Vessel Wall - Tissue Functioning and Remodeling in the Circulatory and Ventilatory Systems - page 347

thin, homogeneous wall]) that results from perpendicularly applied blood pressure
p i ; (3) radial compressive stress developed by blood pressure that has a much
smaller magnitude with respect to axial and circumferential stresses; and (4) wall
shear stress exerted by blood flow at the wetted surface of the vessel wall, i.e.,
friction on the luminal surface of the endothelium.
Stress distribution within large vessel wall is heterogeneous, as the wall is
composed of 3 layers (intima, media, and adventitia) of composite materials.
Moreover, stress field bears large temporal and spatial variations, as blood flow is
three-dimensional, developing (or unestablished, as flow develops at the entrance of
short curved vessels between 2 successive branchings), 2 and unsteady. 3
Elastic properties of vascular wall are usually represented by rheological param-
eters defined at specific pressures, as the pressure-cross-sectional area relationship
is non-linear: (1) either vascular distensibility ( p i ) or wall compliance

and (2) elastic moduli (Vol. 7 - Chap. 5. Rheology). These parameters deal with the
bulk wall behavior and do not represent elastic properties of wall material.

( ∂ A i / A i ) / ∂

7.2 Vasculature Development

Mesodermal cells in the early embryo differentiate into endothelial precursors —
angioblasts — and form blood islands. Fusion of blood islands leads to the primary
capillary plexi. When blood circulation is established, primary plexi remodel into a
hierarchical network of arteries, arterioles, capillaries, venules, and veins.
Vascular smooth myocytes (SMC) are associated with large and mid-sized
vessels, whereas capillaries are covered by pericytes. First lymphatic endothelial
cells sprout from embryonic veins, then they migrate to form lymphatic sacs.
Lymphangiogenesis also involves sprouting, branching, and remodeling. Closed-
end lymphatic capillaries drain into collecting vessels and ducts.
The branchial arch artery apparatus is a transient structure that appears in 6- to
7-week-old human embryos. Five branchial arches exist, each of which contains
an arch artery (1-4 and 6). Blood exits from the heart via branchial arch arteries
to circulate throughout the embryo. The branchial arch artery apparatus is initially
symmetrical with equivalent amounts of blood flow through all of these arteries.

2 Because of the presence of the vessel wall, a boundary layer develops in the entry segment of
any vessel, at least in the inner wall after branching. In other words, a velocity gradient from
wall to flow core occurs and develops along the wetted surface of the conduit wall, whereas the
blood stream in the central region of the duct lumen appears to have an inviscid-flow type, i.e.,
the velocity remains uniform. The thickness of the boundary layer, in which momentum diffuses
toward the vessel axis, grows in the streamwise direction until it reaches a critical length, the so-
called entry, or entrance, length ( L e ). From the entry length, flow becomes established, or fully
developed. Downstream from L e , the pressure gradient that must overcome the resistance to flow
decreases linearly and the cross-sectional velocity distribution is invariant.
3 The action of the cardiac pump imposes a time-dependent flow evolution that is quasi-periodic.