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Microcirculation: Structural adaptation and angiogenesis Timothy W' Secomb Mathematical Biosciences

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Title: Microcirculation: Structural adaptation and angiogenesis Timothy W' Secomb Mathematical Biosciences


1
MicrocirculationStructural adaptation and
angiogenesisTimothy W. SecombMathematical
Biosciences InstituteColumbus, OhioJanuary 19,
2007
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(No Transcript)
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Dynamic 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

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Structural 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
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Poiseuilles law (1840s)
Also
Q flow rate Jwall wall shear stress D
diameter 0 apparent blood viscosity
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Murrays 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.
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Adaptation in response to wall shear stress
Rodbard 1975
See also Kamiya et al., 1984
8
Uneven distribution of shear stress
Rodbard 1975
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Microvascular 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
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Pressure-shear relationship
Pries et al. 1995
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Adaptation to pressure-shear relationship
Pries et al. 1995
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Instability resulting from response to shear
stress
See also Hudetz and Kiani, 1992 Hacking et al.,
1996
Rodbard 1975
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Adaptation in response to wall shear stress and
pressure
Increasing time
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Adaptation in response to wall shear stress,
pressure and metabolic state
Increasing time
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Information transfer
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Schematic diagram of adaptation model
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Diameters and flow rates measured vs. model
Pries al., 2001
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Angiogenic 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
  • Angiopoietin-1 and -2

19
Stages 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

20
Basic concept of antiangiogenic therapy
If we can prevent formation of new blood vessels,
we can limit tumor growth
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Balding and McElwain, 1985
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Ausprunk and Folkman, 1977
1 mm
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Typical scheme for modeling tumor-induced vascular
growth
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Models 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

25
Models 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

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Models 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

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Microcirculatory 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
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