scholarly journals A one-dimensional individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation

2019 ◽  
Vol 475 (2227) ◽  
pp. 20180838 ◽  
Author(s):  
R. J. Murphy ◽  
P. R. Buenzli ◽  
R. E. Baker ◽  
M. J. Simpson
Keyword(s):  
Mechanical Model ◽  
Numerical Solutions ◽  
Cell Movement ◽  
Biological Tissues ◽  
Tissue Level ◽  
Cellular Level ◽  
Coarse Grained ◽  
Mechanical Heterogeneity ◽  
Single Scale ◽  
The Individual

Mechanical heterogeneity in biological tissues, in particular stiffness, can be used to distinguish between healthy and diseased states. However, it is often difficult to explore relationships between cellular-level properties and tissue-level outcomes when biological experiments are performed at a single scale only. To overcome this difficulty, we develop a multi-scale mathematical model which provides a clear framework to explore these connections across biological scales. Starting with an individual-based mechanical model of cell movement, we subsequently derive a novel coarse-grained system of partial differential equations governing the evolution of the cell density due to heterogeneous cellular properties. We demonstrate that solutions of the individual-based model converge to numerical solutions of the coarse-grained model, for both slowly-varying-in-space and rapidly-varying-in-space cellular properties. We discuss applications of the model, such as determining relative cellular-level properties and an interpretation of data from a breast cancer detection experiment.

scholarly journals An individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation

2018 ◽  
Author(s):  
R. J. Murphy ◽  
P. R. Buenzli ◽  
R. E. Baker ◽  
M. J. Simpson
Keyword(s):  
Mechanical Model ◽  
Numerical Solutions ◽  
Cell Movement ◽  
Biological Tissues ◽  
Tissue Level ◽  
Cellular Level ◽  
Coarse Grained ◽  
Mechanical Heterogeneity ◽  
Single Scale ◽  
The Individual

AbstractMechanical heterogeneity in biological tissues, in particular stiffness, can be used to distinguish between healthy and diseased states. However, it is often difficult to explore relationships between cellular-level properties and tissue-level outcomes when biological experiments are performed at a single scale only. To overcome this difficulty we develop a multi-scale mathematical model which provides a clear framework to explore these connections across biological scales. Starting with an individual-based mechanical model of cell movement, we subsequently derive a novel coarse-grained system of partial differential equations governing the evolution of the cell density due to heterogeneous cellular properties. We demonstrate that solutions of the individual-based model converge to numerical solutions of the coarse-grained model, for both slowly-varying-in-space and rapidly-varying-in-space cellular properties. Applications of the model are discussed, including determining relative cellular-level properties and an interpretation of data from a breast cancer detection experiment.

scholarly journals QuickStitch for seamless stitching of confocal mosaics through high-pass filtering and recursive normalization

2016 ◽  
Author(s):  
Pavel A. Brodskiy ◽  
Paulina M. Eberts ◽  
Cody Narciso ◽  
Jochen Kursawe ◽  
Alexander Fletcher ◽  
...  
Keyword(s):  
Open Source ◽  
Large Scale ◽  
Imaging System ◽  
Tissue Level ◽  
Cellular Level ◽  
Specific Information ◽  
Open Source Tool ◽  
The Individual ◽  
User Friendly ◽  
High Pass

ABSTRACTFluorescence micrographs naturally exhibit darkening around their edges (vignetting), which makes seamless stitching challenging. If vignetting is not corrected for, a stitched image will have visible seams where the individual images (tiles) overlap, introducing a systematic error into any quantitative analysis of the image. Although multiple vignetting correction methods exist, there remains no open-source tool that robustly handles large 2D immunofluorescence-based mosaic images. Here, we develop and validate QuickStitch, a tool that applies a recursive normalization algorithm to stitch large-scale immunofluorescence-based mosaics without incurring vignetting seams. We demonstrate how the tool works successfully for tissues of differing size, morphology, and fluorescence intensity. QuickStitch requires no specific information about the imaging system. It is provided as an open-source tool that is both user friendly and extensible, allowing straightforward incorporation into existing image processing pipelines. This enables studies that require accurate segmentation and analysis of high-resolution datasets when parameters of interest include both cellular-level phenomena and larger tissue-level regions of interest.

scholarly journals Multiscale Eulerian CFD of Chemical Processes: A Review

2020 ◽  
Vol 4 (2) ◽  
pp. 23 ◽  
Author(s):  
Son Ich Ngo ◽  
Young-Il Lim
Keyword(s):  
Bubble Columns ◽  
Coarse Grained ◽  
Navier Stokes ◽  
Digital Twins ◽  
Single Scale ◽  
Liquid Bubble ◽  
Coupling Strategy ◽  
Computational Fluid Dynamics Cfd ◽  
Individual Scale ◽  
The Individual

This review covers the scope of multiscale computational fluid dynamics (CFD), laying the framework for studying hydrodynamics with and without chemical reactions in single and multiple phases regarded as continuum fluids. The molecular, coarse-grained particle, and meso-scale dynamics at the individual scale are excluded in this review. Scoping single-scale Eulerian CFD approaches, the necessity of multiscale CFD is highlighted. First, the Eulerian CFD theory, including the governing and turbulence equations, is described for single and multiple phases. The Reynolds-averaged Navier–Stokes (RANS)-based turbulence model such as the standard k-ε equation is briefly presented, which is commonly used for industrial flow conditions. Following the general CFD theories based on the first-principle laws, a multiscale CFD strategy interacting between micro- and macroscale domains is introduced. Next, the applications of single-scale CFD are presented for chemical and biological processes such as gas distributors, combustors, gas storage tanks, bioreactors, fuel cells, random- and structured-packing columns, gas-liquid bubble columns, and gas-solid and gas-liquid-solid fluidized beds. Several multiscale simulations coupled with Eulerian CFD are reported, focusing on the coupling strategy between two scales. Finally, challenges to multiscale CFD simulations are discussed. The need for experimental validation of CFD results is also presented to lay the groundwork for digital twins supported by CFD. This review culminates in conclusions and perspectives of multiscale CFD.

Freezing-Induced Cell-Fluid-Matrix Interaction in Engineered Tissue

2008 ◽  
Author(s):  
Junkyu Jung ◽  
Ka Yaw Teo ◽  
J. Craig Dutton ◽  
Bumsoo Han
Keyword(s):  
Extracellular Matrix ◽  
Biological Tissues ◽  
Tissue Level ◽  
Cellular Level ◽  
Tissue Type ◽  
Freezing And Thawing ◽  
Matrix Interaction ◽  
Engineered Tissues ◽  
Quantitative Understanding ◽  
Engineered Tissue

Freezing of biological tissues occurs in cryomedicine applications such as cryosurgery and cryopreservation. Although cellular level biophysics during freezing and thawing (F/T) has been extensively studied, tissue level biophysics is not fully understood yet. Especially, the effects of F/T on the functionalities of tissue are not well understood so that the outcomes of cryomedicine applications are highly tissue-type dependent [1]. Although many of the functionalities are associated with the extracellular matrix (ECM), the effect of F/T on ECM microstructure has been overlooked. Quantitative understanding on the post-thaw ECM structure is rarely available, but it is essential to design and improve cryopresevation and cryotherapy protocols for a wide variety of native and engineered tissues.

scholarly journals Hierarchical modeling of mechano-chemical dynamics of epithelial sheets across cells and tissue

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yoshifumi Asakura ◽  
Yohei Kondo ◽  
Kazuhiro Aoki ◽  
Honda Naoki
Keyword(s):  
Wound Healing ◽  
Cell Migration ◽  
Continuum Model ◽  
Tissue Level ◽  
Chemical Signals ◽  
Cellular Level ◽  
Mathematical Framework ◽  
Collective Cell Migration ◽  
The Continuum ◽  
Cell Cell

AbstractCollective cell migration is a fundamental process in embryonic development and tissue homeostasis. This is a macroscopic population-level phenomenon that emerges across hierarchy from microscopic cell-cell interactions; however, the underlying mechanism remains unclear. Here, we addressed this issue by focusing on epithelial collective cell migration, driven by the mechanical force regulated by chemical signals of traveling ERK activation waves, observed in wound healing. We propose a hierarchical mathematical framework for understanding how cells are orchestrated through mechanochemical cell-cell interaction. In this framework, we mathematically transformed a particle-based model at the cellular level into a continuum model at the tissue level. The continuum model described relationships between cell migration and mechanochemical variables, namely, ERK activity gradients, cell density, and velocity field, which could be compared with live-cell imaging data. Through numerical simulations, the continuum model recapitulated the ERK wave-induced collective cell migration in wound healing. We also numerically confirmed a consistency between these two models. Thus, our hierarchical approach offers a new theoretical platform to reveal a causality between macroscopic tissue-level and microscopic cellular-level phenomena. Furthermore, our model is also capable of deriving a theoretical insight on both of mechanical and chemical signals, in the causality of tissue and cellular dynamics.

scholarly journals Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization

2014 ◽  
Vol 11 (97) ◽  
pp. 20140352 ◽  
Author(s):  
Alfonso Bueno-Orovio ◽  
David Kay ◽  
Vicente Grau ◽  
Blanca Rodriguez ◽  
Kevin Burrage
Keyword(s):  
Structural Heterogeneity ◽  
Biological Tissues ◽  
Tissue Level ◽  
Fractional Diffusion ◽  
Diffusion Models ◽  
Excitable Media ◽  
Research Fields ◽  
Dispersion Of Repolarization ◽  
Electrical Propagation

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

scholarly journals Extended logistic growth model for heterogeneous populations

2017 ◽  
Author(s):  
Wang Jin ◽  
Scott W McCue ◽  
Matthew J Simpson
Keyword(s):  
Cell Proliferation ◽  
Growth Model ◽  
Numerical Solutions ◽  
Cellular Level ◽  
Logistic Growth ◽  
Logistic Growth Model ◽  
Living Tissues ◽  
Discrete Mathematical Model ◽  
The Continuum

AbstractCell proliferation is the most important cellular-level mechanism responsible for regulating cell population dynamics in living tissues. Modern experimental procedures show that the proliferation rates of individual cells can vary significantly within the same cell line. However, in the mathematical biology literature, cell proliferation is typically modelled using a classical logistic equation which neglects variations in the proliferation rate. In this work, we consider a discrete mathematical model of cell migration and cell proliferation, modulated by volume exclusion (crowding) effects, with variable rates of proliferation across the total population. We refer to this variability as heterogeneity. Constructing the continuum limit of the discrete model leads to a generalisation of the classical logistic growth model. Comparing numerical solutions of the model to averaged data from discrete simulations shows that the new model captures the key features of the discrete process. Applying the extended logistic model to simulate a proliferation assay using rates from recent experimental literature shows that neglecting the role of heterogeneity can, at times, lead to misleading results.

scholarly journals Controlling the length of porphyrin supramolecular polymers via coupled equilibria and dilution-induced supramolecular polymerization

2022 ◽  
Vol 13 (1) ◽  
Author(s):  
Elisabeth Weyandt ◽  
Luigi Leanza ◽  
Riccardo Capelli ◽  
Giovanni M. Pavan ◽  
Ghislaine Vantomme ◽  
...  
Keyword(s):  
Complex Systems ◽  
Self Assembly ◽  
Chiral Discrimination ◽  
Coarse Grained ◽  
Supramolecular Polymers ◽  
Supramolecular System ◽  
Precise Control ◽  
Aggregate Morphology ◽  
The Individual ◽  
Supramolecular Polymerization

AbstractMulti-component systems often display convoluted behavior, pathway complexity and coupled equilibria. In recent years, several ways to control complex systems by manipulating the subtle balances of interaction energies between the individual components have been explored and thereby shifting the equilibrium between different aggregate states. Here we show the enantioselective chain-capping and dilution-induced supramolecular polymerization with a Zn2+-porphyrin-based supramolecular system when going from long, highly cooperative supramolecular polymers to short, disordered aggregates by adding a monotopic Mn3+-porphyrin monomer. When mixing the zinc and manganese centered monomers, the Mn3+-porphyrins act as chain-cappers for Zn2+-porphyrin supramolecular polymers, effectively hindering growth of the copolymer and reducing the length. Upon dilution, the interaction between chain-capper and monomers weakens as the equilibria shift and long supramolecular polymers form again. This dynamic modulation of aggregate morphology and length is achieved through enantioselectivity in the aggregation pathways and concentration-sensitive equilibria. All-atom and coarse-grained molecular simulations provide further insights into the mixing of the species and their exchange dynamics. Our combined experimental and theoretical approach allows for precise control of molecular self-assembly and chiral discrimination in complex systems.

scholarly journals Structure and mechanics of aegagropilae fiber network

2017 ◽  
Vol 114 (18) ◽  
pp. 4607-4612 ◽  
Author(s):  
Gautier Verhille ◽  
Sébastien Moulinet ◽  
Nicolas Vandenberghe ◽  
Mokhtar Adda-Bedia ◽  
Patrice Le Gal
Keyword(s):  
Mechanical Response ◽  
Posidonia Oceanica ◽  
Biological Tissues ◽  
Individual Response ◽  
Fiber Network ◽  
Friction Forces ◽  
Fiber Clustering ◽  
Wide Range ◽  
Natural Aggregates ◽  
The Individual

Fiber networks encompass a wide range of natural and manmade materials. The threads or filaments from which they are formed span a wide range of length scales: from nanometers, as in biological tissues and bundles of carbon nanotubes, to millimeters, as in paper and insulation materials. The mechanical and thermal behavior of these complex structures depends on both the individual response of the constituent fibers and the density and degree of entanglement of the network. A question of paramount importance is how to control the formation of a given fiber network to optimize a desired function. The study of fiber clustering of natural flocs could be useful for improving fabrication processes, such as in the paper and textile industries. Here, we use the example of aegagropilae that are the remains of a seagrass (Posidonia oceanica) found on Mediterranean beaches. First, we characterize different aspects of their structure and mechanical response, and second, we draw conclusions on their formation process. We show that these natural aggregates are formed in open sea by random aggregation and compaction of fibers held together by friction forces. Although formed in a natural environment, thus under relatively unconstrained conditions, the geometrical and mechanical properties of the resulting fiber aggregates are quite robust. This study opens perspectives for manufacturing complex fiber network materials.

scholarly journals Skillful Climate Forecasts of the Tropical Indo-Pacific Ocean Using Model-Analogs

2018 ◽  
Vol 31 (14) ◽  
pp. 5437-5459 ◽  
Author(s):  
Hui Ding ◽  
Matthew Newman ◽  
Michael A. Alexander ◽  
Andrew T. Wittenberg
Keyword(s):  
General Circulation ◽  
General Circulation Models ◽  
Coarse Grained ◽  
Seasonal Forecasts ◽  
Multimodel Ensemble ◽  
Initial State ◽  
The North ◽  
Eastern Equatorial Pacific ◽  
Spread Model ◽  
The Individual

Seasonal forecasts made by coupled atmosphere–ocean general circulation models (CGCMs) undergo strong climate drift and initialization shock, driving the model state away from its long-term attractor. Here we explore initializing directly on a model’s own attractor, using an analog approach in which model states close to the observed initial state are drawn from a “library” obtained from prior uninitialized CGCM simulations. The subsequent evolution of those “model-analogs” yields a forecast ensemble, without additional model integration. This technique is applied to four of the eight CGCMs comprising the North American Multimodel Ensemble (NMME) by selecting from prior long control runs those model states whose monthly tropical Indo-Pacific SST and SSH anomalies best resemble the observations at initialization time. Hindcasts are then made for leads of 1–12 months during 1982–2015. Deterministic and probabilistic skill measures of these model-analog hindcast ensembles are comparable to those of the initialized NMME hindcast ensembles, for both the individual models and the multimodel ensemble. In the eastern equatorial Pacific, model-analog hindcast skill exceeds that of the NMME. Despite initializing with a relatively large ensemble spread, model-analogs also reproduce each CGCM’s perfect-model skill, consistent with a coarse-grained view of tropical Indo-Pacific predictability. This study suggests that with little additional effort, sufficiently realistic and long CGCM simulations provide the basis for skillful seasonal forecasts of tropical Indo-Pacific SST anomalies, even without sophisticated data assimilation or additional ensemble forecast integrations. The model-analog method could provide a baseline for forecast skill when developing future models and forecast systems.

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