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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 i ii 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) KTH University, Guillaume GIBERT 1.2. Overview of MRI 12 • 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. KTH University, Guillaume GIBERT 1.2. Overview of MRI 14 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 KTH University, Guillaume GIBERT 1.2. Overview of MRI 15 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. KTH University, Guillaume GIBERT 1.2. Overview of MRI 16 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 KTH University, Guillaume GIBERT 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. KTH University, Guillaume GIBERT 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. KTH University, Guillaume GIBERT 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). KTH University, Guillaume GIBERT 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 KTH University, Guillaume GIBERT 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 KTH University, Guillaume GIBERT 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. KTH University, Guillaume GIBERT 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 KTH University, Guillaume GIBERT 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 KTH University, Guillaume GIBERT 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 KTH University, Guillaume GIBERT 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. KTH University, Guillaume GIBERT 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 KTH University, Guillaume GIBERT 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). KTH University, Guillaume GIBERT 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 KTH University, Guillaume GIBERT 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 KTH University, Guillaume GIBERT 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. KTH University, Guillaume GIBERT 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. KTH University, Guillaume GIBERT 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. 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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