Complex Cell Geometry Research Articles

A Simulation Framework for Electrochemical Processes with Electrolyte Flow

Software tools for simulating electrochemical processes (e.g. COMSOL Multiphysics, ELSYCA) are mostly of commercial type. Besides, three-dimensional simulations in complex cell geometries are known to become resource-expensive, as typically thin concentration boundary layers need to be resolved. This work presents a simulation framework for electrochemical processes based on the open source platform OpenFOAM. The finite volume method used and combined with domain decomposition is able to efficiently benefit from multi-core computer architectures. Our framework takes into account electrolyte flow, which is well known to affect mass transfer, and allows to consider multi-species electrolytes and forcing of the electrolyte. The stability and fast convergence of the method presented is found to rely on the linearization of the Butler-Volmer condition in the iterative solver. The framework is validated against an analytical solution valid for simplified conditions and an electrodeposition process at a conically shaped electrode in an external magnetic field. The latter exhibits transient departure of the concentration boundary layer from the cathode, and excellent agreement with COMSOL simulation results is found.

Beyond analytic solution: Analysis of FRAP experiments by spatial simulation of the forward problem

Fluorescence redistribution after photobleaching is a commonly used method to understand the dynamic behavior of molecules within cells. Analytic solutions have been developed for specific, well-defined models of dynamic behavior in idealized geometries, but these solutions are inaccurate in complex geometries or when complex binding and diffusion behaviors exist. We demonstrate the use of numerical reaction-diffusion simulations using the Virtual Cell software platform to model fluorescence redistribution after photobleaching experiments. Multiple simulations employing parameter scans and varying bleaching locations and sizes can help to bracket diffusion coefficients and kinetic rate constants in complex image-based geometries. This approach is applied to problems in membrane surface diffusion as well as diffusion and binding in cytosolic volumes in complex cell geometries. In addition, we model diffusion and binding within phase-separated biomolecular condensates (liquid droplets). These are modeled as spherical low-affinity binding domains that also define a high viscosity medium for exchange of the free fluorescently labeled ligand with the external cytosol.

Vat photopolymerization of fly-like, complex micro-architectures with dissolvable supports

Recent advances in additive manufacturing of complex geometries enabled the creation of mechanical metamaterials whose exotic properties are based on local control of complex cell geometries. Overhanging and free-hanging features that lack continuous support layers in the previous build volume cannot be directly manufactured, imposing a major design limitation. The resulting metamaterials are limited to single homogenous structural materials, and inherently self-supporting geometries, resulting in constraints of achievable architectures. Realizing arbitrary features is compelling but is inherently limited by process and material support constraints. Here we present a novel light-based additive manufacturing approach capable of printing arbitrary micro-architectures comprising a large array of internally suspended features, large span overhang, and high aspect ratio struts. This method eliminates the need for manual removal of internal supports and enables a suite of multi-functional metamaterials with a range of designed properties, including wide bandgaps for elastic waves at low frequency, switchable wave transmissions, and products requiring no post support removal. We describe the synthesis and rapid printing of a variety of metamaterials comprising an extensive array of suspended features and demonstrate their metamaterial behaviors. The proposed approach removes scale and unit cell limitations and is capable of achieving embedded features across multiple materials.

Advanced in silico validation framework for three-dimensional traction force microscopy and application to an in vitro model of sprouting angiogenesis

In the last decade, cellular forces in three-dimensional hydrogels that mimic the extracellular matrix have been calculated by means of Traction Force Microscopy (TFM). However, characterizing the accuracy limits of a traction recovery method is critical to avoid obscuring physiological information due to traction recovery errors. So far, 3D TFM algorithms have only been validated using simplified cell geometries, bypassing image processing steps or arbitrarily simulating focal adhesions. Moreover, it is still uncertain which of the two common traction recovery methods, i.e., forward and inverse, is more robust against the inherent challenges of 3D TFM. In this work, we established an advanced in silico validation framework that is applicable to any 3D TFM experimental setup and that can be used to correctly couple the experimental and computational aspects of 3D TFM. Advancements relate to the simultaneous incorporation of complex cell geometries, simulation of microscopy images of varying bead densities and different focal adhesion sizes and distributions. By measuring the traction recovery error with respect to ground truth solutions, we found that while highest traction recovery errors occur for cases with sparse and small focal adhesions, our implementation of the inverse method improves two-fold the accuracy with respect to the forward method (average error of 23% vs. 50%). This advantage was further supported by recovering cellular tractions around angiogenic sprouts in an in vitro model of angiogenesis. The inverse method recovered higher traction peaks and a clearer pulling pattern at the sprout protrusion tips than the forward method. Statement of significanceBiomaterial performance is often studied by quantifying cell-matrix mechanical interactions by means of Traction Force Microscopy (TFM). However, 3D TFM algorithms are often validated in simplified scenarios, which do not allow to fully assess errors that could obscure physiological information. Here, we established an advanced in silico validation framework that mimics real TFM experimental conditions and that characterizes the expected errors of a 3D TFM workflow. We apply this framework to demonstrate the enhanced accuracy of a novel inverse traction recovery method that is illustrated in the context of an in vitro model of sprouting angiogenesis. Together, our study shows the importance of a proper traction recovery method to minimise errors and the need for an advanced framework to assess those errors.

Numerical conformal mapping method vs. geometrical separation attitude: Combustion motor chamber internal flow simulation

AbstractThis paper describes the numerical solution of flow analysis in a two‐dimensional combustion chamber with two parallel inlets aided for propellants entrance, addressing a number of different problems that depend on each other: the flow affected by a discrete point in‐cell vortex, the velocity affected by the flow regime in the cell, and the combustion problem affected by the oxygen and fuel entries from the cell walls. The shape geometry of the combustion chamber is made from a square section connected with a semi‐circular one. The mathematical model of the problem consists of an inhomogeneous stream function Laplace equation coupled to partial differential mass conservation equation subjected to a wall non‐intrusion condition and known mass values in the wall openings. Algebraic conformal mapping transformation has been used for modeling the complex cell geometry. The solution was obtained by using the iterative Gauss–Seidel method for both the current function and the mass calculation. Comparison with another modeling method for calibration purpose was performed; considering each geometrical component separately whereas continuous conditions were applied between the two sections. The grid types are: (1) a uniform grid in Cartesian coordinates in the square part, and (2) a uniform circular grid in polar coordinates. It was found that different initial guesses have not effect on the final solution, but an informed initial guess affects the solution time convergence iterations number to solve the problem. Finally, the effect of the mixing vortex on the location of the flame front in the chamber was investigated.

Image-based multi-scale mechanical analysis of strain amplification in neurons embedded in collagen gel

A general multi-scale strategy is presented for modeling the mechanical environment of a group of neurons that were embedded within a collagenous matrix. The results of the multi-scale simulation are used to estimate the local strains that arise in neurons when the extracellular matrix is deformed. The distribution of local strains was found to depend strongly on the configuration of the embedded neurons relative to the loading direction, reflecting the anisotropic mechanical behavior of the neurons. More importantly, the applied strain on the surrounding extracellular matrix is amplified in the neurons for all loading configurations that are considered. In the most severe case, the applied strain is amplified by at least a factor of 2 in 10% of the neurons' volume. The approach presented in this paper provides an extension to the capability of past methods by enabling the realistic representation of complex cell geometry into a multi-scale framework. The simulation results for the embedded neurons provide local strain information that is not accessible by current experimental techniques.

Numerical Simulation of Multiphase Magnetohydrodynamic Flow and Deformation of Electrolyte–Metal Interface in Aluminum Electrolysis Cells

A computational fluid dynamics based multiphase magnetohydrodynamic (MHD) flow model for simulating the melt flow and bath–metal interface deformation in realistic aluminum reduction cells is presented. The model accounts for the complex physics of the MHD problem in aluminum reduction cells by coupling two immiscible fluids, electromagnetic field, Lorentz force, flow turbulence, and complex cell geometry with large length scale. Especially, the deformation of bath–metal interface is tracked directly in the simulation, and the condition of constant anode–cathode distance (ACD) is maintained by moving anode bottom dynamically with the deforming bath–metal interface. The metal pad deformation and melt flow predicted by the current model are compared to the predictions using a simplified model where the bath–metal interface is assumed flat. The effects of the induced electric current due to fluid flow and the magnetic field due to the interior cell current on the metal pad deformation and melt flow are investigated. The presented model extends the conventional simplified box model by including detailed cell geometry such as the ledge profile and all channels (side, central, and cross-channels). The simulations show the model sensitivity to different side ledge profiles and the cross-channel width by comparing the predicted melt flow and metal pad heaving. In addition, the model dependencies upon the reduction cell operation conditions such as ACD, current distribution on cathode surface and open/closed channel top, are discussed.

A fast platform for simulating semi-flexible fiber suspensions applied to cell mechanics

We present a novel platform for the large-scale simulation of three-dimensional fibrous structures immersed in a Stokesian fluid and evolving under confinement or in free-space in three dimensions. One of the main motivations for this work is to study the dynamics of fiber assemblies within biological cells. For this, we also incorporate the key biophysical elements that determine the dynamics of these assemblies, which include the polymerization and depolymerization kinetics of fibers, their interactions with molecular motors and other objects, their flexibility, and hydrodynamic coupling. This work, to our knowledge, is the first technique to include many-body hydrodynamic interactions (HIs), and the resulting fluid flows, in cellular assemblies of flexible fibers. We use non-local slender body theory to compute the fluid–structure interactions of the fibers and a second-kind boundary integral formulation for other rigid bodies and the confining boundary. A kernel-independent implementation of the fast multipole method is utilized for efficient evaluation of HIs. The deformation of the fibers is described by nonlinear Euler–Bernoulli beam theory and their polymerization is modeled by the reparametrization of the dynamic equations in the appropriate non-Lagrangian frame. We use a pseudo-spectral representation of fiber positions and implicit time-stepping to resolve large fiber deformations, and to allow time-steps not excessively constrained by temporal stiffness or fiber–fiber interactions. The entire computational scheme is parallelized, which enables simulating assemblies of thousands of fibers. We use our method to investigate two important questions in the mechanics of cell division: (i) the effect of confinement on the hydrodynamic mobility of microtubule asters; and (ii) the dynamics of the positioning of mitotic spindle in complex cell geometries. Finally to demonstrate the general applicability of the method, we simulate the sedimentation of a cloud of semi-flexible fibers.

Complex cell geometry and sources distribution model for Monte Carlo single cell dosimetry with iodine 125 radioimmunotherapy

In cellular dosimetry, common assumptions consider concentric spheres for nucleus and cell and uniform radionuclides distribution. These approximations do not reflect reality, specially in the situation of radioimmunotherapy with Auger emitters, where very short-ranged electrons induce hyper localised energy deposition. A realistic cellular dosimetric model was generated to give account of the real geometry and activity distribution, for non-internalizing and internalizing antibodies (mAbs) labelled with Auger emitter I-125. The impact of geometry was studied by comparing the real geometry obtained from confocal microscopy for both cell and nucleus with volume equivalent concentric spheres. Non-uniform and uniform source distributions were considered for each mAbs distribution. Comparisons in terms of mean deposited energy per decay, energy deposition spectra and energy-volume histograms were calculated using Geant4. We conclude that realistic models are needed, especially when energy deposition is highly non-homogeneous due to source distribution.

Lessons from the real bench: non-BRS.

Bench testing of stents used in bifurcations can provide information on the general properties that influence performance including crossing profile, radial strength, recoil, flexibility and radiopacity. Problems with device delivery can be clarified. Bench testing identified that side branch dilatation caused stent distortion and elucidated correction strategies. Bench testing led to a stent design change adding connectors between hoops to help overcome the clinical problem of longitudinal distortion. Testing on the bench can determine best deployment strategies and showed that a two-step post-dilatation strategy produced the best deployment with "crush" stenting. Scanning electron microscopy showed that withdrawal of a coronary guidewire trapped between a stent (or scaffold) and a mock arterial wall during a provisional side branch stenting strategy caused only mild linear polymer coating damage. Stent fracture can cause adverse clinical events and our repetitive bend test identified the stents most resistant to fracture. Causes of obstruction of the passage of a balloon over a wire through the side of a stent include damage to the catheter tip, complex cell geometry and inadvertent passage of a wire behind a strut. Bench testing plays a major role in validation of computer modelling of bifurcation treatments and flow alterations.

An XFEM‐based numerical strategy to model mechanical interactions between biological cells and a deformable substrate

SUMMARYContractile cells are known to constantly probe and respond to their mechanical environment through mechanosensing. Although the very mechanisms responsible for this behavior are still obscure, it is now clear that cells make full use of cross‐talks between mechanics, chemistry, and transport to organize their structure and generate forces. To investigate these processes, it is important to derive mathematical and numerical models that can accurately capture the interactions between cells and an underlying deformable substrate. The present paper therefore introduces a computational framework, based on the extended FEM (XFEM) and the level set method, to model the evolution of two‐dimensional (plane stress) cells lying on an elastic substrate whose properties can be varied. Cells are modeled with a continuum mixture approach previously developed by the authors to describe key phenomena of cell sensing, such as stress fiber formation, mechanosensitive contraction, and molecular transport whereas cell–substrate adhesion is formulated with a linear elastic cohesive model. From a numerical viewpoint, cell and substrate are discretized on a single, regular finite element mesh, whereas the potentially complex cell geometry is defined in terms of a level set function that is independent of discretization. Field discontinuities across the cell membrane are then naturally enforced using enriched shape functions traditionally used in the XFEM formulation. The resulting method provides a flexible platform that can handle complex cell geometries, can avoid expensive meshing techniques, and can potentially be extended to study cell growth and migration on an elastic substrate. In addition, the XFEM formalism facilitates the consideration of the cell's cortical elasticity, a feature that is known to be important during cell deformation. The proposed method is illustrated with a few biologically relevant examples of cell–substrate interactions. Generally, the method is able to capture some key phenomena observed in biological systems and displays numerical versatility and accuracy at a moderate computational cost.Copyright © 2012 John Wiley & Sons, Ltd.

Reality-Based Real-Time Cell Indentation Simulator

Training simulators that provide realistic visual and haptic feedback during cell indentation tasks are currently investigated. Complex cell geometry inherent to biological cells and intricate mechanical properties drive the need for precise mechanical and numerical modeling to assure accurate cell deformation and force calculations. Advances in alternative finite-element formulation, such as the mass-tensor approach, have reached a state, where they are applicable to model soft-cell deformation in real time. The geometrical characteristics and the mechanical properties of different cells are determined with atomic force microscopy (AFM) indentation. A real-time, haptics-enabled simulator for cell centered indentation has been developed, which utilizes the AFM data (mechanical and geometrical properties of embryonic stem cells) to accurately replicate the indentation task and predict the cell deformation during indentation in real time. This tool can be used as a mechanical marker to characterize the biological state of the cell. The operator is able to feel the change in the stiffness during cell deformation between fixed and live cells in real time. A comparative study with finite-element simulations using a commercial software and the experimental data demonstrate the effectiveness of the proposed physically based model.

Velocity interpolation and streamline tracing on irregular geometries

Streamline tracing on irregular grids requires reliable interpolation of velocity fields. We propose a new method for direct streamline tracing on polygon and polytope cells. While some numerical methods provide a basis function that can be used for interpolation, other methods provide only the fluxes at the faces of the elements. We introduce the concept of full- and raw-field methods. Full-field methods have built-in interpolation but are often not defined on general grids such as polygonal and polyhedral grids which we examine here. Also, reliability issues may arise on non-simplicial meshes in terms of not being able to reproduce constant velocity fields. We propose an interpolation in H(div) and H(curl) valid on general grids that is based on barycentric coordinates and that reproduces uniform flow. The interpolation can be used to compute the streamline directly on the complex cell geometry. The method generalizes to convex polytopes in 3D, with a restriction on the polytope topology near corners that is shown to be satisfied by several popular grid types. Numerical results confirm that the method is applicable to general grids and preserves uniform flow.

A Method for Efficient Calculation of Diffusion and Reactions of Lipophilic Compounds in Complex Cell Geometry

A general description of effects of toxic compounds in mammalian cells is facing several problems. Firstly, most toxic compounds are hydrophobic and partition phenomena strongly influence their behaviour. Secondly, cells display considerable heterogeneity regarding the presence, activity and distribution of enzymes participating in the metabolism of foreign compounds i.e. bioactivation/biotransformation. Thirdly, cellular architecture varies greatly. Taken together, complexity at several levels has to be addressed to arrive at efficient in silico modelling based on physicochemical properties, metabolic preferences and cell characteristics. In order to understand the cellular behaviour of toxic foreign compounds we have developed a mathematical model that addresses these issues. In order to make the system numerically treatable, methods motivated by homogenization techniques have been applied. These tools reduce the complexity of mathematical models of cell dynamics considerably thus allowing to solve efficiently the partial differential equations in the model numerically on a personal computer. Compared to a compartment model with well-stirred compartments, our model affords a more realistic representation. Numerical results concerning metabolism and chemical solvolysis of a polycyclic aromatic hydrocarbon carcinogen show good agreement with results from measurements in V79 cell culture. The model can easily be extended and refined to include more reactants, and/or more complex reaction chains, enzyme distribution etc, and is therefore suitable for modelling cellular metabolism involving membrane partitioning also at higher levels of complexity.

Virtual Cell modelling and simulation software environment

The Virtual Cell (VCell; http://vcell.org/) is a problem solving environment, built on a central database, for analysis, modelling and simulation of cell biological processes. VCell integrates a growing range of molecular mechanisms, including reaction kinetics, diffusion, flow, membrane transport, lateral membrane diffusion and electrophysiology, and can associate these with geometries derived from experimental microscope images. It has been developed and deployed as a web-based, distributed, client-server system, with more than a thousand world-wide users. VCell provides a separation of layers (core technologies and abstractions) representing biological models, physical mechanisms, geometry, mathematical models and numerical methods. This separation clarifies the impact of modelling decisions, assumptions and approximations. The result is a physically consistent, mathematically rigorous, spatial modelling and simulation framework. Users create biological models and VCell will automatically (i) generate the appropriate mathematical encoding for running a simulation and (ii) generate and compile the appropriate computer code. Both deterministic and stochastic algorithms are supported for describing and running non-spatial simulations; a full partial differential equation solver using the finite volume numerical algorithm is available for reaction-diffusion-advection simulations in complex cell geometries including 3D geometries derived from microscope images. Using the VCell database, models and model components can be reused and updated, as well as privately shared among collaborating groups, or published. Exchange of models with other tools is possible via import/export of SBML, CellML and MatLab formats. Furthermore, curation of models is facilitated by external database binding mechanisms for unique identification of components and by standardised annotations compliant with the MIRIAM standard. VCell is now open source, with its native model encoding language (VCML) being a public specification, which stands as the basis for a new generation of more customised, experiment-centric modelling tools using a new plug-in based platform.

Cylindrical Cell Membranes in Uniform Applied Electric Fields: Validation of a Transport Lattice Method

The frequency and time domain transmembrane voltage responses of a cylindrical cell in an external electric field are calculated using a transport lattice, which allows solution of a variety of biologically relevant transport problems with complex cell geometry and field interactions. Here we demonstrate the method for a cylindrical membrane geometry and compare results with known analytical solutions. Results of transport lattice simulations on a Cartesian lattice are found to have discrepancies with the analytical solutions due to the limited volume of the system model and approximations for the local membrane model on the Cartesian lattice. Better agreement is attained when using a triangular mesh to represent the geometry rather than a Cartesian lattice. The transport lattice method can be readily extended to more sophisticated cell, organelle, and tissue configurations. Local membrane models within a system lattice can also include nonlinear responses such as electroporation and ion-channel gating.

Effect of Water Chemistry on the Erosion-Corrosion of Aluminum in High Temperature High Velocity Water

Abstract Laboratory experiments were conducted to simulate the erosion-corrosion of aluminum fuel cladding in water-cooled, plutonium producing, nuclear reactors. Water quality was demonstrated to be critical in causing erosion-corrosion attack on aluminum in high temperature pressurized water. Very little attack occurred in distilled water, whereas attack was progressively worse in river water and well water. The extreme attack in well water was simulated by dissolving 50 ppm CaCO3 and 10 ppm SiO2 in distilled water. A distinct corrosion enhancing synergism was apparent between dissolved bicarbonate and silicate ions. In situ recordings of electrochemical potential vs time were characteristic of the extent of erosion-corrosion which was occurring on a particular specimen. Polarization resistance measurements did not have the expected sensitivity to erosion-corrosion, probably because of the complex cell geometry imposed by the erosion-corrosion testing apparatus.