The estimated elastic constants for a single bone osteonal lamella

Micromechanical estimates of the elastic constants for a single bone osteonal lamella and its substructures are reported. These estimates of elastic constants are accomplished at three distinct and organized hierarchical levels, that of a mineralized collagen fibril, a collagen fiber, and a single lamella. The smallest collagen structure is the collagen fibril whose diameter is the order of 20 nm. The next structural level is the collagen fiber with a diameter of the order of 80 nm. A lamella is a laminate structure, composed of multiple collagen fibers with embedded minerals and consists of several laminates. The thickness of one laminate in the lamella is approximately 130 nm. All collagen fibers in a laminate in the lamella are oriented in one direction. However, the laminates rotate relative to the adjacent laminates. In this work, all collagen fibers in a lamella are assumed to be aligned in the longitudinal direction. This kind of bone with all collagen fibers aligned in one direction is called a parallel fibered bone. The effective elastic constants for a parallel fibered bone are estimated by assuming periodic substructures. These results provide a database for estimating the anisotropic poroelastic constants of an osteon and also provide a database for building mathematical or computational models in bone micromechanics, such as bone damage mechanics and bone poroelasticity.     

Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study

Bone remodelling is the process that maintains bone structure and strength through adaptation of bone tissue mechanical properties to applied loads. Bone can be modelled as a porous deformable material whose pores are filled with cells, organic material and interstitial fluid. Fluid flow is believed to play a role in the mechanotransduction of signals for bone remodelling. In this work, an osteon, the elementary unit of cortical bone, is idealized as a hollow cylinder made of a deformable porous matrix saturated with an interstitial fluid. We use Biot’s poroelasticity theory to model the mechanical behaviour of bone tissue taking into account transverse isotropic mechanical properties. A finite element poroelastic model is developed in the COMSOL Multiphysics software. Elasticity equations and Darcy’s law are implemented in this software; they are coupled through the introduction of an interaction term to obtain poroelasticity equations. Using numerical simulations, the investigation of the effect of spatial gradients of permeability or Poisson’s ratio is performed. Results are discussed for their implication on fluid flow in osteons: (i) a permeability gradient affects more the fluid pressure than the velocity profile; (ii) focusing on the fluid flow, the key element of loading is the strain rate; (iii) a Poisson’s ratio gradient affects both fluid pressure and fluid velocity. The influence of textural and mechanical properties of bone on mechanotransduction signals for bone remodelling is also discussed.     

Micromechanical modeling of elastic properties of cortical bone accounting for anisotropy of dense tissue

The paper analyzes the connection between microstructure of the osteonal cortical bone and its overall elastic properties. The existing models either neglect anisotropy of the dense tissue or simplify cortical bone microstructure (accounting for Haversian canals only). These simplifications (related mostly to insufficient mathematical apparatus) complicate quantitative analysis of the effect of microstructural changes – produced by age, microgravity, or some diseases – on the overall mechanical performance of cortical bone. The present analysis fills this gap; it accounts for anisotropy of the dense tissue and uses realistic model of the porous microstructure. The approach is based on recent results of Sevostianov et al. (2005) and Saadat et al. (2012) on inhomogeneities in a transversely-isotropic material. Bone?s microstructure is modeled according to books of Martin and Burr (1989), Currey (2002), and Fung (1993) and includes four main families of pores. The calculated elastic constants for porous cortical bone are in agreement with available experimental data. The influence of each of the pore types on the overall moduli is examined.     

'Universal' microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: micromechanics-based prediction of anisotropic elasticity

Bone materials are characterized by an astonishing variability and diversity. Still, because of 'architectural constraints' due to once chosen material constituents and their physical interaction, the fundamental hierarchical organization or basic building plans of bone materials remain largely unchanged during biological evolution. Such universal patterns of microstructural organization govern the mechanical interaction of the elementary components of bone (hydroxyapatite, collagen, water; with directly measurable tissue-independent elastic properties), which are here quantified through a multiscale homogenization scheme delivering effective elastic properties of bone materials: at a scale of 10nm, long cylindrical collagen molecules, attached to each other at their ends by approximately 1.5nm long crosslinks and hosting intermolecular water inbetween, form a contiguous matrix called wet collagen. At a scale of several hundred nanometers, wet collagen and mineral crystal agglomerations interpenetrate each other, forming the mineralized fibril. At a scale of 5-10microm, the extracellular solid bone matrix is represented as collagen fibril inclusions embedded in a foam of largely disordered (extrafibrillar) mineral crystals. At a scale above the ultrastructure, where lacunae are embedded in extracellular bone matrix, the extravascular bone material is observed. Model estimates predicted from tissue-specific composition data gained from a multitude of chemical and physical tests agree remarkably well with corresponding acoustic stiffness experiments across a variety of cortical and trabecular, extracellular and extravascular materials. Besides from reconciling the well-documented, seemingly opposed concepts of 'mineral-reinforced collagen matrix' and 'collagen-reinforced mineral matrix' for bone ultrastructure, this approach opens new possibilities in the exploitation of computer tomographic data for nano-to-macro mechanics of bone organs.     

Penetration of cutting tool into cortical bone: Experimental and numerical investigation of anisotropic mechanical behaviour

An anisotropic mechanical behaviour of cortical bone and its intrinsic hierarchical microstructure act as protective mechanisms to prevent catastrophic failure due to natural loading conditions; however, they increase the extent of complexity of a penetration process in the case of orthopaedic surgery. Experimental results available in literature provide only limited information about processes in the vicinity of a tool–bone interaction zone. Also, available numerical models the bone-cutting process do not account for material anisotropy or the effect of damage mechanisms. In this study, both experimental and numerical studies were conducted to address these issues and to elucidate the effect of anisotropic mechanical behaviour of cortical bone tissue on penetration of a sharp cutting tool. First, a set of tool-penetration experiments was performed in directions parallel and perpendicular to bone axis. Also, these experiments included bone samples cut from four different cortices to evaluate the effect of spatial variability and material anisotropy on the penetration processes. Distinct deformation and damage mechanisms linked to different microstructure orientations were captured using a micro-lens high-speed camera. Then, a novel hybrid FE model employing a smoothed-particle-hydrodynamic domain embedded into a continuum FE one was developed based on the experimental configuration to characterise the anisotropic deformation and damage behaviour of cortical bone under a penetration process. The results of our study revealed a clear anisotropic material behaviour of the studied cortical bone tissue and the influence of the underlying microstructure. The proposed FE model reflected adequately the experimental results and demonstrated the need for the use of the anisotropic and damage material model to analyse cutting of the cortical-bone tissue.     

A resistor interpretation of general anisotropic cardiac tissue

This paper describes a spatial discretization scheme for partial differential equation systems that contain anisotropic diffusion. The discretization method uses unstructured finite volumes, or the boxes, that are formed as a secondary geometric structure from an underlying triangular mesh. We show how the discretization can be interpreted as a resistive circuit network, where each resistor is assigned at each edge of the triangular element. The resistor is computed as an anisotropy dependent geometric quantity of the local mesh structure. Finally, we show that under certain conditions, the discretization gives rise to negative resistors that can produce non-physical hyperpolarizations near depolarizing stimuli. We discuss how the proper choice of triangulation (anisotropic Delaunay triangulation) can ensure monotonicity (i.e. all resistors are positive).     

Strain Concentrations Surrounding an Ellipsoid Model of Lacunae and Osteocytes

Direct cell sensing of tissue matrix strains is one possible signaling mechanism for mechanically mediated bone adaptation. We utilized homogenization theory lo estimate bone tissue matrix strains surrounding osteocytes using two sets of models. The first set of models estimated the strain levels surrounding the lacunae and canaliculi, taking into account variations in lamellar properties. The second set estimated strain levels in the osteocyte and the surrounding matrix for different cellular mechanical properties. The results showed that the strain levels found in and surrounding osteocytes, 1700 to 2700 microstrain (denoted as μe; 1 =.0001% strain), were significantly greater than the trabecular tissue level strains of [1325 μe, 287 μe, 87 μe] used for model input. Variation in lamellar properties did not affect strain levels, except at lamellar boundaries. Strain in and surrounding the osteocyte was not significantly affected by cellular stiffness ranging between 28 and 28,000 Pascals (Pa). Strain levels surrounding lacunae and canaliculi were approximately equivalent.     

The elastic deformability of closed multilayered membranes is the same as that of a bilayer membrane

The elastic behavior of closed multilayered membranes is analyzed with the assumption that the constituent layers are in close contact but are unconnected in the sense that they are free to slide by one another. The system exhibits three independent elastic deformation modes for any number of the constituent layers equal to or larger than two. These are the area expansivity of the membrane neutral surface, and the local and non-local membrane bending. The corresponding elastic moduli are expressed in terms of the elastic moduli of the constituent layers, their areas, and distances between their neutral surfaces. Closed multilayered membranes only differ from a closed bilayer membrane in that for any of their shapes some of the constituent layers are expanded and some compressed.     

Determination of the viscometric constants for chitosan

The viscometric constants a and K_m in the Mark-Houwink equation have been determined for chitosan in 0.1 m acetic acid 0.2 m sodium chloride solution, using the approach of Sharples and Major. The number-average molecular weights were determined by absorbance measurements on solutions of the phenylosazone derivatives. The values obtained a = 0.93, K_m = 1.81 × 10^?3 cm³ g¹ differ considerably from those reported previously by Lee but are in agreement with values found for other ionic polysaccharides having related β-(1 → 4)-linked structures.     

Measurement of rate constants for actin filament elongation in solution

This paper describes a simple method to measure the rate constants for actin filament elongation using pyrene-actin fluorescence as a measure of the polymer concentration and unlabeled actin filaments as nuclei. With careful selection of conditions, the initial rate of polymerization is directly proportional to the actin monomer concentration above the critical concentration. Plots of initial rate versus actin concentration give the critical concentration (x intercept), the association rate constant, k+ (slope), and the dissociation rate constant, k-(y intercept). By calibrating the system under conditions where the absolute values of these rate constants are known from previous electron microscopic experiments [T. D. Pollard and M. S. Mooseker (1981) J. Cell Biol. 88, 654-659; J. A. Cooper, S. B. Walker, and T. D. Pollard (1983) J. Muscle Res. Cell Motil. 4, 253-262], one can calculate the absolute values of the rate constants under other conditions as well as the length of the filaments used as a nuclei. This approach has proven useful for evaluating the effect of actin-binding proteins on the polymerization process.     

Corrected equations for calculation of constants in enzyme inhibition and activation

Equations for calculation of the constants of biparametrical types of enzyme inhibition and activation were obtained that take into account a ratio of the lengths of L vector projections representing such reactions in the three-dimensional K (m)V I coordinate system. This allows higher accuracy of calculation and is more correct for comparison of these constants. Examples of data analysis of enzyme inhibition and activation by using the traditional equations (they do not take into account the lengths of vector projections) and corrected ones (they take into account the lengths of vector projections) are given. The corrected and traditional equations are used for calculation of the constants of biparametrical types of enzyme inhibition and activation.     

Co-C force constants from resonance Raman spectra of alkylcobalamins: insensitivity to dimethylbenzylimidazole coordination

The Co-C stretching vibration has been identified in resonance Raman spectra of alkyl-cobalamins, via isotope substitution, permitting estimation of the Co-C force constants, f = 1.85, 1.77 and 1.50 mdyn Å⁻¹ for methyl-, ethyl- and deoxyadenosyl-cobalamin, respectively (ν_Co-C = 506, 471 and 442/429 cm⁻¹). These values scale with the reported bond dissociation energies, and support the view that the Co-C bond weakens with increasing bulk of the alkyl group due to steric interaction with the corrin ring. However, the force constants are unaffected by dissociation of the dimethylbenzimidazole ligand at low pH, even though the bond dissociation energy rises significantly upon DMB dissociation in AdoCbl. This increase must therefore reflect destabilization of the Co^II product, rather than Co-C bond strengthening in the AdoCbl ground state. The insensitivity of the force constants to dimethylbenzimidazole dissociation implies that the steric effect of DMB coordination is not transmitted to the Co-C bond by the corrin ring. Consistent with this interpretation, the RR frequencies of the corrin ring modes are minimally perturbed by DMB dissociation, supporting earlier NMR results that indicated little change in the corrin conformation.     

Measurement of three-bond coupling constants in the osmoregulated periplasmic glucan of Burkholderia solanacearum

Summary The cyclic osmoregulated periplasmic glucan produced by Burkholderia solanacearum contains 13 glucose units, all -(1–2) linked except for one -(1–6) linkage. We report here the measurement of the ³J(C1-H2) and ³J(H1-C2) coupling constants, characterizing the glycosidic linkages, through the use of a ¹³C/¹²C double half-filtered NOESY experiment. The values obtained give information about the (, ) angles of the different linkages. The results presented form an important step towards a detailed experimental model of the cyclic glucan, which might allow us to clarify its biological role and establish whether the cavity of these molecules is compatible with the capability of complexing host molecular signals.     

Binding constants of phenylalanine for the four mononucleotides

Summary Earlier work has shown that several properties of amino acids correlate directly with properties of their anticodonic nucleotides. Furthermore, in precipitation studies with thermal proteinoids and homopolyribonucleotides, an anticodonic preference was displayed between Lys-rich, Pro-rich and Gly-rich thermal proteinoids and their anticodonic polyribonucleotides. However, Phe-rich thermal proteinoid displayed a preference for its codonic nucleotide, poly U. This inconsistency seemed to be explained by a folding in of the hydrophobic residues of Phe causing the proteinoid to appear more hydrophilic. The present work used nuclear magnetic resonance techniques to resolve a limited question: To which of the four nucleotides does Phe bind most strongly? The results show quite clearly that Phe binds most strongly to its anticodonic nucleotide, AMP.     

Dihydroxamic acid complexes of iron (III): ligand pKa and coordinated water hydrolysis constants

A series of dihydroxamic acid ligands of the formula [RN(OH)C(O)]₂(CH₂)_n, (n = 2, 4, 6, 7, 8; R = CH₃, H) has been studied in 2.0 M aqueous sodium perchlorate at 25.0 °C. These ligands may be considered as synthetic analogs to the siderophore rhodotorulic acid. Acid dissociation constants (pK_a) have been determined for the ligands and for N-methylacetohydroxamic acid (NMHA). The pK_a1 and pK_a2 values are: n = 2, R = CH₃ (8.72, 9.37); N = 4, R = CH₃ (8.79, 9.37); N = 6, R = CH₃; N = 7, R = CH₃ (8.95, 9.47); N = 8, R = CH₃ (8.93, 9.45); N = 8, R = H (9.05, 9.58). Equilibrium constants for the hydrolysis of coordinated water (log K) have been estimated for the 1:1 feeric complexes of the ligands n = 2, 4, 8; R = CH₃. The N = 8 ligand forms a monomeric complex with Fe(III) while the n = 2 and 4 ligands form dimeric complexes. For hydrolysis of the n = 8 monomeric complex, log K₁ = −6.36 and log K₂ = −9.84. Analysis of the spectrophotometric data for the dimeric complexes indicates deprotonation of all four coordinated waters. The successive hydrolysis constants, log K_1–4, for the dimeric complexes are as follows: n = 2 (−6.37, −5.77, −10.73, −11.8); n = 4 (−5.54, −5.07, −11.57, −10.17). The log K₂ values for the dimers are unexpectedly high, higher in fact than log K₁, inconsistent with the formation of simple ternary hydroxo complexes. A scheme is proposed for the hydrolysis of the ferric dihydroxamate dimers, which includes the possible formation of μ-hydroxo and μ-oxo bridges.     

Flow and Oxygen Transfer Characteristics of an Intravenous Membrane Oxygenator: A Computational Study

Abstract

Spectral element computational simulations of the conservation of mass, momentum and species equations are performed to investigate the flow and oxygen transfer characteristics of an Intravenous Membrane Oxygenator (IMO). The simulations consider a three-dimensional IMO computational model consisting of equally-spaced fibers, an elastic balloon with non-permeable walls positioned longitudinally within the vena cava, and a Newtonian and time-dependent incompressible flow. Flow characteristics and oxygen transfer parameters are determined for operating conditions of a stationary and a pulsating balloon. For the stationary balloon configuration the flow is two-dimensional, parallel, laminar and without secondary flows for the Reynolds number range of 5.7-455.2. Evaluations of the oxygen transfer characteristics for the stationary balloon indicate that the main transport mechanisms are diffusion and convection in the crosswise and streamwise directions, respectively. Additionally, evaluations of oxygen transfer rates and Sherwood numbers in this Reynolds number range indicate that the oxygen transfer rate reaches an asymptotic limit at relatively moderate Reynolds numbers. For the pulsating balloon, flow characteristic results demonstrate the existence of a strong secondary flow around the fiber, and between the balloon and the fiber. This secondary flow induces oscillatory crosswise and streamwise velocities and a seemingly random spanwise flow which enhances the flow mixing as well as the transport of oxygen from the fiber surface to the bulk flow.     

Heteronuclear coupling constants of hydroxyl protons in a water solution of oligosaccharides: trehalose and sucrose

Relatively few details are known about the conformational preferences of hydroxyl groups in carbohydrates in water solution, though these would be informative about solvation and H-bonding. We show that highly concentrated solutions of sucrose and trehalose exhibit surprisingly well-resolved ¹H NMR spectra in a deuterium oxide–water solvent mixture at subzero temperatures. Measurement conditions are suitable to extract nearly all homonuclear and, for the first time, heteronuclear coupling constants of OH groups of carbohydrates in their natural abundance. For ^2,3J_HO,C coupling constants new, powerful variants of HETLOC and HECADE techniques were applied. The present data do not support the presence of persistent H-bonds in these two cryogenic disaccharides.     

Stress–strain behavior of mitral valve leaflets in the beating ovine heart

Excised anterior mitral leaflets exhibit anisotropic, non-linear material behavior with pre-transitional stiffness ranging from 0.06 to 0.09 N/mm² and post-transitional stiffness from 2 to 9 N/mm². We used inverse finite element (FE) analysis to test, for the first time, whether the anterior mitral leaflet (AML), in vivo, exhibits similar non-linear behavior during isovolumic relaxation (IVR). Miniature radiopaque markers were sewn to the mitral annulus, AML, and papillary muscles in 8 sheep. Four-dimensional marker coordinates were obtained using biplane videofluoroscopic imaging during three consecutive cardiac cycles. A FE model of the AML was developed using marker coordinates at the end of isovolumic relaxation (when pressure difference across the valve is approximately zero), as the reference state. AML displacements were simulated during IVR using measured left ventricular and atrial pressures. AML elastic moduli in the radial and circumferential directions were obtained for each heartbeat by inverse FEA, minimizing the difference between simulated and measured displacements. Stress–strain curves for each beat were obtained from the FE model at incrementally increasing transmitral pressure intervals during IVR. Linear regression of 24 individual stress–strain curves (8 hearts, 3 beats each) yielded a mean (±SD) linear correlation coefficient (r²) of 0.994±0.003 for the circumferential direction and 0.995±0.003 for the radial direction. Thus, unlike isolated leaflets, the AML, in vivo, operates linearly over a physiologic range of pressures in the closed mitral valve.     

Reaction rate constants of superoxide scavenging by plant antioxidants

Plant phenols may exert protective effects by scavenging superoxide, which is implicated in tissue damage and accelerated inactivation of vasorelaxing nitric oxide. Preventing the interaction of superoxide with tissue biomolecules depends not only on the extent of superoxide scavenging but also on scavenging velocity. However, information on superoxide scavenging kinetics of plant phenols is scarce. We describe an improved lucigenin-based chemiluminescence assay for kinetic analysis. The use of potassium superoxide (KO₂) as a nonenzymatic superoxide source allowed simple and reliable determination of the second-order reaction rate constants between superoxide and plant antioxidants at physiologically relevant conditions, avoiding unspecific effects of other reactive oxygen species or superoxide-generating enzymes. We calculated the rate constants for phenols of different structures, ranging from 2.9 × 10³ mol⁻¹ l s⁻¹ for morin to 2.9 × 10⁷ mol⁻¹ l s⁻¹ for proanthocyanidins. Compounds with pyrogallol or catechol moieties were revealed as the most rapid superoxide scavengers, and the gallate moiety was found to be the minimal essential structure for maximal reaction rate constants with superoxide.     

Transient response method for evaluating the rate constants of reactions over immobilized enzymes

The transient response method was utilized to evaluate the rate constants of reaction over immobilized enzyme. Glucose oxidation catalyzed by the immobilized glucose oxidase in a fixed-bed reactor was selected as an example. A theoretical model including the effects of axial dispersion, film diffusion, and intraparticle diffusion was established for the reactor. The individual rate constant of each elementary step of this enzymatic reaction was determined through direct fitting of the experimental response data to the model.