Reduced‐order modeling of hemodynamics across macroscopic through mesoscopic circulation scales

Abstract

We propose a hemodynamic reduced-order model bridging macroscopic and mesoscopic blood flow circulation scales from arteries to capillaries. In silico tree like vascular geometries, mathematically described by graphs, are synthetically generated by means of stochastic growth algorithms constrained by statistical morphological and topological principles. Scale-specific pruning gradation of the tree is then proposed in order to fit computational budget requirement. Different compliant structural models with respect to pressure loads are used depending on vessel walls thicknesses and structures, which vary considerably from macroscopic to mesoscopic circulation scales. Nonlinear rheological properties of blood are also included and microcirculation network responses are computed for different rheologies. Numerical results are in very good agreement with available experimental measurements. The computational model captures the dynamic transition between large-to small-scale flow pulsatility speeds and magnitudes and wall shear stresses, which have wide-ranging physiological influences.

Multimodal cardiovascular model for hemodynamic analysis: Simulation study on mitral valve disorders

“…Based on the EDL source description, local strength at position 'x' on the surface of the myocardium (Sv) can be mapped to potential ϕ generated at location 'y' on the body surface as given in Eq (15) where, B(y, x) is the transfer function expressing the volume conductor model, considering geometry and conductivity in the chest cavity, V m is the local transmembrane potential at heart surface and dω(y, x) is the solid angle subtended at y by the surface Volume conductor model as expressed in Eq (15) cannot be solved analytically due to the complex asymmetrical shape of individual compartments; rather, it is solved numerically, using a specialized Boundary element method (BEM) algorithm. The potential at discretized body surface consisting of 'ϕ(t, l)' lead position are expressed as given in Eq (16) where B is a transfer matrix, incorporating the solid angles subtended by source elements as viewed from the nodes of the triangulated surface. The resulting matrix 'ϕ' generates the body surface potential, a subset of which is the standard 12 lead ECG and single-lead ECG configuration.…”

“…These models are commonly used to simulate blood flow regimes for which pulse waves propagate in large compliant arteries [15]. These models are computationally efficient and mostly linked to study the physiological hemodynamic phenomena under various pathological conditions [16,17]. In the integrated multimodal modeling domain, there are some hemodynamic models based on cellular properties such as ion equations, myofilament structure, and fiber orientation [18].…”

Computational Analysis of Flow Structures in Turbulent Ventricular Blood Flow Associated With Mitral Valve Intervention

“…The blood in the LV is modelled as an incompressible Newtonian fluid. Although blood is known to express non-Newtonian properties in smaller blood vessels, see e.g., Pedley and Fung (1980) , and Adjoua and Lucor (2019) , the blood inside the heart chambers is typically modelled as a Newtonian fluid, see Westerhof et al (2010) . To simulate the LV blood flow, we determine the velocity vector u ( x , t ): Ω t → ℝ 3 and scalar pressure p ( x , t ): Ω t → ℝ, such that the Navier-Stokes equations are satisfied: defined over the time-dependent domain Ω t ⊂ ℝ 3 at time t ∈ [0, T ].…”

Uncertainty quantification of a thrombosis model considering the clotting assay PFA‐100®

“…Nevertheless, it remains very costly to quantify the link between multi‐physics, multi‐scale and multi‐parameters phenomena to useful clinical indicators. A large number of model order reduction techniques have been proposed 50,51 …”

“…A large number of model order reduction techniques have been proposed. 50,51 In order to alleviate the computational cost of a parametric study involving the full thrombosis model, a surrogate model will be constructed in place of the direct thrombosis model. The surrogate model should approximate the quantity of interest Y as accurately as possible.…”