Abstract
Blood vessel networks, represented as 3D graphs, help predict disease biomarkers, simulate blood flow, and aid in synthetic image generation, relevant in both clinical and pre-clinical settings. However, generating realistic vessel graphs that correspond to an anatomy of interest is challenging. Previous methods aimed at generating vessel trees mostly in an autoregressive style and could not be applied to vessel graphs with cycles such as capillaries or specific anatomical structures such as the Circle of Willis. Addressing this gap, we introduce the first application of denoising diffusion models in 3D vessel graph generation. Our contributions include a novel, two-stage generation method that sequentially denoises node coordinates and edges. We experiment with two real-world vessel datasets, consisting of microscopic capillaries and major cerebral vessels, and demonstrate the generalizability of our method for producing diverse, novel, and anatomically plausible vessel graphs.
C. Prabhakar and S. Shit—Contributed equally.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
References
Austin, J., Johnson, D.D., Ho, J., Tarlow, D., Van Den Berg, R.: Structured denoising diffusion models in discrete state-spaces. Advances in Neural Information Processing Systems 34, 17981–17993 (2021)
Drees, D., Scherzinger, A., Hägerling, R., Kiefer, F., Jiang, X.: Scalable robust graph and feature extraction for arbitrary vessel networks in large volumetric datasets. BMC bioinformatics 22(1), 1–28 (2021)
Dwivedi, V.P., Bresson, X.: A generalization of transformer networks to graphs. arXiv preprint arXiv:2012.09699 (2020)
Feldman, P., Fainstein, M., Siless, V., Delrieux, C., Iarussi, E.: Vesselvae: Recursive variational autoencoders for 3d blood vessel synthesis. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. pp. 67–76. Springer (2023)
Haefeli, K.K., Martinkus, K., Perraudin, N., Wattenhofer, R.: Diffusion models for graphs benefit from discrete state spaces. arXiv preprint arXiv:2210.01549 (2022)
Ho, J., Jain, A., Abbeel, P.: Denoising diffusion probabilistic models. Advances in neural information processing systems 33, 6840–6851 (2020)
Hua, C., Luan, S., Xu, M., Ying, R., Fu, J., Ermon, S., Precup, D.: Mudiff: Unified diffusion for complete molecule generation. arXiv preprint arXiv:2304.14621 (2023)
Huang, H., Sun, L., Du, B., Fu, Y., Lv, W.: Graphgdp: Generative diffusion processes for permutation invariant graph generation. In: 2022 IEEE International Conference on Data Mining (ICDM). pp. 201–210. IEEE (2022)
Jo, J., Lee, S., Hwang, S.J.: Score-based generative modeling of graphs via the system of stochastic differential equations. In: International Conference on Machine Learning. pp. 10362–10383. PMLR (2022)
Kreitner, L., Paetzold, J.C., Rauch, N., Chen, C., Hagag, A.M., Fayed, A.E., Sivaprasad, S., Rausch, S., Weichsel, J., Menze, B.H., et al.: Synthetic optical coherence tomography angiographs for detailed retinal vessel segmentation without human annotations. IEEE Transactions on Medical Imaging (2024)
Loshchilov, I., Hutter, F.: Decoupled weight decay regularization. arXiv preprint arXiv:1711.05101 (2017)
Luo, T., Mo, Z., Pan, S.J.: Fast graph generative model via spectral diffusion. arXiv preprint arXiv:2211.08892 (2022)
Lyu, X., Cheng, L., Zhang, S.: The reta benchmark for retinal vascular tree analysis. Scientific Data 9(1), 397 (2022)
Menten, M.J., Paetzold, J.C., Dima, A., Menze, B.H., Knier, B., Rueckert, D.: Physiology-based simulation of the retinal vasculature enables annotation-free segmentation of oct angiographs. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. pp. 330–340. Springer (2022)
Paetzold, J.C., McGinnis, J., Shit, S., Ezhov, I., Büschl, P., Prabhakar, C., Sekuboyina, A., Todorov, M., Kaissis, G., Ertürk, A., et al.: Whole brain vessel graphs: A dataset and benchmark for graph learning and neuroscience. In: Thirty-Fifth Conference on Neural Information Processing Systems Datasets and Benchmarks Track (Round 2) (2021)
Paetzold, J.C., Lux, L., Kreitner, L., Ezhov, I., Shit, S., Lotery, A.J., Menten, M.J., Rueckert, D.: Geometric deep learning for disease classification in octa images. Investigative Ophthalmology & Visual Science 64(8), 1098–1098 (2023)
Peng, X., Guan, J., Liu, Q., Ma, J.: Moldiff: Addressing the atom-bond inconsistency problem in 3d molecule diffusion generation. arXiv preprint arXiv:2305.07508 (2023)
Perez, E., Strub, F., De Vries, H., Dumoulin, V., Courville, A.: Film: Visual reasoning with a general conditioning layer. In: Proceedings of the AAAI conference on artificial intelligence. vol. 32 (2018)
Pinheiro, P.O., Rackers, J., Kleinhenz, J., Maser, M., Mahmood, O., Watkins, A., Ra, S., Sresht, V., Saremi, S.: 3d molecule generation by denoising voxel grids. Advances in Neural Information Processing Systems 36 (2024)
Rauch, N., Harders, M.: Interactive Synthesis of 3D Geometries of Blood Vessels. In: Eurographics 2021 - Short Papers. The Eurographics Association (2021). https://doi.org/10.2312/egs.20211012
Reichold, J., Stampanoni, M., Keller, A.L., Buck, A., Jenny, P., Weber, B.: Vascular graph model to simulate the cerebral blood flow in realistic vascular networks. Journal of Cerebral Blood Flow & Metabolism 29(8), 1429–1443 (2009)
Schneider, M., Reichold, J., Weber, B., Székely, G., Hirsch, S.: Tissue metabolism driven arterial tree generation. Medical image analysis 16(7), 1397–1414 (2012)
Todorov, M.I., Paetzold, J.C., Schoppe, O., Tetteh, G., Shit, S., Efremov, V., Todorov-Völgyi, K., Düring, M., Dichgans, M., Piraud, M., et al.: Machine learning analysis of whole mouse brain vasculature. Nature methods 17(4), 442–449 (2020)
Vignac, C., Krawczuk, I., Siraudin, A., Wang, B., Cevher, V., Frossard, P.: Digress: Discrete denoising diffusion for graph generation. arXiv preprint arXiv:2209.14734 (2022)
Vignac, C., Osman, N., Toni, L., Frossard, P.: Midi: Mixed graph and 3d denoising diffusion for molecule generation. arXiv preprint arXiv:2302.09048 (2023)
Wittmann, B., Paetzold, J.C., Prabhakar, C., Rueckert, D., Menze, B.: Link prediction for flow-driven spatial networks. In: Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision. pp. 2472–2481 (2024)
Wolterink, J.M., Leiner, T., Isgum, I.: Blood vessel geometry synthesis using generative adversarial networks. arXiv preprint arXiv:1804.04381 (2018)
Xie, T., Fu, X., Ganea, O.E., Barzilay, R., Jaakkola, T.: Crystal diffusion variational autoencoder for periodic material generation. arXiv preprint arXiv:2110.06197 (2021)
Yang, K., Musio, F., Ma, Y., Juchler, N., Paetzold, J.C., Al-Maskari, R., Höher, L., Li, H.B., Hamamci, I.E., Sekuboyina, A., et al.: Benchmarking the cow with the topcow challenge: Topology-aware anatomical segmentation of the circle of willis for cta and mra. arXiv preprint arXiv:2312.17670 (2023)
Yi, K., Zhou, B., Shen, Y., Liò, P., Wang, Y.: Graph denoising diffusion for inverse protein folding. Advances in Neural Information Processing Systems 36 (2024)
Acknowledgments
This work has been supported by the Helmut Horten Foundation. S. S. is supported by the GRC Travel Grant from UZH. F.M. is funded by the DIZH grant. H. B. Li is supported by an SNF postdoctoral mobility grant.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Ethics declarations
Disclosure of Interests
The authors have no competing interests to declare that are relevant to the content of this article.
1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Prabhakar, C. et al. (2024). 3D Vessel Graph Generation Using Denoising Diffusion. In: Linguraru, M.G., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2024. MICCAI 2024. Lecture Notes in Computer Science, vol 15011. Springer, Cham. https://doi.org/10.1007/978-3-031-72120-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-031-72120-5_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-72119-9
Online ISBN: 978-3-031-72120-5
eBook Packages: Computer ScienceComputer Science (R0)