Methods and utilities to assist in the optimization of image quality and radiation dose in X-ray Computed Tomography

Methods and Utilities to Assist in the

Optimization of Image Quality and

Radiation Dose in X-ray Computed

Tomography

ROBERT BUJILA

Doctoral Thesis in Physics

KTH Royal Institute of Technology

Academic Dissertation which, with due permission of the KTH Royal Institue of Technology,

is submitted for public defence for the Degree of Doctor of Philosophy on Friday the 5th of June 2020, at 9:15 AM in U1, Brinellvägen 28A, Stockholm

© Robert Bujila

ISBN 978-91-7873-541-9 TRITA-SCI-FOU 2020:14

Methods and utilities to assist in the

optimization of image quality and radiation

“It is possible that this technique may open up a new chapter in X-ray diagnosis.”

— Godfrey Newbold Hounsfield, 1973

HISTORY

OF SWEDISH NEURORADIOLOGY

the Serafimer clinic, intrathecal injection of air had

been used by the neurologist JACOBEUS

to treat tuber-

culous meningitis, and incidentally a visiting Norwe-

gian,

S .

WIDEROE,

observed

air

on a spine film of one

of these patients. This observation gave him the idea

of using air for myelography. He and JACOBEUS

pub-

lished reports on the use of gas for myelography in

1921 (60, 123), the first publications on myelogra-

phy. SICARD

&

FORESTIER

published their paper

on

oil

myelography in 1922, and DANDY’S

paper on air my-

elography appeared in 1925. Gas

-

air or oxygen

-

was used at the Serafimer Hospital, and the myelo-

graphic technique was developed by LINDGREN

(73),

and later modified by WESTBERC

(121), to allow dif-

ferentiation between cystic and solid cord lesions.

However, water-soluble media were widely used in

Sweden for lumbar myelography outside the Ser-

afimer clinic. The undesired side-effects of these me-

dia became evident in the beginning of the 1970s.

Modem technical development. The interest in

technical achievements persisted even after the

transfer of the activities from the Serafimer Hospital

to the Karolinska Hospital in 1963. In collaboration

with FREDZELL

(now at the Elema factory), the con-

struction of a new apparatus for neuroradiologic ex-

aminations had begun at the Serafimer Hospital and

was continued at the Karolinska Hospital, finally re-

sulting in the Mimer I11 (30, 31). This apparatus al-

lowed “instant fluoroscopy” and “instant tomogra-

phy” during pneumoencephalography, as well as

easy positioning of the patient thanks to the rotating

chair combined with the unit (Fig.

5

c). A chair spe-

cially designed for the examination of children was

constructed in cooperation with DEREK

HARWOOD-

NASH

(52).

During the last decades, Swedish neuroradiology

has not played the same prominent role in technical

developments as previously, albeit some notable

contributions have been made.

Computed tomography (CT). In September 1972,

Swedish neuroradiologists from 7 universities and

representatives from the radiation technology indus-

try

made a joint application to the major research

foundations, including the Swedish Medical Re-

search Council, for a grant to buy an EM1 scanner

for

CT

and to install it at the Karolinska Hospital.

Because of this early commitment, the EM1 scanner

was installed in October 1973 at the Department of

Neuroradiology of the Karolinska Hospital (Fig. 9),

the third to be delivered outside the UK and the first

on the Continent.

The results of this multi-institutional project were

presented a little over a year later in a supplement of

Acta Radiologiea. This publication (80) contained

not only one of the very first reports on a larger pa-

Fig.

9. a) GODFREY

HOUNSKELD

and TORGNY

GREITZ

flanking the

EM1 scanner at the Department of Neuroradiology, Karolinska

Hospital. The photo was taken while HOUNSFIELD

was in Stock-

holm to receive the Nobel Prize in Medicine. b) The first image

taken with this scanner, which was the first CT machine in Eu-

rope.

tient material but also an account of several method-

ologic innovations. Members of the Department of

Neuroradiology at the Karolinska Hospital were the

first to introduce CT cisternography, as reported in

1974 (43), and proceeded to pioneer

CT

angiogra-

phy (104), dynamic CT

(50),

and later stereotactic

CT, as reported in 1976 (9).

Among radiologists from departments outside the

Karolinska Hospital who took part in the evaluation

of

the new method were PAUL EDHOLM of

Linkoping, who analyzed different algorithms for

image reconstruction; BENGT LILIEQUIST

(Umei),

who compared the size of the lateral ventricles as

Hounsfield (right) making a site visit to the Karolinska Hospital, Stock-holm, Sweden, in conjunction with receiving the Nobel Prize in Physiology or Medicine in 1979. Image courtesy of Acta Radiologica.

Abstract

X-ray Computed Tomography (CT) is a highly utilized tool in diagnos-tic radiology. CT provides radiologists with unobstructed views of patient anatomy. However, image quality in CT is highly dependent on the imaging task, scan technique, beam quality and radiation dose. The size of the patient must be considered and the radiation dose must be subsequently adapted to achieve consistent image quality. As CT is a modality that utilizes radia-tion to generate images, the purpose of this thesis was to explore tools and methodologies that can be utilized to optimize image quality with respect to radiation dose.

In Paper I, fundamental image quality metrics were modeled whereby the e↵ect of radiation dose/beam quality on these metrics could be estimated. The applications of these models were demonstrated by estimating the de-tectability of low contrast details across di↵erent radiation doses/beam qual-ities using a mathematical model observer.

Dose indices are reported by CT scanners to indicate the level of radiation that has been utilized during a scan. As the level of radiation dose is a central aspect in optimization work, methods were deployed to verify the accuracy of CT dose indices for wide beam CT scanners in Paper II.

to adapt the level of radiation dose to obtain consistent image quality across varying sized patients. In Paper III, a comprehensive study was executed to better understand the complex nature of ATCM as it relates to di↵erent vendor implementations as ATCM plays a central role in the optimization of CT scans.

As the beam quality used during an examination has a central role for both dosimetry and image quality, a toolkit was developed that can be used to model x-ray spectra emerging from an x-ray tube in Paper IV. The toolkit underwent a rigorous validation and has since been made available online. In conclusion, this thesis has resulted in a number of methods and utilities that can help unfold the complex relationship between image quality and radiation dose on a practical level in CT.

keywords: X-ray Computed Tomography, Image Quality, Radiation Dosime-try

Sammanfattning

Datortomografi (DT) ¨ar ett mycket anv¨ant verktyg inom diagnostisk ra-diologi. DT tillhandah˚aller radiologer med obehindrade vyer av patien-tanatomi. Bildkvalitet f¨or DT ¨ar emellertid mycket beroende av den kliniska fr˚agest¨allningen, avbildningsteknik, str˚alkvalitet, och str˚aldos. Patientens storlek m˚aste beaktas och str˚aldosen m˚aste anpassas d¨arefter f¨or att uppn˚a j¨amn bildkvalitet. Eftersom DT ¨ar en modalitet som anv¨ander str˚alning f¨or att ta fram bilder ¨ar syftet med denna avhandling att utforska verktyg och metoder som kan anv¨andas f¨or att optimera bildkvalitet med avseende p˚a str˚aldos.

I artikel I, grundl¨aggande bildkvalitetsparametrar modellerades d¨ar e↵ekten av str˚aldos/str˚alkvalitet p˚a dessa parametrar kunde skattas. Applikationer f¨or dessa modeller demonstrerades genom att skatta detekterbarheten av l˚agkontrast objekt ¨over olika str˚aldosniv˚aer/str˚alkvaliteter genom att anv¨anda matematiska modellobservat¨orer.

Dosindex rapporteras av DT system f¨or att indikera niv˚an av str˚alningen som har anv¨ants vid en unders¨okning. Eftersom str˚aldosniv˚an ¨ar en central parameter i optimering, har metoder anv¨ants f¨or att verifiera noggranheten av dosindex som anv¨ands f¨or DT system med breda str˚alf¨alt i artikel II. DT system anv¨ander automatisk r¨orstr¨omsmodulering d¨ar str˚alningsniv˚an

anpassas f¨or att uppn˚a j¨amn bildkvalitet ¨over patienter med varierande stor-lek. Eftersom r¨orstr¨omsmodulering ¨ar en viktig aspekt n¨ar det g¨aller optimer-ing, genomf¨ordes en omfattande studie f¨or att b¨attre f¨orst˚a komplexiteterna kring r¨orstr¨omsmodulering med h¨ansyn tagen till hur olika leverant¨orer har implementerat r¨orstr¨omsmodulering i artikel III.

Eftersom den str˚alkvaliteten som har anv¨ants vid en unders¨okning ¨ar vik-tigt att f¨orst˚a med h¨ansyn till b˚ade dosimetri och bildkvalitet, har ett verk-tyg utvecklats som kan anv¨andas f¨or att modellera r¨ontgen spektra fr˚an ett r¨ontgenr¨or i artikel IV. Verktyget har genomg˚att en noggrann validering och har sedan gjorts tillg¨anglig p˚a n¨atet.

Sammanfattningsvis, denna avhandling har resulterat i ett antal metoder och verktyg som kan hj¨alpa med den praktiska f¨orst˚aelsen av den komplexa f¨orh˚allandet mellan bildkvalitet och str˚aldos inom DT.

List of Publications

The thesis is based on the following Papers:

Paper I Bujila R, Fransson A, Poludniowski G. Practical approaches to approximating MTF and NPS in CT with an example applica-tion to task-based observer studies. Physica Medica. 2017 Jan 1;33:16-25.

Paper II Bujila R, Kull L, Danielsson M, Andersson J. Applying three dif-ferent methods of measuring CTDIfree air to the extended CTDI formalism for wide-beam scanners (IEC 60601–2–44): A compar-ative study. Journal of applied clinical medical physics. 2018 Jul;19(4):281-9.

Paper III Merzan D, Nowik P, Poludniowski G, Bujila R. Evaluating the impact of scan settings on automatic tube current modulation in CT using a novel phantom. The British journal of radiology. 2017 Jan;90(1069):20160308.

Paper IV Bujila R, Omar A, Poludniowski G. A validation of SpekPy: a software toolkit for modelling x-ray tube spectra. Accepted for publication at Physica Medica April 2020.

Other Publications

In addition to the papers included in the thesis, the author has contributed to the following peer-reviewed publications:

• da Silva J, Gr¨onberg F, Cederstr¨om B, Persson M, Sj¨olin M, Alagic Z, Bujila R, Danielsson M. Resolution characterization of a silicon-based, photon-counting computed tomography prototype capable of patient scanning. Journal of Medical Imaging. 2019 Oct;6(4).

• Alagic Z, Bujila R, Enocson A, Srivastava S, Koskinen SK. Ultra-low-dose CT for extremities in an acute setting: initial experience with 203 subjects. Skeletal Radiol (2019).

• Nowik P, Poludniowski G, Svensson A, Bujila R, Morsbach F, Bris-mar TB. The synthetic localizer radiograph–A new CT scan planning method. Physica Medica. 2019 May 1;61:58-63.

• Alagic Z, Alagic H, Bujila R, Srivastava S, Jasim S, Lindqvist M, Wick MC. First experiences of a low-dose protocol for CT-guided mus-culoskeletal biopsies combining di↵erent radiation dose reduction tech-niques. Acta Radiologica. 2019 May.

• Nowik P, Bujila R, Kull L, Andersson J, Poludniowski G. The dosimet-ric impact of including the patient table in CT dose estimates. Physics in Medicine & Biology. 2017 Nov 9;62(23):N538.

• Nordenskj¨old AC, Bujila R, Aspelin P, Flodmark O, Kaijser M. Risk of Meningioma after CT of the Head. Radiology. 2017 Aug 14;285(2):568-75.

• Persson M, Bujila R, Nowik P, Andersson H, Kull L, Andersson J, Bornefalk H, Danielsson M. Upper limits of the photon fluence rate on CT detectors: Case study on a commercial scanner. Medical physics. 2016 Jul;43(7):4398-411.

• Omar A, Bujila R, Fransson A, Andreo P, Poludniowski G. A frame-work for organ dose estimation in x-ray angiography and interventional radiology based on dose-related data in DICOM structured reports. Physics in Medicine Biology. 2016 Mar 23;61(8):3063.

• ¨Od´en J, Zimmerman J, Bujila R, Nowik P, Poludniowski G. On the calculation of stopping-power ratio for stoichiometric calibration in pro-ton therapy. Medical physics. 2015 Sep;42(9):5252-7.

• Nowik P, Bujila R, Poludniowski G, Fransson A. Quality control of CT systems by automated monitoring of key performance indicators: a two-year study. Journal of applied clinical medical physics. 2015 Jul;16(4):254-65.

Contents

1 Introduction 1

1.1 Author’s Contribution . . . 3

2 X-ray Computed Tomography 5 2.1 X-ray Production and Interactions . . . 5

2.2 Tomographic Reconstruction . . . 8

2.3 Radiation Dosimetry Aspects in CT . . . 12

2.4 Image Quality Aspects in CT . . . 14

2.5 Automatic Tube Current Modulation . . . 19 3 Modeling the MTF and NPS with applications in

task-based observer performance 22

4 Validation of Wide Beam CT Dosimetry 28

5 Comprehensive Evaluation of Automatic Tube Current

Mod-ulation 33

6 X-ray Source Modeling 42

7 Conclusions and Outlook 51

Acknowledgements 53

Chapter 1

Introduction

X-ray Computed Tomography (CT) has revolutionized medical diagnostics.[1] Since the introduction of CT in 1973[2], CT has seen an exponential increase in usage due to its wide spread availability and clinical utility. CT has become an important imaging modality when it comes to many medical indications, e.g., in the emergency department[3], among others. However, CT is as-sociated with a relatively high radiation dose, compared to other imaging modalities. CT is considered to be one of the largest contributors to the collective e↵ective radiation dose from medical exposures.[4] Radiation dose in CT has therefore become a major concern in the medical community.[5] At the same time, a radiologist’s ability to interpret images from CT is im-pacted by the radiation dose that has been applied during an examination. To put this into perspective, if a CT examination is carried out with too low of a radiation dose, a radiologist might not be able to confidently iden-tify a pathology. However, if an X-ray examination is carried out with too high of a radiation dose, a radiologist will be able to confidently identify a pathology, but the patient will be exposed to a more than necessary amount

of radiation. While there is no universal consensus on the risk of developing stochastic tissue reactions associated with low levels of exposure to radiation (the radiation doses encountered in diagnostic radiology) it is universally accepted that one should exercise caution and abide by the “As Low As Reasonably Achievable” (ALARA) principle.[6]

Unfortunately, applying the optimal amount of radiation to a CT examina-tion is not trivial as it will depend on, among other things, the indicaexamina-tion, the size of the patient as well as the perception of the radiologists. On top of that, modern CT scanners o↵er a high degree of configurability and sophis-tication where image quality can be manipulated using di↵erent parameters for image reconstruction and the applied radiation dose can be adapted in di↵erent ways to the large range of patient sizes using for example automatic tube current modulation (ATCM). Both radiation dose and image quality also depend on the settings of the x-ray tube that were used during an ex-amination, which is therefore an aspect of the imaging acquisition that is important to be able to estimate.

The purpose of this thesis was to investigate the following research questions covering di↵erent aspects of image quality and radiation dose optimization in CT:

• Can models be used to estimate fundamental image quality metrics, for variable scan settings, with potential applications in evaluating task-based observer performance?

• Does radiation dose determined using the current formalism for wide beam CT dosimetry vary depending on measurement methodology? • What is the impact on ATCM, i.e. potential consequence to image

quality and/or radiation dose, when changing a wide range of scan settings on CT scanners from multiple vendors?

• Can an established model of x-ray tube emission be improved upon? Further, can packaging it into a user-friendly toolkit broaden the utility of the model for research?

Author’s Contribution

Paper I

The author is the primary contributor of this paper including model devel-opment, data acquisition, and analysis. The author was supervised by Gavin Poludniowski and Annette Fransson.

Paper II

The author is the primary contributor of this paper. The study was designed together with Love Kull, Mats Danielsson, and Jonas Andersson. The author acquired data together with Love Kull and Jonas Andersson. The author was supervised by Mats Danielsson and Jonas Andersson.

Paper III

While not the primary contributor (first name) on paper III, the author took a prominent role in the design, data acquisition, data analysis and supervision of this study. This study was made together with Deborah Merzan, Patrik Nowik and Gavin Poludniowski.

Paper IV

The author is the primary contributor of this paper. The implementation of algorithms was done together with Gavin Poludniowski. Monte Carlo simu-lations of electron penetration characteristics in Tungsten and x-ray spectra for validation were done by the author. Artur Omar provided Monte Carlo simulated x-ray spectra for normalization of the implemented model as well as valuable insights into the Monte Carlo method and x-ray spectra. The validation of the implemented model was done by the author. The author was supervised by Gavin Poludniowski.

Chapter 2

X-ray Computed Tomography

X-ray Production and Interactions

X-rays were first reported by Wilhelm Conrad R¨ontgen in 1895.[7] X-rays are photons that are generated through interactions when energetic electrons bombard a target material, for example Tungsten, in the anode of an x-ray tube, producing bremsstrahlung and characteristic emissions.[8]

Bremsstrahlung occurs primarily when an electron is de-accelerated in the presence of atomic nuclei in the target material, emitting its loss of kinetic energy as a photon. The energy that is transferred to the bremsstrahlung photon depends on the initial energy of the electron and the degree to which the electron has been deflected by the atomic nuclei during the interaction. The photons that are emitted through bremsstrahlung can have an energy ranging from ⇠ 0 keV to the incident kinetic energy of the electron, E0.

Characteristic emission occurs through a de-excitation process after an atom in the target material becomes ionized through a direct collision between

an incident and orbital electron (impact ionization) or by a bremsstrahlung photon (photoionization). The ionization creates a vacancy in the inner electron shell of the atom which is then filled by orbital electrons that have a higher binding energy. A photon is emitted with an energy that is equal to the di↵erence between the binding energies of the two shells that an orbital electron traverses to fill the vacancy. As such, photons that are emitted through this mode of interaction have well-defined energies.

An x-ray spectrum, S(E), constitutes the number density, of photons di↵er-ential in energy. The number of electrons per unit time that bombard the target material (tube load given in milli-Ampere-seconds or mAs) will a↵ect the fluence of the emitted photons. The energy of the electrons incident on the target (determined through the tube voltage given in kilo-Volts or kV) will a↵ect both the fluence rate as well as the energy of the photons emitted from the x-ray tube (see figure 2.1b).

There are two main modes of photon interaction with matter that are rel-evant in the energy ranges used in diagnostic radiology, the photo-electric e↵ect ( P E), and Compton scattering ( CS). Collectively, these two modes

of interaction dictate the attenuation of a beam of x-rays as it transmits through matter via the linear attenuation coefficient, µM(E). Note, the

lin-ear attenuation coefficient has a material (Z, ⇢) and energy (E) dependence (see figure 2.1a).

During transmission through an object, the x-ray spectrum will be filtered, i.e., the number density of photons di↵erential in energy will change due to interactions with the object’s material. The photon spectrum exiting an object, can be described with the Lambert-Beer Law,

S(E) = E0 Z 0 S0(E)e R sµ(x,y,E)dsdE, (2.1)

where s is a line through some material as the photons traverse the object and S0is the initial spectrum. In figure 2.1b, an example of spectral filtration

is given where a 120 kV spectrum is filtered with 50 mm of water.

0 50 100 150 Energy [keV] 10-1 100 101 102 103 104 Mass Attenuation [cm 2 g -1] Water Calcium Iodine (a) 0 20 40 60 80 100 120 Energy [keV] 0 0.5 1 1.5 2 2.5 3 3.5 Fluence [cm -2] 107 120 kV 120 kV/50 mm Water 80 kV Characteristic Bremsstrahlung (b)

Figure 2.1: Examples of a) Mass Attenuation Coefficients of di↵erent mate-rials and b) X-ray spectra. The x-ray spectra in b) were estimated using the source model from Paper IV.

The potential applications of x-rays in medicine were immediately under-stood. By placing a patient between an x-ray tube and, e.g., a fluorescent screen, medical doctors could see the internal anatomy of patients, which ush-ered in a new discipline of medicine, radiology. In projection radiography, a beam of x-rays are attenuated along its path from an x-ray tube through the patient before impinging on a detector. As such, areas of lower transmission (for example bone) will have a lower detector signal compared to soft tissue (which would have a higher transmission). One of the drawbacks of projec-tion radiography is that all tissues along a ray-line will be superimposed on top of each other. It is therefore difficult to di↵erentiate the di↵erent tissues individually and understand their context in space.

Tomographic Reconstruction

While the radiological implications were not considered at the time, Johann Radon introduced an integral transform (Radon Transform) in 1917[9] that would later revolutionize radiology. In this transform, the density distribu-tion of an object in a plane is mapped to projecdistribu-tions that represent parallel line integrals through the object, at some angle, ✓, and radial position, r, along an axis that is perpendicular to ✓. X-rays can be used to generate these line integrals by studying the initial spectrum before it traverses the object at some (r, ✓) and the exiting spectrum as,

p(r, ✓) = Z s µ(x, y)ds = ln E0 R 0 S0(E)Ee R sµ(x,y,E)dsdE E0 R 0 S0(E)EdE . (2.2)

A CT scanner collects many projections at di↵erent angles around a patient. As such, a CT scanner has two main components, 1) an x-ray tube and 2) a detector, that are placed opposite each other. Figure 2.2 presents an idealized geometry for CT using conventional notations for the di↵erent axes (x,y,z) that make up the coordinate system. Currently CT scanners use energy integrating detectors that convert the incident photons to an electrical signal that is proportional to the intensity of the incident photons using a scintilator coupled to a photo-diode. However, in the future, a new type of detector may be used that has the ability to both count the number of photons incident on the detector as well as resolve their energy.[10]

X Y Z Z Y X + +

Figure 2.2: The geometry of a CT scanner along three axes (x,y,z). The patient (represented by the oval) is centered in the scanner which has an opening represented by the large circle. X-rays from the tube (top of figure) are transmitted through the patient and impinge on the detector (bottom of the figure). The dashed circle denotes the Field of View (FOV) which demonstrates the area that can be reconstructed into an image.

The projections that are collected around an object form a sinogram, which represents all of the acquired projection measurements as function of ✓ and r (see 2.3b). Images are reconstructed by re-mapping the collected projections back onto the same coordinate system that they were collected from. Until recently, this was done analytically using a method called backprojection (BP), which can be seen as the inverse of the Radon Transform, expressed as,

f (x, y) = Z

p(x cos(✓) + y sin(✓), ✓)d✓, (2.3)

to recover the object f (x, y). However, using BP alone will produce blurred images. An example of using backprojection can be seen in figure 2.3c. To

counteract this blurring of the object in the backprojection, filters can be applied in a method called filtered backprojection (FBP). An example of the same object reconstructed with FBP can be seen in figure 2.3d. A number of di↵erent filters can be selected in the reconstruction of images to smooth or sharpen images depending on the imaging task.

(a)

Projection Angle [ ]

Projection Location [r]

(b)

(c) (d)

Figure 2.3: An example of image reconstruction. Projections around the object a) have been collected to form the sinogram in b). The information in the sinogram has been used to generate a backprojected (BP) image c). A filter has been applied in the backprojection (FBP) when reconstructing the image in d).

A number of advances in the reconstruction of images have occurred. All vendors of CT scanners provide so-called iterative reconstructions. In this type of reconstruction, di↵erent models are used to correct acquired sinogram data over multiple iterations which either improves the quality of the images or allows the user to reconstruct images of diagnostic quality while using lower radiation doses.[11] Vendors have also released products which use Deep Learning to provide a mechanism to reconstruct images of higher quality.[12] CT images represent the attenuation at di↵erent locations in an image. The individual voxel values are given as CT Numbers at some location (x,y) in an image and defined as,

CT Number = 1000_⇥µtissue µwater µwater

(2.4)

where µtissue and µwater are the average linear attenuation coefficients for

some tissue composition and water, respectively. A CT Number is given in Hounsfield Units (HU) and will generally range from -1000 for air to 1000 or more for dense cortical bone.

CT is an inherently 3D imaging modality where a volume of the patient is re-constructed into a number of di↵erent slices. The coverage in the z-direction is called the nominal total collimation width. CT scanners typically have two modes of operation, axial and helical. In axial mode, a patient is trans-lated to predefined locations in the z-direction. Between each subsequent table translation, projection data is acquired by rotating the tube/detec-tor around the patient. In helical mode, the patient is moved continuously throughout the scan while the tube/detector are rotating. Helical pitch, p, denotes the relationship between the nominal total collimation width relative to the distance the table travels per rotation.

Radiation Dosimetry Aspects in CT

The International Commission on Radiological Protection (ICRP) have three general priniciples of radiological protection, 1) justification, 2) optimization of protection and 3) radiation dose limits.[13] In terms of medical exposures, justification relies on a medical practitioner ensuring that the x-ray examina-tion will do more good than harm to the patient. The second principle is used to ensure that excessive amounts of radiation are not used when imaging a patient in accordance with the As Low as Reasonably Achievable (ALARA) principle. Radiation dose limits to the patient are not recommended as this could negatively impact the e↵ectiveness of the diagnosis.[14] The quantifi-cation of radiation dose and subsequently optimization of CT exams with respect to radiation dose therefore plays a central role in radiation protec-tion.

Radiation dose has been a consideration since CT was first introduced.[15] Initially, there was no standardized radiation dose metric in CT. It was quickly established that when estimating dose at any location along a scan, one has to consider contributions from radiation scattered to adjacent loca-tions. Shope et al first introduced the concept of the CT Dose Index (CTDI) in 1983.[16] expressed as, CT DI₁ = 1 nT 1 Z 1 D(z)dz, (2.5)

where D(z) is a dose profile in the longitudinal direction, z, and nT represent the number of rows in the acquisition as well as the nominal thickness of each row, respectively. Practically, the longitudinal dose profile, D(z), was mea-sured using a 100 mm pencil ionization chamber[17], yielding the following

expression, CTDI100= 1 nT 50mm_Z 50mm D(z)dz. (2.6)

In practice, the CT DI100 is measured in axial mode for 3 situations

repre-senting the distribution of air Kerma in 1) head, 2) body, and 3) free-air.[18] For head and body measurements, a cylindrical PMMA phantom with a di-ameter of 16 and 32 cm is used respectively. These phantoms are generally 14-15 cm in the longitudinal direction. In each of these phantoms, there are 5 holes extending in the longitudinal direction in one central location and 4 peripheral locations at 12, 9, 6, and 3 o’clock. The weighted CTDI was intro-duced to provide a readily measured estimate of the CTDI averaged over an irradiated section of an object.[19] The weighted CTDI, CTDIw, is defined

as, CTDIw= 1 3⇥ CTDI100,c+ 2 3⇥ CTDI100,p, (2.7)

where c represents a central measurement of CT DI100 and p represents

the average measurement in the peripheral locations. The Volume CTDI, CT DIV ol takes variable pitch into consideration and is defined as CT DI_pitchW.

The CT DI100 in free-air is a standardized measurement and is acquired

by suspending a pencil ionization chamber without inserting the ionization chamber in a phantom.[18] An example of a 100 mm pencil ionization cham-ber is presented in figure 2.4. In this example, a carbon ficham-ber rod is used to suspend the pencil ionization chamber in free-air.

The CTDI is currently ubiquitously used for the reporting of radiation dose in CT. While the CTDI is not intended to represent the radiation dose to patients, it can be used to gauge the level of radiation dose to standard sized objects (head and body) for a given set of exposure parameters.[20] There has been considerable e↵ort made in the community to develop a metric, the Size Specific Dose Estimate, whereby the CTDI can be adapted to di↵erent sized

Figure 2.4: A 3D rendering of a 100 mm pencil ionization chamber from Paper II where the pencil ionization chamber is attached to a carbon fiber rod to assist in the measurement of CT DIf ree air.

objects to give a more patient specific radiation dose estimate for individual patients,[21] Further, there has been considerable e↵ort made to use Monte Carlo simulations to provide more accurate distributions of radiation dose to individual patients and their specific organs.[22]

Image Quality Aspects in CT

Image quality in radiology has a broad definition and is quantified through varying degrees of sophistication in both the literature and in practice. While there is no unified definition of image quality, it is ultimately related to the imaging task at hand. As an example, detecting low contrast liver lesions requires a certain image quality (image characteristics) while characterizing acute extremity fractures requires another[23]. At its core, image quality is inherently a task-based concept and should relate to the observer’s, e.g. a radiologist’s, ability to perform a required imaging task.[24]

From a technical perspective, image quality can be factorized into the metrics:

• Low Contrast Resolution: the di↵erence in CT Number between regions in an image,

• High Contrast (Spatial) Resolution: the ability to delineate the inter-face between bordering objects in an image.

While not strictly task-based in and of themselves, there exists a complex relationship between these image quality metrics and ones ability to perform an imaging task. Further, these image quality metrics can be manipulated in the acquisition/reconstruction of CT images and will also depend on the object that is being scanned as well as the applied radiation dose and radia-tion qualty. As a first order evaluaradia-tion of image quality simple metrics could be used (see table 2.1)

Table 2.1: Tabulation of first order methods to quantify image quality in CT.

IQ Metric Quantification

Noise Standard deviation of CT Numbers in a

ho-mogeneous region

Contrast The number of detectable objects of varying size and contrast in an image

Spatial Resolution The number of visible line pairs of decreasing spatial frequency.

The types of image quality metrics in table 2.1 have utility from, for example, a quality control perspective to evaluate the constancy of a CT scanner.[25] However, these metrics map poorly to task-based image quality as they are not explicitly evaluated in relation to a clinically relevant imaging task.

Image noise in CT is inherently correlated, that is, the texture of noise is characteristic of the acquisition/reconstruction. For example, images with higher spatial frequency (sharper images) will have a finer texture compared to images with lower spatial frequency content (smoother images).[26] The simple metric of standard deviation of voxel values is not capable of ade-quately describing the correlations in image noise.

By decomposing the image noise into its spatial frequency components, both the standard deviation and correlations in noise can be described.[27] This decomposition of image noise is referred to as the noise power spectrum (NPS) and is expressed with continous variables as[28]:

N P S(u, v, w) = 1

XY Z |F T [I(x, y, z)]|

2 _(2.8)

where FT denotes a Fourier Transform and I(x, y, z) represents a sample of image noise (homogeneous image volume) to be transformed into the NPS with the coordinates x, y, and z. The NPS is calculated by integrating over the volume XY Z.

The 3D NPS can be reduced to a 2D (in-plane) representation by integration along the longitudinal axis, z.[29]

N P S2D(u, v) =

Z

N P S3D(u, v, w)dw (2.9)

It can be noted that the standard deviation, or variance, of image noise can be recovered by integrating the NPS,

2 ₌

Z

N P S2D(u, v)dudv. (2.10)

Further, the normalized NPS (NNPS) denotes the NPS normalized by vari-ance, i.e., N P S

A more advanced metric to quantify resolution can be found in the Modula-tion Transfer funcModula-tion (MTF). As an object is being imaged it gets blurred by the imaging system as it is propagated through the reconstruction. This systematic blurring of the object at the di↵erent stages of the acquisition/re-construction can be characterized using the Point Spread Function (PSF). A PSF can be acquired by imaging a small bead (impulse). Analogous to imaging a point to acquire a 2D PSF, a sharp edge can be imaged to acuqire an Edge Spread Function (ESF) in 1D.

If the ESF is acquired by extracting a radial line profile around a circular object, the in-plane MTF can be expressed as[30]:

M T F (u) = F T ⇥ rESF (r) ⇤ R rESF (r)dr , (2.11)

where r is radial coordinates. Note, in this example, the dependent variable, u represents radial spatial frequencies.

An imaging task, in the spatial frequency domain, can be modeled as the Fourier Transform of the di↵erence between binary hypotheses,

WT ask(u, v) = F T [H1 H0], (2.12)

where DFT is the Fourier Transform and H0 and H1 form the binary

hy-pothesis. For a detection task, H1 would represent that a signal was present

and H0 would represent the absence of a signal. An example of a template

for low detection tasks is presented in figure 2.5 covering a range of di↵erent detail sizes and contrast relative to the background.

The in-plane MTF and NPS can be further be combined with a representation of an imaging task, WT ask, resulting in a detectablity index d0[24],

d02=

⇥R R

M T F (u, v)2_W

T ask(u, v)2dudv

⇤2

R R

N P S(u, v)M T F (u, v)2_W

T ask(u, v)2dudv

Target Diameters [mm]

Nominal

Target Contrast [%]

Figure 2.5: An example of a low contrast detection task template from Pa-per I.

There are a number of variations to the detectability index, d0_{, relating to}

di↵erent aspects of human observation, ranging from the ideal observer to including eye filters which model the human visual system. The detectability index, d0_{, given in equation 2.13 is called the Non Pre-whitening (NPW)}

model observer as it takes the impact of correlations in image noise into consideration.

The detectability index, d0, is related to human observation through Receiver Operator Characteristic (ROC) analyses. In a ROC study, human observers are presented a number of images and they have to decide if they can, for example, detect a detail or not. The number of true positive and false positve observations are plotted against each other. The area under the curve (AUC) can then be calculated where a value of unity means that the, for example, signal present/absent images can be fully di↵erentiated from each other. This form of analysis requires a great deal of time and e↵ort and is difficult to implement in practice as it requires many observers or many images to ac-quire confidence. The detectability index, d0, however, can be transferred to the AUC mathematically.[31] Studies have shown that mathematical model observers correlate well with human observers in CT.[32]

Automatic Tube Current Modulation

Patients come in all shapes and sizes. Using data from Kanal et al [33], the distribution of patients in the USA, in terms of water equivalent diameter (i.e., the diameter of a water cylinder that corresponds to a patient’s cross-sectional attenuation) for abdomen pelvis scans is presented in figure (2.6). Due to the exponential nature of attenuation, a 3.6 cm increase in patient diameter would require a two-fold increase in radiation dose, to maintain constant image noise.[34]

To overcome inconsistent image quality between patients and at di↵erent slice locations in the same scan, due to a patient’s di↵ering anatomy, Auto-matic Tube Current Modulation (ATCM) was introduced as early as 1994.[35] ATCM adapts the applied tube current during a scan to achieve a targeted level of image quality. The size and shape of the patient is determined using a localizer radiograph, which is a planar x-ray image (single projection) of the patient that is acquired prior to a CT scan. An example of a localizer radiograph is presented in figure 2.7b.

There are two types of ATCM, longitudinal and angular. Longitudinal ATCM adapts the tube current at di↵erent z-locations to the size of the anatomy at that location, however, it uses the same tube current during an entire rotation. Angular ATCM, on the other hand, adapts the tube current to the shape of the patient at di↵erent tube angles.

In figure 2.7a, the primary di↵erence between longitudinal and angular ATCM is presented where longitudinal ATCM uses a fixed tube current for all rota-tion angles and angular tube current modularota-tion adapts the tube current at di↵erent rotation angles. Angular ATCM applies more tube current at rota-tion angles where the patient is thicker (e.g., lateral projecrota-tions) and less tube current where the patient is thinner (e.g., anterior-posterior projections).

CT Abdomen Pelvis with Contrast 21 - 25 cm 25 - 29 cm 29 - 33 cm 33 - 37 cm 37 - 41 cm 0 5 10 15 20 25 30 35 Frequency [%]

Figure 2.6: Distribution of patient size in terms of water equivalent diameter across Abdomen/Pelvis scans in the USA. The data for this plot was reported by Kanal et al [33].

In figure 2.7b, an example of what the applied tube current could look like using di↵erent modes of ATCM along the z-direction for a helical scan is presented. The solid line represents fixed tube current, where the same tube current is used throughout a scan. Using a fixed tube current throughout a scan, one could expect inconsistent levels of image noise at di↵erent slice locations due to the patients varying attenuation in the z-direction. The thick dashed line represents longitudinal modulation where the tube current is adapted to the size of the patient in the z-direction. In the longitudinal case, a lower tube current is used over the lungs compared to thicker parts of the patients anatomy (e.g., the abdomen). A further refinement to the ATCM is achieved when using angular tube current modulation which also adapts the tube current at di↵erent rotation angles to account for the shape of the patient (fine dashed line in figure 2.7b). Note, all three modes of tube current modulation exhibit the same mean tube current for the entire scan.

0 50 100 150 200 250 300 350 Rotation Angle [deg]

Tube Current [mA]

Longitudinal ATCM Angular ATCM

(a)

0 200 400 600 800 1000 1200

Slice location (z-direction) [mm]

Tube Current [mA]

Constant mA Longitudinal ATCM Angular ATCM

(b)

Figure 2.7: Example of how di↵erent types of ATCM work as a function of rotation angle a), and what the di↵erent modes of ATCM could look like at di↵erent slice locations throughout a scan in b).

Since its introduction, ATCM has become an integral part of the majority of CT scans. ATCM is widely recognized as leading to a net reduction of radiation dose across patients as the tube current adapts the radiation to patient size.[22]

Chapter 3

Modeling the MTF and NPS

with applications in task-based

observer performance

The MTF and NPS were introduced in chapter 2 (section Image Quality in CT) as image quality metrics that present resolution and noise in the spatial frequency domain. Further, these metrics, together with an imaging task,

WT ask, can be incorporated into a mathematical model observer, see

equa-tion 2.13, to provide a task-based detectability index, d0_{. While relatively}

straightforward to calculate, d0 requires a multitude of image acquisitions. The acquisition of images is further exacerbated if one would like to calcu-late the d0 _{that corresponds to multiple techniques variations (e.g., changing}

the tube current or tube voltage).

In Paper I, a model of the NPS was developed whereby the NPS was fac-torized into one component that described the normalized spatial frequency distribution of noise, N N P S, per reconstruction algorithm, and one

compo-nent that could be used to scale the normalized NPS to arbitrary levels of mAs and kV, S(mAs, kV ). The model of the N P S took on the following form,

N P S1D(mAs, kV ) = S(mAs, kV ) 2nominalN N P S1D, (3.1)

where nominal corresponds to image variance at some nominal level of mAs

and kV, N N P S1D corresponds to the 1D normalized NPS. The scaling

func-tion is expressed as, S(mAs, kV ) = ✓ mAs mAsnominal ◆ 1 A  kV kVnominal B + C ! . (3.2)

The free parameters A, B and C were found by fitting image variance at di↵erent levels of kV.

Further, the N N P S1D and M T F1D were also modeled in Paper I. The

N N P S1D was fit to the following expression,

N N P S1D(u) = aubexp c|ug h|k , (3.3)

where a, b, c, g, h, and k were free parameters in the fit. The M T F1D

cor-responding to each reconstruction algorithm was fit to a linear combination of Gaussian terms, M T F (u) = ⌃iaiexp ✓_{u b} i ci ◆2! , (3.4)

where ai, bi, and ci were free parameters in the fit for i terms.

A CT750HD (GE Healthcare, Waukesha, WI, USA) was used to acquire the images in Paper I. All scans were made in helical mode with a pitch of approximately 1, a slice thickness of 0.625, and using the scanners medium bowtie filter. A nominal technique of 120 kVp and 400 mAs was used to acquire images for the MTF and NPS determinations.

A Catphan 600 phantom (The Phantom Laboratory, Salem, NY, USA) was used for the determination of the MTF whereby the teflon cylindrical insert in the CTP404 of that phantom was used to acquire ESF using di↵erent FBP reconstruction kernels. The MTF for the di↵erent reconstruction kernels were modeled using equation 3.4. A comparison between the determined and modeled MTF can be seen in figure 3.1.

Spatial Frequency [lp cm-1] 0 5 10 15 Modulation 0.0 0.5 1.0 1.5 MTF SOFT STANDARD CHST DETAIL Emp. Model (a) Spatial Frequency [lp cm-1] 0 5 10 15 Modulation 0.0 0.5 1.0 1.5 MTF LUNG BONE BONEPLUS EDGE Emp. Model (b)

Figure 3.1: Comparison between determined and modeled MTF for a range of di↵erent reconstruction filters from Paper I

The NPS was determined using the scanner’s 20 cm water phantom. The N P S3D, see equation 2.8, was determined as the average of 37 64x64x64

vol-umes of interest that covered the water section of the phantom. Five scans were used to decrease the uncertainty in the determination of the N P S3D.

The N P S3D was transformed into a 2D representation, N P S2D, using

equa-tion 2.9. As the N P S2D was rotationally symmetric, a 1D representation,

N P S1D of the NPS was derived by radial averaging. The N P S1D was

de-termined for the 8 reconstruction kernels that were available on the scanner. The N P S1Ds were then modeled using equation 3.3. The scaling function,

S(mAs, kV ) was determined by fitting image varaince at di↵erent kV levels from acquisitions of the same water phantom. Figure 3.2 shows the NPS

model compared to NPS determined at di↵erent scan techniques (mAs and kV) for a smooth (SOFT) and edge enhancing (BONEPLUS) reconstruction kernels.

Spatial Frequency [lp cm-1]

0 2 4 6 8 10

Noise Power [HU

2 cm 2 ] 0.0 1.0 2.0 3.0 4.0 SOFT 400mAs/140kV 400mAs/120kV 400mAs/100kV 100mAs/120kV Kernel Ratio Emp. Model (a) Spatial Frequency [lp cm-1] 0 5 10 15

Noise Power [HU

2 cm 2 ] 0.0 10.0 20.0 30.0 40.0 50.0 BONEPLUS 400mAs/140kV 400mAs/120kV 400mAs/100kV 100mAs/120kV Kernel Ratio Emp. Model (b)

Figure 3.2: Comparison between determined and modeled NPS for di↵erent reconstruction filters and scan techniques from Paper I. Note, the NPS model is shown as the solid black line.

The modeled M T F1D and N P S1D from figures 3.1 and 3.2 were further

val-idated by determining the detectability index, d0, for the tasks presented in figure 2.5 for a range of scan technqiues (di↵erent mAs and kV). Assuming that the M T F1D and N P S1D were rotationally symmetric, 2D

representa-tions of the quantities, M T F2D and N P S2D were calculated. The M T F2D

and N P S2D, along with the detection tasks, WT ask, presented in figure 2.5

were used as input to calculate d0 _{with equation 2.13. Across the}

di↵er-ent scan techniques (mAs and kV), tasks, and reconstruction kernels, the root mean error (RMSE) of d0 _{compared to the NPS determined at those}

same scan techniques was no greater than 0.02. The degree of correspon-dence between the model and actual measurements can be seen in figure 3.3, where d0 _{for one task across di↵erent mAs and reconstruction kernels is}

the highest detectability for the low contrast tasks that were studied and that the detectability of the low contrast details has an mAs (radiation dose) dependence.

Tube Load [mAs]

100 200 300 400 500 600 700 835 Detectability Index (d') 0.0 1.0 2.0 3.0 4.0 5.0 Figure of Merit SOFT STANDARD CHST DETAIL Emp. Model Kernel Ratio (a)

Tube Load [mAs]

100 200 300 400 500 600 700 835 Detectability Index (d') 0.0 0.5 1.0 1.5 2.0 2.5 Figure of Merit LUNG BONE BONEPLUS EDGE Emp. Model Kernel Ratio (b)

Figure 3.3: A comparison of detectability indices calculated with the MTF and NPS models and actual measurements. The detectability index across di↵erent reconstruction kernels and mAs for a detection task consisting of 0.5% nominal contrast and a diameter of 7mm from Paper I. Note, the model is presented as the solid black line.

In summary, Paper I demonstrated that for FBP reconstructions, the NPS could be factorized into a component describing the normalized spatial fre-quency distribution and a component describing the scale of the NPS at varying techniques. The NPS was modeled using equation 3.1. The MTF was assumed to be invariant of exposure technique (di↵erent mAs and kV) so it was not modeled as a function of mAs/kV like the NPS. Together, the modeled NPS and MTF were used to derive detectability indices using tasks from the template in figure 2.5 and showed good agreement with measured MTF/NPS at a range of di↵erent scan technqiues. This method could help alleviate some of the difficulties when trying to understand the trade-o↵s in radiation dose and task-based image quality when optimizing protocols.

The models of the MTF and NPS developed in this work assume that these quantities do not have a non-linear dose or contrast gradient dependence. The models developed in this paper are therefore not likely to be directly applicable to images reconstructed with iterative (non linear) methods. Note, when this work was being conducted, non-linear (iterative) reconstruc-tion methods had not yet become mainstream in the clinic. Since Paper I was published, non-linear reconstruction methods have become increasingly applied to CT reconstructions to either boost image quality or compensate the degradation of image quality when the applied radiation dose is decreased.

Chapter 4

Validation of Wide Beam CT

Dosimetry

When first introduced, CT scanners were equipped with a modest number of slices (1 or 2), limiting their coverage in the z-direction. However, in the late 1990s, fierce competition between vendors, aptly called the ”slice wars”, led to an increasing number of slices (i.e., increasing detector coverage).[36] Today, scanners are equipped with a detector coverage up to 160 mm in width. While the CT DI100, see equation 2.6, is used ubiquitously as a metric

for radiation dose in CT, it can be severely underestimated as the nominal total collimation width increases.[37]

The International Electrotechnical Commission (IEC) approached this prob-lem by introducing a new formalism for the CTDI when the nominal total collimation width exceeds 40 mm[18],

CT DI100,nT =

CTDIfree-air,nT

CTDIfree-air,ref ⇥ CTDI100,ref

, (4.1)

collimation of 20 mm or less.

With the CTDI formalism for wide beams in equation (4.1), accurate CT DIf ree air

measurements are of great importance. The Interantional Atomic Energy Agency (IAEA) suggest that a 100 mm pencil ionization chamber (PIC) can be used to measure the CT DIf ree air.[38] Further, for nominal total

collima-tion widths in excess of the length of the pencil ionizacollima-tion chamber, the IAEA suggest translating the pencil ionization chamber along the z-direction com-bining multiple contiguous measurements to aggregate a CT DIf ree air

mea-surement covering the nominal total collimation width. While the IAEA[38] state that air Kerma profiles measured with a point dosimeter at di↵erent positions in the longitudinal direction could theoretically be used to derive CT DIf ree air, the agreement between point dosimeters and pencil ionization

chambers, to the best of our knowledge, has not been demonstrated using the formalism for wide beam CT dosimetry.

In Paper II, the IAEA method (multiple contiguous pencil ionization cham-ber positions) was compared to the CT DIf ree airderived from high resolution

air Kerma profiles in the z-direction. A point dosimeter, Liquid Ionization Chamber (LIC), was used to acquire the high resolution air Kerma profiles for a range of nominal total collimation widths. The LIC was considered to be a dosimetric reference in this study. A measurement rig was used to translate the LIC in the z-direction (see figure 4.1). Further, a more common/commer-cial point dosimeter was used to acquire high resolution air Kerma profiles. The commercial solution was a CT Dose Profiler (CTDP) (RTI Electronics, M¨olndal, Sweden). The CTDP also comes equiped with a translation device called a Mover.

Figure 4.1: A 3D rendering of the rig that was used to measure longitudinal air Kerma profiles, D(z), in Paper II. Note, the sensitive volume of the Liquid Ionization Chamber (dark disc in the cut-out image) is compared to an American quarter dollar coin.

The measurements were made on a Revolution CT (GE Healthcare, Wauke-sha, WI, USA), which has a nominal total collimation width up to 160 mm. A standard exposure technique given by the scanner’s technical documentation for quality assurance purposes was used. The air Kerma profiles acquired in this study can be seen in figure 4.2. The acquired air Kerma profiles were transferred to CT DIf ree air using equation 2.6, where the integration

lengths were extended to those shown in figure 4.2. These determinations of CT DIf ree air,nT were compared to determinations derived through

translat-ing a pencil ionization chamber to multiple contiguous positions to cover the full extension of the wide beams (>40 mm). Note, in addition to the IAEA positions for translating the pencil ionization chamber, the scanner’s docu-mentation has alternative positions. Both the IAEA and GE positions were used in this study. The CT DIf ree air determinations were subsequently used

to estimate the CT DIw (see equation 2.7 using the wide beam formalism in

Figure 4.2: The high resolution Air Kerma profiles covering the range of nominal total collimation widths (nT ) on the scanner studied in Paper II.

Table 4.1 presents the results from this study where the CT DIw is given

for the di↵erent measurement methods. Table 4.1 includes the expectation values form the scanner’s reference documentation. Note, the output of radi-ation can vary from tube to tube so the LIC is used as a dosimetric reference, rather than the expectation value from the scanner’s documentation.

Table 4.1: Results from Paper II where the CT DIw for wide nominal total

collimation widths (nT) is estimated using a pencil ionization chamber (PIC), liquid ionization chamber (LIC) and CT Dose Profiler (CTDP). The values are presented in mGy. The column GE TRM represents the expectation values from the scanner’s technical documentation.

nT GE TRM PIC IAEA Positions PIC GE Positions LIC CTDP 80 mm 27.0 25.2 25.3 25.4 26.0 120 mm 26.2 24.4 24.4 24.6 25.5 160 mm 25.4 23.8 23.8 23.7 24.9

The results form Paper II suggest that translating a pencil ionization cham-ber to multiple contiguous positions to determine the CT DIf ree air closely

agrees with determinations made with the dosimetric reference (LIC), which has not previously been demonstrated for wide beam CT dosimetry. Note, this includes both of the di↵erent PIC positions suggested by IAEA and in the scanner’s technical documentation. While the CTDP also gave similar results to the LIC, the CTDP is not an as commonly available an instrument as a pencil ionization chamber.

Chapter 5

Comprehensive Evaluation of

Automatic Tube Current

Modulation

Since ATCM is complex and varies widely among vendors, it can be a daunt-ing task to understand the intricacies of ATCM as a user. At the same time, ATCM is highly customizable and the level of radiation dose in a scan can be tuned to radiologists preferences. If, for example, the ATCM is not prop-erly configured on a scanner, it could lead to excessive radiation doses or conversely poor image quality.

The aim of Paper III was to perform a comprehensive investigation of state-of-the-art CT scanners (at the time of publication) from the four major CT manufacturers to understand the subtle and not so subtle nuances of specific vendor implementations of ATCM. A thorough description of the specific vendor implementations can be found in Paper III. While ATCM has been studied in the past, these investigations often focused on a single

manufacturer or single aspect of ATCM and often used di↵erent methods (i.e., di↵erent phantoms), which are therefore difficult to aggregate to cover the specific aims of Paper III. However, from other previous studies[39, 40, 41, 42, 43], specific insights about phantom design can be concluded (summarized in table 5.1).

Table 5.1: Summary of desired features for an ATCM phantom that influ-enced design.

Desired characteristics Design statement

Study longitudinal modulation Sections with di↵erent sizes Study angular modulation Elliptical cross-sections

Avoid sharp transitions Tapered edges

Accommodate wide beam collima-tions

Wide sections in z-direction

Avoid air gaps Manufacture from single block

Evaluate image quality Homogenous material to measure

noise

At the time of this study, no single phantom was available that encompassed all of the desired attributes summarized in table 5.1. For that reason, the scope of the study was expanded to include manufacturing a phantom for the purpose of evaluating ATCM. The final phantom is presented in figure 5.1 and was designed as follows:

1. 3 elliptical sections with an aspect ratio of 3:2 (25, 35, and 30 cm major axes respectively),

3. 10 cm between each section (tapered) and rounded outer edges, 4. Phantom milled from a single block of PMMA.

Figure 5.1: 3D rendering of the ATCM phantom that was developed in Pa-per III.

After the phantom was manufactured, the ATCM functionality from a Revo-lution CT (GE Healthcare, Waukesha, WI, USA), Somatom Force (Siemens Healthineers, Forcheim, Germany), Brilliance iCT 256 (Philips Healthcare, Cleveland, OH, USA), and an Aquilion One Vision Edition (Toshiba Medical Systems, Otawara, Japan) was evaluated. On each of the scanners, a refer-ence protocol was defined and used to determine a baseline ATCM. The ref-erence protocol was scanned several times to determine the inherent variation in ATCM using the same scan settings. On each scanner, the reference pro-tocols were then modified and the ATCM from the modified propro-tocols were compared to the ATCM from the reference protocols using the normalized

root mean square error (NRMSE). If the NRMSE of the modified/reference protocol was greater than the inherent variation of the baseline protocol, the ATCM was deemed to have been a↵ected by that protocol modification. Note that the criteria for whether a protocol modification was a↵ected by a protocol change varied quantitatively between the systems as they had dif-ferent inherent variations between scans of the reference protocol. In the evaluations, tube current values were extracted from the DICOM images at the di↵erent slice locations along the scan.

Di↵erent aspects of protocol modifications were studied. These included modifications to the localizer radiograph settings, which the scanners use to estimate patient size/shape to determine the longitudinal and/or angular modulation profiles for the scan. Modifications to the protocol’s CT scan and reconstruction parameters were also systematically modified as well as the miscentering the phantom.

When using ATCM, the level of applied radiation dose can be specified by the user using a reference IQ parameter. The Revolution CT and Aquilion One scanners apply a level or radiation that targets a desired image noise in the object, reflected in their reference IQ parameters Noise Index and Standard Deviation (SD), respectively. Other vendors instead allow the user to specify a level of radiation relative to a reference sized object. The applied level of radiation is then increased or decreased along pre-defined curves for sizes less than or greater than the reference size. The Somatom Force and Brilliance iCT 256 scanners use this approach through their reference IQ parameters Q-ref-mAs and Dose Right Index (DRI), respectively. ATCM curves from the four vendors are presented in figure 5.2 Note, the ATCM curves are superimposed on top of a graphical representation of the phantom’s size at di↵erent locations in the longitudinal direction.

Figure 5.2: The level of radiation applied with ATCM can be controlled using a reference IQ parameter. This figure, from Paper III, shows the applied ATCM for di↵erent levels of the reference IQ parameter for a) the Noise Index (NI) on the Revolution CT, b) the Dose Right Index (DRI) on the Brilliance iCT 256, c) the Qref mAs on the Somatom Force, and d) the Standard Deviation (SD) on the Aquilion One.

The expected level of image noise throughout a scan is approached di↵erently by the four vendors. The Revolution CT and Aquilion One adapt the ATCM to target constant image noise throughout a scan. The Somatom Force and Brilliance iCT 256 on the other hand do not attempt to maintain a constant level of image noise. On these scanners, ATCM is applied in a way to allow for an increase in image noise as the object size increases (lower level of radiation) and a reduction in image noise (higher level of radiation) as the

object size decreases. The reasoning is that contrast between tissues increases with the amount of interstitial fat. Image noise along the phantom using with ATCM enabled/disabled is presented in figure 5.3.

Figure 5.3: Distribution of image noise along the phantom scanned with ATCM enabled/disabled from Paper III. These results reflect the following scanners, a) Revolution CT, b) Brilliance iCT 256, c) Somatom Force, d) Aquilion One.

Paper III resulted in several tables (for each of the categories of protocol modifications tested) that provide a comprehensive quantitative overview of which scan settings, for each scanner, can impact the applied ATCM. While too exhaustive to report on all findings, figure 5.4 presents some of the more unique findings from each scanner. On the Revolution CT (see figure 5.4a), the level of iterative denoising (given in percent) is coupled to the ATCM.

The ATCM on the Brilliance iCT 256 is sensitive to the tube voltage that was used during the acquisition of the localizer radiograph used to plan the CT scan (see figure 5.4b). The direction with which one scans can impact the applied ATCM on the Somatom Force (see figure 5.4c). The Aquilion One allows the user to apply an image filter (e.g., smoothing or edge enhancing) to the acquired localizer radiograph, which can have an impact on the applied ATCM (see 5.4d).

Figure 5.4: Impact to the ATCM when, a) setting the level of iterative denoising (%) on the Revolution CT, b) using di↵erent tube voltages when acquiring localizer radiographs on the iCT 256, c) scanning the object in di↵erent directions on the Somatom Force, and d) applying di↵erent imaging filters to the localizer radiograph on the Aquilion One. This figure is from Paper III.

In summary, ATCM is an important feature on CT scanners. If used prop-erly, it can provide a target image quality across varying patient sizes and within a scan. However, due to the complexities associated with ATCM, pro-tocol modifications could lead to unexpected consequences with respect to excessive radiation dose or poor image quality. Paper III provides CT users with a comprehensive reference to understand how a protocol modification may, or may not, impact the applied ATCM. Note, ATCM may vary between scanner models from the same vendor and di↵erent software versions on the same scanner.

The phantom design from Paper III was commercialized by The Phantom Laboratory (Salem, NY, USA) and is now available so that other users may test the ATCM on their specific scanners (see figure 5.5).

part number

CCT228

page 1 of 2

ATCM Phantom

Automatic Tube Current Modulation (ATCM) is used on CT scanners to obtain a target image quality across varying patient attenuations along a scan. ATCM is an invaluable tool when optimizing CT scans with respect to radiation dose and image quality. The effectiveness of ATCM varies with different technique param-eters and the applied ATCM differs between manufacturers.

The CCT228 ATCM Phantom, developed in cooperation with researchers from the Karolinska University Hospitial (Deborah Merzan, Patrik Nowik, Gavin Poludniowski and Robert Bujila)[1] assists CT operators in characterizing ATCM performance.

The phantom is cast in a single piece from rugged Catphan® Uniformity Material. This phantom allows for both the image noise as well as applied tube current to be evaluated in three different sized oval sections to demonstrate how the ATCM compensates for variations in torso sizes. The phantom can also be used to assess the effects of variations in patient alignment.

The 65cm long phantom consists of 3 ellipsoidal sections. Each ellipsoid is 15 cm in length with a 3:2 ratio; 25:16.7 cm, 30:20 cm and 35:23.3 cm sizes, which is appropriate for modern CT scanners with spiral collimation widths up to 80 mm and which use simultaneous longitudinal and angular ATCM. Smooth transi-tions are provided between the sectransi-tions and the ends are rounded. The phantom

phone 800-525-1190 or 518-692-1190 fax 518-692-3329 email info@phantomlab.com web www.phantomlab.com mail P.O. Box 511 Salem, New York 12865 shipping 2727 State Route 29 Greenwich, New York 12834 T h e P h a n t o m L a b o r a t o r y

Figure 5.5: Product sheet for the commercial ATCM phantom that is based on the design from Paper III. Image courtesy of The Phantom Laboratory (Salem, NY, USA)

Chapter 6

X-ray Source Modeling

As previously highlighted in this thesis, both image quality and the radiation dose to patients is highly dependent on the x-ray spectrum used during an examination. For this reason, it is of great interest to be able to estimate clinical x-ray spectra. Measuring spectra from an x-ray tube is the most direct method of estimation, however, this method is associated with too many impracticalities (and costs) for it to be a practical option for most clinical Medical Physicists.

Poludniowski et al introduced a model to estimate photon emission from a tungsten anode.[44, 45] This model was later incorporated into the widely popular SpekCalc software tool that allowed users to quickly estimate x-ray spectra covering clinical operating conditions.[46] The Poludniowski et al model can be described as follows where the reference geometry of the model can be seen in figure 6.1. The number of electrons at some depth, t, given an incident kinetic energy, E0, in a Tungsten anode is ⌘e(t; E0). An electron

at the depth has the probability pe(E|t; E0) of having an energy, E. The

number of bremsstrahlung emissions di↵erential in energy is d br

where k is the energy of a bremsstrahlung emission, n is the number density of the atoms in the anode, dl is the distance traveled by the electrons in the target, and d br

dk is the bremsstrahlung cross-section di↵erential in energy.

The bremsstahlung emission (number density per unit energy and solid angle, ⌦) per incident electron can be expressed as:

Nbr k,⌦(↵, ; E0) = 1 4⇡Nbrdtn 1 R 0 dt⌘e(t; E0) E0 R k

dEpe(E|t; E0)d_dkbr(k; E)fint(k, t, ↵, ),

(6.1)

where fint represents intrinsic (self) filtration, dt = dl/dt is the average path

length travelled by an incident electron per penetrated depth and Nbr is an

empirical parameter that can be used normalize the bremsstrahlung emission to benchmark results. Note, the model assumes instant electron di↵usion in the anode so the parameter dt is set to 2.

If a radiative transition between sub-shells in the target material of the an-ode is denoted S0 S1, the probability and energy of that transition are

PS0 S1 and kS0 S1, respectively. The density of characteristic emission can

be expressed as: Nch k (E0) = 1 4⇡⌃S0NS0⌃S1PS0 S1 (k kS0 S1) ⇥Nbrdtn 1 R 0 dt⌘e(t; E0) E0 R kS0 dEp(E_{|t; E}0)d_dkbr(k; E), (6.2)

where kS0 corresponds to the edge energy. Note, the parameter NS0 is an

empirical factor to normalize the characteristic emission to benchmark re-sults.

The bremsstrahlung and characteristic emission contributions, Nbr

k,⌦and Nkch,

are incorporated into the spectrum model as follows:

k(↵, , z; E0) =

fext(k, ↵, )

z2_{(1 + tan}2_{↵ + tan}2 ₎(N br