Machine learning based multiscale calibration of mesoscopic constitutive models for composite materials: application to brain white matter

Abstract

A modular pipeline for improving the constitutive modelling of composite materials is proposed.The method is leveraged here for the development of subject-specific spatially-varying brain white matter mechanical properties. For this application, white matter microstructural information is extracted from diffusion magnetic resonance imaging (dMRI) scans, and used to generate hundreds of representative volume elements (RVEs) with randomly distributed fibre properties. By automatically running finite element analyses on these RVEs, stress-strain curves corresponding to multiple RVE-specific loading cases are produced. A mesoscopic constitutive model homogenising the RVEs’ behaviour is then calibrated for each RVE, producing a library of calibrated parameters against each set of RVE microstructural characteristics. Finally, a machine learning layer is implemented to predict the constitutive model parameters directly from any new microstructure. The results show that the methodology can predict calibrated mesoscopic material properties with high accuracy. More generally, the overall framework allows for the efficient simulation of the spatially-varying mechanical behaviour of composite materials when experimentally measured location-specific fibre geometrical characteristics are provided.

FE$${}^\textrm{ANN}$$: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

“…Furthermore, in order to demonstrate that the chosen tolerance ε tol,1 = 5 % within the multiscale loop is sufficient, the achieved macroscopic solution is compared to a solution in which this tolerance is prescribed to 2.5 %. 14 As shown in Fig. 12, a relative error of below 2 % with respect to the reference solution occurs for the stress P11 .…”

“…For example, in [24], an ML framework for predicting macroscopic yield as a function of crystallographic texture is described. An ML-based multiscale calibration of constitutive models representing the effective response of rate dependent composite materials is applied to brain white matter in [14]. Based on a library of calibrated parameters corresponding to a set of microstructural characteristics, an ML model which predicts the constitutive model parameters directly from a new microstructure is trained.…”

FE${}^\textbf{ANN}$ $-$ An efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

“…For example, in [50], an ML framework for predicting macroscopic yield as a function of crystallographic texture is described. An ML-based multiscale calibration of constitutive models representing the effective response of rate dependent composite materials is applied to brain white matter in [51]. Based on a library of calibrated parameters corresponding to a set of microstructural characteristics, an ML model which predicts the constitutive model parameters directly from a new microstructure is trained.…”

White matter tract transcranial ultrasound stimulation, a computational study

“…where d is the intrinsic free diffusivity given as 1.7 × 10 −3 mm 2 s −1 [51]. The heuristical corrected mean diffusivity, λ h is given as:…”

“…where b is the b-value (a factor that reflects the strength and timing of the gradients used to generate diffusion-weighted images), δ ij is the Kronecker delta function, and λ is the mean diffusivity given by [51]:…”