Biorheology - Volume 47, issue 1

Authors: Duenwald, Sarah E. | Vanderby, Ray | Lakes, Roderic S.

Article Type: Research Article

Abstract: Accurate joint models require the ability to predict soft tissue behavior. This study evaluates the ability of constitutive equations to predict the nonlinear and viscoelastic behavior of tendon and ligament during stress relaxation testing in a porcine model. Three constitutive equations are compared in their ability to model relaxation, recovery and reloading of tissues. Quasi-linear viscoelasticity (QLV) can fit a single stress relaxation curve, but fails to account for the strain-dependence in relaxation. Nonlinear superposition can fit the single relaxation curve and will account for the strain-dependent relaxation behavior, but fails to accurately predict recovery behavior. Schapery's nonlinear viscoelastic model …successfully fits a single relaxation curve, accounts for strain-dependent relaxation behavior, and accurately predicts recovery and reloading behavior. Comparing Schapery's model to QLV and nonlinear superposition, Schapery's method was uniquely capable of fitting the different nonlinearities that arise in stress relaxation curves from different tissues, e.g. the porcine digital flexor tendon and the porcine medial collateral ligament (MCL), as well as predicting subsequent recovery and relaxation curves after initial loads. Show more

Keywords: Viscoelasticity, quasi-linear viscoelasticity, nonlinear superposition, tendon, ligament

DOI: 10.3233/BIR-2010-0559

Citation: Biorheology, vol. 47, no. 1, pp. 1-14, 2010

Authors: Fan, Lijie | Sakai, Jiro | Bessho, Sadao | Wada, Shigeo | Karino, Takeshi

Article Type: Research Article

Abstract: Monocytes are involved in the pathogenesis and localization of intimal hyperplasia and atherosclerosis in regions of disturbed flow in man. Hence, to investigate the mechanism of the localization of these vascular diseases, we created a state of disturbed flow distal to a 0.92 mm into 3.0 mm sudden tubular expansion consisting of a stainless steel upstream tube and a hybrid vascular graft by recirculating a cell culture medium through it in steady flow. Then by introducing fluorescence-labeled human blood monocytes (THP-1 cells) into the medium, we tested the effect of a disturbed flow (an annular vortex) on adhesion of monocytes …to the endothelium of the hybrid graft. It was found that adhesion and invasion of THP-1 cells to the endothelium were the highest around the reattachment point (the toe of the annular vortex) where the flow was the slowest and wall shear stress was the lowest. They were the lowest at a location between the step of the tubular expansion and the reattachment point that was close to the vortex center where the flow was the fastest and wall shear stress was the highest. A similar distribution was also obtained with 20 nm diameter polystyrene microspheres used as a model of low-density lipoproteins (LDL). These results indicated that a disturbed flow itself provided favorable conditions for the adhesion of monocytes and LDL to the endothelium in regions of very slow flow, and hence low wall shear stress, by allowing them to make contact and interact with endothelial cells for a long time. This may explain, in part, why intimal hyperplasia and atherosclerotic lesions develop preferentially in regions of very slow flow. Show more

Keywords: Intimal hyperplasia, atherosclerosis, monocyte, THP-1 cell, adhesion, disturbed flow

DOI: 10.3233/BIR-2010-0562

Citation: Biorheology, vol. 47, no. 1, pp. 15-29, 2010

Authors: Fan, Lijie | Karino, Takeshi

Article Type: Research Article

Abstract: Atherosclerotic lesions and intimal hyperplasia develop preferentially in regions where blood flow is disturbed by the formation of secondary and recirculation flows. Hence, to investigate the mechanism of the localization of these vascular diseases, we constructed a sudden tubular expansion consisting of a 0.92 mm i.d. upstream tube and a 3.0 mm i.d. hybrid vascular graft, and by recirculating a cell culture medium through it in steady flow for 7 days, we tested the effect of a disturbed flow (an annular vortex) on proliferation of smooth muscle cells (SMC) of the hybrid graft. It was found that the thickness of …the cell layer that was considered a measure of the proliferation of SMC underlying the endothelial cells was greatest around the reattachment point (the toe of the annular vortex) where the flow was the slowest and the wall shear stress was the lowest. The thickening of the cell layer also occurred around the stagnation point located at the origin of the expansion but was much less than that around the reattachment point. The cell layer was the thinnest in the middle portion of the vortex where the flow was the fastest and wall shear stress was the highest. These results indicated that a disturbed flow provides favorable conditions for the proliferation of SMC in regions where the flow is very slow and wall shear stress is very low. This may explain, in part, why intimal hyperplasia and atherosclerotic lesions develop preferentially in regions of slow flow. Show more

Keywords: Intimal hyperplasia, atherosclerosis, endothelial cell, smooth muscle cell, cell proliferation, disturbed flow

DOI: 10.3233/BIR-2010-0561

Citation: Biorheology, vol. 47, no. 1, pp. 31-38, 2010

Authors: Moyers-Gonzalez, Miguel A. | Owens, Robert G.

Article Type: Research Article

Abstract: In an earlier paper, Moyers-Gonzalez et al. [J. Fluid. Mech. 617 (2008), 327–354] used kinetic theory to derive a non-homogeneous haemorheological model and applied this to simulate the properties of steady flow of blood in a tube. By adjusting the tube haematocrit to match that of the experimental fitted curve of Pries et al. [Circ. Res. 67 (1990), 826–834] the authors showed that it was possible to quantitatively predict the apparent viscosity values presented in a later paper by Pries et al. [Am. J. Physiol. 263 (1992), 1770–1778]. In the present paper, it is the discharge haematocrit rather than the …tube haematocrit that is prescribed. We further develop the predictive capacities of the original model of Moyers-Gonzalez et al. [J. Fluid. Mech. 617 (2008), 327–354] by introducing a cell-free peripheral layer next to the tube wall where, following the ideas of Sharan and Popel [Biorheology 38 (2001), 415–428], dissipation in this layer is accounted for by allowing the viscosity there to exceed that of plasma. Using both the apparent viscosity data of Pries et al. [Am. J. Physiol. 263 (1992), 1770–1778] and the relative tube haematocrit relation proposed by Sharan and Popel [Biorheology 38 (2001), 415–428], we predict the thickness of the cell-free layer and the relative viscosity in this layer. The predicted thickness of the cell-free layer as a function of both a pseudo-shear rate and the tube diameter for 45% haematocrit blood is shown to be in very close conformity with the experimental measurements of Reinke et al. [Am. J. Physiol. 253 (1987), 540–547]. With increasing discharge haematocrit the cell-free layer thickness is shown to decrease, as observed in several experimental papers [Bugliarello and Hayden, Trans. Soc. Rheol. VII (1963), 209–230, Bugliarello and Sevilla, Biorheology 7 (1970), 85–107, Soutani et al., Am. J. Physiol. 268 (1995), 1959–1965]. Our prediction of the relative viscosity in the cell-free layer shows a similar trend to that computed by Sharan and Popel [Biorheology 38 (2001), 415–428]. Finally, for sufficiently large pseudo-shear rates it is shown that the Deborah number (a non-dimensional relaxation time) may be taken to be a constant, thus greatly simplifying our haemorheological model and allowing for a partially analytic solution to the problem of steady non-homogeneous flow of blood in a tube. Show more

Keywords: Cell-free peripheral layer, non-homogeneous flow, kinetic theory modelling

DOI: 10.3233/BIR-2010-0558

Citation: Biorheology, vol. 47, no. 1, pp. 39-71, 2010

Authors: Mansour, Mohamed H. | Bressloff, Neil W. | Shearman, Cliff P.

Article Type: Research Article

Abstract: Red blood cell (RBC) migration effects and RBC–plasma interactions occurring in microvessel blood flow have been investigated numerically using a shear-induced particle migration model. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear-induced RBC migration in concentrated suspensions. The model couples a non-Newtonian stress/shear rate relationship with a shear-induced migration model of the suspended particles in which the viscosity is dependent on the haematocrit and the shear rate (Quemada model). The focus of this paper is on the determination of the two phenomenological parameters, …Kc and Kμ , in a diffusive flux model when using the non-Newtonian Quemada model and assuming deformable particles. Previous use of the diffusive flux model has assumed constant values for the diffusion coefficients which serve as tuning parameters in the phenomenological equation. Here, previous data [Biophys. J. 92 (2007), 1858–1877; J. Fluid Mech. 557 (2006), 297–306] is used to develop a new model in which the diffusion coefficients depend upon the tube haematocrit and the dimensionless vessel radius for initially uniform suspensions. This model is validated through previous publications and close agreement is obtained. Show more

Keywords: Non-Newtonian, microvessel, cell-depletion, Quemada model, shear-induced migration

DOI: 10.3233/BIR-2010-0560

Citation: Biorheology, vol. 47, no. 1, pp. 73-93, 2010