Individual identification using multi-metric of DTI in Alzheimer's disease and mild cognitive impairment^*

Our 213 participants were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (http://www.loni.ucla.edu/ADNI/). A whole brain DTI is roughly described as following scanning parameters: repetition time (TR), 13000 ms; echo time (TE), 68.3 ms; flip angle, 90°; field strength, 3.0; slice thickness, 2.7 mm; 41 non-collinear directions with a b-value of 1000 s/mm², and 5 images with no diffusion weighting. The exact parameters are varied slightly across scanners. Participants can be divided into four groups according to ADNI baseline diagnosis: HC, EMCI, LMCI, and AD groups. Before scanning, the participants experience cognitive and behavioral assessments. There are no significant differences (P > 0.05) between the four groups when comparing age and gender (See Table 1 for group characteristics). There are differences between groups for demographics including mini-mental state examination (MMSE),^[24] clinical dementia rating (CDR).^[25] According to the comparison of cognitive scores between groups in Fig. 1, a decreasing MMSE and an increasing CDR along with the aggravation of disease can be obviously found. The statistical analysis of basic information is computed in SPSS 22.0.

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The data preprocessing is performed by using PANDA (www.nitrc.org/projects/panda),^[26] which is a pipeline toolbox for diffusion MRI analysis. PANDA is developed by applying the MATLAB software under an Ubuntu Operating System. A number of the processing functions from the FSL,^[27] the Pipeline System for Octave and Matlab (PSOM),^[28] Diffusion Toolkit,^[29] and MRIcron software (http://www.mccauslandcenter.sc.edu/mricro/mricron/) are called by PANDA. Briefly, the preprocessing procedure includes skull-stripping, eddy-current, and head-motion correction, diffusion metrics calculation. FA, MD, AD, and RD maps in the MNI space are generated for each individual. Beyond that, Gong proposed a novel inter-voxel metric referred to as the local diffusion homogeneity (LDH).^[30] This metric is defined to characterize the overall coherence of water molecule diffusion within a neighborhood, and can be used to explore inter-subject variability of WM microstructural properties. Computationally, the LDH metric uses Spearman's rank correlation coefficient (LDHs) or Kendall's coefficient concordance (LDHk) to quantify the overall coherence of the diffusivity series.

The diffusion metrics (i.e., FA, MD, DA, RD, LDHs, and LDHk) characterize microsturctural (e.g., degree of myelination or axonal organization) WM properties.^[31] The regional values for these metrics are extracted using the White Matter Parcellation Map (WMPM), which is a prior WM atlas defined in the MNI space.^[32] The mean of FA, MD, DA, RD, LDHs, and LDHk are calculated for each WMPM region. Here, a total of 50 WMPM regions are selected, and these areas are defined as the "core white matter".^[32] The remaining peripheral WM regions near the cortex are excluded because they are highly variable across individuals.

A SVM method is applied to classify the four groups using diffusion metrics. The leave-one-out cross-validation (LOOCV) is adopted to evaluate the classification performance, which provides a good estimation for the generalizability of the classifiers, particularly when the sample size is small. Similarly, an LR method is reapplied to compare with the SVM method. All machine learning analyses are performed using Python (https://www.python.org/) and the tools are freely available at https://sourceforge.net/projects/scikit-learn.^[33] The process flow chart of machine learning is shown in Fig. 2.

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2.3.1. Feature combination

2.3.2. Feature selection

As is well known, the elimination strategy of the non-informative features is widely employed to enhance classification performance. A recursive feature elimination (RFE)^[34] method combined with SVM or LR is applied in order to obtain an optimum feature dimension. The SVM-RFE or LR-RFE method allows one to minimize redundant and extraneous features which could potentially degrade classifier performance.^[35] It works backwards from the initial set of features and eliminates the least "useful" feature on each recursive pass, and it had been applied successfully for feature selection in several functional neuroimaging studies.^[36,37] Specifically, the process of feature selection is shown in Fig. 2(c). The x axis of the line chart represents the feature dimension, and the y axis indicates the classification score. The peak value marked with a red circle is the optimal feature dimension. Take SVM-RFE for example, the ranking criterion score of the i-th feature is defined as:

$$\begin{eqnarray}&&{c}_{i}={\omega }_{i}^{2}.\end{eqnarray} \tag{ 1 }$$

In each iteration, the feature with minimum ranking criterion score is removed and the remaining features are trained on the SVM classifier. The concrete algorithm of SVM-RFE is as follows:

Input: training samples {x_i, y_i}, y_i ∈ {−1,1}.

Output: feature sorting set R.

(i) Initialization. Original feature set S = {1,2, ..., D}, feature sorting set R = Ø.

(ii) Loop through the following procedure until S = Ø:

ii-1) Acquisition of training samples with candidate feature sets;

ii-2) Receive ω according to Eq. (2):

$$\begin{eqnarray}&&\mathop{\max }\limits_{\alpha }\,\displaystyle \sum _{i=1}^{N}{\alpha }_{i}-\frac{1}{2}\displaystyle \sum _{i=1}^{N}\displaystyle \sum _{j=1}^{N}{\alpha }_{i}{\alpha }_{j}{y}_{i}{y}_{j}({x}_{i}\cdot {x}_{j})\\ &&{\rm{s}}.{\rm{t}}.\,\displaystyle \sum _{i=1}^{N}{\alpha }_{i}{y}_{i}=0;\,0\leqslant {\alpha }_{i}\leqslant C,i=1,2,\ldots,N,\end{eqnarray} \tag{ 2 }$$

where α_i is the Lagrange multiplier and C is the penalty parameter.

ii-3) Calculate the ranking criterion score according to Eq. (1)

$$\begin{eqnarray}&&{c}_{k}={\omega }_{k}^{2},\,k=1,2,\ldots,|S|;\end{eqnarray} \tag{ 3 }$$

ii-4) find out the feature with minimum ranking criterion score

$$\begin{eqnarray}&&p={\rm{\arg }}\mathop{\max }\limits_{k}{c}_{k};\end{eqnarray} \tag{ 4 }$$

ii-5) Update the feature set

$$\begin{eqnarray}&&R=\{p\}\cup R;\end{eqnarray} \tag{ 5 }$$

ii-6) Remove the feature among S

$$\begin{eqnarray}&&S=S/p.\end{eqnarray} \tag{ 6 }$$

2.3.3. Classification

In terms of classification methods, SVM is by far the most popular method and is already known as a tool that discovers informative patterns.^[34] The linear SVM with the LOOCV method is applied to implement the classification. Meanwhile, the logistic regression (LR),^[38] another widely used classification model, is reapplied to validate the robustness of classification results via SVM. The classification diagram for the SVM classifier is shown in Fig. 2(d). Specifically, there exist training samples ${\{{x}_{i},{y}_{i}\}}_{i=1}^{N}$ where x_i ∈ R^D, y_i ∈ {−1,1} is the class labels. N is the number of training samples, and D is the feature dimension of the sample. The goal of SVM is to explore the optimally classified hyperplane:

$$\begin{eqnarray}&&w\cdot x+b=0,\end{eqnarray} \tag{ 7 }$$

where w is the weight vector of the optimal hyperplane and b is the threshold value. This makes the optimally classified hyperplane not only separate the two kinds of samples accurately, but also maximize the classification interval between the two classes. The following optimization problem needs to be solved in order to obtain the weight vector and threshold vector:

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle\mathop{{\rm{\min }}}\limits_{w,b,\xi }\,\frac{1}{2}\Vert w{\Vert }^{2}+C\displaystyle \sum _{i=1}^{N}{\xi }_{i}\\ {\rm{s}}.{\rm{t}}.\,{y}_{i}(w\cdot {x}_{i}+b)\geqslant 1-{\xi }_{i},\,i=1,2,\ldots,N,\,\\ \quad{\xi }_{i}\geqslant 0,\,i=1,2,\ldots,N,\end{array}\end{eqnarray} \tag{ 8 }$$

where C > 0 is the penalty parameter and ξ_i is the slack variable. Parameter C plays a role in controlling the punishment degree of the misclassficaton, and realizes the tradeoff between the proportion of the wrong sample and the complexity of the algorithm. By introducing Lagrange multiplier, the optimization problem of SVM can be transformed into the dual programming problem as Eq. (2). The relationship between weight vector and dual optimization Eq. (2) is as follows:

$$\begin{eqnarray}&&w=\displaystyle \sum _{i=1}^{N}{\alpha }_{i}{y}_{i}{x}_{i}.\end{eqnarray} \tag{ 9 }$$

The discriminant function of SVM is as follows:

$$\begin{eqnarray}&&f(x)={\rm{sgn}}\left(\displaystyle \sum _{i=1}^{N}{\alpha }_{i}{y}_{i}{x}_{i}\cdot x+b\right),\end{eqnarray} \tag{ 10 }$$

where sgn(·) is the sign function.

Similar to the SVM method, the LR method also aims to obtain a linear classifier with a decision function y = f(x), in which y is the classification score and x is the multidimensional feature vector. The training and predicting framework is the same as the SVM method. In contrast, the LR method predicts the probability that a sample belongs to one class, rather than a hard label. The probability is defined as P = e^y / (1 + e^y), and the predicted label will be 1 (i.e., controls) if the probability is bigger than 0.5, otherwise −1 (i.e., AD). According to the algorithm implementation, the LR applies the maximum likelihood estimation to obtain the optimal classifier, rather than maximizing the margin as the SVM.

The principle of leave-one-out cross validation (LOOCV) method is as follows. Suppose there are N samples, each sample is taken as the test sample and the other N − 1 sample as the training sample. In this way, N classifiers and N test results are obtained. The average of these N results is used to measure the performance of the model.

2.3.4. Evaluation of classification performance

Since the machine learning methods used here are supervised learning, we need to know the label of each subject in advance, therefore the neuropsychological scale tests are essential. As is well known, psychometric analysis is applied to cognitive tests to improve their reliability, to allow the comparison of different cognitive tests, and to increase understanding of the cognitive processes underlying each test.

Based on the above purpose, we perform two sample T-tests on the cognitive score differences between different groups. The results are shown in Fig. 1. A decreasing MMSE score and increasing CDR score along with the severity of disease can be investigated obviously. The difference for MMSE score between the EMCI and LMCI group is less significant than that between other groups (P < 0.01). However, there are extremely significant differences in CDR scores among all four groups (P < 0.001). The above results are basically consistent with the statistical results in a recent review.^[40]

The psychological scale of cognitive behavior is subjective and only used in patients with some clinical symptoms. In addition, once the symptoms have emerged and have been measured by the cognitive behavior scale, they have developed to the stage of disease. The effect has been very limited through medication and other therapeutics at this time. However, if we can find the effective markers in imaging diagnosis, we can intervene as early as possible.

The results shown in Table 2 have already experienced feature selection. The SVM and LR classifiers accurately discriminate the four groups using the single-type metric (FA, MD, DA, RD, LDHs, LDHk) and the combined metrics (Table 2). The classification accuracy here is significantly improved compared with previous research.^[41–43] It seems that the combined metrics receive a better accuracy than the single-type metric. Notably, the SVM classifiers show a little advantage over the LR classifiers. To validate the robustness of the classification result, the permutation tests (1000 times) are applied in the combined metrics of between-group comparisons. The results show that the accuracies obtained above are significantly higher than values expected by chance (p < 0.001) except HC-EMCI comparison (p = 0.969) for LR.

The considerable classification accuracy among the compared groups can be well validated with the results of Fig. 1. Our results show that the majority of classifiers using combined metrics performed largely better than single WM metric-based classifiers, suggesting that all these features are jointly affected by AD. It should be noted that the discrimination performance using combined metrics only shows a slight improvement or even a trend compared with HC-AD comparison for SVM and HC-AD, HC-EMCI, and EMCI-AD comparisons for LR (Table 2). This may relate to the limited sample size or classification algorithm of this study, which requires future validation. Although the classification performances of a certain single-metric of certain between-group comparisons for the SVM classifier are worse than that of the LR classifier, the SVM classifier is better than the LR classifier for all between-group comparisons after metric combination, which also indirectly reflects that white matter damage is reflected on different levels. Moreover, it can be found that two novel metrics (i.e., LDHs and LDHk) also receive considerable accuracy, implying which may become imaging markers with great potential. In addition, the results of the permutation test also indirectly show the robustness of the classifiers (see Figs. 3 and 4).

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The application of ROC curve analysis in the evaluation of diagnostic testing has been more and more widely accepted, and has become the standard statistical method of clinical screening and diagnostic evaluation at home and abroad.^[44] The greatest characteristic of ROC curve analysis is the integration of sensitivity and specificity into one index, which is not affected by the incidence of disease. This characteristic is beneficial for both diagnosis and elimination of disease.^[45] The essence of ROC curve analysis is to analyze its sensitivity and specificity under multiple diagnostic thresholds.^[46] These ROC curves and AUCs (Fig. 5) show the classifiers' performance for combined metrics of all between-group comparisons. It can be found that the use of SVM classifiers generally obtain better performance than that of LR classifiers. It seems that the robustness of HCs versus EMCIs is not superior to that of other groups, possibly because the EMCIs marker on brain imaging is similar to that of HCs, even though they exhibit difference in cognitive function. Notably, the above results indirectly reflect the sensitivity and specificity of classifiers. Therefore, the ROC curves and AUCs can be validated by the classification performance of combined multi-type WM metrics and reflected the sensitivity and specificity of the classifiers.

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To further illustrate the importance of different WM tract to classification, the top 10 features with higher weight are selected for each between-group comparison. Meanwhile, the best feature dimensions are shown in Table 3. For any features which appear repeatedly in multiple between-group comparisons, we consider them as the most important features which contribute to classification. Statistically, these features are uncinate fasciculus, cingulum, superior corona radiate, external capsule, internal capsule, corpus callosum, and pontine crossing tract, respectively.

The limbic system and association fiber were the abnormal areas that were being most reported in WM research of AD.^[47–49] Cingulum is the important associative fiber that was tight related with episodic memory between cingulate gyrus and other brain GM structures. An impaired cingulum would lead to interruption of hippocampus and cerebral cortex, even causing dysmnesia in AD patients. Bozoki and colleagues^[50] revealed that descending cingulum integrity declined during both the transition from normal aging to MCI and the transition from MCI to AD. This research strongly verified that the cingulum played an important role in between-group classification. The corpus callosum is a thick plate of fibers that reciprocally interconnected the left and right hemisphere. According to previous studies, the anterior part of the corpus callosum contained interconnecting fibers that associated with the feeling of motivation were from the prefrontal cortex.^[51] Furthermore, the deficiency of the corpus callosum integrity might lead to slow initiation and longer reaction times in ADs. Bozzali and colleagues^[52] discovered a notable decrease of the corpus callosum area from ADs compared with age matched healthy subjects. The aforementioned research illustrated the corpus callosum is an importance WM tract for revealing the developmental stage of AD. Moreover, the relevant studies indicated that AD was associated with changes in the WM of the frontal and temporal lobes.^[53,54] The uncinate fasciculus is a white matter tract that connects the anterior part of the temporal lobe and is considered to play a role in emotion, decision-making, and episodic memory.^[55,56] Review of many experimental studies supported the role of the uncinate fasciculus whose disruption resulted in severe memory impairment.^[55,57] The disruption in connectivity between the temporal and frontal lobes via the uncinate fasciculus was postulated as a possible cause of posttraumatic retrograde amnesia.^[55,58] The internal capsule is the major route that connects with the brainstem and spinal cord and contains both ascending and descending axons. Moreover, the internal capsule contains the pyramidal tracts, which imply its effect in somatic movement. It is likely that the impairment of an internal capsule would lead to movement disturbance in AD. The corona radiata, as the most prominent projection fiber, radiates out from the cortex and comes together in the brain stem, which continue ventrally as the internal capsule. Corona radiata is related to the motor pathway and speculative analysis so that the AD or MCI patients would suffer motor and cognitive dysfunction.^[59] The external capsule and uncinate fasciculus comprise the capsular division of the lateral cholinergic pathway. The capsular division of the lateral cholinergic pathway innervates frontal, parietal, and temporal neocortices.^[60] The damage in the lateral cholinergic pathway is consistent with AD pathology. The above research demonstrated the corona radiate, external capsule, and internal capsule are important WM features for classification in our research.