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| [[File:3D VR Image 200.jpg|right|thumb|A [[Volume rendering|volume rendered]] brain QSM acquired at 3 Teslas and reconstructed with Morphology Enabled Dipole Inversion (MEDI).]]
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| Quantitative [[magnetic susceptibility|Susceptibility]] Mapping (QSM) provides a novel<ref>[http://www.mrt.uni-jena.de/QSM-Workshop.461.0.html?&L=1 1st International Workshop on MRI Phase Contrast and Quantitative Susceptibility Mapping, Jena (2011)]</ref> [[contrast (vision)|contrast]] mechanism in [[MRI|Magnetic Resonance Imaging]] (MRI) different from traditional [[Susceptibility weighted imaging|Susceptibility Weighted Imaging]]. The voxel intensity in QSM is linearly proportional to the underlying tissue apparent [[magnetic susceptibility]], which is useful for chemical identification and quantification of specific [[biomarkers]] including iron, calcium, [[MRI contrast agent|gadolinium]], and super [[paramagnetic]] iron oxide (SPIO) nano-particles. QSM utilizes phase images, solves the [[magnetic field]] to [[magnetic susceptibility|susceptibility]] source inverse problem, and generates a three dimensional [[magnetic susceptibility|susceptibility]] distribution. Due to its quantitative nature and sensitivity to certain kinds of material, potential QSM applications include standardized quantitative stratification of [[cerebral hemorrhage|cerebral microbleeds]] and [[neurodegenerative disease]], accurate [[MRI contrast agent|gadolinium]] quantification in contrast enhanced MRI, and direct monitoring of targeted theranostic drug biodistribution in [[nanomedicine]].
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| == Background ==
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| [[File:zero cone.jpg|right|thumb|A visualization of the cone in Fourier domain.]]
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| In [[Magnetic resonance imaging|MRI]], the local field <math>\delta B</math> induced by non-ferromagnetic biomaterial [[magnetic susceptibility|susceptibility]] along the main polarization [[B₀]] field is the [[convolution]] of the volume susceptibility distribution <math>\chi </math> with the [[dipole]] kernel <math>d</math>: <math>\delta B = d \otimes \chi</math>. This spatial [[convolution]] can be expressed as a point-wise multiplication in [[k-space (MRI)|Fourier domain]]:<ref name="Salomir2003">{{cite journal |last1=Salomir |first1=Rares |last2=De Senneville |first2=Baudouin Denis |last3=Moonen |first3=Chrit TW |title=A fast calculation method for magnetic field inhomogeneity due to an arbitrary distribution of bulk susceptibility |journal=Concepts in Magnetic Resonance |volume=19B |pages=26–34 |year=2003 |doi=10.1002/cmr.b.10083}}</ref><ref name="Marques2003">{{cite journal |last1=Marques |first1=J.P. |last2=Bowtell |first2=R. |title=Application of a Fourier-based method for rapid calculation of field inhomogeneity due to spatial variation of magnetic susceptibility |journal=Concepts in Magnetic Resonance Part B: Magnetic Resonance Engineering |volume=25B |pages=65–78 |year=2005 |doi=10.1002/cmr.b.20034}}</ref> <math>\Delta B = D \cdot \Chi</math>. This [[k-space (MRI)|Fourier]] expression provides an efficient way to predict the field perturbation when the susceptibility distribution is known. However, the field to source inverse problem involves division by zero at a pair of cone surfaces at the [[magic angle]] with respect to [[B₀]] in the [[k-space (MRI)|Fourier domain]]. Consequently, [[magnetic susceptibility|susceptibility]] is underdetermined at the spatial frequencies on the cone surface, which often leads to severe streaking artifacts in the reconstructed QSM.
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| == Techniques ==
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| === Data acquisition ===
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| In principle, any [[Three-dimensional space|3D]] gradient echo sequence can be used for data acquisition. In practice, high resolution imaging with a moderately long echo time is preferred to obtain sufficient [[magnetic susceptibility|susceptibility]] effects, although the optimal imaging parameters depend on the specific applications and the field strength. A multi-echo acquisition is beneficial for accurate [[B₀]] field measurement without the contribution from B<sub>1</sub> inhomogeneity. Flow compensation may further improve the accuracy of [[magnetic susceptibility|susceptibility]] measurement in venous blood, but there are certain technical difficulties to devise a fully flow compensated multi-echo sequence.
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| === Background field removal ===
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| [[File:local field 400.jpg|right|thumb|Estimated local field maps using Left) high-pass filtering method, Right) Projection onto Dipole Fields (PDF) method.]]
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| In human [[brain]] quantitative [[magnetic susceptibility|susceptibility]] mapping, only the local [[magnetic susceptibility|susceptibility]] sources inside the brain are of interest. However, the [[magnetic field]] induced by the local sources is inevitably contaminated by the field induced by the air-tissue interface, whose [[magnetic susceptibility|susceptibility]] difference is orders of magnitudes stronger than that of the local sources. Therefore, the background field generated by the air-tissue interface needs to be removed for clear visualization on phase images and precise quantification on QSM.
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| Traditional heuristic methods, including [[high-pass filter]]ing, are useful for the background field removal, but they also tamper with the local field and degrade the quantitative accuracy. Two recent methods which are based on physical principles, Projection onto Dipole Fields (PDF)<ref name="Liu 2011 PDF">{{cite journal |last1=Liu |first1=Tian |last2=Khalidov |first2=Ildar |last3=de Rochefort |first3=Ludovic |last4=Spincemaille |first4=Pascal |last5=Liu |first5=Jing |last6=Tsiouris |first6=A. John |last7=Wang |first7=Yi |title=A novel background field removal method for MRI using projection onto dipole fields |journal=NMR in Biomedicine |year=2011 |pmid=21387445 |doi=10.1002/nbm.1670 |volume=24 |issue=9 |pages=1129–36}}</ref> and Sophisticated Harmonic Artifact Reduction on Phase data (SHARP),<ref name="Schweser 2011 SHARP">{{cite journal |last1=Schweser |first1=Ferdinand |last2=Deistung |first2=Andreas |last3=Lehr |first3=Berengar Wendel |last4=Reichenbach |first4=Jürgen Rainer |title=Quantitative imaging of intrinsic magnetic tissue properties using MRI signal phase: an approach to in vivo brain iron metabolism? |journal=NeuroImage |volume=54 |issue=4 |pages=2789–2807 |year=2011 |pmid=21040794 |doi=10.1016/j.neuroimage.2010.10.070}}</ref> demonstrated improved contrast and higher precision on the estimated local field. Both methods model the background field as a [[magnetic field]] generated by an unknown background [[magnetic susceptibility|susceptibility]] distribution, and differentiate it from the local field using either the approximate orthogonality or the harmonic property.
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| === Field-to-source inversion ===
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| The field-to-source inverse problem can be solved by several methods with various associated advantages and limitations.
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| ==== Calculation Of Susceptibility through Multiple Orientation Sampling (COSMOS)<ref name="Liu2009">{{cite journal |last1=Liu |first1=Tian |last2=Spincemaille |first2=Pascal |last3=De Rochefort |first3=Ludovic |last4=Kressler |first4=Bryan |last5=Wang |first5=Yi |title=Calculation of susceptibility through multiple orientation sampling (COSMOS): A method for conditioning the inverse problem from measured magnetic field map to susceptibility source image in MRI |journal=Magnetic Resonance in Medicine |volume=61 |issue=1 |pages=196–204 |year=2009 |pmid=19097205 |doi=10.1002/mrm.21828}}</ref><ref name="Wharton2010">{{cite journal |last1=Wharton |first1=Sam |last2=Schäfer |first2=Andreas |last3=Bowtell |first3=Richard |title=Susceptibility mapping in the human brain using threshold-based k-space division |journal=Magnetic Resonance in Medicine |volume=63 |issue=5 |pages=1292–304 |year=2010 |pmid=20432300 |doi=10.1002/mrm.22334}}</ref>====
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| [[File:Gd cosmos.jpg|left|thumb|The first QSM image reconstructed using COSMOS to quantify [[MRI contrast agent|gadolinium]] concentrations in vials. a)magnitude image; b)field map; c)QSM; d)linear regression.]]COSMOS solves the inverse problem by [[oversampling]] from multiple orientations.<ref name="Liu2009"/> COSMOS utilizes the fact that the zero cone surface in the [[k-space (MRI)|Fourier domain]] is fixed at the [[magic angle]] with respect to the [[B₀]] field. Therefore, if an object is rotated with respect to the [[B₀]] field, then in the object's frame, the [[B₀]] field is rotated and thus the cone. Consequently, data that cannot be calculated due to the cone becomes available at the new orientations.
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| COSMOS assumes a model-free [[magnetic susceptibility|susceptibility]] distribution and keeps full fidelity to the measured data. This method has been validated extensively in ''[[in vitro]]'', ''[[ex vivo]]'' and phantom experiments. Quantitative [[magnetic susceptibility|susceptibility]] maps obtained from ''[[in vivo]]'' human [[neuroimaging|brain imaging]] also showed high degree of agreement with previous knowledge about brain anatomy. Three orientations are generally required for COSMOS, limiting the practicality for clinical applications. However, it may serve as a reference standard when available for calibrating other techniques.
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| ==== Morphology Enabled Dipole Inversion (MEDI)<ref name="de Rochefort 2010">{{cite journal |last1=De Rochefort |first1=Ludovic |last2=Liu |first2=Tian |last3=Kressler |first3=Bryan |last4=Liu |first4=Jing |last5=Spincemaille |first5=Pascal |last6=Lebon |first6=Vincent |last7=Wu |first7=Jianlin |last8=Wang |first8=Yi |title=Quantitative susceptibility map reconstruction from MR phase data using bayesian regularization: Validation and application to brain imaging |journal=Magnetic Resonance in Medicine |pages=194–206 |year=2009 |doi=10.1002/mrm.22187}}</ref>====
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| A unique advantage of [[MRI]] is that it provides not only the phase image but also the magnitude image. In principle, the contrast change, or equivalently the edge, on a magnitude image arises from the underlying change of tissue type, which is the same cause for the change of [[magnetic susceptibility|susceptibility]]. This observation is translated into mathematics in MEDI, where edges in a QSM which do not exist in the corresponding magnitude image are sparsified by solving a weighted [[L1 norm|<math>l_1</math>]] norm minimization problem.<ref><nowiki>http://cds.ismrm.org/protected/10MProceedings/files/4996_705.PDF</nowiki>{{dead link|date=January 2011}} Liu J, Liu T, de Rochefort L, Khalidov I, Prince M, Wang Y. 2010 ''Quantitative susceptibility mapping by regulating the field to source inverse problem with a sparse prior derived from the Maxwell Equation: validation and application to brain'' Proc. Intl. Soc. Mag. Reson. Med. 18 (2010):4996.</ref>
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| MEDI has also been validated extensively in phantom, ''[[in vitro]]'' and ''[[ex vivo]]'' experiments. In ''[[in vivo]]'' human [[brain]], MEDI calculated QSM showed similar results compared to COSMOS without statistically significant difference.<ref name="Liu 2011 MEDI COSMOS">{{cite journal |last1=Liu |first1=Tian |last2=Liu |first2=Jing |last3=de Rochefort |first3=Ludovic |last4=Spincemaille |first4=Pascal |last5=Khalidov |first5=Ildar |last6=Ledoux |first6=James |last7=Wang |first7=Yi |title=Morphology enabled dipole inversion (MEDI) from a single-angle acquisition: Comparison with COSMOS in human brain imaging |journal=Magnetic Resonance in Medicine |pmid=21465541 |doi=10.1002/mrm.22816 |volume=66 |issue=3 |date=September 2011 |pages=777–83}}</ref> MEDI only requires a single angle acquisition, so it is a more practical solution to QSM.
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| ==== Thresholded K-space Division (TKD)<ref name="Wharton2010"/><ref name="Shmueli 2009">{{cite journal |last1=Shmueli |first1=Karin |last2=De Zwart |first2=Jacco A. |last3=Van Gelderen |first3=Peter |last4=Li |first4=Tie-Qiang |last5=Dodd |first5=Stephen J. |last6=Duyn |first6=Jeff H. |title=Magnetic susceptibility mapping of brain tissue in vivo using MRI phase data |journal=Magnetic Resonance in Medicine |volume=62 |issue=6 |pages=1510–22 |year=2009 |pmid=19859937 |doi=10.1002/mrm.22135}}</ref>====
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| The underdetermined data in [[k-space (MRI)|Fourier domain]] is only at the location of the cone and its immediate vicinity. For this region in [[k-space (MRI)|k-space]], spatial-frequencies of the dipole kernel are set to a predetermined non-zero value for the division. Investigation of more advanced strategies for recovering data in this [[k-space (MRI)|k-space]] region is also a topic of ongoing research.<ref name="Li 2011 WKD">{{cite journal |last1=Li |first1=Wei |last2=Wu |first2=Bing |last3=Liu |first3=Chunlei |title=Quantitative susceptibility mapping of human brain reflects spatial variation in tissue composition |journal=NeuroImage |volume=55 |issue=4 |pages=1645–56 |year=2011 |pmid=21224002 |doi=10.1016/j.neuroimage.2010.11.088}}</ref> | |
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| Thresholded [[k-space (MRI)|k-space]] division only requires a single angle acquisition, and benefits from the ease of implementation as well as the fast calculation speed. However, streaking artifacts are frequently present in the QSM and the [[magnetic susceptibility|susceptibility]] value is underestimated compared to COSMOS calculated QSM.
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| == Potential clinical applications ==
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| === Differentiating calcification from iron ===
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| [[File:Iron calc 400.jpg|left|thumb|Differentiation between calcification and iron. From left to right are magnitude, phase and QSM.]]
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| It has been confirmed in ''[[in vivo]]'' and phantom experiments that cortical bones, whose major composition is calcification, are [[diamagnetism|diamagnetic]] compared to water.<ref name="Liu2009"/><ref name="de Rochefort2008">{{cite journal |last1=De Rochefort |first1=Ludovic |last2=Brown |first2=Ryan |last3=Prince |first3=Martin R. |last4=Wang |first4=Yi |title=Quantitative MR susceptibility mapping using piece-wise constant regularized inversion of the magnetic field |journal=Magnetic Resonance in Medicine |volume=60 |issue=4 |pages=1003–9 |year=2008 |pmid=18816834 |doi=10.1002/mrm.21710}}</ref> Therefore, it is possible to use this [[diamagnetism]] to differentiate calcifications from iron deposits that usually demonstrate strong [[paramagnetism]].<ref name="Schweser2010">{{cite journal |last1=Schweser |first1=Ferdinand |last2=Deistung |first2=Andreas |last3=Lehr |first3=Berengar W. |last4=Reichenbach |first4=JüRgen R. |title=Differentiation between diamagnetic and paramagnetic cerebral lesions based on magnetic susceptibility mapping |journal=Medical Physics |volume=37 |issue=10 |pages=5165–78 |year=2010 |pmid=21089750 |doi=10.1118/1.3481505}}</ref> This may allow QSM to serve as a problem solving tool for the diagnosis of confounding hypointense findings on T2* weighted images.
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| === Quantification of contrast agent ===
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| For exogenous susceptibility sources, the susceptibility value is theoretically linearly proportional to the concentration of the contrast agent. This provides a new way for ''[[in vivo]]'' quantification of [[MRI contrast agent|gadolinium]] or [[MRI contrast agent|SPIO]] concentrations.<ref name="de Rochefort2008(2)">{{cite journal |last1=De Rochefort |first1=Ludovic |last2=Nguyen |first2=Thanh |last3=Brown |first3=Ryan |last4=Spincemaille |first4=Pascal |last5=Choi |first5=Grace |last6=Weinsaft |first6=Jonathan |last7=Prince |first7=Martin R. |last8=Wang |first8=Yi |title=In vivo quantification of contrast agent concentration using the induced magnetic field for time-resolved arterial input function measurement with MRI |journal=Medical Physics |volume=35 |issue=12 |pages=5328–39 |year=2008 |pmid=19175092 |doi=10.1118/1.3002309}}</ref>
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| == References ==
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| {{reflist}}
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| [[Category:Magnetic resonance imaging]]
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The OXO 1068557 14 piece professional knife block set provides all of this, by utilizing specially hardened stainless steel and complete tang construction as well as sheer durability from the top quality steel and a guarantee of stain cost-free overall performance. 1 consideration when looking at knife sets - particularly in blocks - is how they appear on the shelf. Should you have almost any inquiries about wherever as well as tips on how to work with Very best Cutting Board Styles - click home page -, you'll be able to email us from the webpage. OXO provides a superb set at a quite very good cost, and the knives execute well. I got this set last year (very same price tag, identical store).
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The knife set shown above is just one particular of many Wusthof knife block sets, some considerably bigger, but the set offered here is an average set, and so is depicted right here merely as an example for my overview. I've waited rather a when to initially obtain and then buy a properly-produced knife set that would each enhance my finest kitchen efforts and would also hopefully last a lifetime. The chef's knife in this set passes that test.