ABSTRACT
Dosimetry is the underlying concept generally used to relate imparted energy by radiation exposure in a volume of tissue to a potential biological effect. This effect can be stochastic in nature, such as the induction of cancer after a substantial time after the exposure, or deterministic where particular damages and cell death can be predicted after reaching certain levels of radiation exposure. The basic unit commonly believed to relate an amount of imparted energy to a biological effect (or the risk for an effect) is the absorbed dose expressed as the mean imparted energy in a mass element (J/kg) of the tissue. The process of calculating the absorbed dose is very complicated since it involves several types of coupled photon and charged-particle interactions in a radiation transport that has a stochastic nature. The absorbed dose cannot therefore directly be measured in vivo and, as a consequence of this, all results are really estimates with relatively large error bars. The Medical Internal Radiation Dose Committee of the Society of Nuclear Medicine introduced a formalism for calculating the absorbed dose for medical use of radiopharmaceuticals in the late 1960s [1] and have since then written several publications in the area. The formalism is described by the general equation
D A Sr r r rT S T S= ⋅ ←
(16.1)
where D is the mean absorbed dose to a target volume, A is the cumulated activity (e.g., total number of disintegrations during a time interval) in the
CONTENTS
Dosimetry in General ......................................................................................... 314 Organ-Based 2D Dosimetry ............................................................................... 315 Organ-Based 3D Dosimetry ............................................................................... 317
Activity Quantitation ..................................................................................... 317 Absorbed Dose Calculation with Point-Dose Kernels .............................. 318 Absorbed Dose Calculation Using Full Monte Carlo Simulation ........... 318
Limitations with 3D Dosimetry ........................................................................ 319 References ............................................................................................................. 320
source volume, and S is a factor that de‰nes the mean absorbed dose to the target volume per unit cumulated activity in the source volume. For internally administered radionuclides, the cumulated activity depends on the physical half-life of the radionuclide and biological half-life determined by the biokinetic behavior of the radionuclide (or radiopharmaceutical). The cumulated activity can therefore be calculated from
A A f t t= ∞∫o d( ) 0
(16.2)
where Ao is the initial activity administered at injection time and f(t) is a time-dependent function. Mostly, f(t) is a combination of one or several exponential functions that, in principle, is speci‰c for each individual and radiopharmaceutical. The S value can be described as
S
n E m
=
⋅ ⋅ φ
(16.3)
where n and E are the number of particles emitted per nuclear transition and the energy of the particles, respectively, and m is the mass of the target volume. The term ϕ is called the absorbed fraction and de‰nes the fraction of the energy emitted from the source volume that will be absorbed in the target volume. When broken down into its smallest constituents, Equation 16.1 becomes
D
A n E r r
m r
=
⋅ ⋅ ⋅ ← ⎛
⎝
⎜
⎞
⎠
⎟∑∑ φ ( )
(16.4)
where the absorbed fraction φ( )r rT S← is de‰ned as the fraction of energy emitted from the source rS and absorbed in the target rT. The principles of the MIRD-formalism remain valid for magnitudes ranging from organ levels down to cellular levels but are most commonly used in the calculation of the mean absorbed dose to whole organs. For practical purposes in dosimetry for risk estimates, the S values are precalculated using Monte Carlo calculation on a mathematical phantom.
