Effect of viscoelastic relaxation on moisture transport in foods. Part II: Sorption and drying of soybeans

The general fluid transport equation presented in Part-I of this paper is used for predicting moisture transport and viscoelastic stresses during sorption and drying of soybeans. Predicted drying curves were validated using experimental data obtained from literature (average absolute difference 6-13%). For drying temperatures used in the soybean processing industry (70–93 °C), smooth moisture profiles were obtained, which indicated Fickian (Darcian) transport. As the drying temperature approached the glass transition temperature (25 °C at 10% moisture content), the moisture profiles became sharper, which indicated non-Fickian (non-Darcian) transport. The viscoelastic stress profiles clearly exhibited the role of the force terms during imbibition and drying. Increase in drying temperature tends to decrease the stress relaxation function but reduction in moisture content during drying tends to increase it. The increase in stress due to the reduction in moisture content below 10% was not compensated by an increase in drying temperature. Drying of soybeans below 10% moisture content should be avoided in the industry because this will lead to thicker flakes that reduce the amount of oil recovery. During imbibition of soybeans, a high magnitude of stresses was obtained in the rubbery regions, which may cause critical regions prone to fissuring. The role of glass transition on stress development and critical region development was clearly observed during drying and imbibition of soybeans.Revised version: 5 October 2003     

Viscoelastic behavior of erythrocyte membrane.

A nonlinear viscoelastic relation is developed to describe the viscoelastic properties of erythrocyte membrane. This constitutive equation is used in the analysis of the time-dependent aspiration of an erythrocyte membrane into a micropipette. Equations governing this motion are reduced to a nonlinear integral equation of the Volterra type. A numerical procedure based on a finite difference scheme is used to solve the integral equation and to match the experimental data. The data, aspiration length vs. time, is used to determine the relaxation function at each time step. The inverse problem of obtaining the time dependence of the aspiration length from a given relaxation function is also solved. Analytical results obtained are applied to the experimental data of Chien et al. 1978. Biophys. J. 24:463-487. A relaxation function similar to that of a four-parameter solid with a shear-thinning viscous term is proposed.     

Determining rigid body transformation parameters from ill-conditioned spatial marker co-ordinates

The three-dimensional location of a body-fixed axis system is described by position and orientation parameters that can be calculated knowing local and global coordinates of three or more body-fixed markers. However, marker distribution can become ill-conditioned when marker placement is symmetrical with respect to the mean of the markers. As symmetry and ill-conditioning increases, random errors in marker locations can affect the stability of orientation parameters as a result of the mathematical approach adopted. The present study investigates the methods of Veldpaus et al. [1988; Journal of Biomechanics 21, 45], Challis [1995; Biomechanics 28, 733] and Andriacchi et al. [1998; Journal of Biomedical Engineering 120, 743] for obtaining segment orientation parameters when segment markers ranged from well-defined to highly ill-conditioned depending on the symmetry of segment markers. A novel fourth approach is also presented that enabled comparisons of the root mean square error of reconstructed marker coordinates to verify that an optimal solution was obtained. No single method produced optimal results for all axis orientation parameters when reconstructing movement trials. The best performed was the method of Veldpaus et al. [1988; Journal of Biomechanics 21, 45] based on consistent results and ease of implementation. The fourth approach presented provided a reliable method in all but the highly ill-conditioned markers, however implementation was computationally difficult. The method of Challis [1995; Biomechanics 28, 733] was only suited to well-conditioned marker sets which avoided markers lying in a single plane with symmetries in marker distribution relative to the mean. The method of Andriacchi et al. [1998; Journal of Biomedical Engineering 120, 743] produced, at best, orientation parameters that approximated the results obtained by least squares methods.     

A constituent-based model for the nonlinear viscoelastic behavior of ligaments

This paper presents a constitutive model for predicting the nonlinear viscoelastic behavior of soft biological tissues and in particular of ligaments. The constitutive law is a generalization of the well-known quasi-linear viscoelastic theory (QLV) in which the elastic response of the tissue and the time-dependent properties are independently modeled and combined into a convolution time integral. The elastic behavior, based on the definition of anisotropic strain energy function, is extended to the time-dependent regime by means of a suitably developed time discretization scheme. The time-dependent constitutive law is based on the postulate that a constituent-based relaxation behavior may be defined through two different stress relaxation functions: one for the isotropic matrix and one for the reinforcing (collagen) fibers. The constitutive parameters of the viscoelastic model have been estimated by curve fitting the stress relaxation experiments conducted on medial collateral ligaments (MCLs) taken from the literature, whereas the predictive capability of the model was assessed by simulating experimental tests different from those used for the parameter estimation. In particular, creep tests at different maximum stresses have been successfully simulated. The proposed nonlinear viscoelastic model is able to predict the time-dependent response of ligaments described in experimental works (Bonifasi-Lista et al., 2005, J. Orthopaed. Res., 23, pp. 67-76; Hingorani et al., 2004, Ann. Biomed. Eng., 32, pp. 306-312; Provenzano et al., 2001, Ann. Biomed. Eng., 29, pp. 908-214; Weiss et al., 2002, J. Biomech., 35, pp. 943-950). In particular, the nonlinear viscoelastic response which implies different relaxation rates for different applied strains, as well as different creep rates for different applied stresses and direction-dependent relaxation behavior, can be described.     

Gas transport during oscillatory flow in a network of branching tubes

A transport coefficient was measured for a range of oscillatory flow conditions in a branching network of tubes. Measurements were made both across the first generation of a three-generation network and the second generation of a four-generation network. The results for these two series of tests were similar, indicating that there was no significant effect due to the system boundaries. The results are cast in terms of an effective axial diffusion coefficient of the form (Formula: see text) where kappa is the molecular diffusivity, Vt is the local stroke volume (cc); and f is the oscillation frequency (Hz). These results are compared to those obtained by other investigators in branching systems of similar geometry. At low frequency, this result is found to be in approximate agreement with the steady flow result of Scherer, et al. [15]. This expression differs from the oscillatory flow results of Tarbell, et al. [19] for liquids, primarily in terms of the effects of oscillation frequency.     

On the generalization of the Weinbaum-Jiji bioheat equation to microvessels of unequal size; the relation between the near field and local average tissue temperatures

The extensive series of experiments reported in Lemons et al. [1] show that measureable local tissue temperature fluctuations are observed primarily in the vicinity of the 100-500 micron countercurrent vessels of the microcirculation and thus strongly support the basic hypothesis in the new bioheat equation of Weinbaum and Jiji [2] that these countercurrent microvessels are the principal determinants of local blood-tissue heat transfer. However, the detailed temperature profiles in the vicinity of these vessels indicate that large asymmetries in the local temperature field can result from the significant differences in size between the countercurrent artery and vein. Using the superposition techniques of Baish et al. [9], the paper first presents a solution to the classic problem of an unequal countercurrent heat exchanger with heat loss to the far field. This solution is then used to generalize the Weinbaum-Jiji bioheat equation and the conductivity tensor that appears in this equation to vessels of unequal size. An asymptotic analysis has also been developed to elucidate the relationship between the near field temperature of the artery-vein pair and the local average tissue temperature. This analysis is used to rigorously prove the closure approximation relating the local arterial-venous temperature difference and the mean tissue temperature gradient which had been derived in [2] using a more heuristic approach.     

A new drift-flux model for particle transport and deposition in human airways

Particle deposition and transport in human airways isfrequently modeled numerically by the Lagrangian approach. Current formulations of such models always require some ad hoc assumptions, and they are computationally expensive. A new drift-flux model is developed and incorporated into a commercial finite volume code. Because it is Eulerian in nature, the model is able to simulate particle deposition patterns, distribution and transport both spatially and temporally. Brownian diffusion, gravitational settling, and electrostatic force are three major particle deposition mechanisms in human airways. The model is validated against analytical results for three deposition mechanisms in a straight tube prior to applying the method to a single bifurcation G3-G4. Two laminar flows with Reynolds numbers 500 and 2000 are simulated. Particle concentration contour deposition pattern, and enhancement factor are evaluated. To demonstrate how the diffusion and settling influence the deposition and transport along the bifurcation, particle sizes from 1 nm to 10 microm are studied. Different deposition mechanisms can be combined into the mass conversation equation. Combined deposition efficiency for the three mechanisms simultaneously was evaluated and compared with two commonly used empirical expressions.     

Intraflagellar transport and cilium-based signaling

Cilia are specialized structures that not only play diverse roles in cell motility but also transmit signals to the cytoplasm and nucleus to control gene expression, cell function, animal development, and behavior. Cilia are assembled and maintained by the intraflagellar transport (IFT) machinery, which coordinates rapid, bidirectional transport between the cell body and the distal tip of the cilium. A new study (Wang et al., 2006) illuminates the role of IFT in cilium-based signaling during mating in the alga Chlamydomonas.     

A critical comparison of different residence time measures in aneurysms

Flow stagnation and residence time (RT) are important features of diseased arterial flows that influence biochemical transport processes and thrombosis. RT calculation methods are classified into Eulerian and Lagrangian approaches where several measures have been proposed to quantify RT. Each of these methods has a different definition of RT, and it is not clear how they are related. In this study, image-based computational models of blood flow in an abdominal aortic aneurysm and a cerebral aneurysm were considered and RT was calculated using different methods. In the Lagrangian methods, discrete particle tracking of massless tracers was used to calculate particle residence time and mean exposure time. In the Eulerian methods, continuum transport models were used to quantify RT using Eulerian RT and virtual ink approaches. Point-wise RT and Eulerian indicator RT were also computed based on measures derived from velocity. A comparison of these methods is presented and the implications of each method are discussed. Our results highlight that most RT methods have a conceptually distinct definition of RT and therefore should be utilized depending on the specific application of interest.     

Model transformations to evaluate transient thermal responses at a tissue surface

For a spatially distributed model describing the transient temperature response of a thermistor-tissue system, Wei et al. [J. Biomech. Eng., 117:74-85, 1995] obtained an approximate transformation for fast analysis of the temperature response at the tissue surface. This approximate transformation reduces the model to a single ordinary differential equation. Here, we present an exact transformation that yields a single differential-integral equation. Numerical solutions from the approximate and exact transformations were compared to evaluate the differences with several sets of parameter values. The maximum difference between the exact and approximate solutions did not exceed 15 percent and occurred for only a short time interval. The root-mean-square error of the approximate solution was no more than 5 percent and within the level of experimental noise. Under the experimental conditions used by Wei et al., the approximate transformation is justified for estimating model parameters from transient thermal responses.     

Na+-dependent p-aminohippurate transport at the basolateral side of the isolated perfused rat kidney

The uptake of p-amino[3H]hippurate by isolated perfused rat kidney was studied to characterize the mechanism which was responsible for organic anion transport process. A rapid injection multiple indicator dilution technique and the distributed two-compartment model of Sawada et al. (Computer Methods Programs Biomed., 20 (1985) 51) were employed. Some characteristics of a carrier-mediated transport from the antiluminal space to the intracellular space for p-aminohippurate at the basolateral side were demonstrated: the uptake was stimulated by the countertransport effect and showed Na+ dependency. These findings are consistent with p-amino[3H]hippurate's being taken up into the isolated rat basolateral membrane vesicle by Na+-dependent carrier-mediated transport (J. Pharmacol. Exp. Ther. 227 (1983) 122). It is suggested that the multiple indicator dilution technique is a sensitive new method to study the mechanisms of renal tubular transport in the living kidney as an organ.     

Calculation of the reflection coefficient from measurements of endogenous vascular indicators

The solvent drag reflection coefficient (sigma) for total proteins can be estimated by comparing the relative degrees of concentration of erythrocytes and plasma proteins that occur during fluid filtration in an isolated perfused organ. In this analysis, we evaluated the accuracy of equations proposed by Pilati and Maron [Am. J. Physiol. 247 (Heart Circ. Physiol. 16): H1-H7, 1984] and Wolf et al. [Am. J. Physiol. 253 (Heart Circ. Physiol. 22): H194-H204, 1987] to calculate sigma from these concentration changes. We calculated sigma with each equation using data generated from a mathematical model of fluid and solute flux in membranes with known sigma's. We found that the equation of Wolf et al. provided the closest approximation to the true sigma over the entire range of filtration fractions tested (0.1-0.6), with the differences between the two equations increasing with filtration fraction. At low filtration fractions, the difference in sigma obtained using either approach was found to be inconsequential. At larger filtration fractions, a closer approximation of the true sigma can be obtained using the equation of Wolf et al.     

Evidence for a close link between the thyroid hormone transport system and the aromatic amino acid transport system T in erythrocytes

The transport of [125I]triiodothyronine ([125I]T3) and [3H]tryptophan ([3H]Trp) by washed rat erythrocytes was studied at 25 degrees C in the presence of leucine in order to block the neutral amino acid transport system L. Eadie-Hofstee plots of initial velocity data gave the following values of Km (micromolar) and Vmax (nanomole/min/10(8) cells): 0.122 +/- 0.007 and 0.140 +/- 0.021 for T3, and 558 +/- 28 and 17.4 +/- 2.3 for Trp (n = 5). The Trp transport system in rat erythrocytes is similar to the human erythrocyte aromatic amino acid-specific system T described by Rosenberg et al. (Rosenberg, R., Young, J. D., and Ellory, J. C. (1980) Biochim. Biophys. Acta 598, 375-384). Unlabeled aromatic amino acids (e.g. Trp, phenylalanine, tyrosine) competitively inhibited [125I]T3 uptake and unlabeled iodothyronine analogues (e.g. T3, D-T3, thyroxine, thyronine) competitively inhibited [3H]Trp uptake. The inhibition constants of these competitors measured with each labeled substrate were highly correlated. N-Ethylmaleimide irreversibly inhibited T3 and Trp transport and each substrate protected the transport system of the other from inactivation by N-ethylmaleimide. The Vmax of T3 and Trp transport by human erythrocytes were 500 and 120 times lower, respectively, than those of rat erythrocytes (0.30 and 126 pmol/min/10(8) cells, respectively). The T3 and Trp transport activities of sheep erythrocytes were undetectable. These results indicate that T3 and Trp either share a common multi-specific transport system or are transported by closely linked systems which interact in the erythrocyte membrane.     

Mechanical hemolysis in blood flow: user-independent predictions with the solution of a partial differential equation

This paper presents for the first time numerical predictions of mechanical blood hemolysis obtained by solving a hyperbolic partial differential equation (PDE) modelling the hemolysis in a Eulerian frame of reference. This provides hemolysis predictions over the entire computational domain as an alternative to the Lagrangian approach consisting in evaluating cell hemolysis along their trajectories. The solution of a PDE over a computational domain, such as in the approach presented herein, yields a unique solution. This is a clear advantage over the Lagrangian approach, which requires the human-made choice of a limited number of trajectories for integration and inevitably results in the incomplete coverage of the computational domain. The hyperbolic hemolysis model is solved with a Discontinuous Galerkin finite element method. The solution algorithm also includes adaptive remeshing to provide high accuracy simulations. Predictions of the modified index of hemolysis (MIH) are presented for flows in dialysis cannulae and sudden contractions. MIH predictions for cannulae differ significantly from those obtained by other authors using the Lagrangian approach. The predictions for flows in sudden contractions are used, along with our own experimental measurements, to assess the value of the threshold shear stress required for hemolysis that is included in the hemolysis model.     

Permeability of artificial membranes to a pluridisperse solution of 125I-polyvinylpyrrolidone.

The validity of the transport equation for uncharged macromolecules across a porous membrane developed by Verniory et al. (1973, J. Gen. Physiol. 62:489) has been tested on several types of artificial membranes (Amicon PM-30, XM-50, and XM-100 Diaflo ultrafilters) using a pluridisperse solution of polyvinylpyrrolidone as filtrand. The influence of the filtration pressure on the shape of the sieving curve predicted by the theory has been verified. A mean pore radius and the width of the pore demonstrated that the method used previously to determine the effective filtration pressure in the glomerulus from sieving data is valid. The transport equation previously proposed by Renkin (1954, J. Gen. Physiol. 38:225) gives results that are less consistent than those obtained with the new transport equation.     

FFT method to compute solution X-ray scattering curves

We present an efficient algorithm to compute X-ray intensities scattered by macromolecules in solution, from atomic positions found in crystal structures. The algorithm applied the FAst Fourier Transform to an electron density map created from the atomic coordinates and corrected for solvent density. We compute scattering curves for both allosteric forms of E. coli aspartate carbamoyltransferase. Calculated intensities are in agreement with the ones measured by Moddy et al. [1,2] which shows that the structures observed in solution in the presence or in the absence of a substrate analogue do correspond to those of two crystal forms analyzea by Lipscomb and collaborators [3,4,5].     

A comparison of methods for estimating the kinetic parameters of two simple types of transport process

Sets of experimental data, with known characteristics and error structures, have been simulated for the Michaelis-Menten equation plus a second term, either for linear transport or for competitive inhibition. The Michaelis-Menten equation plus linear term was fitted by several methods and the accuracy and the precision of the parameter estimates from the several methods were compared. The model-fitting methods were: three for least-squares non-linear regression, computer versions of two graphical methods and of two non-parametric methods. The most precise and accurate method was that of D.W. Marquardt (J. Soc. Ind. Appl. Math. 11 (1963) 431–441). The Michaelis-Menten equation with competitive inhibition was also fitted by several methods, viz., two for least-squared non-linear regression, a non-parametric method and four variants of the Preston-Schaeffer-Curran plot (Preston, R.L. et al. (1974) J. Gen. Physiol. 64, 443–467). The most precise and accurate of these was the non-linear regression method of W.W. Cleland (Adv. Enzymol. 29 (1967) 1–32). For both these models, the various graphical methods and non-parametric methods gave poor results and are not recommended.     

Potassium transport across the frog retinal pigment epithelium

Previous experiments indicate that the apical membrane of the frog retinal pigment epithelium contains electrogenic Na:K pumps. In the present experiments net potassium and rubidium transport across the epithelium was measured as a function of extracellular potassium (rubidium) concentration, [K]0 ( [Rb]0). The net rate of retina-to-choroid 42K(86Rb) transport increased monotonically as [K]0 ( [Rb]0) increased from approximately 0.2 to 5 mM on both sides of the tissue or on the apical (neural retinal) side of the tissue. No further increase was observed when [K]0 ( [Rb]0) was elevated to 10 mM. Net sodium transport was also stimulated by elevating [K]0. The net K transport was completely inhibited by 10-4 M ouabain in the solution bathing the apical membrane. Ouabain inhibited the unidirectional K flux in the direction of net flux but had no effect on the back-flux in the choroid-to-retina direction. The magnitude of the ouabain-inhibitable 42K(86Rb) flux increased with [K]0 ( [Rb]0). These results show that the apical membrane Na:K pumps play an important role in the net active transport of potassium (rubidium) across the epithelium. The [K]0 changes that modulate potassium transport coincide with the light-induced [K]0 changes that occur in the extracellular space separating the photoreceptors and the apical membrane of the pigment epithelium.