Review of the Brain's Behaviour after Injury and Disease for Its Application in an Agent-Based Model (ABM).

The brain is the most complex organ in the human body and, as such, its study entails great challenges (methodological, theoretical, etc.). Nonetheless, there is a remarkable amount of studies about the consequences of pathological conditions on its development and functioning. This bibliographic review aims to cover mostly findings related to changes in the physical distribution of neurons and their connections-the connectome-both structural and functional, as well as their modelling approaches. It does not intend to offer an extensive description of all conditions affecting the brain; rather, it presents the most common ones. Thus, here, we highlight the need for accurate brain modelling that can subsequently be used to understand brain function and be applied to diagnose, track, and simulate treatments for the most prevalent pathologies affecting the brain.

Using the Mooney Space to Characterize the Non-Affine Behavior of Elastomers.

The formulation of the entropic statistical theory and the related neo-Hookean model has been a major advance in the modeling of rubber-like materials, but the failure to explain some experimental observations such as the slope in Mooney plots resulted in hundreds of micromechanical and phenomenological models. The origin of the difficulties, the reason for the apparent need for the second invariant, and the reason for the relative success of models based on the Valanis-Landel decomposition have been recently explained. From that insight, a new micro-macro chain stretch connection using the stretch tensor (instead of the right Cauchy-Green deformation tensor) has been proposed and supported both theoretically and from experimental data. A simple three-parameter model using this connection has been suggested. The purpose of this work is to provide further insight into the model, to provide an analytical expression for the Gaussian contribution, and to provide a simple procedure to obtain the parameters from a tensile test using the Mooney space or the Mooney-Rivlin constants. From different papers, a wide variety of experimental tests on different materials and loading conditions have been selected to demonstrate that the simple model calibrated only from a tensile test provides accurate predictions for a wide variety of elastomers under different deformation levels and multiaxial patterns.

An Agent-Based Model to Reproduce the Boolean Logic Behaviour of Neuronal Self-Organised Communities through Pulse Delay Modulation and Generation of Logic Gates.

The human brain is arguably the most complex "machine" to ever exist. Its detailed functioning is yet to be fully understood, let alone modelled. Neurological processes have logical signal-processing and biophysical aspects, and both affect the brain's structure, functioning and adaptation. Mathematical approaches based on both information and graph theory have been extensively used in an attempt to approximate its biological functioning, along with Artificial Intelligence frameworks inspired by its logical functioning. In this article, an approach to model some aspects of the brain learning and signal processing is presented, mimicking the metastability and backpropagation found in the real brain while also accounting for neuroplasticity. Several simulations are carried out with this model to demonstrate how dynamic neuroplasticity, neural inhibition and neuron migration can reshape the brain's logical connectivity to synchronise signal processing and obtain certain target latencies. This work showcases the importance of dynamic logical and biophysical remodelling in brain plasticity. Combining mathematical (agents, graph theory, topology and backpropagation) and biomedical ingredients (metastability, neuroplasticity and migration), these preliminary results prove complex brain phenomena can be reproduced-under pertinent simplifications-via affordable computations, which can be construed as a starting point for more ambitiously accurate simulations.

Reverse-engineering and modeling the 3D passive and active responses of skeletal muscle using a data-driven, non-parametric, spline-based procedure.

In this work we present a non-parametric data-driven approach to reverse-engineer and model the 3D passive and active responses of skeletal muscle, applied to tibialis anterior muscle of Wistar rats. We assume a Hill-type additive relation for the stored energy into passive and active contributions. The terms of the stored energy have no upfront assumed shape, nor material parameters. These terms are determined directly from experimental data in spline form solving numerically the functional equations of the tests from which experimental data is available. To characterize typical longitudinal-to-transverse behavior in rodent's muscle, experiments from Morrow et al. (J. Mech. Beh. Biomed. Mater. 2010; 3: 124-129) are employed. Then, the passive and active behaviors of Wistar rats are determined from the experiments of Calvo et al. (J. Bomech. 2010; 43:318-325) and Ramirez et al. (J. Theor. Biol. 2010; 267:546-553). The twitch shape is not assumed, but reverse-engineered from experimental data. The influence of the strain and the stimulus voltage and frequency in the active response, are also modeled. A convenient stimulus power-related variable is proposed to comprise both voltage and frequency dependencies in the active response. Then, the behavior of the resulting muscle model depends only on the muscle strain maintained during isometric tests in the muscle and the stimulus power variable, along the time from initiation of the tetanus state.

A continuum model for tension-compression asymmetry in skeletal muscle.

Experiments on passive skeletal muscle on different species show a strong asymmetry in the observed tension-compression mechanical behavior. This asymmetry shows that the tension modulus is two orders of magnitude higher than the compression modulus. Until now, traditional analytical constitutive models have been unable to capture that strong asymmetry in anisotropic solids using the same material parameters. In this work we present a model which is able to accurately capture five experimental tests in chicken pectoralis muscle, including the observed tension-compression asymmetry. However, aspects of the anisotropy of the tissue are not captured by the model.

Strain-Level Dependent Nonequilibrium Anisotropic Viscoelasticity: Application to the Abdominal Muscle.

Soft connective tissues sustain large strains of viscoelastic nature. The rate-independent component is frequently modeled by means of anisotropic hyperelastic models. The rate-dependent component is usually modeled through linear rheological models or quasi-linear viscoelastic (QLV) models. These viscoelastic models are unable, in general, to capture the strain-level dependency of the viscoelastic properties present in many viscoelastic tissues. In linear viscoelastic models, strain-level dependency is frequently accounted for by including the dependence of multipliers of Prony series on strains through additional evolution laws, but the determination of the material parameters is a difficult task and the obtained accuracy is usually not sufficient. In this work, we introduce a model for fully nonlinear viscoelasticity in which the instantaneous and quasi-static behaviors are exactly captured and the relaxation curves are predicted to a high accuracy. The model is based on a fully nonlinear standard rheological model and does not necessitate optimization algorithms to obtain material parameters. Furthermore, in contrast to most models used in modeling the viscoelastic behavior of soft tissues, it is valid for the large deviations from thermodynamic equilibrium typically observed in soft tissues.

Determination and Finite Element Validation of the WYPIWYG Strain Energy of Superficial Fascia from Experimental Data.

What-You-Prescribe-Is-What-You-Get (WYPIWYG) procedures are a novel and general phenomenological approach to modelling the behavior of soft materials, applicable to biological tissues in particular. For the hyperelastic case, these procedures solve numerically the nonlinear elastic material determination problem. In this paper we show that they can be applied to determine the stored energy density of superficial fascia. In contrast to the usual approach, in such determination no user-prescribed material parameters and no optimization algorithms are employed. The strain energy densities are computed solving the equilibrium equations of the set of experiments. For the case of superficial fascia it is shown that the mechanical behavior derived from such strain energies is capable of reproducing simultaneously the measured load-displacement curves of three experiments to a high accuracy.

On the tension-compression switch of the Gasser-Ogden-Holzapfel model: Analysis and a new pre-integrated proposal.

Many biological soft tissues are structurally composed of a mostly isotropic matrix (elastin) and fibers (collagen). These fibers are not perfectly aligned but dispersed around some referential, preferred directions. In order to account for the dispersion of the fibers, a probability distribution is assumed. The Generalized Structure Tensor (GST) models perform a pre-integration of the distribution in order to achieve improved computational efficiency. The best known model of this kind is the Gasser-Ogden-Holzapfel (GOH) model. However, in these models no singular treatment of fibers is made. Whenever they suffer compression it is usual to consider that fibers should not contribute to the overall stiffness. At this point, a switch criterion is employed. This switch criterion is important because it changes the model predictions and may also result in unphysical stress predictions or strain ranges at which no compatible equilibrium solution is found. We perform an analysis of different tension-compression switch criteria from the literature for the GOH model and show relevant physical and computational drawbacks when using these criteria. In order to overcome these drawbacks, we make a new proposal which yields continuous stress solutions. In our proposal, pre-integrated expressions given in terms of the usual set of invariants take into account an average amount of fibers working either in tension or in compression for a given deformation gradient and fiber family. Two distinct switches naturally emerge from our procedure. Furthermore, we keep the appealing GST pre-integrated approach for any proposed stored energy, including that of the GOH model.