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GAUSSIAN MARKOV RANDOM FIELDS FOR ASSESSING INTERMODAL REGIONAL ASSOCIATIONS IN PRODROMAL ALZHEIMER’S DISEASE

      Background

      Alzheimer’s disease (AD) is characterized by a cascade of pathological processes that can be assessed in vivo using different neuroimaging methods. Recent research suggests a systematic sequence of pathogenic events on a global biomarker level, but little is known about the associations and dependencies of distinct lesion patterns on a regional level. Markov random fields are a probabilistic graphical modeling approach that represent the interaction between individual random variables by an undirected graph. We propose the novel application of this approach to study the inter-regional associations and dependencies between multimodal imaging markers of AD pathology, and to compare different hypotheses regarding the spread of the disease.

      Methods

      We retrieved multimodal imaging data from 398 subjects with mild cognitive impairment enrolled in the Alzheimer’s Disease Neuroimaging Initiative (ADNI). Mean amyloid load (AV45-PET), glucose metabolism (FDG-PET), and gray matter volume (MRI) were calculated for the six principle nodes of the default mode network – a functional network of brain regions that appears to be preferentially targeted by AD. Gaussian Markov random fields were fitted to the data and estimated the partial correlation between each pair of regions and imaging modalities. The resulting models were compared to previously defined graph structures representing three different hypotheses regarding the spread of the disease: the “intraregional evolution model”, the “trans-neuronal spread” hypothesis, and the “wear-and-tear” hypothesis, (Figure 1 A–C). Evaluation was conducted using tenfold cross-validation with 1000 repetitions.

      Results

      For all pairs of modalities, the estimated graph structures (Figure 2) were most similar to the “wear-and-tear” hypothesis of disease vulnerability (Table 1). For the pairs amyloid-β/gray matter volume and metabolism/gray matter volume, the posterior cingulate cortex provided the main hub node with strongest edges to various other regions. For the pair amyloid-β/metabolism, the hub node medial prefrontal cortex provided best fit. Although strongest associations were found within each modality, significant associations between modalities were most matching the intraregional evolution model (Figure 2).

      Conclusions

      Gaussian Markov random field models offer a convenient framework for studying the associations of distinct lesion patterns in AD. They afford great potential to complement traditional multiple regression analyses in multimodal neuroimaging research.
      Figure thumbnail fx1
      Figure 1Representative graph structures for different hypotheses regarding the spread of Alzheimer's disease. The first imaging modality is located on the left side of each subfigure, the second modality is located on the right side. Both modalities are connected depending on the specific hypothesis. Abbreviations: HPL, HPR – left and right hippocampus, IPL, IPR – left and right inferior parietal cortex, MPC – medial prefrontal cortex, PCC – posterior cingulate cortex.
      Figure thumbnail fx2
      Figure 2Graph structures and partial correlation between nodes obtained from Gaussian Markov random fields. Edges represent the mean partial correlation across the 10000 cross-validation iterations, thresholded at a significance level of P < 0.05. Abbreviations: amy – amyloid-β, fdg – fluorodeoxyglucose metabolism, gmv – gray matter volume, HPL, HPR – left and right hippocampus, IPL, IPR - left and right inferior parietal cortex, MPC – medial prefrontal cortex, PCC – posterior cingulate cortex.
      Table 1Jaccard similarity coefficient for the graph structures learned from the data and the manually specified models
      ModalitiesModel AModel BModel CHub node
      Amyloid – Metabolism0,08±0,020,14±0,000,26±0,01HPL
      0,10±0,000,22±0,01IPL
      0,18±0,010,42±0,02 *MPC
      0,14±0,000,36±0,02 *PCC
      Amyloid – Gray matter volume0.02±0.020.14±0.020.28±0.04HPL
      0.12±0.010.27±0.04IPL
      0.17±0.010.30±0.03MPC
      0.17±0.010.40±0.03 *PCC
      Metabolism – Gray matter volume0.23±0.020.13±0.010.23±0.02HPL
      0.13±0.010.25±0.03IPL
      0.21±0.010.30±0.02MPC
      0.17±0.030.35±0.03 *PCC
      Mean and standard deviation of the Jaccard similarity coefficient for comparing the set of edges obtained from Gaussian graphical models and the manually specified models for the different hypotheses regarding the spread of Alzheimer's disease. Asterisk indicates significant difference of the Jaccard index for the best models in comparison to all other models within the respective pair of modalities (P < 0.05). Abbreviations: Models A, B, and C refer to the networks given in Figure 1. HPL – left hippocampus, IPL – left inferior parietal cortex, MPC – medial prefrontal cortex, PCC – posterior cingulate cortex.