AI-supported Modelling of Brain tissue as Soft Multiscale Multiphysics (Poroelastic) medium

Presentation (2022, January)

ANN-aided incremental multiscale-remodelling-based finite strain poroelasticity

in Computational Mechanics (2021)

Mechanical modelling of poroelastic media under finite strain is usually carried out via phenomenological models neglecting complex micro-macro scales interdependency. One reason is that the mathematical ... [more ▼]

Mechanical modelling of poroelastic media under finite strain is usually carried out via phenomenological models neglecting complex micro-macro scales interdependency. One reason is that the mathematical two-scale analysis is only straightforward assuming infinitesimal strain theory. Exploiting the potential of ANNs for fast and reliable upscaling and localisation procedures, we propose an incremental numerical approach that considers rearrangement of the cell properties based on its current deformation, which leads to the remodelling of the macroscopic model after each time increment. This computational framework is valid for finite strain and large deformation problems while it ensures infinitesimal strain increments within time steps. The full effects of the interdependency between the properties and response of macro and micro scales are considered for the first time providing a more accurate predictive analysis of fluid-saturated porous media which is studied via a numerical consolidation example. Furthermore, the (nonlinear) deviation from Darcy’s law is captured in fluid filtration numerical analyses. Finally, the brain tissue mechanical response under the uniaxial cyclic test is simulated and studied. [less ▲]

Modelling of residually stressed, extended and inflated cylinders with application to aneurysms

in Mechanics Research Communications (2021), 111

The paper presents the localized bifurcation abnormal enlargement associated with certain human diseases such as abdominal aortic aneurysms (AAA), among others. The constitutive framework herewith ... [more ▼]

The paper presents the localized bifurcation abnormal enlargement associated with certain human diseases such as abdominal aortic aneurysms (AAA), among others. The constitutive framework herewith proposed is constructed relying on the modelling of non-linear elastic materials under the action of residual stresses. The suitable incorporation on the mechanical response of residual stresses in the analysis is regarded important for the formation of aneurysms in soft tissues. From a mechanical perspective, the onset of aneurysms formation can be interpreted through bifurcation conditions, whose localization is relatively sensitive to different material and geometrical parameters as it is shown here. In order to reduce the risk and interpret aneurysm formation, we perform a thorough sensitivity analysis of the effect of design parameters such as tube diameter, length, thickness and strength of the residual stress field on bifurcation of a tube under inflation and extesion. A consistent residually stressed material model is formulated in terms of invariants for a general elastic strain-energy function. The dependence of applied pressure, axial stretch and different geometrical and constitutive parameters on bulging and bending bifurcation is illustrated. The numerical procedure to analyse the bifurcation of the finite deformation boundary-value problem at hand is developed based on the modified Riks method. The proposed formulation is implemented in the general-purpose finite element code ABAQUS using user-defined material subroutines.For a given material model, bulging bifurcation is expected for sufficiently large values of the axial stretch while the onset of bifurcation is found to be the bending mode for small values of the axial stretch. This transition zone from bending bifurcation to bulging bifurcation is analyzed for the different parameters considered. [less ▲]

Poroelastic model parameter identification using artificial neural networks: on the effects of heterogeneous porosity and solid matrix Poisson ratio

in Computational Mechanics (2020), 66

Predictive analysis of poroelastic materials typically require expensive and time-consuming multiscale and multiphysics approaches, which demand either several simplifications or costly experimental tests ... [more ▼]

Predictive analysis of poroelastic materials typically require expensive and time-consuming multiscale and multiphysics approaches, which demand either several simplifications or costly experimental tests for model parameter identification. This problem motivates us to develop a more efficient approach to address complex problems with an acceptable computational cost. In particular, we employ artificial neural network (ANN) for reliable and fast computation of poroelastic model parameters. Based on the strong-form governing equations for the poroelastic problem derived from asymptotic homogenisation, the weighted residuals formulation of the cell problem is obtained. Approximate solution of the resulting linear variational boundary value problem is achieved by means of the finite element method. The advantages and downsides of macroscale properties identification via asymptotic homogenisation and the application of ANN to overcome parameter characterisation challenges caused by the costly solution of cell problems are presented. Numerical examples, in this study, include spatially dependent porosity and solid matrix Poisson ratio for a generic model problem, application in tumour modelling, and utilisation in soil mechanics context which demonstrate the feasibility of the presented framework. [less ▲]

The role of microscale solid matrix compressibility on the mechanical behaviour of poroelastic materials

in European Journal of Mechanics. A, Solids (2020), 83

We present the macroscale three-dimensional numerical solution of anisotropic Biot's poroelasticity, with coefficients derived from a micromechanical analysis as prescribed by the asymptotic ... [more ▼]

We present the macroscale three-dimensional numerical solution of anisotropic Biot's poroelasticity, with coefficients derived from a micromechanical analysis as prescribed by the asymptotic homogenisation technique. The system of partial differential equations (PDEs) is discretised by finite elements, exploiting a formal analogy with the fully coupled thermal displacement systems of PDEs implemented in the commercial software Abaqus. The robustness of our computational framework is confirmed by comparison with the well-known analytical solution of the one-dimensional Therzaghi's consolidation problem. We then perform three-dimensional numerical simulations of the model in a sphere (representing a biological tissue) by applying a given constant pressure in the cavity. We investigate how the macroscale radial displacements (as well as pressures) profiles are affected by the microscale solid matrix compressibility (MSMC). Our results suggest that the role of the MSMC on the macroscale displacements becomes more and more prominent by increasing the length of the time interval during which the constant pressure is applied. As such, we suggest that parameter estimation based on techniques such as poroelastography (which are commonly used in the context of biological tissues, such as the brain, as well as solid tumours) should allow for a sufficiently long time in order to give a more accurate estimation of the mechanical properties of tissues. [less ▲]