Multiscale Computational Modeling of Vascular Adaptation: A Systems Biology Approach Using Agent-Based Models

Figures

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  FIGURE 1. Multiscale vascular system. Adapted with permission from Wikimedia Commons, (public domain, https://commons.wikimedia.org/wiki/File:DNA_simple2.svg, https://commons.wikimedia.org/wiki/File:Circulatory_System_no_tags.svg), Blausen.com staff (2014) (https://creativecommons.org/licenses/by/3.0/), and from Blanco et al. (2017) (http://creativecommons.org/licenses/by-nc/4.0/).

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  FIGURE 2. Example of agent-based model (ABM) of vascular wall at the cell-tissue scale implemented on a hexagonal lattice, as in Corti et al. (2020). (A) Three-dimensional patient-specific vessel geometry. (B) Cell-tissue scale ABM of a vessel cross-section implemented on a hexagonal lattice. The vessel wall is composed by the intima, media and adventitia layers. Each layer is populated by cell and extracellular matrix (ECM) agents, with each agent occupying one lattice site. (C) Examples of ABM rules.

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  FIGURE 3. Examples of lattice-free and lattice-based agent-based model (ABM) at the cell scale. (A) Lattice-free ABM. (B) Lattice-based ABM with one lattice site corresponding to a single agent, i.e., cell or extracellular matrix (ECM). (C) Lattice-based ABM with multiple agents (cells and ECM) at one lattice site. (D) Lattice-based ABM with agents (cells and ECM) occupying more than one lattice site. The lattice-based ABMs shown in (B–D) are implemented on a hexagonal lattice, as in Corti et al. (2020).

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  FIGURE 4. Schematic representation of a general multiscale framework of vascular adaptation. The main simulated events at the different spatio-temporal scales are: 1) structural mechanics and fluid dynamics, 2) cellular activity and 3) molecular transport. The modules receive proper inputs (red arrows) and generate suitable outputs (green arrows).

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  FIGURE 5. Results of the multiscale computational fluid dynamics–agent-based model (CFD-ABM) framework of atherosclerosis by Bhui and Hayenga (2017). The temporal evolution of the ABM geometry from the initial configuration (A) to the configuration at 6 months (B) and at 7 months (C) is shown, for the longitudinal (left) and transverse (right) views, with the endothelial cells in green, the arterial cells in red and leukocytes in yellow. The initial condition (A) is characterized by the presence of 15 leukocytes in the arterial wall. Until 6 months (B), thanks to the compensatory Glagov’s remodeling, the plaque growth determined an outward remodeling, while preserving the lumen area. At this point, the plaque area is 40%. At 7 months (C), the plaque growth provokes a reduction of the lumen area. Reprinted with permission from Bhui and Hayenga (2017) (http://creativecommons.org/licenses/by/4.0/).

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  FIGURE 6. Results of the computational fluid dynamics–agent-based model (CFD-ABM) framework of atherosclerosis by Corti et al. (2020). At the top, the idealized 3D geometry of a superficial femoral artery is represented, with the wall shear stress (WSS) luminal distribution computed from steady-state CFD simulation. At the bottom, the ABM temporal evolution of three representative cross-sections is presented at day 0, 30 and 60. Greater plaque formation and lumen area reduction is obtained at luminal regions exposed to low WSS, such as downstream from the curvature (planes B and C). The planes involved in the atherogenic process (planes B and C) present an asymmetric plaque characterized by the presence of a well-defined lipid core (in yellow) and an increased intimal extracellular matrix (ECM) and smooth muscle cell (SMC) content (blue and light-blue, respectively).

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  FIGURE 7. Results of the multiscale agent-based modeling framework of in-stent restenosis of Zun et al. (2019). At the top, the stent geometry is shown, with indications on the position of the four analyzed cross-sections. At the bottom, the results at 28 days are shown for the four cross-sections. For each cross-section: 1) on the left, a quantitative comparison of the predicted (in-silico) and in-vivo neointimal thickness is provided for the 6 struts locations (A–F), 2) in the middle, the in-vivo cross-section is shown and 3) on the right, the in-silico cross-section is represented, with the smooth muscle cells (SMCs) in dark blue, the internal elastic lamina (IEL) in light blue, the external elastic lamina (EEL) in beige, the extracellular matrix (ECM) in red and the stent struts in light grey. Both in the in-vivo and in-silicosilico cross-sections the blue area represents the neointima estimation. Reprinted with permission from Zun et al. (2019) (http://creativecommons.org/licenses/by/4.0/).

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  FIGURE 8. Schematic representation of agent-based model (ABM) rules in Boyle et al. (2010), with contractile smooth muscle cells (SMCs) (green circles), synthetic SMCs (blue circles) and endothelial cells (red circles). (A) When the endothelium and extracellular matrix (ECM) are intact, SMCs are contractile; (B) The injury provoked by the stent placement induces endothelial denudation, ECM reduction and SMCs removal; (C) In the vicinity of degraded ECM, SMCs switch to the synthetic phenotype; (D) Synthetic SMCs randomly migrate (arrows represent possible directions); (E) Synthetic SMCs proliferate (blue circles with dashed lines represent daughter cells); (F) SMCs produce ECM; (G) Lesion formation; (H) Reendothelialization stops lesion growth. Reprinted with permission from Boyle et al. (2010) (http://creativecommons.org/licenses/by/4.0/).

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  FIGURE 9. Results of the multiscale finite-element method–agent-based model (FEM-ABM) framework of in-stent restenosis by Boyle et al. (2010). At the top, the stent expansion configuration obtained from FEM analysis is shown and constitutes the initial condition of the ABM. At the bottom, the ABM evolution along 320 days is provided for a longitudinal section (dashed box). Contractile smooth muscle cells (SMCs) are represented in green, synthetic SMCs in blue and endothelial cells in red. At day 7, the ABM is characterized by a complete endothelial denudation and synthetic SMCs in the injured region (in correspondence of the stent struts). Lesion progression is shown at day 90 and 160. The endothelium starts recovering, leading to a complete reendothelialization at day 320. The lesion growth stops when complete reendothelialization occurs (arrow, day 160) or when the SMCs switch back to a contractile phenotype (arrow, day 320). Reprinted with permission from Boyle et al. (2010) (http://creativecommons.org/licenses/by/4.0/).

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  FIGURE 10. Outputs of two multiscale agent-based modeling framework of vein graft adaptation by Garbey’s research group. (A) Results obtained by Garbey et al. (2019), when an immersed boundary method (IBM) module was added to simulate the vessel wall remodeling. (B) Histological images of rabbit vein graft (Conte et al., 2006). (C) Results obtained by Garbey et al. (2017). The results of panel (A) well resemble the histological images (B). The model captures different possible patterns of neointimal hyperplasia, namely a vertical and horizontal configuration (panels (A,B)). Panel (C) shows a limitation of the model by Garbey et al. (2017). In particular, when the symmetry condition is removed, a non-realistic configuration of the lumen contour is obtained (e.g., detached elements, holes). Figures 9A,B Reprinted with permission from Garbey et al. (2019) (http://creativecommons.org/licenses/by/4.0/). Figure 9C reprinted with permission from Garbey et al. (2017) (http://creativecommons.org/licenses/by/4.0/).

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  FIGURE 11. Results of the continuum-based modeling framework of atherosclerosis by Pleouras et al. (2020). Panels (A,B) depict the artery geometry reconstructed at the initial condition and follow-up, respectively. The contour maps of wall shear stress (WSS) (C), oxidized low-density lipoproteins (LDLs) (D), macrophages (E) and plaque formation input (F) at the initial condition are shown. Panels (G,H) refer to the red dashed line in (A) with the initial input of plaque formation (G) and the computed output cross-section (H). Panels (I,J) refer to the green dashed line in (A) with the initial input of plaque formation (I) and the computed output cross-section (J). Adapted with permission from Pleouras et al. (2020) (http://creativecommons.org/licenses/by/4.0/).

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  FIGURE 12. Agent-based model (ABM) outputs at 2-months follow-up obtained from 9 independent simulations of the same ABM cross-section initialized with equal WSS profile. Figure inspired from the work of Corti et al. (2020).