CN1947655A - Quantitative analysis method for cerebral cortex complexity during treating three-D magnetoencepha-resonance data - Google Patents

Quantitative analysis method for cerebral cortex complexity during treating three-D magnetoencepha-resonance data Download PDF

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CN1947655A
CN1947655A CN 200510109337 CN200510109337A CN1947655A CN 1947655 A CN1947655 A CN 1947655A CN 200510109337 CN200510109337 CN 200510109337 CN 200510109337 A CN200510109337 A CN 200510109337A CN 1947655 A CN1947655 A CN 1947655A
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蒋田仔
李晓波
朱万琳
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Institute of Automation of Chinese Academy of Science
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Abstract

本发明涉及三维结构核磁共振成像技术领域,一种利用离散体素的分形信息维数分析离散数据在三维空间中的分布的方法,对脑皮层形状的复杂性进行定量分析。在采集到三维结构核磁共振数据并经过必要的预处理后,提取全部或局部脑皮层灰质与脑脊液交接处的体素,形成离散的脑灰质外表面。计算离散数据在三维空间的分形信息维,因而获得全脑或局部灰质外皮层的形状复杂性定量描述。这种方法也完全适用于测量灰质内皮层以及白质皮层的形状复杂性。该发明主要用于分析精神与神经疾病所引起的脑皮层形状异常。该方法计算精确,快速,在普通的微机上即可完成。该方法可广泛应用于脑结构核磁共振的临床与基础研究中。

Figure 200510109337

The invention relates to the technical field of three-dimensional structural nuclear magnetic resonance imaging, and relates to a method for analyzing the distribution of discrete data in three-dimensional space by using the fractal information dimension of discrete voxels to quantitatively analyze the complexity of the shape of the cerebral cortex. After collecting the three-dimensional structural MRI data and undergoing necessary preprocessing, the voxels at the junction of all or part of the cerebral cortex gray matter and cerebrospinal fluid are extracted to form a discrete outer surface of cerebral gray matter. Calculate the fractal information dimension of discrete data in three-dimensional space, and thus obtain a quantitative description of the shape complexity of the whole brain or local gray matter cortex. This method is also perfectly applicable for measuring the shape complexity of gray matter endocortex as well as white matter cortex. The invention is mainly used to analyze the abnormal shape of the cerebral cortex caused by mental and nervous diseases. This method is accurate and fast, and can be completed on a common microcomputer. This method can be widely used in clinical and basic research of brain structure MRI.

Figure 200510109337

Description

三维脑磁共振数据处理中的皮层复杂性定量分析方法A Quantitative Analysis Method for Cortical Complexity in 3D Brain Magnetic Resonance Data Processing

技术领域technical field

本发明涉及磁共振成像技术领域,特别是一种利用计算几何分形维数的三维脑磁共振数据处理中的皮层复杂性定量分析方法,对脑结构磁共振数据进行处理。The invention relates to the technical field of magnetic resonance imaging, in particular to a method for quantitatively analyzing cortex complexity in three-dimensional brain magnetic resonance data processing using geometric fractal dimensions to process brain structural magnetic resonance data.

背景技术Background technique

核磁共振成像技术(Magnetic Resonance Imaging,MRI)主要利用氢原子核的核磁共振显像进行成像。图像内核磁共振信号的大小主要由组织的质子密度,纵向和横向驰豫时间,磁场不均匀性等因素决定。脑组织中,白质,灰质和脑脊液这三种组织的纵向驰豫时间差别比较大,因而形成清晰的结构像,使对脑结构的定量分析成为可能。Magnetic Resonance Imaging (MRI) mainly uses nuclear magnetic resonance imaging of hydrogen nuclei for imaging. The size of the MRI signal in the image core is mainly determined by the proton density of the tissue, the longitudinal and transverse relaxation time, the inhomogeneity of the magnetic field and other factors. In the brain tissue, the longitudinal relaxation times of white matter, gray matter and cerebrospinal fluid are relatively different, so a clear structural image is formed, which makes quantitative analysis of brain structure possible.

长期的尸解研究证明,脑皮层的形状复杂性与人脑的发育,病变,及认知功能有密切的联系。在绝大多数的脑结构影像研究中,通过计算脑皮层白质和灰质的体素个数来统计脑皮层实质的体积是唯一的度量皮层复杂性的方法。Long-term autopsy studies have proved that the shape complexity of the cerebral cortex is closely related to the development, pathological changes, and cognitive functions of the human brain. In the vast majority of brain structural imaging studies, counting the volume of cortical parenchyma by counting the number of voxels of white and gray matter in the cortex is the only method to measure the complexity of the cortex.

Thompsom等人,(1998)提出一个度量来精细分析皮层复杂性。他们首先对脑皮层的脑沟进行人工标定,然后用参数化曲面拟合每一个脑沟,再对每个参数化曲面求其退化分形维数,用退化分形维数的大小来度量皮层脑沟复杂性。这个方法有一些重大的缺陷。首先,人工标定脑沟没有严格统一的标准,受人为因素影响大,而且手工工作量大,不利于普遍推广。其次,参数化曲面是一种二阶光顺的曲面,无法表达数据点所描述的细小形状变化,因而精确度低。为此,我们提出了一种直接基于影像数据,计算皮层体素点集的分形信息维数的方法,以定量描述脑皮层形状的复杂性。Thompsom et al., (1998) proposed a metric to fine-tune the analysis of cortical complexity. They first manually calibrated the brain sulcus of the cerebral cortex, then fitted each brain sulcus with a parametric surface, and then calculated the degenerated fractal dimension of each parametric surface, and used the size of the degenerated fractal dimension to measure the cortical sulcus Complexity. This approach has some major drawbacks. First of all, there is no strict and uniform standard for manual calibration of brain sulci, which is greatly affected by human factors, and the manual workload is heavy, which is not conducive to general promotion. Second, the parametric surface is a second-order smooth surface, which cannot express the small shape changes described by the data points, so the accuracy is low. To this end, we propose a method to calculate the fractal information dimension of cortical voxel point sets directly based on image data, so as to quantitatively describe the complexity of the shape of the cortex.

参考文献:references:

Thompson,P.,Moussai,J.,Zohoori,S.,Goldkorn,A.,Khan,A.,Mega,M.,Small,G.,Cummings,J.,Toga,A..Cortical variability and asymmetry innormal aging and Alzheimer’s disease.Cerebral Cortex,1998:Vol.8,pp492-509.Thompson, P., Moussai, J., Zohoori, S., Goldkorn, A., Khan, A., Mega, M., Small, G., Cummings, J., Toga, A..Cortical variability and asymmetry abnormal aging and Alzheimer's disease. Cerebral Cortex, 1998: Vol.8, pp492-509.

发明内容Contents of the invention

一种对脑的结构核磁共振数据进行处理的方法,利用计算机设备,采用三维分形信息维对脑皮层表面的散乱体素集合的分布进行分析,以达到检测脑皮层形状复杂性的目的,三维散乱点云的分形信息维,利用重正化群的理论,对脑皮层体素点云所描述的几何形状进行定量分析,以此对脑皮层复杂性进行研究。A method for processing brain structure nuclear magnetic resonance data, using computer equipment, using three-dimensional fractal information dimension to analyze the distribution of scattered voxel collections on the surface of the cerebral cortex, in order to achieve the purpose of detecting the complexity of the shape of the cerebral cortex, three-dimensional scattered The fractal information dimension of the point cloud, using the theory of renormalization group, quantitatively analyzes the geometric shape described by the voxel point cloud of the cerebral cortex, so as to study the complexity of the cerebral cortex.

所述的对脑的结构核磁共振数据进行处理的方法,对全脑或脑局部灰质,白质皮层,以及子结构表面几何形状复杂性进行测量。The method for processing the structural MRI data of the brain measures the complexity of geometric shapes of the whole brain or partial brain gray matter, white matter cortex, and substructure surfaces.

一种利用离散体素的分形信息维数分析离散数据在三维空间中的分布的方法,对脑皮层形状的复杂性进行定量分析。在采集到三维结构核磁共振数据并经过必要的预处理后,提取全部或局部脑皮层灰质与脑脊液交接处的体素,形成离散的脑灰质外表面。计算离散数据在三维空间的分形信息维,因而获得全脑或局部灰质外皮层的形状复杂性定量描述。这种方法也完全适用于测量灰质内皮层以及白质皮层的形状复杂性。该发明主要用于分析精神与神经疾病所引起的脑皮层形状异常。该方法计算精确,快速,在普通的微机上即可完成。该方法可广泛应用于脑结构核磁共振的临床与基础研究中。A method for analyzing the distribution of discrete data in three-dimensional space using the fractal information dimension of discrete voxels to quantify the complexity of the shape of the brain cortex. After collecting the three-dimensional structural MRI data and undergoing necessary preprocessing, the voxels at the junction of all or part of the cerebral cortex gray matter and cerebrospinal fluid are extracted to form a discrete outer surface of cerebral gray matter. Calculate the fractal information dimension of discrete data in three-dimensional space, and thus obtain a quantitative description of the shape complexity of the whole brain or local gray matter cortex. This method is also perfectly applicable for measuring the shape complexity of gray matter endocortex as well as white matter cortex. The invention is mainly used to analyze the abnormal shape of the cerebral cortex caused by mental and nervous diseases. This method is accurate and fast, and can be completed on a common microcomputer. This method can be widely used in clinical and basic research of brain structure MRI.

本发明的核心部分在于,将三维脑结构核磁共振图像进行组织分割后,对全脑或者感兴趣的脑区,提取位于灰质和脑脊液边界处的体素,将这些体素看成三维空间中的一个离散点集。计算该点集的信息维数,从而对脑区的皮层形状复杂性进行定量分析。这种方法也适用于分析白质皮层的形状复杂性。该方法计算过程快速,稳定,在普通的微机上即可完成。其实现过程可分为4个步骤,如图1所示。The core part of the present invention is that, after the three-dimensional brain structure nuclear magnetic resonance image is segmented, the voxels located at the boundary between the gray matter and the cerebrospinal fluid are extracted from the whole brain or the brain area of interest, and these voxels are regarded as three-dimensional space. A set of discrete points. The information dimension of the point set is calculated to quantitatively analyze the cortical shape complexity of the brain area. This method is also suitable for analyzing the shape complexity of white matter cortex. The calculation process of this method is fast and stable, and can be completed on an ordinary microcomputer. Its implementation process can be divided into four steps, as shown in Figure 1.

附图说明Description of drawings

图1是本发明实现过程的流程图。Fig. 1 is a flow chart of the realization process of the present invention.

图2是前额叶的定义图。Figure 2 is a definition diagram of the prefrontal cortex.

图3是左侧前额叶灰质皮层的提取图。Figure 3 is an extracted image of the left prefrontal gray matter cortex.

具体实施方式Detailed ways

图1所示,As shown in Figure 1,

步骤一(S1)、脑结构核磁共振数据的获取:脑功能结构核磁共振数据的采集在具备能够成T1或T2加权结构像的磁共振扫描仪上完成。成像的具体参数无特殊要求,空间分辨率一般为数毫米,如1×1mm2。,对受试者的配合无特殊要求,只需要告诉受试者安静闭目,尽量保持头部不动。Step 1 (S1), acquisition of brain structure MRI data: acquisition of brain functional structure MRI data is completed on an MRI scanner capable of forming T1 or T2 weighted structural images. There are no special requirements for the specific parameters of the imaging, and the spatial resolution is generally several millimeters, such as 1×1mm 2 . , There are no special requirements for the cooperation of the subjects, only the subjects need to be told to close their eyes quietly and keep their heads as still as possible.

步骤二(S2)、预处理:数据采集完毕后一般需要进行常规预处理,包括头动矫正、空间标准化等,但这些过程要根据使用目的来决定,并非必需的过程。这些基本过程完成后,去除颅脑部分,以及小脑,脑干等,对大脑进行组织分割。然后对感兴趣的脑区进行划分。Step 2 (S2), preprocessing: After the data collection is completed, conventional preprocessing is generally required, including head movement correction, spatial standardization, etc., but these processes are determined according to the purpose of use and are not necessary. After these basic processes are completed, the cranial part, as well as the cerebellum, brainstem, etc., are removed, and the brain is divided into tissues. The brain regions of interest are then segmented.

步骤三(S3)、提取脑皮层体素:预处理完成后,对感兴趣的皮层提取表面的体素,计算每个体素质心在三维空间中的位置,将这些位置看成一个空间离散点集。Step 3 (S3), extracting the voxels of the cerebral cortex: after the preprocessing is completed, extract the voxels on the surface of the interested cortex, calculate the position of each voxel centroid in the three-dimensional space, and regard these positions as a set of discrete points in space .

步骤四(S4)、计算分形信息维数:对步骤三所得到的空间离散点集进行空间归一化,然后计算其分形信息维数。对大脑皮层而言,这个信息维数是一个1和3之间的数值。这个值越靠近3,说明皮层形状的复杂性越大,反之,如果它越靠近1,说明皮层形状的复杂性越小。Step 4 (S4), calculating the fractal information dimension: performing spatial normalization on the spatially discrete point set obtained in Step 3, and then calculating its fractal information dimension. For the cerebral cortex, this information dimension is a value between 1 and 3. The closer this value is to 3, the greater the complexity of the cortical shape, and conversely, if it is closer to 1, the less complex the cortical shape is.

图2是前额叶的定义(竖直线左侧为前额叶部位),一个左侧前额叶灰质皮层的提取示例,其中(a)为所提取的皮层体素,(b)为这些体素质心在三维空间中形成的离散点集。Figure 2 is the definition of the prefrontal lobe (the left side of the vertical line is the prefrontal lobe), an example of the extraction of the gray matter cortex of the left prefrontal lobe, where (a) is the extracted cortical voxel, and (b) is the centroid of these bodies A discrete set of points formed in three-dimensional space.

图3是左侧前额叶灰质皮层的提取。a:皮层体素,b:体素质心在三维空间中形成的离散点集。Figure 3 is an extraction of the left prefrontal gray matter cortex. a: cortical voxel, b: discrete point set formed by the voxel centroid in 3D space.

下面举例说明本发明的实现过程:The implementation process of the present invention is illustrated below by way of example:

步骤一(S1)、数据获取:病例组为12名符合美国精神障碍诊断与统计手册(第四版)(DSM-IV)ADHD诊断标准的男孩,年龄11.67-14.83岁。对照组为来自邻近中学的11名男孩,年龄12.67-13.92岁。所有被试均为右利手,智商>80分,排除广泛性发育障碍,儿童精神分裂症,情绪障碍等其他儿童期常见的精神障碍及神经系统发育障碍,排除器质性疾病所致的注意力缺陷者,排除早产儿(<34周)及有严重脑外伤史(致昏迷)者。本研究的目的是比较正常儿童与患有ADHD的儿童大脑的左右两边前额叶灰质皮层的形状复杂性的差异,以了解该病变对前额叶灰质皮层发育的影响。所有影像学数据均在Siemens Trio3.0T机器上采集,使用标准头部线圈作为发射和接收线圈。在定位扫描后进行常规头部扫描,以排除脑部病变。三维结构像采用SPGR序列进行矢状位全脑扫描,TR=1770ms,TE=3.92ms,IT(反转时间)=1100ms,反转角=12°,扫描范围(FOV)=256mm×256mm,矩阵512×512,层厚=1mm,层间隔=0.5mm,共192层,扫描时间15分钟;扫描时嘱受试者头部尽量保持不动。Step 1 (S1), data acquisition: the case group consisted of 12 boys, aged 11.67-14.83, who met the diagnostic criteria of ADHD in the Diagnostic and Statistical Manual of Mental Disorders (Fourth Edition) (DSM-IV). The control group consisted of 11 boys from neighboring secondary schools, aged 12.67-13.92 years. All subjects were right-handed, with an IQ of >80 points. Pervasive developmental disorders, childhood schizophrenia, emotional disorders, and other common childhood mental and nervous system developmental disorders were excluded. Attention caused by organic diseases were excluded. For those with disabilities, preterm infants (<34 weeks) and those with a history of severe traumatic brain injury (causing coma) were excluded. The purpose of this study was to compare the difference in the shape complexity of the left and right prefrontal gray matter in the brains of normal children and children with ADHD, in order to understand the impact of the lesion on the development of the prefrontal gray matter. All imaging data were acquired on a Siemens Trio 3.0T machine, using standard head coils as transmitting and receiving coils. Routine head scans are done after scout scans to rule out brain lesions. The three-dimensional structure image was scanned by SPGR sequence in sagittal position, TR=1770ms, TE=3.92ms, IT (inversion time)=1100ms, inversion angle=12°, scan field (FOV)=256mm×256mm, matrix 512×512, slice thickness = 1mm, slice interval = 0.5mm, a total of 192 slices, scanning time 15 minutes; the subject was asked to keep his head as still as possible during scanning.

步骤二(S2)、预处理:首先,使用MRIcro( http://www.psychology.nottingham.ac.uk/staff/crl/mricro.html)软件自动去除非脑组织。然后,手动去除脑干,小脑,以及残留的非脑组织。选一个正常人作为模版,使用SPM5b( http://www.fil.ion.ucl.ac.uk/spm/)进行刚体配准,这一步骤是为了通过旋转和平移交正头的位置,以便使用统一的标准进行前额叶分割。前额叶的定义如图1所示,竖直线左侧的脑组织为前额叶。最后,对前额叶进行组织分割。Step 2 (S2), pretreatment: first, use MRIcro ( http://www.psychology.nottingham.ac.uk/staff/crl/mricro.html ) software to automatically remove non-brain tissue. Then, manually remove the brainstem, cerebellum, and residual non-brain tissue. Choose a normal person as a template, and use SPM5b ( http://www.fil.ion.ucl.ac.uk/spm/ ) for rigid body registration. This step is to rotate and translate the position of the orthodox head so that it can be used A unified standard for prefrontal lobe segmentation. The definition of the prefrontal lobe is shown in Figure 1, the brain tissue to the left of the vertical line is the prefrontal lobe. Finally, perform tissue segmentation on the prefrontal cortex.

步骤三(S3)、提取脑皮层体素:预处理完成后,提取前额叶灰质于脑脊液交接表面的所有体素,计算每个体素质心在三维空间中的位置,将这些位置看成一个空间离散点集。图2是一个左侧前额叶灰质皮层的提取示例,其中(a)为所提取的皮层体素,(b)为这些体素质心在三维空间中形成的离散点集。Step 3 (S3), extracting cerebral cortex voxels: after the preprocessing is completed, extract all voxels on the interface surface of prefrontal gray matter and cerebrospinal fluid, calculate the position of each voxel centroid in three-dimensional space, and regard these positions as a spatially discrete point set. Figure 2 is an example of the extraction of the left prefrontal gray matter cortex, where (a) is the extracted cortical voxels, and (b) is the discrete point set formed by these voxel centroids in three-dimensional space.

步骤四(S4)、计算分形信息维数:对步骤三所得到的空间离散点集进行空间归一化,然后计算其分形信息维数。对病人组和对照组的前额叶左右两侧分别进行t统计检验后,发现病人和正常人都有前额叶皮层形状复杂性左大于右的模式。但是,病人的左侧前额叶皮层形状复杂性显著低于正常人,其右侧也低于正常人,但是没有达到显著性水平。这些变化反映了ADHD疾病的确与前额叶皮层形状复杂性的发育不良有密切关系。Step 4 (S4), calculating the fractal information dimension: performing spatial normalization on the spatially discrete point set obtained in Step 3, and then calculating its fractal information dimension. After the t-statistic test was performed on the left and right sides of the prefrontal cortex of the patient group and the control group, it was found that the shape complexity of the left side of the prefrontal cortex was greater than that of the right side in both patients and normal people. However, the shape complexity of the patient's left prefrontal cortex was significantly lower than that of normal people, and its right side was also lower than normal people, but it did not reach the level of significance. These changes reflect that ADHD disease is indeed closely related to the dysplasia of prefrontal cortex shape complexity.

总之,用离散点集的分形维数对脑皮层形状复杂性进行精确测量有非常广泛的应用前景。与传统的方法相比较,本方法有如下主要优点:(1)避免了繁重的手工标定脑沟的工作,以及因没有统一标准而造成的主观误差;(2)无需对离散体素点集进行参数化拟合,因而保证一些皮层形状的细小变化被考察到,有效地提高了测量精确度;(3)整个处理过程速度快,消耗内存少,有利于普遍推广,有非常重要的生理及临床意义。In conclusion, the precise measurement of the shape complexity of the cerebral cortex using the fractal dimension of discrete point sets has a very broad application prospect. Compared with the traditional method, this method has the following main advantages: (1) It avoids the heavy work of manual sulcus calibration and the subjective error caused by the lack of uniform standards; Parametric fitting, thus ensuring that some small changes in the shape of the cortex are investigated, effectively improving the measurement accuracy; (3) The entire processing process is fast and consumes less memory, which is conducive to general promotion and has very important physiological and clinical significance. significance.

Claims (5)

1、一种对脑的结构核磁共振数据进行处理的方法,其特征是,利用计算机设备,采用三维分形信息维对脑皮层表面的散乱体素集合的分布进行分析,以达到检测脑皮层形状复杂性的目的,三维散乱点云的分形信息维,利用重正化群的理论,对脑皮层体素点云所描述的几何形状进行定量分析,以此对脑皮层复杂性进行研究。1. A method for processing the structural nuclear magnetic resonance data of the brain, characterized in that computer equipment is used to analyze the distribution of scattered voxel sets on the surface of the cerebral cortex by using three-dimensional fractal information dimensions, so as to achieve the detection of complex shapes of the cerebral cortex In order to study the complexity of the cerebral cortex, the fractal information dimension of the three-dimensional scattered point cloud is quantitatively analyzed by using the theory of renormalization group to analyze the geometric shape described by the voxel point cloud of the cerebral cortex. 2、根据权利要求1所述的对脑的结构核磁共振数据进行处理的方法,其特征在于,对全脑或脑局部灰质,白质皮层,以及子结构表面几何形状复杂性进行测量。2. The method for processing brain structural MRI data according to claim 1, characterized in that the geometric shape complexity of the whole brain or partial brain gray matter, white matter cortex, and substructure surface is measured. 3、根据权利要求1所述的对脑的结构核磁共振数据进行处理的方法,其特征在于,将三维脑结构核磁共振图像进行组织分割后,对全脑或者感兴趣的脑区,提取位于灰质和脑脊液边界处的体素,将这些体素看成三维空间中的一个离散点集,计算该点集的信息维数,从而对脑区的皮层形状复杂性进行定量分析。3. The method for processing brain structure nuclear magnetic resonance data according to claim 1, characterized in that, after tissue segmentation of the three-dimensional brain structure nuclear magnetic resonance image, the whole brain or the brain region of interest is extracted from the gray matter. Consider these voxels as a discrete point set in three-dimensional space, and calculate the information dimension of the point set, so as to quantitatively analyze the complexity of the cortical shape of the brain region. 4、根据权利要求1所述的对脑的结构核磁共振数据进行处理的方法,其特征在于,在采集到三维结构核磁共振数据并经过必要的预处理后,提取全部或局部脑皮层灰质与脑脊液交接处的体素,形成离散的脑灰质外表面,计算离散数据在三维空间的分形信息维,因而获得全脑或局部灰质外皮层的形状复杂性定量描述。4. The method for processing the structural MRI data of the brain according to claim 1, characterized in that, after collecting the three-dimensional structural MRI data and undergoing necessary preprocessing, all or part of the cerebral cortex gray matter and cerebrospinal fluid are extracted The voxels at the junction form the discrete gray matter outer surface, and calculate the fractal information dimension of the discrete data in three-dimensional space, thus obtaining a quantitative description of the shape complexity of the whole brain or local gray matter outer cortex. 5、根据权利要求1所述的对脑的结构核磁共振数据进行处理的方法,其特征在于,步骤S1、脑结构核磁共振数据的获取:脑功能结构核磁共振数据的采集在具备能够成T1或T2加权结构像的磁共振扫描仪上完成;5. The method for processing brain structural MRI data according to claim 1, characterized in that, step S1, acquisition of brain structural MRI data: the acquisition of brain functional structural MRI data can be performed in T1 or Completed on the magnetic resonance scanner of T2 weighted structural image; 步骤S2、预处理:数据采集完毕后一般需要进行常规预处理,包括头动矫正、空间标准化;Step S2, preprocessing: After the data collection is completed, conventional preprocessing is generally required, including head movement correction and spatial standardization; 步骤S3、提取脑皮层体素:预处理完成后,对感兴趣的皮层提取表面的体素,计算每个体素质心在三维空间中的位置,将这些位置看成一个空间离散点集;Step S3, extracting the voxels of the cerebral cortex: after the preprocessing is completed, extract the voxels on the surface of the interested cortex, calculate the position of each voxel centroid in three-dimensional space, and regard these positions as a set of spatially discrete points; 步骤S4、计算分形信息维数:对步骤S3所得到的空间离散点集进行空间归一化,然后计算其分形信息维数。Step S4, calculating the fractal information dimension: performing spatial normalization on the spatially discrete point set obtained in step S3, and then calculating its fractal information dimension.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101742963B (en) * 2007-06-29 2012-04-25 加藤俊德 White matter enhancing device, white matter enhancing method
CN103717129A (en) * 2011-05-24 2014-04-09 加利福尼亚大学董事会 Magnetoencephalography source imaging
CN105765398A (en) * 2013-11-22 2016-07-13 皇家飞利浦有限公司 System for measuring cortical thickness from MR scan information

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101742963B (en) * 2007-06-29 2012-04-25 加藤俊德 White matter enhancing device, white matter enhancing method
CN103717129A (en) * 2011-05-24 2014-04-09 加利福尼亚大学董事会 Magnetoencephalography source imaging
CN105765398A (en) * 2013-11-22 2016-07-13 皇家飞利浦有限公司 System for measuring cortical thickness from MR scan information

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