A Review on Interpolation Methods for Diffusion Tensor Images

doi:10.11938/cjmr20182688

Abstract

Abstract: Diffusion tensor imaging measures three-dimensional distribution of water molecule displacement in tissues, and has been widely used to study the structure of the brain. The technique has attracted wide research interests in recent years. Interpolation is often needed in the acquisition and reconstruction of diffusion tensor images to improve spatial resolution and/or facilitate visualization, especially when the images are used for white matter fiber tracking and registration in human brain. In this paper, the existing tensor interpolation methods are reviewed. The theory underlying the interpolation methods is described first. The technical challenges and limitations of the currently-used methods are then reviewed, followed by the introduction to the evaluation indices of the interpolation methods. The performance of typical interpolation methods is then compared with simulated data and real experimental data. The future direction of the development of tensor interpolation method is suggested.

Key words: diffusion tensor imaging (DTI), tensor interpolation, Euler angle, quaternion, fractional anisotropy

CLC Number:

JIANG Fan, WANG Yuan-jun. A Review on Interpolation Methods for Diffusion Tensor Images[J]. Chinese Journal of Magnetic Resonance, 2019, 36(3): 392-407.

References

[1] BASSER P J, MATTIELLO J, LEBIHAN D. MR diffusion tensor spectroscopy and imaging[J]. Biophys J, 1994, 66(1):259-267.
[2] HOPTMAN M J, NIERENBERG J, BERTISCH H C, et al. A DTI study of white matter microstructure in individuals at high genetic risk for schizophrenia[J]. Schizophr Res, 2008, 106(2,3):115-124.
[3] FRINDEL C, ROBINI M, SCHAERER J, et al. A graph-based approach for automatic cardiac tractography[J]. Magn Reson Med, 2010, 64(4):1215-1229.
[4] ALEXANDER D C, PIERPAOLI C, BASSER P J, et al. Spatial transformations of diffusion tensor magnetic resonance images[J]. IEEE Trans Med Imaging, 2001, 20(11):1131-1139.
[5] HUI Z, YUSHKEVICH P A, GEE J C. Deformable registration of diffusion tensor MR images with explicit orientation optimization[J]. Med Image Comput Comput Assist Interv, 2006, 8(1):172-179.
[6] LOMBAERT H, PEYRAT J M, CROISILLE P, et al. Statistical analysis of the human cardiac fiber architecture from DT-MRI[C]//New York:International Conference on Functional Imaging and Modeling of the Heart, 2011:171-179.
[7] PEYRAT J M, SERMESANT M, PENNEC X, et al. A computational framework for the statistical analysis of cardiac diffusion tensors:application to a small database of canine hearts[J]. IEEE Trans Med Imaging, 2007, 26(11):1500-1514.
[8] TOUSSAINT N, SERMESANT M, STOECK C T, et al. In vivo human 3D cardiac fibre architecture:reconstruction using curvilinear interpolation of diffusion tensor images[J]. Med Image Comput Comput Assist Interv, 2010:418-425.
[9] LE B D, MANGIN J F, POUPON C, et al. Diffusion tensor imaging:concepts and applications[J]. J Magn Reson Imaging, 2010, 13(4):534-546.
[10] SHAO Y, LIU Y, SUN F C. Overview of tensor valued images interpolation technology[J]. J Imag Graph, 2012, 17(10):4-12. 邵宇, 刘莹, 孙富春. 张量值图像插值方法综述[J]. 中国图象图形学报, 2012, 17(10):4-12.
[11] KINDLMANN G, WEINSTEIN D, HART D. Strategies for direct volume rendering of diffusion tensor fields[J]. IEEE T Vis Comput Gr, 2000, 6(2):124-138.
[12] TSCHUMPERLE D, DERICHE R. Diffusion tensor regularization with constraints preservation[C]//Kauai:Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2001. doi:10.1109/CVPR.2001.990631.
[13] ZHUKOV L, BARR A H. Oriented tensor reconstruction:tracing neural pathways from diffusion tensor MRI[C]//Boston:IEEE Visualization. 2002. doi:10.1109/VISUAL.2002.1183799.
[14] PENG H L, ORLICHENKO A, DAWE R J, et al. Development of a human brain diffusion tensor template[J]. Neuroimage, 2009, 46(4):967-980.
[15] SMITH S M, JENKINSON M, JOHANSEN-BERG H, et al. Tract-based spatial statistics:voxelwise analysis of multi-subject diffusion data[J]. Neuroimage, 2006, 31(4):1487-1505.
[16] KINDLMANN G, ESTÉPAR R S, NIETHAMMER M, et al. Geodesic-loxodromes for diffusion tensor interpolation and difference measurement[J]. Med Image Comput Comput Assist Interv, 2007, 10(1):1-9.
[17] PENNEC X, FILLARD P, AYACHE N. A riemannian framework for tensor computing[J]. Int J Comput Vis, 2006, 66(1):41-66.
[18] FLETCHER P T, JOSHI S. Riemannian geometry for the statistical analysis of diffusion tensor data[J]. Signal Process, 2007, 87(2):250-262.
[19] SON C I, XIA S R. Diffusion tensor interpolation profile control using non-uniform motion on a Riemannian geodesic[J]. Front Inform Tech El, 2012, 13(2):90-98.
[20] BRO R, ACAR E, KOLDA T G. Resolving the sign ambiguity in the singular value decomposition[J]. J Chemomet, 2008, 22(2):135-140.
[21] SHOEMAKE K. Animating rotation with quaternion curves[C]//New York:SIGGRAPH, 85 Processing of the 42th Annal Conference on Computer Graphics and Interactive Techniques, 1985:245-254.
[22] WANG Z Z, VEMURI B C, CHEN Y M, et al. A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from DWI[J]. Inf Process Med Imaging, 2003, 18:660-671.
[23] WARD P, COUNSELL S, ALLSOP J, et al. Reduced fractional anisotropy on diffusion tensor magnetic resonance imaging after hypoxic-ischemic encephalopathy[J]. Pediatrics, 2006, 117(4):e619-e630.
[24] BURGMANS S, VAN BOXTEL M P, GRONENSCHILD E H, et al. Multiple indicators of age-related differences in cerebral white matter and the modifying effects of hypertension[J]. Neuroimage, 2010, 49(3):2083-2093.
[25] CERCIGNANI M, INGLESE M, PAGANI E, et al. Mean diffusivity and fractional anisotropy histograms of patients with multiple sclerosis[J]. AJNR Am J Neuroradiol, 2001, 22(5):952-958.
[26] GASPAROTTI R, VALSECCHI P, CARLETTI F, et al. Reduced fractional anisotropy of corpus callosum in first-contact, antipsychotic drug-naive patients with schizophrenia[J]. Schizophr Res, 2009, 108(1-3):41-48.
[27] VIRTA A, BARNETT A, PIERPAOLI C. Visualizing and characterizing white matter fiber structure and architecture in the human pyramidal tract using diffusion tensor MRI[J]. Magn Reson Imaging, 1999, 17(8):1121-1133.
[28] ROBERTS T P, LIU F, KASSNER A, et al. Fiber density index correlates with reduced fractional anisotropy in white matter of patients with glioblastoma[J]. AJNR Am J Neuroradiol, 2005, 26(9):2183-2186.
[29] CHAO T C, CHOU M C, YANG P C, et al. Effects of interpolation methods in spatial normalization of diffusion tensor imaging data on group comparison of fractional anisotropy[J]. Magn Reson Imaging, 2009, 27(5):681-690.
[30] STRIJKERS G J, BOUTS A, BLANKESTEIJN W M, et al. Diffusion tensor imaging of left ventricular remodeling in response to myocardial infarction in the mouse[J]. NMR Biomed, 2010, 22(2):182-190.
[31] FLETCHER P T, LU C L, PIZER S M, et al. Principal geodesic analysis for the study of nonlinear statistics of shape[J]. IEEE Trans Med Imaging, 2004, 23(8):995-1005.
[32] FLETCHER P T, JOSHI S. Riemannian geometry for the statistical analysis of diffusion tensor data[J]. Signal Process, 2007, 87(2):250-262.
[33] SMITH S T. Covariance, subspace, and intrinsic Crame/spl acute/r-Rao bounds[J]. IEEE T Signal Process, 2005, 53(5):1610-1630.
[34] BATCHELOR P G, MOAKHER M, ATKINSON D, et al. A rigorous framework for diffusion tensor calculus[J]. Magn Reson Med, 2005, 53(1):221-225.
[35] ARSIGNY V, FILLARD P, PENNEC X, et al. Log-Euclidean metrics for fast and simple calculus on diffusion tensors[J]. Magn Reson Med, 2006, 56(2):411-421.
[36] 甄帅. 磁共振扩散张量图像插值方法及其图像配准应用研究[D]. 杭州:浙江大学, 2013.
[37] ZHEN S, SUN C R, JIANG B, et al. MR diffusion tensor image interpolation method based on local features and profile controlling[J]. Space Medicine & Medical Engineering, 2013, 26(4):323-328. 甄帅, 孙创日, 蒋飚, 等. 基于局部特征与轮廓控制的磁共振扩散张量插值方法[J]. 航天医学与医学工程, 2013, 26(4):323-328.
[38] DAM E B, KOCH M, LILLHOLM M. Quaternions, interpolation and animation[R]. Datalogisk Institut, Kobenhavns Universitet, 1998.
[39] COLLARD A, BONNABEL S, PHILLIPS C, et al. Anisotropy preserving DTI processing[J]. Int J Comput Vision, 2014, 107(1):58-74.
[40] XU Y H, GAO S C, HAO X F, et al. An Improved spectral quaternion interpolation method of diffusion tensor imaging[J]. Journal of Biomedical Engineering, 2016, 33(2):362-367. 徐永红, 高上策, 郝小飞. 一种改进的扩散张量成像谱四元数插值方法[J]. 生物医学工程学杂志, 2016, 33(2):362-367.
[41] YANG F, ZHU Y M, MAGNIN I E, et al. Feature-based interpolation of diffusion tensor fields and application to human cardiac DT-MRI[J]. Med Image Anal, 2012, 16(2):459-481.
[42] YANG N, XU P P, LIU P J, et al. Prognostic classification of Alzheimer's disease brain image based on tensor method[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2017, 56(2):40-47. 杨宁, 徐盼盼, 刘佩嘉, 等. 基于张量法的阿尔兹海默症脑图像分类[J]. 中山大学学报(自然科学版), 2017, 56(2):40-47.
[43] WANG Y J, LIU Y. A Groupwise registration method based on topology center of images[J]. Chinese J Magn Reson, 2018, 35(4):457-464. 王远军, 刘玉. 基于图像集拓扑中心的群体配准方法[J]. 波谱学杂志, 2018, 35(4):457-464.
[44] HUTCHINSON E B, SCHWERIN S C, RADOMSKI K L, et al. Population based MRI and DTI templates of the adult ferret brain and tools for voxelwise analysis[J]. Neuroimage, 2017, 152:575-589.
[45] ZHANG S W, ARFANAKIS K. Evaluation of standardized and study-specific diffusion tensor imaging templates of the adult human brain:Template characteristics, spatial normalization accuracy, and detection of small inter-group FA differences[J]. Neuroimage, 2018, 172:40-50.
[46] JIANG F, WANG Y J. Construction of human brain templates with diffusion tensor imaging data:A review[J]. Chinese J Magn Reson, 2018, 35(4):520-530. 蒋帆, 王远军. 扩散张量成像的人脑模板构建[J]. 波谱学杂志, 2018, 35(4):520-530.