  Mathematical models that accurately predict the mechanical behavior of blood
can contribute to the development of biomedical devices and medications which
are relevant in clinical applications. The models existing in the literature
are complex enough in order to agree with various in vitro experimental
observations. Latest technological advancements opened the possibility of
studying blood flow in vivo which could play an important role in the creation
of biocompatible implants for health monitoring and treatment purposes.
However, most of existing models may fail to predict blood behavior in vivo
because they require many parameters which are difficult to find in vivo and
they do not incorporate pertinent coupled chemo-mechanical dynamics specific to
blood flow in a living body. Recently, we used the fractional model of
continuum mechanics proposed by Drapaca and Sivaloganathan [J. Elast.,107:
105-123, 2012] to study blood circulation. In this mathematical formulation the
spatial derivatives of the rate of deformation tensor are expressed using
Caputo fractional derivatives. The aim of this paper is to compare the
Poiseuille flows of blood through an axi-symmetric circular rigid and
impermeable pipe where the blood is described by the above mentioned fractional
model, the Casson's model, and the power law model. Although the velocity
profiles of these three models look similar, the fractional model provides a
better fitting to published experimental data.
