A Thesis

entitled

Automated Signal to Noise Ratio Analysis for Magnetic Resonance Imaging Using a

Noise Distribution Model

by

Abdullah M Aldokhail

Submitted to the Graduate Faculty as partial fulfillment of the requirements for the

Master of Science Degree in Biomedical Sciences - Medical Physics

______E. Ishmael Parsai, Ph.D., Committee Chair

______Kerry Krugh, Ph.D., Committee Member

______Diana Shvydka, Ph.D., Committee Member

______Dr. Amanda Bryant-Friedrich, Dean College of Graduate Studies

The University of Toledo

August 2016 Copyright 2016, Abdullah M Aldokhail

This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author. An Abstract of

Automated Signal to Noise Ratio Analysis for Magnetic Resonance Imaging Using a Noise Distribution Model

by

Abdullah M Aldokhail

Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science in Degree in Biomedical Science - Medical Physics

The University of Toledo

August 2016

Signal to noise ratio (SNR) is a fundamental index of image quality in Magnetic

Resonance Imaging (MRI) and it has traditionally been considered as a sensitive test to monitor the performance of MRI systems. As part of quality assurance program, SNR measurement should have a high level of reproducibility and accuracy. Currently accepted methods to evaluate SNR rely upon manual analysis and are observer dependent. The goal of this project is to develop a robust automated method for SNR analysis to eliminate individual’s variability when performing such a test. This method uses a macro file that has been written using imageJ software to automatically segment the phantom from the background region, measure the mean signal from an area covering

80% of the phantom and determine the noise by fitting a noise distribution model to the background histogram. Fifty-four phantom scans from a variety of RF coils were used to compare the automated SNR analysis method with the manual SNR methods described in the ACR QC Manual. The automated SNR method proved to be accurate, highly reproducible, and relatively insensitive to the existence of minor artifacts in the noise measurement region.

iii Acknowledgements

I would like to express my sincere gratitude to my professor and advisor

Dr. Kerry Krugh for introducing the topic to me and for the continuous guidance and support during my study and my research. This thesis would not have been possible without his help and support.

I would like to thank the MRI staff for giving me the time to spend on the machines and for being helpful and kind.

Finally, I would like to express my deep gratitude to my parents and my wife for the continuous support and encouragement throughout my years of study. This achievement would not have been possible without them.

iv Table of Contents

Abstract iii

Acknowledgements iv

Table of Contents v

List of Tables vii

List of Figures viii

1 Introduction 1

1.1 Basic Principles of MRI 2

1.1.1 Magnetic Proprieties of Nucleus 2

1.1.2 Interaction of Protons with an External Magnetic Feld 3

1.1.3 MR Signal Detection and Image Formation 6

1.2 Primary Components of MRI Scanner 7

1.3 Quality Control for MRI System 9

1.3.1 Signal to Nose Ratio 10

1.3.2 Noise Distribution in Magnitude MR Image 11

1.3.3. Signal to Noise Ratio Measurements 13

1.4 Automated SNR Measurement 17

1.5 Objective of the Study 18

2 Materials and Methods 20

2.1 Materials 20

2.1.1 MRI Scanners

2.1.2 RF Coils and Phantoms 20

2.1.3 Image Analysis Tools 21

v 2.2 Methods 22

2.2.1 Scanning Procedure and Parameters 22

2.2.2 Automated Assessment of Signal to Noise Ratio 23

2.2.3 Validation of the Automated SNR Method 38

2.2.4 Background Artifacts and Noise Estimation 41

3 Results 43

4 Discussion 52

5 Conclusion 57

References 58

Appendix A : Phantom Set Up 61

Appendix B : ImageJ Macro File 62

vi List of Tables

1.1 Properties of selected MR active nuclei ...... 3

1.2 Correction factors for multi-channels coils as a function of channel

numbers ...... 14

2.1 ImageJ built in functions utilized in the automated SNR method…………...21

2.2 Scanning protocols for each RF coil…………………………………………23

3.1 Mean SNR and standard deviation for the automated SNR analysis method

(SNRauto)....………………………………...………………………………...44

3.2 Mean SNR and standard deviation for the single-image SNR analysis method

(SNRsingle)……………………………………………...……………………..44 3.3 Mean SNR and standard deviation for the two-image SNR analysis method

(SNRdual)…………………………………...…………………………………45 3.4 A comparison between the three methods of SNR measurement over all phantom scans of different radiofrequency coils (and number of channels)...46 3.5 Mean (R2), standard deviation (SD), and %CV for different RF coils……………………………………………………………………….….47 3.6 Comparison between noise estimation obtained from the background ROI standard deviation and the noise determined by the noise model fit………...48

3.7 SNR based on SNR single and SNR auto in presence and absence of background artifacts……………………………………………………………………….51

vii List of Figures

1.1: Protons distribution in presence and absence of external magnetic field ...... 4

1.2: precession of a proton in a magnetic field (Bo) ...... 5

1.3: signal localization using read out gradient. The read out gradient induces a change

in the proton precessional frequency (ω) depending on the spatial location

within the sampling volume ...... 8

2.1: Flowchart showing the main steps in the automated SNR measurement…………...24

2.2: A schematic illustration of a typical bimodal distribution………………………….26

2.3: A schematic illustration of a histogram acquired from MRI phantom scan with a threshold value (T) corresponds to the signal intensity at the local minimum between the background and phantom peaks………………………………………………………….27

2.4: Phantom selection in the phase encode direction…………………………………...29

2.5 Background selection for noise measurement…………………………………….…29

2.6: Phantom selection in the phase encode direction…………………………………...30

2.7: background selection for noise measurement……………………………………….30

2.8: Signal truncation along the edges of FOV…………………………………………..31

2.9: Schematic illustration of estimating the number of pixels with zero count…………32

2.10: background signal histogram including signal truncation (left) and after eliminating the truncation artifact (right)……………………………………………………………..33

2.11: Background histogram before and after signal smoothing………………………...34

2.12: SNR report with acquisition parameters…………………………………………...37

2.13: Single image method for SNR measurement………………………………………39

2.14: Two image method for SNR measurement………………………………………...40

viii 2.15: Spine phantom scan shows background ROI placement to include structural artifacts (left) and away from visible artifacts (right)……………………………………41

2.16: Knee phantom scan shows background ROI placement in the phase encode direction to intentionally include structural artifacts (left) and the proper placement of

ROI (right)……………………………………………………………………………….42

Figure 3.1: SNR measurements of six RF coils from three different SNR methods…….46

Figure 3.2: Background histogram for knee coil with artifacts (top) and without artifacts

(bottom)………………………………………………………………………………….49

Figure 3.3: Background histogram for spine coil with artifacts (top) and without artifacts

(bottom)………………………………………………………………………………….50

Figure 4.1: background noise histogram for shoulder coil before smooth (top) and after smooth (bottom)…………………………………………………………………………53

Figure 4.2: difference image artifacts due to temporal instability in MRI data acquisition for breast (left) and spine (right) phantom scan…………………………………………54

Figure 4.2: difference image artifacts due to temporal instability in MRI data acquisition for breast (left) and spine (right) phantom scan…………………………………………56

A-1: Photographs show reference position for phantom set up……….………………...61

ix

x Chapter One Introduction

Magnetic Resonance Imaging (MRI) is a non-invasive medical imaging modality that is used to create cross-sectional images of the internal body structures to aid physicians in the study and diagnosis of disease. MRI uses a very strong magnetic field (most commonly used field strength are 1.5T and 3T) and non-ionizing radiation (radio frequency waves) to generate the MR signal.

MRI is based on principles of Nuclear Magnetic Resonance (NMR) that is when MR active nuclei are placed in a strong magnetic field, the protons will align with the magnetic field in one of two distinct energy states; either parallel (low energy state) or antiparallel (high energy state) to the direction of the applied magnetic field. A few excess protons will align in the low energy level resulting in a net magnetization pointing in the direction of the magnetic field (Mz).

Additionally, the protons will start to precess around the main magnetic field at a specified frequency proportional to the strength of the applied magnetic field (precession frequency). If an external energy (radiofrequency pulse at the precessional frequency) is applied to the sampling volume, some of the protons in the low energy state will absorb the energy and will be flipped to the higher energy state. In addition, the RF pulse will cause protons to synchronize and precess in-phase with each other resulting in a displacement of the net magnetization to the transverse plane (Mx,y). The rotation of the net magnetization on the transverse plane will induce a voltage in an RF receiver coil that could be detected and subsequently used as an MR signal. This phenomenon was independently described by Felix Bloch and Edward Purcell in 1946 for which they shared the Nobel Prize in Physics in 1952. In 1973, Paul Lauterbur and Peter Mansfield, independently proposed a method to spatially localize NMR signals by using magnetic field

1 gradients for which they shared the Nobel Prize for Medicine in 2003. The first MR image of a human body was achieved by Raymond Damadian in 1977. MRI found wide applications in neurological and musculoskeletal imaging due to the excellent contrast resolution for soft tissue this modality provides.

1.1 Basic Principles of MRI

Atoms consist of a central nucleus surrounded by negatively charged electrons. The nucleus contains positively charged particles called protons and electrically neutral particles called neutrons. There are three types of motion within an atom. In addition to the electron motion around the nucleus, both electrons and the nucleus spin around their own axis.

1.1.1 Magnetic properties of the Nucleus

Magnetic properties of the nucleus are determined by the number of protons and neutrons. Nuclei with an odd mass number (i.e. the number of protons plus the number of neutrons is odd) possess a spin or an angular momentum and magnetic moment. Such nuclei, tend to interact with an applied magnetic field (MR active nuclide). On the other hand, nuclei with even mass number and even atomic number (i.e. the number of protons and the number of neutrons are both even), have no spin and no magnetic moment and will not interact with the external magnetic field (MR inactive nuclei )(Mark, Richard, & Thomas, 2004). Table 1.1 lists examples of relevant MR active nuclei.

2 Table 1.1: Properties of selected MR active nuclei (Bushberg, 2012).

Nucleus Spin Number % Isotopes Magnetic Gyromagnetic Relative

Abundance Moment Ratio (MHz/T) sensitivity

H-1 1/2 99.98 2.79 42.58 1

F-19 1/2 100 2.63 40 9 푥 10−6

Na-23 3/2 100 2.22 11.3 1푥10−4

P-31 1/2 100 1.13 17.2 6푥10−5

Of primary interest in MRI is the hydrogen atom (proton). Hydrogen is the most abundant nucleus in the human body. In addition, hydrogen which consists of a single proton, has a relatively large magnetic moment. For these reasons, MRI uses H-1 protons as a source for

MR signals (Bushberg, 2012).

1.1.2 Interaction of Protons with an External Magnetic Feld

Each proton can be considered as a small magnet with a magnetic moment represented by magnitude and direction. In absence of an external magnetic field, the magnetic moment of a sample of protons will be randomly oriented with a net magnet moment of zero (Figure 1.1 A).

When a strong magnetic field is applied to a sample containing a large number of protons, two important phenomena can be observed. The magnetic moment of protons will align with the magnetic field in two distinct energy levels; low energy level (parallel to the direction of magnetic field) and high energy level (antiparallel to the direction of the magnetic field).

Alignment of protons depends on the thermal energy of the nuclide; high thermal energy nuclei will align antiparallel to the magnetic field, while low thermal energy nuclei align with the

3 magnetic field. At equilibrium, a few more protons will align parallel to the magnetic field ( low energy level) resulting in small, but measurable net magnetic moment in the direction of the applied magnetic field (Figure 1.1B) (Westbrook, Roth, & Talbot, 2011).

Figure 1.1: Protons distribution in presence and absence of external magnetic field.

Figure taken from Bushberg, J. T. (2012): The essential physics of medical imaging.

The energy separation between the two energy levels is proportional to the strength of the applied magnetic field (Bushberg, 2012). As the energy separation increases, fewer protons will have thermal energy high enough to oppose the magnetic field. Therefore, a stronger magnetic field increases the net magnetization resulting in higher MR signal.

In addition to the protons alignment in the magnetic field, the protons will start to precess around the magnetic field at specific angular precessional frequency (ω) as shown in Figure1.2.

4

Figure 1.2: precession of a proton in a magnetic field (Bo). Figure taken from Bushberg, J. T.

(2012): The essential physics of medical imaging.

The processional frequency (ω) is governed by Larmor equation:

휔 = 훾 푥 퐵0 (1-1)

Where:

ω: is the angular frequency ( radian/s)

γ: is Gyromagnetic ratio (radian/s-T) ;

B0: is the magnetic field strength (T)

5

In terms of linear frequency (푓), the Larmor equation becomes:

훾 푓 = 퐵0 (1-2) 2휋

Where:

푓 : precessional frequency in MHz.

γ/2π: is Gyromagnetic Ratio in (MHz/T).

B0: is magnetic field strength in (T).

The Larmor equation states that the precessional frequency depends on the magnetic field strength and the gyromagnetic ratio (a constant value for each MR active nuclei). Gyromagnetic ratio for selected MR active nuclei are listed in Table 1.1.

1.1.3 MR Signal Detection and Image Formation

Recall that when protons are placed in a strong magnetic field, they tend to align with the magnetic field with slight majority aligned with direction of the magnetic field ( low energy state) resulting in a net magnetization vector pointing in the direction of the magnetic field (Mz).

When an external radiofrequency pulse (precisely matching the Larmor frequency of protons) is applied to the sampling volume, the net magnetization will be tipped away from the z direction at an angle determined by the magnitude and the duration of the RF pulse. If the RF pulse is left on long enough to flip the net magnetization vector entirely into the x-y plane, a 90O flip angle is

6 achieved. Once the 90O RF pulse is switched off, the transverse net magnetization vector will rotate on the x-y plane and after some time delay will realign with the main magnetic field in the z direction due to a process known as relaxation. During relaxation, the hydrogen atoms release the absorbed RF energy in two simultaneous, but independent process named T1 and T2 relaxation. Relaxation results in regrowth of the net magnetization in the z direction (T1 recovery) and decay of transverse magnetization (T2 decay).The rotation of the transverse magnetization in the x-y plane will induce a voltage in a receiver RF coil as stated by Faraday’s law of electromagnetic induction. The voltage induced in the RF coil is subsequently used as the

MR signal (Westbrook et al., 2011).

The collected data from MR signals are stored in a frequency domain k-space matrix. The horizontal axis of the k-space represents the frequency information and the vertical axis represents the phase information. After the k-space is filled, an inverse Fourier transform is applied to the data to produce a spatial domain representation of the data (Bushberg, 2012).

1.2 Primary Components of MRI Scanner

There are four main components of MRI unit: A strong magnet, gradient coils, radiofrequency system, and computer system.

The magnet is the main and the most expensive part of the MRI system. The strength of magnetic field is measured in tesla (T) (1.0T = 10,000 Gauss). Typical magnetic field strength for clinical applications ranges from 0.3T to 3T with 1.5T and 3T being the most commonly used field strength.

Another important component of the MRI scanner is the gradient coils. To obtain an MR image with spatial information, the MR signal from different physical positions must be

7 localized. Gradient coils are used to produces a slight change in the magnetic field strength across the imaging volume which results in slight change in the precessional frequency of protons across the sampling volume as stated by the Larmor equation. Location of MR signals in a two dimensional image is determined by the frequency and phase of the precessional protons.

Figure 1.3 shows an example of signal localization using the read out gradient.

Figure 1.3: signal localization using read out

gradient. The read out gradient induces a change

in the proton precessional frequency (ω)

depending on the spatial location within the

sampling volume. Taken from Mark, B., Richard,

S., & Thomas, K. N. (2004). MRI: Basic Principles and

Applications, 3rd edition.

The radiofrequency system is composed of a radiofrequency transmitter (to generate radiofrequency pulses tuned at the Larmor frequency) and a sensitive radiofrequency receiver coil to detect MR signals. MRI utilizes different types of RF coils depending on the anatomical area of interest. Volume coils surround the entire imaging tissue and produce a uniform signal intensity and SNR over the entire imaging volume. Volume coils can provide large FOV and are suitable for brain, knee, and total body imaging, however, this type of coils produces images with relatively low SNR compared with other types of coils such as surface coils. Surface coils, on the other hand, are placed adjacent to the imaging tissue and produce high SNR when imaging tissues near the surface of the coil. This type of coils is used to image structures near the surface of the patient such as the spine. Surface coils are usually small and have limited FOV.

8 Another type of MRI coil are phased array coils. This type of coil consists of multiple independent sub-coils that offer the high SNR of surface coils while achieving the large FOV of the volume coils. Phased array coils can be configured as a surface coil as well as volume coil.

Finally, a powerful computer system is needed to control and coordinate the functionality of MRI unit components and process the MRI data.

1.3 Quality Control for MRI System

Image quality, for medical purpose, can be defined as how well the image conveys anatomical or functional information to the interpreting physician (Bushberg, 2012). Like any other medical imaging modality, MRI system needs to be checked periodically to ensure the scanner works properly and to detect any degeneration of image quality that can adversely affect the clinical decision. Recommendations and protocols for image quality assurance have been established by several organization such as the American College of Radiology (ACR: MRI

Quality Control Manual, 2015), American Association of Physics in Medicine (AAPM report

No.100, 2010), and the National Electrical Manufacturers Association (NEMAMS 1-2008).

A comprehensive MRI quality program has been established by The American College of

Radiology (ACR) providing a set of standardized quality control tests and performance criteria to ensure a high level of performance. The image quality portion of this program includes various daily, weekly, and annual assessments of the MRI scanner. The recommended tests include, but are not limited to, slice thickness and slice position accuracy, low and high contrast resolution, magnetic field homogeneity, image uniformity, and signal to noise ratio (ACR: MRI Quality

Control Manual, 2015).

9 1.3.1 Signal to Nose Ratio

Signal to noise ratio (SNR) is an important factor in describing the image quality of MRI scanners. It is often used to evaluate the performance of MRI systems, compare and evaluate pulse sequences and imaging protocols, and to monitor the system performance for ongoing quality control program purposes. (Dietrich, Raya, Reeder, Reiser, & Schoenberg, 2007;

Murphy et al., 1993; Redpath, 1998). Since the contrast sensitivity of the MR image is limited by

SNR (Bushberg, 2012), degeneration of SNR impairs the detectability of low contrast objects. In such case, lesions with signal intensities close to the surrounding tissue can be difficult to be identified by interpreting physician and can result in inaccurate diagnosis. Thus, it is important to have a reliable and accurate method to evaluate SNR in MR imaging to detect a small degeneration in SNR before it adversely impact the clinical decisions.

As the name implies, SNR is the ratio of the signal relative to the noise. MR signal is proportional to the amplitude of the voltage induced in the receiver coil while the noise can be random and/ or nonrandom. Random noise is present in every image and is caused by the electrical fluctuation of the MR system and the presence of the patient in magnet. Nonrandom or structural noise arises from system malfunction or some type of motion artifacts such as ghosting artifact.

Several factors affect SNR in MR image which include, the main magnetic field strength, pulse sequence parameters (TR, TE, and flip angle), scanning parameters such as voxel size, the number of signal averages (NEX), receiver bandwidth (BW), image acquisition and reconstruction algorithms, and RF coil type and location relative to the imaging volume

(Bushberg, 2012; Westbrook et al., 2011). For instance, SNR can be maximized by using a large voxel volume and increasing the number of signal averages (NEX), however, increasing the

10 NEX increases the scan time while using large voxel volume reduces image spatial resolution.

Therefore, scanning parameters are adjusted to produce optimal image quality with reasonable scan time.

1.3.2 Noise Distribution in Magnitude MR Image

In MRI, the acquired complex data in the k-space are assumed to be superimposed by a

Gaussian distributed noise. Since Fourier transform- is a linear operation, it will preserve the

Gaussian distribution of the noise. In clinical practice, however, magnitude reconstruction algorithm is applied to the complex data to produce the image. Magnitude operation is non-linear and it will alter the noise distribution in the magnitude images to a Rician distribution (Sijbers, den Dekker, Van Audekerke, Verhoye, & Van Dyck, 1998).

Noise properties in magnitude images have been studied by Henkelman which shows that image processing used to produce the magnitude image changes the noise distribution in the image and leads to under estimation of the true noise value (σ). In areas with no MR signal(background regions) , the true noise value (σ) was found to be equal to the background standard deviation (SD air) divided by 0.655 (Henkelman, 1985). The correction factor (0.655) arises because the noise distribution in the background region is not Gaussian.

Further analysis of the noise distribution shows that the noise distribution in a magnitude

MR image does not follow Gaussian distribution; in fact, it follows Rician distribution. This is more prominent for areas with low signal intensities, while for areas of high signal intensities

(SNR > 3) the noise distribution approaches Gaussian distribution. It was also shown that in regions with no MR signal (background region), the noise distribution follows a special case of

11 Rician distribution known as Rayleigh distribution with probability distribution function given in equation (1-3) (Gudbjartsson & Patz, 1995; Sijbers et al., 1998).

푆2 푆 −( ) P(S) = 푒 2휎2 (1-3) 휎2

Where:

S: is the noise signal in background area ,

σ : is the noise.

Gaussian standard deviation or the true noise in the image (σ) can be estimated from the

Rayleigh standard deviation (SD air ) using equation (1-4) (Edelstein, Bottomley, & Pfeifer, 1984) which yields the same result presented by Henkelman.

휋 SD air = √(2 − ) σ (1-4. A) 2

σ = 푆퐷(푎푖푟) / 0.655 (1-4. B)

Constantinides C.D et al showed that the number of channels of the receiver coil influences the noise distribution in the magnitude image and proposed equations to evaluate the noise distribution not only for a single channel coils, but also to include multi-channel phased array coils (Constantinides, Atalar, & McVeigh, 1997). Phased array coils consist of multiple independent closely positioned sub-coils (channels). Each sub-coil receives MR signal from a small area of the imaged structure and the output signal from each sub-coil can be displayed as a composite or combined image. The output signal of the composite image in most MRI systems is computed as the root of the sum-of-sqaures of the signal from each sub-coil. According to

Constantinides C.D et al, the composite noise distribution in area with no MR signal

12 (background) was shown to be governed by a central chi statistics with probability distribution function given by:

푆2 2 2푛−1 −( 2 ) P(S) = 2푛 ∗ 푆 ∗ 푒 2휎 (1-5) (휎√2) (푛−1)!

Where

S: is the signal in background areas (noise signal),

n: is the number coil elements,

σ: is the noise.

For a single channel coil (n=1), central chi distribution (1-5) reduces to the Rayleigh distribution function (1-3).

To summarize, in magnitude MR image, the noise distribution in regions with noise signal only (background noise) was found to be governed by Rayleigh distribution for a single channel coils while for multi-channel coils it follows the central chi distribution.

1.3.3. Signal to Noise Ratio Measurements

While measuring the MRI signal is somewhat straight forward, estimating the noise is more challenging. A review of literature has shown many different methods to perform SNR measurement; some are based on a single image acquisition and computing the mean signal from the signal producing phantom and estimating the noise from the standard deviation of the background region (i.e. region with no MR signal) (Henkelman, 1985; Kaufman, Kramer,

Crooks, & Ortendahl, 1989). Another method is based on acquisition of two identical images and computing the noise from the subtracted image (NEMA MS 1, 2008 & AAPM report No. 100,

13 2010). Still another method is based on acquiring an image with no signal producing phantom

(pure noise image) and estimating the noise from the pure noise image (NEMA MS 1, 2008).

The most commonly used methods for QA purposes found during literature review are discussed below.

1.3.3.1 Single Image Method

SNR measurement based on single image acquisition is performed by measuring the mean signal (푆) from the phantom ROI and estimating the noise (σ) from the standard deviation from an artifact-free background region in the phase encode direction (SDair). Since the reconstruction algorithm used in MRI to produce a magnitude image changes the noise distribution in the reconstructed image, true noise in the image for a single channel coil (σ) =

푆퐷(푎푖푟) . The factor (0.655) arises because the noise in the image is not Gaussian distributed 0.655

(Henkelman, 1985; Kaufman et al., 1989). Since the number of channels influences the noise distribution, different correction factors need to be applied for multi-channel coils. Table 1.3 shows appropriate correction factors for multi-channel coils as suggested by NEMA Standards

Publication MS 9-2008.

Table 1.3: correction factors for multi-channels coils as a function of channel numbers.

Number of channels Correction factor (CF)

2 0.68

3 0.69

4-20 0.70

21-256 0-71

14

Signal to noise ratio in this case is given by:

푆 푆푁푅 = 퐶퐹 ∗ (1-6) 푆퐷(푎푖푟)

Although this method is simple to perform, it is sensitive to the presence of structural artifacts in the background region such as ghosting artifacts. Because the single image method assumed the signal in the background region is essentially zero, subtle signal intensities projected in the background region due to image artifacts can lead to artificially elevated SD. As a consequence, the SNR is underestimated (Firbank, Coulthard, Harrison, & Williams, 1999;

Kaufman et al., 1989). An additional factor that complicates the SNR measurement with the single image method is the spatial inhomogeneity of the noise in the background region due to noise correlation (Aja-Fernandez & Tristan-Vega, 2012). In addition, for ongoing QC measurements, it is crucial to reproduce the exact same ROIs in terms of size and location for signal and noise measurement. This is especially true for measuring the mean signal for surface coils where the signal falls significantly depending on the distance from the coil surface (AAPM report No. 100, 2010).

1.3.3.2 Dual Image Method

SNR measurement based on two image acquisition was proposed by the National

Electrical Manufacturers Association (NEMA MS 1-2008). This method required an acquisition of two identical phantom scans with minimum time interval between the two scans (less than five minutes). The signal intensity was suggested to be computed as the mean signal (푆) from a

15 regular phantom ROI covering at least 75% of the phantom. These images are then subtracted from each other and the noise is computed as the standard deviation from the same ROI in the

푆퐷(푑푖푓푓) difference image (SD diff). The noise (σ) in the subtracted image is given by . Since the √2 noise is evaluated in a region within the phantom which has high signal intensity, this method assumed that the noise has a Gaussian distribution and, therefore, no need for a correction factor.

The square root of two, however, arise because the noise is computed from the difference image.

SNR in this case is given by:

푆 SNR= √2 (1-7) 푆퐷(푑푖푓푓)

Since the noise is measured from an area within the phantom, this method is not sensitive to the structural artifacts projected in the background region. However, one of the identified problems of this method is that it is sensitive to temporal system instability which leads to artificially elevated standard deviation in the subtracted image (SD diff) and ,hence, underestimation of SNR. In this case, the method is not valid for noise estimation (Sijbers et al.,

1998). Additionally, unlike the single image method, the dual image method requires two MRI phantom scans (doubling the scanning time) and images need to be manipulated for SNR analysis which makes it time consuming. Finally, like the single image method, it is imperative for ongoing QA tests to reproduce the same size and location of ROIs from previous test which can be challenging.

One can choose either the single or the dual acquisition method to evaluate SNR for the scanner. However, the most important factor when measuring SNR for quality control purposes

16 is reproducibility. In addition to scan parameters and phantom position, the method of noise analysis and measurements must be identical from one test to another (ACR MRI QC

Manual, 2015). For some coils where the signal drops sharply relative to the distance from the coil, it is imperative to have a reference for SNR measurements such as a photograph showing the location of the ROIs to accurately reproduce them each time (AAPM report No. 100, 2010).

To avoid such a burden from individuals performing SNR measurements and to eliminate human variability, an automated method to measure SNR with high accuracy and reproducibility is proposed in this project.

1.4 Automated SNR Measurement.

Review of literatures reveals many proposed methods to evaluate the performance of

MRI scanners using automated approach to keep the human interaction at minimum and to expedite the process of the measurements. Keeping the human interaction to minimum will mitigate the observer dependence and will avoid the subjectivity of individuals performing quality control measurements.

One of the early works toward automating the process of evaluating MRI performance using a custom designed parallel rod test object was proposed to allow a semi-automated assessment of scanners performance in term of image distortion, spatial resolution, slice thickness and separation, and SNR with minimum human interaction (Covell et al., 1986; Hyde,

Ellis, Gardner, Zhang, & Carson, 1994). Bourel et al have developed an automated QC software and a designated cylindrical test object aiming to detect degrading MRI system performance in term of SNR, spatial resolution, slice thickness, image uniformity, and geometric distortion

(Bourel, Gibon, Coste, Daanen, & Rousseau, 1999). Recent published work for an automated

17 MRI quality assurance program to compare and evaluate the MRI systems performance within multicenter studies. In this work, the ACR phantom was utilized to evaluate several scanner performance parameter such as SNR, image uniformity, spatial resolution and linearity (Davids et al., 2014).

Although these approaches were investigated to provide an automated assessment of the main parameters related to the performance of MRI scanner including SNR measurement, those methods utilize software that strictly applied to a particular test object which might not be readily available for clinical medical physicists. In addition, the design and size of the test objects seems to be impractical for evaluating SNR for surface coils and special purpose coils such as breast and knee coils. Finally, the noise measurement is based on the standard deviation measured from the background region or from the difference image. In contrast, the automated SNR method proposed in this project is based on a noise distribution model and it can be used to evaluate SNR for a variety of coil configurations using the readily available quality control phantoms provided by the scanner vendor.

1.5 Objective of the study

SNR is a fundamental index of image quality in MRI and it provides a sensitive measure to monitor the performance of MRI systems. As part of a quality assurance program, the phantom set up, scan parameters and the method for analyzing SNR should have a high level of reproducibility. The main goal of this project is to develop an automated SNR method using a model-based noise determination to improve the reproducibility of the measurement by eliminating individual’s variability when performing such measurements.

18

This study has the following specific objectives:

1) Propose a reliable automated method for SNR analysis by developing a robust

software to efficiently segment the phantom from the background region and

determine the noise by fitting a noise distribution model to the background histogram.

2) Evaluate the robustness of the automated SNR method on a variety of RF coils types

and channel numbers.

3) Assess the accuracy and precision of the proposed automated method by comparison

with the recommended and commonly used methods for evaluating SNR (single and

dual image method).

4) Investigate the impact of the presence of minor background artifacts on the noise

determined by the fit.

19 Chapter Two

Materials and Methods

A total of 54 phantom scans were performed on two different MRI systems using six different radiofrequency coils. The acquired images were used to compare three different methods of measuring SNR, namely: single image method, two-image method and the proposed method in this study (automated method).

2.1 Materials

2.1.1 MRI Scanners

MRI scanners used for this project are a 3.0T GE (Signa Excite HDx, General Electric) and a 1.5T Siemens (Magnetom Espree, Siemens) both are located at The University of Toledo

Medical Center. Toledo, OH.

2.1.2 RF Coils and phantoms

A random sampling of three RF coils were chosen for each scanner to represent a variety of coil configurations ( single-channel volume coil, phased-array surface coil, and phased-array volume coil) over a range of channel numbers. For the 3.0T scanner, phantom scans were performed with a single-channel body coil, 8-channel brain coil, and 8-channel breast coil. While for the 1.5T scanner, phantom scans were performed with a spine coil operated with 3 channels, a4-channel shoulder coil, and a 8-channel knee coil. Scans were performed using the quality assurance fluid-filled phantoms provided by the manufacturer.

20 2.1.3 Image analysis tools

Images were analyzed using the freely available ImageJ software from the National Institute of

Health (NIH) which was also utilized to develop a script for the automated SNR measurement

(Schneider, Rasband, & Eliceiri, 2012). Useful built-in function utilized in this project are listed in Table 2.1

Table 2.1: ImageJ built in functions utilized in the automated SNR method.

Function Description getStatistic( area, mean) Returns the area and the mean pixel value of the image or selection. getHistogram ( values, counts, nBins) Returns the histogram ( pixel values and number of counts) of the image or selection with a bin width of max pixel value / nBin . createSelection Creates a composite selection from a thresholded image setThreshold (lower, upper) Sets the lower and upper threshold values getSelectionbounds (x, y , width , height ) Returns the smallest rectangle that circumscribe the active selection with origin coordinate (x,y) getInfo (DICOM_TAG) Returns the value of a specified DICOM TAG) makeRectangle ( x , y , width, height) Creates a rectangular selection with origin coordinate of (x,y) makeInverse Invert the active selection (creates an inverse selection). Fit.doFit ( equation, xpoints, ypoints) Fits a defined equation to a specified x and y data.

21 2.2 Methods

2.2.1 Scanning Procedure and Parameters:

For the each RF coil used in this project, three identical, consecutive MRI scans were performed in compliance with the ACR MRI QC Manual (ACR:MRI Quality Control Manual,

2015). These scans were repeated three times in three different scanning sessions over a period of two months. Within each scanning session, phantom scans were performed without repositioning the phantom so that the only variable in SNR measurement should be related to the image analysis method such as the size and/ or the location of ROIs. Although care was taken to ensure the same scanning set up for each session, performing the scans on different sessions is important to take into account any possibility of set up changes which may cause some variation in the SNR measurement. It should be noted that after positioning the phantom of interest inside the magnet bore, a period of three minutes was allowed to pass before starting the scan to allow the fluid in the phantom to settle.

As recommended by the ACR QC Manual, all phantom scans were performed with a T1 weighted image using a single spin-echo (SE) sequence with repetition time (TR) of 500 ms, echo time (TE) of 20 ms, number of signal averages (NEX) of one, and matrix size of 256 × 256.

Appropriate field of view (FOV) and slice thickness were chosen according to the RF coil of interest. FOV was chosen to provide a background region, in the frequency encode direction, large enough to obtain adequate sampling of the noise (ACR: MRI Quality Control Manual,

2015). Table (2.2) shows the scanning parameter for each RF coil.

22 Table 2.2: Scanning protocols for each RF coil.

Pulse Matrix Slice RF Coil TR(ms) TE(ms) NEX FOV(cm) Sequence Size Thickness(mm) GE Body SE 500 20 1 2562 48 5 GE Brain SE 500 20 1 2562 35 1 GE SE 500 20 1 2562 40 5 Breast Siem. SE 500 20 1 2562 45 1.5 Spine Siem. SE 500 20 1 2562 25 1.5 Shoulder Siem. SE 500 20 1 2562 25 1.5 Knee

2.2.2 Automated Assessment of Signal to Noise Ratio

The proposed method utilizes a script that has been written using ImageJ software to automatically measure the mean signal intensity (S) from an area covering 80% of the phantom and noise measurement by fitting the noise model discussed in section 1.3.2 to the signal distribution in the background region (excluding the phase encode direction) . The script was developed to perform the following main tasks: 1) automatically segment the phantom from the background region using a histogram-based thresholding technique 2) define signal ROI as an area covering 80% of the phantom and measure the mean signal (S) 3) define the background

ROI in the frequency encode direction and extract the signal distribution 4) background signal processing to correct for signal truncation and to smooth the histogram 5) fit the signal distribution to the noise model in equation (1-5) to obtain the noise fit parameter (σ) 6) calculate

SNR as (S/σ) and print the result along with some optional parameters. Figure 2.1 shows a flowchart of the automated SNR measurement.

23 MRI Phantom Image Segmented Phantom Signal ROI

Define 80% of the phantom & find

mean signal (S) Thresholding

Define background area in Background ROI frequency encode direction

SNR Report

Fit background signal to noise model & determine the noise (σ) from the fit

Bkg. Distribution Noise Model Fit Calculate SNR as (S/σ) and print the result

ofCounts Number

Signal Intensity

Figure 2.1: Flowchart showing the main steps in the automated SNR measurement.

24 2.2.2.1 Phantom Segmentation and Defining the Signal ROI

The first task in the scrip is to segment the phantom from the background region using a histogram-based threshold technique with threshold value (T) corresponding to a signal intensity at the valley (local minimum) between the phantom and background peaks.

Segmentation is a process that subdivides the image into regions with similar properties.

A simple method to segment an image can be obtained by using a thresholding technique by which the image is divided into two categories depending on the pixel intensity. Pixels with a certain range of intensity will be assigned to one category, while the rest of the pixels will be assigned to the other category (Russ, 1995). A histogram-based thresholding technique, was found to work well when the ROI has signal intensity different than that of the background region (Sharma & Aggarwal, 2010).

Since phantom scans show two distinctive histogram peaks (high phantom signals and low background signals), the resultant histogram will be bimodal (Fig 2.2). Is this case, mode method can be used to segment the image with threshold value (T) corresponding to the pixel value at the local minimum between the two peaks (Glasbey, 1993; Sahoo, Soltani, & Wong,

1988).

25 Bimodal Distribution 1000 900 800 700 600 500 400 300

Frequency(arbitrary) 200 100 0 0 100 200 300 400 500 Intensity ( arbitrary)

Figure 2.2: A schematic illustration of a typical bimodal distribution.

In some cases, however, the phantom scan shows a histogram with three peaks separated by two minima due to truncation artifact (Figure.2.3). To circumvent this issue, the valleys in the histogram are sorted and the threshold value (T) is chosen as the pixel value of the second valley

(i.e. the valley between the background peak and phantom peak). Additionally, a pop-up window will appear showing the automated threshold value and the user can change the threshold value if needed. The automated threshold value determined by the algorithm was found to be appropriate for all phantom scans performed on this project.

26 MRI Phantom Histogram 1000 900 Truncation peak 800 700 600 Background peak 500 400 Phantom peak 300

Frequency(arbitrary) 200 100 T 0 0 100 200 300 400 500 Intensity ( arbitrary)

Figure. 2.3: A schematic illustration of a histogram acquired from MRI phantom scan with a threshold value (T) corresponds to the signal intensity at the local minimum between the background and phantom peaks.

Phantom segmentation is accomplished by the following steps:

i- Obtaining the intensity histogram of the image using “getHistogram” function.

ii- Finding the peaks in the histogram using ‘‘findMaxima functions.

iii- Finding and sorting the valleys in the histogram.

iv- Defining the threshold value (T) as the pixel value at the valley between the

background and the phantom peaks.

v- Thresholding the image using “setThreshold” function with threshold value of (T).

After segmenting the phantom from the background region, the boundaries of the phantom are defined using the “create selection” function and the mean signal from an area covering 80% of the selection (phantom) is acquired using the “getStatistics” function. The mean signal (S) is saved as a variable to be used later in SNR calculation.

27

In short, the phantom is segmented from the background using a histogram-based threshold technique with a threshold value corresponding to a pixel value in the valley between the phantom and the background peaks. Then, the mean signal from an area covering 80% of the phantom (S) is obtained and saved to be used in SNR calculation.

2.2.2.2 Defining the Background ROI and Extracting the Noise Signal:

The next step in the script is to define the background region excluding the phase encode direction. The phase encode must be excluded from noise measurement because it is susceptible to major artifact (ghosting artifact) (ACR MRI QC Manual, 2015 & Henkelman, 1985). In order to accomplish this, the script will obtain the phase encode direction from the image DICOM header using the “getInfo” function and the background ROI will be defined accordingly as follows:

i- If the phase encode direction is column (vertical axis of the image), the script will

create a mask covering the phantom (with a buffer to exclude potential artifacts that

may occur at the boundaries of the phantom) in the phase encode direction using the

“makeRectangle” function (Figure 2.4).

28

Phase Encode Direction Direction Encode Phase

Figure 2.4: phantom selection in the phase encode direction.

The selected rectangle in Figure 2.4 represents the area that needs to be excluded from the noise measurement. To exclude this region, the “makeInverse” function is used to select the entire image excluding the previous selection as shown in Figure 2.5.

Phase Encode Direction Direction Encode Phase

Figure 2.5: Background selection for noise measurement

ii- If the phase encode direction is row (along the horizontal axis of the image), a

horizontal rectangle covering the phantom on the phase encode direction will be

29 created using the function “makeRectangle“(Figure 2.6). The selection then will be

inverted and the resulting selection is shown in Figure. 2.7.

Direction Encode Frequency Figure 2.6: Phantom selection in the phase encode direction.

Direction Encode Frequency

Figure2.7: background selection for noise measurement.

30 After defining the background region, signal distribution (noise signal) from the selected area is obtained from the histogram using the “getHistogram” function.

2.2.2.3 Background Signal Processing

After extraction the background signal, the signal is processed to exclude the counts from the truncation area in the image from being included in the noise estimation and to smooth the noise histogram.

It is not uncommon to observe signal truncation artifact (dark bands along the outer edges of the FOV) where the signal has artificially been zeroed by the system (Figure 2.8).

Figure 2.8: Signal truncation along the edges of FOV.

Multiple approaches were investigated to eliminate the signal truncation from the histogram used for noise determination. One approach was to eliminate all the pixels that have zero signal from the background histogram (i.e. assuming the background region has signal intensity greater than zero). Another approach was to approximate the number of pixels that have no signal to an arbitrary number. Yet another approach was to extrapolate the number of pixels that have zero

31 signal intensity from the first three points in the noise histogram (x1, x2, and x3). This approximation is done by using linear regression to determine the y-intercept (Figure 2.9). The number of counts from pixels with no signal in the background region is assumed to be equal to the y-intercept value. Background histograms with signal truncation and after extrapolating the number of pixels with signal intensity of zero are shown in Figure 2.10.

Frequency ( Y)

x1 x2 x3 Intensity (X)

Figure 2.9: Schematic illustration of estimating the number of pixels with zero count.

32 The slope of the three points was found using the line function:

y= mx + b (2-1)

where

y: the number of counts (frequency)

m: the slope of the line

x: is the pixel value (intensity)

b : is the y-intercept

Since the truncation signal represent one point in the histogram, manipulating this point

should have minimum effect on the curve fitting process. Linear regression approach was

implemented to estimate the number of zero counts in the background region since it was shown

to maintain the trend of the noise histogram.

1500 1500

1000 1000

500 500

0 0 0 18 23 28 33 38 43 48 53 58 63 68 73 0 18 23 28 33 38 43 48 53 58 63 68 73

Figure 2.10: background signal histogram including signal truncation (left) and after eliminating

the truncation artifact (right).

33 Histogram signal smoothing is implemented in the software because it was shown to improve the consistency of the automated method. Smoothing of the background signal is done using a five-point moving average technique by which each point in the signal histogram is replaced with an average of five adjacent points prior to applying the noise model fit. Figure 2.11 shows the background histogram before and after signal smoothing.

1200

1000

800 Original Histogram 600 Smoothed Histogram

Frequency 400

200 0 0 20 40 60 80 100 Signal Intensity

Figure 2.11: Background histogram before and after signal smoothing

The noise signal is smoothed using the following equations:

For i=2 to i= n-2:

푆(푖−2)+푆(푖−1)+푆(푖)+푆(푖+1)+푆(푖+2) Ss(i) = (2-2) 5

Where: n : is the total number of points in the histogram

th Ss(i) is the i smoothed point

S(i) is the original ith point in the histogram

34 For the second point( i=1), there is not enough points to perform the five -point average.

Therefore, a three-point smoothing is done as:

푆(0)+푆(1)+푆(2) Ss(1) = (2-3) 3

Similarly, for the first point in the histogram (i=0) the smoothing is done as:

푆(0)+푆(1) Ss(0)= (2-4) 2

Since the last two points are located at the tail of the curve, which is almost flat, these points should have no effect on the noise estimation and, therefore, they can be assumed to be zero

(O'Haver, 1997).

2.2.2.4 Noise Model Fit and Computing the Image Noise:

Recall from equation (1-5) that the probability distribution of the noise in the background region is a function of the signal, the number of channels in the receiver coil, and the noise in the image. The background signal is already obtained in a previous step, but the number of channels is still undefined. It is possible to incorporate a manual input where the user can enter the number of channels. However, a study has shown that the presence of noise correlation in the background region results in a reduction of the effective number of channels of the coil (Aja-

Fernandez & Tristan-Vega, 2012). Therefore, to optimize the accuracy of noise estimation and to make the process fully automated, the algorithm will execute an iteration process to find the number of channels (n) that produce the best fit of the noise model to the background noise distribution. In other words, the program will fit the noise model to the background signal histogram using the “Fit.doFit” function over a range of channel numbers (from n=1 to j ) where j is the number of iterations. In this project, j was chosen to be eight because the maximum

35 number of coil elements utilized in this study was eight channels. After the iteration process, the goodness of the fit is determined by the coefficient of determination (R2) and the number of channels that produces the best fit will be used as the variable (n) for the noise estimation.

The “curve fitter” function uses an iterative procedure by which 1) the parameters of the fitting model are initially estimated, 2) the fitting model is compared with the data points, 3) the initial parameters values are then adjusted to improve the fit, 4) the function will return to step 2.

This iterative process is repeated until the best possible fit is achieved (Schneider et al., 2012).

Figure 2.11 shows the background histogram and the model fit based on the background signal.

Bkg. Distribution

Noise Model Fit Frequency

Signal Intensity

Figure 2.11: Background ROI distribution with noise model fit based on background signal.

The final step in the program is to obtain the noise parameter (σ) from the optimal fit and calculate SNR calculation as:

푆 SNR = (2-5) 휎

36 Where

S : is the mean signal measured from signal ROI

σ: is the noise parameter obtained from the curve fit

The result will be printed on the screen with some optional acquisition parameters as shown in

Figure 2.12.

Figure 2.12: SNR report with acquisition parameters

37

2.2.3 Validation of the Automated SNR Measurement method:

To investigate the reliability of the automated SNR method, accuracy and precision were assessed. Precision was assessed by obtaining three consecutive phantom scans under identical scanning conditions from six different radiofrequency coils (section 2.1.2). These scans were repeated three times in three different scanning sessions in reproducible manner. For each radiofrequency coil, the SNR was measured using the automated method and the variation in the measurements from each scan is determined by the coefficient of variation (CV) as:

푆퐷 퐶푉 = 휇

Where:

SD : is the standard deviation of the three SNR measurements

μ : is the mean value of the three SNR measurements

The CV in the measurements from each scanning session (i.e from consecutive scans without repositioning the phantom) will be referred as intra-session CV and it should reflect only the variation in the image analysis method such as the location and size of ROIs. The CV in the measurements from the three scanning session will be referred as inter-session CV. In addition to the variation in the image analysis method, inter-session CV takes into account a potential variation in the phantom set up and possible slight changes in the scanner performance.

Accuracy of the automated methods was tested on 52 phantom scans from six different radiofrequency coils (section 2.1.2). For each image, the automated SNR measurement value is compared with that obtained from the manual SNR methods described by the ACR QC Manual,

38 namely, single-image SNR method and two- image SNR method (ACR: MRI Quality Control

Manual, 2015). The accuracy of the automated SNR method is reported as the percentage deviation (% Dev) from the manual method as:

퐷푒푣푖푎푡푖표푛 % 퐷푒푣 = ( ) ∗ 100 푚푎푛푢푎푙 푆푁푅 푣푎푙푢푒

As recommended by the ACR manual, SNR measurement using the single-image method is performed by measuring the mean signal from a manually drawn signal ROI covering 80% of the phantom and measuring the standard deviation from an ROI placed in the background region avoiding the phase encode direction and visible artifacts (Figure 2.13). Effort was made to perform the analysis in a reproducible manner. Signal ROI of a regular shaped area was sized to cover 80 ± 2% of the area of the phantom and placed at the center of the phantom. Background measurement is obtained from two identically sized rectangular ROIs covering as large area as possible in the frequency encode direction avoiding signal truncation and visible artifacts.

Mean Signal ROI Background ROIs

SD1 SD2

S

Figure 2.13: Single image method for SNR measurement.

This method will be referred as (SNR single) and it is computed as:

푆 SNR single = 퐶퐹 ∗ 푆퐷(푎푖푟)

39

Where

S : is the mean signal in the phantom

2 2 푆퐷(푎푖푟): is the combined background standard deviation =√(푆퐷1 + 푆퐷2 )/2

CF: is Gaussian equivalent correction factor

For the two-image method, two consecutive identical phantom scans are acquired and the mean signal is measured from two centered ROIs of a regular shape covering 80 ±2% of the area the phantoms. These images are, then, subtracted and the noise is measured as the standard deviation from the same signal ROI in the subtracted image (Figure 2.14). In most cases, the boundaries of the phantom in the difference image are difficult to identify. Therefore, the mean signal ROI is copied and placed in the difference image.

Mean Signal ROI1 Mean Signal ROI2 Difference Image ROI

S1 S2 SDdiff

Image 1 Image 2 Image1-Image2 Figure 2.14: Two image method for SNR measurement.

This method will be referred as (SNR dual) and is computed as:

푆 SNR= √2 푆퐷(푑푖푓푓)

40

Where

S: is the average of the mean signal in ROI1 and ROI2

푆퐷(푑푖푓푓): is the standard deviation in the difference image

√2 : To account for the noise in the difference image.

2.2.4 Background Artifacts and Noise Estimation

To investigate the effect of minor background artifacts in the noise estimation determined by the automated method, structural artifact was intentionally included and excluded in two separate background ROIs. The noise was then estimated using the model-based fit and by the

ROI standard deviation. This experiment was performed on spine phantom scan (Figure 2.15) and knee phantom scan (Figure 2.16). For the knee scan, the background ROI was intentionally placed in the phase encode direction to include ghosting artifact.

Figure 2.15: Spine phantom scan shows background ROI placement to include structural artifacts (left) and away from visible artifacts (right).

41

Figure 2.16: Knee phantom scan shows background ROI placement in the phase encode direction to intentionally include structural artifacts (left) and the proper placement of ROI

(right).

42 Chapter Three

Results

Using the methods described in the previous section, 52 phantom scans from two MRI scanners using different radiofrequency coils were evaluated using the three different SNR methods.

3.1 Reproducibility

For each radiofrequency coil, the mean SNR value (and standard deviation) and the percentage coefficient of variation (%CV) using the automated SNR method (SNR auto), single image SNR method (SNR single), and two image SNR method (SNR dual) are shown in Tables 3.1,

3.2 and 3.3, respectively. Looking at each scanning session, the deviation in the measurements ranges from 0.07 to 0.86 for SNRauto, 0.31 to 3.80 for SNRsingle, and 0.20 to 6.85 for SNRdual. The average intra-session %CV ranges from 0.23 to 0.34 for SNR auto, 0.63 to 1.28 for SNR single, and

1.98 to 2.18 for SNR dual.

Across all scanning sessions, the deviation in the measurements range from 1.27 to 1.83 for SNR auto, 0.85 to 3.10 for SNR single, and 1.13 to 8.58 for SNR dual with an inter-session %CV that on average are 1.48, 1.53, and 4.34 for SNR auto, SNR single, and SNR dual, respectively.

43

Table 3.1: Mean SNR and standard deviation for the automated SNR analysis method (SNRauto) Session 1 Session 2 Session 3 All Phantom Scans

RF Coil SNR (±SD) % CV SNR (±SD) % CV SNR (±SD) % CV SNR (±SD) % CV

Brain (8CH) 131.60(0.41) 0.31 134.75(0.21) 0.16 130.790(0.16) 0.12 132.38(1.83) 1.38

Body (1CH) 81.75(0.15) 0.18 83.41(0.30) 0.36 80.50(0.07) 0.09 81.89(1.27) 1.56

Breast (8CH) 164.15(0.17) 0.10 163.92(0.39) 0.24 161.23(0.38) 0.24 163.10(1.43) 0.88

Knee (8CH) 105.82(0.31) 0.30 102.31(0.25) 0.24 102.71(0.36) 0.35 103.61(1.68) 1.62

Shoulder (4CH) 83.57(0.44) 0.53 83.60(0.12) 0.15 80.80(0.15) 0.19 82.66(1.42) 1.71

Spine (3CH) 84.15(0.22) 0.27 81.32(0.20) 0.25 81.58(0.86) 1.06 82.16(1.43) 1.74

Average 0.28 0.23 0.34 1.48

Table 3.2: Mean SNR and standard deviation for the single-image SNR analysis method

(SNRsingle)

Session 1 Session 2 Session 3 All Phantom Scans

RF Coil SNR (±SD) % CV SNR (±SD) % CV SNR (±SD) % CV SNR (±SD) % CV

Brain (8CH) 149.98(1.22) 0.81 152.77(0.76) 0.49 150.77(0.70) 0.47 151.17(1.48) 0.98

Body (1CH) 81.93(1.03) 1.26 80.20(1.06) 1.32 79.73(0.35) 0.44 80.62(1.26) 1.56

Breast (8CH) 161.68(2.46) 1.52 164.92(0.78) 0.47 160.22(3.80) 2.37 162.27(3.10) 1.91

Knee (8CH) 108.23(0.94) 0.87 105.00(0.47) 0.45 103.73(1.68) 1.62 105.65(2.24) 2.12

Shoulder (4CH) 88.06(0.90) 1.02 88.52(0.57) 0.65 86.28(1.24) 1.44 87.62(1.31) 1.50

Spine (3CH) 76.56(0.91) 1.19 76.35(0.31) 0.40 75.51(1.01) 1.33 76.14(0.85) 1.11

Average 1.11 0.63 1.28 1.53

44 Table 3.3: Mean SNR and standard deviation for the two-image SNR analysis method (SNRdual) Session 1 Session 2 Session 3 All Phantom Scans

RF Coil SNR (±SD) % CV SNR (±SD) % CV SNR (±SD) % CV SNR (±SD) % CV

Brain (8CH) 133.33(6.85) 5.14 138.90(1.47) 1.06 131.16(3.43) 2.61 134.46(5.12) 3.88

Body (1CH) 81.59(0.38) 0.47 82.76(1.05) 1.27 80.59(0.55) 0.68 81.64(1.13) 1.38

Breast (8CH) 146.11(1.44) 0.98 136.09(3.26) 2.40 127.63(5.01) 3.92 136.61(8.58) 6.28

Knee (8CH) 100.58(1.57) 1.56 95.25(3.99) 4.19 96.35(0.20) 0.21 97.39(3.25) 3.34

Shoulder (4CH) 75.93(3.19) 4.20 79.54(1.84) 2.31 77.73(1.04) 1.34 77.73(2.47) 3.18

Spine (3CH) 74.65(0.47) 0.63 73.70(0.49) 0.66 63.31(2.73) 4.32 70.56(5.63) 7.98

Average 2.16 1.98 2.18 4.34

3.2 Accuracy

A comparison between the mean SNR measurements based on the automated SNR method, single image method, and dual image method over all phantom scans are shown in

Table 3.4 and Figure 3.1. The automated SNR measurements show a percentage deviation range from -12.43% to 8.16% and -1.55% to 16.44% relative to the single and the dual image methods, respectively. On average, the automated SNR value is -1.63 ± 6.98% of the single image method and 7.88 ± 8.45% of the dual image method.

45

Table 3.4: A comparison between the three methods of SNR measurement over all phantom scans of different radiofrequency coils (and number of channels). The average percentage deviation is reported ± one standard deviation *.

SNR singe SNR dual SNR auto

% % Dev. of % Dev. of RF Coil SNR (±SD) % CV SNR (±SD) % CV SNR (±SD) CV SNR single SNR dual Brain (8CH) 151.17(1.48) 0.98 134.46(5.12) 3.88 132.38(1.83) 1.38 -12.43 -1.55

Body (1CH) 80.62(1.26) 1.56 81.64(1.13) 1.38 81.89(1.27) 1.56 1.57 0.30

Breast (8CH) 162.27(3.10) 1.91 136.61(8.58) 6.28 163.10(1.43) 0.88 0.51 19.39

Knee (8CH) 105.65(2.24) 2.12 97.39(3.25) 3.34 103.61(1.68) 1.62 -1.93 6.39

Shoulder (4CH) 87.62(1.31) 1.50 77.73(2.47) 3.18 82.66(1.42) 1.71 -5.66 6.33

Spine (3CH) 76.14(0.85) 1.11 70.56(5.63) 7.98 82.35(1.43) 1.74 8.16 16.44

Average 1.53 4.34 1.48 -1.63±6.98* 7.88±8.45*

SNR Measurements of Different Methods 180

160

140

120

100

SNR 80

60

40

20

0 8-Ch Brain 1ch Body 8-Ch Breast 8-Ch Knee 4-Ch Shoulder 3-Ch Spine

SNR single SNR dual SNR auto

Figure 3.1: SNR measurements of six RF coils from three different SNR methods.

46

The goodness of the noise model fit in terms of the mean coefficient of determination

(R2) for each RF coils is shown in Table 3.5. In all phantom measurements, the noise model fit yields

R2 value that on average is 0.98 with an average %CV of 0.34%.

Table3.5: Mean R2, standard deviation (SD), and %CV for different RF coils. Averaged Over All Phantom Scans

RF Coil R2 (±SD) %CV Brain (8CH) 0.9835 0.0069 0.6981

Body (1CH) 0.9313 0.0069 0.7373

Breast (8CH) 0.9875 0.0028 0.2838

Knee (8CH) 0.9990 0.0002 0.0204

Shoulder (4CH) 0.9950 0.0011 0.1134

Spine (3CH) 0.9930 0.0016 0.1608

Average 0.9815 0.3356

47

3.3 Background Artifacts and Noise Measurement

The impact of minor artifacts in the background ROI on the noise estimation obtained by computing the background standard deviation from a manually drawn ROI compared to the model-based noise is presented in Table 3.6. The noise estimation based on the standard deviation of the background region is significantly increased in the presence of artifacts 17.61% and 18.91% for knee coil and spine coil, respectively. The noise determined by the fit in the presence of artifacts increased by 2.71% and 1.59% for the knee coil and the spine coil, respectively. Background histograms and noise model fit with and without artifacts for the knee and spine coils are shown in Figure 3.2 and 3.3, respectively.

Table 3.6: Comparison between noise estimation obtained from the background ROI standard deviation and the noise determined by the noise model fit.

Noise estimation from background SD Noise determined by the fit

Without With Without With % Difference % Difference artifacts artifacts artifacts artifacts Knee 11.53 13.56 17.61 11.44 11.75 2.71 coil Spine 6.77 8.05 18.91 6.30 6.40 1.59 coil

48

Artifact signal Frequency

Signal Intensity

Frequency

Signal Intensity

Figure 3.2: Background histogram for knee coil with artifacts (top) and without artifacts (bottom). The open circles represent the noise signal and solid line shows the model fit. Parameter b represents the noise estimate from the fit.

49

Artifact signal Frequency

Signal Intensity

Frequency

Signal Intensity

Figure 3.3: Background histogram for spine coil with artifacts (top) and without artifacts (bottom). The open circles represent the noise signal and solid line shows the model fit. Parameter b represents the noise estimate from the fit.

50

Table 3.7 shows the effects of the presence of artifacts in the background ROI on the measured SNR using the single image method and the automated SNR method. The reduction in the SNR value based on the single image method in the presence of artifacts is 14.96% and

15.95% for the knee coil and spine coil, respectively. Based on the automated method, the reduction in the measured SNR due to the presence of artifacts is 2.61% and 1.49% for the knee coil and the spine coil, respectively.

Table 3.7: SNR based on SNR single and SNR auto in presence and absence of background artifacts.

SNR based on single image method SNR based on automated method Without With Without With % Difference % Difference artifacts artifacts artifacts artifacts Knee 106.73 90.76 -14.96 105.41 102.66 -2.61 coil Spine 75.79 63.70 -15.95 81.93 80.71 -1.49 coil

51 Chapter Four

Discussion

The proposed method for measuring SNR is fully automated and simple to operate; the user only needs to open the image and the macro file (script) on ImageJ software, execute “Run

Macro” from the tool bar and confirm the selected threshold value. The time a medical physicist spent on analyzing an image and trying to reproduce the exact size and locations of the ROIs from previous tests can be significant. In contrast, the automated SNR measurement is obtained in a few seconds. Background signal truncation was eliminated from the histogram used for noise determination by using linear regression to determine the y-intercept and equating the number pixels with zero count to the value of the y-intercept. Background signal smoothing was incorporated in the automated method since it was found to improve the consistency of the measurements. This is especially true for the shoulder coil. During the early work in developing the program, the SNR measurements for this particular coils were inconsistent from one scan to another. Applying the five-point smooth was shown to improve the consistency of the automated method with insignificant effect on the SNR values. Therefore, smoothing was implemented in the software. Figure 4.1 shows background histogram for shoulder coil scan before and after signal smooth.

52

Frequency

Signal Intensity

Frequency

Signal Intensity

Figure 4.1: background noise histogram for shoulder coil before smooth (top) and after smooth (bottom). Noise determined by the fit for non-smoothed and smoothed histogram are 17.53 and 17.54, respectively.

53 Accuracy of the automated method is demonstrated by comparing the SNR values obtained from the automated method with that obtained by the single and dual image methods described in the ACR manual. Averaged over all phantom measurements, the automated measurements shows a good agreement with the single image method. The deviations in the measurements from the single method were found to be 1.67±6.91%. In term of the dual image method, the deviations in the measurements were 7.88±8.45%. The dual image method was found to be vulnerable to artifacts in the difference image which increase the standard deviation and results in underestimation of SNR (Figure 4.2). These artifacts arise due to temporal instability of the machine which result in miss-registration of the raw data from one scan relative to the other and/or non-cancellation of systemic artifacts (De Wilde, Lunt, & Straughan, 1997;

Sijbers et al., 1998).

Figure 4.2: difference image artifacts due to temporal instability in MRI data acquisition

for breast (left) and spine (right) phantom scan.

54

Consistency of the automated SNR measurement was assessed with repeated phantom scans with and without repositioning of the phantom. The variation in the SNR measurements without repositioning of the phantom attributed only to the methodology of the image analysis is reported as intra-session %CV. The variation in the measurement with repositioning of the phantom is reported as inter-session %CV which takes into account the potential variation of phantom set up and possible change in the scanner performance. Considered together, the results show that the automated method has a higher level of reproducibility compared to the manual methods ( SNR single and SNR dual).

The impact of minor background artifacts on the noise estimation obtained by the automated method was investigated by intentionally including structural artifacts in the background ROI and compared to the effect that these artifacts have on the SNR obtained with the single-image method. The results show that the automated SNR method is less sensitive to the presence of artifacts compared to the single image method. Unlike the single image method which determines noise from the background ROI standard deviation, the noise in the automated method is determined by fitting the background signal to a noise model making it relatively insensitive to minor artifacts.

For a single channel coil, the histogram of the background noise shows asymmetrical intensity distribution as shown in Figure 4.3. The noise distribution in the background region shows a good fit to Rayleigh distribution function. For multi-channel coils, background noise distribution is more symmetrical than that for single channel coil (Figure 4.4). The background noise distribution for multi-channel coils fits well with central chi distribution function. These

55 observations show that the background noise distributions in magnitude MR images are in agreement with the noise models discussed in section 1.3.2.

Background Noise Histogram

1200 1CH Body Coil 1000

800

600

400

200

0 0 5 10 15 20 25 30 35 40 45

Figure 4.3: Background noise distribution for single channel coil. The solid line shows Rayleigh distribution based on the noise signal.

Background Noise Histogram 1800 1600 3CH Spine Coil 1400 1200 1000 800 600 400 200 0 0 5 9 13 17 21 25 29 33 39 43

Figure 4.4: Background noise distribution for three-channel coil. The solid line shows central chi distribution based on the noise signal

56 Chapter 5 Conclusions

 An automated method for SNR analysis using model-based noise determination was

developed utilizing the freely available ImageJ software.

 The SNRauto demonstrated a higher level of reproducibility than the traditional single- and

dual-image methods described in the ACR Manual

 The SNRauto results have good agreement with those obtained by the traditional single-

and dual-image methods

 The noise model fits well with the background noise histogram for a variety of coil types

and channel numbers.

 The SNRauto was proven to be relatively insensitive to the presence of minor artifacts in

background region

 The developed program is fully automated, user friendly, time-efficient and can be a

valuable tool to medical physicists who routinely perform MRI annual QC testing.

57 References

American Association of Physicists in Medicine. AAPM Report No. 100: Acceptance Testing and Quality

Assurance Procedures for Magnetic Resonance Imaging Facilities. College Park, MD: AAPM;2010.

American College of Radiology (ACR). MRI Quality Control Manual 2015.

Aja-Fernandez, S., & Tristan-Vega, A. (2012). Influence of noise correlation in multiple-coil statistical models with sum of squares reconstruction. Magn Reson Med, 67(2), 580-585. doi:10.1002/mrm.23020

Bourel, P., Gibon, D., Coste, E., Daanen, V., & Rousseau, J. (1999). Automatic quality assessment protocol

for MRI equipment. Med Phys, 26(12), 2693-2700. doi:10.1118/1.598809

Bushberg, J. T. (2012). The essential physics of medical imaging: Philadelphia : Wolters Kluwer

Health/Lippincott Williams & Wilkins, c2012. 3rd ed.

Constantinides, C. D., Atalar, E., & McVeigh, E. R. (1997). Signal-to-noise measurements in magnitude

images from NMR phased arrays. Magnetic Resonance in Medicine, 38(5), 852-857.

doi:10.1002/mrm.1910380524

Covell, M. M., Hearshen, D. O., Carson, P. L., Chenevert, T. P., Shreve, P., Aisen, A. M., . . . Martel, W.

(1986). Automated analysis of multiple performance characteristics in magnetic resonance

imaging systems. Med Phys, 13(6), 815-823. doi:10.1118/1.595804

Davids, M., Zollner, F. G., Ruttorf, M., Nees, F., Flor, H., Schumann, G., & Schad, L. R. (2014). Fully-

automated quality assurance in multi-center studies using MRI phantom measurements. Magn

Reson Imaging, 32(6), 771-780. doi:10.1016/j.mri.2014.01.017

De Wilde, J. P., Lunt, J. A., & Straughan, K. (1997). Information in magnetic resonance images: evaluation

of signal, noise and contrast. Med Biol Eng Comput, 35(3), 259-265.

58 Dietrich, O., Raya, J. G., Reeder, S. B., Reiser, M. F., & Schoenberg, S. O. (2007). Measurement of signal-

to-noise ratios in MR images: influence of multichannel coils, parallel imaging, and

reconstruction filters. J Magn Reson Imaging, 26(2), 375-385. doi:10.1002/jmri.20969

Edelstein, W. A., Bottomley, P. A., & Pfeifer, L. M. (1984). A signal‐to‐noise calibration procedure for

NMR imaging systems. Medical Physics, 11(2), 180-185.

doi:doi:http://dx.doi.org/10.1118/1.595484

Firbank, M. J., Coulthard, A., Harrison, R. M., & Williams, E. D. (1999). A comparison of two methods for

measuring the signal to noise ratio on MR images. Phys Med Biol, 44(12), N261-264.

Glasbey, C. A. (1993). An Analysis of Histogram-Based Thresholding Algorithms. CVGIP: Graphical Models

and Image Processing, 55(6), 532-537. doi:http://dx.doi.org/10.1006/cgip.1993.1040

Gudbjartsson, H., & Patz, S. (1995). THE RICIAN DISTRIBUTION OF NOISY MRI DATA. Magnetic Resonance

in Medicine, 34(6), 910-914. doi:10.1002/mrm.1910340618

Henkelman, R. M. (1985). MEASUREMENT OF SIGNAL INTENSITIES IN THE PRESENCE OF NOISE IN MR

IMAGES. Medical Physics, 12(2), 232-233. doi:10.1118/1.595711

Hyde, R. J., Ellis, J. H., Gardner, E. A., Zhang, Y., & Carson, P. L. (1994). MRI scanner variability studies

using a semi-automated analysis system. Magn Reson Imaging, 12(7), 1089-1097.

Kaufman, L., Kramer, D. M., Crooks, L. E., & Ortendahl, D. A. (1989). MEASURING SIGNAL-TO-NOISE

RATIOS IN MR IMAGING. Radiology, 173(1), 265-267.

Mark, B., Richard, S., & Thomas, K. N. (2004). MRI: Basic Principles and Applications, 3rd edition. Medical

Physics, 31(1), 170.

Murphy, B. W., Carson, P. L., Ellis, J. H., Zhang, Y. T., Hyde, R. J., & Chenevert, T. L. (1993). Signal-to-noise

measures for magnetic resonance imagers. Magn Reson Imaging, 11(3), 425-428.

O'Haver, T. (1997). A Pragmatic Introduction to Signal Processing.

59 Redpath, T. W. (1998). Signal-to-noise ratio in MRI. Br J Radiol, 71(847), 704-707.

doi:10.1259/bjr.71.847.9771379

Russ, J. C. (1995). The image processing handbook (2nd ed.). Boca Raton: CRC Press.

Sahoo, P. K., Soltani, S., & Wong, A. K. C. (1988). A survey of thresholding techniques. Computer Vision,

Graphics, and Image Processing, 41(2), 233-260. doi:http://dx.doi.org/10.1016/0734-

189X(88)90022-9

Schneider, C. A., Rasband, W. S., & Eliceiri, K. W. (2012). NIH Image to ImageJ: 25 years of image

analysis. Nat Methods, 9(7), 671-675.

Sharma, N., & Aggarwal, L. M. (2010). Automated medical image segmentation techniques. Journal of

Medical Physics / Association of Medical Physicists of India, 35(1), 3-14. doi:10.4103/0971-

6203.58777

Sijbers, J., den Dekker, A. J., Van Audekerke, J., Verhoye, M., & Van Dyck, D. (1998). Estimation of the

noise in magnitude MR images. Magn Reson Imaging, 16(1), 87-90.

Westbrook, C., Roth, C. K., & Talbot, J. (2011). MRI in practice: Chichester, West Sussex ; Malden, Mass. :

Wiley-Blackwell, c2011. 4th ed.

60 Appendix A

Phantom Set Up

Brain phantom Body phantom

Spine phantom Knee phantom

Figure A-1: Photographs show reference position for phantom set up

61 Appendix B

ImageJ Macro File

Phantom segmentation using a histogram-based threshold technique getDimensions(width,height,chan,slices,frames); getStatistics(im_area,im_mean,im_min,im_max); im_id=getImageID(); getHistogram(bin,count,256); valleys=Array.findMinima(count,50); peaks=Array.findMaxima(count,50); val=newArray(valleys.length); peak=newArray(peaks.length); for (i=0; i

Array.sort(val);

Array.sort(peak); for (i=0; i

}

} for (i=0; i

62 if (val[i]>pk1 && val[i]

} setThreshold(thresh,im_max,"black & white");

Dialog.create("Thresholding");

Dialog.addNumber("Auto-threshold set to " + thresh + ". Adjust manually if needed", thresh);

Dialog.show(); newthresh=Dialog.getNumber(); if (newthresh!=thresh) setThreshold(newthresh,im_max,"black & white");

Defining signal ROI as an area covering 80% of the phantom and measuring the mean signal run("Create Selection"); getStatistics(area); getSelectionBounds(x,y,roi_w,roi_h); area_eighty=area*0.8; while (area>= area_eighty) { getStatistics(area); run("Enlarge...", "enlarge=-1");

} getStatistics(area,mean,min,max,std);

63 Defining the background ROI in the frequency encode direction and extracting the signal distribution pe=getInfo("0018,1312"); if (startsWith(pe," ") == 1) {

pe=substring(pe,1,4);

} if (pe == "COL") { makeRectangle(x-round(width*0.11),0,roi_w+(round(width*0.11)*2),height);

} else { makeRectangle(0,y-round(height*0.11),width,roi_h+(round(height*0.11)*2));

} run("Make Inverse"); getStatistics(bkg_area,bkg_mean,bkg_min,bkg_max,bkg_std);

Eliminating signal truncation from background histogram using linear regression approach getHistogram(bin,count,bkg_max);

Xi=newArray(bin[1],bin[2],bin[3]);

Yi=newArray(count[1],count[2],count[3]); equation=" y = a+(b*x)";

Fit.doFit(equation,Xi,Yi);

Yintercept=round(Fit.p(0)); if (Yintercept < 0) Yintercept=0;

64 count[0]=Yintercept;

Histogram signal smooth using five-point moving average technique count_5ps=newArray(count.length); for (i=2; i

} count_5ps[0] = (count[0] + count[1])/2; count_5ps[1] = (count[0] + count[1] + count[2])/3;

Finding the number of channels that produce the optimum fit of the noise model to the background noise distribution rsquare_5ps=newArray(8); sigma_5ps=newArray(8); for (chan=1; chan<=8; chan++) { fact=1; for (i=1; i

} fitfunc="y=a*exp(-(x*x)/2/(b*b))*pow(x,2*" + chan + "-1)*((2/" + fact + ")/pow(b*sqrt(2),2*" + chan + "))"; initial=newArray(500.00,5.00);

65

Fit.doFit(fitfunc, bin, count_5ps, initial); rsquare_5ps[chan-1]=Fit.rSquared; sigma_5ps[chan-1]=Fit.p(1);

} rank_r2=Array.rankPositions(rsquare_5ps); chan=rank_r2[7]+1; fact=1; for (i=1; i

}

Fitting the background signal to the noise model and determining the noise from the optimum fit fitfunc="y=a*exp(-(x*x)/2/(b*b))*pow(x,2*" + chan + "-1)*((2/" + fact + ")/pow(b*sqrt(2),2*" + chan + "))"; initial=newArray(500.00,5.00);

Fit.doFit(fitfunc, bin, count_5ps, initial);

Fit.plot;

Printing SNR report including acquisition parameters print ("Acquisition Info:"); selectImage(im_id);

66 tags=newArray("0008,103E","0008,0022","0018,0080","0018,0081","0018,0050","0018,0083","

0018,1250","0018,0095","0018,1310"); names = newArray("Series description:","Acquisition date: ","TR: ","TE: ","Slice thickness:

","NEX: ","Coil name: ","Pixel bandwidth:","Matrix size: "); for (i=0; i

} print("PE: " + pe); print("Optimal fit for channel: " + chan); print("mean signal 80% ROI: " + mean); print("noise: " + sigma_5ps[rank_r2[7]]); print("R^2: " + rsquare_5ps[rank_r2[7]]);

SNR=(mean/sigma_5ps[rank_r2[7]]); print("SNR:" + SNR);

67