Blood Flow and Transport Processes in Microvascular Networks
D. Goldman
The primary role of the circulatory system, and in particular the
microcirculation,
is to ensure optimal delivery of oxygen to all living cells,
under both steady and
time-varying conditions.
The structural complexity of the microvasculature
can have a profound effect on the distribution of oxygen to the surrounding
tissue, especially in disease states or when the demand for oxygen is
high.
Following earlier work in the field
we have made significant progress in studying the
effect of geometric and hemodynamic complexity on steady-state oxygen
transport in the microcirculation. This was done through the
development of a flexible, efficient and highly realistic computational
model for simulating microvascular blood flow and oxygen delivery.
This
model has been generalized to study time-dependent oxygen
delivery,
which is of primary interest for understanding physiological
functioning. Current studies use this newly developed model
to study the dynamical behavior of blood flow and oxygen transport in the
microcirculation. This work is
primarily computational, including 3D
visualization of the results obtained,
but also involves detailed mathematical
analysis of the model wherever possible.
The goal of this ongoing project is to increase
understanding of physiological
processes relevant to normal
pathological
phenomena in skeletal muscle and other tissues.
In particular, we are interested in the time-course and spatial distribution
of hypoxia and anoxia, which can cause localized tissue damage.
As found previously
for vasomotion, the interaction
between the structural heterogeneity of the microvasculature and
the nonlinearity of certain processes, such as blood flow and
oxygen consumption,
is expected to have important physiological consequences.
During ischemic events, such as heart attack, a
temporary loss of normal blood supply can
deprive certain tissue regions of oxygen, but it is at present
not known how these regions are spatially distributed at the microvascular
level
or how these regions change as blood flow is lost and then
restored.
The onset of aerobic exercise,
which greatly increases
the oxygen consumption rate, is another time-dependent oxygen
transport process in which the heterogeneity of microvascular geometry
is expected to be important.
We are
investigating the consequences for tissue oxygen delivery
of the interaction between structural
and bio-dynamic complexity in the microcirculation
in order to increase basic understanding, explain
observed phenomena, and examine new approaches for
minimizing tissue damage.
To study the effect of time-varying oxygen consumption rate,
blood flow velocity,
and systemic hematocrit on tissue oxygen distributions,
simulations of the transport equations are being performed using a
previously validated numerical scheme.
This same method was used in
our study of oxygen transport
during vasomotion-induced oscillations of blood flow in capillary networks
and several important new results were obtained.
For example, it was found that under realistic geometric, hemodynamic,
and biophysical conditions, vasomotion can significantly
increase oxygen delivery to
tissue and can decrease or eliminate hypoxic regions.
Shown below are examples of a typical capillary
network and tissue domain used for blood flow and steady-state oxygen transport
simulations. Well-oxygenated regions, where the oxygen partial pressure
(PO2) is relatively high, are
indicated by red, while hypoxic regions are shown as blue.
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