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Physically Informed Deep Learning Technique for Estimating Blood Flow Parameters in Arterial Bifurcations

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Abstract

This research investigates application of physically regularized deep learning for the estimation of blood flow parameters in bifurcations of human arteries. The study presents a comprehensive methodology that combines synthetic data generation and advanced neural network architectures. The initial step involves construction of 3D meshes for bifurcations achieved through the developed mesh generator based on the GMSH library. A diverse dataset is then generated on the basis of 3D blood flow simulations in bifurcations in a physiological range of parameters such as vessel radii, bifurcation angles and inlet and outlet pressures. The generic database for neural network training and testing contains approximately \(1.4\cdot 10^{5}\) data samples. The research focuses on training a feed-forward neural network, which provides the minimum possible error and physically relevant output. Two types of loss functions are explored for assessing the network’s performance, Huber loss function (HLF) and a physically regularized loss function (PRLF). We achieve the relative error of \(12\%\) for HLF. The study demonstrates that PRLF enhances the model’s capability to adhere to physical laws which provides faster convergence of training phase and decrease of the relative error to approximately \(2.5\%\) on the test dataset. We also study sensitivity of PRLF-based neural network convergence to different physical components. We found that adding symmetry property to the mass conservation condition accelerates the training process, decreases fluctuations of PRLF and reduces the relative error.

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Funding

This work has been supported by the Russian Science Foundation, grant number 21-71-30023.

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Authors and Affiliations

  1. Marchuk Institute of Numerical Mathematics of Russian Academy of Science, 119333, Moscow, Russia

    A. Isaev, T. Dobroserdova, A. Danilov & S. Simakov

  2. Sechenov University, 119048, Moscow, Russia

    A. Danilov & S. Simakov

  3. Moscow Institute of Physics and Technology, 141701, Dolgoprudny, Moscow oblast, Russia

    S. Simakov

Authors
  1. A. Isaev
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  2. T. Dobroserdova
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  3. A. Danilov
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  4. S. Simakov
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Correspondence to T. Dobroserdova, A. Danilov or S. Simakov.

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Isaev, A., Dobroserdova, T., Danilov, A. et al. Physically Informed Deep Learning Technique for Estimating Blood Flow Parameters in Arterial Bifurcations. Lobachevskii J Math 45, 239–250 (2024). https://doi.org/10.1134/S1995080224010219

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