A nonlinear biphasic model of flow-controlled infusion in brain: Fluid transport and tissue deformation analyses

A biphasic nonlinear mathematical model is proposed for the concomitant fluid transport and tissue deformation that occurs during constant flow rate infusions into brain tissue. The model takes into account material and geometrical nonlinearities, a hydraulic conductivity dependent on strain, and nonlinear boundary conditions at the infusion cavity. The biphasic equations were implemented in a custom written code assuming spherical symmetry and using an updated Lagrangian finite element algorithm. Results of the model showed that both, geometric and material nonlinearities play an important role in the physics of infusions, yielding important differences from infinitesimal analyses. Geometrical nonlinearities were mainly due to the significant enlargement of the infusion cavity, while variations of the parameters that describe the degree of nonlinearity of the stress–strain curve yielded significant differences in all distributions. For example, a parameter set showing stiffening under tension yielded maximum values of radial displacement and porosity not localized at the infusion cavity. On the other hand, a parameter set showing softening under tension yielded a slight decrease in the fluid velocity for a three-fold increase in the flow rate, which can be explained by the substantial increase of the infusion cavity, not considered in linear analyses. This study strongly suggests that significant enlargement of the infusion cavity is a real phenomenon during infusions that may produce collateral damage to brain tissue. Our results indicate that more experimental tests have to be undertaken in order to determine material nonlinearities of brain tissue over a range of strains. With better understanding of these nonlinear effects, clinicians may be able to develop protocols that can minimize the damage to surrounding tissue.     

A nonlinear biphasic viscohyperelastic model for articular cartilage

Experiments on articular cartilage have shown nonlinear stress-strain curves under finite deformations as well as intrinsic viscous effects of the solid phase. The aim of this study was to propose a nonlinear biphasic viscohyperelastic model that combines the intrinsic viscous effects of the proteoglycan matrix with a nonlinear hyperelastic constitutive equation. The proposed equation satisfies objectivity and reduces for uniaxial loading to a solid type viscous model in which the actions of the springs are represented by the hyperelastic function proposed by Holmes and Mow [1990. J. Biomechanics 23, 1145-1156.]. Results of the model, that were efficiently implemented in an updated Lagrangian algorithm, were compared with experimental infinitesimal data reported by DiSilverstro and Suh [2001. J. Biomechanics 34, 519-525.] and showed acceptable fitting for the axial force (R(2)=0.991) and lateral displacement (R(2)=0.914) curves in unconfined compression as well as a good fitting of the axial indentation force curve (R(2)=0.982). In addition, the model showed an excellent fitting of finite-deformation confined compression stress relaxation data reported by Ateshian et al. [1997. J. Biomechanics 30, 1157-1164.] and Huang et al. [2005. J. Biomechanics 38, 799-809.] (R(2)=0.993 and R(2)=0.995, respectively). The constitutive equation may be used to represent the mechanical behavior of the proteoglycan matrix in a fiber reinforced model of articular cartilage.     

A nonlinear biphasic fiber-reinforced porohyperviscoelastic model of articular cartilage incorporating fiber reorientation and dispersion

A nonlinear biphasic fiber-reinforced porohyperviscoelastic (BFPHVE) model of articular cartilage incorporating fiber reorientation effects during applied load was used to predict the response of ovine articular cartilage at relatively high strains (20%). The constitutive material parameters were determined using a coupled finite element-optimization algorithm that utilized stress relaxation indentation tests at relatively high strains. The proposed model incorporates the strain-hardening, tension-compression, permeability, and finite deformation nonlinearities that inherently exist in cartilage, and accounts for effects associated with fiber dispersion and reorientation and intrinsic viscoelasticity at relatively high strains. A new optimization cost function was used to overcome problems associated with large peak-to-peak differences between the predicted finite element and experimental loads that were due to the large strain levels utilized in the experiments. The optimized material parameters were found to be insensitive to the initial guesses. Using experimental data from the literature, the model was also able to predict both the lateral displacement and reaction force in unconfined compression, and the reaction force in an indentation test with a single set of material parameters. Finally, it was demonstrated that neglecting the effects of fiber reorientation and dispersion resulted in poorer agreement with experiments than when they were considered. There was an indication that the proposed BFPHVE model, which includes the intrinsic viscoelasticity of the nonfibrillar matrix (proteoglycan), might be used to model the behavior of cartilage up to relatively high strains (20%). The maximum percentage error between the indentation force predicted by the FE model using the optimized material parameters and that measured experimentally was 3%.     

Unconfined compression of articular cartilage: nonlinear behavior and comparison with a fibril-reinforced biphasic model

Mechanical behavior of articular cartilage was characterized in unconfined compression to delineate regimes of linear and nonlinear behavior, to investigate the ability of a fibril-reinforced biphasic model to describe measurements, and to test the prediction of biphasic and poroelastic models that tissue dimensions alter tissue stiffness through a specific scaling law for time and frequency. Disks of full-thickness adult articular cartilage from bovine humeral heads were subjected to successive applications of small-amplitude ramp compressions cumulating to a 10 percent compression offset where a series of sinusoidal and ramp compression and ramp release displacements were superposed. We found all equilibrium behavior (up to 10 percent axial compression offset) to be linear, while most nonequilibrium behavior was nonlinear, with the exception of small-amplitude ramp compressions applied from the same compression offset. Observed nonlinear behavior included compression-offset-dependent stiffening of the transient response to ramp compression, nonlinear maintenance of compressive stress during release from a prescribed offset, and a nonlinear reduction in dynamic stiffness with increasing amplitudes of sinusoidal compression. The fibril-reinforced biphasic model was able to describe stress relaxation response to ramp compression, including the high ratio of peak to equilibrium load. However, compression offset-dependent stiffening appeared to suggest strain-dependent parameters involving strain-dependent fibril network stiffness and strain-dependent hydraulic permeability. Finally, testing of disks of different diameters and rescaling of the frequency according to the rule prescribed by current biphasic and poroelastic models (rescaling with respect to the sample's radius squared) reasonably confirmed the validity of that scaling rule. The overall results of this study support several aspects of current theoretical models of articular cartilage mechanical behavior, motivate further experimental characterization, and suggest the inclusion of specific nonlinear behaviors to models.     

A biphasic multilayer computational model of human skin

The present study investigates the layer-specific mechanical behavior of human skin. Motivated by skin’s histology, a biphasic model is proposed which differentiates between epidermis, papillary and reticular dermis, and hypodermis. Inverse analysis of ex vivo tensile and in vivo suction experiments yields mechanical parameters for each layer and predicts a stiff reticular dermis and successively softer papillary dermis, epidermis and hypodermis. Layer-specific analysis of simulations underlines the dominating role of the reticular dermis in tensile loading. Furthermore, it shows that the observed out-of-plane deflection in ex vivo tensile tests is a direct consequence of the layered structure of skin. In in vivo suction experiments, the softer upper layers strongly influence the mechanical response, whose dissipative part is determined by interstitial fluid redistribution within the tissue. Magnetic resonance imaging-based visualization of skin deformation in suction experiments confirms the deformation pattern predicted by the multilayer model, showing a consistent decrease in dermal thickness for large probe opening diameters.

     

A biphasic, anisotropic model of the aortic wall

A biphasic, anisotropic elastic model of the aortict wall is developed and compared to literature values of experimental measurements of vessel wall radii, thickness, and hvdraulic conductivity as a function of intraluminal pressure. The model gives good predictions using a constant wall modulus for pressures less than 60 mmHg, but requires a strain-dependent modulus for pressures greater than this. In both bovine and rabbit aorta, the tangential modulus is found to be approximately 20 times greater than the radial modulus. These moduli lead to predictions that, when perfused in a cylindrical geometry, the aortic volume and its specific hydraulic coonductivity are relatively independent of perfusion pressure, in agreement with experimental measurements. M, the parameter that relates specific hydraulic conductivy, to tissue dilation, is found to be a positive quantity correcting a previous error in the literature.     

Mass transport of macromolecules within an in vitro model of supragingival plaque

The aim of this study was to examine the diffusion of macromolecules through an in vitro biofilm model of supragingival plaque. Polyspecies biofilms containing Actinomyces naeslundii, Fusobacterium nucleatum, Streptococcus oralis, Streptococcus sobrinus, Veillonella dispar, and Candida albicans were formed on sintered hydroxyapatite disks and then incubated at room temperature for defined periods with fluorescent markers with molecular weights ranging from 3,000 to 900,000. Subsequent examination by confocal laser scanning microscopy revealed that the mean square penetration depths for all tested macromolecules except immunoglobulin M increased linearly with time, diffusion coefficients being linearly proportional to the cube roots of the molecular weights of the probes (range, 10,000 to 240,000). Compared to diffusion in bulk water, diffusion in the biofilms was markedly slower. The rate of diffusion for each probe appeared to be constant and not a function of biofilm depth. Analysis of diffusion phenomena through the biofilms suggested tortuosity as the most probable explanation for retarded diffusion. Selective binding of probes to receptors present in the biofilms could not explain the observed extent of retardation of diffusion. These results are relevant to oral health, as selective attenuated diffusion of fermentable carbohydrates and acids produced within dental plaque is thought to be essential for the development of carious lesions.     

A compartmental model for oxygen transport in brain microcirculation in the presence of blood substitutes

A compartmental model is developed for oxygen (O(2)) transport in brain microcirculation in the presence of blood substitutes (hemoglobin-based oxygen carriers). The cerebrovascular bed is represented as a series of vascular compartments, on the basis of diameters, surrounded by a tissue compartment. A mixture of red blood cells (RBC) and plasma/extracellular hemoglobin solution flows through the vascular bed from the arterioles through the capillaries to the venules. Oxygen is transported by convection in the vascular compartments and by diffusion in the surrounding tissue where it is utilized. Intravascular resistance and the diffusive loss of oxygen from the arterioles to the tissue are incorporated in the model. The model predicts that most of the O(2) transport occurs at the level of capillaries. Results computed from the present model in the presence of hemoglobin-based oxygen carriers are consistent with those obtained from the earlier validated model (Sharan et al., 1989, 1998a) on oxygen transport in brain circulation in the absence of extracellular hemoglobin. We have found that: (a) precapillary PO(2) gradients increase as PO(2) in the arterial blood increases, P(50 p) (oxygen tension at 50% saturation of hemoglobin with O(2) in plasma) decreases, i.e. O(2) affinity of the extracellular hemoglobin is increased, the flow rate of the mixture decreases, hematocrit decreases at constant flow, metabolic rate increases, and intravascular transport resistance in the arterioles is neglected; (b) precapillary PO(2) gradients are not sensitive to (i) intracapillary transport resistance, (ii) cooperativity (n(p)) of hemoglobin with oxygen in plasma, (iii) hemoglobin concentration in the plasma and (iv) hematocrit when accounting for viscosity variation in the flow; (c) tissue PO(2) is not sensitive to the variation of intravascular transport resistance in the arterioles. We also found that tissue PO(2) is a non-monotonic function of the Hill coefficient n(p) for the extracellular hemoglobin with a maximum occurring when n(p) equals the blood Hill coefficient. The results of the computations give estimates of the magnitudes of the increases in tissue PO(2) as arterial PO(2) increases,P(50 p) increases, flow rate increases, hematocrit increases, hemoglobin concentration in the plasma increases, metabolic rate decreases, the capillary mass transfer coefficient increases or the intracapillary transport resistance decreases.     

A fully nonlinear viscohyperelastic model for the brain tissue applicable to dynamic rates

Understanding the mechanical response of the brain to external loadings is of critical importance in investigating the pathological conditions of this tissue during injurious conditions. Such injurious loadings may occur at high rates, for example among others, during road traffic or sport accidents, falls, or due to explosions. Hence, investigating the injury mechanism and design of protective devices for the brain requires constitutive modeling of this tissue at such rates. Accordingly, this paper is aimed at critically investigating the physical background for viscohyperelastic modeling of the brain tissue with scrutinizing the elastic fields pertinent to large, time dependent deformations, and developing a fully nonlinear multimode Maxwell model that can mathematically explain such deformations. The proposed model can be calibrated using the simple monotonic uniaxial deformation of the sample extracted from the tissue, and does not require additional information from relaxation or creep experiments. The performance of the proposed model is examined using the experimental results of two different studies, which reveals a desirable agreement. The usefulness, limitations, and future developments of the proposed model are discussed in this paper.     

Mass customization: manufacturing issues and taxonomic analyses

As the field of mass customization (MC) attains the status of a mature discipline, two significant research deficits stand out. First, a through metareview of the entire body of MC research that looks at the application value and rigorousness of research is overdue. Second, manufacturing issues, especially those pertaining to quality and the supply chain have been largely ignored. This issue is dedicated to both of these important areas of research. The conclusion with regards to the status of the MC field is that it is currently vibrant, with growing research volume and applications. The manufacturing issues dealt with in this issue are strategically important, dealing with quality and customization issues. The work on quality is the first of its kind: it seeks to generate a defect-tracking matrix consistent with product configurations, enabling agile identification of defects in a mass customization environment. The use of discrete event simulation to deal with the dynamically evolving customized demand so as to minimize cost and schedule disruption is innovative, timely, and profound.     

A biphasic model for micro-indentation of a hydrogel-based contact lens

The stiffness and hydraulic permeability of soft contact lenses may influence its clinical performance, e.g., on-eye movement, fitting, and wettability, and may be related to the occurrence of complications; e.g., lesions. It is therefore important to determine these properties in the design of comfortable contact lenses. Micro-indentation provides a nondestructive means of measuring mechanical properties of soft, hydrated contact lenses. However, certain geometrical and material considerations must be taken into account when analyzing output force-displacement (F-D) data. Rather than solely having a solid response, mechanical behavior of hydrogel contact lenses can be described as the coupled interaction between fluid transport through pores and solid matrix deformation. In addition, indentation of thin membranes ( approximately 100 microm) requires special consideration of boundary conditions at lens surfaces and at the indenter contact region. In this study, a biphasic finite element model was developed to simulate the micro-indentation of a hydrogel contact lens. The model accounts for a curved, thin hydrogel membrane supported on an impermeable mold. A time-varying boundary condition was implemented to model the contact interface between the impermeable spherical indenter and the lens. Parametric studies varying the indentation velocities and hydraulic permeability show F-D curves have a sensitive region outside of which the force response reaches asymptotic limits governed by either the solid matrix (slow indentation velocity, large permeability) or the fluid transport (high indentation velocity, low permeability). Using these results, biphasic properties (Young's modulus and hydraulic permeability) were estimated by fitting model results to F-D curves obtained at multiple indentation velocities (1.2 and 20 microm/s). Fitting to micro-indentation tests of Etafilcon A resulted in an estimated permeability range of 1.0 x 10(-15) to 5.0 x 10(-15) m(4)N s and Young's modulus range of 130 to 170 kPa.     

A model of interfacial inactivation for papain in aqueous organic biphasic systems

A model was proposed to describe the effects of the main factors in aqueous-organic two-liquid-phase media on the stability of papain. The relationships between the half-life of papain activity and these factors including interfacial tension, stirring rate, phase volume ratio and temperature were investigated. The results showed that these factors had notable effects on papain stability except temperature. The correlation coefficient between the model and the experimental data were 0.829, which indicated the model is practicable.     

A realistic model of biphasic calcium transients in electrically nonexcitable cells.

In many electrically nonexcitable cells, the release of calcium from internal stores is followed by a much slower phase in which the intracellular calcium concentration decreases gradually to a sustained value higher than the concentration before stimulation. This elevated calcium plateau has been shown to be the result of calcium influx. The model presented in this work describes a system consisting of a cytoplasmic calcium store and a plasma membrane calcium channel, both excitable by a membrane receptor; a fast cytoplasmic calcium buffer; and calcium pumps in both the calcium store and cellular membranes. Inherent difficulties in the numerical evaluation of the model, caused by very large calcium fluxes across the store membrane, were overcome by analytically separating the fast processes of calcium release from the slower processes of calcium cycling across the plasma membrane. This enabled the simulation of realistic biphasic calcium transients similar to those observed experimentally. The model predicted 1) a strong correlation between the rate of calcium cycling across the plasma membrane and the rate of calcium decay; and 2) a dependence on the level of cell excitation of the maximum rise in cytoplasmic calcium concentration, the level of the elevated calcium plateau, and the rate of calcium decay. Using the model, we simulated the washout of agonist from the bathing solution and the depletion of the calcium store by a pharmacological agent (such as thapsigargin) under several experimental conditions.     

A model of ovum transport

A theoretical fluid dynamical model of ovum transport in the oviduct incorporating transport mechanisms due to ciliary activity, muscular activity and an applied pressure drop across the oviduct is developed. Theory suggests that the cilia provide the steady component of ovum transport whereas muscular activity results in highly oscillatory motion. If muscular activity is to provide transport in a pro-uterine direction, a coordinated sequence of muscular activity with a strong pro-uterine bias is needed. Changes in pressure are highest in the narrowest sections. The highly convoluted rugae may allow "leakback" around the ovum so relieving the pressure drop across the ovum in narrower sections of the oviduct.     

Weakly nonlinear stability analyses of one-dimensional Turing pattern formation in activator-inhibitor/immobilizer model systems

The development of one-dimensional Turing patterns characteristic of the chlorite-iodide-malonic acid/starch reaction as well as analogous Brussellator/immobilizer and Schnackenberg/immobilizer model systems is investigated by means of a weakly nonlinear stability analysis applied to the appropriately scaled governing equations. Then the theoretical predictions deduced from these pattern formation studies are compared with experimental evidence relevant to the Turing diffusive instabilities under examination in order to explain more fully the transition to such stationary symmetry-breaking spatial structures when the temperature or pool species concentrations vary.     

Microbial genome analyses: comparative transport capabilities in eighteen prokaryotes

Here, we present a comprehensive analysis of solute transport systems encoded within the completely sequenced genomes of 18 prokaryotic organisms. These organisms include four Gram-positive bacteria, seven Gram-negative bacteria, two spirochetes, one cyanobacterium and four archaea. Membrane proteins are analyzed in terms of putative membrane topology, and the recognized transport systems are classified into 76 families, including four families of channel proteins, four families of primary carriers, 54 families of secondary carriers, six families of group translocators, and eight unclassified families. These families are analyzed in terms of the paralogous and orthologous relationships of their protein members, the substrate specificities of their constituent transporters and their distributions in each of the 18 organisms studied. The families vary from large superfamilies with hundreds of represented members, to small families with only one or a few members. The mode of transport generally correlates with the primary mechanism of energy generation, and the numbers of secondary transporters relative to primary transporters are roughly proportional to the total numbers of primary H(+) and Na(+) pumps in the cell. The phosphotransferase system is less prevalent in the analyzed bacteria than previously thought (only six of 14 bacteria transport sugars via this system) and is completely lacking in archaea and eukaryotes. Escherichia coli is shown to be exceptionally broad in its transport capabilities and therefore, at a membrane transport level, does not appear representative of the bacteria thus far sequenced. Archaea and spirochetes exhibit fewer proteins with multiple transmembrane segments and fewer net transporters than most bacteria. These results provide insight into the relevance of transport to the overall physiology of prokaryotes.     

Tryptamine transport in rat brain slices: A comparison with 5-hydroxytryptamine

The uptake of [¹⁴C]tryptamine (¹⁴C-T) and [³H]serotonin (³H-5HT) into slices of rat hypothalamus (HT), fronto-parietal cortex (CX), and caudate nucleus (Cau) has been investigated. In all three brain areas, the uptake of³H-5HT at 37°C was much greater than that in an ice-bath at 1.0–1.5°C. In contrast, the uptake of¹⁴C-T at 37°C was not much greater than uptake at 1.0–1.5°C. While markedly different amounts of³H-5HT were accumulated by each of the brain areas studied, the regional uptake of¹⁴C-T was quantitatively similar. In general the uptake of¹⁴C-T was inhibited less than³H-5HT by cocaine, DNP, ouabain, and decreased Na⁺ concentrations. Similarly,¹⁴C-T was less susceptible to serotonin uptake inhibitors except in the caudate. It was concluded that though a common indoleamine uptake system accumulates both T and 5HT, a non-specific low affinity or diffusional process also transports both amines and is predominantly responsible for T, but not 5HT, uptake. The spontaneous release, or wash-out, of¹⁴C-T from the caudate was much faster than that of³H-5HT. In addition, while depolarizing stimuli caused little or no release of¹⁴C-T, large releases of³H-5HT were observed. T, therefore, does not behave like a conventional neurotransmitter.     

The feasibility of utilizing a mathematical model in studying nonlinear transport processes in living systems

On the basis of proportionality between flow and its conjugated force a mathematical model for volume, current and osmotic flows was designed and a method for the experimental measurement of flows, the transbarrier (trans-segmental) potential and the rate of flow was devised. The results obtained experimentally as well as using the mathematical model indicate that the plant root is differentiated not only according to localization, but also according to the conductivity, permeability and selectivity of these tissues.