Biomedical Engineering Reference
In-Depth Information
plementary mathematical models for RBCs and describe a systematic procedure on
extracting the relevant input parameters from optical tweezers and microfluidic ex-
periments for single RBCs. We then use these validated RBC models to predict the
behaviour of whole healthy blood and compare with experimental results. The same
procedure is applied to modelling malaria, and results for infected single RBCs and
whole blood are presented.
10.1 Introduction
The healthy human red blood cells (RBCs) are discocytes when not subjected to any
external stresses and they are approximately 7.5 to 8.7
μ
m in diameter and 1.7 to
2.2
m in thickness [1]. The membrane of the RBC is made up of a phospholipid
bilayer and a network of spectrin molecules (cytoskeleton), with the latter largely
responsible for the shear elastic properties of the RBC. The spectrin network is con-
nected to bilayer via transmembrane proteins and together with the spectrin filaments
and the cytosol inside the membrane determine the morphological structure of RBCs.
This critical binding between the spectrin network and the lipid bilayer is actively
controlled by ATP [2]. Parasitic infections or genetic factors can drastically change
the viscoelastic properties and even the shape of RBCs [3]. For example, the parasite
Plasmodium falciparum
that invades the RBCs (Pf-RBCs) of most malaria patients
affects drastically the RBC membrane properties resulting in a ten-fold increase of
its shear modulus and a spherical shape at the later stages of the intra-cell parasite
development [3]. In addition, Pf-RBCs develop knobs on their surface that serve
as adhesion sites for the binding to other Pf-RBCs as well as healthy RBCs. This
enhanced cytoadherence of Pf-RBCs in combination with their reduced deformabil-
ity may cause blood flow obstruction especially through the smaller arterioles and
capillaries. Sickle cell anemia is another blood disorder that affects the hemoglobin
inside the RBCs causing dramatic changes in their shape and deformability. These
changes combined with the increased internal viscosity affects the flow of sickled
RBCs through the capillaries leading to flow occlusion [3, 4]. Other hereditary dis-
eases with similar effects are spherocytosis and elliptocytosis [5]. In the former,
RBCs become spherical with reduced diameter and carry much more hemoglobin
than healthy RBCs. In the latter, RBCs are elliptical or oval in shape and of reduced
deformability.
The common problem in the aforementioned hematologic disorders is the re-
modelling of the cytoskeleton and correspondingly a change in the structure and
viscoelastic properties of individual RBCs, so studying their mechanical and rheo-
logical properties in vitro can aid greatly in the understanding and possible discovery
of new treatments for such diseases. To this end, new advanced experimental tools
are very valuable in obtaining the basic properties of single RBCs in health and
disease, which are required in formulating multiscale methods for modelling blood
flow in vitro and in vivo. Specifically, advances in experimental techniques now
allow measurements down to the nanometer scale, and include micropipette aspira-
tion [6, 7], RBC deformation by optical tweezers [8, 9, 10], optical magnetic twisting
μ
