One-dimensional models of the vascular system can capture the physics of pulse waves and provide insights on the onset and development of cardiovascular disease. These models rely on the definition of many parameters which may vary between individuals. To evaluate the robustness of clinical hypotheses at the population level, model parameters should be changed over the physiologic range to finally a population of models that are representative of many individuals rather than small cohorts often considered in modelling studies. The aim of this study was to build such a virtual population through a Monte Carlo analysis.
Physiological ranges of the model parameters were identified from the literature including length, lumen radius, wall Young’s modulus, and the windkessel model parameters used at outlets. A Latin Hypercube algorithm was used to ensure a homogeneous coverage of the input space resulting in 5000 simulations with different combinations of the input parameters. The simulations were run with the openBF 1D code [1,2], which takes between 20 and 30 minutes of execution time for each set of input parameters. Each simulation was run at three mesh density values to ensure mesh independence, leading to a total of 15,000 simulations. These single-core simulations, which will require more than 200 days if executed sequentially, were run with an embarrassingly parallel approach over a multi-cores Virtual Machine (HPC cloud, SURFsara, NL), a tier-1 (Cartesius, SURFsara, NL) and a tier-3 HPC system (ShARC, Sheffield, UK), allowing us to reduce the toal comput time linearly with the number of cores availabel. The convergence of mean and standard deviation across the population for aortic and brachial artery systolic and diastolic pressures was monitored to check Monte Carlo analysis convergence. An analysis of the resulting pulse pressures was performed to exclude non-physiological waveforms and the respective models. Final results were validated through a comparison of diastolic and systolic pressure distributions at specific locations with data published in the literature for similar population studies .
The resulting database of pressure and flow waveforms at several locations of the systemic circulation provides a comprehensive set of boundary conditions for models of local haemodynamics for investigation of clinical hypotheses.
 Melis A, Clayton RH, Marzo A. Bayesian sensitivity analysis of a 1D vascular model with Gaussian process emulators. International Journal for Numerical Methods in Biomedical Engineering. 2017 Jan 1. DOI: 10.1002/cnm.2882
 Melis A, Marzo A. (since 2017) openBF: A 1D blood flow solver in Julia. https://github.com/INSIGNEO/openBF
 Willemet M, Chowienczyk P, Alastruey J. A database of virtual healthy subjects to assess the accuracy of foot-to-foot pulse wave velocities for estimation of aortic stiffness. American Journal of Physiology-Heart and Circulatory Physiology. 2015 Aug 15;309(4):H663-75.