Correction of Partial Volume Effects in Arterial Spin Labeling MRI

By: Tracy Ssali

Supervisors: Dr. Keith St. Lawrence and Udunna Anazodo

Medical Biophysics 3970Z – Six Week Project

April 13th

2012

Introduction

The amount of blood being delivered to brain tissue, also known as brain perfusion, is

indicative of function within a given region. By measuring the amount of perfusion to

each area, it is possible to map out which areas of the brain correspond to various actions.

Using these observations, we can discover how the brain responds to different stimuli. In

addition, we can gain insight on which areas of the brain are under or over stimulated in

some disease states, by comparing the results of healthy subjects and patients.

There are a number of different techniques which can be used to measure perfusion in

the brain. In this experiment, perfusion will be measured using Arterial Spin Labeling

MRI (ASL-MRI). The brain consists of grey matter (GM), white matter (WM) and

cerebral spinal fluids (CSF). Since the majority of the diseases studied show irregular

flow in grey matter (e.g. Alzheimer’s and Parkinson’s disease), most ASL-MRI studies

are interested in grey matter perfusion [1]. Due to the resolution of ASL imaging, it is

difficult to separate the signals coming from the three types of tissue. To give a better

approximation of the perfusion signal coming from the grey matter tissue, a partial

volume effects (PVE) correction is applied to the images. The objective of this

experiment was to determine the signal to noise (SNR) in whole brain signal before and

after the application of an in-house implementation of the PVE correction.

Theory

Arterial Spin Labeling MRI

Perfusion in the brain can be measured using diffusible tracers such as xenon in

Perfusion CT or gadolinium DTPA in Dynamic Contrast enhanced MRI. The use of these

established techniques often require the administration of radioactive or exogenous

tracers which cannot be used on certain patient populations, and require long clearance

times. Arterial Spin Labeling MRI is a novel technique which uses the magnetization of

water molecules in arterial blood as a tracer to measure tissue perfusion non-invasively.

ASL MRI consists of two experiments. The first experiment creates a control image

while the second experiment creates a tagged image. To create a tagged image, arterial

blood water is magnetically labeled by directing radiofrequency pulses at an area

proximal to the desired imaging region. For perfusion images of the brain, the tag pulses

are applied to vessels in the neck. A delay time is given to allow the labeled blood to

reach the brain. When the labeled arterial water interacts with the magnetic field, the

longitudinal magnetization is affected which in turn affects the signal being produced.

The control image is taken to account for the static magnetization that is produced by the

water molecules already present in the brain. Since we are interested in the change of

flow, the difference of the signal produced from the labeled and the control image is

taken. The difference of the control and the label image is known as the ASL signal

change.

The fractional ASL signal change is proportional to the amount of perfusion within a

tissue. This is expressed as a ratio between the difference of the control and the labeled

signal in the tissue (ΔM), scaled by the fully relaxed tissue signal (M0) i.e. (ΔM/M0). The

images are acquired in quick succession using Echo Planar Imaging (EPI). EPI has the

fastest acquisition of images at the expense of having a lower spatial resolution, hence,

the heterogeneity of the signals in each voxel. The partial volume corrected fractional

signal change can be expressed as:

[a]

( ) ( ) ( )

Where; PGM, PWM, and PCSF represent the probability maps of GM, WM and CSF

respectively.

ΔMGM, ΔMWM and ΔMCSF represent the ASL perfusion weighted signal of the gray

matter, white matter and CSF. M0_GM, M0_WM, M0_CSF represent the fully relaxed EPI

magnetization in gray matter, white matter and CSF. The perfusion weighted contribution

Figure 1: Schematic of how the ASL image is created. The first 3 images represent an imaged voxel.

The difference of the control and the label image is taken to get the ASL signal, shown in the third

image. Areas where the signal changes between the control and the label are highlighted in red. The

rightmost image is a CBF image. It is proportional to the signals produced in the ASL image. [2]

from CSF is set to zero since the labeled and the control magnetizations in CSF are

essentially the same [1].

The SNR can be estimated by dividing the mean ASL signal by the standard deviation

or variance of the signal. Since the primary focus is on grey matter, the SNR is expressed

as:

[b]

Where; µMGM is the mean ASL signal and σGM is the standard deviation of the grey

matter signal. In an image, the mean signal is represented by the mean value of all the

voxels at a particular point. The standard deviation is the square root of the variance in

these voxels.

Partial Volume Effects

The intensity of signals acquired from ASL MRI are inherently low. Consequently,

multiple tag and control pairs are collected and averaged to increase the SNR. In the case

of where the brain is atrophic, the resolution of ASL-EPI (which is approximately

3x3x3mm per voxel) is not small enough to distinguish the different tissue types.

Additionally, the problem of point spread blurring is also often run into due to the rapid

image acquisition. As a result of these two tendencies, the contributions from GM WM

and CSF are combined. Since perfusion in the three types of tissues are not the same, a

calculated difference in the flow between two voxels may be caused by the fact that the

voxels are heterogeneous rather than an actual difference in the flow. This is known as

the partial volume effect.

Prior to quantifying blood perfusion, ASL difference images are usually smoothened

with a Gaussian filter to reduce the amount of noise by decreasing the variance. GM

flow can then be estimated by setting a threshold value such that brain tissues that fall

within the specified threshold value are classified accordingly. Generally, a threshold

value of 0.8 is set for GM matter tissue [1]. All voxels which have values greater than 0.8

are used in the estimation of GM flow. This however, does not work well in brain areas

that have voxels with high heterogeneity as it is prone to signal cross contamination (the

combining of the different signals). By using this thresholding method instead of

applying a true PVE correction, GM signal can be underestimated by up to 24% [2].

Kernel Regression Algorithm

Instead of using the threshold to classify the tissue, a kernel regression algorithm can

be used to account for partial volume effect. For this project, a PVE correction was

implemented with, a kernel regression algorithm outlined by Iris Asllaniet. al [1]. The

regression algorithm estimates the partial signal contribution of each tissue type in the

ASL image based on MRI tissue contrast information from high resolution anatomical

(MPRAGE) MRI image volume. The Kernel regression algorithm estimates the value of

the GM, WM and CSF ASL signal contribution from voxels within the radius of a pre-

defined kernel size. Increasing the kernel size will increase the radius of voxel values

included as nearest neighbor points in the calculation. The regression algorithm uses the

assumption that the GM values (or WM or CSF) are homogeneous over the kernel size.

As a result, the kernel size or k-fliter needs to be chosen precisely. Large kernel sizes

tend to smoothen out the image too much whereas small kernel sizes are sensitive to

noise.

Methods

Image Acquisition

5 Chronic Regional Pain syndrome (CRPS) patients were scanned on a Siemens 3.0T

system. For each subject a high-resolution T1-weighted 3D MPRAGE anatomical image

volume, 8 2D EPI-M0 images, and 64 label/control 2D EPI-ASL image pairs were

acquired.

Image Preprocessing

For each subject, the skull was removed from the raw MPRAGE image volume. Using

SPM8 image analysis software (FIL, UCL, London, UK), the MPRAGE image volume

was segmented into GM, WM and CSF probability maps. The raw EPI images were pre-

processed in SPM8 and in-house code written in MATLAB (The MathWorks, Natick,

MA, USA). To remove motion errors, all the EPI images were aligned to the first

acquired image. Average perfusion-weighted images were generated by time averaging

the EPI-ASL images and taking the difference of the image pairs. Since the spatial

resolution of the ASL MRI is coarser than the anatomical MRI images, the anatomical

MRI images are down sampled using a coregistration algorithm to match the ASL MRI

images.

PVE Correction

The PVE correction algorithm was applied to the motion corrected EPI image time

series of 5 CRPS subjects, to estimate partial ΔM and M0 signal contribution for GM,

WM and CSF. This experiment was carried out for a kernel size of 5 and 9. The SNR was

estimated for ΔM in gray matter using formula [b] and compared to ASL data pre and

post-PVE correction to see whether there is a significant improvement in the signal to

noise after the PVE correction is applied. Using an independent two sample t-test the

results from the SNR calculation pre and post-correction were compared once for kernel

size 5 and again for kernel size 9.

K-filter

The kernel size used in the regression model was adjusted to equal a voxel size of 5, 7,

9, 11 and 15. Using the different kernel sizes, the PVE correction was applied on the ASL

images of an arbitrarily chosen subject. For each kernel size, the SNR was calculated.

Results

Over all, the uncorrected SNR calculated from the data is within the range reported by

the literature. In an experiment conducted by Y.Chen et al, the reported average raw

pCASL SNR was 1.58 [3]. The SNR for Subjects 1 through 5 were 1.27, 1.12, 1.33, 1.52

and 1.40 respectively. This yields an average of 1.33.

PVE correction at k=5 for 5 CRPS patients

Following the PVE correction of the images using a kernel size of 5, there was a

significant decrease in SNR (P<0.05). The signal was consistently reduced by over 80%

for each of the patients. These results are depicted in figure 2.

PVE correction at k=9 for 5 CRPS patients

In the second experiment, the kernel size was changed from 5 to 9. As seen in figure 3,

the SNR after the PV correction yielded inconsistent results for each of the patients. The

SNR of the ASL MRI images increased for subject 5, marginally changed for subjects 1

and 2 and considerably decreased for subjects 3 and 4. The results of the student t-test

indicate that there was not a significant change in the SNR (P<0.05) after the application

of the PVE correction. If the data for subject 5 is removed, there is a significant decrease

in the SNR (P<0.1).

0

0.5

1

1.5

2

Subject 1 Subject 2 Subject 3 Subject 4 Subject 5

Sign

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Complex Regional Pain Syndrome Patient

SNR before and after PV correction k = 5

Uncorrected SNR

PV corrected SNR

Figure 2: Graphical representation of SNR before and after the PV correction was applied

for the 5 CRPS patients using a kernel size of 5. The dotted bars represent the uncorrected

SNR and the line patterned bars represent the PVE corrected SNR.

Kernel size and SNR of Subject 5

In the third experiment the k-filter was set equal to a voxel size of 5, 7, 9, 11, and 15.

The results, shown in figure 4, show that as the kernel size increased, the SNR increased.

The uncorrected SNR remains the same since there was no filters or corrections applied

to it.

0

0.5

1

1.5

2

2.5

3

Subject 1 Subject 2 Subject 3 Subject 4 Subject 5

Sign

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Complex Regional Pain Syndrome Patient

SNR before and after PV correction k = 9

Uncorrected SNR

PV corrected SNR

0

0.5

1

1.5

2

2.5

3

3.5

4

5 7 9 11 15

Sign

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Kernel Size

Kernel Size vs SNR

Uncorrected SNR

PV Corrected SNR

Figure 4: Graphical representation of the change in the SNR as the Kernel size changes. The

dotted bars represent the Uncorrected SNR and the line patterned bars represent the PV

corrected SNR.

Figure 3: Graphical representation of the SNR before and after the PV correction for 5 CPRS

patients using a kernel size of 9. The dotted bars represent the uncorrected SNR and the line

patterned bars represent the PV corrected SNR. The error bars represent the standard error

of the data set.

Discussion

PVE Correction at K=5

The results of the PVE correction experiment yielded unexpected results. Using the

kernel size of 5, it was found that the SNR decreased considerably for each of the

patients.

A possible explanation for this trend is that the ASL MRI images had a low resolution

and were noisy. The kernel algorithm works by reassigning a value to the pixel at the

center based on the pixels surrounding it. If there is a lot of noise in the image, the filter

will corrupt the data by assigning incorrect values to the voxels and possibly amplifying

the variation of the voxels. Since the SNR is the signal divided by the noise, and the noise

is the square root of the variance, an increase in variance will cause the SNR to decrease.

In addition, if there is a substantial amount of noise in the image, the voxels which are

being used in the regression algorithm cannot be considered homogenous. This is one of

the assumptions that are made in using the regression algorithm.

The SNR after the PV correction was so low that using it as an image processing

technique is not beneficial. In this scenario, it may be practical to use the crude

thresholding technique that was mentioned in the theory.

PVE Correction at K=9

In the second experiment, the kernel size was increased to 9 and applied to all 5

subjects to test if a larger kernel size would provide a more accurate estimate the partial

signal contribution. The idea was that increasing the kernel filter will include more voxels

in the algorithm and resultantly minimize the effect of noise.

The results from this investigation varied from subject to subject; some of the SNR’s

increased, while the remaining ones either decreased or marginally changed. In terms of

fitting the data, a k-filter of 9 is more stable. While this was an improvement from the k-

filter of 5, the inconsistency of the results suggests that there is an underlying problem.

One of the possibilities could be that there are bugs within the in-house PVE algorithm

code that need to be investigated. Initially the code was intended to find the SNR voxel

wise for each of the horizontal slices as well as the SNR for the entire brain. After

reviewing the code, it appeared that it was calculating the SNR voxel wise vertically for

each slice. With this in mind, there may have been other issues within the code that need

to be ironed out.

The student t-test of this data yielded insignificant results. This suggests that there is

no difference from the mean signal before the PVE correction for this patient population.

By looking at Figure 4, subject 5 had a very high SNR. This produced a relatively large

increase in the P value which affected its significance.

Kernel Filter and SNR

Since the k-filter dictates the number of pixel elements which were used to determine

the value of the signal, a change in the kernel size had a substantial impact on the SNR.

PVE corrected images which used small kernel sizes had lower SNRs while larger kernel

sizes yielded higher SNRs.

The low SNR could be attributed to the fact that the algorithm is unstable at lower

kernel sizes. Since the algorithm is looking at a smaller radius, the variance within that

area is higher. This especially happens at the edges between the background and the

feature. Smaller kernel sizes tend to have lower SNR, take less time to compute and

produce less smoothened images.

The high SNR of the large kernel sizes can be explained by the larger region of voxels

the algorithm uses. The algorithm works with a larger region and thus makes the entire

image more uniform. After the PVE correction, the images are smoothened. As a result

the SNRs tend to be greatly over estimated. In comparison to the small kernel sizes, the

larger ones take less time to compute.

As previously mentioned, it is important to use a kernel which doesn’t smooth the data

too much or break down as a result of variation due to noise. From analyzing the

experimental data in figures 2, 3 and 4 it is difficult to decide on a kernel size which will

optimize the SNR. A kernel size of 5 tends to result in very low SNRs. A kernel size of 9

yields inconsistent results or a significant decrease in the SNR (when patient subject 5 is

removed). Above a kernel size of 9, the images are smoothed. Further tests are required

to get a better idea of which kernel size would be most suitable.

Conclusion

Based on the results from this experiment it would be difficult to justify the use of the

PVE correction we implemented. In ASL MRI imaging it is common to underestimate

the cerebral blood flow (CBF) as a result of partial volume effects. From the

experimental data collected, the use of this PVE correction at a kernel size of 5, results in

a decreased SNR (P<0.05) which would lead to an underestimation of the CBF. This

could lead to misdiagnosis of both healthy and diseased patients. Using a kernel size of 9

would also lead to detrimental effects because the results were inconsistent across the

patient population. As a result of the variance in the SNRs, there was no significant

change in the SNR (P>0.05). By increasing the kernel sizes, we discovered that the SNR

and the smoothness of the images increase. Resultantly, the kernel size has to be selected

with this in mind.

References

[1] Asllani, Iris, AjnaBorogovac, and Truman R. Brown. "Regression Algorithm

Correcting for Partial Volume Effects in Arterial Spin Labeling MRI." Magnetic

Resonance in Medicine 60.6 (2008): 1362-371.

[2] Asllani, Iris, AjnaBorogovac. "Arterial Spin Labeling (ASL) FMRI: Advantages,

Theoretical Constrains and Experimental Challenges in Neurosciences." International

Journal of Biomedical Imaging 2012 (2011).

[3] Chen, Y., M. Korczykowski, and J. Wang. "Comparison of Reproducibility between

Continuous , Pulsed , and Pseudo-continuous Arterial Spin Labeling." Magnetic

Resonance in Medicine 348.1998 (2008): 2008.

[4] Liu, Thomas T., and Gregory G. Brown. "Measurement of Cerebral Perfusion with

Arterial Spin Labeling: Part 1. Methods." Journal of the International

Neuropsychological Society 13.03 (2007).

[5] Wolf, R., and J. Detre. "Clinical Neuroimaging Using Arterial Spin-Labeled

Perfusion Magnetic Resonance Imaging." Neurotherapeutics 4.3 (2007): 346-59.