
6. Indexer (which selects which channel to send the source) functions properly
7. Backup systems function during power/pneumatic failure
8. Mechanical (hand) source retraction system is functional
10. System memory correctly stores information
11. Device shielding adequately limits leakage

#### Applicators

The following tests are recommended by AAPM TG-41 for the acceptance testing of an HDR applicator

Key point: The primary source of potential error in a transfer tube/applicator system would be a systematic positioning error.

1. Guide tube integrity
2. Applicator integrity
3. Source and dummy positioning
• This can be measured using gafchromic film
4. Accurate movement of source through the applicator producing expected dose distributions
• This can be measured using gafchromic film
5. Applicator attenuation (if dose calculation will be attenuation corrected)

# Knowledge Test

1. What is the TG-43U1 specification of source strength?

Question 1 of 3

2. Why was a cutoff energy, delta, included in the definition Air-Kerma Strength in TG-43U1?

Question 2 of 3

3. Match the TG-43 2D formalism component to it's purpose.
 Accounts for inverse square lawUnselectDetermines the dose rate at the reference point from a source of a given strengthUnselectAccounts for variation in dose rate as a function of polar angle relative to the transverse plane of the sourceUnselectAccounts for scatter and attenuationUnselectThe measure of the source strengthUnselect Accounts for inverse square lawUnselectDetermines the dose rate at the reference point from a source of a given strengthUnselectAccounts for variation in dose rate as a function of polar angle relative to the transverse plane of the sourceUnselectAccounts for scatter and attenuationUnselectThe measure of the source strengthUnselect Accounts for inverse square lawUnselectDetermines the dose rate at the reference point from a source of a given strengthUnselectAccounts for variation in dose rate as a function of polar angle relative to the transverse plane of the sourceUnselectAccounts for scatter and attenuationUnselectThe measure of the source strengthUnselect Accounts for inverse square lawUnselectDetermines the dose rate at the reference point from a source of a given strengthUnselectAccounts for variation in dose rate as a function of polar angle relative to the transverse plane of the sourceUnselectAccounts for scatter and attenuationUnselectThe measure of the source strengthUnselect Accounts for inverse square lawUnselectDetermines the dose rate at the reference point from a source of a given strengthUnselectAccounts for variation in dose rate as a function of polar angle relative to the transverse plane of the sourceUnselectAccounts for scatter and attenuationUnselectThe measure of the source strengthUnselect

Question 3 of 3