Table 1. Modelling strategies for mapping of cell and tissue mechanics.
Modelling approaches (top to bottom) are ranked from lowest to highest resolution. Combinations of modelling approaches, where different structures are resolved at different length- and time scales, are termed Multiscale Models. Models in red employ one or multiple phenomenological parameters, models in green are physics-based.
| Modelling approach* | Model scales | Key input | Key output | Modelling principle | Application |
|---|---|---|---|---|---|
| Finite Element Modelling (FEM) | Tissue, organ (mm-cm) | Mechanical moduli, constitutive relations, shape | Organ scale shape changes; mechanical rupture | Different elements that represent local mechanical properties are combined, allowing scalable modelling of heterogeneous tissue | Complex, heterogeneous, multicellular systems in tissue |
| Cellular Potts Model (CPM) | Cell, cell aggregate (μm-cm) | Cell and ECM mechanics, target volume and area, speed | Single-cell and collective dynamics, cell shape, invasiveness, vascularization | Represents cells as domains on a regular lattice, with mathematical rules prescribing their ECM contacts, interactions, proliferation and migration | Cells and cell cluster growth and migration |
| Multiphasic, active and constitutive (SGR) modelling | Cell, tissue (μm-cm) | Constitutive equations; composition, porosity and anisotropy; energy consumption | Mechanical properties, dynamics and response of entire cells | Mathematical equations dictating the flow and elastic response of cell and environment | Predicting cell deformation, relaxation and shape change under applied stress |
| Network models (numerical, analytical) | Cell, microtissue (μm-mm) | Fibril (visco-) elastic response, network architecture | Visco-elastic constitutive (dynamic) response fibrils, incl. bundling and alignment; filopodial dynamics | Fibril bending and extension properties are modelled to predict network deformation responses | Cytoskeletal mechanics, ECM mechanics |
| Coarse grained molecular dynamics (CGMD) | Fibril, bundle (nm-μm) | protein aggregate, arrangement, PMF | Mechanical response of single fibrils; effects of quaternary structural defects and crosslinking | Small particles (i.e. molecules) are aggregated and modelled as single particles, allowing modelling of larger volumes | Protein assembly and mechanical response of single protein fibrils |
| Atomistic models | Protein (≤100 nm) | Amino acid sequence, chemical composition, force fields | Potentials of mean force (PMF) for CGMD, mechanical effects of mutations and molecular damage | Numerical solution of Newton’s equations for the motions of atoms, alone and in molecules | Single protein mechanics and structure |