Quantification of the Cerebral Perfusion with the Arterial Spin Labelling 3D-MRI method. Quantification of the Cerebral Perfusion with the Arterial Spin Labelling 3D-MRI method

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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 modifica- tions 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.

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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 imple- menteras 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.

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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 con- stantly 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.

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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 im- provements 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

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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 highly- developed 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

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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 −→

B₀. The precession occurs at 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= ¹₂) or anti-parallel state (ml= −¹₂). The sum of all the

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microscopic magnetic momenta of the hydrogen protons of a water sample is now considered. 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 B1during 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 rotates −→

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 = γB₁τ_p (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

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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 in- duction 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 180^o 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) = M0e^−t/T² (1.2)

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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 2D- image, 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 de-

KTH University, Guillaume GIBERT

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pends on the position in space. Therefore, at position −→r = x−→x + y−→y + z−→z, the total magnetic field becomes

−

→B =−→ B₀+−→

B_G= (B₀+ G_xx + G_yy + G_zz)−→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 90^o RF pulse, the Larmor frequency will depend on the position in the sample.

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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 :

S(t) ∝ Z

x

Z

y

ρ(x, y)e^{−iφ(x,y,t)}dxdy (1.5)

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:

kx(t) = γ 2π

τ

Z

0

Gx(t)dt (1.7)

ky(t) = γ 2π

τ

Z

0

Gy(t)dt (1.8)

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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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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

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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.

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1.3. State of the art 18

1.3 State of the art

1.3.1 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 N2O concentra- tions 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 N2O concentration in the veins to equilibrate with the concentration in the arteries:

rCBF = (QB)u/W Ru

0(A − V )dt (1.9)

where (QB)_u is the amount of N2O taken up by the brain by time u (time when there is equilibrium between arterial and venous concentration), A is the arterial N2O concentration, V is the venous N2O 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

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image the cerebral perfusion with the PET method using a freely diffusible tissue tracer, oxygen-15-labelled water (¹⁵O − H₂O).[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 Con- trast (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.

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1.3.2 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 endovascu- lar 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 suffer- ing 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 pseudo- continuous arterial spin labeling MRI at multiple postlabeling delays: accounting for

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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.

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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).

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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 perfusion- weighted 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

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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

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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.

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Figure 2.1.3: Inversion profiles of tag and control pulses for FAIR, EPISTAR and PI- CORE. 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.

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2.2. Quantification of perfusion 27

Advantages Disadvantages

PASL Higher tagging efficiency Lower SNR

Lower SAR Increased transit delay

Improved transit time effects

CASL Lower tagging efficiency

Higher SNR than PASL Continuous RF transmit hardware required

Shorter transit delay Higher SAR

Magnetization Transfer effects

PCASL Higher SNR than PASL

Higher tagging efficiency than CASL Higher SAR Improved transit time effect 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 Sub- straction"). Another version of the QUIPSS-II consists in replacing the saturation pulse

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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 in- sufficient to quantify the rCBF without too much uncertainty. The value of the rCBF at KTH University, Guillaume GIBERT

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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 Numerical Fitting

2.3.1 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 develop- ment 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

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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 non- fully-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

2αM_0,af e^−∆t/T^1,a if ∆t ≤ t ≤ ∆t + τ

0 if t > ∆t + τ

(2.2)

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), M_0,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/T^{1,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):

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∆M (t) =







0 if t < ∆t

2

λαM0,tf

T1,ef fe^−∆t/T^1,a

1 − e^{−(t−∆t)/T}^{1,ef f}

if ∆t ≤ t ≤ ∆t + τ

2

λαM0,tf

T1,ef fe^−∆t/T^1,a

e^{τ /T}^{1,ef f}−1

e^{−(t−∆t)/T}^{1,ef f}

if t > ∆t + τ (2.4)

where M0,t is the equilibrium magnetization of the tissue. It is related to M0,a by λthe 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, M_0,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

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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

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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).

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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.

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Figure 2.3.3: Example of fitting at one voxel(up) and information provided by the fitting (down)

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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 exam- ination, 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.

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3.1. First set of experiment 37

3.1 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 2D- slice 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.

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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 20 TF 12 EF 33 Nbe of Segments 4

TA (per TI/total) 0:45/12:45 TI-range 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.

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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 KTH University, Guillaume GIBERT

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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

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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

Quantification of the Cerebral Perfusion with the Arterial Spin Labelling 3D-MRI method. Quantification of the Cerebral Perfusion with the Arterial Spin Labelling 3D-MRI method