Inverse identification of region-specific hyperelastic material parameters for human brain tissue

Model-driven exploration of poro-viscoelasticity in human brain tissue: be careful with the parameters!

The brain is arguably the most complex human organ and modelling its mechanical behaviour has challenged researchers for decades. There is still a lack of understanding on how this multiphase tissue responds to mechanical loading and how material parameters can be reliably calibrated. While previous viscoelastic models with two relaxation times have successfully captured the response of brain tissue, the Theory of Porous Media provides a continuum mechanical framework to explore the underlying physical mechanisms, including interactions between solid matrix and free-flowing interstitial fluid. Following our previously published experimental testing protocol, here we perform finite element simulations of cyclic compression-tension loading and compression-relaxation experiments on human brain white and gray matter specimens. The solid volumetric stress proves to be a crucial factor for the overall biphasic tissue behaviour as it strongly interferes with porous effects controlled by the permeability. An inverse parameter identification reveals that poroelasticity alone is insufficient to capture the time-dependent material behaviour, but a poro-viscoelastic formulation captures the response of brain tissue well. We provide valuable insights into the individual contributions of viscous and porous effects. However, due to the strong coupling between porous, viscous, and volumetric effects, additional experiments are required to reliably determine all material parameters.

Heterogeneous biomechanical/mathematical modeling of spatial prediction of glioblastoma progression using magnetic resonance imaging-based finite element method

BACKGROUND AND OBJECTIVE

Brain tumors are one of the most common diseases and causes of death in humans. Since the growth of brain tumors has irreparable risks for the patient, predicting the growth of the tumor and knowing its effect on the brain tissue will increase the efficiency of treatment strategies.

METHODS

This study examines brain tumor growth using mathematical modeling based on the Reaction-Diffusion equation and the biomechanical model based on continuum mechanics principles. With the help of the image threshold technique of magnetic resonance images, a heterogeneous and close-to-reality environment of the brain has been modeled and experimental data validated the results to achieve maximum accuracy in predicting growth.

RESULTS

The obtained results have been compared with the reported conventional models to evaluate the presented model. In addition to incorporating the chemotherapy effects in governing equations, the real-time finite element analysis of the stress tensors of the surrounding tissue of tumor cells and considering its role in changing the shape and growth of the tumor has added to the importance and accuracy of the current model.

CONCLUSIONS

The comparison of the obtained results with conventional models shows that the heterogeneous model has higher reliability due to the consideration of the appropriate properties for the different regions of the brain. The presented model can contribute to personalized medicine, aid in understanding the dynamics of tumor growth, optimize treatment regimens, and develop adaptive therapy strategies.

Exploring the role of different cell types on cortical folding in the developing human brain through computational modeling

The human brain's distinctive folding pattern has attracted the attention of researchers from different fields. Neuroscientists have provided insights into the role of four fundamental cell types crucial during embryonic development: radial glial cells, intermediate progenitor cells, outer radial glial cells, and neurons. Understanding the mechanisms by which these cell types influence the number of cortical neurons and the emerging cortical folding pattern necessitates accounting for the mechanical forces that drive the cortical folding process. Our research aims to explore the correlation between biological processes and mechanical forces through computational modeling. We introduce cell-density fields, characterized by a system of advection-diffusion equations, designed to replicate the characteristic behaviors of various cell types in the developing brain. Concurrently, we adopt the theory of finite growth to describe cortex expansion driven by increasing cell density. Our model serves as an adjustable tool for understanding how the behavior of individual cell types reflects normal and abnormal folding patterns. Through comparison with magnetic resonance images of the fetal brain, we explore the correlation between morphological changes and underlying cellular mechanisms. Moreover, our model sheds light on the spatiotemporal relationships among different cell types in the human brain and enables cellular deconvolution of histological sections.

A comparison of brain retraction mechanisms using finite element analysis and the effects of regionally heterogeneous material properties

Finite element (FE) simulations of the brain undergoing neurosurgical procedures present us with the great opportunity to better investigate, understand, and optimize surgical techniques and equipment. FE models provide access to data such as the stress levels within the brain that would otherwise be inaccessible with the current medical technology. Brain retraction is often a dangerous but necessary part of neurosurgery, and current research focuses on minimizing trauma during the procedure. In this work, we present a simulation-based comparison of different types of retraction mechanisms. We focus on traditional spatulas and tubular retractors. Our results show that tubular retractors result in lower average predicted stresses, especially in the subcortical structures and corpus callosum. Additionally, we show that changing the location of retraction can greatly affect the predicted stress results. As the model predictions highly depend on the material model and parameters used for simulations, we also investigate the importance of using region-specific hyperelastic and viscoelastic material parameters when modelling a three-dimensional human brain during retraction. Our investigations demonstrate how FE simulations in neurosurgical techniques can provide insight to surgeons and medical device manufacturers. They emphasize how further work into this direction could greatly improve the management and prevention of injury during surgery. Additionally, we show the importance of modelling the human brain with region-dependent parameters in order to provide useful predictions for neurosurgical procedures.

Using dropout based active learning and surrogate models in the inverse viscoelastic parameter identification of human brain tissue

Inverse mechanical parameter identification enables the characterization of ultrasoft materials, for which it is difficult to achieve homogeneous deformation states. However, this usually involves high computational costs that are mainly determined by the complexity of the forward model. While simulation methods like finite element models can capture nearly arbitrary geometries and implement involved constitutive equations, they are also computationally expensive. Machine learning models, such as neural networks, can help mitigate this problem when they are used as surrogate models replacing the complex high fidelity models. Thereby, they serve as a reduced order model after an initial training phase, where they learn the relation of in- and outputs of the high fidelity model. The generation of the required training data is computationally expensive due to the necessary simulation runs. Here, active learning techniques enable the selection of the "most rewarding" training points in terms of estimated gained accuracy for the trained model. In this work, we present a recurrent neural network that can well approximate the output of a viscoelastic finite element simulation while significantly speeding up the evaluation times. Additionally, we use Monte-Carlo dropout based active learning to identify highly informative training data. Finally, we showcase the potential of the developed pipeline by identifying viscoelastic material parameters for human brain tissue.

Histology-informed multiscale modeling of human brain white matter

In this study, we propose a novel micromechanical model for the brain white matter, which is described as a heterogeneous material with a complex network of axon fibers embedded in a soft ground matrix. We developed this model in the framework of RVE-based multiscale theories in combination with the finite element method and the embedded element technique for embedding the fibers. Microstructural features such as axon diameter, orientation and tortuosity are incorporated into the model through distributions derived from histological data. The constitutive law of both the fibers and the matrix is described by isotropic one-term Ogden functions. The hyperelastic response of the tissue is derived by homogenizing the microscopic stress fields with multiscale boundary conditions to ensure kinematic compatibility. The macroscale homogenized stress is employed in an inverse parameter identification procedure to determine the hyperelastic constants of axons and ground matrix, based on experiments on human corpus callosum. Our results demonstrate the fundamental effect of axon tortuosity on the mechanical behavior of the brain's white matter. By combining histological information with the multiscale theory, the proposed framework can substantially contribute to the understanding of mechanotransduction phenomena, shed light on the biomechanics of a healthy brain, and potentially provide insights into neurodegenerative processes.