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.

An integrated finite element method and machine learning algorithm for brain morphology prediction.

The human brain development experiences a complex evolving cortical folding from a smooth surface to a convoluted ensemble of folds. Computational modeling of brain development has played an essential role in better understanding the process of cortical folding, but still leaves many questions to be answered. A major challenge faced by computational models is how to create massive brain developmental simulations with affordable computational sources to complement neuroimaging data and provide reliable predictions for brain folding. In this study, we leveraged the power of machine learning in data augmentation and prediction to develop a machine-learning-based finite element surrogate model to expedite brain computational simulations, predict brain folding morphology, and explore the underlying folding mechanism. To do so, massive finite element method (FEM) mechanical models were run to simulate brain development using the predefined brain patch growth models with adjustable surface curvature. Then, a GAN-based machine learning model was trained and validated with these produced computational data to predict brain folding morphology given a predefined initial configuration. The results indicate that the machine learning models can predict the complex morphology of folding patterns, including 3-hinge gyral folds. The close agreement between the folding patterns observed in FEM results and those predicted by machine learning models validate the feasibility of the proposed approach, offering a promising avenue to predict the brain development with given fetal brain configurations.

Fibrin fiber deformation mechanisms: insights from phenomenological modeling to molecular details.

The deformation mechanism of fibrin fibers has been a long-standing challenge to uncover due to the fiber's complex structure and mechanical behaviors. In this paper, a phenomenological, bilinear, force-strain model is derived to accurately reproduce the fibrin fiber force-strain curve, and then, the phenomenological model is converted to a mechanistic model using empirical relationships developed from particle simulation data. The mechanistic model assumes that the initial linear fibrin fiber force-strain response is due to entropic extension of polypeptide chains, and the final linear response is due to enthalpic extension of protofibrils. This model is the first fibrin fiber tensile force-strain equation to simultaneously (1) reproduce the bilinear force-strain curve of fibrin fibers in tension; (2) explicitly include the number of protofibrils through the fibrin fiber cross section, persistence length of [Formula: see text]-regions, and stiffness of fibrin protofibrils; and (3) make demonstrably reasonable/accurate predictions of fibrin fiber mechanics when tempered against experimental results. The model predicted that the count of protofibrils through the cross section for the analyzed fibrin fibers is between 207 and 421, the persistence length of [Formula: see text]-regions is [Formula: see text], and the stiffness of protofibrils in a deforming fiber is [Formula: see text]. The predicted [Formula: see text]-region persistence length is within the range typical of amino acid residue lengths [Formula: see text] and the predicted protofibril stiffness is shown to correspond to half-staggered protofibrils of unfolded fibrin monomers. Our analysis supports the proposition that entropic extension of [Formula: see text]-regions could be responsible for fibrin fiber's initial force-strain stiffness and suggests a structural change in fibrin protofibrils during fibrin fiber deformation. The results from the model are compared to those from five candidate deformation mechanisms reported in the literature. Our work provides (1) strong quantitative support to a deformation mechanism that was previously supported by anecdote and qualitative argument, and (2) a model for rigorously analyzing fibrin fiber force-strain data and simulating fibrin fibers in tension.

A Tractable, Transferable, and Empirically Consistent Fibrous Biomaterial Model.

Stochastic modeling is a useful approach for modeling fibrous materials that attempts to recreate fibrous materials' structure using statistical data. However, several issues remain to be resolved in the stochastic modeling of fibrous materials-for example, estimating 3D fiber orientation distributions from 2D data, achieving the desired fiber tortuosity distributions, and dealing with fiber-fiber penetration. This work proposes innovative methods to (1) create a mapping from 2D fiber orientation data to 3D fiber orientation probability distributions, and vice versa; and (2) provide a means to select parameters de novo for random walks employing the popularized von Mises-Fisher distribution given that the desired tortuosity of the path is known. The proposed methods are incorporated alongside previously developed stochastic modeling techniques to simulate fiber network structures. First, fiber orientation distributions vary significantly depending on how a fibrous material is formed, and projection distortion affects the measurement of fiber orientation distributions when reported as 2D data such as histograms or polar plots. Relationships are developed to estimate 3D fiber orientation distributions from 2D data, accounting for projection distortion and the variety of orientation distributions observed in fibrous materials. We show that without correcting for projection distortion, fiber orientation distribution parameters could have errors of up to 100%. Second, in stochastic modeling, fiber tortuosity is usually treated with random walks, but no relationship is available for choosing random walk inputs to generate a desired fiber tortuosity. Relationships are also developed to relate the input parameters of von Mises-Fisher random walks to the expected tortuosity of the generated path-a necessary link to modeling fiber tortuosity distributions tractably and with empirical consistency. Using the developed relationships, we show that modeling of tortuous fibers from a distribution could be sped up by ~1200-fold and the uncertainty of selecting appropriate parameters could be eliminated. Third, randomly placing fibers in a simulation domain inevitably results in fiber-fiber penetration, and correcting this issue requires changes to the simulated fibrous material structure through non-penetration conditions. No thorough remedy can be offered here, but we statistically quantify the effects of enforcing non-penetration conditions on the fiber shape and orientation changes as well as the overall fibrous material model. This work offers tractable and transferable methods for treating fiber orientation and tortuosity that allow for empirical consistency in the stochastic modeling of fibrous materials.

Forces, energetics, and dynamics of conjugated-carbon ring tethers adhered to CNTs: a computational investigation.

The strength and nature of the interactions between carbon nanotubes (CNTs) and molecular tethers plays a vital role in technology such as CNT-enzyme sensors. Tethers that attach noncovalently to CNTs are ideal for retaining the electrical properties of the CNTs since they do not degrade the CNT surface and effect its electrical conductivity. However, leaching due to weak CNT-tether attachment is very common when using noncovalent tethers, and this has limited their use in commercial products including biosensors. Thus, understanding the fundamental mechanics governing the strength of CNT-tether adhesion is crucial for the design of highly sensitive, viable sensors. Here, we computationally investigate the adhesion strength of CNT-tether complexes with 8 different tethering molecules designed to adhere noncovalently to the CNT surface. We study the effects of CNT diameter, CNT chirality, and the size/geometry of the tethering molecule on the adhesion energy and force. Our results show an asymptotic relationship between adhesion strength and CNT diameter. Calculations show that noncovalent tethers tested here can reach adhesion forces and energies that are up to 21% and 54% of the strength of the carbon-carbon single bond force and bond energy respectively. We anticipate our results will help guide CNT-enzyme sensor design to produce sensors with high sensitivity and minimal leaching.