Deep Geometric Learning with Monotonicity Constraints for Alzheimer’s Disease Progression

Information Science Artificial Intelligence Neurology Medical Imaging Medicine
Alzheimer's Disease Geometric Modeling Longitudinal Data Missing Value Imputation Neural Ordinary Differential Equations

Using Monotonicity-Constrained Deep Geometric Learning to Predict Alzheimer’s Disease Progression

Background Introduction

Alzheimer’s Disease (AD) is a devastating neurodegenerative disorder that gradually leads to irreversible cognitive decline, eventually resulting in dementia. Early identification and progression prediction of this disease are crucial for clinical diagnosis and treatment, making accurate modeling of AD progression a key research focus.

Currently, many studies employ structural magnetic resonance imaging (MRI) for modeling AD progression, focusing mainly on three aspects: 1) temporal variability; 2) incomplete observational data; 3) temporal geometric features. Despite existing deep learning methods attempting to address data variability and sparsity, there remains insufficient attention to intrinsic geometric characteristics correlated with AD progression, such as the size, thickness, volume, and shape of brain regions.

In this context, the authors of this paper propose a new geometric learning approach that combines longitudinal MRI biomarkers and cognitive scores modeling. Furthermore, they introduce a training algorithm that reflects the irreversibility of measurement changes through monotonicity constraints. The study utilizes a geometric modeling method called ODE-RGRU (Ordinary Differential Equation-based Recurrent Neural Network). However, this method faces limitations in extrapolating positive definite symmetric matrices from incomplete samples, which is particularly prominent in clinical applications.

Paper Source

This paper is authored by Seungwoo Jeong, Wonsik Jung, Junghyo Sohn, and Heung-Il Suk (Senior Member, IEEE), mainly from Korea University’s institutions in South Korea. The paper was published in May 2024 in the IEEE Transactions on Neural Networks and Learning Systems journal.

Detailed Research Process

Research Process

The research process includes the following steps:

  1. Data Preprocessing and Transformation: Transforming input data (s_t) into points (x_t) in Cholesky space.
  2. Combination Modules: The framework includes three modules: the topological space transformation module, ODE-RGRU module, and trajectory estimation module. The topological space transformation module converts data into geometric representation; the ODE-RGRU module learns time trajectories; the trajectory estimation module estimates missing values from incomplete samples.
  3. Training and Optimization: Introducing a new training algorithm combining monotonicity constraints that regularize MRI biomarkers’ trajectories to satisfy specific requirements while maintaining model performance.

Experimental Methods and Algorithms

  1. ODE-RGRU Module:

    • Using Cholesky space and Riemannian geometric operations for time series modeling.
    • Capturing data’s geometric structure by introducing Fréchet mean and manifold ODE operations.

  2. Trajectory Estimation Module:

    • Addressing missing values issue by using ODE solvers and decoders to estimate missing data in incomplete samples.
    • Ensuring feature monotonicity through autoregressive modeling.

  3. Training Algorithm:

    • Optimizing using estimation loss (l{estim}), prediction loss (l{pred}), and monotonic regularization (l_{reg}).
    • Ensuring all modules’ learning objectives are achieved by adjusting hyperparameters (\lambda_1), (\lambda_2), and (\lambda_3).

Experiments and Results

The authors evaluated the method using the publicly available TADPOLE dataset. Experimental results indicate that the proposed method outperforms existing techniques in various longitudinal scenarios, especially in irregular time settings.

  1. Longitudinal Clinical State Prediction:

    • The results show the proposed method achieves higher MAUC and accuracy in multi-classification tasks of predicting CN (Cognitively Normal), MCI (Mild Cognitive Impairment), and AD states, outperforming existing methods.

  2. Cognitive Score Prediction:

    • In cognitive score prediction, the method achieves the lowest MAPE and performs significantly in ADAS-Cog11 and ADAS-Cog13 aspects.

  3. MRI Biomarker Prediction under Incomplete Observation:

    • The method accurately predicts time-discontinuous or complex pathological features, demonstrating robust missing value prediction capability.

Research Significance and Value

The geometric learning framework proposed in this paper provides a novel and effective method for modeling AD progression by combining longitudinal data’s temporal variability, geometric characteristics, and monotonicity constraints. This method:

  1. Scientific Value: By introducing geometric and monotonic constraints, the framework enhances the modeling performance of longitudinal MRI and cognitive scores data, improving the model’s efficacy in handling sparse and incomplete sample data.
  2. Application Value: Effectively used for clinical progression prediction and diagnosis, providing more accurate AD progression predictions that aid in improving early diagnosis and treatment outcomes.

Research Highlights and Future Work

Research Highlights

  1. Proposes a new geometric learning framework that integrates temporal variability and geometric characteristics.
  2. Develops a monotonicity-constrained training algorithm, ensuring model stability and effectiveness.
  3. Demonstrates superior performance in clinical and cognitive score prediction through detailed experiments and comparisons.

Future Work

Future research will focus on the following aspects:

  1. Improving Missing Value Estimation Accuracy: Enhancing the accuracy of missing value estimation by more precisely tracking trajectories within the manifold space.
  2. Optimizing Clinical State Prediction: Enhancing model accuracy in clinical state prediction by deeply reflecting the irreversible properties of AD.
  3. Expanding Application Scenarios: Extending the method to other neurodegenerative diseases or complex datasets with similar characteristics for validation and application.

Through these efforts, the research aims to further advance studies and clinical applications in AD and related fields, providing more scientifically reliable tools for early detection and treatment of related diseases.