Schulich School of Medicine & Dentistry - Western …...QUALITY ASSURANCE OF MAGNETIC RESONANCE IMAGING FOR ADAPTIVE RADIOTHERAPY: PRELIMINARY INVESTIGATIONS Chemical Shifts The examples

QUALITY ASSURANCE OF MAGNETIC RESONANCE

IMAGING FOR ADAPTIVE RADIOTHERAPY:

PRELIMINARY INVESTIGATIONS

TREVOR THANG1

Supervisors: Dr. Eugene Wong2, Dr. Rob Bartha1 Department of Medical Biophysics

1, Department of Physics

2 Western University

2 | QUALITY ASSURANCE OF MAGNETIC RESONANCE IMAGING FOR ADAPTIVE RADIOTHERAPY: PRELIMINARY INVESTIGATIONS

INTRODUCTION

Cancer is one of the leading causes of death in Canada. It is an endogenous disease which

arises from the spontaneous mutation of normal tissue cells causing them to divide rapidly.

About 40% of Canadians will develop cancer in their lifetime and over half of them will die from

it. [1] Thus, cancer detection and treatment research has become very prevalent in today’s

society and is needed to help fight off this disease. One technique used to treat cancer is the use

of Radiation Therapy. The protocol for radiotherapy is first acquiring a Computed Tomography

(CT) scan of the tumor area and then creating a treatment plan which irradiates the tumor.

Radiation can come in the form of x-rays or gamma rays, and the goal is to have these ionizing

rays damage and destroy the DNA of the tumor cells, to prevent them from multiplying further.

However, radiation cannot be perfectly targeted so some healthy cells are also irradiated in the

process. Therefore, in order to avoid a lethal dose of radiation to healthy tissue, the process is

spread out over a few weeks. [1]

The long length of treatment allows for many variables to change throughout the

treatment process. These factors include: patient position, patient weight, organ movement,

tumor movement and tumor aggressiveness. Currently, once a treatment plan has been created by

medical physicists and oncologists, the plan rarely get revised. For example, if the patient loses a

lot of weight (a side effect of chemotherapy), instead of changing the dose to account for the

weight loss, an entirely new treatment plan is create; increasing costs, wasting time and

resources. If the tumor moves slightly to the left, the patient is moved slightly to the right in

order to compensate. This is the established norm which is designed to maximize patient care

and hopefully extend the life of the patient.


One key element missing from the radiation therapy is functional information. Currently,

treatment plans only use anatomical and x-ray attenuation data from the CT image. Functional

imaging could give insight towards the aggressiveness of certain areas of the tumor, as well as

potentially allow for the detection of smaller tumors that can’t be seen using traditional CT

imaging. Also, this data can be tracked throughout the treatment process. Any changes seen can

be reflected in the treatment plan by an appropriate adaption which best treats the immediate

needs of the patient. However, one obstacle that all imaging scientist must always consider is

whether the changes seen on the image are true biological changes or a result of inconsistent

imaging environments.

Of the many forms of functional imaging, the one being explored is Magnetic Resonance

Imaging (MRI), specifically, Magnetic Resonance Spectroscopy (MRS). MRS can be used to

detect in vivo metabolites, some of which may be flags for the aggressiveness of cancerous cells.

The drawback to MRS is how many more variables the technology introduces. The biggest factor

and the factor to be explored is the homogeneity of the main magnetic field (B0).

Furthermore, MRS data requires specialized programs to process and display them

properly. Thus, it would be ideal to avoid actually processing and analyzing the MRS before first

determining whether or not it is ‘good’ data. The idea proposed is to use more conventional MRI

data as surrogates for the quality of MRS data. Whether this can be done and how it can be done

will be explored in this experiment.

The overall purpose of the project is to calculate quality assurance metrics which can

used as thresholds which govern the validity of the imaging data. This experiment will contribute

to this project by determining a surrogate metric which can flag the presence of an


inhomogeneous magnetic field (B0), thus giving insight towards the accuracy of the Magnetic

Resonance Spectroscopy data.

THEORY

Magnetic Resonance Imaging (MRI), involves nuclear resonance within a strong

magnetic field. The main magnetic field (B0) generated by the MRI machine can range from

1.5T – 7T. This magnetic field is typically generated by a super-cooled solenoid and by

convention, the field generated is pointing in the ẑ direction of a Cartesian plane.

Magnetic Dipole Physics

In order to understand Magnetic Resonance (MR) physics, it is important to understand how a

singular dipole exists in a magnetic field, and thus, this report will explain the physics of one

dipole in a magnet. Though samples contain multiple dipoles, their effects will not be explained

as it does not facilitate further understanding to the report.

MR data is acquired by taking advantage of the magnetic dipole of certain molecules,

mainly 1H,

31P, and

13C. This magnetic dipole (µ) is produced by electrons orbiting the atomic

nucleus. (Figure 1) [2] When the magnetic field (B0) is turned on, the atomic dipole within the

machine begins to align with the magnetic field. This is due to the fact that this is the most

energetically favorable position for the dipoles to exist. (Figure 2)

Figure 1: Atomic Magnetic Dipole created by Orbiting Electron

http://fr.wikipedia.org/wiki/%E1%BA%90


Figure 2: Magnetic Dipoles in a Sample

Left: No B0 Right: Large B0

Once the dipole is aligned with the magnetic field, the MRI machine uses radiofrequency

(RF) pulses to excite the dipole into a higher energy state such that it no longer aligns with the

magnetic field but instead points at some angle away from B0. (Figure 3) The most common RF

pulse is a 90° flip angle pulse which rotates the dipole 90° or into the xy plane, where the

magnetic field is defined as the direction of ẑ.

Based on magnetostatics, the

magnetic dipole (µ) will begin to precess

about the z-axis because of a torque created

by the magnetic field. This force and

direction of this precession is defined by

Equation 1.

Figure 3: RF Pulse Rotating Magnetic Dipole (µ)

B0

http://fr.wikipedia.org/wiki/%E1%BA%90


The frequency at which a dipole precesses (Larmor Frequency) is one of the most

fundamental principles of MRI. The Larmor Frequency is dependent on each dipole’s (1H,

31P,

and 13

C) gyromagnetic ratio ( ) which relates the precession frequency and the magnetic field.

The gyromagnetic ratio of 1H is 267.5 MHz/T.

Torque of a Magnetic Dipole in a Magnetic Field

Equation 1

is the torque vector on the dipole

is the magnetic dipole vector

is the magnetic field vector

Larmor Frequency

Equation 2

is the angular frequency (rads/sec)

is the precession frequency (cycles/sec)

is the gyromagnetic ratio

is the magnetic field strength

The precession about the z-axis however does not remain in the xy plane. As the dipole

emits an electromagnetic signal, there is a loss of energy. As a result,, the magnetic dipole cannot

remain in this excited state and thus begins to tilt back towards the main magnetic field. As it

tilts back, there is a recovery of longitudinal magnetization and a loss of transverse

magnetization. The rates of longitudinal recovery and transverse decay can be expressed using

the exponential time constants T1 and T2 respectively.

Summary: After a RF pulse (90° flip angle pulse), the magnetic dipole is excited into the xy

plane and begins to precess at the Larmor frequency as defined by Equation 1 and 2. As the

dipole begins to lose its energy, it must return to its ground state (aligned with the magnetic

field). The rate at which the loss of magnetization in the transverse plane (xy plane) and the gain


of magnetization in the longitudinal direction (z) can be expressed as the exponential time

constants T2 and T1 respectively.

Magnetic Resonance Spatial Imaging [3]

Magnetic Resonance Imaging is used to measure a variety of variables concerning

magnetic dipoles. Common variables are T1 and T2 values and atomic diffusion. However, these

signals from the sample have to be labeled in order to create a three dimensional image and this

is done through the use of magnetic gradients. These gradients along the x, y and z axis are used

to encode spatial data into the spinning dipole by change the magnetic field strength along any

axis.

Slice Encoding (Z Coordinate)

A magnetic gradient is applied in the direction. This gradient causes slight variations in

the magnetic field along the z axis and thus, there is a slight energy difference between the

ground and excited dipole states. Thus, when a 90° flip angle RF pulse, with the chosen energy

is applied to the sample, only the dipoles with that exact energy gap (between ground and

excited) will precess and give off signal. As a result, any signal picked up from the sample must

have been emitted from the known xy plane. It is important to note that the magnetic field is

always pointing in the z direction; gradients simply change the magnitude of the magnetic

vector.

Phase Encoding (Y Coordinate)

A magnetic gradient is applied along the direction. The slight changes in magnetic field

affect the precession frequency of the dipoles as explained by Equation 2. This gradient is only

applied for a short period of time so that the dipoles are no longer in phase with one another;

instead, only dipoles in the same y co-ordinate will have the same phase.


Frequency Encoding (X Coordinate)

The final magnetic gradient is applied along the x direction. This causes the Larmor

frequency to change and thus some dipoles will rotate faster than others. When this final gradient

is turned on, the signal is acquired thus allowing the frequencies to be encoded.

Summary: In order to encode spatial information, MRI machines use 3 magnetic gradient

encode a three dimensional Cartesian coordinate into the magnetic dipoles. The z coordinate is

selected with the use of a specific RF pulse which only excites one slice of the sample. The y

coordinate is encoded in the dipole phase which resulted from a temporary magnetic gradient,

dephasing the dipoles. Finally, the x coordinate is encoded in the dipole frequencies in the

presence of a third magnetic field. All of this information is summarized by Figure 4.

Figure 4: Magnetic Resonance Imaging and Spatial Encoding


Chemical Shifts

The examples and discussion used throughout this section will pertain to using 1H as the dipole.

However, the basic concepts remain the same for any dipole.

Magnetic Resonance Spectroscopy (MRS) is a technique used to gather metabolic data

in-vivo from a sample. It can detect protons within slightly different chemical environments and

thus protons belonging to specific molecules can be identified and quantified.

Typically, magnetic dipoles do not exist by themselves; instead, they are bound to a

molecule. When bound to a molecule, the effects of neighboring atoms and their electrons are

especially influential on the dipole and its magnetic environment. Electrons can partially shield

nuclei from the magnetic field thus changing the ‘effective’ magnetic field felt by the dipole.

However, this effect is very minute: approximately 0.1% of the B0. Though small, this change in

magnetic field is what causes a slight change in Larmor Frequency which is the key to

differentiating nuclei from one another. [2]

This ‘slight change’ in frequency can be quantified and must be experimentally

determined. This change in frequency is called the chemical shift and is defined by Equation 3.

Chemical Shifts

Equation 3

represents the chemical shift (ppm)

represents the change in frequency due to altered chemical environment (Hz)

represents the frequency of the reference molecule (Hz)

(for 1H, the reference molecule is TMS, trimethylsilane)

NOTE: The chemical shift values are independent of the main magnetic field strength.


For example, examine the molecule, choline below. (Figure 5)

Figure 5: Choline with Highlighted Hydrogen Atoms

All hydrogen atoms colored in with the same color are chemically identical due to identical

bonding sequences. Thus, it would be expected that the signal received from the blue protons

would by nine times the signal received from the green protons. [2] The chemical shifts for each

set of protons have been determined by experimentally, the most important chemical shift is the

one for the blue protons. This is because there is significantly more signal available and thus, is

more noticeable on the trace. (Figure 6) The chemical shift for the blue protons is approximately

3.24ppm. [4]

Figure 6: Data from a Prostate Cancer Patient illustrating the Choline Peak at 3.2ppm


Summary: Based on the peaks seen on an MRS trace, metabolites can be identified based on the

frequency shifts due to their chemical environments. These shifts are quantified as chemical

shift.

METHODS

In order to generate thresholds, it is important to understand how the data is currently

being acquired and the condition/accuracy of the images taken. From London’s Cancer Institutes

of Health Research (CIHR), multiple types of MR data (T2w, DW-EPI) were gathered from

prostate cancer patients who were imaged just prior to their prostatectomy. These images were

acquired at Robart’s Research Institute using a 3T General Electric (GE) MRI Machine. Of the

many patients data files (~ 45), only a small subset (11) were identified to have had MRS data

along with the standard MR images.

Two types of images were identified to have the largest variability in accuracy: Diffusion

Weight Echo Planar Imaging (DW-EPI) and Magnetic Resonance Spectroscopy (MRS). It was

suspected that the two resulted in ‘poor’ data because of inhomogeneous magnetic fields as

supported by the MR Physics described in the Theory section of this report.

MRS data is deemed poor if the peaks are not clearly resolved. This can result from

having thick peaks that have a large Full Width at Half Max (FWHM) (Figure 7). Large FWHM

can arise due to many variations in the magnetic field. The peaks blur together and thus, specific

metabolites cannot be differentiated from one another.


Figure 7: Large FWHM & Blurring of Peaks 1 & 2

DW-EPI data is deemed poor when here is warping of the image. This is a result of poor

spatial encoding. As mentioned previously, the spatial encoding is coded with the use of

magnetic gradients. If the magnetic field is non-uniform, multiple additional gradients may exist

within the machine which the computer processes unknowingly. The result is a distorted image,

such as Figure 8 below.

Figure 8: Large Deformation in DW-EPI

Since both imaging modalities (MRS and DW-EPI) are theoretically susceptible to an

inhomogeneous magnetic field, it is hypothesized that the quality of the two may be correlated.


The quality of the images can be quantified using the Full Width at Half Max (FWHM) for MRS

and Volumetric Distortion for DW-EPI.

Gathering the FWHM – Water and Lipid

The MRS data gathered from the MRI is imported into a computer as a P-File, a specially

encoded data format which GE uses to protect their data. Using a program developed by Dr. Rob

Bartha called fitMAN, the P-File is converted in a more appropriate format which fitMAN is

able to open and display. A sample raw data is presented in Figure 9. A noise filter is then

applied in order to reduce the noise as shown in Figure 10.

The largest peak is from water (4.7ppm) within the prostate. The FWHM of this peak is

acquired. Afterwards, in order to gather information about smaller peaks, such as the lipid peak,

the water peak must be removed from the spectrum using another filtering tool. (Figure 11)

Finally, the FWHM of the Lipid peak (1.5ppm) can also be acquired.

Figure 9:

Raw MRS data from Prostate

Figure 10:

Noise Filtered MRS

Water FWHM

Figure 11:

Water and Noise Filtered MRS data

Lipid FWHM

Quantifying the Magnetic Distortion

There are many ways to quantify the amount of distortion within the image but the

method used in this experiment is a volumetric percent change. Using the Cancer Treatment


Planning System, Pinnacle, manual contours of the prostate were made in two sets of MR

images: DW-EPI and T2 Weighted – Fast Spin Echo (T2w-FSE) (Figure 12). Unlike DW-EPI

which is susceptible to an inhomogeneous magnetic field, T2w-FSE is not due to a special pulse

sequence known as a 180° Refocusing Pulse. Since the T2w-FSE volume is closest to the

“truth”, it will be used as the gold standard which the DW-EPI will be compared with. The

volumetric percent change was calculated using Equation 4.

Figure 12: Manual Contours on Pinnacle of DW-EPI (left) and T2w-FSE (right)

Volumetric Percent Change

Equation 4

represents the volumetric percent change

represents the T2w-FSE Volume of the Prostate

represents the DW-EPI Volume of the Prostate

The Statistics

After completing these important appropriate measurements, statistical analysis was

performed to determine whether or not a correlation exists. Also, based on the resulting trends, a

suitable threshold was determined.


RESULTS

The first correlation was done with the FWHM of the water peak and the Volumetric

Distortion. As the water peak is typically the largest peak, it is a good place to start. The

correlation is shown below in Figure 13.

The second largest peak, lipid peak was also analyzed. This was done for consistency to

ensure that the FWHM dependency was not associated with certain metabolites. The results of

the lipid correlation are shown below in Figure 14.

R² = 0.82

0

5

10

15

20

25

0 5 10 15 20

Vo

lum

etri

c P

erce

nt

Ch

ang

e (%

)

FWHM of Water Peak (Hz)

Volumetric Distortion as a Surrogate for MRS Quality - Water

%Δ = 1.03 ∙ FWHM - 1.13

Figure 13: Correlating FWHM of the Suppressed Water Peak with the Volumetric Distortion

Plotting FWHM of Suppressed Water Peak vs. Volumetric Percent Change shows a positive

correlation with an R2 value of 0.83. ( N=11) It is important to note that the x-intercept is not

0. This is due to MR Physics which even in a perfectly uniform magnetic field, prevents a

infinitely thin peak from existing.


Though the correlation between the 2 variables is slightly weaker (R2 = 0.63), the

correlation is definitely still present. The reason for a weaker correlation is due to an outlier

present (Point A). There are many factors which could have resulted in such a large volumetric

percent change (ie. patient movement). Thus, in order generate a threshold, outliers need to be

ignored. Therefore, Point A was removed from this data set as shown in Figure 15.

R² = 0.63

0

5

10

15

20

25

10 20 30 40 50 60 70

Vo

lum

etri

c P

erce

nt

Ch

ang

e (%

)

FWHM of Lipid Peak (Hz)

Volumetric Distortion as a Surrogate for MRS Quality - Lipid

Figure 14: Correlating FWHM of The Lipid Peak with the Volumetric Distortion

Plotting FWHM of Lipid Peak vs Volumetric Percent Change shows a posistive correlation

with an R2 value of 0.63. ( N=11) One outlier is present amoungst the data.

%Δ = 0.52 ∙ FWHM - 9.9

Point A


This change results in a much stronger correlation with an R2 value of 0.87. However, with only

10 data points, the correlation would be strengthened if the number of patients available were

doubled.

R² = 0.87

0

5

10

15

20

25

10 20 30 40 50 60 70

Volu

met

ric

Per

cent

Chan

ge

(%)

FWHM of Lipid Peak (Hz)

Volumetric Distortion as a Surrogate for MRS Quality

Lipid (Revised)

%Δ = 0.67 ∙ FWHM - 16.19

Figure 15: Correlating FWHM of The Lipid Peak with the Volumetric Distortion - Revised

Plotting FWHM of Lipid Peak vs Volumetric Percent Change shows a posistive correlation

with an R2 value of 0.87. ( N=10)


DISCUSSION

Since there are strong correlations between MRS FWHM and DW-EPI distortions,

quality assurance thresholds can be generated. The R2 values for the water peak (0.82) and for

the lipid peak (0.87) suggest that there is likely to be an underlining cause which is damaging

both imaging techniques. It is hypothesized that it may be an inhomogeneous magnetic field, but

this was not proven during this experiment.

Based off of numerous scientific reports, the typical FWHM for a suppressed water peak

should be approximately 8 Hz. [5] Thus, based on the line of best fit in Figure 13, an appropriate

threshold for Volumetric Percent Change would be 7%. Of the 11 patients (2 data points are

identical), 7 were deemed to be acceptable since they were above the threshold. A similar result

was seen for the revised lipid peak data. With a threshold of 7% and the corresponding lipid

FWHM threshold of 35Hz, the same 4 patients were deemed unacceptable.

In regards to omitting the Point A, the goal of this project is to create a set of thresholds

that can be used to quickly check the validity of the MR data. Thus, when generating each

threshold, it is not necessary for each threshold to individually differentiate all the good data

from the bad. It is hopefully, a cumulative effort of all the quality assurance metrics which gives

the best complete picture of the image accuracy. Although, it is expected that even though by our

threshold, Point A would be deemed unacceptable (greater than 7% change), other quality

assurance metrics could help identify it as being good MRS data (lipid FWHM less than 35Hz).

There are many revisions that can be made to improve the results, such as how

volumetric distortion was quantified. In this experiment, a volumetric percent change was

employed but may not reflect a true value for distortion as shown in Figure 16. Alternatives


include Surface Area-to-Volume ratio and Percent Overlap. Correlations for these new metrics

should also be done.

Figure 16: Equal Volumes (0% Percent Change) with Large Distortion

The scale of this project is very large and thus the results presented in this paper are

merely the first of many potential quality assurance metrics. In order to validate this threshold,

Receiver Operator Curve analysis must be performed, more patient data must be gathered to

strengthen the correlation value. Furthermore, this threshold may be replaced in the future as

there are special pulses sequences have been developed that can directly measure the

homogeneity of the magnetic field. These techniques include Phase Difference Method ( [6]

and Bandwidth-Difference ( ) [7] However, at the time of this research, this data was not

being acquired at Robart’s and thus a surrogate had to be used. Whether or not these new types

of data are beneficial is up to further research which must balance the amount of new

information gained with the increased patient scanning time.

CONCLUSION

In this experiment, DW-EP images were used as a surrogate for MRS quality. The reason for this

is due to the hypothesized effect of an inhomogeneous magnetic field on the two data types.

Using data acquired from the London’s CIHR project, images taken at Robart’s were processed

and metrics were calculated to quantify the quality of both the DW-EPI and MRS images.

Volumetric percent change and FWHM metrics were shown to have a strong correlation. An R2


value of 0.82 for the water peak and 0.87 for the lipid peak (0.87) allowed a threshold of 7%

volumetric percent change to be calculated. Of the 11 patients, 4 were deemed to have

unacceptable data. Further studies for this project include alternative quantification of distortion,

analyzing the FWHM of functional metabolites such as citrate and choline, and exploring the

effectiveness of new pulse sequence which can directly measure the magnetic field. As more of

these quality assurance metrics are determined, medical physicist and oncologist will have more

flexibility in their treatment plan. As long as their treatment plan fits within these metrics, the

physician is free to adapt the plan giving more power and meaning to the world of Adaptive

Radiotherapy.

REFERENCES

[1] Canadian Cancer Statistics 2011: Featuring Colorectal Cancer, Canadian Cancer Society.

Accessed: Feb. 2012

[2] Dr. Neil Gelman. MEDBIO 3505F Lecture Notes: Fall 2011. Western University

[3] Functional Magnetic Resonance Imaging. Scott A. Huettel. Sinauer Associates, Inc.

Sunderland, Massachusetts, USA.

[4] MR Spectroscopy – Quick Guide. Siemens Medical.

[5] Prostate cancer metabolite quantification relative to water in 1H-MRSI in vivo at 3 Tesla.

Mclean.

[6]

Magnetic Resonance Imaging Quality Control Manual (American College of Radiology),

Weinreb, 1991

[7]

Routine Testing of Magnetic Field Homogeneity on clinical MRI Systems. Hua-Hsuan

Chen, 2006

Documents

Schulich School of Medicine & Dentistry - Western …...QUALITY ASSURANCE OF MAGNETIC RESONANCE IMAGING FOR ADAPTIVE RADIOTHERAPY: PRELIMINARY INVESTIGATIONS Chemical Shifts The examples