The Physics of CT Dosimetry

CTDI and Beyond

Robert L. Dixon

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9780429662775
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

This book explores the physics of CT dosimetry and provides practical guidance on best practice for medical researchers and practitioners. A rigorous description of the basic physics of CT dosimetry is presented and illustrates flaws of the current methodology.

It also contains helpful (and rigorous) shortcuts to reduce the measurement workload for medical physicists. The mathematical rigor is accompanied by easily-understood physical explanations and numerous illustrative figures.

Features:

• Authored by a recognised expert in the field and award-winning teacher
• Includes derivations for tube current modulation and variable pitch as well as stationary table techniques
• Explores abnormalities present in dose-tracking software based on CTDI and presents methods to correct them

Chapter 1

Introduction and History

1.1 INTRODUCTION

In most books or textbooks, CT dosimetry is presented in “cookbook” form, namely a 100 mm pencil chamber measurement in a phantom and a formula for CTDI ₁₀₀ to be “plugged” (including that of its offspring CTDI _w and CTDI _vol), without providing a derivation of the formula or discussion of its many limitations. In this book, derivations and physical rigor are employed throughout, making these limitations and their required corrections readily apparent to the reader, and made plausible by accompanying the results with clear physical descriptions for the less mathematically inclined reader. An effort has been made to keep each chapter self-contained to avoid too much “page flipping.”

1.2 A HISTORICAL VIEW OF CT DOSIMETRY

The following historical vignette lends some perspective on the development of CT dosimetry. This chapter will also serve as an introduction to this book and may not be strictly chronological (and some “literary license” has been employed).

These early workers could not have imagined the explosive growth in CT methodology over the ensuing decades.

1.2.1 The Early Universe

The early measurement of CT dose and mapping of the dose distribution was primarily done using thermoluminescent dosimetry (TLD) which was tedious and had relatively low spatial resolution. In the early days of CT when scan times were slow and x-ray tube heat capacities were low, obtaining the dose (or dose distribution) resulting from multiple axial slices was difficult. Ed McCollough and Tom Payne (beginning in 1976) did some early work using TLD.

In 1977, the pencil chamber method was introduced by Jucius and Kambic – the same year the Apple II computer was released, and people were playing the Atari game, PONG.

Bob Jucius and George Kambic of Ohio Nuclear, Inc. (a US CT manufacturer) provided the first comprehensive look at CT dosimetry, presenting various options including TLD as well as the introduction of the long pencil ion chamber which they commissioned Capintec, Inc. to manufacture for them (Jucius et al. 1977). They derived an equation which showed that the integral of a single-slice dose profile could be used to predict the average dose about the central scan location (z = 0) for multiple slices. This is far from obvious, and their insight was quite impressive. Their derivation involved a (relatively opaque) summation of integrals. They also mapped dose distributions using TLD and surface dose using Kodak RP/M (mammography) film, but concluded that “at this time, TLD is the technique of choice.”

Dixon and Ekstrand (1978) independently introduced surface dose mapping using a slower radiation therapy verification film (Kodak Xomat/V), digitized using a scanning densitometer for various scanners of the day (resulting in some unexpected dose spikes).

1.2.2 The Birth of CTDI – 1981

Perhaps the best-known paper was that of a US FDA group – Shope, Gagne, and Johnson (Shope et al. 1981) – who refined the integral concept of Jucius and Kambic described in the previous section. To avoid confusion, we will henceforth adopt the notation used throughout this book. They defined the “multiple slice average dose” (MSAD) resulting from a series of N identical axial dose profiles f(z) spaced at equal intervals of b = Δd along z as,

$$MSAD=D_L(0)=\frac{1}{b}{\displaystyle \underset{-L/2}{\overset{L/2}{\int }}f(z^{\prime })d{z}^{\prime }}$$

(1.1)

where the MSAD is the average dose over ± b/2 about z = 0 (at the center of the scan length L) and where L = Nb. For axial scans the dose distribution over the scan length is quasi-periodic of period b, hence the average is over one period (± b/2) about z = 0. Note that their nomenclature “multiple scan average dose” (MSAD) is rather misleading, since it is not the average dose over the total scan length, but rather only about the center of the scan length z = 0. They also stated that L in the above MSAD equation was intended to be long enough for the dose at the center of the scan length to reach its limiting, equilibrium value. From this they defined a “dose index” CTDI as,

$$CTD{I}_{\infty }=\frac{1}{T}{\displaystyle \underset{-\infty }{\overset{\infty }{\int }}f(z^{\prime })d{z}^{\prime }}$$

(1.2)

where

Tis “the slice thickness as stated by the manufacturer” and

f(z)is the dose profile generated by a single axial scan centered at z = 0.

CTDI _∞ is the value of MSAD when L is large enough such that MSAD approaches its limiting (equilibrium) value (which we denote by D _eq) – such that profiles beyond z = ± L/2 contribute negligible scatter back to z = 0; z = 0 being the relevant location for MSAD or CTDI. Note also that CTDI _∞ represents the dose that accrues at the center of the scan length for a table increment b = T, which represented “contiguous axial scans.” With the advent of multi-detector CT (MDCT), T is replaced by “N × T” (nT in our more concise notation used herein). A common misconception is that T or nT represent a beam width, but physically (in any dose formula) they represent a table increment, as will become clear from our derivations in Chapter 2.

The derivation of the MSAD equation by Shope and Gagne (Shope et al. 1981) involved a tedious summation of integrals (following Jucius and Kambic). The derivation for axial scans has been simplified to a few steps (Dixon 2003) using convolution mathematics; this derivation produces the “running mean” dose D _L(z) as an average over z ± b/2 at all values of z (and not just z = 0 as for the MSAD of Shope et al.). This derivation is shown in Chapter 2.

1.2.3 Enter the Regulators – 1989

Codification of physical law rarely turns out well, and once the law has been laid down it is devilishly hard to change (or “too many cooks spoil the broth”).

The original definition of CTDI put forth by Shope et al. (1981), as well as the original US FDA regulatory pro...

Table of contents

• Cover
• Half-Title
• Series
• Title
• Copyright
• Contents
• Preface
• Acknowledgments
• Author
• About the Series
• Chapter 1 ■ Introduction and History
• Chapter 2 ■ Derivation of Dose Equations for Shift-Invariant Techniques and the Physical Interpretation of the CTDI-Paradigm
• Chapter 3 ■ Experimental Validation of a Versatile System of CT Dosimetry Using a Conventional Small Ion Chamber
• Chapter 4 ■ An Improved Analytical Primary Beam Model for CT Dose Simulation
• Chapter 5 ■ Cone beam CT Dosimetry
• Chapter 6 ■ Analytical Equations for CT Dose Profiles Derived Using a Scatter Kernel of Monte Carlo Parentage Having Broad Applicability to CT Dosimetry Problems 6.1 INTRODUCTION
• Chapter 7 ■ Dose Equations for Tube Current Modulation in CT Scanning and the Interpretation of the Associated CTDIvol
• Chapter 8 ■ Dose Equations for Shift-Variant CT Acquisition Modes Using Variable Pitch, Tube Current, and Aperture, and the Meaning of their Associated CTDIvol
• Chapter 9 ■ Stationary Table CT Dosimetry and Anomalous Scanner-Reported Values of CTDIvol
• Chapter 10 ■ Future Directions of CT Dosimetry and A Book Summary
• Index