346:. Two recent methods based on physical principles, projection onto dipole fields (PDF) and sophisticated harmonic artifact reduction on phase data (SHARP), 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 susceptibility distribution, and differentiate it from the local field using either the approximate orthogonality or the harmonic property. The background field can also be directly computed by solving the Laplace's equation with simplified boundary values, as demonstrated in the Laplacian boundary value (LBV) method.
315:
363:
96:
509:
490:
The underdetermined data in
Fourier domain is only at the location of the cone and its immediate vicinity. For this region in 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
436:
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 susceptibility. This observation is translated into
334:
Ideally, the background field can be directly measured with a separate reference scan, where the sample of interest is replaced by a uniform phantom with the same shape while keeping the scanner shimming identical. However, for clinical application, such an approach is impossible and post-processing
494:
Thresholded 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 susceptibility value is underestimated compared to COSMOS calculated QSM.
330:
induced by the local sources is inevitably contaminated by the field induced by other sources such as main field inhomogeneity (imperfect shimming) and the air-tissue interface, whose susceptibility difference is orders of magnitudes stronger than that of the local sources. Therefore, the
423:
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.
74:
to susceptibility source inverse problem, and generates a three-dimensional susceptibility distribution. Due to its quantitative nature and sensitivity to certain kinds of material, potential QSM applications include standardized quantitative stratification of
1278:
De
Rochefort, Ludovic; Nguyen, Thanh; Brown, Ryan; Spincemaille, Pascal; et al. (2008). "In vivo quantification of contrast agent concentration using the induced magnetic field for time-resolved arterial input function measurement with MRI".
265:. This 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
781:
Schweser, Ferdinand; Deistung, Andreas; Lehr, Berengar Wendel; Reichenbach, Jürgen Rainer (2011). "Quantitative imaging of intrinsic magnetic tissue properties using MRI signal phase: an approach to in vivo brain iron metabolism?".
305:
inhomogeneity. Flow compensation may further improve the accuracy of susceptibility measurement in venous blood, but there are certain technical difficulties to devise a fully flow compensated multi-echo sequence.
481:
human brain, MEDI calculated QSM showed similar results compared to COSMOS without statistically significant difference. MEDI only requires a single angle acquisition, so it is a more practical solution to QSM.
1234:
Schweser, Ferdinand; Deistung, Andreas; Lehr, Berengar W.; Reichenbach, JüRgen R. (2010). "Differentiation between diamagnetic and paramagnetic cerebral lesions based on magnetic susceptibility mapping".
873:"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"
273:
in the
Fourier domain. Consequently, susceptibility is underdetermined at the spatial frequencies on the cone surface, which often leads to severe streaking artifacts in the reconstructed QSM.
660:
Salomir, Rares; De
Senneville, Baudouin Denis; Moonen, Chrit TW (2003). "A fast calculation method for magnetic field inhomogeneity due to an arbitrary distribution of bulk susceptibility".
263:
222:
1015:"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"
128:
463:
163:
294:
effects, although the optimal imaging parameters depend on the specific applications and the field strength. A multi-echo acquisition is beneficial for accurate
290:
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
187:
526:
compared to water. Therefore, it is possible to use this diamagnetism to differentiate calcifications from iron deposits that usually demonstrate strong
401:
COSMOS assumes a model-free susceptibility distribution and keeps full fidelity to the measured data. This method has been validated extensively in
1014:
974:"Quantitative susceptibility map reconstruction from MR phase data using bayesian regularization: Validation and application to brain imaging"
398:
field is rotated and thus the cone. Consequently, data that cannot be calculated due to the cone becomes available at the new orientations.
825:
Zhou, Dong; Liu, Tian; Spincemaille, Pascal; Wang, Yi (2014). "Background field removal by solving the
Laplacian boundary value problem".
1328:
689:"Application of a Fourier-based method for rapid calculation of field inhomogeneity due to spatial variation of magnetic susceptibility"
17:
437:
mathematics in MEDI, where edges in a QSM which do not exist in the corresponding magnitude image are sparsified by solving a weighted
530:. This may allow QSM to serve as a problem solving tool for the diagnosis of confounding hypointense findings on T2* weighted images.
339:, are useful for the background field removal, although they also tamper with the local field and degrade the quantitative accuracy.
83:, accurate gadolinium quantification in contrast enhanced MRI, and direct monitoring of targeted theranostic drug biodistribution in
538:
For exogenous susceptibility sources, the susceptibility value is theoretically linearly proportional to the concentration of the
331:
non-biological background field needs to be removed for clear visualization on phase images and precise quantification on QSM.
44:
1056:"Morphology enabled dipole inversion (MEDI) from a single-angle acquisition: Comparison with COSMOS in human brain imaging"
326:
quantitative susceptibility mapping, only the local susceptibility sources inside the brain are of interest. However, the
354:
The field-to-source inverse problem can be solved by several methods with various associated advantages and limitations.
318:
Estimated local field maps using left) high-pass filtering method, right) projection onto dipole fields (PDF) method.
342:
More recent background field removal methods directly or indirectly exploit the fact that the background field is a
104:
231:
80:
1195:"Quantitative MR susceptibility mapping using piece-wise constant regularized inversion of the magnetic field"
192:
291:
287:
131:
55:
578:
2nd
International Workshop on MRI Phase Contrast & Quantitative Susceptibility Mapping, Cornell (2013)
600:
4th
International Workshop on MRI Phase Contrast & Quantitative Susceptibility Mapping, Graz (2016)
589:
3rd
International Workshop on MRI Phase Contrast & Quantitative Susceptibility Mapping, Duke (2014)
1288:
1244:
1097:"Quantitative susceptibility mapping of human brain reflects spatial variation in tissue composition"
567:
1st
International Workshop on MRI Phase Contrast and Quantitative Susceptibility Mapping, Jena (2011)
1029:
76:
1054:
Liu, Tian; Liu, Jing; de
Rochefort, Ludovic; Spincemaille, Pascal; et al. (September 2011).
954:
902:
850:
807:
736:
547:
367:
63:
512:
Differentiation between calcification and iron. From left to right are magnitude, phase and QSM.
24:
brain QSM acquired at 3 Tesla and reconstructed with morphology enabled dipole inversion (MEDI).
1304:
1260:
1216:
1175:
1126:
1077:
995:
946:
894:
842:
799:
763:
642:
613:"Quantitative susceptibility mapping (QSM): Decoding MRI data for a tissue magnetic biomarker"
566:
343:
110:
36:
871:
Liu, Tian; Spincemaille, Pascal; De Rochefort, Ludovic; Kressler, Bryan; et al. (2009).
730:
Liu, Tian; Khalidov, Ildar; de Rochefort, Ludovic; Spincemaille, Pascal; et al. (2011).
1296:
1252:
1206:
1165:
1157:
1144:
Shmueli, Karin; De Zwart, Jacco A.; Van Gelderen, Peter; Li, Tie-Qiang; et al. (2009).
1116:
1108:
1067:
985:
936:
884:
834:
791:
753:
745:
710:
700:
669:
632:
624:
336:
295:
135:
21:
522:
and phantom experiments that cortical bones, whose major composition is calcification, are
441:
148:
1292:
1248:
370:
concentrations in vials. a) magnitude image; b) field map; c) QSM; d) linear regression.
1170:
1145:
1121:
1096:
758:
731:
637:
612:
539:
378:
from multiple orientations. COSMOS utilizes the fact that the zero cone surface in the
327:
172:
71:
1322:
1112:
958:
795:
732:"A novel background field removal method for MRI using projection onto dipole fields"
527:
379:
225:
906:
811:
854:
523:
420:
375:
84:
67:
972:
De Rochefort, Ludovic; Liu, Tian; Kressler, Bryan; Liu, Jing; et al. (2009).
925:"Susceptibility mapping in the human brain using threshold-based k-space division"
383:
266:
142:
1146:"Magnetic susceptibility mapping of brain tissue in vivo using MRI phase data"
314:
224:. This spatial convolution can be expressed as a point-wise multiplication in
59:
16:
58:, which is useful for chemical identification and quantification of specific
358:
Calculation of susceptibility through multiple orientation sampling (COSMOS)
54:
intensity in QSM is linearly proportional to the underlying tissue apparent
1308:
1264:
1220:
1179:
1130:
1081:
999:
950:
898:
846:
803:
767:
646:
508:
403:
1193:
De Rochefort, Ludovic; Brown, Ryan; Prince, Martin R.; Wang, Yi (2008).
705:
688:
673:
413:
and phantom experiments. Quantitative susceptibility maps obtained from
70:
iron oxide (SPIO) nano-particles. QSM utilizes phase images, solves the
715:
518:
438:
415:
409:
1300:
1256:
1211:
1194:
1161:
1072:
1055:
990:
973:
941:
924:
889:
872:
628:
577:
362:
335:
based methods are preferred. Traditional heuristic methods, including
95:
838:
749:
693:
Concepts in Magnetic Resonance Part B: Magnetic Resonance Engineering
166:
588:
507:
361:
323:
313:
94:
51:
15:
390:
field. Therefore, if an object is rotated with respect to the B
433:
40:
366:
The first QSM image reconstructed using COSMOS to quantify
599:
923:
Wharton, Sam; Schäfer, Andreas; Bowtell, Richard (2010).
491:
this k-space region is also a topic of ongoing research.
1013:
Liu, J; Liu, T; de Rochefort, L; Khalidov, I (2010).
469:
MEDI has also been validated extensively in phantom,
444:
234:
195:
175:
151:
113:
457:
257:
216:
181:
157:
122:
301:field measurement without the contribution from B
918:
916:
99:A visualization of the cone in Fourier domain.
8:
258:{\displaystyle \Delta B=D\cdot \mathrm {X} }
866:
864:
428:Morphology enabled dipole inversion (MEDI)
145:of the volume susceptibility distribution
1210:
1169:
1120:
1071:
989:
940:
888:
757:
714:
704:
636:
449:
443:
250:
233:
194:
174:
150:
130:induced by non-ferromagnetic biomaterial
112:
1095:Li, Wei; Wu, Bing; Liu, Chunlei (2011).
394:field, then in the object's frame, the B
559:
504:Differentiating calcification from iron
217:{\displaystyle \delta B=d\otimes \chi }
374:COSMOS solves the inverse problem by
7:
687:Marques, J.P.; Bowtell, R. (2005).
29:Quantitative susceptibility mapping
486:Thresholded K-space division (TKD)
251:
235:
14:
43:(MRI) different from traditional
1113:10.1016/j.neuroimage.2010.11.088
1022:Proc. Intl. Soc. Mag. Reson. Med
796:10.1016/j.neuroimage.2010.10.070
534:Quantification of contrast agent
499:Potential clinical applications
45:susceptibility weighted imaging
1199:Magnetic Resonance in Medicine
1150:Magnetic Resonance in Medicine
1060:Magnetic Resonance in Medicine
978:Magnetic Resonance in Medicine
929:Magnetic Resonance in Medicine
877:Magnetic Resonance in Medicine
662:Concepts in Magnetic Resonance
617:Magnetic Resonance in Medicine
542:. This provides a new way for
1:
134:along the main polarization
466:norm minimization problem.
1345:
1329:Magnetic resonance imaging
41:magnetic resonance imaging
516:It has been confirmed in
350:Field-to-source inversion
81:neurodegenerative disease
62:including iron, calcium,
550:or SPIO concentrations.
310:Background field removal
123:{\displaystyle \delta B}
56:magnetic susceptibility
1028:: 4996. Archived from
513:
459:
432:A unique advantage of
371:
319:
259:
218:
183:
159:
124:
100:
25:
511:
460:
458:{\displaystyle l_{1}}
386:with respect to the B
365:
317:
260:
219:
184:
160:
158:{\displaystyle \chi }
125:
98:
19:
442:
232:
193:
173:
149:
111:
77:cerebral microbleeds
1293:2008MedPh..35.5328D
1249:2010MedPh..37.5165S
1035:on October 16, 2015
706:10.1002/cmr.b.20034
674:10.1002/cmr.b.10083
477:experiments. In an
337:high-pass filtering
35:) provides a novel
827:NMR in Biomedicine
737:NMR in Biomedicine
546:quantification of
514:
455:
372:
320:
286:In principle, any
255:
214:
179:
155:
120:
107:, the local field
101:
26:
1301:10.1118/1.3002309
1257:10.1118/1.3481505
1212:10.1002/mrm.21710
1162:10.1002/mrm.22135
1073:10.1002/mrm.22816
991:10.1002/mrm.22187
942:10.1002/mrm.22334
890:10.1002/mrm.21828
629:10.1002/mrm.25358
611:Wang, Yi (2014).
344:harmonic function
269:with respect to B
182:{\displaystyle d}
1336:
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920:
911:
910:
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868:
859:
858:
839:10.1002/nbm.3064
822:
816:
815:
790:(4): 2789–2807.
778:
772:
771:
761:
750:10.1002/nbm.1670
727:
721:
720:
718:
708:
684:
678:
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382:is fixed at the
282:Data acquisition
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1338:
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1333:
1319:
1318:
1317:
1316:
1287:(12): 5328–39.
1281:Medical Physics
1277:
1276:
1272:
1243:(10): 5165–78.
1237:Medical Physics
1233:
1232:
1228:
1192:
1191:
1187:
1143:
1142:
1138:
1094:
1093:
1089:
1053:
1052:
1048:
1038:
1036:
1032:
1017:
1012:
1011:
1007:
971:
970:
966:
935:(5): 1292–304.
922:
921:
914:
870:
869:
862:
824:
823:
819:
780:
779:
775:
729:
728:
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22:volume rendered
12:
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5:
1342:
1340:
1332:
1331:
1321:
1320:
1315:
1314:
1270:
1226:
1185:
1156:(6): 1510–22.
1136:
1107:(4): 1645–56.
1087:
1046:
1005:
984:(1): 194–206.
964:
912:
883:(1): 196–204.
860:
817:
773:
744:(9): 1129–36.
722:
679:
652:
603:
592:
581:
570:
558:
557:
555:
552:
540:contrast agent
535:
532:
505:
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487:
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452:
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380:Fourier domain
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328:magnetic field
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292:susceptibility
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226:Fourier domain
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132:susceptibility
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72:magnetic field
13:
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1227:
1222:
1218:
1213:
1208:
1205:(4): 1003–9.
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1189:
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1177:
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1167:
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1074:
1069:
1066:(3): 777–83.
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1016:
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623:(1): 82–101.
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528:paramagnetism
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421:brain imaging
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141:field is the
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61:
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39:mechanism in
38:
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18:
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1202:
1198:
1188:
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1139:
1104:
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1090:
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1059:
1049:
1037:. Retrieved
1030:the original
1025:
1021:
1008:
981:
977:
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932:
928:
880:
876:
833:(3): 312–9.
830:
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376:oversampling
373:
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321:
285:
102:
85:nanomedicine
68:paramagnetic
66:, and super
49:
32:
28:
27:
1039:January 26,
716:2066/195319
524:diamagnetic
384:magic angle
267:magic angle
143:convolution
1101:NeuroImage
784:NeuroImage
554:References
548:gadolinium
368:gadolinium
277:Techniques
91:Background
64:gadolinium
60:biomarkers
959:206278637
699:: 65–78.
668:: 26–34.
322:In human
248:⋅
236:Δ
212:χ
209:⊗
197:δ
165:with the
153:χ
115:δ
1323:Category
1309:19175092
1265:21089750
1221:18816834
1180:19859937
1131:21224002
1082:21465541
1000:19953507
951:20432300
907:41444063
899:19097205
847:24395595
812:19593094
804:21040794
768:21387445
647:25044035
471:in vitro
404:in vitro
37:contrast
1289:Bibcode
1245:Bibcode
1171:4275127
1122:3062654
855:1815936
759:3628923
638:4297605
544:in vivo
519:in vivo
479:in vivo
475:ex vivo
416:in vivo
410:ex vivo
169:kernel
1307:
1263:
1219:
1178:
1168:
1129:
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1080:
998:
957:
949:
905:
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766:
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645:
635:
419:human
167:dipole
1033:(PDF)
1018:(PDF)
955:S2CID
903:S2CID
851:S2CID
808:S2CID
324:brain
52:voxel
1305:PMID
1261:PMID
1217:PMID
1176:PMID
1127:PMID
1078:PMID
1041:2011
996:PMID
947:PMID
895:PMID
843:PMID
800:PMID
764:PMID
643:PMID
473:and
79:and
50:The
1297:doi
1253:doi
1207:doi
1166:PMC
1158:doi
1117:PMC
1109:doi
1068:doi
986:doi
937:doi
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