Transcript Harnessing Chemical Patterning to Direct the Flow of

Modeling Tumor Growth and Angiogenesis
Rui Travasso
Centro de Física Computacional
Universidade de Coimbra
Cancer
 Group of diseases presenting
 Uncontrolled cell growth
 Invasion (and metastasis)
 Computer simulation in cancer:
Khain et al, Phys.Rev.Lett. (2006)
prognostic and control
 Complex problem
 Interaction between different cellular types
 Processes at different scales
 Microscopic: protein reaction networks, mutations
 Macroscopic: cell diffusion
 Focus: Solid tumors
Tumor growth
 Phase 1: Genetic mutations
 Cellular cycle and apoptosis disruption
 Uncontrolled reproduction, no cell death
 Phase 2: Interaction with immune system
 Cancer cells inhibit immune system
 Phase 3: Solid tumor
 Cancer cell diffusion
 Necrotic zones
Necrotic zone
Uncontrolled
Reproduction
 Solid tumor diameter 1-2 mm
Healthy cells
Angiogenesis and Metastasis
 Tumor growth requires nutrients
 Active nutrient search
 Phase 4: Angiogenesis
 Segregation of proteins which promote
blood vessel growth
 Aberrant vascular network
 Phase 5: Metastasis
 Cancer cells enter in blood network
 New colonies in healthy regions
M. D. Anderson Cancer Center, Univ. of Texas
Tumor Topics
 Cancer cells’ uncontrolled reproduction
 Genetic material diversity
 Large adaptability
 Tumor surroundings are extremely hostile
 Host destruction is adaptation victory
 Fragile blood vessels
 A tumor bleeds
 Continuous angiogenesis
 A tumor is a wound which does not heal
Tumor Growth - Spheroids
 Tumor growth in vitro
 ~106 cells
R
 ~2 mm diameter
 Many different models
t
Necrotic
Quiescent
Proliferative
High Pressure
+ Nutrients
+ Elasticity
Pressure gradients
Interstitial fluid flow
+ ECM and other cells
Multiphase models
Many constitutive equations
Cell based
Tumor Growth - Cadherin Switch - Permeable Phenotype
 E-Cadherin connect nearby cells of epithelium
 Proliferation regulated by E-cadherin
signal pathway
 In case of failure may lead to uncontrolled
proliferation
 Cadherin switch at the onset of solid tumor growth
 Motile tumor cells
 Move in search for nutrients
 Metastasis
Tumor Growth - Angiogenesis Switch - Vascular Phase
 The tumor promotes the
development of nearby
vessels to have oxygen
 Challenging simulations
Chaplain et al, Annu Rev Biomed Eng 2006
 Many parameters
 Cell based
 Continuous
 Hybrid
MackLin et al, J Math Biol 2009
Tumor Growth - Competition - Evolution
 Deregulated proliferation
 Mutations
 Darwin selection

Acid
Metabolism and migration
 Anaerobic matabolism
 2 ATP instead of 36
 No need of Oxygen
 Produces acid
 Helps migration
 Prevailing phenotype
 Acid resistant
Gerlee, Anderson, J Theor Biol 2007
Angiogenesis
 Sprouting of new blood vessels from existing ones
 Relevant in varied situations
 Morphogenesis
Gerhardt et al, Cell (2003)
 Inflammation
 Wound healing
 Neoplasms
 Diabetic Retinopathy
 For tumors
 Altered vessel network
Lee et al, Cell (2007)
 Dense, no hierarchical structure
 Capillaries are fragile, permeable, with variable diameter
 Capillary network carries both nutrients and drugs
Two types of cells
 Tip cells are special
 Have filopodia
 Produce MMPs which degrade ECM
 Construct path
 Do not proliferate
Gerhardt et al, Cell (2003)
 Stalk cells
 Proliferation regulated by VEGF
 Not diggers

Follow tip cell created pathway
Gerhardt et al, Cell (2003)
Angiogenesis in a Nutshell
 Capillaries are constituted by
 Endothelial cells
Endothelial cells
Pericites, smooth muscle cells…
 Pericites, muscle cells
 VEGF weakens capillary wall
 Endothelial cells may divide
VEGF
 Cells follow VEGF gradient
 The first cell is activated and opens way in ECM
 Cells organize to form lumen
Meyer et al, Am.J.Path. (1997)
 Blood flows when capillaries form loops
 Blood reorganizes network
Tip cells: Notch and Dll-4
 New branches do not form everywhere
 Tip cells regulated by Notch pathway
 VEGF activates cell receptor (VEGFR2)
 Many pathways (reproduction, survival, cell activation)
 Promotes Dll-4
 Dll-4 activates Notch in
VEGFR2
reproduction
survival
neighboring cell
activation
 Notch represses VEGFR2
Notch
Dll-4
 Tip cells are not neighbors (salt and pepper pattern)
The Way to Look at it
 Capillary walls divide space
 Inside/Outside considered as different phases
 Different phases separated by interfaces
 Interfaces grow and move
Rodriguez-Manzaneque et al, PNAS (2001)
 Phase field models
 Describe interface dynamics
 Applied to different problems
Solidification
 Biological membranes
 Fluid interfaces

Phase-Field Models
 Approach to moving boundary problems
 Phases associated with value of
Interface implies f = 0
 Diffuse interface
 Original problem obtained
when e → 0
f
f= 1

Phase 1
e
f= -1
Phase 2
 Correct interface physics in varied situations
 Interfaces in elastic, viscoelastic or fluid media
 Fracture dynamics
 Can be derived from a free energy F[f,e]
 Computationally effective since no frontier conditions at interface
Examples


Canham-Helfrisch energy
Multiscale modelling


Dendritic growth
Phase separation of elastic phases
The Model
 Two equations
 Diffusion: concentration of VEGF, T
 Phase-Field: order parameter dynamics
The penetration length  of
T inside the capillary
is given by D
t f     f Tf(f)
2
 Tip cell
 f 2 f 4 e 2
2 
F    
Ginzburg-Landau
free energyradius
 Characteristic
Rc 2 4  2 f dr
 Perfect Notchsignaling
F

 f  f 3  e 2 2f
Chemical
potential
 Introduced when
f T > Tc
D T
 Velocity: v t 
f f
  
Cahn-Hilliard dynamics


f = 1 inside capillary
f = -1 outside capillary
T
t
 tension
f regulates
thematerial
proliferation
and
Surface
driven, bulk
conservation
Df the chemotaxis
Simulation
 Starting configuration
Artery
Cells in hypoxia
 Artery close to tissue
in hypoxia
 Concentration at cells: Ts
QuickTime™ and a
Video decompressor
are needed to see this picture.

A blood vessel network emerges
 Df = 250 and f = 3.0
Proliferation
 Varying
f for Df = 250
f = 1.0
f = 3.0
f = 4.0
 Higher proliferation rate leads to thicker and ramified vessels
Chemotaxis
 Varying Df for f = 3.0
Df = 100
Df = 300
Df = 400
 Higher tip cell velocity leads to thinner and more ramified vessels
VEGF Prodution
 Varying Ts, for f and D2 constants
Ts = 1.0
Ts = 1.2
Gerhardt et al.,
Develop. Biol. (2003)
 Higher production of VEGF leads to more vessels but not thicker
vessels
Matrix Metalloproteinase
 MMPs implementation:
bound to matrix if cMMP high
 cMMP high in a radius RMMP
of tumor cell
 Diffusion in function of Th
low cMMP
D
high cMMP
Th
 Formation of thick vessels
 Thin vessel merging
MMP-9 Overexpressed MMP-9 Inhibition
 Heavy VEGF isoforms get
Rodriguez-Manzaneque et al, PNAS (2001)
Conclusion
 Introduced phase-field model for angiogenesis
 Able to be extended in order to describe
tissue dynamics
Gerhardt et al, Cell (2003)
 Delicate balance between proliferation and chemotaxis
 High proliferation leads to thick and ramified vessels
 Strong chemotaxis leads to thin and ramified vessels
 High production VEGF levels lead to increased vessel density
 Experimental agreement
 Future work
 Anastomosis
Rodriguez-Manzaneque et al, PNAS (2001)
 Incorporation of experimental results
A Pretty One
QuickTime™ and a
Video decompressor
are needed to see this picture.
Coimbra Group
 Susana Silva
 Pedro Oliveira
 Inês Lopes
 Fernando Nogueira
 Claudia Cardoso
 Apostolos Marinopoulos
 Duan-Jun Cai
 Paulo Abreu
 Bruce Milne
 Myrta Grünning