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title={Bayesian Windkessel calibration using optimized 0D surrogate models},
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author={Jakob Richter and Jonas Nitzler and Luca Pegolotti and Karthik Menon and Jonas Biehler and Wolfgang A. Wall and Daniele E. Schiavazzi and Alison L. Marsden and Martin R. Pfaller},
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year={2024},
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volume={2404.14187},
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journal={arXiv},
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}
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@MISC{eigenweb,
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author = {Ga\"{e}l Guennebaud and Beno\^{i}t Jacob and others},
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title = {Eigen v3},
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howpublished = {http://eigen.tuxfamily.org},
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year = {2010}
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title={Bayesian Windkessel calibration using optimized zero-dimensional surrogate models},
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author={Richter, Jakob and Nitzler, Jonas and Pegolotti, Luca and Menon, Karthik and Biehler, Jonas and Wall, Wolfgang A and Schiavazzi, Daniele E and Marsden, Alison L and Pfaller, Martin R},
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@@ -124,7 +124,7 @@ The zero-dimensional simulations performed by `svZeroDSolver` are governed by no
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We integrate these equations in time using the implicit generalized-alpha scheme [@JANSEN2000305] with Newton-Raphson iterations to solve the linearized system.
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Under the hood, these linearized governing equations for each block are implemented as local contributions to a system of linear (matrix) equations, which are then assembled into a global linear system based on the user-specified configuration.
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Details on the modular implementation of the blocks, along with their governing equations, are provided in the documentation's [Developer Guide](https://simvascular.github.io/svZeroDSolver/developer_guide.html).
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We use the [Eigen package](https://gitlab.com/libeigen/eigen) to represent and solve these sparse linear systems[@eigenweb].
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We use the [Eigen package](https://gitlab.com/libeigen/eigen) to represent and solve these sparse linear systems.
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Mathematical details on this implementation are provided in the [`SparseSystem`](https://simvascular.github.io/svZeroDSolver/class_sparse_system.html#details) and [`Integrator`](https://simvascular.github.io/svZeroDSolver/class_integrator.html#details) classes in the documentation.
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`svZeroDSolver` currently has implementations of different types of blood vessel blocks with non-linear resistors to model vascular stenoses, junctions between blood vessels, a heart valve block modeled using a hyperbolic tangent function, a cardiac chamber block modeled as a time-varying capacitor and inductor, and several boundary condition blocks including simple flow, pressure and resistors blocks, windkessel boundary conditions, coronary boundary conditions that include the intramyocardial pressure experienced by coronary arteries, as well as two-sided versions of windkessel and coronary boundary conditions that allow a user to build closed-loop circulation models [@Vignon-Clementel2006; @Kim2009; @kimcoronary; @Mirramezani2019; @menon2023predictors; @menon2024personalized].
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