J. D. Hellums

Involvement of large plasma von Willebrand factor (vWF) multimers and unusually large vWF forms derived from endothelial cells in shear stress-induced platelet aggregation.

A fluid shear stress of 180 dyn/cm2 was applied for 0.5 and 5 min to platelets in citrated plasma or blood in a cone and plate viscometer with minimal platelet-surface interactions. Platelets aggregated in the shear field if large von Willebrand Factor (vWF) multimers were present. Aggregation did not require ristocetin, other exogenous agents, or desialation of vWF. Unusually large vWF multimers produced by human endothelial cells were functionally more effective than the largest plasma vWF forms in supporting shear-induced aggregation. Shear-induced aggregation was inhibited by monoclonal antibodies to platelet glycoprotein Ib or the IIb/IIIa complex, but was little affected by the absence of fibrinogen. vWF-dependent platelet aggregation under elevated shear stress in partially occluded vessels of the arterial microcirculation may contribute to thrombosis, especially if unusually large vWF multimers are released locally from stimulated or disrupted endothelial cells.

Red Blood Cell Damage by Shear Stress

A series of careful studies has been made on blood damage in a rotational viscometer. Specific attention has been focused on the effects of solid surface interaction, centrifugal force, air interface interaction, mixing of sheared and unsheared layers, cell-cell interaction, and viscous heating. The results show that there is a threshold shear stress, 1500 dynes/cm(2), above which extensive cell damage is directly due to shear stress, and the various secondary effects listed above are negligible. By analysis of these results and those of prior workers it is shown that the exposure time-shear stress plane is divided into two distinct regimes. In the regime of relatively low stresses and exposure times there is relatively little damage, and the damage is dominated by solid surface interaction effects. In the other regime, at high stresses and exposure times, stress effects alone dominate and very high rates of hemolysis occur. The experimental findings of all prior workers are shown to be consistent when interpreted in this way.

Hemodynamic forces induce the expression of heme oxygenase in cultured vascular smooth muscle cells.

Both nitric oxide (NO) and carbon monoxide (CO) are vessel wall-derived messenger molecules that cause platelet inhibition and vasodilation by activating guanylyl cyclase in target cells. Since vascular smooth muscle cells (SMCs) are exposed to shear and tensile stresses, this study examined the effects of these hemodynamic forces on the enzymes that generate NO and CO in SMCs. Monolayers of cultured rat aortic SMCs were subjected to shear stress using a modified cone and plate viscometer, or cyclic elongational stretch using a compliant silastic culture membrane. Shear stress stimulated time-dependent increases in mRNA and protein for inducible heme oxygenase-1 (HO-1), the enzyme which forms CO as a byproduct of heme degradation. The threshold level of shear necessary to induce HO-1 expression was between 5 and 10 dynes/cm2. In contrast, shear stress did not stimulate inducible NO synthase (iNOS) expression. Cyclic stretch also induced the expression of HO-1 but not of iNOS mRNA. Exposure of vascular SMCs to shear stress stimulated the production and release of CO as demonstrated by the CO-dependent increase in intracellular cGMP levels in coincubated platelets. In addition, ADP-stimulated aggregation was inhibited in platelets exposed to sheared SMCs but not in platelets exposed to untreated control SMCs. Treatment of sheared SMCs with the HO-1 inhibitor, tin protoporphyrin-IX, blocked the antiaggregatory effect of the cells, whereas the iNOS inhibitor, methyl--arginine, had no effect. These results indicate that hemodynamic forces induce HO-1 gene expression and CO production in vascular SMCs, and that SMC-derived CO inhibits platelet aggregation. Thus, CO is a novel endogenous vessel wall-derived messenger molecule that may be selectively induced by hemodynamic forces to inhibit platelet reactivity and preserve blood fluidity at sites of vascular injury.

Numerical Solution of the Three‐Dimensional Equations of Motion for Laminar Natural Convection

A method is presented for numerical finite difference solution of the equations of motion in three dimensions. The complete Navier‐Stokes equations are transformed and expressed in terms of vorticity and a vector potential. The transformed equations are solved using an alternating direction method for the parabolic portion of the problem, and successive over‐relaxation for the elliptic portion. The classical problem of convection in fluid layers bounded by solid walls and heated from below is solved in both two and three dimensions. Comparison with other methods and with prior work in two dimensions shows that the new method presented here has important advantages in speed and accuracy. Apparently, there has been no successful prior work in three dimensions except in cases where one component of the equation of motion is highly simplified.

The resistance to oxygen transport in the capillaries relative to that in the surrounding tissue

Abstract Previous workers on mathematical analysis of oxygen transport from blood in the microcirculation have all either treated the blood as a continuum or neglected the resistance to transport in the radial direction in the capillary. In this work, an approximate analysis is given in which the red cells are approximated as cylinders which fill the lumen of the capillary such that the oxygen transport is by radial diffusion in the cell. The results indicate that the resistance to oxygen transfer in the capillaries is significantly higher than previously reported and is of approximately equal importance to the resistance in the surrounding tissue.

Molecular dynamics of the transition from L-selectin- to beta 2-integrin-dependent neutrophil adhesion under defined hydrodynamic shear.

Homotypic adhesion o2 neutrophils stimulated with chemoattractant is analogous to capture on vascular endothelium in that both processes depend on L-selectin and beta 2-integrin adhesion receptors. Under hydrodynamic shear, cell adhesion requires that receptors bind sufficient ligand over the duration of intercellular contact to withstand hydrodynamic stresses. Using cone-plate viscometry to apply a uniform linear shear field to suspensions of neutrophils, we conducted a detailed examination of the effect of shear rate and shear stress on the kinetics of cell aggregation. A collisional analysis based on Smoluchowskis flocculation theory was employed to fit the kinetics of aggregation with an adhesion efficiency. Adhesion efficiency increased with shear rate from approximately 20% at 100 s-1 to approximately 80% at 400 s-1. The increase in adhesion efficiency. Adhesion efficiency increased with shear rate from approximately 20% at 100 s-1 to approximately 80% at 400 s-1. The increase in adhesion efficiency with shear was dependent on L-selectin, and peak efficiency was maintained over a relatively narrow range of shear rates (400-800 s-1) and shear stresses (4-7 dyn/cm2). When L-selectin was blocked with antibody, beta 2-integrin (CD11a, b) supported adhesion at low shear rates (< 400 s-1). The binding kinetics of selectin and integrin appear to be optimized to function within discrete ranges of shear rate and stress, providing an intrinsic mechanism for the transition from neutrophil tethering to stable adhesion.

Studies on the Mechanisms of Shear-Induced Platelet Activation

The importance of flow-related phenomena in thrombotic and thrombembolic events has been appreciated by a number of workers for several years. In the last decade, a series of studies have focused specifically on the action of shear stress due to fluid motion on human blood platelets. The shear field may modify the platelet directly, in addition to the role of increasing platelet motion, collision, and contact with solid surfaces. Also, it is clear that both the rates and the extent of response of platelets to various agonists depend heavily on the shear field. A review is available [24], as well as several recent papers [5–7, 21, 25, 35, 37, 44–47].

Aggregation and disaggregation kinetics of human blood platelets: Part II. Shear-induced platelet aggregation

A population balance equation (PBE) mathematical model for analyzing platelet aggregation kinetics was developed in Part I (Huang, P. Y., and J. D. Hellums. 1993. Biophys. J. 65: 334-343) of a set of three papers. In this paper, Part II, platelet aggregation and related reactions are studied in the uniform, known shear stress field of a rotational viscometer, and interpreted by means of the model. Experimental determinations are made of the platelet-aggregate particle size distributions as they evolve in time under the aggregating influence of shear stress. The PBE model is shown to give good agreement with experimental determinations when either a reversible (aggregation and disaggregation) or an irreversible (no disaggregation) form of the model is used. This finding suggests that for the experimental conditions studied disaggregation processes are of only secondary importance. During shear-induced platelet aggregation, only a small fraction of platelet collisions result in the binding together of the involved platelets. The modified collision efficiency is approximately zero for shear rates below 3000 s-1. It increases with shear rates above 3000 s-1 to about 0.01 for a shear rate of 8000 s-1. Addition of platelet chemical agonists yields order of magnitude increases in collision efficiency. The collision efficiency for shear-induced platelet aggregation is about an order of magnitude less at 37 degrees C than at 24 degrees C. The PBE model gives a much more accurate representation of aggregation kinetics than an earlier model based on a monodispersed particle size distribution.

Modeling the reversible kinetics of neutrophil aggregation under hydrodynamic shear

Neutrophil emigration into inflamed tissue is mediated by beta 2-integrin and L-selectin adhesion receptors. Homotypic neutrophil aggregation is also dependent on these molecules, and it provides a model system in which to study adhesion dynamics. In the current study we formulated a mathematical model for cellular aggregation in a linear shear field based on Smoluchowskis two-body collision theory. Neutrophil suspensions activated with chemotactic stimulus and sheared in a cone-plate viscometer rapidly aggregate. Over a range of shear rates (400-800 s-1), approximately 90% of the single cells were recruited into aggregates ranging from doublets to groupings larger than sextuplets. The adhesion efficiency fit to these kinetics reached maximum levels of > 70%. Formed aggregates remained intact and resistant to shear up to 120 s, at which time they spontaneously dissociated back to singlets. The rate of cell disaggregation was linearly proportional to the applied shear rate, and it was approximately 60% lower for doublets as compared to larger aggregates. By accounting for the time-dependent changes in adhesion efficiency, disaggregation rate, and the effects of aggregate geometry, we succeeded in predicting the reversible kinetics of aggregation over a wide range of shear rates and cell concentrations. The combination of viscometry with flow cytometry and mathematical analysis as presented here represents a novel approach to differentiating between the effects of hydrodynamics and the intrinsic biological processes that control cell adhesion.

Basic theory of blood flow in capillaries

Abstract A model of capillary blood flow is studied theoretically by considering the mechanics of a flexible solid object (cell) suspended in a fluid (plasma) flowing in a conduit (capillary). The cell is similar in size to the conduit and deforms in compliance to the fluid stresses. Only axially symmetric systems in two and three dimensions are treated, and several approximations are made in the equations of motion of the plasma and the cell. A nonlinear boundary value problem is thus formulated and is solved numerically over a range of parameter values, including values of physiological interest. The calculations result in parachute-shaped cells whose sides do not touch the conduit wall. When the cell size is approximately equal to the conduit size, the ratio of cell to plasma velocity is 1.67 and the apparent viscosity of the two-phase mixture is 1.05, relative to plasma. These results agree semiquantitatively with experiment.