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SCIENTIA SINICA Informationis, Volume 49, Issue 6: 663(2019) https://doi.org/10.1360/N112017-00273

Progress in brain fiber voxel microstructure estimation algorithms

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  • ReceivedJun 27, 2018
  • AcceptedAug 13, 2018
  • PublishedJun 10, 2019

Abstract

Diffusion magnetic resonance imaging (dMRI) is the only available technique for the noninvasive and in vivo reconstruction of white matter microarchitecture. A crucial aspect of the image results is the accuracy of the estimation of fiber orientation. Recently, a number of high angular resolution imaging techniques have been used to estimate fiber orientation. In this paper, we review several white fiber reconstruction algorithms, including the widely used spherical deconvolution. We describe advances in the spherical deconvolution optimization algorithm by the development of the optimization algorithm, including $L_2$ regularization, $L_1$ regularization, $L_1$, and $L_2$ regularization. In addition, we conduct experiments to analyze typical reconstruction algorithm. Finally, future research and development of reconstruction algorithm are discussed.


Funded by

国家自然科学基金(61379020,61703369)

浙江省自然科学基金(LQ16F030009,LY13F030007)

浙江省重点研发计划(2017C03039)

温州市重大科技专项(ZS2017007)


Acknowledgment

感谢 Dipy 库和 Angelos Barm poutis 提供用于计算模型的开源代码,以及 Westin CF 在数据上的支持和方法上的指导. 本文是在浙江工业大学信息工程学院信息处理与自动化研究所以及浙江省嵌入式系统联合重点实验室的共同支持下完成的.


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  • Figure 1

    (Color online) FOD comparison at single voxel model. Comparison of the results for the reconstructed FOD obtained using DTI, CSA-QBI, CT-FOD, SD, RC-CSD, Sparse-SD and spatial-SD, synthetic data with parameters b= 3000 s/mm$^2$, 81 DW directions, and SNR = 40. Each image is colored by RGB. In addition, the grey line represents the actual fiber direction, the red dotted line represents the local optimum of the FOD. The uppermost layer represents the actual fiber intersection angle within the voxel

  • Figure 2

    (Color online) Comparison of angular resolution limitation. Using 5 different $b$ value for comparison, (a) b= 1000 s/mm$^2$, (b) b= 2000 s/mm$^2$, (c) b= 3000 s/mm$^2$, (d) b= 4000 s/mm$^2$, (e) b= 5000 s/mm$^2$, respectively. Each graph indicates the size of the $b$-value of the data used; the $y$-axis represents the minimum angular resolution and the $x$-axis represents the model order. The model represented by each polyline is indicated in the upper right corner of the graph

  • Figure 3

    (Color online) Comparison of fiber detection accuracy. Using different orders for comparison, the orders areprotect łinebreak (a) l= 8, (b) l= 10, (c) l= 12, respectively; the $b$ value of the data is set to 3000 s/mm$^2$

  • Figure 4

    (Color online) Fiber direction estimation results of ISBI data. (a) DTI; (b) CT-FOD; (c) CSA-QBI. The lower left corner of the figure corresponds to the yellow box, respectively

  • Figure 5

    (Color online) Fiber direction estimation results of ISBI data. (a) SD; (b) RC-CSD; (c) Sparse-SD; (d) Spatial-SD. The lower left corner of the figure corresponds to the yellow box, respectively

  • Figure 6

    (Color online) Quantification of the reconstruction accuracy. The results of 7 models in terms of (a) AAE,protect łinebreak (b) N${^+}$ and (c) N${^-}$ using ISBI data with SNR = 10, SNR = 20, SNR = 30, respectively

  • Figure 7

    (Color online) Visualization of FOD reconstructed in the posterior thalamic radiation. (a) DTI; (b) CT-FOD; (c) CSA-QBI. The lower left corner of the figure corresponds to the yellow box

  • Figure 8

    (Color online) Visualization of FOD reconstructed in the posterior thalamic radiation. (a) SD; (b) RC-CSD; (c) Sparse-SD; (d) Spatial-SD. The lower left corner of the figure corresponds to the yellow box

  • Figure 9

    (Color online) Visualization of FOD reconstructed in the superior temporal gyrus WM and the middle temporal gyrus WM. (a) DTI; (b) CT-FOD; (c) CSA-QBI. The lower left corner of the figure corresponds to the yellow box

  • Figure 10

    (Color online) Visualization of FOD reconstructed in the superior temporal gyrus WM and the middle temporal gyrus WM. (a) SD; (b) RC-CSD; (c) Sparse-SD; (d) Spatial-SD. The lower left corner of the figure corresponds to the yellow box

  • Table 1   List of deconvolution framework
    Method $F(v)$ $R(g,v)$
    Basser et al. [3] $\delta~(D;{D_0})$ ${{\rm~e}^{~-~{g^{\rm~T}}Dg}}$
    Tuch et al. [29] ${w_k}\delta~(D;{D_k})$ ${{\rm~e}^{~-~{g^{\rm~T}}Dg}}$
    Tournier et al. [6,34] $a_{lm}Y_{lm}$ ${{\rm~e}^{~-~{{(gv)}^2}}}$
    Anderson [43] $a_{lm}Y_{lm}$ ${{\rm~e}^{~-~{g^{\rm~T}}D_\lambda~^vg}}$
    Alexander [59] ${w_k}{{\rm~e}^{~-~\frac{{\arccos~{{(|~{v~\cdot~{v_k}}|)}^2}}}{{{\sigma~^2}}}}}$ ${{\rm~e}^{~-~{g^{\rm~T}}Dg}}$
    Jian et al. [60] ${w_k}{\gamma~_{p,D_\lambda~^{{v_k}}}}$ ${{\rm~e}^{~-~{g^{\rm~T}}Dg}}$
    Ramirez-Manzanareas et al. [61] ${w_k}\delta~(v;{v_k})$ ${{\rm~e}^{~-~{g^{\rm~T}}D_\lambda~^vg}}$

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