CMBs CHARACTERIZATION USING PHASE-CONTRAST 

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CMBs denition on MRI

As seen above CMBs are paramagnetic and are, thus, visible on MRI sequences that are sensitive to magnetic susceptibility dierences (such as GRE T2*-weighted sequence). According to Greenberg et al. [Greenberg et al., 2009] CMBs should be black or very hypointense on T2*- weighted MRI, round or ovoid (excluding tubular or linear structures such as those representing vessels or a resorbed macrobleed), blooming (larger or more conspicuous on GRE than Spin-Echo (SE) MRI, see Figure 1.1.2), devoid of T1- or T2-weighted hyperintensity (such as cavernous malformation), and at least half surrounded by brain parenchyma (permitting supercial CMB as seen in CAA). Other mimics such as mineralization of the basal ganglia or diuse axonal injury are excluded based on appearance or clinical history. The size may be relatively unimportant for correctly categorizing lesions that otherwise meet these criteria and should be applied conservatively if at all.

MR magnetic susceptibility and Phase MR image

In order to better understand how CMBs can be detected on MRI, this chapter briey reviews the physical basis of magnetic susceptibility and how it aects the signal of MRI sequences that are sensitive to magnetic susceptibility1.
Whereas an electric charge is the basis for an electric eld, an electric charge in motion produces a magnetic eld. For example, a loop carrying current produces a magnetic eld equivalent to the one produced by a magnetic dipole (see Figure (1.2.1)).
A magnetic dipole is a basic physical entity that acts as a source of the magnetic eld [Haacke and Reichenbach, 2011]. It is dened by two poles that attract or repel one another. A magnetic dipole is characterized by a vector quantity called the magnetic moment, m. When a material is placed into a magnetic eld, electrons and nucleons acquire dierent energy states. A physical quantity, the spin, is used to describe these energy states; the spin is proportional to the magnetic moment of either an electron or a nucleon. The total magnetic moment of an atom can be calculated by vector summation of the individual spins from nucleons and electrons. Since the gyromagnetic ratio2 of an electron is several hundreds of times larger than the gyromagnetic ratio of a nucleon, the magnetic moment of an atom is usually dominated by the overall electronic spin. Due to thermal energy at ambient temperature, the individual atom magnetic dipole moments point randomly in dierent directions and the resulting vector is in fact negligible in the absence of external magnetic eld. However, when placed in an external magnetic eld, the individual magnetic moments tend to counteract thermal eects and align with the external eld, thus resulting in a macroscopic magnetic moment. If a large number of atoms contained in a given volume are considered, the magnetization can be dened as the average magnetic moments over the volume, enabling to dene a property called the magnetic susceptibility as dened below. It can be noted that these macroscopic magnetic properties are dominated by electronic eects, and that it will produce deformation of the external magnetic eld in MRI. However, most biological tissues contain predominantly water molecules, and 63% of the human body is consequently hydrogen atoms. The nuclear magnetic moments are the basis for the nuclear magnetic resonance (NMR) phenomenon: a nuclear magnetization can be produced for protons of hydrogen atoms, thus making MRI possible [Haacke and Reichenbach.

GRE Phase MR image and its relationship to susceptibility

MRI provides a complex image, with an amplitude and a phase. Amplitude image can be modulated to generate contrast. The phase image is more complex to analyze and has thus been discarded from MR-based analysis till recently. Generally speaking, the phase describes the orientation across time of the magnetization vector in the transverse plane, see Figure 1.2.10. MR signal is received using a quadrature detection, which results in two data streams with a 90° phase dierence. The digitized values from these signals are the real part and the imaginary part of each complex data point in k-space. Magnitude and phase images result from the Fourier transform of data and are dened as p x2 + y2 for the magnitude and as tan􀀀1 􀀀 y x for phase image. As presented in the previous section, the phase can provide information on the local magnetic eld.

CMBs imaging techniques

In order to better identify CMBs, new MRI sequences and reconstruction techniques were proposed, as described below.
T2*-weighted GRE T2*-weighted gradient recalled-echo (GRE) sequence has a high sensitivity for dierences in magnetic susceptibility and is the most commonly used for CMBs detection as illustrated in (a) on Figure 1.3.1 (a). However, CMB identication is very sensitive to MRI sequence parameters such as eld strength, slices thickness, TE, interslice gap, TR, ip angle or matrix size. A higher eld strength allows higher resolution and more susceptibility eect, but rating may become barely feasible. Longer TEs enhance susceptibility eects but also other susceptibility artifacts and may thus hamper identication of CMBs near air-tissue interfaces. Interslice gap needs to be chosen carefully with respect to CMBs size, as some can be missed if the interslice gap is too large.

Discussion/Comparison of state of the art methods for CMBs detection

Five methods were described in this section that require experts intervention to reach nal results. Table 1.3.1 summarizes their results as published. Over all the ve methods display a large number of false positives, with varying degrees of sensitivity as shown in Table 1.3.1. Remaining false positives yielded additional time for manual reviewing which usually required three to ten minutes per patient. Methods were based on shape, intensity and location criteria. They all appear were very ecient to detect large CMBs, perfectly round and completely surrounded by the parenchyma. However very small CMBs were often missed. When considering each method, some drawbacks may be pointed out. The mask used in MIDAS seems sub-optimal; in fact, the mask to remove artifacts built from control subjects seems unsuited as artifacts localization is more likely to be subject dependent. Furthermore, the result from the SVM method can be biased, since learning datasets are the same as test datasets and generalizability of the SVM approach for new datasets is not proven. Radial symmetry transform gave the lowest number of false positives and it seems more robust and more adapted to the denition of CMBs. However, when binarizing the resulting maps, the applied threshold was not successfully explained and justied, thus, issues regarding its generalization for other data may arise. Moreover, CMBs criteria dealing with multi-contrast (using combined information derived from T1, T2, T2* weighted images), as described in [Greenberg et al., 2009], were not investigated and no method has been validated on a large population with a large number of CMBs.

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Internal eld computation with 2D harmonic ltering (2DHF)

Extraction of relevant internal eld information from phase images requires two preliminary steps: phase unwrapping and background eld removal. In most proposed methods, this problem is solved in two separated steps; which may be iterative [Bilgic et al., 2012, de Rochefort et al., 2010a, 2008, Liu et al., 2012, de Rochefort et al., 2010b]. A particularly relevant phase unwrapping technique based on solving Poisson equation was proposed by Song et al. [Song et al., 1995] and extended in 3D to the QSM context [de Rochefort et al., 2010b]. Harmonic ltering, such as SHARP [Schweser et al., 2011], have shown to be extremely ecient in removing the harmonic component due to background sources. However, these methods were validated on 3D phase maps, and may not deal with potential slice-to-slice phase inconsistency that may occur in 2D datasets.
The linear approximation of Maxwell equations is considered relevant in the MRI framework [de Rochefort et al., 2008]; the eld inside the brain, B, can thus be decomposed as the sum of variations due to internal sources, Bin, and variations induced by external sources, Bout. From Maxwell equations, the external eld is harmonic inside the brain [Li and Leigh, 2001, Schweser et al., 2011], resulting in 4Bout = 0, thus leading to 4B = 4Bin (4 denotes the Laplacian). Consequently, external eects can be ltered out through a second order derivative, followed by a second order integration using adequate boundary conditions. Note that any additional linear term is ltered out by the 2nd order derivative.
Unwrapping using Poisson equation and background eld removal using harmonic ltering are the basis of the 2D harmonic lter (2DHF) that will be described below and that were applied on the phase image of the 2D multi-slice T2* GRE sequence. Its principle is also given in Figure 2.3.2.
1. Slice-by-slice phase unwrapping was performed by calculating the 2D phase gradient image as the point-by-point dierence between neighbors. This ‘unwrapping’ method does not actually compute the unwrapped phase (‘) but rather yields an unwrapped phase gradient maps (r’) prior to the second order derivation.Wraps were then detected using the modulo function which shifts phase values within the range[􀀀; [ [Song et al., 1995]. This method assumes that phase gradients are smaller than and was proven to be ecient for large SNR [Conturo and Smith, 1990].
2. The divergence of the estimated unwrapped phase gradient map was then calculated to get 4B: using the point-by-point dierence between neighbors similarly as for the gradient. In this second step, the Laplacian was then nulled-out outside a brain mask, dening at the same time the ‘internal’ region-of-interest (ROI).

Comparison with other ltering methods

Background eld removal techniques may be split into two classes as a function of their underlying assumptions. One method from each class was implemented here for comparison with the 2DHF ltering approach. The rst class is based on the assumption that variations of the background eld are spatially slower than those of the internal eld[Deistung et al., 2008, Haacke and Reichenbach, 2011, Hammond et al., 2008, Rauscher et al., 2003]. The high pass ltering (HPF) method is commonly used [McAuley et al., 2011, 2010, Schweser et al., 2013] and was implemented here for comparison. To obtain high-pass-ltered phase images, complex-valued images were rst generated from the magnitude and phase images. They were then low pass ltered slice-by-slice by multiplying with a two dimensional Gaussian lter in Fourier domain. The Fourier domain center is plotted, with the same cut-o frequency for the two lters (a = 0.2 for illustration, equivalent to 20% of the central frequencies attenuated). standard deviation of the Gaussian lter was chosen so that the half-width-at-half-maximum of the HPF was the same as the one of the 2DHF lter, namely = = 2.3.3). High-pass ltered phase images were then computed as the phase of the ratio between complex-valued and low-pass-ltered images.

Table of contents :

Contents
List of Figures
List of Tables
Glossary
INTRODUCTION
1 CONTEXT 
1.1 Clinical context
1.1.1 History of cerebral microbleeds
1.1.2 CMBs denition on MRI
1.1.3 Clinical relevance
1.2 MR magnetic susceptibility and Phase MR image
1.3 State-of-the-art: identication and detection of CMBs
1.3.1 CMBs imaging techniques
1.3.2 Visual identication
1.3.3 Fully/semi automatic identication
1.4 Objectives
2 CMBs CHARACTERIZATION USING PHASE-CONTRAST 
2.1 Requirements to process GRE phase images
2.2 INTRODUCTION
2.3 MATERIALS AND METHODS
2.3.1 Data acquisition
2.3.2 Internal eld computation with 2D harmonic ltering (2DHF)
2.3.3 Comparison with other ltering methods
2.3.4 Numerical simulation
2.3.5 Regularization parameter
2.4 RESULTS
2.4.1 Numerical Eciency
2.4.2 Simulation results
2.4.3 Results and comparison on clinical data
2.4.4 Application: Magnetic signature of CMBs and CMCs with 2DHF
2.5 DISCUSSION
2.6 ACKNOWLEDGMENTS
2.7 Conclusion
3 CLINICAL VALIDATION: A COMPARISON STUDY 
3.1 INTRODUCTION
3.2 Material and Methods
3.2.1 Evaluation dataset
3.2.2 Methods
3.2.2.1 Susceptibility Weighted Imaging (SWI)
3.2.2.2 Advanced phase image (IFM and QSM)
3.2.3 Evaluation experiments
3.2.3.1 Rating comparison
3.2.3.2 Building-up of the reference
3.3 Results
3.3.1 Reference
3.3.2 Rating results: lesion-based point of view
3.3.3 Rating results: subject-type point of view
3.4 Discussion
3.5 ACKNOWLEDGMENTS
4 AUTOMATIC SEGMENTATION: Proof-of-concept 
4.1 Introduction
4.2 Proof-of-concept design
4.3 Pre-processing
4.3.1 3D T1 segmentation
4.3.2 Ane registration
4.3.3 Intra cranial and cerebral mask calculation
4.4 PROOF-OF-CONCEPT: Automatic CMBs identication
4.4.1 Candidates selection: multi-contrast statistical thresholding
4.4.2 Classication
4.5 Experiment and preliminary results
4.5.1 Thresholding results
4.5.2 Classication results
4.6 Discussion & Perspectives
5 CONCLUSION & PERSPECTIVES 
Bibliography 

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