^{1}

^{1}

^{2,3}

^{1}

^{2}

^{1}

^{2}

^{3}

Diffusion Tensor Imaging (DTI) image registration is an essential step for diffusion tensor image analysis. Most of the fiber bundle based registration algorithms use deterministic fiber tracking technique to get the white matter fiber bundles, which will be affected by the noise and volume. In order to overcome the above problem, we proposed a Diffusion Tensor Imaging image registration method under probabilistic fiber bundles tractography learning. Probabilistic tractography technique can more reasonably trace to the structure of the nerve fibers. The residual error estimation step in active sample selection learning is improved by modifying the residual error model using finite sample set. The calculated deformation field is then registered on the DTI images. The results of our proposed registration method are compared with 6 state-of-the-art DTI image registration methods under visualization and 3 quantitative evaluation standards. The experimental results show that our proposed method has a good comprehensive performance.

Diffusion Tensor Imaging (DTI) is a Magnetic Resonance Imaging (MRI) technique which measures diffusion properties of water molecules in tissue to gained neural bundle images, which cannot be obtained by other imaging modalities [

According to the object of the registration algorithm, the existing DTI image registration algorithms can be divided into three categories: the scalar image based registration algorithm, the tensor image based registration algorithm, and the fiber bundle based registration algorithm [

In the fiber bundle based registration method, fiber tracking is a very important step, and the correctness of fiber tracking directly affects the accuracy of the registration [

Probabilistic tractography uses a deterministic streamline algorithm to generate thousands of trajectories by Monte Carlo methods. The directions of the line segments are repeatedly sampled from a Bayesian posterior distribution [

To resolve this disadvantage, a typical active sample selection learning method called bootstrap [

Based on the above analysis, in this paper, we proposed a DTI image registration method under probabilistic fiber bundles tractography learning. We improve the residual error estimation step in bootstrap method used in active sample selection learning for the probabilistic tractography. Our method assumes that, in the case of independent and identically distributed error, the residuals can be adjusted and the error model is then modified by using finite sample set, therefore, improving the study ability of samples. Subsequently, the tracked fiber bundles can be registered by using symmetric image standardization registration algorithm. The results of our proposed registration method are compared with 6 state-of-the-art DTI image registration methods under visualization and 3 quantitative evaluation standards [

DTI registration methods are mainly divided into three parts by the processing object: the scalar image based registration algorithm, the tensor image based registration algorithm, and the fiber bundle based registration algorithm.

Scalar image based registration methods convert tensor images into scalar images, for example, fractional anisotropy (FA) images, by rotationally invariant measures, and then perform registration on the scalar images. Studholme et al. [

Diffeomorphic mapping is a smooth spatial transform, in which the topology of the images is preserved, as well as voxel correspondence based on the second-order tensor field of Riemannian manifold. It was combined with Lie group [

Based on the above advantages, Cao et al. [

The registration of tensor image is more difficult than scalar image based registration. One reason is multidimensionality of the data. Another is that anatomical structure has changed after image transformations. We need to ensure the tensor orientations to keep consistence with the anatomy.

In 2003, Park et al. [

With direct registration of fiber, we can avoid the estimation error of DTI direction and improve the accuracy as well as robustness of the registration. In 2007, Mayer and Greenspan [

Compared to the deterministic fiber tracking technology, probabilistic tractography technique can more reasonably trace to the structure of the nerve fibers and in a certain extent overcome the internal defect of the single tensor model. Since the probability statistics method is introduced, probabilistic tractography can effectively reduce uncertainty of tracking results by noise and other environmental factors and thus has better performance of antinoise interference. But there are few researches on the DTI image registration based on the probabilistic fiber bundles tractography.

To improve the efficiency of DTI image registration, we proposed a DTI image registration method under probabilistic fiber bundles tractography learning. We first get the distribution of the whole brain white matter fiber bundles based on probabilistic tractography. Then, the tracked fiber bundles can be registered by using symmetric image standardization registration algorithm, and the calculated deformation field acts on the DTI images, finally implementing the accurate DTI images registration. For the experiments, we compared our method with the state of the art methods under visualization and three quantitative evaluation standards and gave a comprehensive analysis.

Our method is innovative in the following two aspects:

Using fiber bundles tracked by probabilistic tractography to calculate the deformation field of DTI image registration: Registration based on white matter fiber bundles can avoid the estimation error of DTI direction. Furthermore, probabilistic tractography technique can more reasonably trace to the structure of the nerve fibers and can effectively reduce uncertainty of tracking results by noise and other environmental factors.

Improving the residual error estimation step in bootstrap method used in active sample selection learning for the probabilistic tractography: Our method assumes that, in the case of independent and identically distributed error, the residuals can be adjusted and the error model is then modified by using finite sample set, therefore, improving the study ability of samples.

Given a brain diffusion MRI image, the DTI can be modeled as a simple diffusion with a Gaussian profile [

To sample the ellipsoid structure based on probability distribution, the

Probabilistic tracking algorithm devised by Friman et al. [

In order to make (

In the probabilistic tractography, sample selection is a very important step. Through the sample selection step, a large number of samples describing the fiber paths starting from region

Sample selection learning is one kind of learning methods which learn from the environment to obtain a number of concept related examples and derive general concept after the induction. Bootstrap [

Having observed a random sample

The wild bootstrap (WB) proposed originally by Wu [

Our method assumes that, in the case of independent and identically distributed error, the residuals can be adjusted and the error model is then modified by using finite sample set. Consequently, our method generates each bootstrap sample using

^{2} (repetition time = 11894.44 ms; echo time = 51 ms). More parameter information can be found at the website.

2D views of the template (the color images are encoded as follows: red for left-right, green for anterior-posterior, and blue for inferior-superior).

DTI axial image

DTI sagittal image

DTI coronal image

FA axial image

FA sagittal image

FA coronal image

TR axial image

TR sagittal image

TR coronal image

Brain Extraction Tool (BET) in FMRIB software Library was used to extract brain tissue for each subject and template. The mask used for skull stripping was generated from each subject or template individually and checked manually. Before tensor estimation, diffusion weighted images (DWIs) in 15 diffusion gradient directions were eddy-current corrected with FMRIB software Library.

In this paper, the symmetric image standardization algorithm (also called symmetric image normalization, SyN) proposed by Avants et al. [

In the spatial domain of fiber bundles

Through the integration of time and smooth velocity field, the diffeomorphism transformation

The Euler-Lagrange equation is then used for algorithm optimization. For computation from the fiber bundle to be registered to the standard template fiber bundle or from the standard template fiber bundle to the fiber bundle to be registered, the path is the same

SyN algorithm can deal with both small and large deformation. The results will not change by the input data order, and the diffeomorphic mapping ensures the precision of the reversible consistency transform.

After the eigen decomposition of the diffusion tensor, the eigenvalues could be denoted in descending order as

The overlap of eigenvalue-eigenvector pairs is defined as

The cross-correlations of the WM voxels between subjects and template are computed by using the FA and TR:

In order to test the performance of the proposed registration method based on probabilistic fiber bundles tractography learning, in this paper, we compare our method with 6 state-of-the-art methods, which are 5 scalar based methods: Rigid [

The result of fiber bundles tracking will affect the accuracy of the following registration method as tracking result is the input of registration step; as a result, fiber bundles tracking is an important step in the whole algorithm system. Figure

Fiber bundles tracking results (8 ROIs is Genu of the Corpus Callosum (Genu), Splenium of the Corpus Callosum (Splenium), Left Anterior Thalamic Radiations (ATR), Right ATR, Left Inferior Frontooccipital Fasciculi (IFO), Right IFO, Left Corticospinal/Corticobulbar Tracts (CST), and Right CST).

Global display of fiber bundles tracking results.

In this section, we test the registration effectiveness by visualization. The results of 7 registration algorithms are shown in Figure

The results of 7 registration algorithms.

Template

Subject

Rigid result

Elastic result

Affine result

FSL result

SyN result

DTI-TK result

Proposed result

The higher dyadic coherence value indicates better eigenvectors alignment and anatomical structure consistency. The empirical CDFs of dyadic coherence are presented in Figure

The empirical CDFs of dyadic coherence and OVL. (a) is the empirical CDFs of dyadic coherence; (b) is the empirical CDFs of OVL.

A higher OVL values represents a greater correspondence in anatomical structure between subjects. The empirical CDFs of OVL are presented in Figure

For the cross-correlation, higher value represents the higher similarity between two maps. The empirical CDFs of cross-correlation for FA and TR are presented in Figures

The empirical CDFs of cross-correlation. (a) is the empirical CDFs of the cross-correlations for FA; (b) is the empirical CDFs of the cross-correlations for TR.

From three evaluation criteria and visualization experimental results, our proposed method shows a high comprehensive performance. DTI-TK method is the currently recognized best registration method; our method shows the quite equal comprehensive performance. DTI-TK is a nonparametric, diffeomorphic deformable image registration, taking tensors as a whole and explicating the optimization of tensor reorientation. The disadvantage of the DTI-TK is that the image boundary is not smooth and the computing is complicated. Meanwhile, it only supports the affine transformation with the least parameters. Our method is based on the completely different algorithm theory; we completes the DTI Image registration method under probabilistic fiber bundles tractography learning. The distribution of the whole brain white matter fiber bundles is first obtained based on probabilistic tractography. Then, the tracked fiber bundles are registered by using symmetric image standardization registration algorithm, and the calculated deformation field acts on the DTI images. Those steps all have the advantages to improve the registration accuracy and robustness.

For the empirical CDFs of

In this paper, we proposed a DTI Image registration method under probabilistic fiber bundles tractography learning, as the probabilistic tractography technique can more reasonably trace to the structure of the nerve fibers and in a certain extent overcome the internal defect of the single tensor model. We improved the residual error estimation step in bootstrap method used in active sample selection learning for the probabilistic tractography. The results of our proposed method were compared with 5 scalar based methods (Rigid, Affine, Elastic, SyN, and FSL) and one tensor based method (DTI-TK). The visualization and 3 quantitative evaluation standards were used to give a comprehensive analysis. The experimental results show that our proposed probabilistic fiber bundles tracking method has the ability to track white matter fiber bundles of diffusion MRI image accurately. Our registration method gives a quite equal comprehensive performance with DTI-TK, much better than the others. Consequently, our method can be used for accurate and efficient DTI image registration.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported in part by the National Natural Science Foundation of China under Grants 61303123, 61402371, and 61461025, Natural Science Basic Research Plan in Shaanxi Province of China under Grants 2015JM6317 and 2015JQ6256, and the Fundamental Research Funds for the Central Universities under Grant 3102015JSJ0008.