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CHAPTER 11. Dosimetry Fundamentals

Jenghwa Chang, Ph.D. D.A.B.R.

Associate Professor Radiation Medicine, Hofstra Northwell School of Medicine at Hofstra University

Associate Adjunct Professor Physics and Astronomy, Hofstra University

J. Chang, PhD, DABR

Introduction

• Radiation dosimetry deals with the determination (i.e., by measurement or calculation) of the absorbed dose or dose rate resulting from the interaction of ionizing radiation with matter

• Other radiologically relevant quantities are exposure, kerma, fluence, dose equivalent, energy imparted, etc. can be determined

• Measuring one quantity (usually the absorbed dose) another one can be derived through calculations based on the defined relationships

J. Chang, PhD, DABR

Dosimeter

• A dosimeter can be generally defined as any device that is capable of providing a reading R that is a measure of the absorbed dose 𝐷𝑔 deposited in its

radiation sensitive volume (RSV) V by ionizing radiation

• If the dose is not homogeneous throughout the RSV, then R is a measure of mean value ഥ𝐷𝑔.

J. Chang, PhD, DABR

RSV

Dosimeter

• Ordinarily one is not interested in measuring the absorbed dose in a dosimeter’s RSV itself, but rather as a means of determining the dose (or a related quantity) for another medium in which direct measurements are not feasible

• Interpretation of a dosimeter reading is the central problem in dosimetry, usually exceeding in difficulty the actual measurement

J. Chang, PhD, DABR

RSV

Simple dosimeter model

• A dosimeter can generally be considered as consisting of an RSV filled with a medium g, surrounded by a wall (or envelope, container, etc.) of another medium w having a thickness t≥0

• A simple dosimeter can be treated in terms of cavity theory, the RSV being identified as the “cavity”, which may contain a gaseous, liquid, or solid material g

J. Chang, PhD, DABR

RSV

Simple dosimeter model

• The dosimeter wall can serve a number of functions simultaneously:

– Being a source of secondary charged particles that contribute to the dose in RSV , and provide CPE or TCPE in some cases

– Shielding RSV from charged particles that originate outside the wall

– Protecting RSV from “hostile” influences such as mechanical damage, dirt, humidity, light, electrostatic or RF fields, etc., that may alter the reading

– Serving as a container for g that is a gas, liquid, or powder

– Containing radiation filters to modify the energy dependency of the dosimeter

J. Chang, PhD, DABR

Interpretation of dosimeter measurements for photons and neutrons

• Under CPE condition

𝐷 = CPE

𝐾𝑐 = Ψ Τ𝜇𝑒𝑛 𝜌

• Consider a dosimeter with a wall of medium w, thick enough to exclude all charged particles generated elsewhere, and at least as thick as the maximum range of secondary charged particles generated in it by the photon or neutron field

• If the wall is uniformly irradiated, CPE exists in the wall near the cavity, therefore knowing 𝐷𝑤 can calculate energy fluence Ψ of the primary field

J. Chang, PhD, DABR

𝑫𝒙 for photons under CPE

• The dosimeter reading provides us with a measure of the dose 𝐷𝑔 in dosimeter’s RSV

• If the latter is small enough to satisfy the B-G conditions, we can find 𝐷𝑤 from 𝐷𝑔

• The dose 𝐷𝑥 in any other medium 𝑥 replacing the dosimeter and given an identical irradiation under CPE conditions can be obtained from

𝐷𝑥 = CPE

𝐷𝑤 Τ𝜇𝑒𝑛 𝜌 𝑥 Τ𝜇𝑒𝑛 𝜌 𝑤

for photons

J. Chang, PhD, DABR

RSV

CPE

B-G or S-A

𝑫𝒙 for neutrons under CPE

• For neutrons the CPE condition results in

𝐷 = CPE

𝐾 = Φ𝐹𝑛 • 𝐹𝑛 is kerma-factor, Φ is neutron fluence

• Therefore the dose 𝐷𝑥 in the medium of interest 𝑥

𝐷𝑥 = CPE

𝐷𝑤 𝐹𝑛 𝑥

𝐹𝑛 𝑤 for neutrons

J. Chang, PhD, DABR

RSV

CPE

B-G or S-A

For higher photon/neutron energies, use TCPE instead

• For higher-energy radiation (ℎ𝜈  1 MeV or Tn  10 MeV), CPE fails but TCPE takes its place in dosimeters with walls of sufficient thickness

• For photons TCPE condition provides relationship

𝐷 = TCPE

𝐾𝑐 1 + 𝜇′ ҧ𝑥 ≡ 𝐾𝑐𝛽 = Ψ Τ𝜇𝑒𝑛 𝜌 𝛽

• For neutrons

𝐷 = TCPE

𝐾 1 + 𝜇′ ҧ𝑥 ≡ 𝐾𝛽 = Φ𝐹𝑛𝛽

• Relating 𝐷𝑤 to Ψ or Φ then requires evaluation of 𝛽 = Τ𝐷 𝐾𝑐 for each case

J. Chang, PhD, DABR

Convert to exposure for in-air measurement

• 𝐷air = CPE

𝐷𝑤 Τ𝜇𝑒𝑛 𝜌 air Τ𝜇𝑒𝑛 𝜌 𝑤

• The exposure 𝑋 (C/kg) for photons can in turn be derived from 𝐷air (for x = air) through this relation:

𝑋 = 𝐾𝑐 Τ𝑊 𝑒

air

= CPE 𝐷air

Τ𝑊 𝑒 air

= 𝐷air

33.97

• This relationship can be extended for higher energies where TCPE exists, dividing 𝐷air by 

J. Chang, PhD, DABR

CPE

B-G or S-A

air

RSV

Dair

Uncertainties due to  and d

• The value of 𝛽 = Τ𝐷 𝐾𝑐 is generally not much greater than unity for radiation energies up to a few tens of MeV, and it is not strongly dependent on atomic number

• Thus for media w and x not differing very greatly in Z, the equations for 𝐷𝑥 are still approximately valid

• If the dosimeter has too large a sensitive volume for the application of B-G theory, Burlin theory can be used to calculate the equilibrium dose 𝐷𝑤 from ഥ𝐷𝑔

– Need to know the 𝑑 ≡ ഥΦ𝑤

Φ𝑤 𝑒 which might not equal to the simple form

1−𝑒−𝛽𝐿

𝛽𝐿 .

J. Chang, PhD, DABR

Advantages of Media matching

• Media matching indicates materials of medium (𝑥), wall (𝑤), and/or gas (𝑔) are similar for the following parameters:

– Atomic compositions

– The density state (gaseous vs. condensed), which influences the collision- stopping-power ratios for electrons by the polarization effect

• If these media are matched:

– The measurement directly provides the dose of interest

– Influence of cavity theory is minimized

– No need to know the radiation energy spectrum

J. Chang, PhD, DABR

Media matching

• 𝑤 = 𝑔 : if the wall and sensitive-volume media of the dosimeter are identical with respect to composition and density, then 𝐷𝑤 = 𝐷𝑔 for all homogeneous irradiations

• 𝑤 = 𝑔 = 𝑥: the dosimeter would be truly representative of that medium with respect to radiation interactions, and 𝐷𝑥 = 𝐷𝑤 = 𝐷𝑔

• Unfortunately, dosimeters are only available in a finite variety, therefore must rely on cavity theory

J. Chang, PhD, DABR

Media matching in photon dosimeters (𝑤 = 𝑔 )

• The Burlin cavity relation

ഥ𝐷𝑔

𝐷𝑤 = 𝑑 ∙ 𝑚 ҧ𝑆𝑤

𝑔 + 1 − 𝑑

ഥ𝜇𝑒𝑛

𝜌 𝑤

𝑔

• If 𝑤 and 𝑔 are matched, the doses 𝐷𝑤 = 𝐷𝑔 and

𝑚 ҧ𝑆𝑤 𝑔 =

ഥ𝜇𝑒𝑛

𝜌 𝑤

𝑔 = 1

• This relationship is hard to satisfy, especially for w and g of different atomic compositions

J. Chang, PhD, DABR

Media matching in photon dosimeters (𝑤 = 𝑔 )

• A more flexible and practical relationship

𝑚 ҧ𝑆𝑤 𝑔 =

ഥ𝜇𝑒𝑛

𝜌 𝑤

𝑔 = 𝑛

• The Burling relation then becomes independent of 𝑑 as Τഥ𝐷𝑔 𝐷𝑤 = 𝑛

• It is relevant, e.g., if photons interact only by the Compton effect:

– Τҧ𝜇𝑒𝑛 𝜌 ≈ 𝜎

𝜌 =

𝑁𝐴𝑍

𝐴 𝑒 𝜎 ∝

𝑍

𝐴 , or the number of electrons per gram

– 𝑑𝑇

𝜌𝑑𝑥 𝑐 = …

𝑍

𝐴 … ∝

𝑍

𝐴 (1st approximation for similar 𝑍 bt. 𝑔 and 𝑤.)

– Therefore, 𝑛 ≈ Τ𝑍 𝐴 𝑔

Τ𝑍 𝐴 𝑤

J. Chang, PhD, DABR

Matching the dosimeter to the medium of interest when 𝑤 ≠ 𝑔

• If the wall material 𝑤 ≠ 𝑔 , matching to medium 𝑥 depends on the RSV size

• If RSO is small (𝑑 = 1 in Burlin’s cavity theory), then the wall should be matched to medium 𝑥, to minimize the need for spectral information

• Dose in 𝑥 can be obtained from ഥ𝐷𝑔

𝐷𝑥 =

ഥ𝐷𝑔

𝐷𝑤 ∙ 𝐷𝑤

𝐷𝑥 = 𝑚 ҧ𝑆𝑤

𝑔 ഥ𝜇𝑒𝑛

𝜌 𝑥

𝑤 𝑤,𝑥 𝑚𝑎𝑡𝑐ℎ ഥ𝐷𝑔

𝐷𝑥 = 𝑚 ҧ𝑆𝑤

𝑔

J. Chang, PhD, DABR

B-G

Matching the dosimeter to the medium of interest when 𝑤 ≠ 𝑔

• If the sensitive volume is large (𝑑 = 0 in Burlin’s cavity theory), the wall influence on the dose in the medium g is entirely lost

• Medium 𝑥 should be matched to g and dose in 𝑥 can be obtained from

ഥ𝐷𝑔

𝐷𝑥 =

ഥ𝐷𝑔

𝐷𝑤 ∙ 𝐷𝑥

𝐷𝑥 =

ഥ𝜇𝑒𝑛

𝜌 𝑤

𝑔 ഥ𝜇𝑒𝑛

𝜌 𝑥

𝑤 =

ഥ𝜇𝑒𝑛

𝜌 𝑥

𝑔 𝑔,𝑥 𝑚𝑎𝑡𝑐ℎ ഥ𝐷𝑔

𝐷𝑥 = 1

• For a general case of intermediate size cavity (0 < 𝑑 < 1) full Burlin equation can be used to obtain 𝐷𝑤 from 𝐷𝑔

J. Chang, PhD, DABR

Attenuation Correction

• The problem arises from the difference in attenuation by media 𝑥 (for example, water), 𝑤 (thickness t) and 𝑔 (radius r)

• The photon energy fluence reaching the center of a dosimeter

Ψ𝑑𝑜𝑠 ≅ Ψ0𝑒 −

𝜇𝑒𝑛 𝜌 𝑤

𝜌𝑤𝑡− 𝜇𝑒𝑛 𝜌 𝑔

𝜌𝑔𝑟 ≅ Ψ0 1 −

𝜇𝑒𝑛

𝜌 𝑤 𝜌𝑤𝑡 −

𝜇𝑒𝑛

𝜌 𝑔 𝜌𝑔𝑟

• The photon energy fluence reaching the water sphere replacing the dosimeter

Ψ𝑤𝑎𝑡 ≅ Ψ0𝑒 −

𝜇𝑒𝑛 𝜌 𝑤𝑎𝑡

𝜌𝑤𝑎𝑡 𝑡+𝑟 ≅ Ψ0 1 −

𝜇𝑒𝑛

𝜌 𝑤𝑎𝑡 𝜌𝑤𝑎𝑡 𝑡 + 𝑟

• The dosimeter reading should be multiplied by ΤΨ𝑤𝑎𝑡 Ψ𝑑𝑜𝑠 to correct for the difference of attenuation in determining the dose to water at the dosimeter midpoint

J. Chang, PhD, DABR

Importance of dosimeter wall thickness

• Dosimeter wall thickness requirement depends on measurement goal:

a) Local photon or neutron field: the dosimeter wall should be at least as thick as the maximum range of the charged particles present, to provide CPE or TCPE

b) Local secondary charged-particle field: the dosimeter wall and sensitive volume should both be thin enough not to interfere with the passage of incident charged particles

• If the wall is neither thick nor thin, dose in sensitive volume is due to

a) A mixture of locally and distantly originating charged particles, or by

b) A supply of secondary charged particles inadequate for equilibrium.

c) Need to know the fractions to perform dose conversion e.g.,  for Pwall in TG21.

J. Chang, PhD, DABR