Physical aspects of cortical folding.

The characteristically folded surface of the human brain is critical for brain function and allows for higher cognitive abilities. Recent mostly computational research advances have shown that mechanical instabilities play a crucial role during early brain development and cortical folding. However, it is difficult to investigate such mechanisms in vivo. To experimentally gain deeper insights into the physical mechanisms that underlie the development of brain shape, we use a setup of swelling polymers. We investigate the influence of cortical thickness and the stiffness ratio between cortex and subcortex on the resulting surface pattern by taking the initially smooth fetal brain geometry at week 22 into consideration. The gel specimens possess a two-layered structure accounting for gray and white matter tissue and yield complex surface morphologies that well resemble patterns in the human brain. The results are in good agreement with analytical predictions. Through the variation of cortical thickness and stiffness, it is possible to reproduce cortical malformations such as polymicrogyria and lissencephaly. The results suggest that wrinkling with subsequent transition into folding is the driving instability mechanism during brain development. In addition, the experiments provide valuable insights towards the distinction between wrinkling and creasing instabilities. Taken together, the presented swelling experiments impressively demonstrate the purely physical aspects of brain shape and constitute a valuable tool to advance our understanding of human brain development.

Symmetry Breaking in Wrinkling Patterns: Gyri Are Universally Thicker than Sulci.

Wrinkling instabilities appear in soft materials when a flat elastic layer on an elastic substrate is sufficiently stressed that it buckles with a wavy pattern to minimize the energy of the system. This instability is known to play an important role in engineering, but it also appears in many biological systems. In these systems, the stresses responsible for the wrinkling instability are often created through differential growth of the two layers. Beyond the instability, the upper and lower sides of the elastic layer are subject to different forces. This difference in forces leads to an interesting symmetry breaking whereby the thickness becomes larger at ridges than at valleys. Here we carry out an extensive analysis of this phenomenon by combining analytical, computational, and simple polymer experiments to show that symmetry breaking is a generic property of such systems. We apply our idea to the cortical folding of the brain for which it has been known for over a century that there is a thickness difference between gyri and sulci. An extensive analysis of hundreds of human brains reveals a systematic region-dependent thickness variation. Our results suggest that the evolving thickness patterns during brain development, similar to our polymer experiments, follow simple physics-based laws: Gyri are universally thicker than sulci.

The role of mechanics during brain development.

Convolutions are a classical hallmark of most mammalian brains. Brain surface morphology is often associated with intelligence and closely correlated to neurological dysfunction. Yet, we know surprisingly little about the underlying mechanisms of cortical folding. Here we identify the role of the key anatomic players during the folding process: cortical thickness, stiffness, and growth. To establish estimates for the critical time, pressure, and the wavelength at the onset of folding, we derive an analytical model using the Föppl-von-Kármán theory. Analytical modeling provides a quick first insight into the critical conditions at the onset of folding, yet it fails to predict the evolution of complex instability patterns in the post-critical regime. To predict realistic surface morphologies, we establish a computational model using the continuum theory of finite growth. Computational modeling not only confirms our analytical estimates, but is also capable of predicting the formation of complex surface morphologies with asymmetric patterns and secondary folds. Taken together, our analytical and computational models explain why larger mammalian brains tend to be more convoluted than smaller brains. Both models provide mechanistic interpretations of the classical malformations of lissencephaly and polymicrogyria. Understanding the process of cortical folding in the mammalian brain has direct implications on the diagnostics of neurological disorders including severe retardation, epilepsy, schizophrenia, and autism.

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.

Accuracy meets simplicity: A constitutive model for heterogenous brain tissue.

We present a general, hyperelastic, stretch-based potential that shows promise for modeling the mechanics of brain tissue. A specific four-parameter model derived from this general potential outperforms alternative models, such as the modified Ogden model, the Gent model, Demiray model, and machine-learning models, in capturing brain tissue elasticity. Specifically, the stretch-based model achieved R2 values of 0.997, 0.992, and 0.993 (tension, compression, and shear) for the cortex, 0.995, 0.983, and 0.983 for the basal ganglia, 0.994, 0.929, and 0.970 for the corona radiata, and 0.990, 0.896, and 0.969 for the corpus callosum. This work has the potential to advance our understanding of brain tissue mechanics and provides a valuable tool to improve finite element models for the investigation of brain development, injuries, and disease.

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.

Engineering peptide-modified alginate-based bioinks with cell-adhesive properties for biofabrication.

Alginate (ALG) and its oxidised form alginate-dialdehyde (ADA) are highly attractive materials for hydrogels used in 3D bioprinting as well as drop-on-demand (DoD) approaches. However, both polymers need to be modified using cell-adhesive peptide sequences, to obtain bioinks exhibiting promising cell-material interactions. Our study explores the modification of ALG- and ADA-based bioinks with the adhesive peptides YIGSR (derived from laminin), RRETEWA (derived from fibronectin) and IKVAV (derived from laminin) for 3D bioprinting. Two coupling methods, carbodiimide and Schiff base reactions, were employed to modify the polymers with peptides. Analytical techniques, including FTIR and NMR were used to assess the chemical composition, revealing challenges in confirming the presence of peptides. The modified bioinks exhibited decreased stability, viscosity, and stiffness, particularly-ADA-based bioinks in contrast to ALG. Sterile hydrogel capsules or droplets were produced using a manual manufacturing process and DoD printing. NIH/3T3 cell spreading analysis showed enhanced cell spreading in carbodiimide-modified ADA, Schiff base-modified ADA, and PEG-Mal-modified ADA. The carbodiimide coupling of peptides worked for ADA, however the same was not observed for ALG. Finally, a novel mixture of all used peptides was evaluated regarding synergistic effects on cell spreading which was found to be effective, showing higher aspect ratios compared to the single peptide coupled hydrogels in all cases. The study suggests potential applications of these modified bioinks in 3D bioprinting approaches and highlights the importance of peptide selection as well as their combination for improved cell-material interactions.

Breast Tumor Cell Survival and Morphology in a Brain-like Extracellular Matrix Depends on Matrix Composition and Mechanical Properties.

Triple-negative breast cancer (TNBC) is the most invasive type of breast cancer with high risk of brain metastasis. To better understand interactions between breast tumors with the brain extracellular matrix (ECM), a 3D cell culture model is implemented using a thiolated hyaluronic acid (HA-SH) based hydrogel. The latter is used as HA represents a major component of brain ECM. Melt-electrowritten (MEW) scaffolds of box- and triangular-shaped polycaprolactone (PCL) micro-fibers for hydrogel reinforcement are utilized. Two different molecular weight HA-SH materials (230 and 420 kDa) are used with elastic moduli of 148 ± 34 Pa (soft) and 1274 ± 440 Pa (stiff). Both hydrogels demonstrate similar porosities. The different molecular weight of HA-SH, however, significantly changes mechanical properties, e.g., stiffness, nonlinearity, and hysteresis. The breast tumor cell line MDA-MB-231 forms mainly multicellular aggregates in both HA-SH hydrogels but sustains high viability (75%). Supplementation of HA-SH hydrogels with ECM components does not affect gene expression but improves cell viability and impacts cellular distribution and morphology. The presence of other brain cell types further support numerous cell-cell interactions with tumor cells. In summary, the present 3D cell culture model represents a novel tool establishing a disease cell culture model in a systematic way.

Predicting the hyperelastic properties of alginate-gelatin hydrogels and 3D bioprinted mesostructures.

Additive manufacturing has been widely used in tissue engineering, as 3D bioprinting enables fabricating geometrically complicated replacements for different tissues and organs. It is vital that the replacement mimics the specific properties of native tissue and bears the mechanical loading under its physiological conditions. Computational simulations can help predict and tune the mechanical properties of the printed construct-even before fabrication. In this study, we use the finite element (FE) method to predict the mechanical properties of different hydrogel mesostructures fabricated through various print patterns and validate our results through corresponding experiments. We first quantify the mechanical properties of alginate-gelatin hydrogels used as matrix material through an inverse approach using an FE model and cyclic compression-tension experimental data. Our results show that the fabrication process can significantly affect the material properties so that particular caution needs to be paid when calibrating FE models. We validate our optimized FE model using experimental data and show that it can predict the mechanical properties of different mesostructures, especially under compressive loading. The validated model enables us to tune the mechanical properties of different printed structures before their actual fabrication. The presented methodology can be analogously extended for cell bioprinting applications, other materials, and loading conditions. It can help save time, material, and cost for biofabrication applications in the future.

Mechanisms of mechanical load transfer through brain tissue.

Brain injuries are often characterized by diffusely distributed axonal and vascular damage invisible to medical imaging techniques. The spatial distribution of mechanical stresses and strains plays an important role, but is not sufficient to explain the diffuse distribution of brain lesions. It remains unclear how forces are transferred from the organ to the cell scale and why some cells are damaged while neighboring cells remain unaffected. To address this knowledge gap, we subjected histologically stained fresh human and porcine brain tissue specimens to compressive loading and simultaneously tracked cell and blood vessel displacements. Our experiments reveal different mechanisms of load transfer from the organ or tissue scale to single cells, axons, and blood vessels. Our results show that cell displacement fields are inhomogeneous at the interface between gray and white matter and in the vicinity of blood vessels-locally inducing significant deformations of individual cells. These insights have important implications to better understand injury mechanisms and highlight the importance of blood vessels for the local deformation of the brain's cellular structure during loading.

Multilayer 3D bioprinting and complex mechanical properties of alginate-gelatin mesostructures.

In the biomedical field, extrusion-based 3D bioprinting has emerged as a promising technique to fabricate tissue replacements. However, a main challenge is to find suitable bioinks and reproducible procedures that ensure good printability and generate final printed constructs with high shape fidelity, similarity to the designed model, and controllable mechanical properties. In this study, our main goal is to 3D print multilayered structures from alginate-gelatin (AG) hydrogels and to quantify their complex mechanical properties with particular focus on the effects of the extrusion process and geometrical parameters, i.e. different mesostructures and macroporosities. We first introduce a procedure including a pre-cooling step and optimized printing parameters to control and improve the printability of AG hydrogels based on rheological tests and printability studies. Through this procedure, we significantly improve the printability and flow stability of AG hydrogels and successfully fabricate well-defined constructs similar to our design models. Our subsequent complex mechanical analyses highlight that the extrusion process and the mesostructure, characterized by pore size, layer height and filament diameter, significantly change the complex mechanical response of printed constructs. The presented approach and the corresponding results have important implications for future 3D bioprinting applications when aiming to produce replacements with good structural integrity and defined mechanical properties similar to the native tissue, especially in soft tissue engineering. The approach is also applicable to the printing of gelatin-based hydrogels with different accompanying materials, concentrations, or cells.

Exploring the role of the outer subventricular zone during cortical folding through a physics-based model.

The human brain has a highly complex structure both on the microscopic and on the macroscopic scales. Increasing evidence has suggested the role of mechanical forces for cortical folding - a classical hallmark of the human brain. However, the link between cellular processes at the microscale and mechanical forces at the macroscale remains insufficiently understood. Recent findings suggest that an additional proliferating zone, the outer subventricular zone (OSVZ), is decisive for the particular size and complexity of the human cortex. To better understand how the OSVZ affects cortical folding, we establish a multifield computational model that couples cell proliferation in different zones and migration at the cell scale with growth and cortical folding at the organ scale by combining an advection-diffusion model with the theory of finite growth. We validate our model based on data from histologically stained sections of the human fetal brain and predict 3D pattern formation. Finally, we address open questions regarding the role of the OSVZ for the formation of cortical folds. The presented framework not only improves our understanding of human brain development, but could eventually help diagnose and treat neuronal disorders arising from disruptions in cellular development and associated malformations of cortical development.

Simulating the mechanical stimulation of cells on a porous hydrogel scaffold using an FSI model to predict cell differentiation.

3D-structured hydrogel scaffolds are frequently used in tissue engineering applications as they can provide a supportive and biocompatible environment for the growth and regeneration of new tissue. Hydrogel scaffolds seeded with human mesenchymal stem cells (MSCs) can be mechanically stimulated in bioreactors to promote the formation of cartilage or bone tissue. Although in vitro and in vivo experiments are necessary to understand the biological response of cells and tissues to mechanical stimulation, in silico methods are cost-effective and powerful approaches that can support these experimental investigations. In this study, we simulated the fluid-structure interaction (FSI) to predict cell differentiation on the entire surface of a 3D-structured hydrogel scaffold seeded with cells due to dynamic compressive load stimulation. The computational FSI model made it possible to simultaneously investigate the influence of both mechanical deformation and flow of the culture medium on the cells on the scaffold surface during stimulation. The transient one-way FSI model thus opens up significantly more possibilities for predicting cell differentiation in mechanically stimulated scaffolds than previous static microscale computational approaches used in mechanobiology. In a first parameter study, the impact of the amplitude of a sinusoidal compression ranging from 1% to 10% on the phenotype of cells seeded on a porous hydrogel scaffold was analyzed. The simulation results show that the number of cells differentiating into bone tissue gradually decreases with increasing compression amplitude, while differentiation into cartilage cells initially multiplied with increasing compression amplitude in the range of 2% up to 7% and then decreased. Fibrous cell differentiation was predicted from a compression of 5% and increased moderately up to a compression of 10%. At high compression amplitudes of 9% and 10%, negligible areas on the scaffold surface experienced high stimuli where no cell differentiation could occur. In summary, this study shows that simulation of the FSI system is a versatile approach in computational mechanobiology that can be used to study the effects of, for example, different scaffold designs and stimulation parameters on cell differentiation in mechanically stimulated 3D-structured scaffolds.

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

The identification of material parameters accurately describing the region-dependent mechanical behavior of human brain tissue is crucial for computational models used to assist, e.g., the development of safety equipment like helmets or the planning and execution of brain surgery. While the division of the human brain into different anatomical regions is well established, knowledge about regions with distinct mechanical properties remains limited. Here, we establish an inverse parameter identification scheme using a hyperelastic Ogden model and experimental data from multi-modal testing of tissue from 19 anatomical human brain regions to identify mechanically distinct regions and provide the corresponding material parameters. We assign the 19 anatomical regions to nine governing regions based on similar parameters and microstructures. Statistical analyses confirm differences between the regions and indicate that at least the corpus callosum and the corona radiata should be assigned different material parameters in computational models of the human brain. We provide a total of four parameter sets based on the two initial Poisson's ratios of 0.45 and 0.49 as well as the pre- and unconditioned experimental responses, respectively. Our results highlight the close interrelation between the Poisson's ratio and the remaining model parameters. The identified parameters will contribute to more precise computational models enabling spatially resolved predictions of the stress and strain states in human brains under complex mechanical loading conditions.

Dried Vegetables as Potential Clean-Label Phosphate Substitutes in Cooked Sausage Meat.

While phosphates are key additives in sausage production, their use conflicts with consumer preferences for "natural" foods. In this study, we investigated the potential of using vegetables as "clean-label" phosphate substitutes and their effects on water holding capacity, consumer acceptance, color, softness, and tenderness. Six freeze-dried vegetables with a pH above 6.0 were added to sausage meat on a laboratory scale. Adding 1.6% freeze-dried Brussels sprouts or Red Kuri squash resulted in a similar weight gain (7.0%) as the positive control of 0.6% commercial phosphate additive. Higher vegetable concentrations (2.2-4.0%) caused a significant increase in weight (p ≤ 0.05, 10.4-18.4% weight gain). Similar stress was needed to compress sausages containing 1.6/4.0% Brussels sprouts (14.2/11.2 kPa) and the positive control (13.2 kPa). Indentation tests also led to similar softness results for the sausages prepared with 1.6/4.0% Brussels sprouts (15.5 kPa/16.6 kPa) and the positive control (16.5 kPa). A force of 1.25 N was needed to shear the positive control, while 1.60 N/1.30 N was needed for the samples (1.6/4% Brussels sprouts). In summary, the present study indicates that freeze-dried vegetables have the potential to effectively replace phosphate in meat products.

Poro-viscoelastic material parameter identification of brain tissue-mimicking hydrogels.

Understanding and characterizing the mechanical and structural properties of brain tissue is essential for developing and calibrating reliable material models. Based on the Theory of Porous Media, a novel nonlinear poro-viscoelastic computational model was recently proposed to describe the mechanical response of the tissue under different loading conditions. The model contains parameters related to the time-dependent behavior arising from both the viscoelastic relaxation of the solid matrix and its interaction with the fluid phase. This study focuses on the characterization of these parameters through indentation experiments on a tailor-made polyvinyl alcohol-based hydrogel mimicking brain tissue. The material behavior is adjusted to ex vivo porcine brain tissue. An inverse parameter identification scheme using a trust region reflective algorithm is introduced and applied to match experimental data obtained from the indentation with the proposed computational model. By minimizing the error between experimental values and finite element simulation results, the optimal constitutive model parameters of the brain tissue-mimicking hydrogel are extracted. Finally, the model is validated using the derived material parameters in a finite element simulation.

Mechanical behavior of the hippocampus and corpus callosum: An attempt to reconcile ex vivo with in vivo and micro with macro properties.

Mechanical properties of brain tissue are very complex and vary with the species, region, method, and dynamic range, and between in vivo and ex vivo measurements. To reconcile this variability, we investigated in vivo and ex vivo stiffness properties of two distinct regions in the human and mouse brain - the hippocampus (HP) and the corpus callosum (CC) - using different methods. Under quasi-static conditions, we examined ex vivo murine HP and CC by atomic force microscopy (AFM). Between 16 and 40Hz, we investigated the in vivo brains of healthy volunteers by magnetic resonance elastography (MRE) in a 3-T clinical scanner. At high-frequency stimulation between 1000 and 1400Hz, we investigated the murine HP and CC ex vivo and in vivo with MRE in a 7-T preclinical system. HP and CC showed pronounced stiffness dispersion, as reflected by a factor of 32-36 increase in shear modulus from AFM to low-frequency human MRE and a 25-fold higher shear wave velocity in murine MRE than in human MRE. At low frequencies, HP was softer than CC, in both ex vivo mouse specimens (p < 0.05) and in vivo human brains (p < 0.01) while, at high frequencies, CC was softer than HP under in vivo (p < 0.01) and ex vivo (p < 0.05) conditions. The standard linear solid model comprising three elements reproduced the observed HP and CC stiffness dispersions, while other two- and three-element models failed. Our results indicate a remarkable consistency of brain stiffness across species, ex vivo and in vivo states, and different measurement techniques when marked viscoelastic dispersion properties combining equilibrium and non-equilibrium mechanical elements are considered.

Fiber alignment in 3D collagen networks as a biophysical marker for cell contractility.

Cells cultured in 3D fibrous biopolymer matrices exert traction forces on their environment that induce deformations and remodeling of the fiber network. By measuring these deformations, the traction forces can be reconstructed if the mechanical properties of the matrix and the force-free matrix configuration are known. These requirements limit the applicability of traction force reconstruction in practice. In this study, we test whether force-induced matrix remodeling can instead be used as a proxy for cellular traction forces. We measure the traction forces of hepatic stellate cells and different glioblastoma cell lines and quantify matrix remodeling by measuring the fiber orientation and fiber density around these cells. In agreement with simulated fiber networks, we demonstrate that changes in local fiber orientation and density are directly related to cell forces. By resolving Rho-kinase (ROCK) inhibitor-induced changes of traction forces, fiber alignment, and fiber density in hepatic stellate cells, we show that the method is suitable for drug screening assays. We conclude that differences in local fiber orientation and density, which are easily measurable, can be used as a qualitative proxy for changes in traction forces. The method is available as an open-source Python package with a graphical user interface.

Tissue-Scale Biomechanical Testing of Brain Tissue for the Calibration of Nonlinear Material Models.

Brain tissue is one of the most complex and softest tissues in the human body. Due to its ultrasoft and biphasic nature, it is difficult to control the deformation state during biomechanical testing and to quantify the highly nonlinear, time-dependent tissue response. In numerous experimental studies that have investigated the mechanical properties of brain tissue over the last decades, stiffness values have varied significantly. One reason for the observed discrepancies is the lack of standardized testing protocols and corresponding data analyses. The tissue properties have been tested on different length and time scales depending on the testing technique, and the corresponding data have been analyzed based on simplifying assumptions. In this review, we highlight the advantage of using nonlinear continuum mechanics based modeling and finite element simulations to carefully design experimental setups and protocols as well as to comprehensively analyze the corresponding experimental data. We review testing techniques and protocols that have been used to calibrate material model parameters and discuss artifacts that might falsify the measured properties. The aim of this work is to provide standardized procedures to reliably quantify the mechanical properties of brain tissue and to more accurately calibrate appropriate constitutive models for computational simulations of brain development, injury and disease. Computational models can not only be used to predictively understand brain tissue behavior, but can also serve as valuable tools to assist diagnosis and treatment of diseases or to plan neurosurgical procedures. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC.