Biomedical Engineering Reference
In-Depth Information
rates, and suggests that particles other than RBCs have little effect on the viscosity.
The measured values for whole blood are more consistent than those for erythro-
cyte solutions, which may reflect differences in the preparation of the latter. The
LD-RBC model underestimates somewhat the experimental data, but is generally
in good agreement over the whole range of shear rates, and again demonstrates the
effect of aggregation. This is remarkable in view of the simplicity and economy of
that model.
The dependence of whole blood and erythrocyte solution viscosity on hematocrit
(
H
t
)
is demonstrated in Fig. 10.17(b). The curves are measured viscosities correlated
with
H
t
at constant shear rate by Chien et al. [77], and the points are calculated with
the LD-RBC model. This clearly shows how the latter captures the
H
t
dependence
of viscosity, and that the model again demonstrates aggregation to be crucial for a
quantitative account of the difference between the viscosity of whole blood and that
of washed erythrocyte suspensions.
10.5 Application to malaria modelling
Plasmodium falciparum
(Pf) causes one of the most serious forms of malaria re-
sulting in several million deaths per year. Pf-parasitized cells (Pf-RBCs) experience
progressing changes in their mechanical and rheological properties as well as in their
morphology [79, 80] during intra-erythrocytic parasite development, which includes
three stages from the earliest to the latest: ring
schizont. Progres-
sion through these stages leads to considerable stiffening of Pf-RBCs as found in
optical tweezers stretching experiments [9] and in diffraction phase microscopy by
monitoring the membrane fluctuations [12]. Pf development also results in vacuoles
formed inside of RBCs possibly changing the cell volume. Thus, Pf-RBCs at the final
stage (schizont) often show a “near spherical” shape, while in the preceding stages
maintain their biconcavity. These changes greatly affect the rheological properties
and the dynamics of Pf-RBCs, and may lead to obstruction of small capillaries [80]
impairing the ability of RBCs to circulate.
In vitro
experiments [81] to investigate
the enhanced cytoadherence of Pf-RBCs in flow chambers revealed that their adhe-
sive dynamics can be very different than the well-established adhesive dynamics of
leukocytes. For example, the adhesive dynamics of Pf-RBCs on purified ICAM-1 is
characterized by stable and persistent flipping (rolling) behaviour for a wide range
of wall shear stresses [81] but also by intermittent pause and sudden flipping due to
the parasite mass inertia.
In this section, we apply the computational framework we developed for healthy
RBCs to Pf-RBCs. In particular, we first consider single RBCs for validation pur-
poses and subsequently we simulate whole infected blood as suspension of a mix-
ture of healthy and Pf-RBCs. We examine the mechanical, dynamic and rheologic
responses as well as the adhesive dynamics of infected RBCs.
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trophozoite
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