Information-based similarity analysis

We conducted the information-based similarity method [51] to evaluate the similarity of structural patterns in brain regions between AD and CN groups. The method was developed to discover the hidden structure of sequence data and compare the similarity of two sequences. The information-based similarity index quantifies the distance (or dissimilarity) between two sequences using the occurrence proportion of defined elements. It has been applied to analyse symbolic sequences including heart rate time series [51], literary authorship disputes [55], and genetic sequences [56]. In these studies, the “words” were elements defined in a given length, representing a unique pattern in the sequence (e.g., fluctuations in time series and n-tuple nucleotides in genetic sequences). These words are then ranked according to their occurrence probabilities in the sequence in descending order. The first rank word corresponds to the most common pattern in the symbolic sequence. Using the rank order of words, the weighted distance, denoted as D and ranging from zero to one, defined the dissimilarity of two sequences, S₁ and S₂.

The weighting function F(w_k) derived from Shannon's entropy is as follows, where Z indicates the normalization factor.

Here R₁(w_k) and p₁(w_k) denote the rank and probability of a given word, w_k, in the sequence S₁. R₂(w_k) and p₂(w_k) represent the same in sequence S₂. N₁₂ is the total number of shared words in sequence S₁ and S₂.

To capture the structural pattern in micro-scale (i.e., words in the IBS method), we defined the structural pattern indices by relationships of grey matter intensity in adjacent voxels relative to a given voxel. For a voxel x, its grey matter intensity was compared to its six adjacent voxels. If the grey matter intensity in voxel x was greater than or equal to its neighbor voxel n (v1, v2, …, v6), the symbol Sn (S1, S2, …, S6) was marked with a one; otherwise, it was marked with a zero.

We mapped the six symbols to a binary sequence, following the order: right, left, anterior, posterior, superior, and inferior voxels. The binary sequence, representing intensity relationships, was then converted into a decimal number (see more details in Fig. ​Fig.1A).1A). These decimal numbers, identified as structural pattern indices, were integers between zero and 63 (i.e., 2⁶ = 64 combinations), with each index corresponding to a unique spatial pattern.

Flowchart. A Grey matter relationships with neighboring six voxels identified structural pattern indices. The binary symbol sequence, which represented the combination of intensity relationships, was then converted to a decimal pattern index. B Preprocessed grey matter maps were mapped using a zero-padded grey matter mask. This step ensured the retention of voxels and their neighbors for morphological similarity analysis. Subsequently, these were mapped with the grey matter mask. C We measured the IBS distances as dissimilarity between two AAL brain regions based on the probabilities and rank orders of structural patterns. D The IBS distance between the original and spatial shuffled grey matter intensities assessed the structural randomness. The stepwise regression was used to examine the relationship of the MMSE score with structural randomness. E We applied the one-sample t-test to investigate the regional structural similarity and the independent t-tests to explore group differences in inter-regional structural similarity and structural randomness. AAL: automated anatomical labeling; IBS: information-based similarity; MMSE: Mini-Mental State Examination

To ensure grey matter voxels and their neighbors were included in the analysis and to preserve the boundary information, the preprocessed structural MRI data of all participants were mapped with a zero-padded grey matter mask. This study only included grey matter voxels with six intact neighboring voxels. Next, we filled the structural pattern indices into the corresponding voxels to generate a map for each participant. The resulting images were mapped with the standard grey matter mask again and applied for morphological similarity analysis (Fig. ​(Fig.11B).

In this study, we performed a word rank frequency analysis on 64 structural pattern indices in a specific brain area. We calculated the occurrence probability of each index and sorted it in descending order. Subsequently, the IBS distance between two brain areas was measured based on their respective index rank orders, allowing us to assess inter-regional structural similarity (Fig. ​(Fig.1C).1C). The small IBS distances between brain regions are expressed as structural similarity.

We conducted two sections of examination to explore the alterations in structural similarity in AD. First, we computed the index rank for each brain region based on the group average probability of each index. The similarity between a specific brain region of the two groups was then defined as the regional structural similarity. Brain areas with small regional structural similarity to the CN group represented the affected regions in AD. Second, we calculated the inter-regional similarities between pairs of brain regions, resulting in 4005 (C(90,2) = 4005) structural similarities for each participant. The inter-regional similarities were examined to investigate whether the morphological associations varied with AD progression.

To quantify the organizational characteristics of structural patterns in a brain region, we calculated the nonrandomness index derived from the IBS method [51]. The nonrandomness index is the average IBS distance between the original signal and its randomized surrogates. A high nonrandomness index means that the original signal is not similar to the randomized one, suggesting that it is a more regular organization. In contrast, a low nonrandomness index indicates a more random configuration. The nonrandomness index was applied to quantify underlying dynamics features of heart rate time series and effectively discriminate the healthy subjects and subjects with congestive heart failure [51].

In addition to structural similarity reflecting structural coordination between groups and brain regions, we explored structural randomness to find the underlying organization of regional structure. The IBS distance between the structural pattern of the original and voxel-shuffled grey matter density map evaluated the degree of structural nonrandomness. For every AAL brain region, we generated a regional zero-padded mask to extract neighboring voxels. Next, we created ten randomly shuffled surrogates, remaining with the grey matter intensity information but disrupting the spatial distribution. Each surrogate was denoted with voxel-wise structural pattern indices and compared the IBS distance to the structural pattern map derived from the raw grey matter intensity. Finally, the average of ten distances was computed as the nonrandomness index for each brain region (Fig. ​(Fig.1D).1D). The low nonrandomness index of a brain region is denoted as structural randomness.