Biological cells and coupled electro-mechanical effects: The role of organelles, microtubules, and nonlocal contributions

Mechanics of Small-Scale Spherical Inclusions Using Nonlocal Poroelasticity Integrated with Light Gradient Boosting Machine

Detecting inclusions in materials at small scales is of high importance to ensure the quality, structural integrity and performance efficiency of microelectromechanical machines and products. Ultrasound waves are commonly used as a non-destructive method to find inclusions or structural flaws in a material. Mathematical continuum models can be used to enable ultrasound techniques to provide quantitative information about the change in the mechanical properties due to the presence of inclusions. In this paper, a nonlocal size-dependent poroelasticity model integrated with machine learning is developed for the description of the mechanical behaviour of spherical inclusions under uniform radial compression. The scale effects on fluid pressure and radial displacement are captured using Eringen's theory of nonlocality. The conservation of mass law is utilised for both the solid matrix and fluid content of the poroelastic material to derive the storage equation. The governing differential equations are derived by decoupling the equilibrium equation and effective stress-strain relations in the spherical coordinate system. An accurate numerical solution is obtained using the Galerkin discretisation technique and a precise integration method. A Dormand-Prince solution is also developed for comparison purposes. A light gradient boosting machine learning model in conjunction with the nonlocal model is used to extract the pattern of changes in the mechanical response of the poroelastic inclusion. The optimised hyperparameters are calculated by a grid search cross validation. The modelling estimation power is enhanced by considering nonlocal effects and applying machine learning processes, facilitating the detection of ultrasmall inclusions within a poroelastic medium at micro/nanoscales.

Three-Phase-Lag Bio-Heat Transfer Model of Cardiac Ablation

Significant research efforts have been devoted in the past decades to accurately modelling the complex heat transfer phenomena within biological tissues. These modeling efforts and analysis have assisted in a better understanding of the intricacies of associated biological phenomena and factors that affect the treatment outcomes of hyperthermic therapeutic procedures. In this contribution, we report a three-dimensional non-Fourier bio-heat transfer model of cardiac ablation that accounts for the three-phase-lags (TPL) in the heat propagation, viz., lags due to heat flux, temperature gradient, and thermal displacement gradient. Finite element-based COMSOL Multiphysics software has been utilized to predict the temperature distributions and ablation volumes. A comparative analysis has been conducted to report the variation in the treatment outcomes of cardiac ablation considering different bio-heat transfer models. The effect of variations in the magnitude of different phase lags has been systematically investigated. The fidelity and integrity of the developed model have been evaluated by comparing the results of the developed model with the analytical results of the recent studies available in the literature. This study demonstrates the importance of considering non-Fourier lags within biological tissue for predicting more accurately the characteristics important for the efficient application of thermal therapies.

Nonlocal models in the analysis of brain neurodegenerative protein dynamics with application to Alzheimer's disease

It is well known that today nearly one in six of the world’s population has to deal with neurodegenerative disorders. While a number of medical devices have been developed for the detection, prevention, and treatments of such disorders, some fundamentals of the progression of associated diseases are in urgent need of further clarification. In this paper, we focus on Alzheimer’s disease, where it is believed that the concentration changes in amyloid-beta and tau proteins play a central role in its onset and development. A multiscale model is proposed to analyze the propagation of these concentrations in the brain connectome. In particular, we consider a modified heterodimer model for the protein–protein interactions. Higher toxic concentrations of amyloid-beta and tau proteins destroy the brain cell. We have studied these propagations for the primary and secondary and their mixed tauopathies. We model the damage of a brain cell by the nonlocal contributions of these toxic loads present in the brain cells. With the help of rigorous analysis, we check the stability behaviour of the stationary points corresponding to the homogeneous system. After integrating the brain connectome data into the developed model, we see that the spreading patterns of the toxic concentrations for the whole brain are the same, but their concentrations are different in different regions. Also, the time to propagate the damage in each region of the brain connectome is different.

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable attention in the research community, the same cannot be said about nonlocality in time, in particular when nonlocal initial conditions are present. This paper aims at filling this gap, providing an overview of the current status of nonlocal models and focusing on the mathematical treatment of such models when nonlocal initial conditions are at the heart of the problem. Specifically, our representative example is given for a nonlocal-in-time problem for the abstract Schrödinger equation. By exploiting the linear nature of nonlocal conditions, we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of the complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem’s well-posedness and the existence of its solution under different regularities. Furthermore, we present new sufficient conditions for the existence of the solution that extend the existing results in this field to the case when some nonlocal parameters are unbounded. Two further examples demonstrate the developed methodology and highlight the importance of its computer algebra component in the reduction procedures and parameter estimations for nonlocal models. Finally, a connection of the considered models and developed analysis is discussed in the context of other reduction techniques, concentrating on the most promising from the viewpoint of data-driven modelling environments, and providing directions for further generalizations.

Organic and inorganic equivalent models for analysis of red blood cell mechanical behaviour

Experimental investigation into the mechanical response of red blood cells is presently impeded with the main impediments being the micro dimensions involved and ethical issues associated with in vivo testing. The widely employed alternative approach of computational modelling suffers from its own inherent limitations being reliant on precise constitutive and boundary information. Moreover, and somewhat critically, numerical computational models themselves are required to be validated by means of experimentation and hence suffer similar impediments. An alternative experimental approach is examined in this paper involving large-scale equivalent models manufactured principally from inorganic, and to lesser extent organic, materials. Although there presently exists no known method providing the means to investigate the mechanical response of red blood cells using scaled models simultaneously having different dimensions and materials, the present paper aims to develop a scaled framework based on the new finite-similitude theory that has appeared in the recent open literature. Computational models are employed to test the effectiveness of the proposed method, which in principle can provide experimental solution methods to a wide range of practical applications including the design of red-blood cell nanorobots and drug delivery systems. By means of experimentally validated numerical experiments under impact loading it is revealed that although exact prediction is not achieved good accuracy can nevertheless be obtained. Furthermore, it is demonstrated how the proposed approach for first time provides a means to relate models at different scales founded on different constitutive equations.

Auxeticity in biosystems: an exemplification of its effects on the mechanobiology of heterogeneous living cells

Auxeticity (negative Poisson's ratio) is the unique mechanical property found in an extensive variety of materials, such as metals, graphene, composites, polymers, foams, fibers, ceramics, zeolites, silicates and biological tissues. The enhanced mechanical features of the auxetic materials have motivated scientists to design, engineer and manufacture man-made auxetic materials to fully leverage their capabilities in different fields of research applications, including aeronautics, medical, protective equipments, smart sensors, filter cleaning, and so on. Atomic force microscopy (AFM) indentation is one of the most widely used methods for characterizing the mechanical properties and response of the living cells. In this contribution, we highlight main consequences of auxeticity for biosystems and provide a representative example to quantify the effect of nucleus auxeticity on the force response of the embryonic stem cells. A parametric study has been conducted on a heterogeneous stem cell to evaluate the effect of nucleus diameter, nucleus elasticity, indenter's shape and location on the force-indentation curve. The developed model has also been validated with the recently reported experimental studies available in the literature. Our results suggest that the nucleus auxeticity plays a profound role in cell mechanics especially for large size nucleus. We also report the mechanical stresses induced within the hyperelastic cell model under different loading conditions that would be quite useful in decoding the interrelations between mechanical stimuli and cellular behavior of auxetic biosystems. Finally, current and potential areas of applications of our findings for regenerative therapies, tissue engineering, 3 D/4D bioprinting, and the development of meta-biomaterials are discussed.

On the Coupling between Mechanical Properties and Electrostatics in Biological Membranes

Cell membrane structure is proposed as a lipid matrix with embedded proteins, and thus, their emerging mechanical and electrostatic properties are commanded by lipid behavior and their interconnection with the included and absorbed proteins, cytoskeleton, extracellular matrix and ionic media. Structures formed by lipids are soft, dynamic and viscoelastic, and their properties depend on the lipid composition and on the general conditions, such as temperature, pH, ionic strength and electrostatic potentials. The dielectric constant of the apolar region of the lipid bilayer contrasts with that of the polar region, which also differs from the aqueous milieu, and these changes happen in the nanometer scale. Besides, an important percentage of the lipids are anionic, and the rest are dipoles or higher multipoles, and the polar regions are highly hydrated, with these water molecules forming an active part of the membrane. Therefore, electric fields (both, internal and external) affects membrane thickness, density, tension and curvature, and conversely, mechanical deformations modify membrane electrostatics. As a consequence, interfacial electrostatics appears as a highly important parameter, affecting the membrane properties in general and mechanical features in particular. In this review we focus on the electromechanical behavior of lipid and cell membranes, the physicochemical origin and the biological implications, with emphasis in signal propagation in nerve cells.

All Wired Up: An Exploration of the Electrical Properties of Microtubules and Tubulin

Microtubules are hollow, cylindrical polymers of the protein α, β tubulin, that interact mechanochemically with a variety of macromolecules. Due to their mechanically robust nature, microtubules have gained attention as tracks for precisely directed transport of nanomaterials within lab-on-a-chip devices. Primarily due to the unusually negative tail-like C-termini of tubulin, recent work demonstrates that these biopolymers are also involved in a broad spectrum of intracellular electrical signaling. Microtubules and their electrostatic properties are discussed in this Review, followed by an evaluation of how these biopolymers respond mechanically to electrical stimuli, through microtubule migration, electrorotation and C-termini conformation changes. Literature focusing on how microtubules act as nanowires capable of intracellular ionic transport, charge storage, and ionic signal amplification is reviewed, illustrating how these biopolymers attenuate ionic movement in response to electrical stimuli. The Review ends with a discussion on the important questions, challenges, and future opportunities for intracellular microtubule-based electrical signaling.

Microtubule Biomechanics and the Effect of Degradation of Elastic Moduli

The present study aims at quantifying the effect of mechanical degradation of microtubules on their electro-elastic response. A three-dimensional continuum-based hollow cylindrical domain of a microtubule has been considered in this work. A fully coupled electro-mechanical model has been developed for conducting the comparative analysis considering three different cases, viz., no degradation, 50% degradation and 90% degradation of elastic modulus of the microtubule. The microtubule has been subjected to dynamic forces adopted from the commonly used loading-unloading conditions in nanoindentation experiments. The results show that the degradation of microtubules significantly influences their electro-elastic response when subjected to externally applied forces. The transient response of the model in terms of induced displacement, electric potential and volumetric strain has also been analyzed for different magnitudes of mechanical degradation. The modelling study presented here represents a more accurate electro-mechanical model compared to the classical mechanical model for quantifying the effects of mechanical transductions on microtubules biomechanics.