Postoperative morbidity after cardiopulmonary bypass most commonly manifests as bleeding diatheses or pulmonary dysfunction. The pathophysiology has been attributed to the activation of cellular and humoral components of blood after contact with an artificial surface. Development of a surface that would be nonthrombogenic and also would constitute a less potent inflammatory stimulus would therefore be beneficial. In the following experiments, we evaluated the heparin-bonded Carmeda Bioactive Surface (Medtronics Cardiopulmonary, Anaheim, Calif.) in an in vitro model of extracorporeal circulation at standard-dose heparin (5 U/ml), to examine the effects of the surface treatment on activation of blood elements, and at reduced-dose heparin (1 U/ml), to determine whether surface-bound heparin would serve as an effective anticoagulant. During the initial recirculation period, platelet counts in the Carmeda (n = 12) circuits were preserved at both doses of heparin and compared with control values (n = 12): At 5 U/ml, control 36% +/- 4% (mean +/- standard error of the mean) versus Carmeda 81% +/- 5%; at 1 U/ml, 43% +/- 3% versus 61% +/- 10%, expressed as a percent of baseline at 30 minutes, p < 0.05. Furthermore, plasma levels of platelet factor 4 and beta-thromboglobulin were significantly reduced in the Carmeda circuits throughout the experiment: At heparin 5 U/ml, 2500 +/- 340 ng/ml versus 604 +/- 191 ng/ml; at 1 U/ml, 2933 +/- 275 ng/ml versus 577 +/- 164 ng/ml of platelet factor 4 at 2 hours (p < 0.05). The pattern of beta-thromboglobulin release was similar, with effects more pronounced at the lower dose of heparin. Surface modification also reduced leukocyte depletion (p < 0.05) and release of elastase at both concentrations of heparin (5 U/ml, 0.72 +/- 0.29 ng/ml versus 0.33 +/- 0.23 ng/ml; 1 U/ml, 0.85 +/- 0.08 ng/ml versus 0.20 +/- 0.05 ng/ml, at 2 hours, p < 0.05). Moreover, as heparin concentration was reduced, Carmeda surface treatment significantly decreased generation of C3a des Arg (1 U/ml, 14,410 +/- 3558 ng/ml versus 3053 +/- 1039 ng/ml at 2 hours, p < 0.05). Although heparin bonding was originally intended to obviate the need for systemic heparinization, Carmeda treatment did not reduce fibrinopeptide A generation at the lower dose of heparin. In summary, Carmeda treatment failed to exhibit anticoagulant efficacy in this model; however, the data suggest that surface modification may have a role in ameliorating the typical inflammatory response initiated by blood contact with an artificial surface.
This paper presents a stabilized formulation for the generalized Navier-Stokes equations for weak enforcement of essential boundary conditions. The non-Newtonian behavior of blood is modeled via shear-rate dependent constitutive equations. The boundary terms for weak enforcement of Dirichlet boundary conditions are derived via locally resolving the fine-scale variational equation facilitated by the Variational Multiscale (VMS) framework. The proposed method reproduces the consistency and stabilization terms that are present in the Nitsche type approaches. In addition, for the shear-rate fluids, two more boundary terms appear. One of these terms is the viscosity-derivative term and is a function of the shear-rate, while the other term is a zeroth-order term. These terms play an important role in attaining optimal convergence rates for the velocity and pressure fields in the norms considered. A most significant contribution is the form of the stabilization tensors that are also variationally derived. Employing edge functions the edge stabilization tensor is numerically evaluated, and it adaptively adjusts itself to the magnitude of the boundary residual. The resulting formulation is variationally consistent and the weakly imposed no-slip boundary condition leads to higher accuracy of the spatial gradients for coarse boundary-layer meshes when compared with the traditional strongly imposed boundary conditions. This feature of the present approach will be of significance in imposing interfacial continuity conditions across non-matching discretizations in blood-artery interaction problems. A set of test cases is presented to investigate the mathematical attributes of the method and a patient-specific case is presented to show its clinical relevance.
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