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Cortical Surface Diffusion Generative Models

Zhenshan Xie, Simon Dahan, Logan Z. J. Williams, M. Jorge Cardoso, Emma C. Robinson

TL;DR

This work develops a diffusion-based generative framework for cortical surface data by integrating a surface-aware diffusion model with a surface vision transformer (SiT) backbone. The forward DDPM process adds Gaussian noise to curvature maps on a sixth-order icosahedral grid, and the learned reverse process denoises to generate realistic cortical surfaces, with conditioning on postmenstrual age (PMA) via additional input tokens and classifier-free guidance. Evaluated on the dHCP dataset, the model produces PMA-conditioned curvature maps that align with developmental patterns, demonstrated by a high $R^2$ of $0.96$ and comparable PMA regression performance, and qualitative visual examples. This approach advances normative neurodevelopmental modeling by enabling high-fidelity, non-Euclidean surface generation, with potential extensions to image-to-image translation and anomaly detection in cortical morphology.

Abstract

Cortical surface analysis has gained increased prominence, given its potential implications for neurological and developmental disorders. Traditional vision diffusion models, while effective in generating natural images, present limitations in capturing intricate development patterns in neuroimaging due to limited datasets. This is particularly true for generating cortical surfaces where individual variability in cortical morphology is high, leading to an urgent need for better methods to model brain development and diverse variability inherent across different individuals. In this work, we proposed a novel diffusion model for the generation of cortical surface metrics, using modified surface vision transformers as the principal architecture. We validate our method in the developing Human Connectome Project (dHCP), the results suggest our model demonstrates superior performance in capturing the intricate details of evolving cortical surfaces. Furthermore, our model can generate high-quality realistic samples of cortical surfaces conditioned on postmenstrual age(PMA) at scan.

Cortical Surface Diffusion Generative Models

TL;DR

This work develops a diffusion-based generative framework for cortical surface data by integrating a surface-aware diffusion model with a surface vision transformer (SiT) backbone. The forward DDPM process adds Gaussian noise to curvature maps on a sixth-order icosahedral grid, and the learned reverse process denoises to generate realistic cortical surfaces, with conditioning on postmenstrual age (PMA) via additional input tokens and classifier-free guidance. Evaluated on the dHCP dataset, the model produces PMA-conditioned curvature maps that align with developmental patterns, demonstrated by a high of and comparable PMA regression performance, and qualitative visual examples. This approach advances normative neurodevelopmental modeling by enabling high-fidelity, non-Euclidean surface generation, with potential extensions to image-to-image translation and anomaly detection in cortical morphology.

Abstract

Cortical surface analysis has gained increased prominence, given its potential implications for neurological and developmental disorders. Traditional vision diffusion models, while effective in generating natural images, present limitations in capturing intricate development patterns in neuroimaging due to limited datasets. This is particularly true for generating cortical surfaces where individual variability in cortical morphology is high, leading to an urgent need for better methods to model brain development and diverse variability inherent across different individuals. In this work, we proposed a novel diffusion model for the generation of cortical surface metrics, using modified surface vision transformers as the principal architecture. We validate our method in the developing Human Connectome Project (dHCP), the results suggest our model demonstrates superior performance in capturing the intricate details of evolving cortical surfaces. Furthermore, our model can generate high-quality realistic samples of cortical surfaces conditioned on postmenstrual age(PMA) at scan.
Paper Structure (13 sections, 5 equations, 4 figures, 1 table)

This paper contains 13 sections, 5 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Method
  3. DDPM formulation
  4. Surface Diffusion Model
  5. Surface Vision Transformer
  6. Decoding
  7. Conditioning
  8. Experiments and Results
  9. Data
  10. Implementation Details
  11. Evaluation of Conditional Generation
  12. Conclusion
  13. Acknowledgments

Figures (4)

  • Figure 1: The directed graphical model of diffusion process on cortical surface
  • Figure 2: The figure shows the architecture of the cortical surface diffusion model. First, the flattened input will be projected by linear embedding. Then, positional embedding and condition embeddings (class embedding and time embedding) would be added to the input tokens. After N transformer blocks, the prediction of noise would be projected out by the linear decoding layer.
  • Figure 3: Unconditional generated curvature surface compared with real sample
  • Figure 4: Samples of cortical surfaces generated by surface diffusion model conditioned on birth age of 30, 34, 38 and 42 weeks, compared to the real samples in dHCP dataset(First line)