Rheological Properties of Living Materials. From Cells to Tissues

Salt Effects on the Mechanical Properties of Ionic Conductive Polymer: A Molecular Dynamics Study

Functional polymers can be used as electrolyte and binder materials in solid-state batteries. This often requires performance targets in terms of both the transport and mechanical properties. In this work, a model ionic conductive polymer system, i.e., poly(ethylene oxide)-LiTFSI, was used to study the impact of salt concentrations on mechanical properties, including different types of elastic moduli and the viscoelasticity with both nonequilibrium and equilibrium molecular dynamics simulations. We found an encouragingly good agreement between experiments and simulations regarding Young's modulus, bulk modulus, and viscosity. In addition, we identified an intermediate salt concentration at which the system shows high ionic conductivity, high Young's modulus, and short elastic restoration time. Therefore, this study laid the groundwork for investigating ionic conductive polymer binders with self-healing functionality from molecular dynamics simulations.

Acoustic Wave-Induced Stroboscopic Optical Mechanotyping of Adherent Cells

In this study, a novel, high content technique using a cylindrical acoustic transducer, stroboscopic fast imaging, and homodyne detection to recover the mechanical properties (dynamic shear modulus) of living adherent cells at low ultrasonic frequencies is presented. By analyzing the micro-oscillations of cells, whole populations are simultaneously mechanotyped with sub-cellular resolution. The technique can be combined with standard fluorescence imaging allowing to further cross-correlate biological and mechanical information. The potential of the technique is demonstrated by mechanotyping co-cultures of different cell types with significantly different mechanical properties.

Fabrication and characterization of an antibacterial chitosan-coated allantoin-loaded NaCMC/SA skin scaffold for wound healing applications

The field of tissue engineering has recently emerged as one of the most promising approaches to address the limitations of conventional tissue replacements for severe injuries. This study introduces a chitosan-coated porous skin scaffold based on sodium carboxymethyl cellulose (NaCMC) and sodium alginate (SA) hydrogels, incorporating allantoin (AL) as an antibacterial agent. The NaCMC/SA hydrogel was cross-linked with epichlorohydrin (ECH) and freeze-dried to obtain a three-dimensional porous structure. The coated and non-coated scaffolds underwent comprehensive evaluation and characterization through various in-vitro analyses, including SEM imaging, swelling, degradation, and mechanical assessments. Furthermore, the scaffolds were studied regarding their allantoin (AL) release profiles, antibacterial properties, cell viability, and cell adhesion. The in-vitro analyses revealed that adding a chitosan (CS) coating and allantoin (AL) to the NaCMC/SA hydrogel significantly improved the scaffolds' antibacterial properties and cell viability. It was observed that the NaCMC:SA ratio and ECH concentration influenced the swelling capacity, biodegradation, drug release profile, and mechanical properties of the scaffolds. Samples with higher NaCMC content exhibited enhanced swelling capacity, more controlled allantoin (AL) release, and improved mechanical strength. Furthermore, the in-vivo results demonstrated that the proposed skin scaffold exhibited satisfactory biocompatibility and supported cell viability during wound healing in Wistar rats, highlighting its potential for clinical applications.

Bioabsorbable Composites Based on Polymeric Matrix (PLA and PCL) Reinforced with Magnesium (Mg) for Use in Bone Regeneration Therapy: Physicochemical Properties and Biological Evaluation

Improvements in Tissue Engineering and Regenerative Medicine (TERM)-type technologies have allowed the development of specific materials that, together with a better understanding of bone tissue structure, have provided new pathways to obtain biomaterials for bone tissue regeneration. In this manuscript, bioabsorbable materials are presented as emerging materials in tissue engineering therapies related to bone lesions because of their ability to degrade in physiological environments while the regeneration process is completed. This comprehensive review aims to explore the studies, published since its inception (2010s) to the present, on bioabsorbable composite materials based on PLA and PCL polymeric matrix reinforced with Mg, which is also bioabsorbable and has recognized osteoinductive capacity. The research collected in the literature reveals studies based on different manufacturing and dispersion processes of the reinforcement as well as the physicochemical analysis and corresponding biological evaluation to know the osteoinductive capacity of the proposed PLA/Mg and PCL/Mg composites. In short, this review shows the potential of these composite materials and serves as a guide for those interested in bioabsorbable materials applied in bone tissue engineering.

Fast polarization-sensitive second-harmonic generation microscopy based on off-axis interferometry

We propose polarization-sensitive second-harmonic generation microscopy based on off-axis interferometry (OI-PSHG) by recording the complex field of a wide-field second-harmonic generation (SHG) image and performing polarization measurements. With the ability to record the SHG signals associated with different positions simultaneously, the proposed method exhibits a higher imaging frame rate than raster scanning-based SHG microscopy. The molecular orientation (in terms of their symmetric axis) of tendon collagen fibrils and myosin in muscle is resolved in three dimensions from a subset of polarization-resolved SHG holograms. With the present configuration, it takes approximately 0.01 s to acquire an image with 128 × 128 pixels, which is mainly limited by the excitation power density for wide-field illumination. For the same data throughput using pixel-by-pixel scanning, 0.16-s-long acquisition is required, with the pixel dwell time of 10 µs. Offering the ability to perform wide-field imaging and polarization measurements, the present work lays the foundation for fast SHG microscopy using complex deconvolution and harmonic tomography.

Exploring cell and tissue mechanics with optical tweezers

Cellular and tissue biosystems emerge from the assembly of their constituent molecules and obtain a set of specific material properties. To measure these properties and understand how they influence cellular function is a central goal of mechanobiology. From a bottoms-up, physics or engineering point-of-view, such systems are a composition of basic mechanical elements. However, the sheer number and dynamic complexity of them, including active molecular machines and their emergent properties, makes it currently intractable to calculate how biosystems respond to forces. Because many diseases result from an aberrant mechanotransduction, it is thus essential to measure this response. Recent advances in the technology of optical tweezers have broadened their scope from single-molecule applications to measurements inside complex cellular environments, even within tissues and animals. Here, we summarize the basic optical trapping principles, implementations and calibration procedures that enable force measurements using optical tweezers directly inside cells of living animals, in combination with complementary techniques. We review their versatility to manipulate subcellular organelles and measure cellular frequency-dependent mechanics in the piconewton force range from microseconds to hours. As an outlook, we address future challenges to fully unlock the potential of optical tweezers for mechanobiology.

Viscoelasticity of Low-Molecular-Weight Polyelectrolytes

Shear-thickening fluids that absorb the impact energy of high-velocity projectiles are of great interest for aerospace and body-armor applications. In such a frame, we investigate transient states of neat and aqueous polyelectrolytes (PE) having low molecular weights and containing poly([2-(methacryloyloxy)ethyl]trimethylammonium) as polycations and poly(acrylamide-co-acrylic acid) as polyanions. We compare results with those of bulk water. We employ nonequilibrium molecular dynamics to simulate oscillatory shear, mainly in the linear viscoelastic regime. We find that neat PE exhibits properties of a viscoelastic solid, whereas water and the aqueous mixture of PE conform to viscoelastic liquids with Maxwellian behavior at low angular frequencies. Terminal relaxation times are ∼0.499 and ∼1.385 ps for water and the aqueous mixture of PE, respectively. At high angular frequencies, storage moduli show anomalous behaviors that correspond to transitions between shear thinning and shear thickening in complex shear viscosities. The change in potential energy with the increase of the angular frequency is mainly driven by intramolecular interactions for neat PE, whereas short-range Coulomb interactions are the major contributions for water and the aqueous mixture of PE. Upon observation of the molecular configurations, only the local polyionic structure in the aqueous mixture of PE shows improvement when increasing the angular frequency, whereas the rest remains barely affected. Thus, the water structure in the aqueous mixture of PE allows the storage of energy elastically through the hydrogen-bond network at large angular frequencies, whereas the mechanical contribution of polyions weakens and fully vanishes at the beginning of shear thinning, explaining the superimposed data with data of bulk water. Our method and findings set the path for future molecular simulations in the nonlinear viscoelastic regime with more complex underlying molecular mechanisms.

A biaxial tensional model for early vertebrate morphogenesis

We propose a simple biaxial tensional model which is able to reproduce at a qualitative level several aspects of early stages of vertebrate morphogenesis. The model is based on subsequent excitable contractions of an orthoradial and periclinal (radial) set of contracting lines, which generate first the basic embryonic pattern (a motile tube), and second the lateral orifices such as ears, eyes, mouth, gills, etc. An important aspect of the model is the self-arresting character of the process, akin to wound healing. At later stages, the biaxial lines may also work in extension, and this generates a developmental feedback which is quadratic with respect to curvature.

Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid

Parallel-plate compression of multicellular spheroids (MCSs) is a promising and popular technique to quantify the viscoelastic properties of living tissues. This work presents two different approaches to the simulation of the MCS compression based on viscoelastic solid and viscoelastic fluid models. The first one is the standard linear solid model implemented in ABAQUS/CAE. The second one is the new model for 3D viscoelastic free surface fluid flow, which combines the Oldroyd-B incompressible fluid model and the incompressible neo-Hookean solid model via incorporation of an additional elastic tensor and a dynamic equation for it. The simulation results indicate that either approach can be applied to model the MCS compression with reasonable accuracy. Future application of the viscoelastic free surface fluid model is the MCSs fusion highly-demanded in bioprinting.

Mechanical and genetic control of ascidian endoderm invagination during gastrulation

Gastrulation is a near universal developmental process of animal embryogenesis, during which dramatic morphogenetic events take place: the mesodermal and endodermal tissues are internalized, the ectoderm spreads to cover the embryo surface, and the animal body plan and germ layers are established. Morphogenesis during gastrulation has long been considered the result of spatio-temporally localised forces driven by the transcriptional programme of the embryo. Recent work has shown that tissue rheological properties, which define the mechanical response of tissues to internally-generated or external forces, are also important dynamic regulators of gastrulation. Here, we first introduce how embryonic mechanics can be represented, before outlining current knowledge of the mechanical and genetic control of gastrulation in ascidians, invertebrate marine chordates which develop with invariant cell lineages and a solid-like rheological behaviour until the neurula stages. We discuss the potential of these organisms for the experimental and computational whole-embryo characterisation of the mechanisms shaping gastrulation, and how they may inform the more complex tissue internalization strategies used by other model organisms.

Measuring viscoelasticity of soft biological samples using atomic force microscopy

Mechanical properties play important roles at different scales in biology. At the level of a single cell, the mechanical properties mediate mechanosensing and mechanotransduction, while at the tissue and organ levels, changes in mechanical properties are closely connected to disease and physiological processes. Over the past three decades, atomic force microscopy (AFM) has become one of the most widely used tools in the mechanical characterization of soft samples, ranging from molecules, cell organoids and cells to whole tissue. AFM methods can be used to quantify both elastic and viscoelastic properties, and significant recent developments in the latter have been enabled by the introduction of new techniques and models for data analysis. Here, we review AFM techniques developed in recent years for examining the viscoelastic properties of cells and soft gels, describe the main steps in typical data acquisition and analysis protocols, and discuss relevant viscoelastic models and how these have been used to characterize the specific features of cellular and other biological samples. We also discuss recent trends and potential directions for this field.

Effect of cell sample size in atomic force microscopy nanoindentation

Single-cell technologies are powerful tools to evaluate cell characteristics. In particular, Atomic Force Microscopy (AFM) nanoindentation experiments have been widely used to study single cell mechanical properties. One important aspect related to single cell techniques is the need for sufficient statistical power to obtain reliable results. This aspect is often overlooked in AFM experiments were sample sizes are arbitrarily set. The aim of the present work was to propose a tool for sample size estimation in the context of AFM nanoindentation experiments of single cell. To this aim, a retrospective approach was used by acquiring a large dataset of experimental measurements on four bone cell types and by building saturation curves for increasing sample sizes with a bootstrap resampling method. It was observed that the coefficient of variation (CV_%) decayed with a function of the form y = ax^b with similar parameters for all samples tested and that sample sizes of 21 and 83 cells were needed for the specific cells and protocol employed if setting a maximum threshold on CV_% of 10% or 5%, respectively. The developed tool is made available as an open-source repository and guidelines are provided for its use for AFM nanoindentation experimental design.

Magnetic Resonance Elastography of Rodent Brain

Magnetic resonance elastography (MRE) is a non-invasive imaging technique, using the propagation of mechanical waves as a probe to palpate biological tissues. It consists in three main steps: production of shear waves within the tissue; encoding subsequent tissue displacement in magnetic resonance images; and extraction of mechanical parameters based on dedicated reconstruction methods. These three steps require an acoustic-frequency mechanical actuator, magnetic resonance imaging acquisition, and a post-processing tool for which no turnkey technology is available. The aim of the present review is to outline the state of the art of reported set-ups to investigate rodent brain mechanical properties. The impact of experimental conditions in dimensioning the set-up (wavelength and amplitude of the propagated wave, spatial resolution, and signal-to-noise ratio of the acquisition) on the accuracy and precision of the extracted parameters is discussed, as well as the influence of different imaging sequences, scanners, electromagnetic coils, and reconstruction algorithms. Finally, the performance of MRE in demonstrating viscoelastic differences between structures constituting the physiological rodent brain, and the changes in brain parameters under pathological conditions, are summarized. The recently established link between biomechanical properties of the brain as obtained on MRE and structural factors assessed by histology is also studied. This review intends to give an accessible outline on how to conduct an elastography experiment, and on the potential of the technique in providing valuable information for neuroscientists.

Rheological determinants for simultaneous staging of hepatic fibrosis and inflammation in patients with chronic liver disease

The purpose of this study is to investigate the use of fundamental rheological parameters as quantified by MR elastography (MRE) to measure liver fibrosis and inflammation simultaneously in humans. MRE was performed on 45 patients at 3 T using a vibration frequency of 56 Hz. Fibrosis and inflammation scores were obtained from liver biopsies. Biomechanical properties were quantified in terms of complex shear modulus G* as well as shear wave phase velocity c and shear wave attenuation α. A rheological fractional derivative order model was used to investigate the linear dependence of the free model parameters (dispersion slope y, intrinsic speed c0 , and intrinsic relaxation time τ) on histopathology. Leave-one-out cross-validation was then utilized to demonstrate the effectiveness of the model. The intrinsic speed c0 increases with hepatic fibrosis, while an increased relaxation time τ is reflective of more inflammation of the liver parenchyma. The dispersion slope y does not depend either on fibrosis or on inflammation. The proposed rheological model, given this specific parameterization, establishes the functional dependences of biomechanical parameters on histological fibrosis and inflammation. The leave-one-out cross-validation demonstrates that the model allows identification, from the MRE measurements, of the histology scores when grouped into low-/high-grade fibrosis and low-/high-grade inflammation with significance levels of P = 0.0004 (fibrosis) and P = 0.035 (inflammation). The functional dependences of intrinsic speed and relaxation time on fibrosis and inflammation, respectively, shed new light onto the impact hepatic pathological changes on liver tissue biomechanics in humans. The dispersion slope y appears to represent a structural parameter of liver parenchyma not impacted by the severity of fibrosis/inflammation present in this patient cohort. This specific parametrization of the well-established rheological fractional order model is valuable for the clinical assessment of both fibrosis and inflammation scores, going beyond the capability of the plain shear modulus measurement commonly used for MRE.

Suppression of Myogenic Differentiation of Mammalian Cells Caused by Fluidity of a Liquid-Liquid Interface

There is growing evidence to suggest that the prevailing physical microenvironment and mechanical stress regulate cellular functions, including adhesion, proliferation, and differentiation. Moreover, the physical microenvironment determines the stem-cell lineage depending on stiffness of the substrate relative to biological tissues as well as the stress relaxation properties of the viscoelastic substrates used for cell culture. However, there is little known regarding the biological effects of a fluid substrate, where viscoelastic stress is essentially absent. Here, we demonstrate the regulation of myogenic differentiation on fluid substrates by using a liquid-liquid interface as a scaffold. C2C12 myoblast cells were cultured using water-perfluorocarbon (PFC) interfaces as the fluid microenvironment. We found that, for controlled in vitro culture at water-PFC interfaces, expression of myogenin, myogenic regulatory factors (MRF) family gene, is remarkably attenuated even when myogenic differentiation was induced by reducing levels of growth factors, although MyoD was expressed at the usual level (MyoD up-regulates myogenin under an elastic and/or viscoelastic environment). These results strongly suggest that this unique regulation of myogenic differentiation can be attributed to the fluid microenvironment of the interfacial culture medium. This interfacial culture system represents a powerful tool for investigation of the mechanisms by which physical properties regulate cellular adhesion and proliferation as well as their differentiation. Furthermore, we successfully transferred the cells cultured at such interfaces using Langmuir-Blodgett (LB) techniques. The combination of the interfacial culture system with the LB approach enables investigation of the effects of mechanical compression on cell functions.

Damage threshold in adult rabbit eyes after scleral cross-linking by riboflavin/blue light application

Several scleral cross-linking (SXL) methods were suggested to increase the biomechanical stiffness of scleral tissue and therefore, to inhibit axial eye elongation in progressive myopia. In addition to scleral cross-linking and biomechanical effects caused by riboflavin and light irradiation such a treatment might induce tissue damage, dependent on the light intensity used. Therefore, we characterized the damage threshold and mechanical stiffening effect in rabbit eyes after application of riboflavin combined with various blue light intensities. Adult pigmented and albino rabbits were treated with riboflavin (0.5 %) and varying blue light (450 ± 50 nm) dosages from 18 to 780 J/cm(2) (15 to 650 mW/cm(2) for 20 min). Scleral, choroidal and retinal tissue alterations were detected by means of light microscopy, electron microscopy and immunohistochemistry. Biomechanical changes were measured by shear rheology. Blue light dosages of 480 J/cm(2) (400 mW/cm(2)) and beyond induced pathological changes in ocular tissues; the damage threshold was defined by the light intensities which induced cellular degeneration and/or massive collagen structure changes. At such high dosages, we observed alterations of the collagen structure in scleral tissue, as well as pigment aggregation, internal hemorrhages, and collapsed blood vessels. Additionally, photoreceptor degenerations associated with microglia activation and macroglia cell reactivity in the retina were detected. These pathological alterations were locally restricted to the treated areas. Pigmentation of rabbit eyes did not change the damage threshold after a treatment with riboflavin and blue light but seems to influence the vulnerability for blue light irradiations. Increased biomechanical stiffness of scleral tissue could be achieved with blue light intensities below the characterized damage threshold. We conclude that riboflavin and blue light application increased the biomechanical stiffness of scleral tissue at blue light energy levels below the damage threshold. Therefore, applied blue light intensities below the characterized damage threshold might define a therapeutic blue light tolerance range.

Mathematical modelling of peristaltic propulsion of viscoplastic bio-fluids

This article studies theoretically the transportation of rheological viscoplastic fluids through physiological vessels by continuous muscle contraction and relaxation, that is, peristalsis. Both cases of planar and cylindrical physiological vessels are considered. A mathematical model is developed under long wavelength and low Reynolds number approximations. Expressions for axial velocity in core region, axial velocity in plug flow region, volume flow rate and pressure gradient in non-dimensional form are obtained. A comparative study of velocity profiles, pressure distribution, friction force and mechanical efficiency for different viscoplastic liquids is conducted. The influence of width of plug flow region, shear rate strain index and yield stress index on the pressure distribution, friction force and mechanical efficiency is elaborated. The study is relevant to gastric fluid mechanics and also non-Newtonian biomimetic pump hazardous waste systems exploiting peristaltic mechanisms.

Length scales of interactions in magnetic, dielectric, and mechanical nanocomposites

It is investigated how figures of merits of nanocomposites are affected by structural and interaction length scales. Aside from macroscopic effects without characteristic lengths scales and atomic-scale quantum-mechanical interactions there are nanoscale interactions that reflect a competition between different energy contributions. We consider three systems, namely dielectric media, carbon-black reinforced rubbers and magnetic composites. In all cases, it is relatively easy to determine effective materials constants, which do not involve specific length scales. Nucleation and breakdown phenomena tend to occur on a nanoscale and yield a logarithmic dependence of figures of merit on the macroscopic system size. Essential system-specific differences arise because figures of merits are generally nonlinear energy integrals. Furthermore, different physical interactions yield different length scales. For example, the interaction in magnetic hard-soft composites reflects the competition between relativistic anisotropy and nonrelativistic exchange interactions, but such hierarchies of interactions are more difficult to establish in mechanical polymer composites and dielectrics.

In vivo magnetic resonance elastography of human brain at 7 T and 1.5 T

PURPOSE

To investigate the feasibility of quantitative in vivo ultrahigh field magnetic resonance elastography (MRE) of the human brain in a broad range of low-frequency mechanical vibrations.

MATERIALS AND METHODS

Mechanical vibrations were coupled into the brain of a healthy volunteer using a coil-driven actuator that either oscillated harmonically at single frequencies between 25 and 62.5 Hz or performed a superimposed motion consisting of multiple harmonics. Using a motion sensitive single-shot spin-echo echo planar imaging sequence shear wave displacements in the brain were measured at 1.5 and 7 T in whole-body MR scanners. Spatially averaged complex shear moduli were calculated applying Helmholtz inversion.

RESULTS

Viscoelastic properties of brain tissue could be reliably determined in vivo at 1.5 and 7 T using both single-frequency and multifrequency wave excitation. The deduced dispersion of the complex modulus was consistent within different experimental settings of this study for the measured frequency range and agreed well with literature data.

CONCLUSION

MRE of the human brain is feasible at 7 T. Superposition of multiple harmonics yields consistent results as compared to standard single-frequency based MRE. As such, MRE is a system-independent modality for measuring the complex shear modulus of in vivo human brain in a wide dynamic range.

A stochastic model of cell aggregation under planar flow in the dilute regime

Models of the adhesion of a population of cells in a plane flow are developed, considering the dilute regime. Cells considered as rigid punctual entities are virtually injected at regular times within a plane channel limited by two fixed planes. The pressure profile is supposed to be triangular (constant gradient), in accordance with the assumptions of a Poiseuille flow. The cell adherence to the channel wall is governed by the balance of forces, accounting for gravity, non-specific physical interactions, such as electrostatic effects (repulsive) and Van der Waals forces (attractive), specific adhesive forces representing the ligand-receptor interactions, and friction between cells and the fluid in the vicinity of the endothelium wall. The spatial distribution of the adhesion molecules along the wall is supposed to be a random event, accounted for by a stochastic spatial variability of the dipolar moments of those molecules, according to a Gaussian process. Experimental trends reported for the rate of aggregation of L-selectin mediated leukocytes under shear flow are in qualitative accordance with the evolution versus time of adhering cells obtained by the present simulations. The effect of the maximal injection pressure on those kinetics is assessed.

Fractal ladder models and power law wave equations

The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers-Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters.

Multiscale modeling of cell mechanics and tissue organization

Nowadays, experimental biology gathers a large number of molecular and genetic data to understand the processes in living systems. Many of these data are evaluated on the level of cells, resulting in a changed phenotype of cells. Tools are required to translate the information on the cellular scale to the whole tissue, where multiple interacting cell types are involved. Agent-based modeling allows the investigation of properties emerging from the collective behavior of individual units. A typical agent in biology is a single cell that transports information from the intracellular level to larger scales. Mainly, two scales are relevant: changes in the dynamics of the cell, e.g. surface properties, and secreted molecules that can have effects at a distance larger than the cell diameter.

The compaction of gels by cells: a case of collective mechanical activity

To understand mechanotransduction, purely mechanical phenomena resulting from the crosstalk between contractile cells and their elastic surroundings must be distinguished from adaptive responses to mechanical cues. Here, we revisit the compaction of freely suspended collagen gels by embedded cells, where a small volume fraction of cells (osteoblasts and fibroblasts) compacts the surrounding matrix by two orders of magnitude. Combining micropatterning with time-lapse strain mapping, we find gel compaction to be crucially determined by mechanical aspects of the surrounding matrix. First, it is a boundary effect: the compaction propagates from the edges of the matrix into the bulk. Second, the stress imposed by the cells irreversibly compacts the matrix and renders it anisotropic as a consequence of its nonlinear mechanics and the boundary conditions. Third, cell polarization and alignment follow in time and seem to be a consequence of gel compaction, at odds with current mechanosensing conceptions. Finally, our observation of a threshold cell density shows gel compaction to be a cooperative effect, revealing a mechanical interaction between cells through the matrix. The intricate interplay between cell contractility and surrounding matrix mechanics provides an important organizing principle with implications for many physiological processes such as tissue development.

Kidney damage in extracorporeal shock wave lithotripsy: a numerical approach for different shock profiles

In shock-wave lithotripsy--a medical procedure to fragment kidney stones--the patient is subjected to hypersonic waves focused at the kidney stone. Although this procedure is widely applied, the physics behind this medical treatment, in particular the question of how the injuries to the surrounding kidney tissue arise, is still under investigation. To contribute to the solution of this problem, two- and three-dimensional numerical simulations of a human kidney under shock-wave loading are presented. For this purpose a constitutive model of the bio-mechanical system kidney is introduced, which is able to map large visco-elastic deformations and, in particular, material damage. The specific phenomena of cavitation induced oscillating bubbles is modeled here as an evolution of spherical pores within the soft kidney tissue. By means of large scale finite element simulations, we study the shock-wave propagation into the kidney tissue, adapt unknown material parameters and analyze the resulting stress states. The simulations predict localized damage in the human kidney in the same regions as observed in animal experiments. Furthermore, the numerical results suggest that in first instance the pressure amplitude of the shock wave impulse (and not so much its exact time-pressure profile) is responsible for damaging the kidney tissue.

Traction patterns of tumor cells

The traction exerted by a cell on a planar deformable substrate can be indirectly obtained on the basis of the displacement field of the underlying layer. The usual methodology used to address this inverse problem is based on the exploitation of the Green tensor of the linear elasticity problem in a half space (Boussinesq problem), coupled with a minimization algorithm under force penalization. A possible alternative strategy is to exploit an adjoint equation, obtained on the basis of a suitable minimization requirement. The resulting system of coupled elliptic partial differential equations is applied here to determine the force field per unit surface generated by T24 tumor cells on a polyacrylamide substrate. The shear stress obtained by numerical integration provides quantitative insight of the traction field and is a promising tool to investigate the spatial pattern of force per unit surface generated in cell motion, particularly in the case of such cancer cells.

Orientation fields of nonlinear biological fibrils by second harmonic generation microscopy

The orientation of fibrils within biological tissues is of primary importance. In this study, we propose a simple method based on second harmonic generation (SHG) microscopy to map, pixel by pixel, the orientation of the symmetry axis of the second-order nonlinear susceptibility tensor of fibrils that produce SHG. The method uses only four images acquired at specific polarizations of the input laser beam, and can be easily and cheaply implemented on a confocal microscope. In addition to orientation informations, the method also provides polarization independent images and estimations of the ratio of the nonlinear susceptibility components. We demonstrate the relevance of our concept by studying the orientation fields of the collagen meshwork in a healthy rat liver that provides well separated fibrils. By correlating the mean orientation of the nonlinear susceptibility to the fibril orientation itself for many fibril segments, and using circular statistics, it is shown that both orientations are truly parallel at the fibril scale. Our polarimetric method allows to map fibril orientation fields, independently of individual fibril contrast in the SHG image.

Modeling cell interactions under flow

In this review, we summarize the current state of understanding of the processes by which leukocytes, and other cells, such as tumor cells interact with the endothelium under various blood flow conditions. It is shown that the interactions are influenced by cell-cell adhesion properties, shear stresses due to the flow field and can also be modified by the cells microrheological properties. Different adhesion proteins are known to be involved leading to particular mechanisms by which interactions take place during inflammation or metastasis. Cell rolling, spreading, migration are discussed, as well as the effect of flow conditions on these mechanisms, including microfluidic effects. Several mathematical models proposed in recent years capturing the essential features of such interaction mechanisms are reviewed. Finally, we present a recent model in which the adhesion is given by a kinetics theory based model and the cell itself is modeled as a viscoelastic drop. Qualitative agreement is found between the predictions of this model and in vitro experiments.

MR elastography of breast lesions: understanding the solid/liquid duality can improve the specificity of contrast-enhanced MR mammography

The purpose of this analysis is to explore the potential diagnostic gain provided by the viscoelastic shear properties of breast lesions for the improvement of the specificity of contrast enhanced dynamic MR mammography (MRM). The assessment of viscoelastic properties is done via dynamic MR elastography (MRE) and it is demonstrated that the complex shear modulus of in vivo breast tissue follows within the frequency range of clinical MRE a power law behavior. Taking benefit of this frequency behavior, data are interpreted in the framework of the exact model for wave propagation satisfying the causality principle. This allows to obtain the exponent of the frequency power law from the complex shear modulus at one single frequency which is validated experimentally. Thereby, scan time is drastically reduced. It is observed that malignant tumors obtain larger exponents of the power law than benign tumors indicating a more liquid-like behavior. The combination of the Breast Imaging Reporting and Data System (BIRADS) categorization obtained via MRM with viscoelastic information leads to a substantial rise in specificity. Analysis of 39 malignant and 29 benign lesions shows a significant diagnostic gain with an increase of about 20% in specificity at 100% sensitivity.

Fractal approach to the rheology of concentrated cell suspensions

Results on the rheological behavior of Chinese hamster ovary cell suspensions in a large range of concentrations are reported. The concentration-dependent yield stress and elastic plateau modulus are formalized in the context of fractal aggregates under shear, and quite different exponents are found as compared to the case of red blood cell suspensions. This is explained in terms of intrinsic microscopic parameters such as the cell-cell adhesion energy and cell elasticity but also the cell's individual dynamic properties, found to correlate well with viscoelastic data at large concentrations (phi>or=0.5).

Modeling emergent tissue organization involving high-speed migrating cells in a flow equilibrium

There is increasing interest in the analysis of biological tissue, its organization and its dynamics with the help of mathematical models. In the ideal case emergent properties on the tissue scale can be derived from the cellular scale. However, this has been achieved in rare examples only, in particular, when involving high-speed migration of cells. One major difficulty is the lack of a suitable multiscale simulation platform, which embeds reaction diffusion of soluble substances, fast cell migration and mechanics, and, being of great importance in several tissue types, cell flow homeostasis. In this paper a step into this direction is presented by developing an agent-based mathematical model specifically designed to incorporate these features with special emphasis on high-speed cell migration. Cells are represented as elastic spheres migrating on a substrate in lattice-free space. Their movement is regulated and guided by chemoattractants that can be derived from the substrate. The diffusion of chemoattractants is considered to be slower than cell migration and, thus, to be far from equilibrium. Tissue homeostasis is not achieved by the balance of growth and death but by a flow equilibrium of cells migrating in and out of the tissue under consideration. In this sense the number and the distribution of the cells in the tissue is a result of the model and not part of the assumptions. For the purposes of demonstration of the model properties and functioning, the model is applied to a prominent example of tissue in a cellular flow equilibrium, the secondary lymphoid tissue. The experimental data on cell speed distributions in these tissues can be reproduced using reasonable mechanical parameters for the simulated cell migration in dense tissue.

A modelling approach towards epidermal homoeostasis control

In order to grasp the features arising from cellular discreteness and individuality, in large parts of cell tissue modelling agent-based models are favoured. The subclass of off-lattice models allows for a physical motivation of the intercellular interaction rules. We apply an improved version of a previously introduced off-lattice agent-based model to the steady-state flow equilibrium of skin. The dynamics of cells is determined by conservative and drag forces, supplemented with delta-correlated random forces. Cellular adjacency is detected by a weighted Delaunay triangulation. The cell cycle time of keratinocytes is controlled by a diffusible substance provided by the dermis. Its concentration is calculated from a diffusion equation with time-dependent boundary conditions and varying diffusion coefficients. The dynamics of a nutrient is also taken into account by a reaction-diffusion equation. It turns out that the analysed control mechanism suffices to explain several characteristics of epidermal homoeostasis formation. In addition, we examine the question of how in silico melanoma with decreased basal adhesion manage to persist within the steady-state flow equilibrium of the skin. Interestingly, even for melanocyte cell cycle times being substantially shorter than for keratinocytes, tiny stochastic effects can lead to completely different outcomes. The results demonstrate that the understanding of initial states of tumour growth can profit significantly from the application of off-lattice agent-based models in computer simulations.

Direct Measurement of Mechanical and Adhesive Properties of Living Cells Using Surface Forces Apparatus

The adhesive and mechanical properties of living cells assembled into a monolayer on two different substrates were investigated using the surface forces apparatus (SFA) technique. The force measurements allowed elastic and bending moduli of the cells plated on substrates to be determined. The moduli are in good agreement with data reported in the literature for single cells determined using atomic force microscopy. Results confirm that the nature of the cell–substrate interactions can mediate cell mechanical and adhesive properties.

Analysis of lung parenchyma as a parametric porous medium

The dynamic behavior of the lung in health and disease depends on its viscoelastic properties. To better understand these properties, several mathematical models have been utilized by many investigators. In the present work, we present a new approach that characterizes the dynamics of gas flow into a viscoelastic porous medium that models the lung structure. This problem is considered in terms of the lung input impedance on a macro level and parenchymal tissue impedance on the level of an alveolar wall. We start from a basic theoretical analysis in which macroscopic tissue deformations are represented in accordance with the linearized Navier-Stokes equations. This approach has strong theoretical underpinnings in other situations but has not been applied to analyze the impedance of the inflated lung. Our analysis provides a theoretical basis for analyzing the interaction between flow into the lungs as a biophysical diffusion process and parenchymal viscoelasticity described phenomenologically, within the frameworks of standard viscoelasticity and structural damping. This lung impedance incorporates parameters of porosity, permeability, and viscoelasticity on micro and macro levels of parenchymal tissue. The analysis shows the theoretical basis of the transformation from the impedance of alveolar walls or isolated tissue strips to that of the intact parenchyma. We also show how the loading impedance at the lung boundary may have a significant impact on the dynamic behavior of whole lung viscoelasticity. Our analysis may be useful in directing specific tests of different models and for analyzing experimental measurements of viscoelastic parameters of lung material under normal and pathological conditions.

A master relation defines the nonlinear viscoelasticity of single fibroblasts

Cell mechanical functions such as locomotion, contraction, and division are controlled by the cytoskeleton, a dynamic biopolymer network whose mechanical properties remain poorly understood. We perform single-cell uniaxial stretching experiments on 3T3 fibroblasts. By superimposing small amplitude oscillations on a mechanically prestressed cell, we find a transition from linear viscoelastic behavior to power law stress stiffening. Data from different cells over several stress decades can be uniquely scaled to obtain a master relation between the viscoelastic moduli and the average force. Remarkably, this relation holds independently of deformation history, adhesion biochemistry, and intensity of active contraction. In particular, it is irrelevant whether force is actively generated by the cell or externally imposed by stretching. We propose that the master relation reflects the mechanical behavior of the force-bearing actin cytoskeleton, in agreement with stress stiffening known from semiflexible filament networks.

Multicellular tumor spheroid in an off-lattice Voronoi-Delaunay cell model

We study multicellular tumor spheroids by introducing a new three-dimensional agent-based Voronoi-Delaunay hybrid model. In this model, the cell shape varies from spherical in thin solution to convex polyhedral in dense tissues. The next neighbors of the cells are provided by a weighted Delaunay triangulation with on average linear computational complexity. The cellular interactions include direct elastic forces and cell-cell as well as cell-matrix adhesion. The spatiotemporal distribution of two nutrients--oxygen and glucose--is described by reaction-diffusion equations. Viable cells consume the nutrients, which are converted into biomass by increasing the cell size during the G1 phase. We test hypotheses on the functional dependence of the uptake rates and use computer simulations to find suitable mechanisms for the induction of necrosis. This is done by comparing the outcome with experimental growth curves, where the best fit leads to an unexpected ratio of oxygen and glucose uptake rates. The model relies on physical quantities and can easily be generalized towards tissues involving different cell types. In addition, it provides many features that can be directly compared with the experiment.