Computational analysis of the deformability of leukocytes modeled with viscous and elastic structural components

Abstract

The objective of this work is to systematically include non-Newtonian effects in a previous Newtonian model of the leukocyte and to study the effects thereof on leukocyte rheology. The standard Newtonian-drop model of the cell is enhanced in three respects: (1) The cortical layer is treated as an elastic membrane with a nonlinear stress–strain curve to simulate unfolding of the excess surface area of the membrane. (2) A power-law shear thinning fluid is used for the cytoplasm. (3) A three-layer or compound cell model is used, which is comprised of the membrane cortex, cytoplasm and nucleus. Combinations of these aspects are also investigated. The governing equations for this multifluid system are solved in the Stokes limit. The immersed boundary technique is used to simulate the interaction of the elastic membrane with the flow field. Results indicate that each of these additional elements in the leukocyte model yield significant deviations from the Newtonian deformation and recovery behavior of the leukocyte. However, the added modeling sophistication does not appear to be sufficient to fully capture all the distinctive responses of the leukocytes under a wide variety of deformation and recovery protocols. It is shown that although a comprehensive model for the leukocyte remains elusive, the three-layer leukocyte model with cortical elasticity is a promising candidate.

Modeling cell entry into a micro-channel

“…The compound drop model effectively explains the observed rapid initial response in micro-pipette aspiration and fast recoil on recovery Kan et al 1998). Applications of the compound drop model include cell recovery under extensional flows (Kan et al 1999), micropipette aspiration and shear flow (Agresar et al 1998), cell adhesion, andmigration (N'Dri et al 2003) as well as shear thinning and membrane elasticity (Marella and Udaykumar 2004). More recent works include shear-induced drop breakup and cell-surface adhesion (Khismatullin and Truskey 2005).…”

Dissipative Particle Dynamics (DPD): An Overview and Recent Developments

“…Compare with above mentioned Newtonian liquid drop, the compound drop model can effectively explain the rapid initial response in micro-pipette aspiration and fast recoil on recovery [148]. The compound drop model was also used to model cell under shear flow [149] and extensional flows [150], cell adhesion, and migration [151] as well as shear thinning and membrane elasticity [152]. Recently, Leong et al presented a modified compound drop model, which can consider stiffness, elasticity, and viscosity of both the cortex and the nucleus to model breast cancer cell entry into a constricted micro-channel.…”

Algorithms for Fluid–Structure Interaction

“…The previous equations may appear to represent a rather limited setting for fluidstructure interaction problems, but in reality encompass a wide range of biologically relevant FSI problems. Examples include the deformation of cells [11][12][13], the pumping action of the heart [14], deformation of blood vessels [15], the operation of heart valves [16,17], locomotion of cells due to flagellar motion [18,19], and a host of others. The previous system of equations also provides a platform to examine general concepts and challenges associated with solving coupled fluid-structure interaction problems.…”

“…The numerical implementation and other details can be found in Marella and Udaykumar [13]. The velocity at an interface is continuous across it and is obtained at an interfacial point from bilinear interpolation of the fluid velocities stored at grid points around it.…”

“…5.3. By suitable pressure boundary conditions at the boundaries of the domain, including the portion of the domain boundary that lies within the micropipette, the cell is aspirated [13]. The surface of the micropipette is a no-slip solid boundary that is enforced sharply, while the cell membrane is treated with the immersed boundary method.…”