Download Quantification of the Cerebral Perfusion with the Arterial Spin

Quantification of the
Cerebral Perfusion with the
Arterial Spin Labelling
3D-MRI method
Guillaume GIBERT
KTH Supervisor : Massimiliano COLARIETI TOSTI
KTH Reviewer : Anna BJÄLLMARK
Siemens Healthcare Reviewer : Josef PFEUFFER
Master of Science Thesis in Medical Engineering
Stockholm 2014
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Abstract
The Arterial Spin Labelling (ASL) method is a Magnetic Resonance technique used to
quantify the cerebral perfusion. It has the big advantage to be non-invasive so doesn’t
need the injection of any contrast agent. But due to a relatively low Signal-to-Noise
Ratio (SNR) of the signal acquired (only approximately 1% of the image intensity), it
has been hampered to be widely used in a clinical setting so far.
The primary objective of this project is to make the method more robust by improving the quality of the images, the SNR, and by reducing the acquisition time. Different
ASL protocols with different sets of parameters have been investigated. The modifications performed on the protocol have been investigated by analyzing images acquired on
healthy volunteers. An optimized protocol leading to a good trade-off between the different aspects of the method, has been suggested. It is characterized by a 3.4×3.4×4.0mm3
with a two-segment acquisition.
A more advanced ASL method implies the acquisition of images at different inversion
times (TI), which is called the mutli-TI method. The influence of the range of TI used in
the method has been explored. An optimized TI range (from 410ms to 3860ms, sampled
every 150ms) has been suggested to make the ASL method as performant as possible.
A numerical model and a fitting algorithm have been used to extract the information
on the perfusion from the images acquired. Different models have been investigated as
well as their influence on the reliability of the results.
Finally, a criterion has been implemented to evaluate the reliability of the results so
that the clinician or the user of the method can figure out how much he can count on
the results provided by the method.
Sammanfattning
Den Arterial Spin Märkning (ASL) metoden är en Magnetic Resonance teknik som
används för att kvantifiera cerebral perfusion. Det har den stora fördelen att vara icke
invasiva så det behöver inte administrering av något kontrastmedel. På grund av ett
relativt lågt signal-to-noise ratio (SNR) av signalen, har man misslyckats med att implementeras kliniskt hittills .
Projekts mål är att göra metoden mer robust genom att förbättra kvaliteten på
bilderna, SNR, och genom att minska anskaffningstiden. Olika ASL-sekvenser med annan
uppsättning parametrar har undersökts. De ändringar som utförs på sekvensen har
validerats genom att analysera bilder som förvärvats på friska frivilliga. En optimerad
sekvens som leder till en god avvägning mellan de olika aspekterna av metoden, har
föreslagits.
ASL-metoden innebär förvärv av bilder vid olika inversion gånger (TI), som kallas
den multi-TI metoden. Inflytandet av intervallet indexen som används i metoden har
undersökts. En optimerad TI sortimentet har föreslagits för att göra ASL metoden
presterande som möjligt.
En numerisk modell och en passande algoritm används för att extrahera information
om perfusionen från bilderna förvärvat. Olika modeller har undersökts, liksom deras
inverkan på tillförlitligheten av resultaten.
Slutligen har ett kriterium genomförts för att utvärdera godhet av resultaten så att
läkaren eller användaren av metoden kan räkna ut hur mycket kan litas på resultaten
från metoden.
Acknowledgements
I would like to thank Siemens Healthcare company and more especially Heiko Meyer
for having offered me the possibility to work on this project. It enabled me to participate,
at a really tiny scale, in the process of improving the MR systems which is an amazing
tool to improve our today’s ability to treat patients and save lives.
I also would like to thank Dr Josef Pfeuffer who welcomed me in the Neuro team,
supervised me and guided me during these six months. By his experience and his perfect
knowledge of the MRI, he helped me to improve my skills in the MR domain, and to constantly work methodically and scientifically. Many thanks to my supervisor and reviewer
from KTH, Massimiliano Colarieti Tosti and Anna Bjällmark, for having supervised and
given me advice throughout the project.
I would like to thank the whole Neuro crew who welcomed me in their working environment. They helped me professionally by answering my questions and sharing their
experience, and personally by making me feel comfortable in their team. And a special
thanks to Martin for the amazing cave experience.
I cannot forget my co-workers Rainer Schneider and Damien Nguyen who I spent the
most time with. They helped me to handle the more difficult days and made the nice
days even nicer by participating in the good atmosphere of the team. We shared really
great moments both at work and out of work.
Finally, I would like to thank my flatmates Nici, Benni and Patrick who made my stay
in Erlangen memorable. Nici’s happiness, Benni’s german lessons and Patrick’s acting
funny moments helped me to fully enjoy my six months in Germany.
Contents
1 Introduction
1.1
7
Késako . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.1.1
Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.1.2
Cerebral perfusion . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.2
Overview of MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.3
State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.1
Measuring perfusion . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.2
Measuring perfusion with ASL . . . . . . . . . . . . . . . . . . . . 20
2 Theory and Methods
2.1
2.2
2.3
22
ASL Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1.1
Continuous ASL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.2
Pulsed ASL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.3
Pseudo-Continuous ASL (PCASL) . . . . . . . . . . . . . . . . . . 25
Quantification of perfusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.1
Quantification correction . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.2
Multi-TI data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Numerical Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.1
Numerical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.2
Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3 Improving the PASL method
3.1
3.2
36
First set of experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.1.1
First protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.1.2
First results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.1.3
First conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.1.4
First discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Protocol Parameter Settings . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4
Table of Contents
3.3
3.4
5
3.2.1
Protocol - Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.2
Results - Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.3
Discussion - Sequence . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2.4
Conclusions - Sequence . . . . . . . . . . . . . . . . . . . . . . . . . 50
Optimization of the range of TI . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.1
Protocol - TI range . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.2
Results - TI range . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.3
Discussion - TI range . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3.4
Conclusions - TI range . . . . . . . . . . . . . . . . . . . . . . . . . 57
Improvement of the Numerical Model . . . . . . . . . . . . . . . . . . . . . 58
3.4.1
Results - Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.2
Discussion - Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.4.3
Conclusions - Model . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4 Evaluation of the reliability of the data
62
4.1
Implementation of a criterion . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2
High-flow Vs Low-flow regions . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5 Ending
69
5.1
Discussion and Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
List of Abbreviations
ASL Arterial Spin Labelling
BAT Bolus Arrival Time
CASL Continuous Arterial Spin Labelling
CSF Cerebro Spinal Fluid
EF EPI Factor
EPI Echo-Planar Imaging
GM Gray Matter
FID Free induction Decay
FOV Field Of View
MRI Magnetic Resonance Imaging
MT Magnetization Transfer
NMR Nuclear Magnetic Resonance
PASL pulsed Arterial Spin Labelling
PCASL pseudo-Continuous Arterial Spin Labelling
PWI Perfusion-Weighted Image
rCBF regional Cerebral Blood Flow
RF Radio Frequency
SNR Signal-to-Noise Ratio
ROI Region Of Interest
TA Acquisition Time
TE Echo Time
TF Turbo Factor
TI Inversion Time
TR Repetition Time
WM White matter
Chapter 1
Introduction
1.1
Késako
Késako is an old word from the south of France which means «What is it about? ».
1.1.1
Objectives
The main objective of this project is to improve the robustness of the Arterial Spin
Labelling method in order to be able to quantify the cerebral perfusion. This main
objective can be divided in several sub-goals which represent a guideline throughout the
project:
• Adjusting the parameters of the sequence: finding a good balance between the
duration of the sequence, the resolution of the image, the signal-to-noise ratio to
name a few.
• Developing a robust fitting processing algorithm: extracting information from the
images acquired with the MR scan, and performing a post processing analysis to
obtain quantified values of the perfusion, as well as other parameters.
• Incorporating and implementing the improved sequence in the MR scan in-line
processing.
• Acquiring images on volunteer subjects to perform tests and to validate the improvements throughout the project, in parallel of the other tasks.
1.1.2
Cerebral perfusion
The term blood perfusion describes the supply of blood to a region of the body. Cerebral
perfusion is defined as the steady-state supply of nutrients and oxygen to the neurons and
glial cells of the brain (brain tissue parenchyma) via the blood flow. Four main arteries
7
1.1. Késako
8
are supplying the blood to the brain: the left and right internal carotid arteries and the
left and right vertebral arteries. The internal carotid arteries provide blood mainly to the
frontal region of the brain whereas the vertebral arteries provide blood to the occipital
regions. The four arteries meet at a junction called the circle of Willis (see figure 1.1.1).
Figure 1.1.1: Illustration of the main arteries in the neck supplying blood to the head
and the brain.
The perfusion is usually measured in milliliters of blood per 100g of brain tissue per
minute. For a healthy patient, an average value of the rCBF is 60 mL/100g/min [2]. As
tissue weighs approximately 1 gram per cm3 , it is also common practice to express this
as 60 ml/100ml/min, or equivalently 0.01 s−1 . This is also equivalent to saying that the
blood in the capillaries replaces approximately 1% of the tissue volume every second.
In this project, the s−1 will be used. However, in the perfusion MR imaging, the term
’perfusion’ includes several other parameters related to the tissue hemodynamic, such as
the regional cerebral blood flow (rCBF), the cerebral blood volume (CBV), and the arterial
transit time (AAT). Throughout this project,unless otherwise stated, the term perfusion
will be used as a synonym of regional cerebral blood flow.
The ability to measure cerebral perfusion is a really powerful tool in the diagnosis
of several pathologies related to abnormal blood flow such as strokes, stenosis, tumors,
dementia, and migraine.[30] The cerebral perfusion measurements provide maps of the
hemodynamic parameters in the brain, and can facilitate the identification of the limits of
lesions. In the case of tumors, the degree of vascularization of the tumor gives information
on its grade. For example, a high perfusion (rCBF) in the tumor’s region means a highlydeveloped tumor. On the contrary, a too low value of the rCBF in a region of the brain
can be due to a stenosis (a narrowing of the vessel lumen). Thus, several pathologies can
KTH University, Guillaume GIBERT
1.2. Overview of MRI
9
be related to either hypo-perfusion or hyper-perfusion.
1.2
Overview of MRI
The Magnetic Resonance Imaging is a medical engineering technique that enables to
acquire 2D and 3D images of the inside of the body with high resolution and contrast. It
enables to investigate the anatomy and the functions of the body of both healthy and sick
patients. The use of this technique has been rapidly growing in the past few years [26].
Its main advantage over Computational Tomography is the absence of ionizing radiation,
which makes it safer for the patients. MRI is also particularly useful for displaying the
soft tissues of the body such as cartilages and ligaments, and organs such as the heart, the
brain and the eyes. Finally, MRI is also really efficient for showing the blood circulation
through several organs and blood vessels, and thus for identifying pathologies related to
abnormal blood flow.
Nuclear magnetic resonance
MRI relies on the principle of the Nuclear Magnetic Resonance, which uses the quantum properties of the atomic nuclei. The hydrogen nuclei are the most abundant in the
human body, that’s why the MRI is based on imaging the single proton of the hydrogen
nucleus. Protons and neutrons possess an intrinsic angular momentum referred to as
spin, and nuclei which consist of an odd total number of protons and neutrons combined
have a net spin. The spin of these nuclei causes them to behave like a tiny magnet which
can interact with other magnetic fields. In a magnetic field B0 produced by a magnet
(the usual value of the external magnetic field is between 1 and 3 Tesla), the nucleus
undergoes a force which tries to align it with the field. But due to its angular momentum,
the spin resists to this alignment, and rotates around the magnetic field. This is called
−
→
−
the precession of the magnetic dipole moment →
µ around B . The precession occurs at
0
the Larmor frequency which is proportional to the external magnetic field: f0
ω0 = 2πf0 = γB0
where γ is the gyromagnetic ratio (for hydrogen, γ = 42.6 MHz/Tesla).
The Bulk Magnetization
According to its magnetic quantum number ml , the nucleus can have two possible
states: the parallel state (ml = 21 ) or anti-parallel state (ml = − 12 ). The sum of all the
KTH University, Guillaume GIBERT
1.2. Overview of MRI
10
microscopic magnetic momenta of the hydrogen protons of a water sample is now con−→
sidered. This sum is called the bulk magnetization and noted M0 . Without an external
−
→
magnetic field, the bulk magnetization is null. In a magnetic field B0 , the spins rotate,
and are more numerous in the parallel state, because its energy level is lower. This results
in a bulk magnetization in the same direction than the magnetic field (figure 1.2.1). The
−→
bulk magnetization M0 is somehow proportional to our MR signal.
Figure 1.2.1: Sum of the precessing anti-parallel spins and parallel spins, resulting in
a bulk magnetization vector in the same direction than the magnetic field. Figure from
[20]
The RF pulse
The equilibrium magnetization M0 is not strong enough to be observed. In order
to measure a signal, the magnetization is perturbed from the equilibrium by applying
another magnetic field B1 during a short period (a Radio Frequency pulse). This field B1
is perpendicular to the field B0 . If the RF pulse frequency is also the Larmor frequency,
resonance happens, perturbing the magnetic momentum of the spins. The RF pulse ro−→
−→
tates M0 away from the z-axis. The angle between the z-axis and M0 after rotation is
called the flip-angle. The flip-angle depends on the magnitude of the RF pulse and on
its duration τp . By calibrating correctly the RF pulse, any flip-angle can be achieved.
α = γB1 τp
(1.1)
where α is the flip-angle. If the duration of the pulse is longer (higher τp ), more protons
spins will change state, and the magnetization M (sum of all the spins) will rotate
−
→
more (higher α). All the nuclei contributing to this M field start precessing around B0 .
After the RF pulse, the spins keep on precessing and create a fluctuating magnetic field
inducing an oscillating current in the coils of the MR scan which can be measured. The
same coil is often used both to transmit the RF pulse and to detect the signal from the
KTH University, Guillaume GIBERT
1.2. Overview of MRI
11
precessing M .
Figure 1.2.2: Motion of the bulk magnetization vector in the presence of a rotating
RF field as observed in (a) the RF-rotating frame, and (b) the laboratory frame. Figure
from [21]
Relaxation times
When the B1 excitation stops, the resulting magnetization tipped from its original
position returns to the equilibrium under the action of B0 . The signal is called free induction decay (FID). We call relaxation time the time needed by the magnetization to
go back to equilibrium. Two different relaxation times are distinguished: the transversal
relaxation time T2 and the longitudinal relaxation time T1 .
• Transversal relaxation time T2
Due to really small variations of the B0 field, which is not perfectly constant, several
protons will precess at slightly different frequencies and will lose coherence. The magnitude of the magnetization M will decay due to this loss of coherence. Some fluctuations
of the B0 field are fixed and can be refocused by applying a 180o RF pulse. These fluctuations induce the apparent transverse relaxation T2∗ . Other fluctuations are random
and induce the transverse relaxation T2 . During the transverse relaxation, the transverse
vector Mxy decays at a certain rate which depends on T2 . At typical MRI field strengths,
the T2 of both grey and white matter is approximately 100 ms
Mxy (t) = M0 e−t/T2
(1.2)
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1.2. Overview of MRI
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• Longitudinal relaxation time T1
The longitudinal relaxation time T1 corresponds to the return to the energetic equilibrium of the system after excitation. When B1 is suppressed , the resulting magnetization
goes back to the equilibrium. T1 is called the longitudinal relaxation time because it
refers to the time needed for the spins to realign along the longitudinal z-axis
Mz (t) = M0 (1 − e−t/T1 )
(1.3)
The longitudinal relaxation time T1 is always longer than the transversal relaxation time
T2 . Thus when the decay of the magnetization in the xy plane is complete, the recovery of
the z-component of the magnetization is not finished yet. At typical MRI field strengths,
in the white matter and in the gray matter of the cerebrum, T1 is usually between 800
and 1000 ms . [17]
Figure 1.2.3: The recovery of longitudinal magnetization and the decay of transverse
magnetization occur independently. The decay is faster than the recovery. Figure from
[24]
Slice selection
To obtain images of a volume of the body, a series of several 2D-images are acquired,
and reconstituted as a 3D-volume during a post-processing treatment. To acquire a 2Dimage, the slice of interest needs to be selected. To do that, a Gradient Field is applied
perpendicularly to the slice that we want to image. When applying a gradient, a new
component is added to the total magnetic field. The magnitude of this component deKTH University, Guillaume GIBERT
1.2. Overview of MRI
13
−
−
−
−
pends on the position in space. Therefore, at position →
r = x→
x + y→
y + z→
z , the total
magnetic field becomes
→
−
−
→ −→
−
B = B0 + BG = (B0 + Gx x + Gy y + Gz z)→
z
(1.4)
where Gx , Gy and Gz are the gradient component over the three directions of the
space.
The precessing frequency of the spins depends on the magnetic field, and therefore
on the position. Then, by adjusting correctly the frequency of the RF pulse applied, one
can excite only a certain region of the space or so called slice. Or, by fixing the value
of the RF pulse frequency, one can change the magnitude of the gradient to change the
position of the selected slice. Usually, we choose to play with the RF pulse frequency,
because modifying the gradient field quickly induces Eddy currents and different sources
of artefacts.
A RF pulse has actually both a central frequency, and a small range of frequencies
(around 1kHz). Indeed the RF pulse is not perfectly concentrated on the central frequency. The thickness of the selected slice is inversely proportional to the magnitude of
the gradient field applied, and depends also on the bandwidth of frequencies of the RF
pulse. The gradient direction determines the slice orientation. [16] The slice selection
gradient introduces a linear phase shift along the slice thickness. It can be removed by
a refocusing gradient in the opposite direction to the slice selection gradient. We can
already notice that it is also possible to excite the whole volume with a non-selective RF
pulse in the case of 3D-imaging.
Frequency and phase encoding k space
As we are trying to perform images of parts of the body, it is needed to determine
where the signal measured is coming from. The slice imaged is divided into pixels (image
elements), or more exactly into voxels (since the slice has a finite thickness). We want
to be able to measure the signal coming from each of these voxels. The coils of the MR
scanners enable to add linear gradients to the external magnetic field B0 in the x, y and
z directions. As explained in the slice selection process, if a gradient field is applied after
a 90o RF pulse, the Larmor frequency will depend on the position in the sample.
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1.2. Overview of MRI
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If M was initially along the z-axis, and rotated on the xy-plane by the RF pulse,
a linear gradient is applied on the x-direction at the moment of the signal read out
(the read-out gradient). The signal measured is then composed of a range of frequency
components. Each component depends on the position along the x-axis within a single
selected slice. By applying a Fourier transform of the signal, a 1D profile image of our
sample is obtained, illustrating the relative magnitude of the different frequency components. We are more interested in a 2D image of our sample. In order to do that, the
gradient applied at the time of signal out-reading (the read-out gradient) is preceded by
a second gradient, perpendicular to the first one (the phase-encoding gradient). This
extra gradient allows the phase of each spin within the sample to become a function of
its position in both the x and y directions.[6] The signal obtained from an excited slice
and measured by the receiving coils is given by :
Z Z
S(t) ∝
x
ρ(x, y)e−iφ(x,y,t) dxdy
(1.5)
y
where ρ(x, y) is the density of spins in the excited slice, and φ(x, y, t) is the phase of
the spins at the point (x, y) relative to the Larmor Frequency. The phase can be broken
down into two components: one due to the phase-encoding gradient, and another one
due to the read-out gradient.
φ(x, y, t) = 2π(kx (t) + ky (t))
(1.6)
with:
γ
kx (t) =
2π
Zτ
Gx (t)dt
(1.7)
Gy (t)dt
(1.8)
0
γ
ky (t) =
2π
Zτ
0
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1.2. Overview of MRI
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The expression of the signal S(t) has the form of a Fourier transform of the spin
density with kx and ky the frequency coordinates in the reciprocal space. This reciprocal space is called the k-space. The read-out gradient (Gx (t)) and the phase-encoding
gradient(Gy (t)) determine the trajectory in the k-space during the image-acquisition
process, as illustrated on the Figure 1.2.4. The position of the data in the k-space is determined by the gradients. Without any encoding gradient, we are situated in the center
of the k-space. The bigger the magnitude of the gradient, the further we are from the
center of the k-space. The gradients are bipolar, what enables to move in both positive
and negative directions so that the whole k-space can be covered. From the information
in the k-space, the image can be reconstructed in each voxel of the excited slice by applying an inverse 2D-Fourier transform. This process is called the image reconstruction.
Each point of the k-space is coding for one component of the whole image whereas each
point of the image is coded by the whole k-space.[18]
Figure 1.2.4: (a) A basic pulse sequence diagram and (b) the corresponding path
traced in the k-space. The dashed line in (a) shows the consequences of changing the
phase-encoding gradient on the path (b). Figure from [6]
During one sequence (one RF pulse), a certain part of the k-space is covered by the
path defined by the two encoding gradients. To cover the whole k-space, the sequence
has to be repeated several times. Each time, the encoding gradients are shifted in order
to cover the remaining part of the k-space. The time between two repetition of the RF
pulse is called the repetition time (TR).
As the k-space is a reciprocal space, the resolution at which the k-space is sampled is
related to the field of view (FOV) of the image. And inversely, the range of the sampled
k-space is related to the resolution of the image.
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1.2. Overview of MRI
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Echo-Planar Imaging (EPI)
In order to reduce the acquisition time, the idea is to fill the k-space with as few shots
(RF pulses) as possible. The ideal method is called the single-shot EPI, and consists in
going through the whole k-space with a read-out gradient during only one magnetization
decay. If the duration of the read-out is longer than the T2 decay, the image will appear
blurry. Basically the fewer the number of RF pulses to go through the k-space, the faster
the acquisition time. If TA is higher (with multi-shot EPIs), the acquisition has a higher
susceptibility to motion artefacts.
3D Imaging
The specificities of the spatial encoding in MRI enable to perform a 3D imaging,
with acquisition of a direct complete volume, instead of a slice-by-slice imaging. The 3D
imaging is characterized by excitation of a complete volume at each repetition, instead
of only one thin slice. The spatial encoding is performed in three dimensions by adding
a phase encoding in the third dimension, compared to the phase and frequency encoding
used in 2D imaging. The number of repetitions increases linearly with the number of
slices in the third dimension used to cover the 3D k-space. For the image reconstruction,
an inverse 3D Fourier transform is performed.
The acquisition time has to be limited as much as possible. Either short TR are
used (with gradient echo sequences for example), or optimized paths are chosen to cover
as much k-space as possible during one repetition time. At each repetition, the signal
comes from the whole volume, and not from only one slice. Thus, there is more signal
recorded and less interference. Moreover the partitions can be thinner than the classic
2D slices since the signal-to-noise ratio (SNR) is better compared to a thick-equivalent
slice acquired in 2D. Finally the spatial resolution is better since the volume of interest is
fully explored without any spacing or mismatch between the slices. However, due to two
phase-encoding, aliasing artefacts and truncation artefacts can be seen in two different
directions.
Image contrast
According to the description of the imaging process, a good tissue contrast relies mainly
on the proton-density in the sample we are imaging. If many protons are inverted, more
signal will be acquired. However, by selecting appropriate pulse sequences, or by changing
KTH University, Guillaume GIBERT
1.2. Overview of MRI
17
acquisition parameters, we are able to modulate the inherent proton-density weighting.
For example, in the case of short TR , the species with a short longitudinal relaxation
time T1 will have more time to recover their equilibrium magnetization than the species
with high T1 . Thus, when applying the next RF pulse, the rotated magnetization on the
xy-plane will have a bigger magnitude than the one for the long T1 which did not recover
so much. Consequently, the species with low T1 will appear brighter. If the TR is larger,
both species with low and high T1 have time to recover. The influence of the parameters
on the image contrast is more complex than this, but we will not go more deeply into
explanations.
Figure 1.2.5: (a) long TR and short TE . (b) long TR and long TE . (c) short TR and
short TE . Figure from [15]
The Signal-to-Noise Ratio (SNR)
The SNR is the difference in intensity between the signal coming from the area of
interest and the noise coming from the background. Most of the time this background
noise is measured in the air surrounding the object. The difference between the signal
and the background noise is divided by the standard deviation of the signal from the
background. SNR is proportional to the volume of the voxel. So the better the resolution, the smaller the voxel and thus the lower the SNR. The SNR is also proportional
to the square root of the number of scans (phase encodings). Then, a longer acquisition obviously provides a better SNR. An increase of the slice thickness also increases
the SNR. Likewise, increasing the FOV will improve the SNR. Consequently, one of the
big challenge will be to find a good trade-off between resolution, acquisition time, slice
thickness, FOV and SNR.
KTH University, Guillaume GIBERT
1.3. State of the art
1.3
1.3.1
18
State of the art
Measuring perfusion
Several methods have been explored in the last fifty years to be able to measure the blood
flow in the brain. In order to measure the blood perfusion in the brain, it is needed to
mark a sample of blood and trace it throughout its flowing in the brain. One common
feature of all the following methods is the use of an exogenous tracer, or so-called contrast
agent.
Nitrous Oxide inhalation method
Key and Schmidt were the first, in 1945, to be able to perform experimental measurements of the human rCBF at the resting state.[27] They made the patient inhale a defined
amount of nitrous oxide. Then, they took blood samples from the jugular vein at different
time points after the injection of the gas. They compared the different N2 O concentrations in the veins and in the brachial or femoral artery at each time point. With the
Fick’s law, the rCBF can be calculated using the time taken by the N2 O concentration
in the veins to equilibrate with the concentration in the arteries:
(QB )u /W
rCBF = R u
0 (A − V )dt
(1.9)
where (QB )u is the amount of N2 O taken up by the brain by time u (time when
there is equilibrium between arterial and venous concentration), A is the arterial N2 O
concentration, V is the venous N2 O concentration and W is the mass of the brain.
By modifying the concentration of CO2 and O2 in the gas inhaled, Key and Schmidt
were also able to demonstrate that the brain changes the rCBF to regulate its environment. This method provides good efficiency in measuring the perfusion in the brain.
However the use of Nitrous oxide has to be really carefully controlled. Indeed, a too
large exposure to this gas can cause a decrease of the mental performances, the manual
dexterity and the visual ability .[10]
Positron Emission Tomography (PET)
In the positron emission tomography method, a radioactive contrast agent, or so-called
tracer, is injected. This radioactive tracer emits positrons which are going to collide with
electrons of the environment producing the emission of a pair of photons travelling in
opposite directions. The patient is surrounded with photo-detector tubes to detect the
photons emitted, and reconstruct an image of the tracer concentration. It is possible to
KTH University, Guillaume GIBERT
1.3. State of the art
19
image the cerebral perfusion with the PET method using a freely diffusible tissue tracer,
oxygen-15-labelled water (15 O − H2 O).[14]
Despite the fact that PET provides results significantly close to those provided by
ASL [13], ASL has the big advantage and to produce no ionising radiation and to be a
non-invasive method, enabling to save time, and to avoid any type of allergy or immune
reaction during the measurement.
Single Photon Emission Computed Tomography(SPECT)
The SPECT technique relies on the injection of a gamma-emitting radioisotope, so-called
radionuclide, into the bloodstream of the patient. The radioisotope has been combined
to a specific ligand creating a radio-ligand, which is likely to bind with certain types of
tissues. This combination of ligand and radioisotope can be transported and attached to
a region of interest in the body. The isotope is going to emit gamma-rays, measured by
the gamma-camera, allowing to follow its concentration throughout the body. The rate
of decay of signal then gives us information on the rCBF.
The SPECT method appeared to give qualitatively close results to ASL results [29].
However, the resolution available with the ASL method is better than with the SPECT
method. And once again, the ASL method doesn’t require injection or inhalation of any
marker agent.
Dynamic Susceptibility Contrast (DSC)
DSC MRI, on the contrary to the PET and SPECT methods, is the only method with
ASL, using the MRI to measure the cerebral perfusion. Dynamic Susceptibility Contrast (DSC) MRI relies on imaging the flow of a contrast agent (Gadolinium) to measure
the cerebral perfusion. This tracer shortens the T2∗ relaxation time, much like in BOLD
imaging. Then, by identifying the voxels where the arterial signal comes from the arterial
input function can be determined. From the deconvolution of the curve representing the
tracer passage in the brain and from the arterial input function, an estimated rCBF can
be given.
The DSC MRI method of measuring the cerebral perfusion is the most widely used
method clinically [19]. It requires only a few minutes to perform the imaging and produce
qualitative rCBF maps of the brain. However, it remains really difficult to identify the
different arterial input functions. Moreover, the dose of Gadolinium that can be injected
is limited, and there is still a risk of allergic reaction to the tracer.
KTH University, Guillaume GIBERT
1.3. State of the art
1.3.2
20
Measuring perfusion with ASL
Today, we can distinguish two main methods used to measure perfusion with MRI: the
dynamic susceptibility contrast method (DSC) which relies on an exogenous endovascular tracer and arterial spin labelling (ASL) which relies on an endogenous tracer (see 2.1).
The ASL method is totally non-invasive, what makes it really adapted for measuring
perfusion of healthy volunteers, or of groups of patients, where repetitive follow-ups are
required. This non-invasiveness is particularly necessary in the case of patients suffering from particular pathological conditions, such as kidney failure. It is also important
in the paediatric domain where it is restricted to use radioactive contrast agents and
endogenous tracers. In the recent years, ASL has started to be used clinically mainly
due to these different advantages[9]. Moreover, the important increase of high-field MR
scans(> 3T) has enabled ASL method to move progressively from the research domain
towards the clinical world. Indeed, higher magnetic fields provide higher signal-to-noise
ratio, signal-to-noise ratios and spectral resolution. This will help to obtain better spatial
and temporal resolution [28].
However several sources of errors or uncertainties remain and make the ASL method
not robust enough to be fully extended as a clinical routine. The main burning issue is
the low signal-to-noise ratio (SNR). As the image analyzed to measure the perfusion is
actually the difference between two images (see 2.1), the SNR is really low. It is therefore
needed to perform averages of several of these images which makes the acquisition time
a bit longer and the method really sensitive to motion of the patient [9].
Even if this method has been investigated for over 20 years, it has only recently
started to be implemented in a clinical environment. From these 20 years of study, a
plethora of different protocols has emerged, with different labelling schemes, different
read-out parameters, and several different fitting models [5]. It is difficult for a clinician
to figure out which method is more appropriate, hence the need to make this method
more robust and to optimize the parameters of the sequence.
Recently, a study from the research team of Johns Hopkins University in Baltimore
published in August 2013, in the journal NMR in Biomedicine has showed promising
results in measuring the cerebral perfusion with the ASL method. The publication related, untitled «Three-dimensional whole-brain perfusion quantification using pseudocontinuous arterial spin labeling MRI at multiple postlabeling delays: accounting for
KTH University, Guillaume GIBERT
1.3. State of the art
21
both arterial transit time and impulse response function »[22], deals with similar issues
to those I worked on such as the quantification of the regional Cerebral Blood Flow in
three dimensions in the whole brain. They used the pseudo-continuous Arterial-Spin
Labelling method at multiple post-labelling delays(see 2.1). They also investigated the
efficiency of different fitting models with different numbers of parameters. This article is
really close to what I have been working on throughout my whole project. We used it as
a good reference to compare and evaluate the relevancy of our results, but also to try to
put the analysis and the experiments further.
KTH University, Guillaume GIBERT
Chapter 2
Theory and Methods
2.1
ASL Principle
Arterial Spin Labelling is an MR imaging method to measure the cerebral perfusion. This
method is non-invasive, so it doesn’t need injection of an exogenous tracer in the blood
flow. On the contrary, the ASL method uses the blood water as a natural endogenous
contrast agent. While the blood is flowing towards the brain in the arteries of the neck
region, a part of this flowing blood is going to be tagged, that is to say, magnetically
labelled. Usually, the tagging region is located at the neck level, or below the cerebellum,
or more generally below the region of interest that is to be imaged. To perform this labelling, a 180-degree RF inversion pulse is applied. It inverts the net magnetization of the
blood water protons. The time needed by the tagged blood to flow from the tagging region to the imaging region is called the Mean Transit Time or Bolus Arrival Time(BAT).
A first image of the tagged blood in the brain is acquired, and is referred as the tag
image. Then a second image, without tagging pulse, is acquired. This image is referred
as the control image, and is used a little bit as a reference. Both images together refer
as a pair of control/tag images. The subtraction of these two images is sensitive to the
cerebral perfusion, and it is from the subtracted image that the value of the rCBF can be
extracted. The subtracted image is often called the Perfusion-Weighted image (PWI).
The typical SNR obtained with the ASL method is ∼ 1, which is quite low. So usually
several pairs of tag/control images are acquired and then averaged, enabling to higher a
little bit the SNR and to smooth the motion-related artefacts.
Depending on the way the blood is labelled and the image acquired, different ASL
sub-methods can be distinguished: the continuous ASL (CASL), the pulse ASL (PASL),
and the pseudo-continuous ASL (PCASL).
22
2.1. ASL Principle
23
Figure 2.1.1: Basic principle of ASL: arterial blood is tagged and then moves towards
the imaging region during the arterial transit time. During this time, the signal undergoes
a T1 decay. Images are acquired in tag and control conditions. The difference of both
images (the perfusion-weighted image) gives information on the rCBF. Figure from [25]
2.1.1
Continuous ASL
In the continuous ASL method, the tag is applied continuously to the blood flowing
through a thin slice in the neck. The spins in the blood plasma are inverted by a low RF
pulse in the presence of a gradient. This inversion is called the adiabatic fast passage. As
the tag is applied continuously, the net magnetization within the imaging region reaches
a steady state.
The continuous ASL method provides good SNR which is a key point for cerebral
perfusion measurement. However, this method faces an important number of challenges.
The continuous tagging pulse can directly affect the water protons of the blood plasma
situated in the imaging region, even if the tagging pulse is applied to a separate labelling
region lower in the neck. This phenomenon is called Magnetization Transfer (MT) and is
not dependent on perfusion. It has to be reproduced during the acquisition of the control
image so that it is suppressed when subtracting both images and it keeps the perfusionweighted image purely dependent on the perfusion. In order to do this, a similar pulse
as the tagging pulse is applied before the acquisition of the control image, but with the
tagging point in a distal position to the imaging region (see 2.1.2)
The off-resonance saturation of the region of interest produced by the RF pulse is hard
to correct accurately in multiple slices. The continuous ASL approach can be used more
KTH University, Guillaume GIBERT
2.1. ASL Principle
24
Figure 2.1.2: Continuous ASL with suppression of the Magnetization Transfer. For
the control image, the same RF pulse as for the tag image, is applied with tagging point
distal to imaging region.
efficiently to image a single slice. A separate small RF coil could enable to overcome this
problem but it requires a specific hardware. The implementation of this method is made
difficult by the limited technical support to perform continuous tagging, and long RF
pulses. The SNR has been proved to be greater with the CASL than with the PASL, but
this advantage is counterbalanced by the imprecisions of the practical implementation
[31].
2.1.2
Pulsed ASL
The pulsed ASL method relies on a sharp RF pulse applied to the volume of blood located
in the tagging region at the time of the pulse. On the contrary to the CASL, the blood
labelled is not the blood flowing through a thin slice during a long period of time, but the
blood located in a thick slice during a short period of time. So the width of the tagging
slab determines the volume of tagged blood. In PASL, the MT also has to be taken into
account but it is really lower than with the CASL.
Depending on the method to perform the tagging pulse and the corresponding control
pulse, we can distinguish three different sub-methods within the PASL method:
FAIR (Flow sensitive Alternating Inversion Recovery) : the tag produces a non selective inversion across the whole area covered by the the RF coil. The control is
performed after an inversion over an area just a bit wider than the imaging region
EPISTAR (Echo-Planar Imaging and Signal Targeting with Alternating RF) : the tag
is performed in a region proximal to the imaging region. The control corresponds
KTH University, Guillaume GIBERT
2.1. ASL Principle
25
to the same slab located distal to the imaging region, similarly to the CASL method.
PICORE (Proximal Inversion with a Control for Off-Resonance Effects) : The tag is the
same as in the EPISTAR method but the control acquisition follows an off-resonance
RF pulse without any gradient.
The labelling efficiency is higher in the PASL than in the CASL method. But, as the
magnetization undergoes the T1 decay when flowing to the imaging region, the signal is
lower for long inflow times. The increased availability of high-field MR scans has enabled
to improve the PASL method, not only by providing higher SNR but also by lengthening
the T1 , allowing more spin to accumulate [8]. High-field MR scans also help to have
better spatial and temporal resolution.
There is no clear agreement on which of the sub-methods is the the most efficient one
for any particular application. The differences between each of them lie in their relative
ability to reduce the influence of several sources of artefacts. These different contributions
are difficult to quantify. Throughout this project, the PASL method has been investigated
and improved. All the measurements and results presented in the followings come from
acquisitions of data performed with a PASL sequence, unless otherwise stated.
2.1.3
Pseudo-Continuous ASL (PCASL)
The pseudo-Continuous ASL method relies in tagging the blood flowing through a thin
plane or slice during a certain amount of time : the labelling duration. The post-labelling
delay (PLD) is the duration between the moment when the labelling is stopped and the
moment when the imaging starts. It is set up by the user. With the PCASL method,
the blood is labelled during a longer duration than with the PASL. The inversion of
the blood is then more efficient, leading to an increased SNR in the perfusion-weighted
images. The higher the SNR, the easier it is to visualize the blood perfusion on the maps
of the brain.
KTH University, Guillaume GIBERT
2.1. ASL Principle
26
Figure 2.1.3: Inversion profiles of tag and control pulses for FAIR, EPISTAR and PICORE. The tag profile is solid, and the control profile is dashed. Example slice locations
for a five slice experiment are shown as bold vertical lines.
KTH University, Guillaume GIBERT
2.2. Quantification of perfusion
Advantages
PASL
Higher tagging efficiency
Lower SAR
Improved transit time effects
CASL
Higher SNR than PASL
Shorter transit delay
PCASL
Higher SNR than PASL
Higher tagging efficiency than CASL
Improved transit time effect
27
Disadvantages
Lower SNR
Increased transit delay
Lower tagging efficiency
Continuous RF transmit hardware required
Higher SAR
Magnetization Transfer effects
Higher SAR
Limited clinical availability
Table 2.1: Pros and cons of the 3 different ASL methods
2.2
Quantification of perfusion
As noticed before, the perfusion-weighted image, referring as the subtraction between the
tag and the control images, is providing information on the blood perfusion that is to be
quantified. However, in the PASL technique, the subtraction of the two images provides
only qualitative information on the rCBF. Indeed, the delay in the transit of blood from
the tagging region to the imaging region can vary depending on the spatial region. The
tagged blood can flow through different paths, inside different arteries, which influence
the duration of the inflowing to the imaging region. This fluctuating transit time cannot
be measured with only one pair of control/tag images. The resulting uncertainty on the
rCBF would be too big. From now on, we will call BAT (Bolus Arrival Time) the time
needed by the tagged blood to reach the imaging region from the tagging region.
2.2.1
Quantification correction
Two main problems with the PASL method cause a misestimation of the perfusion: the
inflow of untagged blood into the imaging region before the mapping of the labelled
blood has been fully performed, and variations in the transit time. In order to improve
the accuracy of the perfusion measurement, a saturation pulse is applied to the tagging
region just after the blood tagging, in both the tag and control image acquisition. This
method is called QUIPSS-II (for "Quantitative Imaging of Perfusion using a Single Substraction"). Another version of the QUIPSS-II consists in replacing the saturation pulse
KTH University, Guillaume GIBERT
2.2. Quantification of perfusion
28
by periodic saturation pulses applied on thin slices distal to the tagging region.It is called
the Q2TIPS method [11][12].
So the basic structure of a PASL sequence is composed of three main steps. The
tagging is performed by the inversion pulse and can be preceded by pre-saturation pulses
and followed by post-saturation pulses to reduce the direct effects of the inversion pulse
on the imaging region. The tag saturation is performed by the QUIPSS-II or the Q2TIPS
method. And finally, the image read-out is performed at a time TI after the inversion
pulse(see figure 2.2.1).
Figure 2.2.1: Pulse sequence diagram. Top line is RF waveform; the second line is
for the slice selection; the third and fourth lines for phase and read-out gradients. The
dashed line in Gss shows the gradient in the control condition.
2.2.2
Multi-TI data
To be distinguished from the BAT is the Inversion Time (TI). The Inversion Time is
defined as as the duration between the end of the tagging and the beginning of the image
acquisition in the region of interest. If the TI is short, the bolus of tagged blood has just
left the tagging region when the image acquisition starts, and hasn’t reached the imaging
region yet. On the other hand, if the TI is long, the MR signal starts to decay because
of the T1 relaxation. According to the perfusion model in the brain, the blood reaching the region of interest is considered being in a "sink" and cannot leave out this area.
The Inversion Time is set by the user and has to be known in order to quantify the rCBF.
As just explained above, the acquisition of only one pair of control/tag images is insufficient to quantify the rCBF without too much uncertainty. The value of the rCBF at
KTH University, Guillaume GIBERT
2.3. Numerical Fitting
29
each voxel is related to the difference of magnetization between the tag and the control
image. The method to quantify the rCBF consists in acquiring several pairs of control/tag images at different TI. By varying the TI, the curve representing the wash-in
and wash-out of the bolus from the imaging region is sampled. The set of TI investigated
is called the range of TI. For each voxel, a kinetic curve of the difference in magnetization
in respect to the inversion times, is obtained (see Figure 2.2.2). This curve is going to be
fitted with a numerical model describing the kinetics of the passage of the tagged bolus
through the imaging region. The fitting of the kinetic curve with the model will provide
a quantified value of the rCBF as well as other information on the perfusion.
Figure 2.2.2: For each voxel, the difference of magnetization is extracted from the
Perfusion-Weighted image at each TI. A kinetic curve of the magnetization in respect to
the TI is obtained for each voxel.
2.3
2.3.1
Numerical Fitting
Numerical Model
The kinetic curve extracted from the perfusion weighted-images for each voxel is fitted
to a kinetic model describing the flow of the tagged bolus through the imaging region
for an healthy patient. To perform the fitting, we worked a full month on the development of a fitting algorithm in C-language. Because it is not robust enough to be used
for the moment, a Matlab algorithm called "lsqcurvefit" has been used throughout the
project. It relies on the least squares method. The model we have been using, was first
approached by Buxton et al [23], refers as the Balloon Model, and has been taken from
the literature. Then, we implemented it numerically in the Matlab code to be able to
perform the fitting. This model relies on an intuitive approach of the different steps that
KTH University, Guillaume GIBERT
2.3. Numerical Fitting
30
the blood tracer undergoes. The general form [22] for the difference of magnetization is
given by:
∆M (t) = c(t) ⊗ r(t)
(2.1)
where c(t) is the Arterial Input Function (AIF), and represents the delivery of nonfully-relaxed magnetization into a voxel.r(t) is the Impulse Response Function (IRF) and
accounts for the relaxation of the tagged blood (the decay of the tag). The symbol ⊗
denotes convolution.
The AIF for a PASL labelling can be described as:
c(t) =



 0
if 0 < t < ∆t
2αM0,a f


 0
e−∆t/T1,a
if ∆t ≤ t ≤ ∆t + τ
(2.2)
if t > ∆t + τ
where α represents the degree of inversion achieved by the tag (α = 1 refers to a
100% efficient labelling), τ is the temporal width of the tagged bolus (bolus duration),
M0,a is the equilibrium magnetization of the arterial blood, ∆t is the BAT, T1,a is the
relaxation constant for arterial blood.
The IRF decay function can be described as:
r(t) = e−t/T1,ef f
if t > 0
(2.3)
where T1,ef f is an effective T1 relaxation constant.
Then, the difference in magnetization between the tag and the control images is given
by the convolution of the AIF and the IRF functions (cf 2.1):
KTH University, Guillaume GIBERT
2.3. Numerical Fitting
∆M (t) =

0




31
if t < ∆t
e
−∆t/T1,a
T1,ef f e
−∆t/T1,a
2
λ αM0,t f T1,ef f
2
λ αM0,t f
1−e
−(t−∆t)/T1,ef f
τ /T1,ef f
e
−1 e−(t−∆t)/T1,ef f
if ∆t ≤ t ≤ ∆t + τ
if t > ∆t + τ
(2.4)
where M0,t is the equilibrium magnetization of the tissue. It is related to M0,a by
λ the equilibrium tissue/blood partition coefficient of water. f is the regional Cerebral
Blood Flow expressed in (mL/g of tissue/s). Considering that tissue weights 1 gram per
cm3 we can then notice that:
60 · rCBF(mL/100g/min) = 36000 · f (mL/g/s) = 0.01s−1
(2.5)
The tagged blood is assumed to progress to the imaging region under "plug flow",
i.e. there is no temporal dispersion of the tagged bolus. The values of the T1 relaxation
constants are set based on information found in the literature [22][33]: α = 1.0, λ = 0.9,
M0,a = 1.0, T1,a = 1.7s, τ = 0.7s.
Figure 2.3.1: Typical output from PASL Numerical Model, as described by equation
2.4 with ∆t = 0.5s, f = 0.01s−1 , τ = 0.7s.
On the figure 2.3.1, the three different parts defined in the equation of the model can
KTH University, Guillaume GIBERT
2.3. Numerical Fitting
32
be recognized.
First part (1) : The first part of the curve is null. It corresponds to the period of time
when the bolus of tagged blood has not reached the imaging region yet. So when
imaging the region of interest, there is no difference in magnetization between the
tag and the control image. Therefore, the width of this part is the BAT.
Second part (2) : The first point of the second part represents the first "drop" of
tagged blood reaching the imaging region. The increasing part represents the inflow
of tagged blood in the imaging region. The increase reaches its maximum when all
the tagged blood is in the region of interest. Therefore, the duration of the second
part is the bolus duration τ .
Third part (3) : The third part represents the decay of the magnetization. The inverted spins of the water protons are going back to their equilibrium positions (see
explanations on relaxation in the section 1.2.) The convexity of the decay is related
to the T1 relaxation constants. In the model, it is considered that the tagged blood,
once in the imaging region, flows through the big arteries, then through smaller
arteries, and finally in capillaries to feed the tissues. Therefore, it is considered that
the tagged blood flows through different arteries routes without ever leaving the
imaging region. The decreasing part of the model curve is only due to the decay of
the magnetization, and not of the flow of tagged blood out of the imaging region.
Two-parameter model
Some of the variables of the model are fixed, depending on the protocol (τ , α, λ).
Others are considered independent of the patient and are fixed as well (T1,ef f , T1,a ). The
two remaining variables (the rCBF f and the BAT ∆t) are the parameters of the model.
Those two degrees of freedom are going to be adjusted by the algorithm to fit as much as
possible the acquired data. The BAT gives information about how much time is needed
by the tagged blood to reach the imaging region.
From a clinical point of view, a low value of the BAT can indicate difficulties for the
blood to flow through some arteries. Possibly due to a stenosis (reduction of the size of
the lumen) of the arteries, it can help in the diagnosis of arteriosclerosis which induces
risks of stroke. The rCBF gives information about how much blood feeds the cerebral
tissues per unit of time. A low rCBF indicates a poor blood supply to the brain and
leads to poor oxygen supply. This condition is known as brain ischemia, and can lead
to the death of brain tissue and ischemic stroke. On the contrary, a too high rCBF can
KTH University, Guillaume GIBERT
2.3. Numerical Fitting
33
also be the indication of a pathological state. For example a tumor, characterized by a
high vascularization, will appear as an area with abnormally high rCBF values.[4]
The figure 2.3.2 represents the influence of each parameter value on the shape of
the numerical model. A shorter BAT induces a higher peak. Indeed, more labelled
blood has reached the imaging region before the beginning of the decay, hence a higher
magnetization.
2.3.2
Fitting
The resulting values of the rCBF and the BAT provide the information about the brain
perfusion of the patient. Finally, five different pieces of information are going to be
provided by the fitting:
• The value of the Bolus Arrival Time BAT
• The uncertainty on the BAT value (expressed in percentage of the value). From
now on, we will refer at the error-on-BAT
• The value of the regional Cerebral Blood Flow rCBF
• The uncertainty on the rCBF value (expressed in percentage of the value). From
now on, we will refer at the error-on-CBF
• The Correlation Coefficient of the fitting R2
The errors are obtained by taking the square root of the covariance matrix, which is
calculated from the Jacobian matrix and the residual values (difference between the kinetic curve and the fitted curve at each point). The Jacobian and the residual values are
directly provided by the "lsqcurvefit" function [3]. These five pieces of information are
resulting from the fitting of the model and the kinetic curve at each voxel. Therefore, by
reconstituting the slices of the brain from the values at each voxel, five different maps of
the brain are obtained (one for each of the five information provided by the fitting).
KTH University, Guillaume GIBERT
2.3. Numerical Fitting
34
Figure 2.3.2: (a) Influence of the parameter BAT on the shape of the numerical model.
(b) Influence of the parameter rCBF on the shape of the numerical model.
KTH University, Guillaume GIBERT
2.3. Numerical Fitting
35
Figure 2.3.3: Example of fitting at one voxel(up) and information provided by the
fitting (down)
KTH University, Guillaume GIBERT
Chapter 3
Improving the PASL method
The PASL method can be improved and made more robust at different levels. The sequence itself can be adjusted to improve the resolution of the image, to increase the SNR,
to reduce the acquisition time (TA)... It is also possible to investigate how to optimize
the range of TI acquired in order to reduce the error-on-BAT and the error-on-CBF, and
to provide the most reliable estimation of the rCBF and the BAT. Finally, the efficiency
of the fitting algorithm and the consistency of the numerical model also have to be investigated. All these aspects of the PASL method were explored during the project and
are going to be discussed in this chapter.
Throughout the project,a total of 19 different subjects of random ages underwent
perfusion measurements with the ASL method. Notice that, for some patients, images
were performed to investigate both the change in protocol (previous part) and the change
in TI-range. That’s why the total number of patients (19) imaged during the project, is
inferior to the sum of the number of patients imaged in each part of the following section.
The subjects were volunteers, in a healthy state and were registered, after medical examination, on a volunteer list for experimental measurements at Siemens Healthcare. But
no investigation was performed on the influence of the patients characteristics. During
the project, two different Siemens MR scanners were used: the 3-Tesla Magnetom Skyra
and the 3-Tesla Magnetom Prisma.
Finally, as it is impossible to quantify the impact of certain aspects of the method
(the impact of the acquisition time for example), the optimized set of protocol and
the optimized TI-range were decided by a subjective trade-off between the quantitative
results of the performance of the method, and the acquisition time.
36
3.1. First set of experiment
3.1
37
First set of experiment
3.1.1
First protocol
Throughout the project, a couple of parameters of the PASL sequence are going to
be adjusted. Below are the most important parameters that we are going to investigate.
Some of them will be modified to try to improve the sequence, others will remain constant,
but need to be pointed out:
Number of slices : The number of slices of the brain acquired. The more slices you
have, the better coverage of the brain you obtain (for a constant thickness of the
slices).
Slice oversampling : Increase of the effective area of accurate measurement to avoid
aliasing artefacts. it relies on more kz sampled with constant ∆kz .
EPI factor (EF) : Gives an indication of the number of EPI shots (RF pulses)(see
section 1.2) needed to go through the k-space in the in-plane dimension(the 2Dslice dimension). If the EPI factor is equal to the base resolution, a single-shot
is required to go through the whole k-space for a 2D-slice. If the EPI Factor is
halved, twice as many pulses are needed, and therefore the acquisition time (TA)
is doubled.
Turbo Factor (TF) : Equivalent of the EPI Factor in the third dimension (orthogonal
to the slices). If the TF is equal to the number of slices, only a single-shot is
required to go through the third dimension of the k-space. If the TF is halved,
twice as many pulse are required and the TA is doubled.
Number of Segments : It is the number of shots required to go through the whole
k-space (in 3D). It is the product of the number of shots required by the EPI
factor, by the number of shots due to the value of the TF. The higher the number
of segments, the longer the TA.
Repetition Time (TR) : It represents the duration between successive pulse sequences
applied to the same slice. It affects the contrast of the image and also have strong
influence on the total TA.
Resolution : It represents the size of one single voxel (a 3-dimension pixel). The size
of the voxel in the third dimension is actually the thickness of the slice.
Inversion Time (TI) : More a parameter of the PASL method than a parameter of the
sequence. The PASL sequence is going to be repeated for each TI of the TI-range.
KTH University, Guillaume GIBERT
3.1. First set of experiment
38
From now on, we will adopt the new notation [TImin :TIinterval :TImax ] to specify the
TI-range investigated (expressed in milliseconds on the contrary to the other time constants). For example, [800:200:4000] refers to the TI-range [800,1000,1200,1400..4000]ms.
A first set of experiment has been performed on 5 different volunteers, using the 3T
Skyra MR scan, with the sequence with parameters specified in the table 3.1.
Nbe of Slices
TF
EF
Nbe of Segments
TA (per TI/total)
TI-range
20
12
33
4
0:45/12:45
800:200:4000
Table 3.1: Parameters of the first PASL sequence investigated for the 5 × 5 × 5 mm
resolution
Three different resolutions have been investigated : 5 × 5 × 5mm3 , 4 × 4 × 5mm3 and
3 × 3 × 2.5mm3 . For each resolution, the measurements were repeated 3 times to be able
to investigate the repeatability of the results, and to base our evaluation on statistical
data.
3.1.2
First results
The figure 3.1.1 shows an example of the different maps (from top to bottom) of the
BAT, the error-on-BAT, the rCBF, the error-on-CBF and the R2 , for the three different
resolutions (from left to right) 5 × 5 × 5mm3 , 4 × 4 × 5mm3 and 3 × 3 × 2.5mm3 . All
these maps are acquired for the same patient and represent the same slice.
There is no apparent anatomical correspondence between high and low values of the
BAT, no matter the resolution. High values of the BAT are both in the outer region (Gray
Matter and vessels) and in the inner part (White Matter and CerebroSpinal Fluid) of
the brain. The change in resolution has a low impact on the value of the BAT. However,
the error-on-BAT seems to be more important in the White Matter part of the slice,
especially for the 3 × 3 × 2.5mm3 resolution.
There is a clear anatomical correspondence between the different values of the rCBF.
The rCBF is higher in the gray matter part of the slice and way lower in the white
matter part. The gray matter and vessels are mainly located in the outer part of the
slice whereas the white matter and the cerebro-spinal fluid are located in the center.
KTH University, Guillaume GIBERT
3.1. First set of experiment
39
KTH University, Guillaume GIBERT
Figure 3.1.1: Maps of one slice of the brain for the first PASL sequence investigated.
From the left to the right, the different resolutions 5 × 5 × 5mm3 , 4 × 4 × 5mm3 and
3 × 3 × 2.5mm3 . From the top to the bottom, the BAT, the error-on-BAT, the rCBF,
the error-on-CBF, the correlation coefficient
3.1. First set of experiment
40
Here as well, the rCBF doesn’t seem to be affected by the change in resolution. The
error-on-CBF is also anatomically related since there is significantly higher error in the
center part (white matter and cerebro-spinal fluid) than in the outer part (gray matter
and vessels) of the slice. It is even more visible with the best resolution 3 × 3 × 2.5mm3 .
Finally, it seems that the correlation coefficient values are higher for bigger resolution
(5 × 5 × 5mm3 ) than for the smallest one (3 × 3 × 2.5mm3 ). For the 3 × 3 × 2.5mm3
resolution, the R2 values are higher in the high-flow region (GM and vessels) than in the
low-flow region (white matter and cerebro-spinal fluid).
The figure 3.1.2 shows, for both the BAT (left) and the rCBF(right), the relations
between the correlation coefficient and the relative errors on the parameters (at the top),
between the correlation coefficient and the values of the parameters (in the middle), and
between the relative errors and the values of the parameters (at the bottom). The figure
refers to the results for one patient at one resolution ( 4 × 4 × 5mm3 ). The results
from one patient to another, and from one resolution to another, show really similar
behaviors. As the repeatability is important, our analysis is based on this example which
is representative of the results.
For the rCBF, there is a significant correspondence between the voxels where the
R2
is good (close to 1) and the voxels where the relative error is low. Similarly, voxels
with low R2 have a high error-on-CBF. This relation is not so significant for the BAT.
Therefore, at some voxels of the slice, the R2 is really high (good fitting of the kinetic
curve by the model) but the error-on-BAT is big.
Similarly, there is a significant correspondence between voxels where the value of the
rCBF is high and where the R2 is high. On the contrary, the R2 is high in both voxels
where the BAT is high and voxels where the BAT is low.
Finally, the relative errors on the parameters, for both the rCBF and the BAT, tend
to be higher when the value of the parameter is low (especially for the rCBF).
Quantitative comparisons are now going to be performed between the different maps
for the different resolutions in order to estimate which protocol provides the best performance, and which aspects still have to be improved. The table 3.2 gives, for each
resolution, the mean values of each metric over one slice, averaged on the number of
series performed for repeatability.
There are small fluctuations in the value of the parameters (BAT and rCBF) when
KTH University, Guillaume GIBERT
3.1. First set of experiment
41
Figure 3.1.2: Correspondence of the values of the R2 in respect to the error-on-BAT
(top left), in respect to the error-on-CBF (top right), in respect to the BAT (middle
left), in respect to the rCBF (middle right), of the error-on-BAT in respect to the BAT
(bottom left) and of the error-on-CBF in respect to the rCBF (bottom right). Each point
represents one voxel of the slice investigated.
changing the resolution. Especially, both the values of the rCBF and the BAT are lower
with the 5 × 5 × 5 mm resolution. Indeed, if the size of the voxels is bigger, the measures
of the rCBF and the BAT at this voxel, are related to the signal coming from all the
KTH University, Guillaume GIBERT
3.1. First set of experiment
42
R2
BAT
Error-on-BAT
rCBF
Error-on-CBF
0.72 (0.02)
9.1 (0.5)
0.027 (0.003)
7.9 (0.4)
0.74 (0.01)
4 × 4 × 5mm3
0.80 (0.02)
11.1 (0.3)
0.0050 (0.002)
8.2 (0.6)
0.72 (0.01)
3 × 3 × 2.5mm3
0.76 (0.01)
19.7 (1.1)
0.0054 (0.005)
16.3 (1.0)
0.54 (0.02)
5 × 5 × 5mm3
Table 3.2: Average values of the BAT (s), error-on-BAT (%), rCBF (s−1 ), error-onCBF (%) and correlation coefficient over the whole slice investigated, for each of the three
resolutions. The standard deviations relative to the series performed for repeatability are
put into brackets.
brain tissues included in this voxel. That’s why these values change from one resolution
to another. However, these fluctuations are probably smoothed by our averaging of the
values over the whole slice.
Secondly, there is a significant increase of the error-on-BAT and of the error-on-CBF
when the resolution gets better (from 9.1% to 19.07% for the error-on-BAT, and from
7.9% to 16.3% for the error-on-CBF).
Finally, the correlation coefficient is quite stable from the 5 × 5 × 5mm3 resolution
(0.74) to the 4 × 4 × 5mm3 resolution (0.72). But there is a strong drop of the correlation
coefficient when improving the resolution to 3 × 3 × 2.5mm3 (0.54).
3.1.3
First conclusions
Three different protocols were investigated. Each protocol had the same acquisition time
but different resolutions, and therefore different SNRs. A couple of conclusions arose
from our study. First of all, there is a good anatomical correspondence between the
voxels where the rCBF is high, the error-on-CBF is low and the correlation coefficient
R2 is high. Those voxels are located in the outer part (GM and vessels) of the brain.
On the contrary, the voxels where the CBF is low have a high error-on-CBF and low
R2 . Those voxels are located in the inner part (WM and CSF) of the brain. There is no
such correspondence for the BAT. Moreover, in some voxels, the error-on-BAT is high
whereas the R2 is also high.
We also investigated quantitatively the different protocols with different resolutions.
It came out that when the resolution is improved (smaller size of the voxels), the errorKTH University, Guillaume GIBERT
3.1. First set of experiment
43
on-BAT and the error-on-CBF increase significantly. Moreover, the correlation coefficient
R2 undergoes a strong drop when improving the resolution from 5 × 5 × 5mm3 to 3 ×
3 × 2.5mm3 . When the resolution is improved, the uncertainty on the parameters values
increases and the correlation coefficient decreases.
3.1.4
First discussion
The main goal is to improve the resolution of the images while keeping reasonable values
of the uncertainties on the parameters, and good correlation coefficient. The previous
analysis gives the illustration that improving one aspect of the method will negatively
impact on another aspect. The main challenge of improving the PASL method will be
to find the best balance between all the inputs of this method.
Figure 3.1.3: Relation between the FOV and the sampling interval in k-space, and
between the size of the k-space and the pixel size of the image.∆kx is the sampling
interval in k-space; FOV is the Field of View; kx is the size of the k-space; ∆x is the
pixel size of the image. Figure from [24]
In the previous case, the resolution is changed from one protocol to another. If the
size of the pixel is reduced, the size of the k-space kx increases (see figure 3.1.3). From
this change in the size of the k-space can result two different adaptations:
• The number of acquisition steps (∝ ∆kx /kx ) is kept identical. In this case, the
size of the sampling interval ∆kx has to be increased. But the SNR decreases with
FOV2 [7]. In this first case when improving the resolution, the TA is kept similar,
but the SNR decreases.
• The size of the sampling interval ∆kx is kept identical. As kx increases, the number
of acquisition steps is bigger. But the FOV doesn’t change, hence the same SNR.
KTH University, Guillaume GIBERT
3.2. Protocol Parameter Settings
44
In this second case, when improving the resolution, the SNR is kept similar but
the TA increases.
In the case studied before, the TA was remaining constant, but the SNR was lowered
for the best resolutions. It explains why the uncertainty on the parameters value increased and why the correlation coefficient decreased when improving the resolution. We
could have also used the second solution and kept the same SNR. But if the TA is longer,
the patient is more likely to move during the acquisition, hence an increase of the motion
artefacts. Once again it puts forward the need for a good trade-off between the different
aspects of the method, and especially between a good SNR and a short acquisition time
(TA).
It is also possible to increase the thickness of the slice (that is to say the third
dimension of the resolution) in order to increase the SNR. However, if the thickness of
the slice is too high, the number of slices decreases, leading to a worse coverage of the
brain. From a clinical point of view, it is important to keep a high number of slices,
so the practitioner can investigate as much area of the brain as possible. Moreover, a
too important slice thickness leads to a decrease of the signal detection. It is strongly
recommended to investigate the pixel size in 2D, and to assume that cubic voxels provide
the best signal detection [1].
3.2
3.2.1
Protocol Parameter Settings
Protocol - Sequence
In order to find the best trade-off between quality of the image, acquisition time, and
other parameters, we are going to investigate three different protocols. The table 3.3
shows the value of the main parameters for the different protocols.
The main differences between each protocol are the values of the Turbo Factor (TF)
and the EPI Factor (EF), which induce different numbers of segments for each sequence.
That’s why, from now on, these protocols will be named the 4-segment, the 2-segment
and the 1-segment protocols. In the table 3.3, the TF and the EF for the 2-segment
and the 1-segment protocols are equal. According to the definition that given in the
section 3.1.1, it should lead to the same number of segments. But, an acceleration mode
GRAPPA is used. In our case, the acceleration factor is 2, which means that only every
other line in the k-space is acquired. It will reduce the acquisition time since only half
of the number of shots is needed compared to the 2-segment protocol. But, as less "information" is acquired, the results provided with this protocol could worsen. It can also
KTH University, Guillaume GIBERT
3.2. Protocol Parameter Settings
Nbe of Slices
Slice Oversampling
Resolution
TF
EF
PAT
Nbe of Segments
Bolus Duration
TA
TR
45
4-segment protocol
2-segment protocol
1-segment protocol
20
0%
3.4 × 3.4 × 4.0mm3
20
0%
3.4 × 3.4 × 4.0mm3
20
0%
3.4 × 3.4 × 4.0mm3
10
31
Off
20
31
Off
4
2
700 ms
9 min 43 s
3600 ms
700 ms
4 min 55 s
3600 ms
20
31
On
Pat mode : GRAPPA
Acc. Factor : 2
1
700 ms
2 min 33 s
3600 ms
Table 3.3: Parameters of the three different PASL protocols investigated: the 4-segment,
the 2-segment, and the 1-segment protocols.
be noticed that the TA also depends on the number of TI acquired. The values of the
TA in the table 3.3 are calculated for the acquisition of 20 TI. These values are going to
change depending on the TI-range but give a good indication of each sequence duration.
Data were acquired on 8 volunteers, of random ages, in healthy state, with the 3T
MAGNETOM Prisma (Siemens Healthcare). For each sequence, series of images were
acquired for different TI-ranges. And for each TI-range, the same series was performed
3 times identically in order to evaluate the repeatability of the method, and to be able
to base our results on statistical data.
Moreover, another step in the post-processing has been added compared to the first
measurement in the section 3.1. A cubic interpolation of the perfusion-weighted images
has been performed. By inserting one point between every other point, the edges are
smoothed, providing a better quality of the image.
3.2.2
Results - Sequence
In order to draw scientifically relevant conclusions, we will compare qualitatively the
increase and decrease of the metrics when changing the protocol, within the same patient,
and from one patient to another. But we will only compare quantitatively the metrics
within the same patient, since the values of those metrics depend on the volunteer. Finally
KTH University, Guillaume GIBERT
3.2. Protocol Parameter Settings
46
we will perform the same evaluation on two different slices of the brain to ensure that
the performance of the sequence doesn’t depend on the localization of the measurement.
The figure 3.2.1 displays the different maps (from top to bottom) of the BAT, the
error-on-BAT, the rCBF, the error-on-CBF and the R2 for each of the different protocol (from left to right): 4-segment protocol, 2-segment protocol and 1-segment protocol.
Theses maps correspond to the 12th slice from the bottom out of the 20 slices acquired.
The figure 3.2.1 shows that the BAT maps look quite similar for each protocol, even if
the BAT values seem higher in the occipital region of the brain for the 4-segment protocol
than for the other protocols. The BAT is higher in the frontal and occipital regions of
the brain and lower in the central part.
It seems that the error-on-BAT is lower with the 2-segment protocol than with the 4segment, and even lower than with the 1-segment protocol (darker blue indicates a lower
error). As it was already the case with our first results (section 3.1), the error-on-BAT
seems to be higher in the WM part of the brain, in the ventricles area.
The value of the rCBF is higher in the GM than in the WM, what confirms our first
results. The value of the rCBF, for the 4-segment protocol, seems to be averagely higher
than with the two other protocols. There is no value of the rCBF (for the 2-segment and
1-segment protocols) in the region of the occipital artery. The blood flow in this artery
is really important since it provides a great part of the blood supply to the brain. The
value of the rCBF might be so important that the fitting doesn’t manage to find suitable
values of the parameters.
The error-on-CBF seems to be significantly lower with the 2-segment protocol than
with the two other protocols. The error is more important in the WM part of the brain,
around the area of the ventricles than in the GM.
Finally, the correlation coefficient R2 seems slightly inferior with the 1-segment protocol than with the two others. As it is the case with the error maps, there is a significant
split between the voxels of the GM where R2 seems to be good (close to 1) and the voxels
of the WM where the correlation coefficient is way lower.
As observed in our first results, the figure 3.2.2 confirms the good correspondence
between the points where the error-on-CBF is low and the correlation coefficient is high.
But, on the contrary to what came out of our first study, the voxels where the errorKTH University, Guillaume GIBERT
3.2. Protocol Parameter Settings
47
on-BAT is low correspond to the voxels where the correlation coefficient is good, which
represents a good improvement.
Moreover, there is still a relation between the voxels where the rCBF is high and the
error-on-CBF is low, whereas there is no anatomical correspondence between the value
of the BAT and the error-on-BAT. Indeed, if the rCBF is lower, the kinetic curve at one
voxel will be flatter. It becomes more difficult for the fit to detect the peak of the curve
(which is proportional to the rCBF), hence a higher uncertainty on the error-on-CBF if
the value of the rCBF itself is lower. For the BAT, the error-on-BAT doesn’t depend on
the value itself.
We are now going to evaluate quantitatively the results provided by each of the three
protocols. When analysing the data acquired on each volunteer, really similar behaviour
of the metrics values are observed when changing the protocol. The tables 3.4 and 3.5
show the results for a representative patient. Two slices (the 7th and 12th out of 20)
are investigated, and the figures are resulting of an averaging over the different identical
series performed for repeatability. Different TI-ranges are investigated, but the influence
of the TI-range will be fully explored in the section 3.3. Therefore, the influence of the
protocol for a fixed TI-range is explored. The results in the table refer to protocols performed with the TI-range [500:160:2900].
Protocol
BAT
R2
Error-on-BAT
rCBF
Error-on-CBF
TA
1-segment 0.67 (0.03)
18.9 (0.6)
0.0178 (0.002)
28.3 (1.2)
0.61 (0.03) 2:02
2-segment 0.68 (0.02)
16.5 (0.6)
0.0156 (0.003)
24.9 (1.0)
0.67 (0.02) 3:56
4-segment 0.73 (0.03)
15.7 (0.8)
0.0243 (0.005)
24.3 (1.3)
0.66 (0.02) 7:46
Table 3.4: Average values of the BAT (s), error-on-BAT (%), rCBF (s−1 ), error-onCBF (%) and correlation coefficient over the whole slice investigated, for each of the
three protocols for the 7th slice. The standard deviations relative to the series performed
for repeatability are put into brackets.
The tables 3.4 and 3.5 show the values of the different metrics (BAT, error-on-BAT,
rCBF, error-on-CBF, R2 ) for the three different protocols (1-segment, 2-segment and
4-segment). Those tables refer respectively to investigation of the 12th and the 7th slices.
KTH University, Guillaume GIBERT
3.2. Protocol Parameter Settings
Protocol
BAT
48
R2
Error-on-BAT
rCBF
Error-on-CBF
TA
1-segment 0.62 (0.03)
21.4 (1.6)
0.0168 (0.012)
27.7 (1.6)
0.60 (0.02) 2:02
2-segment 0.61 (0.04)
19.2 (1.1)
0.0149 (0.011)
23.5 (1.4)
0.66 (0.02) 3:56
4-segment 0.62 (0.03)
20.0 (1.8)
0.0200 (0.008)
25.2 (1.6)
0.62 (0.05) 7:46
Table 3.5: Average values of the BAT (s), error-on-BAT (%), rCBF (s−1 ), error-onCBF (%) and correlation coefficient over the whole slice investigated, for each of the three
protocols for the 12th slice. The standard deviations relative to the series performed for
repeatability are put into brackets
The value of the BAT is not significantly affected by the different protocols, no matter
the slice investigated. The error-on-BAT is slightly lower (2 to 3% lower) with the 2segment and 4-segment protocols than with the 1-segment protocol. Our visual analysis
of the rCBF maps is confirmed by the quantitative results.
The value of the rCBF is averagely higher with the 4-segment protocol than with
the two other protocols (from 0.0178 s−1 and 0.0156 s−1 to 0.0243 s−1 for the first slice
investigated, and from 0.0168 s−1 and 0.0149 s−1 to 0.0200 s−1 for the second slice) (see
figure 3.2.1). No relevant explanation has been found to explain this increase in the value
of the rCBF with the 4-segment protocol. The error-on-CBF is quite similar with the
4-segment and the 2-segment protocol, even if the 2-segment protocol provides slightly
lower error-on-CBF in the second slice (23.5% compared to 25.2%). The error-on-CBF
is significantly higher with the 1-segment protocol (3 to 5% higher). It is probably due
to the use of the PAT accelerator which induces the acquisition in the k-space of only
half of the points compared to the 2-segment and 4-segment protocols.
Finally the correlation coefficient R2 is higher with the 2-segment protocol compared
to the 1-segment protocol (from 0.67 to 0.61 for the first slice, and form 0.66 to 0.60 for
the second slice).
3.2.3
Discussion - Sequence
It is quite obvious from this evaluation that the 1-segment protocol doesn’t provide as
good performance as the two other protocols. The 2-segment and the 4-segment protocols, despite slightly better error-on-CBF and R2 for the 2-segment, provide similar
performances. But those performances have to be put into perspective with the acquisiKTH University, Guillaume GIBERT
3.2. Protocol Parameter Settings
49
tion time (TA). The 2-segment is twice as fast as the 4-segment protocol. Therefore, even
if those two protocols provide quite similar uncertainties, the best trade-off is offered by
the 2-segment protocol.
It has to be underlined that, the longer the duration of the sequence, the more likely
the patient is to move during the acquisition. The volunteer, whom results have been
presented in the tables 3.4 and 3.5 was quite young. Therefore the impact of a longer
sequence is not so significant since he was able to stay motionless for a long time. On
the contrary, the influence of a longer sequence would appear more significantly for an
older patient or for children who are not able to stay still so long. For example, the
table 3.6 shows the results of the 2-segment and the 4-segment protocols for an older
volunteer (76 year old). The difference between the uncertainties from one protocol to
another is much more significant than for a younger patient: +5% in the error-on-BAT,
+8.3% in the error-on-CBF and -0.14 for the R2 . From a clinical perspective, it is more
likely that older patients will have to undergo measurements of the brain perfusion with
this method. Indeed, the pathologies related to an abnormal blood flow detected by
this method (stroke, tumors, neurodegenerative diseases) are more likely to appear in
elderly people. That’s why the TA plays an important role in the investigation of the
best protocol.
Protocol
BAT
Error-on-BAT
rCBF
Error-on-CBF
R2
TA
2-segment
0.95
23.5
0.0192
43.0
0.42
3:56
4-segment
0.88
28.6
0.0216
53.6
0.37
7:46
Table 3.6: Average values of the BAT (s), error-on-BAT (%), rCBF (s−1 ), error-onCBF (%) and correlation coefficient over the whole slice investigated, for th 2-segment
and 4-segment protocols for the 12th slice for an elder patient. The standard deviations
relative to the series performed for repeatability are put into brackets
Regarding the different results which came out of this chapter, it is suggested to use
the 2-segment protocol. This protocol provides the best trade-off between low uncertainty
on the parameter, good correlation coefficient and short acquisition duration.
Apart from the protocol itself, one of the major aspects of the PASL method is
the range of TI acquired. Indeed, if the number of TI acquired increases, the TA will
increase as well. Depending on the sampling of the TI-range, the quality of the fitting
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3.2. Protocol Parameter Settings
50
might change, as well as the uncertainty on the parameters. All these points are going to
be investigated in the next section in order to be able to suggest an optimized TI-range.
3.2.4
Conclusions - Sequence
The new protocols investigated confirm the correspondence between voxels where rCBF
is high, error-on-CBF is low and R2 is high. Those voxels are located in the GM. There
is now a good correspondence between voxels where the error-on-BAT is low and the
voxels where R2 is high. However the uncertainty on the BAT doesn’t depend on the
value of the BAT itself.
It appears that the BAT value is not affected by the different protocols used. The
error-on-BAT is slightly better with the 2-segment and 4-segment protocols. The erroron-CBF and the R2 are significantly lower with the 2- and 4-segment protocols than with
the 1-segment protocol, and slightly better with the 2-segement than with the 4-segment.
Therefore, the 2-segment protocol is kept as the optimized set of parameters.
KTH University, Guillaume GIBERT
3.2. Protocol Parameter Settings
51
KTH University, Guillaume GIBERT
Figure 3.2.1: Maps of one slice of the brain for the three PASL protocols investigated.
From the left to the right, the different protocols: 4-segment, 2-segment and 1-segment
protocol. From the top to the bottom, the BAT, the error-on-BAT, the rCBF, the erroron-CBF, the correlation coefficient
3.2. Protocol Parameter Settings
52
Figure 3.2.2: For the two-segment protocol, correspondence of the values of the R2
in respect to the error-on-BAT (top left), in respect to the error-on-CBF (top right), in
respect to the BAT (middle left), in respect to the rCBF (middle right), of the erroron-BAT in respect to the BAT (bottom left) and of the error-on-CBF in respect to the
rCBF (bottom right). Each point represents one voxel of the slice investigated.
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3.3. Optimization of the range of TI
3.3
53
Optimization of the range of TI
As we explained in the section 2.2.2, several pairs of Tag/Control images are acquired for
different Inversion Times (TI). The Inversion Time is the duration between the moment
we finish tagging the blood and the moment when we start imaging in the region of
interest. With the value of the magnetization at each voxel for each TI, the kinetic curve
is obtained, which after fitting with the model, give access to the information on the
perfusion. Performing a multi-TI acquisition enables to quantify the perfusion without
too much uncertainty (which would be the case with only one TI).
Therefore, it appears important to investigate the influence of the TI-range on the
efficiency of the PASL method. Two aspects of the TI-range are going to be explored:
the width of the TI-range (the width between the smallest and the biggest TI) and its
sampling (the interval between two successive TI).
3.3.1
Protocol - TI range
Measurements were performed on 8 healthy volunteers of random ages with the 2-segment
protocol. For each TI-range, three identical series were performed to study the repeatability of the method and to base our evaluation on statistical data. First different series
were acquired with a constant sampling interval and different widths. Then, other series
were acquired with another sampling interval and the same different widths. The different TI-ranges (in milliseconds) investigated are:
• 410:120:3890
• 410:150:3860
• 410:120:3410
• 410:150:3410
• 410:120:2690
• 410:150:2660
In order to perform the multi-TI acquisition, a multi-TI mode is used on the software
of the MR scan. This mode sets a certain number of constraints in the choice of the TI.
Therefore, the user is not completely free to set the TI-range as wanted. The sampling
interval and the width of the range are somehow related. That’s why, we cannot obtain
exactly the same width of TI-range with the two different samplings. However, for our
analysis, we will assume that the differences between 3890ms and 3860ms as well as
between 2690ms and 2660ms can be neglected.
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3.3. Optimization of the range of TI
3.3.2
54
Results - TI range
A good repeatability of the qualitative results from one patient to another is obtained.
Therefore, from a qualitative point of view, the results presented in the table 3.7 are
representative of the data acquired in different volunteers. The results can only be
quantitatively investigated within the same patient, since the value of the metrics depends
on each volunteer (further details about this point will be given in the chapter 4).
TI-range
BAT
Error-on-BAT
rCBF
Error-on-CBF
R2
TA
410:120:3890
0.76 (0.03)
14.7 (1.0)
0.0104 (0.002)
22.7 (1.5)
0.58 (0.3)
8:44
410:120:3410
0.71 (0.04)
16.2 (0.8)
0.0108 (0.003)
24.4 (1.4)
0.57 (0.3)
6:48
410:120:2690
0.71 (0.04)
16.3 (1.1)
0.0109 (0.004)
29.3 (2.8)
0.59 (0.5)
4:17
410:150:3860
0.77 (0.02)
15.6 (1.1)
0.0111 (0.003)
24.6 (1.2)
0.59 (0.01)
5:08
410:150:3410
0.75 (0.04)
17.7 (1.5)
0.0134 (0.005)
30.4 (0.8)
0.55 (0.02)
4:30
410:150:2660
0.75 (0.04)
18.8 (1.0)
0.0162 (0.008)
34.6 (2.1)
0.56 (0.03)
3:25
Table 3.7: Average values of the BAT (s), error-on-BAT (%), rCBF (s−1 ), error-on-CBF
(%) and correlation coefficient over the whole slice investigated, for different TI-ranges
investigated. The standard deviations relative to the series performed for repeatability
are put into brackets
To investigate the influence of the width of the range, the three first lines of the table
3.7 are compared between each other, as well as the three last lines. To evaluate the
influence of the sampling interval, the first line is compared with the fourth, the second
with the fifth, and the third with the sixth, so only one parameter (width or sampling)
is changing while the other stays fixed.
Width of the TI-range
There is no significant variation of the BAT value when changing the width of the
range, no matter the sampling interval. There is a significant increase of the error-onBAT when the width of the range decreases (from 14.7% to 16.3% with the first sampling
interval, and from 15.6% to 18.8% for the second sampling interval).
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3.3. Optimization of the range of TI
55
With the first sampling interval, the rCBF value slightly increases when the width
of the range decreases. It increases more significantly with the second sampling interval
(from 0.011 to 0.0162 s−1 ). No matter the sampling interval, there is also a strong increase of the error-on-CBF when the TI-range is shortened (from 22.7% to 29.3% for the
first sampling interval, and from 24.6% to 34.6% for the second one).
Finally the correlation coefficient doesn’t seem to be affected by the changes of the
TI-range width, no matter the sampling interval.
Sampling interval of the TI-range
No matter the width of the TI-range, the BAT value is not affected by the change
in the sampling interval. For each width of the TI-range, the error-on-BAT slightly increases when the sampling interval increases (1 to 2.5% higher).
The value of the rCBF also slightly increases when the sampling interval increases.
The increase is even more significant when the width of the TI-range decreases. Therefore, for the widest range, the rCBF increases from 0.0104 s−1 for the 120ms interval
to 0.0111 s−1 for the 150ms interval. It increases from 0.0109 s−1 to 0.0162s−1 for the
shortest range. The error-on-CBF significantly increases with the sampling interval. For
the widest TI-range, the error-on-CBF soars from 22.7% to 24.6%, from 24.4% to 30.4%
for the intermediate range width, and from 29.3% to 34.6% for the shortest TI-range.
Finally, the correlation coefficient R2 doesn’t seem to be affected by the variation of
the sampling interval of the TI-range.
The acquisition time (TA) is affected by the TI-range since it is almost proportional
to the number of TI acquired (not exactly because the TR can actually be a little bit
adjusted). That’s why, with the 2-segment protocol, the widest range with the smallest
interval requires 8’44", the widest range with the biggest interval requires 5’8", whereas
the smallest range with the biggest interval only needs 3’25".
3.3.3
Discussion - TI range
The value of the BAT is not influenced by the modifications in the TI-range, whereas
the rCBF value tends to increase when the width of the range gets shorter. Indeed,
as it is illustrated on the figure 3.3.1, if the width of the TI-range is shorter, there are
fewer points in the decay part of the kinetic curve. The fitting cannot appreciate the
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3.3. Optimization of the range of TI
56
real convexity of the decay part and misestimates its slope. But, as the rCBF value is
related to the peak of the kinetic curve, an approximate fit of the decay part can lead
to an overestimation or underestimation of the real value of the rCBF. And as we are
trying to provide quantified values of the rCBF in this project, this approximation is
significant. Therefore, it is important to put the emphasis on the width of the TI-range
when concluding on the optimized one.
Figure 3.3.1: Illustration of the difference in fitting the kinetic curve at one voxel,
depending on the width of the TI-range. X and Y are the coordinates of the voxel
studied on the slice’s map.
On the contrary, the BAT is not affected by changes in the TI-range. Indeed, its
value is related to the starting point of the increasing part of the curve. That’s why the
width of the range has no impact on the BAT value. A better sampling interval should
enable to find a more precise value, but the variation of the interval investigated is not
important enough to show significant modifications of the BAT value.
From the first set of experiment to the ones performed with the 2-segment protocol
with different TI-ranges, the quality of the maps, especially of the BAT maps, has been
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3.3. Optimization of the range of TI
57
considerably improved and the TA has been significantly reduced. The improvement of
the BAT maps quality is not only due to the switch to 2-segment protocol, but especially to the fact that the starting point of the TI-range has been lowered. Indeed, the
first TI-ranges investigated were starting at 800ms. It corresponds to usual values of
the BAT. It was complicated for the fit to find the intersection between the null part
and the increasing part of the curve since the first point acquired was really close to
this intersection. By lowering the first TI of the range, the number of points before the
intersection has been increased. The real value of the BAT can be found with more
precision. Switching the first TI of the range from 800ms to 400 or 500ms contributed
significantly to an improvement of the BAT maps and the uncertainty on the BAT values.
The widest range with the smallest sampling interval has provided logically the lowest
uncertainties on the parameters. As seen before, it enables to obtain relevant values of
the rCBF, which is also important from a quantification perspective. However, it has to
be balanced with the important TA of these ranges.
There is no possibility to quantify in what extent a shorter TA has more or less influence than a wide, more-sampled TI-range. Especially because the TA will not have the
same impact depending on the patient. Some of them can stay still no matter the duration of the acquisition, whereas others will be more likely to move when it gets longer.
Therefore, we have to suggest an optimized TI-range finding the best trade-off between
performance and acquisition time.
Our results have suggested to give more importance to the width of the range than
to the sampling interval. Moreover,it seems important to reduce as much as possible
the TA. Therefore, the TI-range [410:120:3890] has a too long TA. The two TI-ranges
[410:120:3410] and [410:150:3860] provides similar results. But we suggest to choose the
second one [410:150:3860] which has a significantly shorter TA (5:08 compared to 6:48).
It also respects our putting more importance on the width than the sampling since it as
an important width but a relatively high sampling interval.
3.3.4
Conclusions - TI range
The shorter the width of the range, the bigger the error-on-BAT and the error-on-CBF.
The rCBF value is also affected by the width of the TI-range since it increases when
the width of the range is reduced. However the value of the BAT and the correlation
coefficient R2 are not affected by the change in the width of the TI-range.
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3.4. Improvement of the Numerical Model
58
Secondly, no matter the width of the TI-range, the error-on-BAT and the error-onCBF always increase when the sampling interval increases. But the increase of the errors
is more important when the width of the range decreases than when the sampling interval
increases.
Finally, the TA is closely related to the number of TI acquired. A wider range, or a
smaller sampling interval leads to a longer acquisition time. On the contrary, a narrower
range or a bigger sampling interval leads to a shorter acquisition time.
The optimized TI-range that is suggested after this investigation is therefore:
[ 410 : 150 : 3860 ] ms
3.4
Improvement of the Numerical Model
Until now, the kinetic curve has been fitted with a two-parameter model defined in section 2.3.1. Based on a visual analysis, it has been noticed that the fitting of the decay
part of the kinetic curve wasn’t always performed accurately. As the curve 3.4.2 illustrates it, the convexity of the decay part of the kinetic curve doesn’t match perfectly the
convexity of the decay part of the model. It leads to a misestimation of the quantified
value of the rCBF, which is related to the peak value of the curve.
As we are trying to quantify the regional cerebral blood flow, it is important to improve the fitting in order to get a more reliable value of the rCBF. The convexity of the
decay part of the curve is related to the relaxation time constant T1ef f described in the
model. If the value of this constant is kept fixed for each measurement, the decay part
of the fitting model cannot be adjusted precisely to the experimental kinetic curve.
That’s why a new fitting model with three parameters has been investigated. The
effective relaxation time T1ef f is now set as the third parameter of the model. Everything
else remains the same. T1ef f gives information on how fast the spins go back to their
equilibrium position.
3.4.1
Results - Model
We analyse the influence of the new model with the results of a representative set of data.
The figure 3.4.2 illustrates the different fittings with the two-parameter model and with
the three-parameter model. The overall fitting is more accurate with the three-parameter
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3.4. Improvement of the Numerical Model
59
Figure 3.4.1: Influence of the parameter T1 on the shape of the numerical model
model. It is confirmed by the difference in the value of the correlation coefficient. From
the two-parameter to the three-parameter model, R2 increases from 0.76 to 0.97 for the
voxel investigated. Moreover, the absolute value of the rCBF given by the fitting increases from 0.052 to 0.10 s−1 . The BAT value is also affected by the new model, since
it increases from 0.59 to 0.72 s.
If we look at the modifications over the whole slice, the correlation coefficient map
for the three-parameter model has higher values than the map for the two-parameter
model. It is confirmed by the average value of the correlation coefficient over the whole
slice, which increases from 0.66 to 0.70.
The rCBF map confirms what was observed for one voxel. The value of the rCBF
is affected by the fitting model used. The rCBF value is underestimated by the twoparameter model, since the rCBF map for the three-parameter model seems to have
higher values of the rCBF. It is also confirmed by the average value of the rCBF over
the whole slice which increases from 0.013 for the two-parameter model to 0.016 for the
three-parameter model.
The BAT map is also affected by the change in the fitting model. From a visual
analysis of the BAT maps, it seems that the three-parameter model leads to lower values
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3.4. Improvement of the Numerical Model
60
Figure 3.4.2: Difference in fitting the kinetic curve at one voxel of the slice, using
respectively the two-parameter model (at the top) and the three-parameter model (at
the bottom).
of the BAT but these differences are really slight. Over the whole slice, the average value
of the BAT decreases from 0.73 to 0.71.
Finally, both the error-on-CBF and the error-on-BAT seem to be lower with the twoparameter than with the three-parameter model. Quantitatively, over the whole slice, the
average value of the error-on-CBF increases from 21.74 with the two-parameter model
to 23.29 with the three-parameter model. The error-on-BAT increases from 13.82 for the
two-parameter model to 14.65 for the three-parameter model.
3.4.2
Discussion - Model
Now that a three-parameter model is used, the fitting provides two extra pieces of information: the T1ef f value and the uncertainty on this value. Therefore, for each slice of
the brain, two extra maps are obtained. Due to a lack of time, these maps haven’t been
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3.4. Improvement of the Numerical Model
61
investigated, nor if the T1ef f map could be potentially useful clinically. It would also be
possible to increase even more the number of parameters of the model, resulting is even
more reliable and accurate values of the rCBF and the BAT. However, increasing the
number of parameters would lead to an increase of the fitting complexity. The fit would
require more time and the other parameters might not be useful information for a clinical diagnosis. A three-, four- and five-parameter model were investigated in the article
[22] and only insignificant differences between the different models came out of this study.
When the fitting algorithm tries to fit the kinetic curve with the model, it adapts the
value of each parameter in order to make the fitting as accurate as possible. So if the
number of parameters is bigger, there are more degrees of freedom to adjust the curve to
the model. The resulting fitting will be better. But the uncertainty on each parameter is
going to be bigger because the constraint on each variable is more important. If a model
has an infinite number of parameters, it is possible to perfectly fit the curve, but there
will also be infinite combinations of parameters resulting in the perfect fitting. Thus, the
uncertainty on each parameter will be more important.
3.4.3
Conclusions - Model
The new three-parameter model provides a more accurate fitting of the kinetic curve for
each voxel. Moreover the misestimation of the quantified rCBF value is corrected by
the new model since the decay part is fitted more accurately. The change in the model
also affects the BAT values. However, we have noticed that the error-on-BAT and more
significantly the error-on-CBF are higher with the three-parameter model.
But as the final goal of this method is to quantify the cerebral perfusion, the threeparameter model is chosen because it provides more reliable results of the CBF and the
BAT. Despite a slightly higher uncertainty on the parameters, the rCBF and BAT values
are more accurate.
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Chapter 4
Evaluation of the reliability of the
data
From a clinical perspective, it is important that the clinicians are aware of how much
they can rely on the results provided by the ASL method. If the patient moves during
the measurement, the values of the rCBF and the BAT can be significantly altered. This
alteration cannot be quantified, that’s why a criterion has to be implemented in order to
determine if the results are reliable or not.
4.1
Implementation of a criterion
Several metrics can be used to measure the reliability of the rCBF and BAT values: the
correlation coefficient, the error-on-BAT and the error-on-CBF. If the correlation coefficient is high (close to 1), it means that the fitted curve (provided by the algorithm) is
close to the kinetic curve (extracted from the measurement), but it doesn’t give information on the uncertainty on the parameters value. Theoretically, the fitted curve can
fit perfectly the kinetic curve but along with a high value on the parameters uncertainty.
On the contrary, the fitted curve can be only approximately fitting the kinetic curve, but
with low uncertainty on the parameters value.
From now on, we are going to work on one slice of the brain to explain the implementation of the criterion. For this slice of the brain, we investigate the three maps of the
error-on-BAT, of the error-on-CBF and of the correlation coefficient. The figure 4.1.1
represents how the metrics values at each voxel are distributed throughout the whole
map. For example, on the error-on-CBF distribution, a high peak around 15% means
that, at a high number of voxels, the value of the error-on-CBF is 15 %. The final goal
is to be able to provide to the clinician enough information so that he can figure out
62
4.1. Implementation of a criterion
63
how the perfusion maps provided are reliable. The first idea was to implement on these
distributions an arbitrary threshold which would separate the reliable voxels and the
unreliable ones and then to provide other maps of the brain displaying only the voxels
selected by the criterion.
Figure 4.1.1: Distribution of the values of the Correlation coefficient, the error-on-BAT
and the error-on-CBF for one slice. If the value at R2 = 0.9 is 400, it means that at 400
voxels of the map,R2 = 0.9
To implement the criterion on each of these three metrics, each distribution is first
fitted with a non-central beta law[32].
f (x) =
∞
X
1 λ 2 −λ/2 xa+j−1 (1 − x)β−1
e
j! 2
B(α + j, β)
(4.1)
j=0
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4.1. Implementation of a criterion
64
where B is the beta function,
Z
B(α + j, β) =
1
tα+j−1 (1 − t)β−1 dt
(4.2)
0
and α and β are shape parameters of the law, and λ is the non-centrality parameter. For the correlation coefficient distribution, the threshold criterion is going to be the
value of R2 where the distribution is maximum minus the standard deviation of this fitted distribution. For the error-on-CBF and the error-on-BAT distributions, the criterion
is going to be the maximum plus the standard deviation since the reliable voxels have a
low uncertainty but a high correlation coefficient.
The figure 4.1.2 illustrates the different steps of the criterion implementation with the
example of the R2 distribution. The distribution is fitted with the non-central beta law
(red curve). The maximum of this red curve minus its standard deviation gives access
to the criterion (blue line). The bottom left map is the initial map before thresholding.
The top right map is the map once the unreliable voxels have been cut. Finally, the
bottom right map is a binary map representing the reliable voxels kept by the criterion
(red) and the unreliable cut by the criterion (green).
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4.2. High-flow Vs Low-flow regions
65
Figure 4.1.2: Implentation of a criterion to evaluate the goodness of the data. Fitting of
the R2 distribution by a non-central beta law (top left), map of the correlation correlation
before thresholding (bottom left), and after the thresholding (top right). Binary map of
the cut and kept voxels (bottom right).
4.2
High-flow Vs Low-flow regions
One question arises from the implementation of the criterion: should this criterion be
independent of the patient or not? In the previous paragraph, the criterion is dependent
of the patient since the maximum and the standard deviation are dependent on the distribution. As the figure 4.1.1 illustrates it, the shape of the distribution really depends
on the patient. If the patient is older for example, the kinetic curve is flatter and harder
to fit. It can result in higher uncertainty on the parameter. Moreover, it has been noticed 3.1 that the voxels with high uncertainty and low reliability are located mainly in
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4.2. High-flow Vs Low-flow regions
66
the WM part of the brain, in the ventricle where the Cerebro Spinal Fluid (CSF) flows.
Therefore, the shape of the distributions will be highly related to the proportion of white
matter and gray matter in the brain, and to the size of the ventricles. For example with
the correlation coefficient, if the proportion of white matter is big, the distribution is going to be flatter and wider than for a small proportion of white matter. This proportion
depends on the patients, who can have different ventricle sizes, and also on the slice of
the brain which is under investigation. That’s why it seems more relevant to implement
a patient-depending criterion.
The value of the perfusion in the low-flow regions is hardly significant compared to
its value in the high-flow regions. As seen before, the proportion of the white matter
impacts the distribution of the different metrics. Therefore it seems more relevant to base
our analysis only on the high-flow region of the brain and to characterize the cerebral
perfusion only in this area. We noticed that the first criterion (with the non-central beta
law) provides a good demarcation between the high-flow and the low-flow regions for
each of the three metrics distributions. Basically, the arbitrary criterion that was to be
used in a first time, seems to provide a good threshold limit between the two regions of
the brain (gray matter and vessels, and white matter and cerebro-spinal fluid).
Our second idea was to use this criterion to separate the voxels of the high-flow region and the voxels of the low-flow region and then, to provide another information to
characterize the results for the high-flow voxels only. This final information would be
given to the clinician and would enable him to figure out how much he can rely on the
results provided by the method. Once the high-flow part of the distributions isolated,
the mean and the standard deviation of this part is calculated. Those two metrics are
the final two pieces of information provided. They enable to have a good overview of
how reliable the value at those voxels is.
Now, we may wonder if this process should be applied three times to each of the
three distributions (error-on-CBF, error-on-BAT and correlation coefficient). During the
analysis of our first set of experiment (see figure 4.1.1) we have noticed that at some
voxels, the error on the parameters was low but the correlation coefficient wasn’t close
to one. And on the contrary, at some voxels the correlation coefficient could be good but
with high error on the parameters. So it seemed necessary to apply the criterion process
to the three distributions. But when improving the method, the figure 3.2.2 showed that
there is now an almost linear relation between the correlation coefficient and the error-on
the parameters. The voxels with good correlation coefficient correspond to the voxels
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4.2. High-flow Vs Low-flow regions
67
Figure 4.2.1: Different steps in evaluating the goodness of the results. First, the limit
between the GM part and the WM part of the R2 distribution is determined. The
GM part is selected, and its mean and standard deviation are given as indicators of the
goodness of the data.
with low error. Therefore, no matter on which distribution the criterion is applied, the
voxels selected will be the same. It is sufficient to apply this process to only one of three
distributions. It has been decided to choose the correlation coefficient which gives a more
global evaluation of the goodness of the data.
The figure 4.2.1 illustrates the overall process to characterize the goodness of the
results. First the part of the R2 distribution corresponding to the gray matter is selected.
Secondly, the mean and the standard deviation of the remaining part are calculated and
provided to give information on the reliability and the goodness of the data.
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4.4. Conclusion
4.3
68
Discussion
When implementing the criterion to evaluate the goodness of the results, a lot of steps
have been performed arbitrarily. For example, a non-central beta law has been chosen to
fit the distributions of the three metrics. It hasn’t been proved that this law is the closest
to the classic shape of distribution encountered when performing the method. Moreover,
it has been stated that the threshold implemented from this law appears to be a good
demarcation between the high-flow region and the low-flow region of the brain. But this
statement actually comes out from our observations on all our data acquired. But it
obviously needs to be verified with more data.
Finally it would be important to get in contact with clinicians to understand their
needs and what kind of information they need, and to discuss the requirements for a
good criterion and the goodness of the data.
4.4
Conclusion
The final criterion provided are the mean and the standard deviation of the high-flow part
of the correlation coefficient distribution. They give a good illustration of the goodness
of the results. For example, a high mean with a small standard deviation implies that all
the values of the correlation coefficient are concentrated close to 1 and that the results
are really reliable.
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Chapter 5
Ending
5.1
Discussion and Perspectives
In order to improve the robustness of the ASL method, it was often necessary to arbitrarily state a trade-off between different aspects of the method (the acquisition duration,
the resolution, the range of inversion times...). The improvement of one of these aspects
often lead to the worsening of another. It is difficult to quantify the impact of certain
aspects of the method on the results. For example, the influence of a longer acquisition
time will probably differ from one patient to another.
The number of patients investigated seems to be sufficient to consider our results
reliable from a scientific point of view. However, it could be interesting to investigate
the impact of people characteristics (age, gender) on our results. It could enable to have
a more quantized idea of the influence of the acquisition duration, and to find a less
arbitrary trade-off between the different aspects of the method.
It has also been noticed that the reliability of the results gets lower when the CBF
decrease. Indeed, for a low CBF, the kinetic curve is flatter, making it harder to perform
the fitting. So we may wonder how the method would react with extremely low CBF, for
example in pathological cases related to abnormally slow blood flow. Therefore, I could
be interesting to perform images acquisition on non-healthy patients to figure out how
the method can face abnormal values of the different parameters.
Our conclusions were based on average values of the parameters over brain slices.
Even if this method is scientifically relevant, the CBF and BAT values appeared to fluctuate depending on the brain area. Especially the outer region with grey matter provides
higher CBF values than the inner part of the brain with white matter and cerebro-spinal
69
fluid. It could be interesting in the future to perform regional investigations of the brain.
However, during all this project, the relatively low speed of the fitting algorithm
tended to limit our investigations. It was especially difficult to investigate every slice of
the brain because it would have required too much time. Similarly, it appeared complicated to perform the regional analysis of the brain because of a too long fitting time
needed. However, the fitting algorithm in C language that we started to work on, could
provide a really faster fitting process. One of the big outlook of this project would be to
enhance this algorithm and to implement it. It could enable to perform deeper investigations of the map.
Moreover, it would also be possible to implement the post-processing and the calculation of the CBF and BAT maps directly in the in-line MR scan (Until now, it has
been performed after the image acquisition on a separate computer). It could enable to
perform on-live feedbacks and allow the clinician to adapt the image acquisition to the
first CBF and BAT maps obtained. If an abnormal blood flow is detected, he will be
able to perform a second acquisition in a more specific region of the brain.
Finally, the next big step of this project is to investigate the su-bmethod PCASL
(pseudo-continuous ASL) the same way that we investigated the PASL (pulsed ASL) in
this project. The PCASL method is supposed to provide a better Signal-to-Noise Ratio,
which could improve the results. But this sub-method hasn’t been fully implemented
yet.
5.2
Conclusion
During this project we attempted to make the ASL method more robust. Among the
various available ASL methods, the pulsed ASL was investigated. An optimized set of
parameters was suggested, referring as the "2-segment protocol". It was demonstrated
that this protocol, among those investigated, provided the best trade-off between performance (reliable values of the regional Cerebral Blood Flow and the Bolus Arrival Time),
acquisition time, resolution and SNR.
We also evaluated the influence of the range of inversion times used to acquire the
images. It appeared that both the width and the sampling interval of this range affect
the value of the rCBF and the BAT. As the cerebral perfusion is quantified through
these metrics, we widely explored the TI range until being able to suggest an optimized
TI-range to provide reliable values of the perfusion within a reasonable acquisition time.
The suggested TI-values range from 400 ms to 3900 ms, sampled every 150 ms.
A numerical model and a fitting algorithm were used to extract the information on
the perfusion from the images acquired. The comparison of a two-parameter and a threeparameter model revealed that the three-parameter model provided a better fitting of
the kinetic curve to the model, resulting in more reliable values of the rCBF and the BAT.
Finally, a metric and a criterion were implemented to evaluate the goodness of the
data. As it is difficult to quantify how much the quantitative value of the perfusion is
affected by movements of the patients and other artefacts, it is important for the clinician or the user to have an error metric on the reliability of the results provided. To
deliver information on the results level of confidence, we investigated the distribution of
correlation coefficients for one single slice. A non-central beta metric enabled to select
the voxels of the high-flow region of the brain (related to gray matter). Secondly, the
mean and the standard deviation of the high-flow part of the R2 distribution were given
to inform on the reliability of the data. A high mean with a low standard deviation did
indicate that all the values of the correlation coefficient are close to 1, hence a good set
of data.
Several aspects of the ASL method still remain to be explored for a better and robust
implementation in clinical routine. Moreover, the fitting algorithm speed has to be
optimized to be able to perform an in-line calculation during the MR acquisition. The
PCASL method also has to be investigated since it can provide a better SNR compared to
the PASL method.The mid-term aim is that the non-invasive, non-contrast agent based
ASL method can substitute the contrast agent MR perfusion.
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Appendix
75
SLICE 12
DISTRIBUTION
BAT
mean
error on BAT
std
mean
CBF
std
mean
error on CBF
std
mean
R2
std
mean
std
Patient Serie
6
4
0,87
0,45
15,88
16,22
0,07
0,29
25,43
20,05
0,5
0,27
EPI 25
6
6
6
0,87
0,85
0,86
0,44
0,44
0,44
16,27
17,28
16,74
16,4
17,37
16,69
0,06
0,07
0,07
0,25
0,41
0,56
25,29
26,85
26,34
18,83
20,64
20,14
0,48
0,47
0,48
0,26
0,27
0,27
3.4x3.4x4.0 800:100:3200
3.4x3.4x4.0 800:100:3200
MOY
STD
0,86
0,01
0,44
0,00
16,54
0,52
16,67
0,44
0,068
0,004
0,38
0,12
25,98
0,65
19,92
0,67
0,48
0,01
0,27
0,00
0,88
0,89
0,87
0,92
0,46
0,46
0,44
0,47
17,38
17,5
17,48
18,28
16,77
16,66
16,79
17,64
0,10
0,10
0,08
0,09
0,82
0,53
0,34
0,44
27,96
28,22
28,89
31,34
20,15
20,19
20,81
21,14
0,54
0,54
0,53
0,51
0,28
0,27
0,28
0,27
0,89
0,02
0,46
0,01
17,66
0,36
16,97
0,39
0,093
0,008
0,53
0,18
29,10
1,34
20,57
0,42
0,53
0,01
0,28
0,01
0,96
0,44
14,45
15,4
0,08
0,3
26,85
18,38
0,58
0,26
0,96
0
0,44
0
14,45
0
15,4
0
0,080
0,000
0,3
0
26,85
0
18,38
0
0,58
0
0,26
0
no all-Tis method
2 SEGMENTs
6
6
6
6
3.4x3.4x4.0 800:150:3200
3.4x3.4x4.0 800:150:3200
5
6
7
1
2
3
8
MOY
STD
7
1
3.4x3.4x4.84800:150:3200
3.4x3.4x4.84800:150:3200
MOY
STD
all-Tis method
2 SEGMENTs
8
11
0,64
0,29
18,1
15,82
0,01
0,05
32,4
22,27
0,62
0,25
EPI 25
8
8
12
13
0,66
0,67
0,26
0,26
18,65
15,4
16,2
14,65
0,01
0,02
0,07
0,1
36,14
31,315
21,93
21,86
0,62
0,65
0,25
0,27
3.4x3.4x4.0 500:60:1880
3.4x3.4x4.0 500:60:1880
MOY
STD
0,66
0,01
0,27
0,01
17,38
1,42
15,56
0,66
0,013
0,005
0,07
0,02
33,29
2,07
22,02
0,18
0,63
0,01
0,26
0,01
0,69
0,69
0,69
0,69
0,29
0,29
0,29
0,29
15,47
15,79
14,67
14,12
15,41
16,23
15,24
14,16
0,01
0,01
0,01
0,01
0,06
0,05
0,04
0,02
25,87
24,86
23,61
24,28
20,17
19,4
19,12
19,6
0,66
0,66
0,69
0,69
0,26
0,26
0,25
0,25
0,69
0,00
0,29
0,00
15,01
0,66
15,26
0,74
0,010
0,000
0,04
0,01
24,66
0,83
19,57
0,38
0,68
0,02
0,26
0,01
0,76
0,76
0,3
0,3
14,63
14,37
14,76
14,61
0,01
0,01
0,04
0,02
27,45
27,24
20
20,02
0,69
0,68
0,24
0,25
0,76
0,00
0,30
0,00
14,50
0,13
14,69
0,08
0,010
0,000
0,03
0,01
27,35
0,11
20,01
0,01
0,69
0,00
0,25
0,01
0,74
0,76
0,77
0,76
0,36
0,37
0,35
0,4
15,89
15,13
16,92
17,05
15,62
15
14,64
15,33
0,02
0,01
0,02
0,02
0,05
0,03
0,1
0,06
24,32
24,01
27,86
25,86
17,97
17,45
17,33
17,61
0,64
0,64
0,59
0,61
0,26
0,25
0,23
0,24
0,76
0,01
0,37
0,02
16,25
0,79
15,15
0,37
0,018
0,004
0,06
0,03
25,51
1,53
17,59
0,24
0,62
0,02
0,25
0,01
0,72
0,67
0,68
0,61
0,64
0,59
0,8
0,81
0,77
0,61
0,61
0,63
0,29
0,32
0,31
0,25
0,3
0,29
0,36
0,35
0,34
0,29
0,3
0,31
19,76
24,57
23,22
16,94
17,87
19,86
23,63
23,26
25,44
18,79
20,55
19,67
16,38
18,62
18,42
14,51
15,62
15,48
18,96
17,47
19,31
16,62
17,55
15,83
0,0126
0,0111
0,0135
0,0165
0,0131
0,0132
0,0135
0,0119
0,0122
0,0152
0,0153
0,0142
0,0501
0,0456
0,0618
0,0944
0,0242
0,0818
0,0483
0,0324
0,0326
0,0458
0,0593
0,0325
34,53
36,01
35,13
25,32
27,99
28,83
42,65
42,51
41
26,45
28,06
29,52
20,62
21,74
20,38
17,97
19,29
19,26
21,84
22,02
22,24
18,8
19,54
19,36
0,53
0,48
0,49
0,61
0,59
0,55
0,44
0,49
0,45
0,61
0,57
0,57
0,25
0,25
0,25
0,24
0,24
0,23
0,26
0,25
0,25
0,24
0,25
0,23
0,68
0,08
0,31
0,03
21,13
2,66
17,06
1,49
0,0135
0,0015
0,0507
0,0201
33,17
6,08
20,26
1,37
0,53
0,06
0,25
0,01
0,24
8
8
8
8
3.4x3.4x4.0 520:100:2420
3.4x3.4x4.0 520:100:2420
MOY
STD
8
8
3.4x3.4x4.84520:100:2420
3.4x3.4x4.84520:100:2420
1 SEGMENT
EPI 31 TF20
3.4x3.4x4.0 520:100:2420
3.4x3.4x4.0 520:100:2420
9
10
MOY
STD
8
8
8
8
3.4x3.4x4.0 500:160:3220
3.4x3.4x4.0 500:160:3220
1
2
3
4
5
6
7
8
MOY
STD
9
9
9
10
10
10
11
11
11
12
12
12
1
2
3
1
2
3
1
2
3
1
2
3
MOY
STD
9
4
0,69
0,34
23,61
17,04
0,0150
0,0618
34,34
20,38
0,51
9
5
0,75
0,31
20,62
16,16
0,0138
0,0447
33,93
20,86
0,54
0,24
9
10
6
4
0,71
0,65
0,33
0,3
23,28
19,85
18,07
15,37
0,0163
0,0131
0,1091
0,0255
34,38
29,17
20,99
18,96
0,5
0,58
0,25
0,24
10
5
0,68
0,29
17,89
14,5
0,0173
0,0907
29,22
18,66
0,61
0,23
10
6
0,65
0,3
20,35
15,48
0,0152
0,0745
29,99
18,63
0,57
0,23
11
4
0,85
0,36
22,55
18,56
0,0198
0,0687
40,32
21,53
0,46
0,25
11
5
0,82
0,36
23,75
18,37
0,0170
0,0970
40,65
21,99
0,46
0,25
11
12
12
12
6
4
5
6
0,79
0,67
0,69
0,65
0,36
0,29
0,34
0,3
25,4
18,49
19,35
19,1
18,65
16,89
16,81
16,18
0,0126
0,0175
0,0179
0,0181
0,0383
0,0286
0,0586
0,1266
40,78
28,16
29,16
27,71
21,69
19,89
19,39
19,96
0,46
0,62
0,59
0,62
0,24
0,25
0,25
0,24
0,72
0,07
0,32
0,03
21,19
2,33
16,84
1,31
0,0161
0,0021
0,0687
0,0309
33,15
4,84
20,24
1,13
0,54
0,06
0,24
0,01
0,66
0,66
0,65
0,27
0,33
0,3
19,12
21,69
19,61
16,96
17,98
16,22
0,0184
0,0178
0,0207
0,0537
0,0718
0,133
30,44
32,99
30,9
20,89
21,23
20,79
0,65
0,62
0,65
0,25
0,25
0,24
0,66
0,00
0,30
0,02
20,14
1,11
17,05
0,72
0,02
0,00
0,09
0,03
31,44
1,11
20,97
0,19
0,64
0,01
0,25
0,00
3.4x3.4x4.0 500:160:2900
3.4x3.4x4.0 500:160:2900
MOY
STD
truncature of 7.4 7.5 and 7.6
12
12
12
3.4x3.4x4.0 500:160:2420
3.4x3.4x4.0 500:160:2420
MOY
STD
2 SEGMENTs
EPI 31 TF20
3.4x3.4x4.0 520:100:2420
3.4x3.4x4.0 520:100:2420
44
55
66
9
11
0,67
0,32
18,17
15,86
0,0095
0,0223
29,49
20,83
0,6
0,25
9 11_moco
0.64_moco 0.30_moco 19.16_moco 16.61_moco 0.01_moco 0.02_moco 29.63_moco 21.26_moco 0.59_moco 0.26_moco
9
12
0,68
0,3
21
16,32
0,0101
0,0483
32,27
21,14
0,54
0,25
9
13
0,68
0,3
21,71
16,51
0,0111
0,0314
34,36
21,42
0,52
0,24
10
7
0,62
0,29
15,82
13,95
0,0121
0,0158
25,36
17,99
0,64
0,22
10
8
0,63
0,28
14
13,07
0,0123
0,0472
22,79
17,66
0,7
0,22
10
9
0,6
0,28
15,32
12,94
0,0119
0,0237
23,75
17,78
0,67
0,22
11
7
0,79
0,34
20,53
17,62
0,0118
0,0327
37,12
22,98
0,54
0,27
11
8
0,76
0,34
20,18
17,65
0,0117
0,0391
34,77
23,15
0,58
0,27
11
9
0,78
0,35
18,96
16,61
0,0106
0,0505
34,71
21,79
0,6
0,26
12
7
0,61
0,29
16,24
14,31
0,0133
0,0136
24,06
18,49
0,65
0,23
12
8
0,66
0,33
16,2
13,82
0,0137
0,0378
25,99
18,6
0,64
0,23
12
9
0,63
0,33
20,11
15,73
0,0123
0,0135
29,57
19,21
0,57
0,23
MOY
STD
9
9
9
10
10
10
11
11
11
12
12
12
14
15
16
10
11
12
10
11
12
10
11
12
0,68
0,06
0,31
0,02
18,19
2,47
15,37
1,61
0,0117
0,0012
0,0313
0,0130
29,52
4,84
20,09
1,94
0,60
0,05
0,24
0,02
0,74
0,77
0,7
0,68
0,67
0,66
0,8
0,85
0,83
0,68
0,71
0,67
0,37
0,36
0,35
0,3
0,29
0,28
0,36
0,37
0,36
0,33
0,3
0,3
25,32
26,35
26,89
15,71
16,73
15,73
19,44
18,96
21,01
17,09
14,65
17,72
19,16
18,64
19,02
13,43
13,3
13,87
16,76
17,27
18,1
15,12
14,17
15,88
0,0193
0,0190
0,0150
0,0123
0,0120
0,0127
0,0133
0,0124
0,0152
0,0156
0,0160
0,0151
0,0831
0,0826
0,0531
0,0218
0,0220
0,0155
0,0357
0,0390
0,0494
0,0628
0,0271
0,0226
37,14
39,23
36,92
25,59
27,05
24,43
33,85
34,16
36,04
25,8
23,29
25,65
21,87
21,37
21,57
17,69
18,02
17,47
21,08
21,82
23,25
18,77
17,77
18,25
0,45
0,44
0,43
0,67
0,65
0,68
0,58
0,59
0,53
0,66
0,7
0,65
0,25
0,25
0,25
0,22
0,21
0,22
0,25
0,26
0,27
0,24
0,23
0,24
3.4x3.4x4.0 500:160:2900
3.4x3.4x4.0 500:160:2900
MOY
STD
0,73
0,06
0,33
0,03
19,63
4,15
16,23
2,13
0,0148
0,0024
0,0429
0,0225
30,76
5,67
19,91
2,00
0,59
0,10
0,24
0,02
truncature of 7.4 7.5 and 7.6
12 1010
12 1111
12 1212
0,66
0,69
0,66
0,32
0,29
0,3
19,15
15,82
19,17
16,54
14,49
15,91
0,0145
0,0168
0,0155
0,0559
0,0683
0,0412
29,03
26,36
29,4
20,51
18,94
20,06
0,69
0,73
0,67
0,24
0,22
0,24
3.4x3.4x4.0 500:160:2420
3.4x3.4x4.0 500:160:2420
MOY
STD
0,67
0,01
0,30
0,01
18,05
1,57
15,65
0,86
0,0156
0,0009
0,06
0,01
28,26
1,35
19,84
0,66
0,70
0,02
0,23
0,01
0,76
0,33
14,72
14,80
0,0114
0,0193
22,69
17,03
0,58
0,26
0,76
0,00
0,33
0,00
14,72
0,00
14,80
0,00
0,0114
0,0000
0,0193
0,0000
22,69
0,00
17,03
0,00
0,58
0,00
0,26
0,00
0,71
0,72
0,32
0,33
15,92
16,56
14,65
15,72
0,0108
0,0108
0,0210
0,0113
23,94
24,80
16,75
17,61
0,57
0,57
0,24
0,25
0,71
0,01
0,32
0,01
16,24
0,32
15,18
0,54
0,0108
0,0000
0,0161
0,0049
24,37
0,43
17,18
0,43
0,57
0,00
0,25
0,00
0,73
0,70
0,28
0,30
15,55
16,95
13,52
14,98
0,0117
0,0101
0,0170
0,0196
29,61
29,08
19,18
19,43
0,59
0,59
0,23
0,23
0,71
0,01
0,29
0,01
16,25
0,70
14,25
0,73
0,0109
0,0008
0,0183
0,0013
29,34
0,27
19,30
0,12
0,59
0,00
0,23
0,00
0,74
0,79
0,33
0,35
15,56
15,71
15,60
14,42
0,0107
0,0114
0,0115
0,0166
23,49
25,73
18,23
18,47
0,60
0,58
0,26
0,25
3 SEGMENTs
EPI 19 TF8
3.4x3.4x4.0 410:120:3890
3.4x3.4x4.0 410:120:3890
13
1
13
2
MOY
STD
13
13
3.4x3.4x4.0 410:120:3410
3.4x3.4x4.0 410:120:3410
MOY
STD
13
13
3.4x3.4x4.0 410:120:2690
3.4x3.4x4.0 410:120:2690
3
4
5
6
MOY
STD
13
13
7
8
3.4x3.4x4.0 410:150:3860
3.4x3.4x4.0 410:150:3860
MOY
STD
13
13
3.4x3.4x4.0 410:150:3260
3.4x3.4x4.0 410:150:3260
9
10
MOY
STD
13
13
11
12
0,77
0,02
0,34
0,01
15,63
0,08
15,01
0,59
0,0111
0,0003
0,0140
0,0026
24,61
1,12
18,35
0,12
0,59
0,01
0,26
0,01
0,75
0,75
0,35
0,31
19,50
15,84
16,18
13,93
0,0147
0,0121
0,0668
0,0246
33,12
27,59
21,38
19,08
0,50
0,60
0,26
0,25
0,75
0,00
0,33
0,02
17,67
1,83
15,06
1,12
0,0134
0,0013
0,0457
0,0211
30,36
2,76
20,23
1,15
0,55
0,05
0,26
0,01
0,76
0,74
0,33
0,32
19,50
18,07
17,26
15,34
0,0179
0,0144
0,1023
0,0416
35,37
33,80
21,31
21,49
0,55
0,56
0,25
0,25
0,75
0,01
0,33
0,01
18,79
0,71
16,30
0,96
0,0162
0,0017
0,0720
0,0304
34,58
0,78
21,40
0,09
0,56
0,00
0,25
0,00
3.4x3.4x4.0 410:150:2660
3.4x3.4x4.0 410:150:2660
MOY
STD
4 SEGMENTs
9
9
17
18
0,74
0,76
0,32
0,35
20,56
21,56
15,32
16,78
0,0179
0,0185
0,0555
0,0949
36,13
38,31
22,73
23,27
0,53
0,52
0,24
0,24
10
10
11
11
12
12
13
14
13
14
13
14
0,69
0,74
0,9
0,87
0,69
0,72
0,3
0,3
0,33
0,33
0,31
0,31
15,48
13,5
21,15
18,79
14,35
13,49
13,18
11,94
18,21
17,29
12,75
12,54
0,0139
0,0145
0,0348
0,0168
0,0251
0,0236
0,0762
0,0529
0,1386
0,0518
0,2252
0,1760
27,84
27,3
44,1
37,58
26,19
25,13
20,11
19,47
23,88
24,42
20,3
19,47
0,67
0,68
0,49
0,58
0,68
0,7
0,21
0,21
0,26
0,28
0,23
0,23
0,76
0,07
0,32
0,02
17,36
3,29
14,75
2,29
0,0206
0,0065
0,1089
0,0606
32,82
6,61
21,71
1,94
0,61
0,08
0,24
0,02
0,84
0,92
0,78
0,76
0,97
0,93
0,69
0,76
0,37
0,41
0,33
0,32
0,41
0,44
0,34
0,34
20,61
17,72
16,15
14,65
21,03
25,94
17,11
14,3
16,44
16,05
13,90
12,48
17,54
19,94
15,03
13,68
0,0238
0,0221
0,0154
0,0144
0,0166
0,0217
0,0259
0,0227
0,1458
0,0706
0,0626
0,0410
0,0317
0,0866
0,1096
0,1728
35,72
35,4
28,42
25,68
39,36
46,73
25,77
22,9
22,23
21,15
19,21
17,8
23,47
23,86
19,21
17,74
0,49
0,52
0,6
0,65
0,48
0,37
0,63
0,69
0,26
0,24
0,24
0,22
0,26
0,25
0,25
0,23
0,83
0,09
0,37
0,04
18,44
3,65
15,63
2,24
0,0203
0,0040
0,0901
0,0465
32,50
7,66
20,58
2,28
0,55
0,10
0,24
0,01
EPI 31 TF10
3.4x3.4x4.0 520:100:2420 MOY
3.4x3.4x4.0 520:100:2420 STD
9
9
10
10
11
11
12
12
3.4x3.4x4.0 500:160:3220
3.4x3.4x4.0 500:160:3220
MOY
STD
19
20
15
16
15
16
15
16
SLICE 7
DISTRIBUTION
BAT
mean
1 SEGMENT
EPI 31
3.4x3.4x4.0 520:100:2420
3.4x3.4x4.0 520:100:2420
2 SEGMENTs
EPI 31
3.4x3.4x4.0 520:100:2420
3.4x3.4x4.0 520:100:2420
mean
std
mean
error on CBF
std
mean
R2
std
mean
std
0,66
0,59
0,61
0,6
0,64
0,57
0,69
0,65
0,68
0,57
0,56
0,63
0,31
0,29
0,31
0,27
0,3
0,29
0,38
0,35
0,39
0,31
0,32
0,32
22,14
24,67
23,7
18,75
18,19
21,07
26,95
26,71
27,47
21,17
23,47
20,551
16,58
17,16
16,24
15,17
14,87
16,06
19,92
18,68
19,34
17,46
18,27
15,46
0,0100
0,0100
0,0100
0,0200
0,0200
0,0146
0,0117
0,0112
0,0120
0,0150
0,0132
0,0122
0,0200
0,0800
0,0400
0,0400
0,0500
0,0332
0,0298
0,0224
0,0276
0,0743
0,0755
0,0179
31,29
33,71
33,13
26,84
28,53
28,56
39,99
38,15
39,51
26,32
28,31
29,34
19,54
19,89
18,68
18,11
19,25
18,19
20,66
20,86
21,58
18,83
19,35
19,1
0,5
0,46
0,48
0,58
0,6
0,56
0,42
0,43
0,43
0,57
0,52
0,55
0,23
0,22
0,23
0,24
0,22
0,22
0,24
0,24
0,23
0,24
0,24
0,23
MOY
STD
0,62
0,04
0,32
0,03
22,90
3,00
17,10
1,59
0,0133
0,0034
0,0426
0,0215
31,97
4,71
19,50
1,03
0,51
0,06
0,23
0,01
0,62
0,69
0,66
0,6
0,67
0,61
0,78
0,75
0,71
0,6
0,65
0,6
0,35
0,31
0,32
0,3
0,29
0,28
0,35
0,36
0,36
0,32
0,33
0,34
25,04
20,82
22,84
22
17,24
20,68
24,56
24,81
26,23
21,07
22
21,13
17,69
15,63
17,22
16,24
13,18
15,68
17,79
17,68
18,05
17,48
16,3
16
0,0100
0,0100
0,0100
0,0100
0,0200
0,0200
0,0126
0,0122
0,0117
0,0139
0,0209
0,0156
0,0100
0,0500
0,0300
0,0300
0,0800
0,3000
0,0254
0,0277
0,0270
0,0157
0,2494
0,1638
31,17
31,49
31,73
28,39
27,16
28,62
39,83
38,8
37,8
26,54
29,55
26,87
18,61
18,99
18,39
17,66
16,74
17,85
21,03
20,76
20,11
18,04
18,99
18,91
0,53
0,55
0,51
0,58
0,63
0,6
0,48
0,48
0,47
0,6
0,59
0,62
0,22
0,22
0,24
0,22
0,21
0,23
0,22
0,22
0,22
0,23
0,22
0,22
0,66
0,06
0,33
0,03
22,37
2,38
16,58
1,33
0,0139
0,0040
0,0841
0,0946
31,50
4,56
18,84
1,22
0,55
0,06
0,22
0,01
0,61
0,62
0,6
0,62
0,59
0,58
0,69
0,68
0,7
0,56
0,59
0,6
0,33
0,31
0,31
0,28
0,29
0,28
0,37
0,36
0,35
0,31
0,33
0,34
19,99
20,89
23,27
15,21
15,48
16,06
21,13
19,37
19,21
17,47
19,32
19,95
16,09
15,47
16,44
12,59
13,19
12,48
16,67
15,97
15,8
14,4
15,6
14,46
0,0100
0,0100
0,0100
0,0200
0,0100
0,0200
0,0103
0,0109
0,0112
0,0137
0,0129
0,0121
0,0600
0,0200
0,0100
0,0400
0,0300
0,0700
0,0208
0,0232
0,0351
0,0909
0,1218
0,0151
27,46
30,22
31,48
24,48
21,69
23,59
33,56
30,82
31,68
22,11
25,08
27,4
18,67
19,36
19,2
16,9
16,14
17,61
21,21
21,35
20,8
16,52
17,92
17,22
0,6
0,56
0,51
0,66
0,68
0,67
0,54
0,57
0,59
0,65
0,61
0,56
0,24
0,23
0,23
0,21
0,22
0,21
0,25
0,26
0,24
0,21
0,24
0,22
0,62
0,04
0,32
0,03
18,95
2,35
14,93
1,42
0,0126
0,0035
0,0447
0,0329
27,46
3,89
18,58
1,75
0,60
0,05
0,23
0,02
0,64
0,66
0,64
0,63
0,62
0,64
0,74
0,76
0,77
0,61
0,62
0,61
0,35
0,34
0,33
0,3
0,29
0,28
0,37
0,4
0,36
0,34
0,3
0,37
27
26,1
26,4
18,03
17,91
16,78
19,18
19,7
21,37
19,46
17,61
20,45
18,51
18,54
18,45
14,2
13,9
13,22
15,42
16,68
17,4
16,07
15,03
17,25
0,0100
0,0100
0,0200
0,0100
0,0200
0,0200
0,0125
0,0120
0,0148
0,0152
0,0145
0,0150
0,1100
0,0300
0,1600
0,0300
0,0300
0,0400
0,0267
0,0358
0,0535
0,1642
0,1081
0,0771
35,13
34,82
34,93
24,92
25,26
24,98
31,13
31,53
34,67
23,39
22,6
24,6
19,99
19,37
20,06
16,64
16,44
17,08
19,34
20,67
21,98
16,86
16,14
16,31
0,46
0,47
0,47
0,65
0,64
0,67
0,59
0,6
0,53
0,66
0,68
0,63
0,23
0,24
0,24
0,21
0,22
0,21
0,23
0,24
0,24
0,22
0,21
0,23
0,66
0,06
0,34
0,04
20,83
3,49
16,22
1,80
0,0145
0,0037
0,0721
0,0492
29,00
4,90
18,41
1,95
0,59
0,08
0,23
0,01
0,68
0,35
16,46
13,43
0,0126
0,0131
24,00
18,36
0,56
0,25
4
5
6
4
5
6
4
5
6
4
5
6
MOY
STD
9
9
9
10
10
10
11
11
11
12
12
12
11
12
13
7
8
9
7
8
9
7
8
9
MOY
STD
9
9
9
10
10
10
11
11
11
12
12
12
3.4x3.4x4.0 500:160:2900
3.4x3.4x4.0 500:160:2900
std
CBF
Patient Serie
9
1
9
2
9
3
10
1
10
2
10
3
11
1
11
2
11
3
12
1
12
2
12
3
9
9
9
10
10
10
11
11
11
12
12
12
3.4x3.4x4.0 500:160:2900
3.4x3.4x4.0 500:160:2900
error on BAT
14
15
16
10
11
12
10
11
12
10
11
12
MOY
STD
3 SEGMENTs
EPI 19 TF8
13
1
13
2
0,69
0,34
13,86
12,33
0,0131
0,0202
19,22
14,14
0,63
0,22
3.4x3.4x4.0 410:120:3890
MOY
0,68
0,35
15,16
12,88
0,0128
0,0167
21,61
16,25
0,59
0,24
3.4x3.4x4.0 410:120:3890
STD
0,00
0,00
1,30
0,55
0,0002
0,0035
2,39
2,11
0,04
0,02
0,62
0,63
0,35
0,34
18,12
17,79
15,46
15,37
0,0121
0,0125
0,0274
0,0193
20,95
21,98
14,81
15,48
0,61
0,61
0,21
0,22
13
13
3
4
3.4x3.4x4.0 410:120:3410
MOY
0,63
0,34
17,96
15,41
0,0123
0,0233
21,46
15,14
0,61
0,21
3.4x3.4x4.0 410:120:3410
STD
0,01
0,01
0,17
0,05
0,0002
0,0040
0,52
0,34
0,00
0,00
0,60
0,63
0,29
0,29
17,50
14,97
13,69
12,22
0,0116
0,0133
0,0333
0,0366
25,45
23,94
17,34
17,38
0,61
0,65
0,21
0,21
0,61
0,02
0,29
0,00
16,23
1,26
12,95
0,74
0,0124
0,0008
0,0349
0,0017
24,69
0,75
17,36
0,02
0,63
0,02
0,21
0,00
0,66
0,69
0,33
0,32
15,58
15,27
14,56
13,86
0,0125
0,0141
0,0226
0,0566
20,76
21,60
16,24
16,20
0,63
0,63
0,24
0,23
0,68
0,01
0,33
0,01
15,42
0,16
14,21
0,35
0,0133
0,0008
0,0396
0,0170
21,18
0,42
16,22
0,02
0,63
0,00
0,24
0,00
0,67
0,61
0,35
0,30
19,05
16,99
15,31
14,38
0,0158
0,0112
0,0718
0,0115
28,02
23,13
19,11
16,96
0,58
0,65
0,24
0,22
0,64
0,03
0,32
0,02
18,02
1,03
14,84
0,47
0,0135
0,0023
0,0417
0,0301
25,57
2,45
18,03
1,08
0,61
0,04
0,23
0,01
0,56
0,61
0,29
0,33
22,49
20,92
16,31
16,05
0,0143
0,0128
0,0631
0,0262
30,30
29,84
19,10
20,06
0,58
0,60
0,23
0,23
0,59
0,02
0,31
0,02
21,71
0,79
16,18
0,13
0,0136
0,0008
0,0446
0,0185
30,07
0,23
19,58
0,48
0,59
0,01
0,23
0,00
17,83
17,56
0,0100
0,0200
0,0200
0,1300
31,7
33,19
21,14
21,54
0,51
0,5
0,24
0,23
13
13
3.4x3.4x4.0 410:120:2690
3.4x3.4x4.0 410:120:2690
MOY
STD
13
13
3.4x3.4x4.0 410:150:3860
3.4x3.4x4.0 410:150:3860
7
8
MOY
STD
13
13
3.4x3.4x4.0 410:150:3260
3.4x3.4x4.0 410:150:3260
5
6
9
10
MOY
STD
13
13
11
12
3.4x3.4x4.0 410:150:2660
3.4x3.4x4.0 410:150:2660
MOY
STD
4 SEGMENTs
4
4
17
18
0,59
0,61
0,33
0,35
24,14
23,96
5
13
0,63
0,33
17,58
14,7
0,0200
0,0500
27,5
20,34
0,64
0,23
5
14
0,64
0,32
16,44
13,69
0,0200
0,0400
27,19
20,07
0,64
0,22
6
13
0,76
0,34
22,09
18,2
0,0238
0,0729
39,26
23,25
0,47
0,26
6
14
0,71
0,36
20,75
17,49
0,0133
0,0362
33,39
23,1
0,54
0,26
7
13
0,58
0,34
19,31
15,86
0,0150
0,0629
25,2
20,18
0,62
0,24
7
14
0,59
0,33
18,19
15,83
0,0172
0,1236
23,66
18,99
0,63
0,25
0,64
0,06
0,34
0,01
20,31
2,72
16,40
1,53
0,0174
0,0042
0,0670
0,0377
30,14
4,84
21,08
1,40
0,57
0,07
0,24
0,01
0,69
0,77
0,7
0,68
0,76
0,73
0,61
0,63
0,34
0,4
0,35
0,33
0,4
0,41
0,34
0,36
21,77
19,92
18,34
16,56
21,8
25,65
22,13
17,82
17,1
16,31
15,15
14,012
17,72
19,79
17,83
15,8
0,0200
0,0200
0,0200
0,0200
0,0163
0,0202
0,0234
0,0163
0,0700
0,0500
0,0500
0,0500
0,0416
0,0739
0,0593
0,0609
30,64
32,18
27,86
25,5
33,43
37,98
28,13
22,17
20,05
19,46
18,98
17,69
21,69
23,1
19,73
17,55
0,53
0,51
0,6
0,64
0,51
0,42
0,57
0,66
0,24
0,24
0,24
0,23
0,27
0,27
0,25
0,24
0,70
0,05
0,37
0,03
20,50
2,74
16,71
1,68
0,0195
0,0022
0,0570
0,0104
29,74
4,61
19,78
1,76
0,56
0,07
0,25
0,01
EPI 31
3.4x3.4x4.0 520:100:2420
3.4x3.4x4.0 520:100:2420
MOY
STD
4
4
5
5
6
6
7
7
3.4x3.4x4.0 500:160:3220
3.4x3.4x4.0 500:160:3220
MOY
STD
19
20
15
16
15
16
15
16