# On the periodicity of cardiovascular fluid dynamics simulations

arXiv: https://arxiv.org/abs/2102.00107 · HTML: https://mlsanity.com/paper/2102.00107/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2021.

## Built on by (most cited first, 5 of 5)

- [Learning Reduced-Order Models for Cardiovascular Simulations with Graph Neural Networks](https://mlsanity.com/paper/2303.07310/) (2023)
- [Liquid Fourier Latent Dynamics Networks for fast GPU-based numerical simulations in computational cardiology](https://mlsanity.com/paper/2408.09818/) (2024)
- [Data-Driven Bifurcation Handling in Physics-Based Reduced-Order Vascular Hemodynamic Models](https://mlsanity.com/paper/2508.21165/) (2025)
- [Physics-informed self-supervised learning for predictive modeling of coronary artery digital twins](https://mlsanity.com/paper/2512.03055/) (2025)
- [Cross-Anatomy Transfer Versus Sparse Interpolation in Digital-Twin-Oriented Aortic Fluid-Structure Interaction Surrogates](https://mlsanity.com/paper/2609.16322/) (2026)

## Abstract (arXiv)

Three-dimensional cardiovascular fluid dynamics simulations typically require computation of several cardiac cycles before they reach a periodic solution, rendering them computationally expensive. Furthermore, there is currently no standardized method to determine whether a simulation has yet reached that periodic state. In this work, we propose use of the asymptotic error measure to quantify the difference between simulation results and their ideal periodic state using lumped-parameter modeling. We further show that initial conditions are crucial in reducing computational time and develop an automated framework to generate appropriate initial conditions from a one-dimensional model of blood flow. We demonstrate the performance of our initialization method using six patient-specific models from the Vascular Model Repository. In our examples, our initialization protocol achieves periodic convergence within one or two cardiac cycles, leading to a significant reduction in computational cost compared to standard methods. All computational tools used in this work are implemented in the open-source software platform SimVascular. Automatically generated initial conditions have the potential to significantly reduce computation time in cardiovascular fluid dynamics simulations.