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Modelling cell-extracellular matrix interactions

Modelling cell-extracellular matrix interactions. Luigi Preziosi. Luigi.preziosi@polito.it calvino.polito.it/~preziosi. (degenerate parabolic). Tumours as multicomponent tissues. Dipartimento di Matematica. Dipartimento di Matematica. Mechanics in Multiphase Models. Growth. Stress.

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Modelling cell-extracellular matrix interactions

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  1. Modelling cell-extracellular matrix interactions Luigi Preziosi Luigi.preziosi@polito.it calvino.polito.it/~preziosi

  2. (degenerate parabolic) Tumours as multicomponent tissues Dipartimento di Matematica Dipartimento di Matematica

  3. Mechanics in Multiphase Models Growth Stress Interaction force Mechanical effects in: (P. Friedl, K. Wolf)‏ http://jcb.rupress.org/cgi/content/full/jcb.200209006/DC1 Dipartimento di Matematica

  4. Cell-ECM interaction • Baumgartner et al. PNAS97 (2000)‏ Dipartimento di Matematica Dipartimento di Matematica

  5. Human Brain Tumor 35 pN Sun et al. Biophys J.89 (2005)‏

  6. Interactionforce Adhesionstrength mcm Darcy's-type law scm vrel Modelling the interaction between cells and ECM - if cells are not pulled strong enough they stick to the ECM - otherwise they move relative to the ECM • L.P. & A. Tosin, J. Math. Biol.58, 625-656, (2009) Dipartimento di Matematica

  7. Interactionforce Adhesionstrength Modelling the interaction between cells and ECM - if cells are not pulled strong enough they they stick to the ECM - otherwise they move relative to the ECM Dipartimento di Matematica

  8. Modelling the interaction between cells and ECM G. Vitale & L.P., M3AS, (2010)

  9. v Modelling the interaction between cells and ECM Contribution due to porosity and tortuosity (in 3D) Contribution due to adhesion Dipartimento di Matematica

  10. Modelling the adhesive contribution Evolution equation In the limit: bond age << travel time Breaking length << cell diameter Dipartimento di Matematica

  11. If z z0 F F0 Modelling the adhesive contribution If z z0 F Dipartimento di Matematica

  12. z mD+mad mad F Fm FM Modelling the adhesive contribution Dipartimento di Matematica

  13. Modelling the interaction between cells and ECM

  14.  Different clones have different thresholds Different invasiveness moves slows down stops Some concluding remarks Adhesion depends on the amount of ECM,

  15. Modelling the interaction between cells and ECM Volume ratio Interfacial force Dipartimento di Matematica

  16. Cellular Potts Model Dipartimento di Matematica

  17. Sub-Cellular Components in CPM M. Scianna M. Scianna & L.P., Multiscale Model. Simul. (2012) Dipartimento di Matematica

  18. Moving cell morphology with CPM Dipartimento di Matematica

  19. Effect of adhesion in 2D Palecek et al., Nature385, 537-540 (1997)

  20. Effect of pore size M. Scianna, L.P., & K. Wolf, Biosci. Engng. (2012)

  21. Effect of deformability Varying fiber elasticity Varying nucleus elasticity

  22. Direct and Inverse Problem Dipartimento di Matematica

  23. Dipartimento di Matematica

  24. Dipartimento di Matematica

  25. Dipartimento di Matematica

  26. Cell Traction V. Peschetola, V. Laurent, A. Duperray, L. Preziosi, D. Ambrosi, C. Verdier, Comp. Methods Biomech. Biomed. Engng. 14, 159-160 (2011). Dipartimento di Matematica time

  27. Traction on a stiff gel Ambrosi, Peschetola,Verdier SIAM J. Appl. Math, (2006) T24 cancer cells Dipartimento di Matematica

  28. Traction on softer gel T24 cancer cells • Conclusions • minor traction ability than fibroblasts • larger forces on stiffer gels Dipartimento di Matematica

  29. Traction in 3D G. Vitale, D. Ambrosi, L.P., J. Math. Anal. Appl. 395, 788-801 (2012). Inverse Problems 28, 095013 (2012) : f→u Penalty function for the minimization problem Self-adjoint problem Dipartimento di Matematica

  30. Traction in 3D Dipartimento di Matematica

  31. D. Ambrosi A. Tosin G. Vitale V. Peschetola A. Chauviere C. Verdier S. Astanin C. Giverso M. Scianna

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