Valves
3-4 2/1/12
Heart cm2
4-6 cm2
Calcified heart valve. Rosenhek et al. (2000) NEJM
www.heartcenteronline.com
1
2/1/12
St. Louis University School of Medicine
www.echobyweb.com
Mark Kittleson, UCD VMTH
Ball and cage valve
Bjork-Shiley valve
Carpentier Edwards stented porcine valve
Leeds polyurethane valve
All images from Leeds University School of Mechanical Engineering
2
2/1/12
AXIAL VELOCITY PROFILES at systolic peak flow
Native valve
Valve prosthesis
Native valve: "blunted" velocity profiles; Prosthetic valve: "two jet" velocity profiles
Native valve
Valve prosthesis
Axial WSS is higher downstream of the aortic valve prosthesis
when compared to the native configuration (note the difference is
measurement scales!)
3
2/1/12
Velocity profile of flow through normal healthy heart valve
Velocity profile of flow through mechanical heart valve
Images courtesy of BIDMC, Boston, MA
Blood vessels arent just tubes!
4
2/1/12
Dynamics of flow in the heart
5
2/1/12
Curved Vessels
Curved Vessels
a
=
R
De = Re
A scaling of the Re
by the ratio of the tube
radius (a) to the radius
of curvature (R).
velocity
profile
6
2/1/12
Curved Vessels
For De<34 and <<1:
v
De 2 cos
rz r =a =
1 +
and
4a
73728
r
r =a =
v De sin
4a
72
The wall shear stress rz due to the primary flow is greatest at the outer
wall and lowest at the inner wall.
r arises from the secondary flow and is smaller than the value for the
main component.
7
2/1/12
Changes in flow at branches
Flow separation areas that
diverge from fully-developed flow,
often presenting as regions in
which some of the fluid moves in a
reverse direction.
Separation point the location at
which flow first reverses direction.
Conversely, the reattachment point
is the location where all of the fluid
again moves in the same direction.
Flow through carotid
70% of flow from common
carotid goes into internal
carotid!
32% of
area of
CCA
50% of area of CCA
120% of area of CCA
8
2/1/12
David Steinman
Univ. of Toronto
Pulsatile flow in an idealized normal carotid bifurcation
In this animation, particles shaded blue represent blood flowing to the left,
highlighting the region of recirculating blood in the carotid bulb. This is where
atherosclerotic plaques commonly occur, suggesting a link between hemodynamics
and vascular disease.
David Steinman
Univ. of Toronto
Computational imaging of pulsatile flow in a normal human carotid bifurcation
Magnetic resonance imaging (MRI) of a live subject provides the boundary
conditions (i.e. geometry and flow rates) for a computational fluid dynamic (CFD)
simulation of the blood flow patterns. In this animation, streak length and color
intensity are proportional to the blood velocity. Color distinguishes particles exiting
the external and internal branches. Note the complex swirling flow patterns and
mixing of red and blue particles.
9
2/1/12
Putative profiles in endothelial gene expression
Atheroprotective:
Anti-inflammatory
Anti-thrombotic
Anti-oxidative
Anti-proliferative
Nonadhesive
Atherosusceptible:
Pro-inflammatory
Pro-thrombotic
Oxidative
Proliferative
Adhesive
David Steinman
Univ. of Toronto
Image-based CFD of a mildly diseased carotid bifurcation
Particle path animation of pulsatile flow in a mildly diseased carotid bifurcation
CFD model reconstructed from black blood MRI.
10
2/1/12
David Steinman
Univ. of Toronto
Pulsatile flow in two models of the stenosed carotid bifurcation
Different patterns of post-stenotic recirculation can be observed in models having
the same stenosis severity but different stenosis geometries. Investigators are
currently investigating whether geometric or hemodynamic information can help
to better identify patients at risk of stroke, since such flow patterns may provide
ideal conditions for the formation of the blood clots that cause many strokes.
David Steinman
Univ. of Toronto
Computational imaging of pulsatile flow in a canine aneurysm
This aneurysm model was reconstructed from an MR angiogram of a dog with an
implanted vein-pouch aneurysm.
11
2/1/12
ECs responsive
Sato are M et al. in Tissue Engineering for Therapeutic Use 4,
Ikada Y, Shimizu Y, eds., 2000, p. 123.
ECs are responsive
Butcher, J. T. et al. Arterioscler Thromb Vasc Biol 2004;24:1429-1434
Images of PAECs (A, C, E, and G) and PAVECs (B, D, F, and H) in static and
steady fluid flow environments
12
2/1/12
Spatial scaling of endothelial phenotypes
Davies et al. Biorheology 39
(2002), 299-306.
Passerini et al. PNAS 101
(2004), 2482-2487.
Davies et al. Biorheology 39 (2002), 299-306.
Davies et al. Circ Res 92
(2003), 359-370.
Helmke et al. Circ Res 86
(2000), 745-752.
ECs are responsive
Disturbed flow
Undisturbed flow
NFB (p65)
GPX3 Ab
Passerini et al. (2004) PNAS 101:2482-2487
13
2/1/12
Progression of atherosclerosis
ECs are responsive
Nerem RM et al. Am J Med Sci 1998; 316:169-175.
14
2/1/12
Increased WSS
increased NO
Increased NO
increased dilation/
diameter
Fluid ow
applied
perpend
icular to
the
direc3on of
collagen
bril
orienta3on.
(A)
Sheared,
unstrained.
(B)
Sheared,
strained.
(C)
Unsheared,
unstrained
sample.
Imber3 et al., The Response of Endothelial Cells to Fluid Shear Stress
Using a CoCulture Model of the Arterial Wall. Endothelium (2002).
15
2/1/12
ECs are responsive
Endothelial cell migra0on assay
Peter
Lelkes,
Drexel
Revzan et al., Steady Unidirec0onal Laminar Flow Inhibits Monolayer Forma0on by
Human and Rat Microvascular Endothelial Cells, Endothelium (2004).
ECs are responsive
Kenneth Barbee, Drexel
The three-dimensional surface topography of an endothelial monolayer aligned
by flow in vitro. The surface geometry was measured by AFM on living cells.
Computational Fluid Dynamics was used to calculate the shear stress
distribution on the endothelial surface due to flow over the surface. Shear stress
values, shown in pseudocolor, vary from the nominal wall shear stress by +/29%.
16
2/1/12
ECs are responsive
h = 3.5 m
h = 1.8 m
= 1 + (h havg )
w
where, is the local shear stress
w is the wall shear stress in the absence of the cell
h-havg is the variation in surface height about the mean over a single cell
is a constant
0.120 m-1 for cells not exposed to flow
0.08 m-1 after a 24-h exposure of cells to flow
Determine the maximum shear stress acting on a cultured endothelial
cell exposed to a shear stress of 15 dyne/cm2 when
(1) the cell has not been exposed to flow in culture
(2) after exposure to flow for 24 hours.
= 1 + (h havg )
w
dyne
cm 2
CASE 1
CASE 2
= 0.12 m 1
= 0.08m -1
h = 3.5m
dyne
= 21.3 2
cm
h = 1.8m
dyne
= 18.2 2
cm
w = 15
17
2/1/12
Therapeutic intervention and device failure
Therapeutic intervention and device failure
18
2/1/12
hLp://www.biouids.net/media.html
Implications of Responsive ECs in Tissue Engineering
Tangential pressure
Normal pressure
Biomimetic conditions accelerated
adaptation at 28 days compared to
static conditions demonstrated by:
1. Improved bursting strength
2. Reduced losses in wall thickness and
suture strength
Hoerstrup et al., Eur J Card Surg
2001; 20:164-169.
19
2/1/12
Implications of Responsive ECs in Tissue Engineering
xenograft
autologous/preimplantation
Niklason et al., Science (1999) 284:489 - 493
autologous/
postimplantation 24 d
20
2/1/12
EXAM 1
Topics covered
Chapter 1: Introduc3on to Biotransport
Transport in the body (types, deni3ons)
Chapter 2: Conserva3on Rela3ons and Momentum Balances
Fluid sta3cs (cor3cal & surface tension)
Using mass, momentum, and force balances to nd
velocity prole, Q, and shear stress for various
geometries
Newtons Law of Viscosity; Poiseuilles Law
Rheology of blood
Chapter 3: Conserva3on Rela3ons for Fluid Transport
Equa3on of con3nuity (conserva3on of mass)
Equa3ons of mo3on (NavierStokes)
Dimensional analysis (Buckingham Pi Theorem)
Chapter 4: Approximate Methods for Analysis of Complex Flow
Bernoulli equa3on (simplied)
Chapter 5: Fluid Flow in the Circula3on and Tissues
Flow in Curved Vessels
Responsiveness of ECs to ow
21