TABLE 1.
Multiscale agent-based modelling frameworks of vascular adaptation.
| Authors (Year) | Pathology | Multiscale framework | Agents | Domain |
|---|---|---|---|---|
| Bhui and Hayenga (2017) | Atherosclerosis | Tissue-scale module (seconds) | EC, SMC (inert agents), Leukocytes (Neutrophils, monocytes, macrophages, foam cells and lymphocytes) | Simplified 3D model of coronary artery |
| Hemodynamics module: FEM. I: vessel geometry; O: WSS | ||||
| Cell-scale module (hours/days) | ||||
| ABM; I: WSS; O: vessel geometry and wall composition | ||||
| Molecular-scale module (seconds) | ||||
| Cytokine and LDL transport in the ABM | ||||
| Corti et al. (2019), Corti et al. (2020) | Atherosclerosis | Tissue-scale module (seconds) | SMC, ECM (collagen, elastin), LDL, Fibroblasts | Idealized 3D model of superficial femoral artery, with 2D ABM cross-sections |
| Hemodynamics module: FVM. I: vessel geometry; O: WSS | ||||
| Cell-scale module (hours/days) | ||||
| ABM; I: WSS; O: vessel geometry and wall composition | ||||
| Caiazzo et al. (2011); Tahir et al. (2011); Tahir et al. (2013); Tahir et al. (2014); Zun et al. (2017); Zun et al. (2019) | In-stent restenosis | Tissue-scale module (seconds) | SMC, IEL (Caiazzo et al. (2011); Tahir et al. (2011); Tahir et al. (2013); Tahir et al. (2014)); SMC, IEL, EEL (Zun et al. (2017)); SMC, ECM, IEL, EEL (Zun et al. (2019)) | 2D longitudinal section of idealized straight artery with 2 stent struts (Caiazzo et al. (2011)),Tahir et al. (2011); Tahir et al. (2013) - 6 stent struts (Tahir et al. (2014)); 3D straight artery (Zun et al. (2017)); Idealized curved artery with stent reconstructed from micro-CT. (Zun et al. (2019)) |
| Hemodynamics module: Lattice Boltzmann. I: vessel geometry; O: WSS/OSI | ||||
| Cell-scale module (hours/days) | ||||
| ABM - physical solver: stent deployment and structural cell dynamics. I: vessel geometry; O: equilibrium position, vessel geometry and structural stress | ||||
| ABM - biological solver: SMC cell-cycle. I: WSS/OSI, drug concentration, structural stress. O: vessel geometry | ||||
| Molecular-scale module (seconds) | ||||
| Drug diffusion: FD. I: vessel geometry; O: drug concentration in the tissue. Included in (Caiazzo et al. (2011); Tahir et al. (2011)) | ||||
| Boyle et al. (2010) | In-stent restenosis | Tissue-scale module (seconds) | SMC, EC ECM, matrix degrading factors and growth factors modeled as agent internal variables | Solid mechanics module: artery as 3D cylinder (symmetry: 1/8th model circumferentially). Lattice-based model: 2D longitudinal section |
| Solid mechanics module: FEM. Stent expansion. I: vessel geometry; O: vessel geometry, minimum principal stress | ||||
| Cell-scale module (hours/days) | ||||
| ABM. I: vessel geometry, minimum principal stress. O: updated vessel geometry and wall composition | ||||
| Boyle et al. (2011) | In-stent restenosis | Tissue-scale module (seconds) | SMC ECM, matrix degrading factors, growth factors and damage modeled as agent internal variables | 2D cross-section of an ideal cylindrical artery with 6 stent struts. 1/6th of the model considered for symmetry |
| Solid mechanics module: FEM. Stent expansion. I: vessel geometry; O: vessel geometry, von Mises stress | ||||
| Cell-scale module (hours/days) | ||||
| ABM. I: vessel geometry, damage, matrix degrading factors, growth factors, ECM; O: updated vessel geometry and wall composition | ||||
| Molecular-scale module (seconds) | ||||
| Inflammation module: Set of ODEs. I: von Mises stress. O: damage, matrix degrading factors, growth factors, ECM | ||||
| Zahedmanesh et al. (2014) | In-stent restenosis | Tissue-scale module (seconds) | SMC, EC ECM, matrix degrading factors and damage modeled as agent internal variables | 2D longitudinal section (axisymmetric model) of artery and single stent strut |
| Solid mechanics module: FEM. Stent expansion. I: vessel geometry; O: vessel geometry, von Mises stress | ||||
| Cell-scale module (hours/days) | ||||
| ABM. I: vessel geometry, damage (sigmoid function of von Mises stress); O: updated vessel geometry and wall composition | ||||
| Nolan and Lally (2018) | In-stent restenosis | Tissue-scale module (seconds) | SMC, EC, ECM, matrix degrading factors, growth factors, phenotype and damage modeled as agent internal variables | 2D quarter cylinder of artery in the radial-circumferential plane |
| Solid mechanics module: FEM. Stent expansion. I: vessel geometry; O: vessel geometry, von Mises stress | ||||
| Cell-scale module (hours/days) | ||||
| ABM. I: vessel geometry, damage, matrix degrading factors, growth factors, ECM, phenotype; O: updated vessel geometry and wall composition | ||||
| Molecular-scale module (seconds) | ||||
| Inflammation module: Set of ODEs. I: von Mises stress. O: damage, matrix degrading factors, growth factors, ECM, phenotype | ||||
| Li et al. (2019) | In-stent restenosis | Tissue-scale module (seconds) | SMC, EC ECM, matrix degrading factors, growth factors, cell phenotype and damage modeled as agent internal variables | 2D longitudinal section (axisymmetric model) of artery and single stent strut |
| Solid mechanics module: FEM. Stent expansion and structural equilibrium following geometrical changes. I: vessel geometry; O: vessel geometry, von Mises stress | ||||
| Cell-scale module (hours/days) | ||||
| ABM. I: vessel geometry, damage, matrix degrading factors, growth factors, ECM; O: updated vessel geometry and wall composition | ||||
| Molecular-scale module (seconds) | ||||
| Inflammation module: set of ODEs. I: von Mises stress. O: damage, matrix degrading factors, growth factors, ECM, cell phenotype | ||||
| Garbey et al. (2015) | Vein graft remodeling | Tissue-scale module (seconds) | SMC, ECM | 2D circular vein graft model |
| Hemodynamics module: FVM and immersed boundary implementation. I: vessel geometry; O: WSS. | ||||
| Solid mechanics module: FEM. I: vessel geometry; O: loaded vessel geometry, wall tension | ||||
| Cell-scale module (hours/days) | ||||
| ABM. I: WSS, wall tension; O: updated unloaded vessel geometry and wall composition | ||||
| Garbey et al. (2017) | Vein graft remodeling | Tissue-scale module (seconds) | SMC, ECM | 2D circular vein graft model |
| Hemodynamics module: Analytical solution (Poisson problem). I: vessel geometry; O: WSS. | ||||
| Solid mechanics module: Analytical solution thick wall cylinder. I: vessel geometry; O: wall tension | ||||
| Cell-scale module (hours/days) | ||||
| ABM. I: WSS, wall tension; O: updated vessel geometry and wall composition | ||||
| Garbey et al. (2019) | Vein graft remodeling | Tissue-scale module (seconds) | SMC, ECM | 2D circular vein graft model |
| Hemodynamics module: Analytical solution (Poisson problem). I: vessel geometry; O: WSS. | ||||
| Solid mechanics module: Analytical solution thick wall cylinder. I: vessel geometry; O: wall tension | ||||
| Cell-scale module (hours/days) | ||||
| ABM. SMC/ECM activities. I: WSS, wall tension; O: updated vessel geometry and wall composition | ||||
| IBM. SMC migration and wall remodeling. I: ABM vessel geometry; O: updated vessel geometry and composition | ||||
| Molecular-scale module (seconds) | ||||
| Diffusion of growth factor. PDE. I: WSS; O: spatio-temporal evolution of growth factor | ||||
| Zahedmanesh and Lally (2012) | Remodeling of a vascular tissue-engineered scaffold | Tissue-scale module (seconds) | SMC, ECM | 2D longitudinal section (axisymmetric model) of vascular scaffold |
| Solid mechanics module: FEM. I: vessel geometry and wall composition; O: vessel geometry, cyclic strain, pore fluid velocity | ||||
| Cell-scale module (hours/days) | ||||
| ABM. I: vessel geometry, cyclic strain, pore fluid velocity. O: updated vessel geometry and wall composition | ||||
| Keshavarzian et al. (2018) | Arterial growth and remodeling under different conditions: growth factors, chemicals, blood pressure | Tissue-scale module (seconds) | EC, SMC, fibroblasts, ECM | 3D model of coronary artery |
| Solid mechanics module: FEM. I: vessel geometry and wall composition (use of a content-based strain energy density function); O: maximum principal stress and strain under different loading condition | ||||
| Cell-scale module (hours/days) | ||||
| ABM. I: vessel geometry, stress, strain. O: updated vessel geometry and wall composition |
ABM: agent-based model; FEM: finite element method; FVM: finite volume method; FD: finite difference; ODE: ordinary differential equation; PDE: partial differential equation; IBM: immersed boundary method; I: input; O: output; WSS: wall shear stress; OSI: oscillatory shear index; SMC: smooth muscle cell; EC: endothelial cell; ECM: extracellular matrix; LDL: low density lipoprotein; IEL: internal elastic lamina; EEL: external elastic lamina; 2D: bidimensional; 3D three-dimensional.