A novel two-layer, coupled finite element approach for modeling the nonlinear elastic and viscoelastic behavior of human erythrocytes

Contraction of the rigor actomyosin complex drives bulk hemoglobin expulsion from hemolyzing erythrocytes

Erythrocyte ghost formation via hemolysis is a key event in the physiological clearance of senescent red blood cells (RBCs) in the spleen. The turnover rate of millions of RBCs per second necessitates a rapid efflux of hemoglobin (Hb) from RBCs by a not yet identified mechanism. Using high-speed video-microscopy of isolated RBCs, we show that electroporation-induced efflux of cytosolic ATP and other small solutes leads to transient cell shrinkage and echinocytosis, followed by osmotic swelling to the critical hemolytic volume. The onset of hemolysis coincided with a sudden self-propelled cell motion, accompanied by cell contraction and Hb-jet ejection. Our biomechanical model, which relates the Hb-jet-driven cell motion to the cytosolic pressure generation via elastic contraction of the RBC membrane, showed that the contributions of the bilayer and the bilayer-anchored spectrin cytoskeleton to the hemolytic cell motion are negligible. Consistent with the biomechanical analysis, our biochemical experiments, involving extracellular ATP and the myosin inhibitor blebbistatin, identify the low abundant non-muscle myosin 2A (NM2A) as the key contributor to the Hb-jet emission and fast hemolytic cell motion. Thus, our data reveal a rapid myosin-based mechanism of hemolysis, as opposed to a much slower diffusive Hb efflux.

Effect of cell geometry in the evaluation of erythrocyte viscoelastic properties

The red blood cell membrane-cytoskeleton is a complex structure mainly responsible for giving the cell rigidity and shape. It also provides the erythrocyte with the ability to pass through narrow capillaries of the vertebrate blood circulatory system. Although the red blood cell viscoelastic properties have been extensively studied, reported experimental data differ by up to three orders of magnitude. This could be attributed to the natural cell variability, to the different techniques employed, and also to the models used for the cell response, which are highly dependent on cell geometry. Here, we use two methodologies based on optical tweezers to investigate the viscoelastic behavior of healthy human red blood cells, one applying small cell deformations (microrheology) and another imposing large deformations (tether extraction). We also establish a defocusing microscopy-based method to characterize the cell geometry and thus the erythrocyte form factor, an essential parameter that allows comparisons among the viscoelastic properties at different conditions. Moreover, for small deformations, a soft glassy rheology model is used to discuss the results, while for large deformations two surface shear moduli and one surface viscosity are determined, together with the surface tension and bending modulus of the erythrocyte membrane lipid component. We also show that F-actin is not detected in tethers, although the erythrocyte membrane has physical properties like those of other adherent cells, known to have tethers containing F-actin inside. Altogether, our results show good agreement with the reported literature and we argue that, to properly compare the viscoelastic properties of red blood cells in different situations, the task of cell geometry characterization must be accomplished. This may be especially important when the influence of agents, like the malaria parasite, induces changes in both the geometry and chemical constituents of the erythrocyte membrane. Together, the new methodologies and procedures used in this study would allow the erythrocyte community to better explore the mechanical behavior of red blood cells and may be useful to characterize erythrocyte viscoelasticity changes in several blood diseases.

Plasmodium falciparum maturation across the intra-erythrocytic cycle shifts the soft glassy viscoelastic properties of red blood cells from a liquid-like towards a solid-like behavior

The mechanical properties of erythrocytes have been investigated by different techniques. However, there are few reports on how the viscoelasticity of these cells varies during malaria disease. Here, we quantitatively map the viscoelastic properties of Plasmodium falciparum-parasitized human erythrocytes. We apply new methodologies based on optical tweezers to measure the viscoelastic properties and defocusing microscopy to measure the erythrocyte height profile, the overall cell volume, and its form factor, a crucial parameter to convert the complex elastic constant into complex shear modulus. The storage and loss shear moduli are obtained for each stage of parasite maturation inside red blood cells, while the former increase, the latter decrease. Employing a soft glassy rheology model, we obtain the power-law exponent for the storage and loss shear moduli, characterizing the soft glassy features of red blood cells in each parasite maturation stage. Ring forms present a liquid-like behavior, with a slightly lower power-law exponent than healthy erythrocytes, whereas trophozoite and schizont stages exhibit increasingly solid-like behaviors. Finally, the surface elastic shear moduli, low-frequency surface viscosities, and shape recovery relaxation times all increase not only in a stage-dependent manner but also when compared to healthy red blood cells. Overall, the results call attention to the soft glassy characteristics of Plasmodium falciparum-parasitized erythrocyte membrane and may provide a basis for future studies to better understand malaria disease from a mechanobiological perspective.

A coupled approach for identification of nonlinear and compressible material models for soft tissue based on different experimental setups - Exemplified and detailed for lung parenchyma

In this paper, a coupled inverse analysis is proposed to identify nonlinear compressible hyperelastic material models described by two sets of experiments. While the overall approach is applicable for different materials, here it will be presented for viable lung parenchyma. Characterizing the material properties of lung parenchyma is essential to describe and predict the mechanical behavior of the respiratory system in health and disease. During breathing and mechanical ventilation, lung parenchyma is mainly subjected to volumetric deformations along with isochoric and asymmetric deformations that occur especially in diseased heterogeneous lungs. Notwithstanding, most studies examine lung tissue in predominantly isochoric tension tests. In this paper, we investigate the volumetric material behavior as well as the isochoric deformations in two sets of experiments: namely, volume-pressure-change experiments (performed with 287 samples of 26 rats) and uniaxial tension tests (performed with 30 samples of 5 rats). Based on these sets of experiments, we propose a coupled inverse analysis, which simultaneously incorporates both measurement sets to optimize the material parameters. Accordingly, we determine a suitable material model using the experimental results of both sets of experiments in one coupled identification process. The identified strain energy function with the corresponding material parameters [Formula: see text] is validated to model both sets of experiments precisely. Hence, this constitutive model describes the complex volumetric and isochoric nonlinear material behavior of lung parenchyma. This derived material model can be used for nonlinear finite element simulations of lung parenchyma and will help to quantify the stresses and strains of lung tissue during spontaneous and artificial breathing; thus, allowing new insights into lung function and biology.

A monolithic fluid-structure interaction framework applied to red blood cells

A parallel fully coupled (monolithic) fluid-structure interaction (FSI) algorithm has been applied to the deformation of red blood cells (RBCs) in capillaries, where cell deformability has significant effects on blood rheology. In the present FSI algorithm, fluid domain is discretized using the side-centered unstructured finite volume method based on the Arbitrary Lagrangian-Eulerian (ALE) formulation; meanwhile, solid domain is discretized with the classical Galerkin finite element formulation for the Saint Venant-Kirchhoff material in a Lagrangian frame. In addition, the compatible kinematic boundary condition is enforced at the fluid-solid interface in order to conserve the mass of cytoplasmic fluid within the red cell at machine precision. In order to solve the resulting large-scale algebraic linear systems in a fully coupled manner, a new matrix factorization is introduced similar to that of the projection method, and the parallel algebraic multigrid solver BoomerAMG is used for the scaled discrete Laplacian provided by the HYPRE library, which we access through the PETSc library. Three important physical parameters for the blood flow are simulated and analyzed: (1) the effect of capillary diameter, (2) the effect of red cell membrane thickness, and (3) the effect of red cell spacing (hematocrit). The numerical calculations initially indicate a shape deformation in which biconcave discoid shape changes to a parachute-like shape. Furthermore, the parachute-like cell shape in small capillaries undergoes a cupcake-shaped buckling instability, which has not been observed in the literature. The instability forms thin riblike features, and the red cell deformation is not axisymmetric but three-dimensional.

Effect of the object 3D shape on the viscoelastic testing in optical tweezers

Viscoelastic testing of biological cells has been performed with the optical tweezers and stretcher. Historically, the cells were modeled by the spring-dashpot network or the power-law models, which can however characterize only the homogeneous, isotropic viscoelastic material, but not the 3D cell itself. Our mechanical and finite element analyses show that the cell elongations are different significantly for different cell 3D shapes in the creep testing. In the dynamic testing the loss tangent, which is measurable directly in the experiment, is not sensitive to the cell shape. However, the stress-strain hysteresis loop still depends on the cell 3D shape.

Biofilm growth: a multi-scale and coupled fluid-structure interaction and mass transport approach

In this paper, we propose a novel approach for modelling biofilm growth. It is based on a finite element method and includes both fluid-structure interaction (FSI) as well as scalar transport effects. Due to the different time-scales of the involved phenomena, the growth of the biofilm structure is coupled with the FSI and mass transport through a multi-scale approach in time. In each hydrodynamic time step, first the non-linear FSI problem is solved followed by the scalar transport equations, using the information on velocities and deformations obtained in the FSI step. After a steady state solution is reached, information on mass fluxes and stresses are passed to the growth model. At this point, the growth is calculated for a biological time step larger than the hydrodynamic one and based on the mass flux through the interface and on normal and shear stresses on it. This type of approach can significantly contribute to the understanding of biofilm development in fluid flows, since the influence of hydrodynamic conditions and availability of nutrients is well known to have effects on biofilm development. Therefore, for the purpose of understanding biofilm macro-scale dynamics, it is essential to adopt a modeling approach, which takes into account all the relevant aspects, like fluid flow, structure deformation, mass transport and their effect on biofilm growth and erosion. First numerical examples demonstrate the suitability of the proposed model to catch the main features of a growing biofilm structure.

Finite-element modeling of viscoelastic cells during high-frequency cyclic strain

Mechanotransduction refers to the mechanisms by which cells sense and respond to local loads and forces. The process of mechanotransduction plays an important role both in maintaining tissue viability and in remodeling to repair damage; moreover, it may be involved in the initiation and progression of diseases such as osteoarthritis and osteoporosis. An understanding of the mechanisms by which cells respond to surrounding tissue matrices or artificial biomaterials is crucial in regenerative medicine and in influencing cellular differentiation. Recent studies have shown that some cells may be most sensitive to low-amplitude, high-frequency (i.e., 1-100 Hz) mechanical stimulation. Advances in finite-element modeling have made it possible to simulate high-frequency mechanical loading of cells. We have developed a viscoelastic finite-element model of an osteoblastic cell (including cytoskeletal actin stress fibers), attached to an elastomeric membrane undergoing cyclic isotropic radial strain with a peak value of 1,000 µstrain. The results indicate that cells experience significant stress and strain amplification when undergoing high-frequency strain, with peak values of cytoplasmic strain five times higher at 45 Hz than at 1 Hz, and peak Von Mises stress in the nucleus increased by a factor of two. Focal stress and strain amplification in cells undergoing high-frequency mechanical stimulation may play an important role in mechanotransduction.