Jointly constrained group sparse connectivity representation improves early diagnosis of Alzheimer’s disease on routinely acquired T1-weighted imaging-based brain network

Abstract

Background

Radiomics-based morphological brain networks (radMBN) constructed from routinely acquired structural MRI (sMRI) data have gained attention in Alzheimer's disease (AD). However, the radMBN suffers from limited characterization of AD because sMRI only characterizes anatomical changes and is not a direct measure of neuronal pathology or brain activity.

Purpose

To establish a group sparse representation of the radMBN under a joint constraint of group-level white matter fiber connectivity and individual-level sMRI regional similarity (JCGS-radMBN).

Methods

Two publicly available datasets were adopted, including 120 subjects from ADNI with both T1-weighted image (T1WI) and diffusion MRI (dMRI) for JCGS-radMBN construction, 818 subjects from ADNI and 200 subjects solely with T1WI from AIBL for validation in early AD diagnosis. Specifically, the JCGS-radMBN was conducted by jointly estimating non-zero connections among subjects, with the regularization term constrained by group-level white matter fiber connectivity and individual-level sMRI regional similarity. Then, a triplet graph convolutional network was adopted for early AD diagnosis. The discriminative brain connections were identified using a two-sample t-test, and the neurobiological interpretation was validated by correlating the discriminative brain connections with cognitive scores.

Results

The JCGS-radMBN exhibited superior classification performance over five brain network construction methods. For the typical NC vs. AD classification, the JCGS-radMBN increased by 1–30% in accuracy over the alternatives on ADNI and AIBL. The discriminative brain connections exhibited a strong connectivity to hippocampus, parahippocampal gyrus, and basal ganglia, and had significant correlation with MMSE scores.

Conclusion

The proposed JCGS-radMBN facilitated the AD characterization of brain network established on routinely acquired imaging modality of sMRI.

Supplementary Information

The online version of this article (10.1007/s13755-023-00269-0) contains supplementary material, which is available to authorized users.

Introduction

Brain networks have been widely adopted in the research of brain abnormalities in Alzheimer’s disease, AD [1]. The brain networks can be constructed using a variety of neuroimaging techniques [2] including functional magnetic resonance imaging, fMRI [3], diffusion magnetic resonance imaging, dMRI [4], and structural magnetic resonance imaging, sMRI [5] etc. Comparing with the advanced sequences of fMRI and dMRI, the morphological brain network (MBN) established on the conventional sMRI such as T1-weighted image (T1WI) has attracted increased attentions in the AD investigation [6–8] because the routinely acquired imaging modality of sMRI is the most clinically accessible brain imaging for diagnosis and monitoring AD progression [9, 10]. Regardless the specific patterns of brain atrophy related to AD measured on sMRI [11], MBN can characterize interregional similarities by morphological features such as regional cortical thickness or gray matter volume [6]. Recently, radiomics-based MBN (called radMBN) has emerged as a powerful technique in AD analysis with solid biological bases [12, 13]. However, the radMBN still suffers from the limited characterization of AD because sMRI only characterizes anatomical changes in cortical and subcortical gray matter regions and is not a direct measure of neuronal pathology or brain activity [14]. Although the redundant connection in the brain network often acts as a neuroprotective mechanism to support brain communication in neuroscience [15, 16], an approximate sparse connectivity representation of the radMBN could better characterize the AD representation when fed into the graph convolutional network (GCN) for early AD diagnosis [17]. Therefore, a sparse connectivity representation of radMBN established on conventional sMRI but with neuronal pathology-guided construction is expected in AD analysis.

In brain network-based diagnostics, GCN exhibits distinct advantages over traditional machine learning methods as they can better capture the topological information of networks and explore meaningful patterns related to diseases in brain network connectivity [18–21]. However, improperly constructed graphs cannot fully exploit the power of GCN and may even lead to worse performance [22], in which case, the sparse representation is preferred to optimize the graph connectivity. Specifically, the sparse connectivity representation method can represent the linear relationships between brain regions by taking into account multiple region effects from other brain regions [23–25]. The group sparse connectivity representation allows joint estimation of brain region connectivity across all subjects and keeps the network connectivity structure of each subject consistent [26], and thus enables better between-group comparability [26]. However, the sparse connectivity representation-related investigation on sMRI-based radMBN is rarely reported particularly in AD application.

Since the dMRI is able to map the trajectory of bundles of white matter axons throughout the brain, the sparse connectivity representation of radMBN would benefit from the regulation of dMRI-based connectivity, and produce more neurobiologically plausible brain networks [27]. The brain network fusion between dMRI and fMRI has been widely investigated by fMRI assisting dMRI, dMRI assisting fMRI, or joint dMRI/fMRI fusion [28]. However, there is still a literature gap regarding the brain network fusion between sMRI-based radMBN and dMRI-based connectivity, which hinders the generalization of the sMRI-based radMBN.

In the present study, a joint constrained group sparse connectivity representation of radMBN for AD analysis was proposed on conventional T1WI images (called JCGS-radMBN). Specifically, the group sparse representation-based framework was adopted to construct brain network by jointly estimating the non-zero connections among subjects with $l_{2,1}\text{-norm}$ regularization. Besides, the $l_{2,1}\text{-norm}$ regularization was weighted by devising a joint constraint factor which was established by group-level white matter fiber connectivity and individual-level sMRI regional similarity. After the sparse brain network was constructed, a triplet GCN which was with the similar triplet network strategy [29, 30], was adopted for early AD diagnosis. The triplet GCN could mine potential high-order relations of subjects between groups and within a group by learning the similarity between anchor and positive/negative samples. Ultimately, the diagnosis was determined by the similarity between test samples and labelled samples. To verify the superiority of the JCGS-radMBN network, two public available datasets were adopted, including 932 participants from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database and 200 participants from the Australian Imaging Biomarkers and Lifestyle (AIBL) database, achieving surpassing performance in early AD diagnosis. The most discriminative brain connections between different groups were also identified to carry out the neurobiological interpretation of the JCGS-radMBN network.

Related works

Radiomics-based morphological brain network (radMBN) construction

The radMBN is constructed based on radiomics feature similarities between brain regions by Pearson correlation operation [12]. Specifically, the radiomics features calculated in study [12] consist of 14 intensity features, 8 shape features, and 33 textural features. However, the redundancy features which has high correlations with other features (R > 0.9) were removed in study [12], generating 25 radiomics features for subsequent analysis (7 intensity features and 18 textural features). In our study, the same 25 radiomics features were adopted.

Assume the radiomics features of the whole brain are denoted as $\mathbf{X}=\left[{\mathbf{x}}_1,,,{\mathbf{x}}_2,,,\cdots ,,,{\mathbf{x}}_{N_b}\right]\in {\mathbb{R}}^{N_f\times N_b}$, $N_f$ represents the dimension of radiomics features, $N_b$ refers to the number of brain regions. For the ith subject, the radiomics similarity ${\phi }_i^{s,t}$ between the sth and tth brain regions can be defined by Pearson correlation operation as follows:

$${\phi }_i^{s,\text{t}}=\frac{{\left({\mathbf{x}}_s,-,{\overline{\mathbf{x}}}_s\right)}^T\left({\mathbf{x}}_t,-,{\overline{\mathbf{x}}}_t\right)}{\sqrt{{\left({\mathbf{x}}_s,-,{\overline{\mathbf{x}}}_s\right)}^T\left({\mathbf{x}}_s,-,{\overline{\mathbf{x}}}_s\right)}\sqrt{{\left({\mathbf{x}}_t,-,{\overline{\mathbf{x}}}_t\right)}^T\left({\mathbf{x}}_t,-,{\overline{\mathbf{x}}}_t\right)}}$$ 1

which constituted the radMBN matrix ${\mathbf{\Psi }}_{\mathit{i}}$ as follows:

$${\mathbf{\Psi }}_{\mathit{i}}={\left[\begin{array}{ccc}{\phi }_i^{1,1}& \cdots & {\phi }_i^{1,N_b}\\ ⋮& {\phi }_i^{s,\text{t}}& ⋮\\ {\phi }_i^{N_b,1}& \cdots & {\phi }_i^{N_b,N_b}\end{array}\right]}_{N_b\times N_b}.$$ 2

This Pearson correlation-based fully connected brain network (called PC_BN) may have a large amount of redundant information. Therefore, a common strategy is to apply a threshold that forces brain connectivity to be 0 or 1 as defined in Eq. (3) (called BinaryPC_BN). This approach simplifies the network structure by removing weak connections and retaining strong connections.

$${\mathbf{A}}_i=\left\{\begin{array}{c}1,{\mathbf{\Psi }}_{\mathit{i}}\ge threshold,\\ 0,otherwise,\end{array}\right)$$ 3

where ${\mathbf{A}}_i$ denotes the binary adjacency matrix of the ith subject, ${\mathbf{\Psi }}_{\mathit{i}}$ denotes the non-binary adjacency matrix of the ith subject defined in Eq. (2).

Sparse connectivity representation

Sparse representation [31] is an approach of representing a signal by finding a linear combination of a set of basis vectors such that the linear combination has a minimum number of nonzero coefficients. The sparse network was constructed under $l_1\text{-norm}$ regularization as defined in Eq. (4):

$${\mathbf{v}}_i^s=\text{arg}\underset{{\mathbf{V}}_i^s}{\mathit{min}}\left(\frac{1}{2},{\Vert {\mathbf{y}}_i^s-\sum _{\begin{array}{c}t=1\\ t\ne s\end{array}}^{N_b}{\mathbf{y}}_i^t{\alpha }_i^{\text{s},t}\Vert }_2^2\right)+\lambda {||{\mathbf{v}}_i^s||}_1,$$ 4

where ${\mathbf{y}}_i^s$ represents the radiomics feature vector of the sth brain region for the ith subject. The vector ${\mathbf{v}}_i^s={\left[{\alpha }_i^{\text{s},1},,,\cdots ,,,{\alpha }_i^{\text{s},s-1},,,{\alpha }_i^{\text{s},s+1},,,\cdots ,,,{\alpha }_i^{\text{s},N_b}\right]}^T\in {\mathbb{R}}^{N_b-1}$ ($N_b$ is the number of brain regions) is the weighted value of the ith subject to linearly represent the sth brain region using other brain regions. The parameter λ controls the sparsity of the network. However, the sparse connectivity representation defined in Eq. (3) cannot consider the relationships or alleviate topological difference between different subjects, and thus the group sparse representation framework is adopted in our study below.

Graph convolutional network for brain network analysis

The GCN generalizes traditional convolutional neural network from Euclidean data (e.g., 2D or 3D images) to the non-Euclidean domain (e.g., graphs and manifolds), and has emerged as a promising method for graph mining [32]. Each brain network can be defined as a graph $G=\{V,E\}$. The vertex set $V=\left\{v_1,,,v_2,,,\cdots ,,,v_{N_b}\right\}$ refers to the nodes in the brain with $N_b$ being the number of brain regions. Each brain region (or node in the brain) is generally characterized with a feature vector, generating a feature matrix $\mathbf{X}=\left[{\mathbf{x}}_1,,,{\mathbf{x}}_2,,,\cdots ,,,{\mathbf{x}}_{N_b}\right]\in {\mathbb{R}}^{N_f\times N_b}$ for the whole brain regions where $N_f$ is the number of features in each node. Besides, $E$ is the set of edges between different nodes with each edge weighted by a connectivity value, generating a adjacency matrix $\text{A}\in {\mathbb{R}}^{N_b\times N_b}$. Based on the above graph definition, the graph convolution is defined as:

$${\text{H}}^{l+1}=\sigma \left({\tilde{\text{D}}}^{-\frac{1}{2}},\tilde{\text{A}},{\tilde{\text{D}}}^{-\frac{1}{2}},{\text{H}}^l,{\text{W}}^l\right),$$ 5

where ${\text{H}}^0=\mathbf{X}$, ${\text{H}}^l\in {\mathbb{R}}^{N_b\times N_f^l}$ is the output of the lth graph convolution layer,$N_b$ is the number of brain regions, $N_f^l$ is the feature dimension of lth layer, $\tilde{\text{A}}=\text{A}+\text{I}$ is the adjacency matrix of graph with self-loops, $\text{I}{\in \mathbb{R}}^{N\times N}$ is the identity matrix, $\tilde{\text{D}}$ is the diagonal degree matrix with ${\tilde{\text{D}}}_{i,j}={\sum }_j{\tilde{\text{A}}}_{i,j}$, and ${\text{W}}^l\in {\mathbb{R}}^{N_f^l\times N_f^{l+1}}$ are the learnable parameters, $\sigma$ is the activation function.

Materials and methods

Data acquisition

Two publicly available datasets were adopted, including 120 subjects from ADNI with both T1WI and dMRI for brain network construction, 818 subjects from ADNI and 200 subjects from AIBL solely with T1WI for validation in early AD diagnosis. The study was approved by institutional review boards of all participating institutions and written informed consent was obtained from all participants or authorized representatives. The participants were divided into NC (normal control), MCI (Mild Cognitive Impairment), and AD groups, and the detailed information of these datasets can be found in Table 1.

Table 1.

Demographic characteristics of the participants

Dataset	Modality	Group	Age	Sex (M/F)	MMSE
ADNI	sMRI	AD (269)	75.13 ± 7.53	142/127	23.22 ± 2.12
		NC (281)	74.12 ± 6.43	131/150	29.14 ± 1.09
		MCI (268)	73.8 ± 7.85	174/94	27.16 ± 1.75
	sMRI + dMRI	AD (42)	74.81 ± 8.18	26/16	22.08 ± 2.10
		NC (47)	71.90 ± 8.18	27/20	28.78 ± 1.98
		MCI (31)	74.11 ± 4.11	18/13	25.44 ± 2.31
AIBL	sMRI	AD (79)	74.84 ± 7.79	33/46	20.42 ± 5.46
		NC (121)	74.16 ± 6.59	66/55	28.80 ± 1.28

NC normal control, MCI mild cognitive impairment, AD Alzheimer’s disease

Data preprocessing

For the T1WI image, the gray matter volume of the whole brain was calculated using the CAT12 toolbox. Then, the same 25 radiomics features with study [12] were calculated for each brain region derived from automatic anatomical labelling (AAL, N = 90), generating a radiomics feature matrix of 25 $\times$ 90. The radiomics feature matrix was normalized among all brain regions using the common minimum–maximum method.

For dMRI data, the PANDA toolbox was used for pre-processing [33]. Specifically, fractional anisotropy (FA) was calculated and the mean FA of the fiber which linked different brain nodes was defined as the connectivity weight in the brain network, generating a 90 × 90 dMRI-based connectivity network for each individual.

The construction of the proposed JCGS-radMBN brain network

The construction of the proposed JCGS-radMBN brain network was summarized in Fig. 1, consisting of two key components: (1) a group sparse connectivity representation framework defined in Eq. (6) to mitigate the topological difference between different subjects by conducting similar topological structures for all subjects and enhance the generalization ability of the proposed JCGS-radMBN brain network when fed into GCN model, and (2) a joint constraint factor ${\mathbf{\Phi }}_{\mathit{g}}$ defined in Eq. (9) established by group-level white matter fiber connectivity and individual-level sMRI regional radiomics similarity to enhance the neurobiological basis for each individual and increase the difference of weighted value of brain connectivity between different individuals.

Fig. 1.

The construction framework of the proposed JCGS-radMBN brain network (FACT Fiber Assignment by Continuous Tracking)

The group sparse connectivity representation

To mitigate the topological difference between different subjects and enhance the generalization ability of the proposed JCGS-radMBN brain network when fed into deep learning model, the group sparse connectivity representation framework defined in Eq. (6) was adopted to achieve a shared graph connectivity by jointly estimating the non-zero connections among subjects with $l_{2,1}\text{-norm}$ regularization based on group LASSO.

$${\mathbf{M}}^s=\text{arg}\underset{{\mathbf{M}}^s}{\mathit{min}}\sum _{i=1}^{N_s}\left(\frac{1}{2},{\Vert {\mathbf{y}}_i^s-\sum _{\begin{array}{c}t=1\\ t\ne s\end{array}}^{N_b}{\mathbf{y}}_i^t{\alpha }_i^{\text{s},t}\Vert }_2^2\right)+\lambda {||{\mathbf{M}}^s||}_{2,1},$$ 6

$${\mathbf{M}}^s=\left[{\mathbf{v}}_1^s,,,\cdots ,,,{\mathbf{v}}_i^s,,,\cdots ,,,{\mathbf{v}}_{N_s}^s\right]={\left[\begin{array}{cc}\begin{array}{ccc}{\alpha }_1^{\text{s},1}& \cdots & {\alpha }_i^{\text{s},1}\\ ⋮& ⋮& ⋮\\ {\alpha }_1^{s,s-1}& \cdots & {\alpha }_i^{\text{s},s-1}\end{array}& \begin{array}{cc}\cdots & {\alpha }_{N_s}^{\text{s},1}\\ ⋮& ⋮\\ \cdots & {\alpha }_{N_s}^{\text{s},s-1}\end{array}\\ \begin{array}{ccc}{\alpha }_1^{s,s+1}& \cdots & {\alpha }_i^{\text{s},s+1}\\ ⋮& ⋮& ⋮\\ {\alpha }_1^b& \cdots & {\alpha }_i^b\end{array}& \begin{array}{cc}\cdots & {\alpha }_{N_s}^{\text{s},s+1}\\ ⋮& ⋮\\ \cdots & {\alpha }_{N_s}^b\end{array}\end{array}\right]}_{(N_b-1)\times N_s},$$ 7

where ${\mathbf{y}}_i^s$ represented the feature of the sth brain region for the ith subject. Same as Eq. (4), the vector ${\mathbf{v}}_i^s={\left[{\alpha }_i^{\text{s},1},,,\cdots ,,,{\alpha }_i^{\text{s},s-1},,,{\alpha }_i^{\text{s},s+1},,,\cdots ,,,{\alpha }_i^{\text{s},N_b}\right]}^T\in {\mathbb{R}}^{N_b-1}$ was the weighted value of the ith subject to linearly represent the sth brain region using other brain regions, and the matrix ${\mathbf{M}}^s=\left[{\mathbf{v}}_1^s,,,\cdots ,,,{\mathbf{v}}_{N_s}^s\right]\in {\mathbb{R}}^{(N_b-1)\times N_s}$ ($N_b$ was the number of brain regions and $N_s$ was number of subjects) concatenated the weighted vector ${\mathbf{v}}_i^s$ of the sth brain region representation for all $i=1,\cdots ,N_s$ subjects. The parameter λ controlled the sparsity of the network. The brain network constructed by group sparse representation shared similar topological structures by imposing similar non-zero or zero connectivity across all subjects to reduce inter-subject variability.

The joint constraint factor established by group-level white matter fiber connectivity and individual-level sMRI regional radiomics similarity

Under the group sparse connectivity representation, a joint constraint factor was devised to further enhance the neurobiological basis for each individual and increase the difference of weighted value of brain connectivity between different individuals. Specifically, the joint constraint factor ${\mathbf{B}}^{\text{s}}$ was added to the above Eq. (6) to establish an element-wise product with the weighted matrix ${\mathbf{M}}^s\in {\mathbb{R}}^{(N_b-1)\times N_s}$ ($N_b$ was the number of brain regions and $N_s$ was number of subjects), and thus was re-formulated as Eq. (8):

$${\mathbf{M}}^s=\text{arg}\underset{{\mathbf{M}}^s}{\mathit{min}}\sum _{i=1}^{N_s}\left(\frac{1}{2},{\Vert {\mathbf{y}}_i^s-\sum _{\begin{array}{c}t=1\\ t\ne s\end{array}}^{N_b}{\mathbf{y}}_i^t{\alpha }_i^{\text{s},t}\Vert }_2^2\right)+\lambda {||{\mathbf{B}}^{\text{s}}\odot {\mathbf{M}}^s||}_{2,1}.$$ 8

The definition of the joint constraint factor ${\mathbf{B}}^{\text{s}}$ was conducted based on a group-level white matter fiber connectivity matrix ${\mathbf{\Phi }}_{\mathit{g}}$ in Eq. (9) and an individual-level radMBN matrix ${\mathbf{\Psi }}_{\mathit{i}}$ defined in Eq. (2).

$${\mathbf{\Phi }}_{\mathit{g}}={\left|\frac{\frac{1}{N_{\mathit{NC}}}{\sum }_{i=1}^{\mathit{NC}}{\mathbf{\Phi }}_{\mathit{i}}+\frac{1}{N_{\mathit{MCI}}}{\sum }_{i=1}^{\mathit{MCI}}{\mathbf{\Phi }}_{\mathit{i}}+\frac{1}{N_{\mathit{AD}}}{\sum }_{i=1}^{\mathit{AD}}{\mathbf{\Phi }}_{\mathit{i}}}{3}\right|}_{N_b\times N_b}.$$ 9

In Eq. (9), ${\mathbf{\Phi }}_{\mathit{g}}$ represented the group-level averaged white matter fiber connectivity matrix, where ${\mathbf{\Phi }}_{\mathit{i}}$ represented the fiber connectivity matrix of subject $i$ from NC, MCI, or AD group with subject numbers in each group being $N_{\mathit{NC}}$, $N_{\mathit{MCI}}$, $N_{\mathit{AD}}$.

The group-level white matter fiber connectivity matrix ${\mathbf{\Phi }}_{\mathit{g}}\in {\mathbb{R}}^{N_b\times N_b}$ in Eq. (9) and an individual-level radMBN matrix ${\mathbf{\Psi }}_{\mathit{i}}\in {\mathbb{R}}^{N_b\times N_b}$ defined in Eq. (2) were then multiplied as follows, generating ${\mathrm{T}}_i\in {\mathbb{R}}^{N_b\times N_b}(i=1,\cdots ,N_s)$ with $N_s$ being the number of subjects.

$${\mathrm{T}}_i=\text{exp}\left(\frac{-{{\mathbf{\Phi }}_{\mathit{g}}}^2}{{\sigma }_1}\right)\times \text{exp}\left(\frac{-{{\mathbf{\Psi }}_{\mathit{i}}}^2}{{\sigma }_2}\right),$$ 10

where the ${\sigma }_1$ and ${\sigma }_2$ are positive parameter used to adjust the weight’s decay for the group-level white matter fiber connectivity strength and individual-level region similarity of radMBN matrix. The adoption of group-level average white matter fiber connectivity matrices instead of individual white matter fiber connection matrices in Eq. (10) is due to the relative scarcity of paired individual dMRI/sMRI data in clinical settings. Employing group-level connectivity matrices is beneficial in addressing the issue of multimodal data absence, thereby facilitating the clinical translation of brain networks.

Based on the matrix ${\mathrm{T}}_i\in {\mathbb{R}}^{N_b\times N_b}$ established for each individual, the factor ${\mathbf{B}}^s$ for the sth brain region representation constraint was conducted as follows:

$${\mathbf{B}}^s=\left[{\mathbf{T}}_1^s,,,\cdots ,,,{{\mathbf{T}}_i^s,\cdots ,\mathbf{T}}_{N_s}^s\right]={\left[\begin{array}{cc}\begin{array}{ccc}{\mathrm{\beta }}_1^{\text{s},1}& \cdots & {\mathrm{\beta }}_i^{\text{s},1}\\ ⋮& ⋮& ⋮\\ {\mathrm{\beta }}_1^{\text{s},s-1}& \cdots & {\mathrm{\beta }}_i^{\text{s},s-1}\end{array}& \begin{array}{cc}\cdots & {\mathrm{\beta }}_{N_s}^{\text{s},1}\\ ⋮& ⋮\\ \cdots & {\mathrm{\beta }}_{N_s}^{\text{s},s-1}\end{array}\\ \begin{array}{ccc}{\mathrm{\beta }}_1^{\text{s},s+1}& \cdots & {\mathrm{\beta }}_i^{\text{s},s+1}\\ ⋮& ⋮& ⋮\\ {\mathrm{\beta }}_1^{\text{s},N_b}& \cdots & {\mathrm{\beta }}_i^{\text{s},N_b}\end{array}& \begin{array}{cc}\cdots & {\mathrm{\beta }}_{N_s}^{\text{s},s+1}\\ ⋮& ⋮\\ \cdots & {\mathrm{\beta }}_{N_s}^{\text{s},N_b}\end{array}\end{array}\right]}_{(N_b-1)\times N_s},$$ 11

where ${\mathbf{B}}^{\mathit{s}}\in {\mathbb{R}}^{(N_b-1)\times N_s}$ was the weighted matrix for an element-wise product with the weighted matrix ${\mathbf{M}}^s$ denoted with $\odot$ in Eq. (8). Specifically, the weighted matrix ${\mathbf{B}}^{\mathit{s}}$ in Eq. (11) concatenated the same sth column of the all matrices ${\mathrm{T}}_i\in {\mathbb{R}}^{N_b\times N_b}(i=1,\cdots ,N_s)$ with element ${\mathrm{\beta }}_{\text{i}}^s$ removed because we only considered linearly representing the sth brain region using other brain regions in the ith subject, generating the jointly constraint matrix of ${\mathbf{B}}^s\in {\mathbb{R}}^{(N_b-1)\times N_s}$.

Given the definition of the jointly constraint matrix of ${\mathbf{B}}^s\in {\mathbb{R}}^{(N_b-1)\times N_s}$, the group LASSO regression was adopted to optimize the Eq. (8), and the weighted matrix ${\mathbf{M}}^s\in {\mathbb{R}}^{(N_b-1)\times N_s}$ was obtained for all brain regions ($s=1,\cdots ,N_b$). Since the optimized matrix ${\mathbf{M}}^s$ concatenated the sth brain region representation of all subjects but the JCGS-radMBN brain network was required to be established for each individual which contained all $N_b$ brain regions, the same ith column of the optimized matrix ${\mathbf{M}}^s\in {\mathbb{R}}^{(N_b-1)\times N_s}(s=1,\cdots ,N_b)$ corresponding to the sth brain region representation of the ith subject was taken out and concatenated to be the final JCGS-radMBN brain network for each individual. Note that the JCGS-radMBN brain network was conducted with size of $N_b\times N_b$ by adding the diagonal element of 0 because we only considered linearly representing the sth brain region using other brain regions in the ith subject (not including the sth brain region itself) and removed the ${\alpha }_i^s$ in the definition ${\mathbf{M}}^s$ of Eq. (7) for the sth brain region representation of the ith subject.

Assume that the JCGS-radMBN brain network was defined by the adjacency matrix $A_{\text{JCGS}-\text{radMBN}}$, the $A_{\text{JCGS}-\text{radMBN}}$ for the ith subject was defined below based on the optimized ${\mathbf{M}}^s\in {\mathbb{R}}^{(N_b-1)\times N_s}(s=1,\cdots ,N_b)$ in Eq. (12).

$$A_{\text{JCGS}-\text{radMBN}}\left(i\right)=\left[\begin{array}{cccccc}0& {\alpha }_i^{2,1}& {\alpha }_i^{3,1}& {\alpha }_i^{4,1}& \cdots & {\alpha }_i^{N_b,1}\\ {\alpha }_i^{1,2}& 0& {\alpha }_i^{3,2}& {\alpha }_i^{4,2}& \cdots & {\alpha }_i^{N_b,2}\\ {\alpha }_i^{1,3}& {\alpha }_i^{2,3}& 0& {\alpha }_i^{4,3}& \cdots & {\alpha }_i^{N_b,3}\\ {\alpha }_i^{1,4}& {\alpha }_i^{2,4}& {\alpha }_i^{3,4}& 0& \cdots & {\alpha }_i^{N_b,4}\\ ⋮& ⋮& ⋮& ⋮& \cdots & ⋮\\ {\alpha }_i^{1,N_b}& {\alpha }_i^b& {\alpha }_i^b& {\alpha }_i^b& \cdots & 0\end{array}\right].$$ 12

Then, the symmetric representation was adopted in the present study by carrying out a symmetric operation $A_{\text{JCGS}-\text{radMBN}}=\left(A_{\text{JCGS}-\text{radMBN}},+,{\text{A}}_{\text{JCGS}-\text{radMBN}}^T\right)/2$ after performing a max–min normalization per-column.

Triplet graph convolutional network strategy for early AD diagnosis

Given the JCGS-radMBN brain network conducted above with adjacency matrix $A_{\text{JCGS}-\text{radMBN}}$ and its associated radiomics-based feature matrix $\mathbf{X}$ defined in "Radiomics-based morphological brain network (radMBN) construction" section, a triplet GCN which was with similar triplet network strategy [29, 30] was adopted for early AD diagnosis. As displayed in Fig. 2, the triplet GCN learning strategy consisted of three channels with each channel containing two graph convolutional layers and three linear layers. The network in the three channels shared the same network parameters.

Fig. 2.

Illustration of triplet graph convolutional network

In the training stage, the triplet GCN was fed with a triplet $\left\{{\mathbf{G}}_a,,,{\mathbf{G}}_p,,,{\mathbf{G}}_n\right\}$, including an reference sample ${\mathbf{G}}_a$ (called anchor), a matching sample ${\mathbf{G}}_p$ (called positive, indicating the sample was from the same class of anchor input), and a non-matching sample ${\mathbf{G}}_n$ (called negative, indicating the sample was from a different class of anchor input). Based on the given adjacency matrix $A_{\text{JCGS}-\text{radMBN}}$ and feature matrix $\mathbf{X}$, the similarity between the anchor and positive input was minimized in the output layer, while the similarity between the anchor and negative input was maximized. Besides, we randomly selected $k=10$ positive samples of ${\mathbf{G}}_p$ and $k=10$ negative samples of ${\mathbf{G}}_n$ from the training set for each anchor ${\mathbf{G}}_a$ to reduce the influence of the noise in the data to early AD diagnosis, generating a triple set ${\left\{{\mathbf{G}}_a,,,{\mathbf{G}}_p^k,,,{\mathbf{G}}_n^k\right\}}_{k=1}^{10}$. The same strategy of the triple set ${\left\{{\mathbf{G}}_a,,,{\mathbf{G}}_p^k,,,{\mathbf{G}}_n^k\right\}}_{k=1}^{10}$ was also adopted in the testing stage. Besides, based on the above triple setting of ${\left\{{\mathbf{G}}_a,,,{\mathbf{G}}_p^k,,,{\mathbf{G}}_n^k\right\}}_{k=1}^{10}$ above, the triplet loss function was defined as follows:

$$\begin{array}{c}L\left({\mathbf{G}}_a,,,{\mathbf{G}}_p,,,{\mathbf{G}}_n\right)={\sum }_{k=1}^{10}[{||f\left({\mathbf{G}}_a\right)-f\left({\mathbf{G}}_p^k\right)||}_2^2\left(-,{||f\left({\mathbf{G}}_a\right)-f\left({\mathbf{G}}_n^k\right)||}_2^2,+,d\right],\end{array}$$ 13

where $f$ represented the embedding generated by the triplet GCN, the margin parameter $d=1$ was employed to enlarge the distance between different categories. The proposed triplet GCN was implemented on PyTorch 1.7.1 using the optimizer Adam with initial learning rate of 0.001, weight decay rate of 5 × 10⁻⁴, batch size of 45, and the training time was set to 50 epochs.

Experimental settings and evaluation metrics

To evaluate the superiority of our proposed brain network construction method, a total of six brain network construction methods were compared, including PC_BN brain network [12], BinaryPC_BN brain network [34, 35], K-nearest neighbors-based brain network (KNN_BN) [36], sparse representation defined in Eq. (4) (SR_BN) [23, 24], group sparse representation defined in Eq. (6) (GSR_BN) [26], and the proposed JCGS-radMBN brain network defined in Eq. (8). Specifically, PC_BN is a fully-connected brain network, BinaryPC_BN, KNN_BN, and SR_BN are individual-level sparse brain networks, GSR_BN and JCGS_radMBN are group-level sparse brain networks. The binarization threshold of 0.8 and K = 10 was adopted in the BinaryPC_BN brain network and KNN_BN brain network, respectively. The sparse representation and group sparse representation was implemented using the SLEP toolkit [37] with the regularization parameter λ = 0.1. which are all determined by the grid search strategy when the highest accuracy was achieved. The grid search details for determining the regularization parameter λ of JCGS-radMBN are provided in Supplementary Material S1. Besides, the same radiomics-based feature matrix $\mathbf{X}$ defined in "Radiomics-based morphological brain network (radMBN) construction" section was adopted for a fair comparison.

The experimental comparison was implemented by feeding the six brain networks constructed above into the triplet GCN model and training the model for the classification task of NC vs. AD under a 10-fold cross-validation strategy. The pre-trained model of NC vs. AD was also applied in the classification task of NC vs. MCI, AD vs. MCI, and pMCI vs. sMCI (pMCI and sMCI were defined as whether to convert to AD within 36 months, respectively. pMCI = progressive MCI, sMCI = stable MCI) for further validation of the superiority of the proposed JCGS-radMBN brain network. Besides, the accuracy (ACC), sensitivity (SEN), specificity (SPE) defined below, and the receiver operating characteristic (ROC) curve and its associated area under the curve (AUC) value were adopted for performance evaluation. The detailed description of AUC can be found in Supplementary Material S2.

$$\text{ACC}=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{FP}+\text{TN}+\text{FN}},$$ 14

$$\text{SEN}=\frac{\text{TP}}{\text{TP}+\text{FN}},$$ 15

$$\text{SPE}=\frac{\text{TN}}{\text{TN}+\text{FP}},$$ 16

where TP, TN, FP, and FN denote true positive, true negative, false positive and false negative, respectively.

Results

Classification comparison between different brain network construction methods

Given the six different brain network construction methods in "Experimental settings and evaluation metrics" section and the same radiomics-based feature matrix $\mathbf{X}$ defined in "Radiomics-based morphological brain network (radMBN) construction" section, Table 2 summarized the comparison results when feeding them into the triplet GCN model. Specifically, the PC_BN brain network exhibited the lowest performance no matter NC vs. AD, NC vs. MCI, AD vs. MCI, or pMCI vs. sMCI. After a sparsification setting such as BinaryPC_BN, KNN_BN, SR_BN, and GSR_BN, the classification performance increased accordingly, and the proposed JCGS-radMBN brain network achieved the best performance. For example, regarding the NC vs. AD classification, the JCGS-radMBN achieved ACC = 0.902, SEN = 0.861, SPE = 0.941, and AUC = 0.936, rising by about 20% over the typical PC_BN in all indices of ACC = 0.708, SEN = 0.687, SPE = 0.728, and AUC = 0.766. The associated ROC curve exhibition was presented in the Supplementary Material S3.

Table 2.

The classification comparison when feeding brain networks constructed by different methods into triplet GCN model

Task	Methods	ACC	SEN	SPE	AUC
NC vs. AD	PC_BN	0.708	0.687	0.728	0.766
	BinaryPC_BN	0.815	0.766	0.863	0.886
	KNN_BN	0.792	0.760	0.823	0.872
	SR_BN	0.850	0.812	0.886	0.909
	GSR_BN	0.883	0.841	0.923	0.920
	JCGS-radMBN	0.902	0.861	0.941	0.936
NC vs. MCI	PC_BN	0.608	0.553	0.659	0.643
	BinaryPC_BN	0.670	0.514	0.819	0.722
	KNN_BN	0.673	0.515	0.824	0.733
	SR_BN	0.720	0.598	0.837	0.775
	GSR_BN	0.734	0.550	0.908	0.783
	JCGS-radMBN	0.744	0.615	0.865	0.807
AD vs. MCI	PC_BN	0.618	0.654	0.582	0.653
	BinaryPC_BN	0.668	0.825	0.512	0.707
	KNN_BN	0.664	0.685	0.644	0.714
	SR_BN	0.694	0.781	0.608	0.732
	GSR_BN	0.689	0.761	0.619	0.743
	JCGS-radMBN	0.706	0.779	0.618	0.747
pMCI vs. sMCI	PC_BN	0.530	0.612	0.462	0.554
	BinaryPC_BN	0.553	0.558	0.548	0.589
	KNN_BN	0.558	0.576	0.508	0.609
	SR_BN	0.594	0.728	0.485	0.642
	GSR_BN	0.618	0.580	0.660	0.672
	JCGS-radMBN	0.634	0.693	0.571	0.691

Best values indicate in bold

Ablation study

To demonstrate the superiority of the triplet GCN over the typical GCN in early AD diagnosis, we implemented the experiments by feeding the six different brain networks into the single-channel GCN in Table 3. The single-channel GCN referred to the shared channel in the triplet GCN which consisted of two graph convolutional layers and three linear layers. The experimental results demonstrated that the triplet GCN achieved superior classification performance than the typical single-channel GCN. For example, regarding the JCGS-radMBN brain network, the triplet GCN improved the accuracy and AUC by 0.037 and 0.021 when compared to the single-channel GCN regarding the NC vs. AD classification. The associated ROC curve exhibition was presented in the Supplementary Material S4.

Table 3.

The classification comparison when feeding brain networks constructed by different methods into the typical single-channel GCN model (sGCN) and the triplet GCN model (tGCN)

Task	Networks	ACC		SEN		SPE		AUC
		sGCN	tGCN	sGCN	tGCN	sGCN	tGCN	sGCN	tGCN
NC vs. AD	PC_BN	0.702	0.708	0.718	0.687	0.686	0.728	0.761	0.766
	BinaryPC_BN	0.809	0.815	0.795	0.766	0.822	0.863	0.878	0.886
	KNN_BN	0.775	0.792	0.774	0.760	0.776	0.823	0.858	0.872
	SR_BN	0.844	0.850	0.822	0.812	0.865	0.886	0.899	0.909
	GSR_BN	0.842	0.883	0.814	0.841	0.868	0.923	0.904	0.920
	JCGS-radMBN	0.865	0.902	0.825	0.861	0.904	0.941	0.915	0.936

Best values indicate in bold

Of note that the triplet GCN only achieved limited improvement over sGCN on the individual-level brain networks such as PC_BN, BinaryPC_BN, and SR_BN, or even with lower sensitivity. The reason is that the individual-level brain network may suffer the great inter-subject variability in topological structures and connections [38], and the connectivity changes in AD compared to the controls are likely to be overwhelmed by such large inter-subject variability [26]. Thus, the triplet GCN only achieved limited improvement over sGCN on these brain network.

The ablation experiment was also conducted by comparing the joint constraint factor ${\mathbf{B}}^{\text{s}}$ defined in Eq. (8) with the single constraint factor of sole group-level white matter fiber connectivity (called group-level constraint factor) or sole individual-level sMRI regional radiomics similarity (called individual-level constraint factor). Specifically, the group-level constraint factor was constructed by removing the other term of the individual-level constraint factor $\text{exp}\left(\frac{-{{\mathbf{\Psi }}_{\mathit{i}}}^2}{{\sigma }_2}\right)$, and vice versa. The experimental results demonstrated that the joint constraint factor achieved superior performance in NC vs. AD classifications (Table 4). The associated ROC curve exhibition was presented in the Supplementary Material S3.

Table 4.

Comparison of classification results using joint constraint factor or single constraint factor for JCGS-radMBN brain network construction

Task	Regularization	ACC	SEN	SPE	AUC
NC vs. AD	Group-level constraint factor	0.872	0.835	0.907	0.925
	Individual-level constraint factor	0.886	0.843	0.928	0.930
	Joint constraint factor	0.902	0.861	0.941	0.936

Group-level constraint factor the single constraint factor of sole group-level white matter fiber connectivity, Individual-level constraint factor the single constraint factor of sole individual-level sMRI regional radiomics similarity. Joint constraint factor was the strategy adopted in our study

Best values indicate in bold

Evaluation on external dataset

To verify the generalizability and superiority of the JCGS-radMBN, we trained the model using the ADNI dataset and conducted external testing with the AIBL dataset. As indicated in Table 5, the JCGS-radMBN still achieved the best classification performance, with an ACC of 0.879 and an AUC of 0.927. In contrast, the PC_BN based on fully-connected exhibited the lowest ACC and AUC values of only 0.550 and 0.514, suggesting that excessive connectivity may reduce the model's generalization performance. Although other brain networks showed slight improvements over PC_BN, they still did not match the performance of JCGS-radMBN. These results demonstrated the robust generalization capabilities of JCGS-radMBN due to the group sparse strategy coupled with joint constraint factors. The associated ROC curve was presented in Fig. S5 of the Supplementary Material.

Table 5.

Classification comparison of brain networks constructed by different methods on an external test set

Task	Methods	ACC	SEN	SPE	AUC
NC vs. AD	PC_BN	0.550	0.371	0.668	0.514
	BinaryPC_BN	0.706	0.623	0.764	0.769
	KNN_BN	0.643	0.411	0.791	0.648
	SR_BN	0.810	0.714	0.870	0.908
	GSR_BN	0.856	0.738	0.931	0.913
	JCGS-radMBN	0.879	0.776	0.944	0.927

Most discriminative brain connections

To investigate the most discriminative brain region connections associated with AD analysis, the two-sample t-test (p < 0.05) was carried out between NC vs. AD, NC vs. MCI, and AD vs. MCI in terms of connection strength represented by the adjacency matrix $A_{\text{JCGS}-\text{radMBN}}$ defined in Eq. (12). The TOP 10 brain connectivity identified by the T-value of the statistical analysis regarding each group comparison were listed in Table 6. Note that only 8 brain connectivity between NC vs. MCI and 3 brain connectivity between AD vs. MCI were with statistically significant difference.

Table 6.

The TOP 10 brain connectivity identified by the T-value of the statistical analysis regarding each group comparison of NC vs. AD, NC vs. MCI, and AD vs. MCI

Group	ROI 1		ROI 2		T	p
	Index	Name	Index	Name
NC vs. AD	38	Right hippocampus	75	Left pallidum	12.007	< 0.0001
	37	Left hippocampus	41	Left amygdala	7.7511	< 0.0001
	37	Left hippocampus	35	Left posterior cingulate	7.6203	< 0.0001
	38	Right hippocampus	78	Right thalamus	7.4980	< 0.0001
	39	Left parahippocampal gyrus	72	Right caudate	7.3693	< 0.0001
	38	Right hippocampus	84	Right superior temporal pole	7.2219	< 0.0001
	38	Right hippocampus	88	Right middle temporal pole	7.0477	< 0.0001
	39	Left parahippocampal gyrus	74	Right putamen	6.4783	< 0.0001
	42	Right amygdala	73	Left putamen	5.4750	< 0.0001
	57	Left postcentral	85	Right middle temporal gyrus	5.4374	< 0.0001
NC vs. MCI	38	Right hippocampus	75	Left pallidum	8.4596	< 0.0001
	35	Left posterior cingulate	37	Left hippocampus	6.2470	< 0.0001
	10	Right orbitofrontal middle gyrus	41	Left amygdala	5.3831	< 0.0001
	38	Right hippocampus	88	Right middle temporal pole	4.7905	0.0009
	38	Right hippocampus	84	Right superior temporal pole	4.4788	0.0038
	39	Left parahippocampal gyrus	72	Right caudate	4.4279	0.0048
	63	Left supramarginal gyrus	76	Right pallidum	4.0053	0.0295
	16	Left frontal inferior orbital	30	Right Insula	3.9572	0.0395
AD vs. MCI	37	Left hippocampus	41	Left amygdala	4.4141	0.0051
	38	Right hippocampus	78	Right thalamus	4.0083	0.0292
	38	Right hippocampus	75	Left pallidum	3.9082	0.0439

Best values indicate in bold

T absolute value of T value, p p value (Bonferroni-corrected)

Regarding the TOP 10 brain connectivity in the results of the NC vs. AD comparison, six of them were hippocampus-related connections, two of them were parahippocampal gyrus-related connections, four of them were basal ganglia-related connections which referred to putamen, caudate nucleus, or pallidum. Regarding the TOP 8 brain connectivity in the results of the NC vs. MCI comparison, four of them were hippocampus-related connections, one of them were parahippocampal gyrus-related connections, three of them were basal ganglia-related connections including connections to caudate nucleus, or pallidum. Regarding the TOP 3 brain connectivity in the results of the AD vs. MCI comparison, all of them were hippocampus-related connections, and one of them was basal ganglia-related connections which referred to pallidum. All the highlighting discriminative brain region connections indicated the strong connectivity with those brain regions above. Figure 3 also displayed the above TOP 10 discriminative brain connections in each group comparison between NC vs. AD, NC vs. MCI, and AD vs. MCI, where the line thickness represented the T-value obtained by the statistical comparison.

Fig. 3.

The scatter plot between connection strength and clinical measures

Association between discriminative brain connections and cognitive scores

To validate the biological basis of the JCGS-radMBN, we correlated the connectivity strength of the discriminative brain connections in "Most discriminative brain connections" section to the Mini-Mental State Examination (MMSE) scores after controlling for the effects of age and gender.

Given the discriminative 10 brain connections between NC vs. AD listed in Table 6 (called NA set), the discriminative 8 brain connections between NC vs. MCI (called NM set), and the discriminative 3 brain connections between AD vs. MCI (called AM set), the intersections of any of two sets such as (NA ∩ NM), (NA ∩ AM), and (NM ∩ AM) were obtained, and the union set of intersections was obtained to calculate the correlation between the discriminative brain connections and MMSE scores in NC, MCI, and AD groups. The final union set included seven connections of right hippocampus to left pallidum, right hippocampus to right superior temporal pole, right hippocampus to right middle temporal pole, left hippocampus to left posterior cingulate, left parahippocampal gyrus to right caudate, left hippocampus to left amygdala, right hippocampus to right thalamus.

Figure 4 displayed the scatter plots of the seven brain connections in the final union set with all of them being significant correlated with MMSE scores, which demonstrated the biological basis of the JCGS-radMBN. Particularly, the connection of right hippocampus to left pallidum exhibited the most correlation with abs(R value) = 0.42. The reason was that the brain connectivity of right hippocampus to left pallidum was the only connection identified in all the three group comparisons in Table 6 indicating the importance of the brain connectivity in characterizing different stages of AD.

Fig. 4.

The visualization of the discriminative brain connections listed in Table 6

Discussion

In the present study, the brain network JCGS-radMBN established on the routinely acquired T1WI image was proposed for early AD diagnosis. Specifically, the JCGS-radMBN established a group sparse connectivity representation of the radMBN under a joint constraint of group-level white matter fiber connectivity and individual-level sMRI regional similarity. The experimental results demonstrated that the JCGS-radMBN brain network achieved superior classification performance over five brain network construction methods under comparison, including PC_BN, BinaryPC_BN, KNN_BN, SR_BN, and GSR_BN no matter NC vs. AD, NC vs. MCI, AD vs. MCI, or pMCI vs. sMCI according to Table 2. The discriminative brain connections exhibited a strong connectivity to hippocampus, parahippocampal gyrus, and basal ganglia (Table 6), and had significant correlation with Mini-Mental State Examination (MMSE) scores (Fig. 3).

To demonstrate the superiority of the proposed JCGS-radMBN, we also summarized brain network construction studies that solely using sMRI [39–41], joint dMRI/sMRI [42], and joint sMRI/fMRI/dMRI [43]. The proposed JCGS-radMBN was established in the mode of dMRI assisting sMRI. Of note that the joint multi-modality is totally different from another modality assisting sMRI in brain network construction. For the joint multi-modality such as joint dMRI/sMRI [42], and joint sMRI/fMRI/dMRI [43] for brain network construction, the deep learning model requires to be fed with the multi-modality imaging simultaneously at each training or testing stage, which might hinder its clinical translation because the multi-modality imaging is not always available clinically. For another modality assisting sMRI in the brain network construction such as the proposed JCGS-radMBN, although the topological connectivity is conducted under the guidance of the advanced sequence such as dMRI, the dMRI is not acquired anymore in the clinical application once the brain network is conducted, which would facilitate the clinical translation of the brain network because the sMRI is the routinely acquired imaging modality. According to Table 7, the proposed JCGS-radMBN achieved better classification performance than not only solely using sMRI using sMRI [39–41] but also joint dMRI/sMRI [42] and joint sMRI/fMRI/dMRI [43], demonstrating the superiority of the JCGS-radMBN in brain network construction and its application in early AD diagnosis.

Table 7.

Comparison with GNN-based methods for AD and NC classification

Methods	Modality	Subjects	ACC	SEN	SPE	AUC
Sampathkumar [39]	sMRI	61NC + 60AD	0.834	NA	NA	NA
Wee et al. [41]	sMRI	960NC + 592AD	0.852	0.812	0.885	NA
Wei et al. [42]	sMRI, dMRI	113NC + 96AD	0.861	0.885	0.833	NA
Tian et al. [43]	sMRI, fMRI, dMRI	167NC + 191AD	0.887	0.867	0.908	0.881
Fan et al. [40]	sMRI	330NC + 336AD	0.890	0.860	0.923	NA
Proposed	sMRI, dMRI	281NC + 269AD	0.902	0.861	0.941	0.936

The superiority of the JCGS-radMBN in brain network construction benefited from the topology consistency achieved by group sparse representation strategy, the group-level constraint of the dMRI using the white matter fiber connectivity (called group-level constraint factor), and the individual-level constraint of the sMRI using regional radiomics similarly (called individual-level constraint factor). Specifically, the group sparse representation of the radMBN alleviated the individual difference in terms of brain network topology, forcing the brain network focusing on the group difference. The group-level constraint factor conducted by dMRI could enhance the physical connectivity between gray matter regions in the brain network construction. The individual-level constraint factor conducted by sMRI facilitated the connectivity strength difference in the brain network construction. The above efforts enhanced the representation of the JCGS-radMBN in AD analysis even established on conventional T1WI image.

Neurobiological interpretation of brain networks is important for understanding brain disease mechanisms and early diagnosis [44, 45]. Table 6 and Fig. 4 in this study showed that a large number of connections were associated with the hippocampus. The hippocampus is often considered to be one of the earliest brain regions affected in AD patients [46–48], and various neuroimaging studies have demonstrated the structural and functional connectivity abnormalities of the hippocampus in patients with AD and MCI [49–52]. Meanwhile, these discriminative connections identified in our study were also associated with the basal ganglia and thalamus, which was also reported previously [53–55]. This suggests that Alzheimer's disease (AD) is associated with neuronal loss not only in the hippocampus and amygdala but also in the thalamus and basal ganglia [56]. Furthermore, alterations in the structure and connectivity of the parahippocampal gyrus are also recognized as early biomarkers of Alzheimer's disease [57, 58]. Previous longitudinal studies have shown significant volume loss in the hippocampus during the progression of AD with a direct relationship with cognitive decline [59, 60]. In this study, we also found a significant correlation (p < 0.0001) between all seven connections and the clinical cognitive score MMSE. Interestingly, we found that the connections associated with the left hippocampus were all positively correlated, whereas those associated with the right hippocampus were mostly negatively correlated (three out of four included), and we speculated that this might be related to the asymmetric atrophy of the right and left hippocampi found previously [61, 62].

This study still has some limitations: (1) we only studied the ADNI dataset and further validation is needed for other diseases and databases. (2) Due to limitations of the unpaired data between dMRI and sMRI, we used group-level dMRI connectivity strength as a constraint factor, while individual-level dMRI connectivity constraint may provide more beneficial information based on paired data. (3) The network construction is limited to a single spatial scale, and it may be beneficial to use multiple brain atlas in network construction and incorporate them into the learning process [63].

Conclusion

In the present study, a joint constrained group sparse connectivity representation of radMBN for AD analysis was proposed on conventional T1WI images (JCGS-radMBN). The JCGS-radMBN achieved superior classification performance compared with other brain network under comparison, and the most discriminative brain connections between different groups were also identified with neurobiological interpretation. The proposed JCGS-radMBN facilitated the AD characterization of brain network and its clinical translation when established on routinely acquired imaging modality of sMRI.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Chuanzhen Zhu and Honglun Li: Conceptualization, Methodology, Data curation, Software, Experiments, and Writing—Original Draft. Zhiwei Song: Methodology, Data curation, Writing—Original Draft. Minbo Jiang: Validation, Formal analysis. Limei Song, Lin Li and Xuan Wang: Writing—Original Draft, Investigation. Qiang Zheng: Conceptualization, Supervision, Project administration and Funding acquisition.

Funding

This work was supported by the National Natural Science Foundation of China (61802330, 61802331), Natural Science Foundation of Shandong Province (ZR2020QH048) and Yantai City Science and Technology Innovation Development Plan (2023XDRH006).

Data availability

The data utilized in this study were sourced from the Alzheimer's Disease Neuroimaging Initiative (ADNI), available at http://adni.loni.usc.edu/data-samples/access-data, and the Australian Imaging, Biomarkers and Lifestyle Flagship Study of Ageing (AIBL), available at http://aibl.csiro.au.

Declarations

Conflict of interest

The authors have no potential conflicts of interest to disclose.

Ethical approval

This study has ethical approval, consent to participate, and consent for publication. The Institutional Review Board of all participating centers approved the study procedures.

Informed consent

This study has consent to participate.

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