Chemo-mechanical Model Research Articles

Mathematical Modeling of Invasive Carcinoma: Biomechanics of Small Groups of Cancer Cells

According to the latest research, cancer is a complex biological system that evolves over time and space. This means that cancer cells differ from each other in their functions in the tumor. They engage in various interactions with the microenvironment and compete for available nutrients to survive. The main problem of mathematical modeling in oncology today is the heterogeneity of a typical malignant neoplasm. In this work, we propose a chemomechanical model of the pattern formation of small groups of cancer cells of invasive carcinoma of a non-special type (IC NST). The model assumes that carcinoma is a heterogeneous formation, which consists of cells of different phenotypes performing different tasks to maintain the existence of the tumor. In the model, each cell is represented as a deformable polygon that changes its shape and size as the tissue develops. Numerical modeling implements various subtypes of IC NST structures. These patterns are compared with morphological structures identified in clinical studies.

Chemomechanical Simulation of Microtubule Dynamics With Explicit Lateral Bond Dynamics

We introduce and parameterize a chemomechanical model of microtubule dynamics on the dimer level, which is based on the allosteric tubulin model and includes attachment, detachment and hydrolysis of tubulin dimers as well as stretching of lateral bonds, bending at longitudinal junctions, and the possibility of lateral bond rupture and formation. The model is computationally efficient such that we reach sufficiently long simulation times to observe repeated catastrophe and rescue events at realistic tubulin concentrations and hydrolysis rates, which allows us to deduce catastrophe and rescue rates. The chemomechanical model also allows us to gain insight into microscopic features of the GTP-tubulin cap structure and microscopic structural features triggering microtubule catastrophes and rescues. Dilution simulations show qualitative agreement with experiments. We also explore the consequences of a possible feedback of mechanical forces onto the hydrolysis process and the GTP-tubulin cap structure.

Strain gradient enhanced chemo-mechanical modeling of fracture in cathode materials for lithium-ion batteries

Next generation lithium-ion batteries (LIBs) cathodes are composed of polycrystalline microstructures where spatial heterogeneity such as grain size is often comparable to the geometric dimension of the cathodes. Incorporating the influence of the aforementioned heterogeneity in a chemo-mechanical continuum description is necessary to address the diffusion induced stress field during electrochemical cycling. Therefore, in the present study, the micro-structural size-dependent characteristic length of the cathode is embedded through a non-classical continuum mechanics approach known as the strain gradient elasticity (SGE) theory. Accordingly, a thermodynamically consistent multi-physics framework is developed where nonlinear diffusion kinetics is included along with the energetic interaction between the lithium-ions and host lattice of the electrode. The coupled governing equations are derived for the spherical cathode, and the generalized differential quadrature (GDQ) method is utilized to build the numerical procedure. The role of material heterogeneity length scale is addressed for strongly coupled chemo-mechanical process. Subsequently, the growth of potential surface flaws is examined under multiple length scales, particle size, and charge rate conditions. Ultimately, a comprehensive fracture map is established to illustrate the regime of flaw insensitivity, partial breakage and complete disintegration. Thus, the present findings can provide a suitable design perspective for fail-safe particulate type composite cathodes.

A chemo-mechanical damage model at large deformation: numerical and experimental studies on polycrystalline energy materials

The unique mechanical properties and transport features of grain boundaries (GBs) in polycrystalline materials have been widely investigated. However, studies which focus on the unique chemo-mechanics phenomena resulting from GBs’ are exceedingly sparse. In this work, a thermodynamically consistent framework has been developed to explore the multi-physics coupling between mechanics and species diffusion. Constitutive laws for the bulk and the across-GB interaction laws have been derived for large deformations from the system free energies. A chemo-mechanically coupled cohesive zone model is developed which takes into account mode-dependent fracture properties in the presence of GBs. Polycrystalline LiNixMnyCozO2 (NMC) particles and LixV2O5 nanowires haveüeen selected to demonstrate the impact of GBs on the modeled and observed chemo-mechanics. The model has been implemented in the open-source finite element (FE) package MOOSE. Simulation results indicate that the chemical process and the mechanical degradation go hand-in–hand, where enhanced intergranular chemical inhomogeneities weaken the mechanical strength of the GBs, while damage to the GBs affects or even block transport across the GB. Furthermore, experimentally observed characteristics of chemo-mechanical degradation, e.g., chemical “hot-spots” and surface layer delamination can be accurately predicted by the model.

Chemo-mechanical modelling of swelling and crosslinking reaction kinetics in alginate hydrogels: A novel theory and its numerical implementation

Hydrogels are mechanically stabilized through the action of external agents which induce the formation of crosslinks in the polymer network as a consequence of transport and reactive mechanisms. Crosslinking increases the stiffness of the construct, produces inelastic deformations in the polymer network and interacts with the swelling capacity of hydrogels. The control of this process is hence crucial for fulfilling functional criteria in several technological fields, like drug-delivery or bioprinting. Nevertheless, experimental approaches for monitoring the crosslinking kinetics with the required resolution are currently missing. The development of new computational models in the field might open the way to novel investigation tools. This paper presents a thermodynamically consistent chemo-mechanical model in large deformation for reactive–diffusive mechanisms occurring during crosslinking in alginate hydrogels. The system accounts for shrinking and swelling effects, fluid movements, as well as the reaction kinetics of calcium-induced crosslinking. Crosslinks alter mechanical and diffusive properties in the hydrogel. Moreover, on the basis of thermodynamic arguments, internal stresses directly affect the crosslinking kinetics, revealing a two-way coupling between mechanics and chemistry. The model is implemented in a finite element framework, considering a monolithic coupling between chemical transport and mechanics. The computational framework allows characterizing the (experimentally inaccessible) heterogeneous distribution of mechano-chemical quantities and properties in the hydrogel. Parametric campaigns of simulations are presented to investigate hydrogels’ behaviour and compare numerical outcomes with available experimental evidence.

Transport of secondary carriers in a solid lithium-ion conductor

Inorganic-solid lithium electrolytes are typically thought of as single-ion conductors, but the presence of secondary carriers can strongly affect their performance. Conventional descriptions of multi-carrier transport neglect both interactions between mobile species and stress diffusion — phenomena which can markedly impact the electrical response. We apply irreversible thermodynamics to develop a chemomechanical transport model for elastic-solid ionic conductors containing two mobile ions. We simulate lithium-ion conducting Li5La3Nb2O12 (LLNO) garnet oxide, a material within which experiments have shown that mobile protons can be freely substituted for lithium to form Li5(1−y)H5yLa3Nb2O12. When subjected to a current, we find that proton-substituted LLNO exhibits bulk lithium polarization, whose extent is partially controlled by cation/cation interactions. Secondary carriers segregate naturally if their global concentration is low, accumulating in a thin boundary layer near the cathode. We quantify the limiting current and Sand’s time, and analyze experimental data to show how competitive proton transport affects LLNO performance.

Chemo-mechanical coupling model of off-shore concrete structures

Seawater represents a complex phenomenon due to the presence of multiple ions. Previous researches aimed to estimate the resistance losses due to sulphate and chloride attacks based on probabilistic approaches. Few studies have focused on the complex chemo-mechanical modeling by coupling all the ions present in seawater and in concrete. In this study, the model proposed is based on the coupling between two codes CemPP- for the microstructure generation of the cementitious material, the evolution of the hydration and chemical reactions - and Cast3M - for the mechanical calculations and damage modeling. Results highlight the importance of considering each effect of cement paste’s ion reacting with seawater and their role on the overall mechanical behaviour of the structure affected by the chemical phases present at equilibrium.

Recursive feedback between matrix dissipation and chemo-mechanical signaling drives oscillatory growth of cancer cell invadopodia.

Most extracellular matrices (ECMs) are known to be dissipative, exhibiting viscoelastic and often plastic behaviors. However, the influence of dissipation, in particular mechanical plasticity in 3D confining microenvironments, on cell motility is not clear. In this study, we develop a chemo-mechanical model for dynamics of invadopodia, the protrusive structures that cancer cells use to facilitate invasion, by considering myosin recruitment, actin polymerization, matrix deformation, and mechano-sensitive signaling pathways. We demonstrate that matrix dissipation facilitates invadopodia growth by softening ECMs over repeated cycles, during which plastic deformation accumulates via cyclic ratcheting. Our model reveals that distinct protrusion patterns, oscillatory or monotonic, emerge from the interplay of timescales for polymerization-associated extension and myosin recruitment dynamics. Our model predicts the changes in invadopodia dynamics upon inhibition of myosin, adhesions, and the Rho-Rho-associated kinase (ROCK) pathway. Altogether, our work highlights the role of matrix plasticity in invadopodia dynamics and can help design dissipative biomaterials to modulate cancer cell motility.

Simulation of hardened cement degradation and estimation of uncertainty in predicted failure times with peridynamics

Modeling the degradation of cement-based infrastructure due to aqueous environmental conditions continues to be a challenge. In order to develop a capability to predict concrete infrastructure failure due to chemical degradation, we created a chemomechanical model of the effects of long-term water exposure on cement paste. The model couples the mechanical static equilibrium balance with reactive–diffusive transport and incorporates fracture and failure via peridynamics (a meshless simulation method). The model includes fundamental aspects of degradation of ordinary Portland cement (OPC) paste, including the observed softening, reduced toughness, and shrinkage of the cement paste, and increased reactivity and transport with water induced degradation. This version of the model focuses on the first stage of cement paste decalcification, the dissolution of portlandite. Given unknowns in the cement paste degradation process and the cost of uncertainty quantification (UQ), we adopt a minimally complex model in two dimensions (2D) in order to perform sensitivity analysis and UQ. We calibrate the model to existing experimental data using simulations of common tests such as flexure, compression and diffusion. Then we calculate the global sensitivity and uncertainty of predicted failure times based on variation of eleven unique and fundamental material properties. We observed particularly strong sensitivities to the diffusion coefficient, the reaction rate, and the shrinkage with degradation. Also, the predicted time of first fracture is highly correlated with the time to total failure in compression, which implies fracture can indicate impending degradation induced failure; however, the distributions of the two events overlap so the lead time may be minimal. Extension of the model to include the multiple reactions that describe complete degradation, viscous relaxation, post-peak load mechanisms, and to three dimensions to explore the interactions of complex fracture patterns evoked by more realistic geometry is straightforward and ongoing.

Multivalent molecular tension probes as anisotropic mechanosensors: concept and simulation

Cells use protein-based mechanosensors to measure the physical properties of their surroundings. Synthetic tension sensors made of proteins, DNA, and other molecular building blocks have recently emerged as tools to visualize and perturb the mechanics of these mechanosensors. While almost all synthetic tension sensors are designed to exhibit orientation-independent force responses, recent work has shown that biological mechanosensors often function in a manner that is highly dependent on force orientation. Accordingly, the design of synthetic mechanosensors with orientation-dependent force responses can provide a means to study the role of orientation in mechanosensation. Furthermore, the process of designing anisotropic force responses may yield insight into the physical basis for orientation-dependence in biological mechanosensors. Here, we propose a DNA-based molecular tension sensor design wherein multivalency is used to create an orientation-dependent force response. We apply chemomechanical modeling to show that multivalency can be used to create synthetic mechanosensors with force response thresholds that vary by tens of pN with respect to force orientation.

Chemo-mechanical model of a cell as a stochastic active gel

While it is commonly observed that the shape dynamics of mammalian cells can undergo large random fluctuations, theoretical models aiming at capturing cell mechanics often focus on the deterministic part of the motion. In this paper, we present a framework that couples an active gel model of the cell mechanical scaffold with the complex cell metabolic system stochastically delivering the chemical energy needed to sustain an active stress in the scaffold. Our closure assumption setting the magnitude of the fluctuations is that the chemo-mechanical free energy of the cell is controlled at a target homeostatic value. Our model rationalizes the experimental observation that the cell shape fluctuations depend on the mechanical environment that constraints the cell. We apply our framework to the simple case of a cell migrating on a one dimensional track to successfully capture the different regimes of the cell mean square displacement along the track as well as the magnitude of the long time scale effective diffusive motion of the cell.

Chemo-mechanical modeling of static fatigue of high density polyethylene in bleach solution

High density polyethylene (HDPE) is increasingly used in infrastructure applications with a design service lifetime of several decades. In many cases, the HDPE member is exposed to a corrosive environment, such as in pipes carrying potable water, where the dissolved bleach selectively attacks the loosely packed amorphous phase of the polymer. The failure mechanism of HDPE transitions from a ductile to a brittle mode as the corrosion level increases. This leads to subcritical crack propagation, which deteriorates the load capacity of the structure. In this study, we develop a coupled chemo-mechanical model to simulate stress corrosion cracking (SCC) in HDPE members exposed to a bleach solution. The mechanical response of the polymer is described by a constitutive model that separately considers the individual deformation and damage behaviors of the amorphous and the crystalline phases. The model accounts for the intermolecular deformation and homogeneous void growth in the crystalline and amorphous phases, along with the resistance of the entangled network and craze damage in the amorphous phase. The embrittlement due to corrosion is captured by relating the constitutive parameters of amorphous phase to the molecular weight of the polymer. The diffusion and chemical reaction of bleach are described by a reduced order kinetics model that links the extent of polymer oxidation to the reduction of the molecular weight. The material constitutive model and diffusion–reaction model are combined in a single finite element (FE) code to investigate the SCC behavior of double edge notched HDPE specimens. The simulation yields the stress-life curves and fracture kinetics under different environments. The predicted stress-life curve qualitatively matches the measured stress-life data of polymer pipes. It is shown that the stress-life curve exhibits different regimes corresponding to distinct failure mechanisms, as indicated by the stress and strain distributions in the specimen.

A Chemomechanical Model for Regulation of Contractility in the Embryonic Brain Tube.

Morphogenesis is regulated by genetic, biochemical, and biomechanical factors, but the feedback controlling the interactions between these factors remains poorly understood. A previous study has found that compressing the brain tube of the early chick embryo induces changes in contractility and nuclear shape in the neuroepithelial wall. Assuming this response involves mechanical feedback, we use experiments and computational modeling to investigate a hypothetical mechanism behind the observed behavior. First, we measured nuclear circularity in embryonic chick brains subjected to transverse compression. Immediately after loading, the circularity varied regionally and appeared to reflect the local state of stress in the wall. After three hours of culture with sustained compression, however, the nuclei became rounder. Exposure to a gap junction blocker inhibited this response, suggesting that it requires intercellular diffusion of a biochemical signal. We speculate that the signal regulates the contraction that occurs near the lumen, altering stress distributions and nuclear geometry throughout the wall. Simulating compression using a chemomechanical finite-element model based on this idea shows that our hypothesis is consistent with most of the experimental data. This work provides a foundation for future investigations of chemomechanical feedback in epithelia during embryonic development.

A common ATP-dependent stepping model for kinesin-5 and kinesin-1: Mechanism of bi-directionality of kinesin-5

Kinesin-5 and kinesin-1 proteins are two families of kinesin superfamily molecular motors that can move processively on microtubules powered by ATP hydrolysis. Kinesin-1 is a unidirectional motor. By contrast, some yeast kinesin-5 motors are bidirectional and the directionality can be switched by changing the experimental conditions. Here, on the basis of a common chemomechanical coupling model, the dynamics of kinesin-1 and in particular the dynamics of kinesin-5 is studied theoretically, explaining the available experimental data. For example, the experimental data about different movement directions under different experimental conditions for kinesin-5 are explained well. The origin of why kinesin-1 can only make unidirectional movement and kinesin-5 can make bidirectional movements is revealed. The origin of mutations or deletions of several structural elements affecting the directionality of kinesin-5 is revealed. Moreover, some predicted results for kinesin-5 are provided.

Chemo-Mechanical Phase-Field Modeling of Iron Oxide Reduction with Hydrogen

The reduction of iron ore with carbon-carriers is one of the largest sources of greenhouse gas emissions in the industry, motivating global activities to replace the coke-based blast furnace reduction by hydrogen-based direct reduction (HyDR). Iron oxide reduction with hydrogen has been widely investigated both experimentally and theoretically. The process includes multiple types of chemical reactions, solid state and defect-mediated diffusion (by oxygen and hydrogen species), several phase transformations, as well as massive volume shrinkage and mechanical stress buildup. In this work, a chemo-mechanically coupled phase-field (PF) model has been developed to explore the interplay between phase transformation, chemical reaction, species diffusion, large elasto-plastic deformation and microstructure evolution. Energetic constitutive relations of the model are based on the system free energy which is calibrated with the help of a thermodynamic database. The model has been first applied to the classical core-shell (w\ustite-iron) structure. Simulations show that the phase transformation from w\ustite to alpha-iron can result in high stress and rapidly decelerating reaction kinetics. Mechanical stresses can contribute elastic energy to the system, making phase transformation difficult. Thus slow reaction kinetics and low metallization are observed. However, if the stress becomes comparatively high, it can shift the shape of the free energy from a double-well to a single-well case and speed up the transformation. The model has been further applied to simulate an actual iron oxide specimen with its complex microstructure, characterized by electron microscopy. The simulation results show that isolated pores in the microstructure are filled with water vapor during reduction, an effect which influences the local reaction atmosphere and dynamics.

Stress Evolution in Lithium Metal Electrodes and the Impact of Artificial Passivating Layers

The potential advantages of lithium (Li) metal anodes have been widely touted (lowest reduction potential, etc.). However, the poor stability of Li metal / liquid electrolyte interfaces leads to chronic problems, such as dendrite formation and capacity loss. The possible impact of mechanical effects on interface stability and dendrite formation is a critical question that is difficult to probe directly. In-situ curvature measurements are an important tool for monitoring stresses during battery cycling. Using this technique during Li plating and examining film thickness effects, it is possible to separate contributions from the bulk lithium metal and the solid electrolyte interphase (SEI). These investigations show that significant stresses are created in the SEI films. Similar stress evolution measurements were also performed during lithium plating and stripping using both soft (PEO) and hard (LiF) artificial surface layers. The results indicate that stresses in surface films can be tuned to improve performance when artificial SEI layers are employed. A basic chemo-mechanical model indicates that hybridizing the two layers may benefit interface stability and performance in Li metal anodes.

Effect of myofibril architecture on the active contraction of dystrophic muscle. A mathematical model

Duchenne muscular dystrophy (DMD) is a muscle degenerative disease caused by a mutation in the dystrophin gene. The lack of dystrophin leads to persistent inflammation, degeneration/regeneration cycles of muscle fibers, Ca2＋ dysregulation, incompletely regenerated fibers, necrosis, fibrotic tissue replacement, and alterations in the fiber ultrastructure i.e., myofibril misalignment and branched fibers. This work aims to develop a comprehensive chemo-mechanical model of muscle-skeletal tissue accounting for dispersion in myofibrillar orientations, in addition to the disorders in sarcomere pattern and the fiber branching. The model results confirm a significant correlation between the myofibrillar dispersion and the reduction of isometric force in the dystrophic muscle and indicate that the reduction of contraction velocity in the dystrophic muscle seems to be associated with the local disorders in the sarcomere patterns of the myofibrils. Also, the implemented model can predict the force–velocity response to both concentric and eccentric loading. The resulting model represents an original approach to account for defects in the muscle ultrastructure caused by pathologies as DMD.

Microstructure evolution and intermediate phase-induced varying solubility limits and stress reduction behavior in sodium ion batteries particles of Na[formula omitted]FePO[formula omitted] ([formula omitted

The cathode material NaxFePO4 (0<x<1) of sodium-ion batteries displays complex phase segregation processes with the existence of an intermediate phase, and large volume change during charging/discharging. A chemo-mechanical phase-field model is developed to capture the thermodynamics of phase segregation along with the structural change that occurs in NaxFePO4. The multiwell potential of NaxFePO4 for the full range of concentration is constructed for the first time. This new model not only captures phase segregation into a sodium-poor phase FePO4 and a sodium-rich phase Na2∕3FePO4 but also the solid-solution phase NaxFePO4 (2∕3<x<1). The microstructure evolution in the whole processes of sodiation and desodiation is investigated. The stress assisted diffusion induces the striking behavior of the maximum solubility limit going beyond 2/3 even within two-phase coexistence. Further, the formation of an intermediate phase leads to varying solubility limits which agrees with recent experimental observation, as well as a stress reduction behavior. Finally, our work suggests that prolate NaxFePO4 particles are mechanically more reliable due to nearly stress-free phases. We expect that the intermediate phase-induced stress reduction behavior provides a new concept for improving mechanical stability and thus better battery performance.

Chemo-mechanical modeling of stress evolution in all-solid-state lithium-ion batteries using synchrotron transmission X-ray microscopy tomography

Abstract In this study, a chemo-mechanical modeling framework was developed by adopting a reconstructed three-dimensional morphology of all-solid-state lithium-ion battery (ASSB) composite electrodes, using a synchrotron transmission X-ray microscopy tomography system. The developed model aimed to elucidate the effects of the electrode microstructure, specifically solid electrolyte/active material (SE/AM) interface and void space, toward the lithiation-induced stress evolution. The results show that the peak stress points happen at the SE/AM interface, while void space can partially accommodate the AM swelling and alleviate the stress formation. Although applying higher pressing pressure during the electrode fabrication can improve the ion pathways, it adversely affects the stress formation and may cause crack propagation. The results reveal that SE stiffness has a key impact on stress formation and AM displacement. Although employing SE with a lower stiffness can attenuate the stress within the microstructure, it can exacerbate the anisotropic displacement of AM particles. In contrast, applying external pressing pressure can prevent anisotropic displacement of AM particles. The developed framework highlights the significance of microstructural design of ASSBs and provides invaluable insights.

Progressive interface debonding in composite electrodes of Li-ion batteries via mixed-mode cohesive zone model: Effects of binder characteristics

A considerable portion of the electrode is made of non-active materials such as binders, these not only regulate the ionic and electronic diffusion pathways, but also play an important role in enhancing the mechanical stability of the active materials. The volumetric expansion/contraction associated with lithiation/delithiation of the active material may lead to particle–binder interfacial debonding, which in turn disrupts the lithium and electronic conduction in the electrode. Since the morphological and material properties of the binder greatly vary in the particle–binder network, in this paper, the effects of binder features on interfacial debonding are investigated using two-way coupling of the chemo-mechanical and mixed-mode cohesive-zone models. The series of simulations we carried out showed that increases in active particle size and binder content prevent debonding, in contrast, increases in the Young’s modulus and ionic conductivity of the binder promote debonding.