Comparison of two model frameworks for fiber dispersion in the elasticity of soft biological tissues

This study compares two models that are used to describe the elastic properties of fiber-reinforced materials with dispersed fibers, in particular some soft biological tissues such as arterial walls and cartilages. The two model approaches involve different constitutive frameworks, one being based on a generalized structure tensor (GST) and the other on the method of angular integration (AI). By using two representative examples, with the same number of parameters for each model, it is shown that the predictions of the two models are virtually identical for a significant range of large deformations, which contradicts conclusions contained in several papers that are based on faulty analysis. Additionally, each of the models is fitted to sets of uniaxial data from the circumferential and axial directions of the adventitia of a human aorta, both models providing excellent agreement with the data. While the predictions of the two models are comparable and exclusion of compressed fibers can be accommodated by either model, it is well known that the AI model requires more computational time than the GST model when used within a finite element environment, in particular if compressed fibers are excluded

An affine continuum mechanical model for cross-linked F-actin networks with compliant linker proteins

Cross-linked actin networks are important building blocks of the cytoskeleton. In order to gain deeper insight into the interpretation of experimental data on actin networks, adequate models are required. In this paper we introduce an affine constitutive network model for cross-linked F-actin networks based on nonlinear continuum mechanics, and specialize it in order to reproduce the experimental behavior of in vitro reconstituted model networks. The model is based on the elastic properties of single filaments embedded in an isotropic matrix such that the overall properties of the composite are described by a free-energy function. In particular, we are able to obtain the experimentally determined shear and normal stress responses of cross-linked actin networks typically observed in rheometer tests. In the present study an extensive analysis is performed by applying the proposed model network to a simple shear deformation. The single filament model is then extended by incorporating the compliance of cross-linker proteins and further extended by including viscoelasticity. All that is needed for the finite element implementation is the constitutive model for the filaments, the linkers and the matrix, and the associated elasticity tensor in either the Lagrangian or Eulerian formulation. The model facilitates parameter studies of experimental setups such as micropipette aspiration experiments and we present such studies to illustrate the efficacy of this modeling approach

Modeling of fibrous biological tissues with a general invariant that excludes compressed fibers

Dispersed collagen fibers in fibrous soft biological tissues have a significant effect on the overall mechanical behavior of the tissues. Constitutive modeling of the detailed structure obtained by using advanced imaging modalities has been investigated extensively in the last decade. In particular, our group has previously proposed a fiber dispersion model based on a generalized structure tensor. However, the fiber tension–compression switch described in that study is unable to exclude compressed fibers within a dispersion and the model requires modification so as to avoid some unphysical effects. In a recent paper we have proposed a method which avoids such problems, but in this present study we introduce an alternative approach by using a new general invariant that only depends on the fibers under tension so that compressed fibers within a dispersion do not contribute to the strain-energy function. We then provide expressions for the associated Cauchy stress and elasticity tensors in a decoupled form. We have also implemented the proposed model in a finite element analysis program and illustrated the implementation with three representative examples: simple tension and compression, simple shear, and unconfined compression on articular cartilage. We have obtained very good agreement with the analytical solutions that are available for the first two examples. The third example shows the efficacy of the fibrous tissue model in a larger scale simulation. For comparison we also provide results for the three examples with the compressed fibers included, and the results are completely different. If the distribution of collagen fibers is such that it is appropriate to exclude compressed fibers then such a model should be adopted

Bis[(1,1'-biphenyl-2,2'-diyl)di-tert-butylphosphonium] di-l-chlorido-bis[dichloridopalladate(II)]

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trans-Bis[bis­(2-methoxy­phen­yl)phenyl­phosphine-κP]dichloridopalladium(II)

The structure of the title compound, [PdCl2(C20H19O2P)2], shows a square-planar geometry for the PdII ion within a Cl2Pd[PPh(PhOMe)2]2 ligand set. The PdII atom sits on an inversion centre and therefore the asymmetric unit contains the PdII atom, one Cl atom and one bis­(2-methoxy­phen­yl)phenyl­phosphine ligand. The trans arrangement of ligands is also imposed by symmetry

An arterial constitutive model accounting for collagen content and cross-linking

It is apparent from the literature that the density of cross-links in collagenous tissue has a stiffening effect on the mechanical response of the tissue. This paper represents an initial attempt to characterize this effect on the elastic response, specifically in respect of arterial tissue. Two approaches are presented. First, a simple phenomenological continuum model with a cross-link-dependent stiffness is considered, and the influence of the cross-link density on the response in uniaxial tension is illustrated. In the second approach, a 3D model is developed that accounts for the relative orientation and stiffness of (two families of) collagen fibers and cross-links and their coupling using an invariant-based strain-energy function. This is also illustrated for uniaxial tension, and the influence of different cross-link arrangements and material parameters is detailed. Specialization of the model for plane strain is then used to show the effect of the cross-link orientation (relative to the fibers) and cross-link density on the shear stress versus the amount of shear deformation response. The elasticity tensor for the general (3D) case is provided with a view to subsequent finite element implementation

Composite infrared bolometers with Si_3N_4 micromesh absorbers

We report the design and performance of 300-mK composite bolometers that use micromesh absorbers and support structures patterned from thin films of low-stress silicon nitride. The small geometrical filling factor of the micromesh absorber provides 20× reduction in heat capacity and cosmic ray cross section relative to a solid absorber with no loss in IR-absorption efficiency. The support structure is mechanically robust and has a thermal conductance, G < 2 × 10^(−11) W/K, which is four times smaller than previously achieved at 300 mK. The temperature rise of the bolometer is measured with a neutron transmutation doped germanium thermistor attached to the absorbing mesh. The dispersion in electrical and thermal parameters of a sample of 12 bolometers optimized for the Sunyaev–Zel’dovich Infrared Experiment is ±7% in R (T), ±5% in optical efficiency, and ±4% in G

trans-Dichloridobis[tris­(2-methoxy­phen­yl)phosphine]palladium(II)

The structure of the title compound, [PdCl2(C21H21O3P)2], shows a nearly square-planar geometry for the PdII atom within the Cl2Pd[P(PhOMe)3]2 ligand set. The PdII atom sits on a centre of inversion and therefore the asymmetric unit contains one half-mol­ecule, i.e. half of one PdII atom, one Cl atom and one tris­(2-methoxy­phen­yl)phosphine ligand

trans-Dichloridobis[tris­(4-methoxy­phen­yl)phosphine]palladium(II) benzene monosolvate

The structure of the title compound, [PdCl2(C21H21O3P)2]·C6H6, shows a square-planar geometry for the PdII atom within a Cl2[P(PhOMe)3]2 ligand set. The crystal structure contains benzene as solvent. The PdII atom sits on a centre of inversion and therefore the asymmetric unit contains the PdII atom, one Cl atom, one tris­(4-methoxy­phen­yl)phosphine ligand and one half of the benzene solvent mol­ecule

Biomechanical relevance of the microstructure in artery walls with a focus on passive and active components

The microstructure of arteries, consisting, in particular, of collagen, elastin and vascular smooth muscle cells, plays a very significant role in their biomechanical response during a cardiac cycle. In this paper we highlight the microstructure and the contributions of each of its components to the overall mechanical behavior. We also describe the changes of the microstructure which occur as a result of abdominal aortic aneurysms and disease such as atherosclerosis. We also focus on how the passive and active constituents are incorporated into a mathematical model without going into detail of the mathematical formulation. We conclude by mentioning open problems towards a better characterization of the biomechanical aspects of arteries that will be beneficial for a better understanding of cardiovascular pathophysiology