Title: Microcirculation: Structural adaptation and angiogenesis Timothy W' Secomb Mathematical Biosciences
1MicrocirculationStructural adaptation and
angiogenesisTimothy W. SecombMathematical
Biosciences InstituteColumbus, OhioJanuary 19,
2007
2(No Transcript)
3Dynamic aspects of vascular structure
- Regulation of blood flow (short-term)
- Growth and maturation
- Wound healing
- Uterine growth and regression
- Response to exercise (or lack thereof)
- Remodeling of vascular grafts
- Tumor growth
4Structural changes
Chick embryo chorio- allantoic membrane Ribatti
et al., 2001 Bar 50 µm
- Vasculogenesis formation of an initial vascular
plexus - Sprouting angiogenesis formation of new vessels
by sprouting and elongation of existing vessels - Intussusception formation of new vessels by
splitting of existing vessels - Pruning loss of vessels
- Structural adaptation, angioadaptation, vascular
remodeling, arterialization changes in wall
structure of existing vessels
Rat mesentery Hansen-Smith, 2000 Bar 50 µm
Grafting to arterial position passive distension
Venous graft
Angioadaptation remodeling
5Poiseuilles law (1840s)
Also
Q flow rate Jwall wall shear stress D
diameter 0 apparent blood viscosity
6Murrays law (1926)
For a set of segments with prescribed flows Qi,
the total energy dissipation is minimized for a
given total blood volume when this condition is
satisfied.
7Adaptation in response to wall shear stress
Rodbard 1975
See also Kamiya et al., 1984
8Uneven distribution of shear stress
Rodbard 1975
9Microvascular networks in rat mesentery
Networks N 6 tissue area 25 - 80 mm2
segments per network 432102 Measurements
Network topology segment lengths, diameters,
hematocrits, flow velocities Model Hemodynamic
simulations, giving estimates of pressure and
wall shear stress in each segment
10Pressure-shear relationship
Pries et al. 1995
11Adaptation to pressure-shear relationship
Pries et al. 1995
12Instability resulting from response to shear
stress
See also Hudetz and Kiani, 1992 Hacking et al.,
1996
Rodbard 1975
13Adaptation in response to wall shear stress and
pressure
Increasing time
14Adaptation in response to wall shear stress,
pressure and metabolic state
Increasing time
15Information transfer
16Schematic diagram of adaptation model
17Diameters and flow rates measured vs. model
Pries al., 2001
18Angiogenic factors
- TAF (tumor angiogenesis factor)
- VEGF (vascular endothelial growth factor)
- FGF (fibrobast growth factor)
- aFGF, bFGF
- TGF-b (transforming growth factor b)
Vascular stabilizing factors
19Stages in tumor growth
- Avascular
- growth limited by diffusion from exterior
- maximum size 1 mm
- Vascular
- growth limited by diffusion from vessels
- size limited only by host survival
20Basic concept of antiangiogenic therapy
If we can prevent formation of new blood vessels,
we can limit tumor growth
21Balding and McElwain, 1985
22Ausprunk and Folkman, 1977
1 mm
23Typical scheme for modeling tumor-induced vascular
growth
24Models for tumor-induced vascular growth I
http//www.maths.dundee.ac.uk/sanderso/discmod7.h
tm
- Anderson and Chaplain, 1998
- 2D continuum model
- three variables, endothelial-cell density, TAF
concentration, fibronectin concentration - also considered discrete model, endothelial cells
on square mesh
- Balding and McElwain, 1985
- 1D continuum model
- two variables, capillary density and capillary
tip density - TAF diffuses from tumor edge
25Models for tumor-induced vascular growth II
- Levine et al., 2001
- 2D continuum model
- many variables (angiogenic factor, proteolytic
enzyme, protease inhibitor, fibronectin,
angiostatin, endothelial cell density)
- Tong and Yuan, 2001
- 2D discrete model of sprout growth
- diffusion of bFGF, uptake by vessels
26Models for vascular growth in tumors
- Hahnfeldt et al., 1999 Sachs et al., 2001
- ODE models
- two variables, number of cells and vascular
carrying capacity - consider effects of anti-angiogenic therapy
- Liotta et al., 1977
- 1D (spherical) continuum model
- two variables, density of tumor cells and
vascular surface area per volume
27Microcirculatory adaptation and angiogenesis
Current and future theoretical topics
- Structural adaptation role of axial tension and
growth, relationship to cellular-level processes - Angiogenesis roles of multiple growth factors
- Intussusceptive growth
- Relationship to pattern formation in early
development - Medical applications cancer, heart disease,
stroke