基于高斯平均的DTI脑模板构建方法

doi:10.11938/cjmr20212957

摘要/Abstract

摘要：

在获取被试的张量数据后通常对其进行多通道线性平均以得到张量模板.但线性平均不仅会忽略张量中的向量信息，还会使灰质和白质的交界处过于平滑，降低模板的分辨率.为了解决以上问题，本文引入了四元数及高斯加权平均来构建高斯扩散张量成像（Diffusion Tensor Imaging，DTI）脑模板.本文首先对55个健康被试的DTI数据进行预处理，使得数据伪影最小化；再通过扩散张量成像工具包（Diffusion Tensor Imaging ToolKit，DTI-TK）将预处理后的数据进行初步空间标准化；然后将张量通过特征分解得到特征向量和特征值；最后，将由特征向量转化的四元数标量和特征值分别进行高斯加权平均得到平均后的特征向量和特征值，并对其进行重建得到张量模板.实验结果表明相比于线性DTI模板，高斯DTI模板在DTED、COH、DVED、OVL、corr_FA评估指标上表现更优，而IA指标较差，说明本文提出的高斯DTI模板在整体信息保留方面有所优化，但方向信息有所丢失.

关键词: 扩散磁共振成像, 脑模板, DTI配准, 高斯平均

Abstract:

The tensor data of subjects are usually averaged linearly over multiple channels to obtain the tensor template. However, linear averaging ignores the vector information in the tensor. Additionally, it will render the interface between the gray matter and white matter too smooth, resulting in resolution reduction. To address the above problems, this paper introduced quaternion and Gaussian weighted average to construct a Gaussian diffusion tensor imaging (DTI) brain template. First, the DTI data of 55 healthy subjects were preprocessed to minimize data artifacts. The obtained data were then subjected to preliminary spatial standardization. Then, the tensor was decomposed to acquire eigenvectors and eigenvalues. Finally, the eigenvalues and quaternion converted from the eigenvectors were followed by Gaussian weighted average to gain the averaged eigenvectors and eigenvalues. The tensor template was obtained by reconstructing the averaged eigenvectors and eigenvalues. The experimental results show that compared with the linear DTI template, the Gaussian DTI template performs better on the DTED, COH, DVED, OVL, and corr_FA evaluation indicators but poorer on the IA indicator. The Gaussian DTI template proposed in this paper has certain advantage on the overall information retention, but is to be further improved on the orientation information.

Key words: diffusion magnetic resonance imaging, brain template, DTI registration, Gaussian average

中图分类号:

O482.53

邓岚,王远军. 基于高斯平均的DTI脑模板构建方法[J]. 波谱学杂志, 2022, 39(4): 413-427.

Lan DENG,Yuan-jun WANG. DTI Brain Template Construction Based on Gaussian Averaging[J]. Chinese Journal of Magnetic Resonance, 2022, 39(4): 413-427.

图/表 9

图1

图2

图3

图4

图5

表1

表2

脑模板参数评估

被试编号	DTED/(×10⁴)		COH		DVED/(×10⁵)		OVL		corr_FA/(×10^?1)
被试编号	Gauss	linear	Gauss	linear	Gauss	linear		linear	Gauss	linear
1	0.141±0.428	3.83±10.2	0.029±0.055	0.026±0.061	2.61±7.93	44.6±126	0.152±2.80	0.148±4.38	6.31	6.30
2	0.128±0.396	3.81±10.1	0.084±0.024	0.028±0.053	2.65±8.01	44.6±126	0.156±2.65	0.151±8.91	7.14	7.13
3	0.131±0.397	3.82±10.2	0.026±0.056	0.091±0.036	2.70±8.15	44.7±130	0.145±2.30	0.142±2.87	6.70	6.69
4	0.128±0.391	3.82±10.2	0.045±0.058	0.028±0.031	2.65±7.98	44.7±126	0.150±4.36	0.118±43.3	6.98	6.97
5	0.130±0.397	3.83±10.2	0.037±0.036	0.031±0.022	2.67±8.05	44.7±126	0.155±1.24	0.158±2.78	6.84	6.83
6	0.128±0.393	3.83±10.2	0.054±0.023	0.041±0.041	2.84±8.62	44.8±127	0.140±1.34	0.139±2.67	6.61	6.60
7	0.123±0.380	3.84±10.2	0.023±0.010	0.139±0.025	2.74±8.29	44.7±126	0.148±1.19	0.147±0.95	7.11	7.10
8	0.131±0.400	3.83±10.2	0.050±0.063	0.080±0.036	2.70±8.17	44.7±126	0.141±6.34	0.155±15.1	6.74	6.73
9	0.133±0.407	3.82±10.2	0.047±0.050	0.033±0.058	2.65±8.00	44.7±126	0.148±5.28	0.151±0.24	6.83	6.82
10	0.123±0.380	3.82±10.1	0.142±0.008	0.010±0.026	2.77±8.34	44.8±127	0.148±1.18	0.147±0.72	7.09	7.08
11	0.101±0.342	3.86±10.1	0.138±0.025	0.101±0.062	2.71±8.91	44.7±127	0.164±3.53	0.100±7.95	6.58	6.35
12	0.129±0.337	3.88±10.1	0.096±0.036	0.051±0.051	2.83±7.03	44.5±127	0.143±4.53	0.126±8.53	6.29	5.65
13	0.156±0.382	3.81±10.2	0.122±0.008	0.045±0.039	2.62±8.63	44.7±126	0.167±5.52	0.143±7.85	6.42	5.07
14	0.140±0.392	3.90±10.1	0.060±0.028	0.052±0.065	2.79±8.12	44.5±127	0.154±3.09	0.123±5.32	5.84	5.48
15	0.144±0.309	3.84±10.1	0.093±0.021	0.060±0.013	2.59±7.47	44.6±127	0.140±2.57	0.130±0.24	7.32	6.91
16	0.109±0.307	3.87±10.2	0.064±0.025	0.039±0.034	2.82±8.25	44.6±127	0.180±5.44	0.160±1.38	8.88	6.20
17	0.129±0.348	3.85±10.2	0.147±0.024	0.116±0.058	2.56±8.17	44.8±127	0.167±5.32	0.150±10.9	8.22	7.53
18	0.127±0.336	3.71±10.1	0.105±0.043	0.124±0.069	2.84±7.26	44.8±127	0.158±5.42	0.155±8.95	7.25	6.31
19	0.151±0.325	3.83±10.2	0.192±0.041	0.131±0.014	2.50±7.34	44.7±127	0.162±4.44	0.122±6.68	7.36	5.01
20	0.109±0.388	3.74±10.2	0.102±0.042	0.093±0.065	2.42±8.71	44.7±127	0.144±6.24	0.142±2.03	8.16	5.01
21	0.105±0.331	3.77±10.2	0.092±0.030	0.100±0.024	2.89±8.48	44.7±126	0.164±5.94	0.129±8.58	8.69	7.94
22	0.146±0.377	3.89±10.2	0.119±0.009	0.040±0.060	2.80±8.77	44.6±127	0.140±4.00	0.112±8.26	6.93	6.56
23	0.103±0.327	3.80±10.2	0.128±0.015	0.039±0.036	2.55±7.38	44.8±127	0.145±4.77	0.124±4.26	8.26	5.26
24	0.156±0.334	3.71±10.1	0.119±0.058	0.090±0.043	2.59±7.85	44.7±126	0.143±7.00	0.112±9.71	8.61	6.49
25	0.153±0.353	3.71±10.2	0.115±0.014	0.048±0.029	2.44±7.40	44.5±126	0.156±5.54	0.121±6.75	7.07	5.42
26	0.131±0.308	3.87±10.1	0.120±0.068	0.019±0.031	2.73±8.47	44.8±126	0.129±1.49	0.112±0.01	7.42	6.84
27	0.145±0.334	3.70±10.1	0.108±0.029	0.044±0.014	2.43±7.54	44.8±127	0.144±4.53	0.123±14.9	7.18	5.40
28	0.139±0.317	3.72±10.1	0.071±0.020	0.057±0.020	2.83±7.56	44.5±126	0.141±4.94	0.124±2.40	7.06	5.92
29	0.148±0.358	3.88±10.1	0.071±0.031	0.037±0.049	2.42±7.47	44.8±126	0.168±3.14	0.133±9.15	8.99	7.98
30	0.143±0.373	3.70±10.0	0.078±0.052	0.023±0.068	2.67±8.10	44.9±127	0.157±1.20	0.147±3.91	7.71	6.79
31	0.135±0.363	3.77±10.2	0.047±0.056	0.046±0.012	2.77±7.37	44.8±126	0.164±2.98	0.126±13.1	8.22	5.29
32	0.155±0.348	3.79±10.1	0.065±0.031	0.012±0.019	2.41±7.28	44.8±126	0.129±3.88	0.131±12.0	7.93	5.66
33	0.154±0.386	3.87±10.1	0.078±0.045	0.053±0.019	2.43±7.95	44.6±126	0.167±3.67	0.145±0.51	6.71	5.64
34	0.140±0.350	3.76±10.1	0.078±0.037	0.025±0.048	2.81±8.49	44.8±126	0.133±2.14	0.110±4.14	7.72	7.36
35	0.119±0.334	3.73±10.1	0.060±0.023	0.028±0.059	2.67±7.63	44.8±126	0.147±6.51	0.103±13.5	7.15	5.59
36	0.134±0.346	3.79±10.2	0.116±0.057	0.042±0.043	2.82±8.31	44.6±127	0.156±2.83	0.155±7.21	7.95	6.31
37	0.111±0.317	3.77±10.1	0.065±0.029	0.063±0.067	2.45±8.75	44.9±126	0.147±4.15	0.128±8.15	6.49	5.36
38	0.119±0.330	3.76±10.2	0.112±0.045	0.053±0.034	2.45±7.38	44.5±127	0.157±2.48	0.157±12.9	8.24	7.68
39	0.148±0.362	3.72±10.1	0.082±0.019	0.021±0.016	2.72±8.93	44.6±127	0.131±2.08	0.115±14.8	8.91	6.90
40	0.117±0.341	3.82±10.1	0.116±0.007	0.036±0.054	2.89±8.79	44.5±126	0.138±2.21	0.136±3.82	7.82	5.62
41	0.120±0.385	3.81±10.1	0.106±0.009	0.102±0.048	2.62±7.47	44.7±126	0.154±5.13	0.141±7.91	6.20	6.12
42	0.107±0.315	3.73±10.1	0.057±0.056	0.039±0.027	2.44±8.07	44.5±126	0.147±1.55	0.128±3.60	6.36	6.22
43	0.134±0.302	3.85±10.2	0.100±0.053	0.064±0.063	2.50±8.16	44.7±127	0.125±3.48	0.105±13.1	7.86	5.95
44	0.149±0.323	3.70±10.1	0.136±0.034	0.093±0.031	2.41±7.63	44.6±127	0.150±3.10	0.129±9.21	7.52	6.17
45	0.123±0.353	3.79±10.2	0.088±0.011	0.052±0.018	2.45±8.37	44.8±127	0.168±2.52	0.147±5.73	6.88	6.40
46	0.142±0.389	3.86±10.1	0.128±0.045	0.034±0.061	2.67±8.76	44.7±126	0.144±3.27	0.127±11.2	8.25	7.54
47	0.143±0.339	3.76±10.1	0.114±0.018	0.102±0.063	2.84±8.38	44.7±126	0.142±4.46	0.117±6.08	7.17	6.00
48	0.153±0.335	3.74±10.1	0.091±0.045	0.085±0.061	2.70±7.17	44.9±127	0.158±6.75	0.111±9.43	8.02	5.59
49	0.103±0.327	3.77±10.1	0.115±0.018	0.057±0.058	2.82±8.32	44.7±126	0.168±3.25	0.146±4.33	6.38	5.59
50	0.151±0.385	3.80±10.2	0.081±0.054	0.034±0.038	2.89±7.81	44.8±127	0.180±6.90	0.170±11.6	8.62	8.54
51	0.104±0.367	3.89±10.2	0.081±0.047	0.047±0.037	2.82±7.80	44.9±127	0.166±2.62	0.107±10.7	7.80	7.74
52	0.146±0.363	3.84±10.2	0.024±0.011	0.017±0.023	2.54±8.21	44.6±127	0.167±2.14	0.124±9.07	6.27	5.14
53	0.138±0.345	3.87±10.1	0.110±0.021	0.020±0.043	2.83±8.20	44.9±126	0.157±4.31	0.153±6.69	7.50	5.07
54	0.121±0.344	3.73±10.1	0.087±0.053	0.073±0.067	2.42±7.17	44.7±127	0.166±3.10	0.162±11.6	8.26	5.00
55	0.112±0.331	3.80±10.1	0.108±0.024	0.033±0.043	2.49±8.26	44.6±127	0.128±6.65	0.116±10.7	6.77	6.65
平均值±标准差	0.132±0.016	3.80±0.058	0.089±0.035	0.055±0.032	2.65±0.156	44.7±0.116	0.152±0.013	0.133±0.017	7.37±0.802	6.32±0.880

表2

图6

表3

通过高斯DTI模板与线性DTI模板进行空间标准化前后张量的IA参数比较

被试编号	Gauss	linear	linear2
1	0.146±0.785	0.115±0.794	0.126±0.778
2	0.146±0.806	0.118±0.810	0.126±0.821
3	0.158±0.869	0.125±0.871	0.137±0.887
4	0.153±0.912	0.125±0.919	0.135±0.915
5	0.149±0.894	0.117±0.899	0.128±0.899
6	0.162±0.871	0.130±0.877	0.140±0.880
7	0.154±0.953	0.123±0.957	0.130±0.955
8	0.155±0.794	0.124±0.799	0.130±0.798
9	0.148±0.844	0.117±0.848	0.127±0.850
10	0.146±0.915	0.116±0.918	0.128±0.911
11	0.151±0.649	0.135±0.792	0.109±0.704
12	0.142±0.603	0.120±0.724	0.114±0.719
13	0.146±0.689	0.119±0.606	0.129±0.618
14	0.170±0.826	0.131±0.853	0.129±0.910
15	0.135±0.761	0.113±0.743	0.120±0.916
16	0.155±0.907	0.122±0.714	0.117±0.897
17	0.140±0.927	0.126±0.938	0.117±0.609
18	0.137±0.730	0.102±0.838	0.115±0.903
19	0.151±0.833	0.114±0.739	0.128±0.663
20	0.148±0.776	0.134±0.645	0.140±0.716
21	0.167±0.668	0.121±0.897	0.105±0.765
22	0.155±0.640	0.135±0.887	0.126±0.803
23	0.155±0.793	0.113±0.872	0.140±0.806
24	0.150±0.627	0.103±0.939	0.109±0.700
25	0.139±0.864	0.117±0.967	0.109±0.606
26	0.166±0.739	0.139±0.721	0.109±0.983
27	0.166±0.914	0.137±0.757	0.122±0.783
28	0.160±0.879	0.114±0.914	0.136±0.880
29	0.142±0.995	0.131±0.608	0.137±0.736
30	0.150±0.773	0.129±0.723	0.110±0.911
31	0.162±0.847	0.117±0.740	0.131±0.880
32	0.157±0.787	0.116±0.672	0.109±0.633
33	0.136±0.691	0.128±0.606	0.113±0.655
34	0.155±0.947	0.101±0.698	0.108±0.820
35	0.142±0.695	0.110±0.994	0.124±0.608
36	0.133±0.911	0.131±0.805	0.110±0.758
37	0.136±0.840	0.114±0.771	0.106±0.854
38	0.156±0.801	0.101±0.797	0.129±0.872
39	0.160±0.762	0.113±0.987	0.104±0.605
40	0.151±0.892	0.120±0.624	0.129±0.999
41	0.143±0.773	0.136±0.931	0.122±0.722
42	0.152±0.884	0.108±0.635	0.113±0.620
43	0.154±0.752	0.109±0.855	0.131±0.842
44	0.142±0.681	0.133±0.757	0.118±0.770
45	0.148±0.853	0.107±0.989	0.104±0.702
46	0.144±0.708	0.108±0.656	0.102±0.899
47	0.154±0.807	0.111±0.947	0.119±0.670
48	0.147±0.771	0.118±0.978	0.113±0.957
49	0.156±0.653	0.101±0.948	0.116±0.654
50	0.145±0.662	0.112±0.829	0.130±0.909
51	0.153±0.998	0.122±0.890	0.124±0.722
52	0.136±0.685	0.123±0.894	0.118±0.772
53	0.132±0.646	0.124±0.782	0.126±0.636
54	0.154±0.638	0.108±0.653	0.117±0.708
55	0.143±0.677	0.121±0.895	0.121±0.678
平均值±标准差	0.150±0.009	0.119±0.010	0.121±0.010

表3

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