Modeling Tumor Growth and Angiogenesis

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• Modeling Tumor Growth and Angiogenesis

Rui Travasso
Centro de Física Computacional Universidade de
Coimbra
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Cancer

• Group of diseases presenting
• Uncontrolled cell growth
• Invasion (and metastasis)
• Computer simulation in cancerprognostic and
  control
• Complex problem
• Interaction between different cellular types
• Processes at different scales
• Microscopic protein reaction networks, mutations
• Macroscopic cell diffusion
• Focus Solid tumors

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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
• Solid tumor diameter 1-2 mm

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Angiogenesis and Metastasis

• Tumor growth requires nutrients
• Active nutrient search
• Phase 4 Angiogenesis
• Segregation of proteins which promoteblood
  vessel growth
• Aberrant vascular network
• Phase 5 Metastasis
• Cancer cells enter in blood network
• New colonies in healthy regions

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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

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Tumor Growth - Spheroids

• Tumor growth in vitro
• 106 cells
• 2 mm diameter
• Many different models

Nutrients Elasticity Pressure gradients
Interstitial fluid flow ECM and other cells
Multiphase models Many constitutive
equations Cell based
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Tumor Growth - Cadherin Switch - Permeable
Phenotype

• E-Cadherin connect nearby cells of epithelium
• Proliferation regulated by E-cadherinsignal
  pathway
• In case of failure may lead to uncontrolledprolif
  eration
• Cadherin switch at the onset of solid tumor
  growth
• Motile tumor cells
• Move in search for nutrients
• Metastasis

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Tumor Growth - Angiogenesis Switch - Vascular
Phase

• The tumor promotes thedevelopment of
  nearbyvessels to have oxygen
• Challenging simulations
• Many parameters
• Cell based
• Continuous
• Hybrid

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Tumor Growth - Competition - Evolution

• Deregulated proliferation
• Mutations
• Darwin selection
• Metabolism and migration
• Anaerobic matabolism
• 2 ATP instead of 36
• No need of Oxygen
• Produces acid
• Helps migration
• Prevailing phenotype
• Acid resistant

Acid
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Angiogenesis

• Sprouting of new blood vessels from existing ones
• Relevant in varied situations
• Morphogenesis
• Inflammation
• Wound healing
• Neoplasms
• Diabetic Retinopathy
• For tumors
• Altered vessel network
• Dense, no hierarchical structure
• Capillaries are fragile, permeable, with variable
  diameter
• Capillary network carries both nutrients and
  drugs

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Two types of cells

• Tip cells are special
• Have filopodia
• Produce MMPs which degrade ECM
• Construct path
• Do not proliferate
• Stalk cells
• Proliferation regulated by VEGF
• Not diggers
• Follow tip cell created pathway

Gerhardt et al, Cell (2003)
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Angiogenesis in a Nutshell

• Capillaries are constituted by
• Endothelial cells
• Pericites, muscle cells

? VEGF weakens capillary wall ?
Endothelial cells may divide
? Cells follow VEGF gradient ? The first
cell is activated and opens way in ECM
? Cells organize to form lumen
? Blood flows when capillaries form loops
? Blood reorganizes network
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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 neighboring cell
• Notch represses VEGFR2
• Tip cells are not neighbors (salt and pepper
  pattern)

VEGFR2
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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
• Phase field models
• Describe interface dynamics
• Applied to different problems
• Solidification
• Biological membranes
• Fluid interfaces

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Phase-Field Models

• Approach to moving boundary problems
• Phases associated with value of f
• Interface implies ? 0
• Diffuse interface
• Original problem obtained when e ? 0
• Correct interface physics in varied situations
• Interfaces in elastic, viscoelastic or fluid
  media
• Fracture dynamics
• Can be derived from a free energy F?,?
• Computationally effective since no frontier
  conditions at interface

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Examples
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The Model

• Two equations
• Diffusion concentration of VEGF, T
• Phase-Field order parameter dynamics
• Tip cell
• Characteristic radius Rc
• Perfect Notch signaling
• Introduced when T gt Tc
• Velocity
• ?? regulates the proliferation and D? the
  chemotaxis

The penetration length ??of T inside the
capillary is given by ?????D????
? 1 inside capillary ? -1 outside capillary
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Simulation

• Starting configuration
• Artery close to tissue in hypoxia
• Concentration at cells Ts

? A blood vessel network emerges ? D?
250 and ?? 3.0
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Proliferation

• Varying ???for D? 250
• Higher proliferation rate leads to thicker and
  ramified vessels

?? 1.0
?? 3.0
?? 4.0
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Chemotaxis

• Varying D??for ?? 3.0
• Higher tip cell velocity leads to thinner and
  more ramified vessels

D? 100
D? 300
D? 400
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VEGF Prodution

• Varying Ts,?for ?? and D2 constants
• Higher production of VEGF leads to more vessels
  but not thicker vessels

Ts 1.0
Ts 1.2
Gerhardt et al., Develop. Biol. (2003)
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Matrix Metalloproteinase

• MMPs implementation
• Heavy VEGF isoforms getbound to matrix if cMMP
  high
• cMMP high in a radius RMMP of tumor cell
• Diffusion in function of Th
• Formation of thick vessels
• Thin vessel merging

MMP-9 Inhibition
MMP-9 Overexpressed
Rodriguez-Manzaneque et al, PNAS (2001)
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Conclusion

• Introduced phase-field model for angiogenesis
• Able to be extended in order to describe tissue
  dynamics
• 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
• Incorporation of experimental results

Gerhardt et al, Cell (2003)
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A Pretty One
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Coimbra Group

• Susana Silva
• Pedro Oliveira
• Inês Lopes
• Fernando Nogueira
• Claudia Cardoso
• Apostolos Marinopoulos
• Duan-Jun Cai
• Paulo Abreu
• Bruce Milne
• Myrta Grünning