Influence of sickle hemoglobin polymerization and membrane properties on deformability of sickle erythrocytes in the microcirculation

Abstract

The rheological properties of normal erythrocytes appear to be largely determined by those of the red cell membrane. In sickle cell disease, the intracellular polymerization of sickle hemoglobin upon deoxygenation leads to a marked increase in intracellular viscosity and elastic stiffness as well as having indirect effects on the cell membrane. To estimate the components of abnormal cell rheology due to the polymerization process and that due to the membrane abnormalities, we have developed a simple mathematical model of whole cell deformability in narrow vessels. This model uses hydrodynamic lubrication theory to describe the pulsatile flow in the gap between a cell and the vessel wall. The interior of the cell is modeled as a Voigt viscoelastic solid with parameters for the viscous and elastic moduli, while the membrane is assigned an elastic shear modulus. In response to an oscillatory fluid shear stress, the cell--modeled as a cylinder of constant volume and surface area--undergoes a conical deformation which may be calculated. We use published values of normal and sickle cell membrane elastic modulus and of sickle hemoglobin viscous and elastic moduli as a function of oxygen saturation, to estimate normalized tip displacement, d/ho, and relative hydrodynamic resistance, Rr, as a function of polymer fraction of hemoglobin for sickle erythrocytes. These results show the transition from membrane to internal polymer dominance of deformability as oxygen saturation is lowered. More detailed experimental data, including those at other oscillatory frequencies and for cells with higher concentrations of hemoglobin S, are needed to apply fully this approach to understanding the deformability of sickle erythrocytes in the microcirculation. The model should be useful for reconciling the vast and disparate sets of data available on the abnormal properties of sickle cell hemoglobin and sickle erythrocyte membranes, the two main factors that lead to pathology in patients with this disease.

Analysis of Mechanical Behavior of Red Cell Membrane in Sickle Cell Disease

“…Therefore, the rheological properties of normal RBCs appear to be largely determined by the red cell membrane .Altered membrane properties in SCD play a primary role in the altered rheology that characterizes the disease and that tied directly to sickle hemoglobin polymerization [18]. Mean that, in sickle cell, assumed that the viscous behavior is dominated by the cell interior, however, having indirect effect on the cell membrane [7]. In sickle cell disease (SCD) the intracellular polymerization of sickle cell hemoglobin upon deoxygenation leads to marked increase in internal viscosity, and elastic stiffness.…”

“…In sickle cell disease (SCD) the intracellular polymerization of sickle cell hemoglobin upon deoxygenation leads to marked increase in internal viscosity, and elastic stiffness. The interior of the cell is modeled as a voigt viscoelastic solid with parameters for the viscous and elastic modulus while the membrane is assigned an elastic shear modulus [7]. As Pucci and Saccomadi [19] reviewed that the Kelvin-Viogt models of non-linear viscoelastic constitutive equations for the Cauchy stress may be split in the sum of two terms: an elastic part and dissipative part .An incompressible viscoelastic continuum is adopted for the cell interior [7].…”

“…The interior of the cell is modeled as a voigt viscoelastic solid with parameters for the viscous and elastic modulus while the membrane is assigned an elastic shear modulus [7]. As Pucci and Saccomadi [19] reviewed that the Kelvin-Viogt models of non-linear viscoelastic constitutive equations for the Cauchy stress may be split in the sum of two terms: an elastic part and dissipative part .An incompressible viscoelastic continuum is adopted for the cell interior [7]. Thus, the generalization of an incompressible Voigt viscoelastic solid model can be thought of as a "mixture" in the following sense, A general viscoelastic constitutive equation for erythrocyte membrane may be written in terms of principal strains and stresses.…”

“…In sickle cell syndromes, abnormal rheological properties are caused primarily by the increase in internal red cell viscosity due to the aggregation or polymerization of sickle hemoglobin (HbS) upon deoxygenation, as well as biochemical abnormalities in the membrane of the sickle erythrocytes [7]. These membrane changes, both reversible and irreversible, are thought to occur due to repeated cycles of polymerization -depolymerization during the life of the sickle erythrocyte circulation [8].…”

“…Polymerization of deoxygenation HbS reduces the cell concentra-tion of osmotically active particles, and also assumed to induce cell shrinkage [10]. Dong et al [7] developed a simple mathematical model of whole cell deformability in narrow vessel wall to estimate the components of abnormal cell rheology due to the polymerization process and that due to the membrane abnormalities. The model uses hydrodynamic lubrication theory to describe the pulsatile flow in the gap between a cell and the vessel wall.…”