1. Modeling Tumor Growth and Angiogenesis Rui Travasso Centro de Física Computacional Universidade de Coimbra

2. Cancer  Group of diseases presenting  Uncontrolled cell growth  Invasion (and metastasis)  Computer simulation in cancer: 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 Khain et al, Phys.Rev.Lett. (2006)

3. 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 Necrotic zone Uncontrolled Reproduction Healthy cells

4. 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

5. 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

6. Tumor Growth - Spheroids  Tumor growth in vitro  ~10 6 cells  ~2 mm diameter  Many different models Necrotic Quiescent Proliferative + Nutrients + Elasticity Pressure gradients Interstitial fluid flow + ECM and other cells Multiphase models Many constitutive equations Cell based t R High Pressure

7. 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

8. Tumor Growth - Angiogenesis Switch - Vascular Phase  The tumor promotes the development of nearby vessels to have oxygen  Challenging simulations  Many parameters  Cell based  Continuous  Hybrid MackLin et al, J Math Biol 2009 Chaplain et al, Annu Rev Biomed Eng 2006

9. 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 Gerlee, Anderson, J Theor Biol 2007 Acid

10. 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 Gerhardt et al, Cell (2003) Lee et al, Cell (2007)

11. 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)

12. Angiogenesis in a Nutshell  Capillaries are constituted by  Endothelial cells  Pericites, muscle cells Endothelial cells Pericites, smooth muscle cells… VEGF  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 Meyer et al, Am.J.Path. (1997)

13. 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 survival activation reproduction Dll-4 Notch

14. 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 Rodriguez-Manzaneque et al, PNAS (2001)

15.  Approach to moving boundary problems  Phases associated with value of   Interface implies  = 0  Diffuse interface  Original problem obtained when  → 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 Phase-Field Models Phase 1 Phase 2  = -1  = 1 

16. Examples  Canham-Helfrisch energy  Multiscale modelling  Phase separation of elastic phases  Dendritic growth

17. The Model The penetration length  of T inside the capillary is given by    D     = 1 inside capillary  = -1 outside capillary T  Two equations  Diffusion: concentration of VEGF, T  Phase-Field: order parameter dynamics  Tip cell  Characteristic radius R c  Perfect Notch signaling  Introduced when T > T c  Velocity:    regulates the proliferation and D  the chemotaxis Ginzburg-Landau free energy Chemical potential Cahn-Hilliard dynamics Surface tension driven, bulk material conservation

18. Simulation  Starting configuration  Artery close to tissue in hypoxia  Concentration at cells: T s Artery Cells in hypoxia  A blood vessel network emerges  D  = 250 and   = 3.0

19. Proliferation  Varying    for D  = 250  Higher proliferation rate leads to thicker and ramified vessels   = 1.0   = 3.0   = 4.0

20. Chemotaxis  Varying D   for   = 3.0  Higher tip cell velocity leads to thinner and more ramified vessels D  = 100D  = 300D  = 400

21. VEGF Prodution  Varying T s,  for   and D 2 constants  Higher production of VEGF leads to more vessels but not thicker vessels T s = 1.0T s = 1.2 Gerhardt et al., Develop. Biol. (2003)

22. Matrix Metalloproteinase  MMPs implementation:  Heavy VEGF isoforms get bound to matrix if c MMP high  c MMP high in a radius R MMP of tumor cell  Diffusion in function of T h  Formation of thick vessels  Thin vessel merging Rodriguez-Manzaneque et al, PNAS (2001) MMP-9 Inhibition MMP-9 Overexpressed ThTh D high c MMP low c MMP

23.  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 Rodriguez-Manzaneque et al, PNAS (2001) Conclusion Gerhardt et al, Cell (2003)

24. A Pretty One

25. Coimbra Group  Susana Silva  Pedro Oliveira  Inês Lopes  Fernando Nogueira  Claudia Cardoso  Apostolos Marinopoulos  Duan-Jun Cai  Paulo Abreu  Bruce Milne  Myrta Gr ü nning