Blog post written by: Lukas Niekerke

Based on: F. J. Martinez-Murcia, A. Ortiz, J. -M. Gorriz, J. Ramirez and D. Castillo-Barnes, "Studying the Manifold Structure of Alzheimer's Disease: A Deep Learning Approach Using Convolutional Autoencoders," in IEEE Journal of Biomedical and Health Informatics, vol. 24, no. 1, pp. 17-26, Jan. 2020. https://ieeexplore.ieee.org/abstract/document/8737996

Introduction

Alzheimer's disease (AD) is a neurodegenerative disorder characterized by progressive cognitive decline and memory loss, significantly impacting millions worldwide [2]. Understanding the underlying mechanisms of AD and identifying early biomarkers for accurate diagnosis are important to develop effective treatments and interventions. Traditional approaches to studying Alzheimer's disease have relied heavily on clinical assessments, neuroimaging, and histopathological analyses. However, these methods often fail to capture the complex, high-dimensional nature of the disease's progression and manifestation.

Recent advances in machine learning, particularly deep learning, offer promising new avenues for exploring and understanding Alzheimer's disease. Deep learning techniques, with their ability to model complex patterns and relationships within vast amounts of data, provide powerful tools for uncovering the intricate structures underlying neurodegenerative diseases.

This paper explores the application of convolutional autoencoders (CAE) in studying the manifold structure of Alzheimer's disease. It discusses the architecture and training of CAEs and the interpretation of the latent space representations. Furthermore, it demonstrates how these representations can be used to identify potential biomarkers, track disease progression, and predict clinical variables.

Methods

Convolutional Autoencoders

Convolutional autoencoders, a type of unsupervised neural network, are designed to learn efficient representations of input data by compressing it into a lower-dimensional latent space and then reconstructing it back to its original form.

In the context of Alzheimer's disease, CAEs can be leveraged to learn the manifold structure of brain imaging data, providing insights into patterns associated with the neurodegeneration. By mapping high-dimensional neuroimaging data onto a lower-dimensional latent space, researchers can identify distinct features and trajectories that differentiate healthy aging from pathological changes associated with AD. This approach not only aids in early diagnosis but also enhances our understanding of the disease's progression and the underlying biological processes.

Dataset

Data for the article were sourced from the ADNI database [3], part of the Alzheimer's Disease Neuroimaging Initiative. This study used the "ADNI1:Complete 2Yr" dataset, involving a 2-year follow-up of patients with MCI and healthy control targets (CTL), including cognitive assessments and MRI scans.

The dataset includes 2182 T1-weighted MRI images from 479 subjects. Additional variables used were age, tau protein levels, ApoE4 variant, MMSE scores, ADAS-cog subscales, and CDRSB, which serve as output variables in the regression model.

Evaluation

The work conducted two experiments to examine the relationships between the dataset's structure, neuropsychological test scores, biological markers, and diagnosis categories

Additionally, visual aid is provided by plotting the subjects in the CAE space. Each neuron's influence is estimated via a linear model, focusing on those most correlated with clinical variables.

Experiment 1: Classification

The study involves classifying AD clusters under two scenarios:

• AD vs CTL: Classifying images labeled as AD and control (CTL).
• MCIC vs MCIS: Using the latest image of each MCI Stable (MCIS) subject and the last image of each MCI Converter (MCIC) subject before conversion to AD

Three different supervised learning algorithms were used for these classifications:

• Linear Support Vector Machine Classifier (SVC)  [4]: Used twice, first as a baseline with the Voxels-As-Features (VAF) approach [5], and then trained/tested on latent space of the CAE (CAE-SVC).
• Neural Classifier (MLP) [6]: With two hidden layers of 64 neurons, ReLU activations, softmax output, dropout (p=0.5), and batch normalization (CAE-MLP).

Experiment 2: Prediction

Prediction of neuropsychological tests and other clinical variables using a neural regression model. This model is a multilayer perceptron (MLP) with two hidden layers of 64 neurons, using ReLU activation, batch normalization, dropout (p=0.5), and a single neuron with linear activation in the output layer to predict the following variables:

• ADAS-11 (Alzheimer’s Disease Assessment Scale)
• ADAS-13 (Alzheimer’s Disease Assessment Scale)
• ADAS-Q4 (Alzheimer’s Disease Assessment Scale)
• Age
• ApoE4 (Presence of the Apolipoprotein E)
• CDRSB (Clinical Dementia Rating)
• MMSE (Mini Mental State Examination)
• TAU (Tau protein concentration in Cerebro-Spinal Fluid)

Performance Estimation

For Experiment 1, 10-fold stratified cross-validation was used to estimate the generalization ability of the classification methodology [7]. The actual error upper bound was estimated using a procedure ensuring the difference between actual and resubstitution error is bounded by the actual risk for any significance η < 0.05.

where l is the sample size [8].

For Experiment 2, the prediction error between the original target variables $//<![CDATA[ \begin{array}{l}y_i\end{array} //]]>$ (neuropsychological scores or clinical markers) and model outputs $//<![CDATA[ \begin{array}{l}\hat{y}_i\end{array} //]]>$ was measured using Mean Squared Error (MSE). Additionally, Pearson's Correlation Coefficient (PCC) and the Coefficient of Determination (R2) were used to assess correlation and regression performance. PCC measures the linear correlation between $//<![CDATA[ \begin{array}{l}y\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}\hat{y}_i\end{array} //]]>$, while R2 explains the proportion of variance in the target variables explained by the model outcomes $//<![CDATA[ \begin{array}{l}\hat{y}_i\end{array} //]]>$:

where $//<![CDATA[ \begin{array}{l}\mu_y\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}\mu_{\hat{y}}\end{array} //]]>$ are the means of all $//<![CDATA[ \begin{array}{l}y_i\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}\hat{y}_i\end{array} //]]>$ respectively.

Results

In both experiments, the effectiveness of features extracted by the autoencoder in the latent space is evaluated. For the first experiment, the ability of these features to distinguish between different classes in the dataset is accessed. In the second experiment, it is examined how well these features predict clinical variables. Specifically, it is focused on how the performance varies with the number of neurons in the latent space for each tissue map.

Evolution of the accuracy of the AD vs CTL setting when varying the number of neurons in the latent space (Z layer) for the first experiment.

Evolution of the PCC when varying the number of neurons in the latent space (Z layer) for the second experiment.

The classification performance improves as the number of neurons Z increases, stabilizing at different Z values for different tissue maps: approximately Z=20 for GM (gray matter) for both experiments. For comparative purposes, Z=20 is chosen for further analysis.

Experiment 1:Classification

It was observed that GM and WM maps achieve better performance in SVC than the MLP. The highest accuracy in the AD vs. CTL scenario is achieved using GM tissue maps, followed closely by WM maps, with precisions exceeding 84%. This suggests that the autoencoder's z-layer effectively clusters subjects, revealing underlying disease structures.

Experiment 2: Regression Analysis

Overall just like in experiment 1 GM maps show the highest correlations with all clinical variables, outperforming other tissue maps significantly. The highest correlation is with ADAS-11 (PCC = 0.638, R2 = 0.381), followed by other ADAS-cognitive measures, CDRSB, and MMSE. These variables are directly related to Alzheimer's disease progression and cognitive state. The only variables that has a low corralation with GM maps is ApoE4 and therefore does not seem to be important for the CAE for identifying AD. The highest correlation in WM maps is with Age (PCC = 0.396, R2 = 0.141)

Comparison

To contextualize the classification results, they are compared to methods proposed in three recent studies:

1. Spherical Brain Mapping (SBM) [9]: This technique creates a two-dimensional map from three-dimensional MRI volumes, representing radial statistical texture values. It is used for both classification and regression .
2. Stacked Autoencoder (SAE) [10]: This approach uses regional gray matter (GM) tissue low-level features (LLFs) for classification .
3. PCA Decomposition [11]: This method decomposes GM MRI images using PCA and applies the extracted features to a regression model predicting MMSE yearly changes .

Classification Perfomance

The method proposed by this paper outperformed the VAF baseline and the SAE features, suggesting the Z-layer features from the CAE are more optimal. However, SAE combined with LLF and SBM reported higher accuracies.

Regression Perfomance

A significant contribution of this work is the regression analysis conducted in Experiment 2, which examines the correlation between pure imaging characteristics and various clinical variables. This type of analysis is rare but crucial for validating diagnoses and deepening the understanding of neurodegeneration processes. The results are similar to the ones found using SBM and suggests a strong link between the CAE-extracted features and cognitive state. The correlation of the CAE method with MMSE was also high, though not as high as the PCA-based approach. However, this analysis did not use a separate test set or cross-validation, indicating that the reported performance might be overestimated. The differences in correlation between GM and WM (and Norm images) were larger in regression analysis. This is consistent with literature indicating that Alzheimer's disease (AD) affects GM first and progresses to WM over time [12].

Visualization of Areas of Influence

The CAE trained with each tissue dataset (GM, WM, and Norm) defines a new space for projecting brain maps from their original image space, which allows to explore their non-linear manifold structure and relate them to clinical variables. It is focused on combinations that better characterize AD, as measured by dementia scales and biological markers like TAU. When examining the distribution of the Z-layer neurons of the CAE for AD and CTL subjects, the greatest differences are observed in the 14th neuron, followed by the 3rd. This indicates that these neurons contain important information about the structure of the disease.

To identify regions that better classify AD, we estimate the Areas of Influence (AoI) of each neuron. When looking at the AoIs of neuron 14 in the Z-layer, trained with GM maps, it can be seen that regions traditionally linked to AD progression, such as parts of the temporal and parietal lobes and cerebellum shrinkage, are highlighted [13], emphasizing the AoI's utility in linking neurodegeneration's structural causes to Z-manifold coordinates.

Conclusion

The demonstrated links between the CAE's data-driven decomposition and various clinical and neuropsychological variables offer a new tool for studying neurodegeneration in AD. The Z-manifold effectively predicts classes and clinical variables, and the identified patterns and regions align with known brain degeneration processes. The strong correlation between automatically extracted features and clinical examinations can enhance dementia diagnosis and provide deeper insights into the structural processes of neurodegeneration and their relationship to cognitive impairment.

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References

[1] F. J. Martinez-Murcia, A. Ortiz, J. -M. Gorriz, J. Ramirez and D. Castillo-Barnes, "Studying the Manifold Structure of Alzheimer's Disease: A Deep Learning Approach Using Convolutional Autoencoders," in IEEE Journal of Biomedical and Health Informatics, vol. 24, no. 1, pp. 17-26, Jan. 2020, doi: 10.1109/JBHI.2019.2914970.

[2] H. Niu, I. Álvarez Álvarez, F. Guillén-Grima and I. Aguinaga-Ontoso, "Prevalencia e incidencia de la enfermedad de Alzheimer en europa: metaanálisis", Neurologia, vol. 32, no. 8, 2017.

[3] ADNI Database: https://adni.loni.usc.edu/

[4] C.-C. Chang and C.-J. Lin, "LIBSVM: A library for support vector machines", ACM Trans. Intell. Syst. Technol., vol. 2, no. 3, Apr. 2011.

[5] J. Stoeckel, N. Ayache, G. Malandain, P. M. Koulibaly, K. P. Ebmeier and J. Darcourt, "Automatic classification of SPECT images of Alzheimers disease patients and control subjects", Proc. Int. Conf. Med. Image Comput. Comput. Assisted Intervention, vol. 3217, pp. 654-662.

[6] D. W. Ruck, S. K. Rogers, M. Kabrisky, M. E. Oxley and B. W. Suter, "The multilayer perceptron as an approximation to a Bayes optimal discriminant function", IEEE Trans. Neural Netw., vol. 1, no. 4, pp. 296-298, Dec. 1990.

[7] R. Kohavi and G. H. John, "Wrappers for feature subset selection", J. Artif. Intell., vol. 97, pp. 273-324, 1997.

[8] J. M. Górriz et al., "A machine learning approach to reveal the NeuroPhenotypes of autisms", Int. J. Neural Syst., vol. 29, Jan. 2019.

[9] F. J. Martinez-Murcia et al., "Assessing mild cognitive impairment progression using a spherical brain mapping of magnetic resonance imaging", J. Alzheimers Disease, vol. 65, pp. 713-729, 2018.

[10] H.-I. Suk et al., "Latent feature representation with stacked auto-encoder for ad/mci diagnosis", Brain Struct. Function, vol. 220, no. 2, pp. 841-859, 2015.

[11] S. Duchesne, A. Caroli, C. Geroldi, G. B. Frisoni and D. L. Collins, "Predicting clinical variable from MRI features: Application to MMSE in MCI", Lecture Notes in Computer Science, pp. 392-399, 2005.

[12] N. Villain et al., "Sequential relationships between grey matter and white matter atrophy and brain metabolic abnormalities in early Alzheimers disease", Brain, vol. 133, no. 11, pp. 3301-3314, 2010.

[13] J. Zhang, C. Yu, G. Jiang, W. Liu and L. Tong, "3D texture analysis on MRI images of Alzheimers disease", Brain Imag. Behav., vol. 6, no. 1, pp. 61-69, 2012.