Luigi Preziosi - Department of Mathematical Sciences, Politecnico di Torino
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Scuole Estive
Modelli Matematici in Biomeccanica e Biomedicina
Mathematical Models in Biomechanics and Biomedicine
  1. ► Equazione di diffusione
    Diffusion equation
  2. ► Il ciclo cellulare e la carcinogenesi
    Cell cycle and carcinogenesis
  3. ► Primi modelli matematici di crescita tumorale
    Early mathematical models of tumor growth
  4. ► Moto delle cellule
    Cell motion
  5. ► Meccanotrasduzione
    Mechanotrandsuction
  6. ► Propagazione di segnali nervosi
    Neurons and signal propagation
  7. ► Individual cell-based models
    Individual cell-based models
  8. ► Modelli multifase di crescita tumorale
    Multiphase models of tumor growth
  9. ► Cellular Potts models
    Cellular Potts models
  10. ► Formazione di reti vascolari (vasculogenesi)
    Vascular networks formation (vasculogenesis)
  11. ► Angiogenesi notes
    Angiogenesis
Alcuni filmati mostrati durante le lezioni
Some movies shown during the lectures

Check also these links for more movies of experiments and simulations:
Lecture 1 - Motion of a fibroblast that stops and rounds up to duplicate. Lecture 2 - Free growth of a glioblastoma (simulation by E. Mottola and M. Trucco). Lecture 2 - Artificial regression due to continuous infusion of a chemotherapeutic drug (simulation by E. Mottola and M. Trucco). Lecture 2 - Convection enhanced delivery: diffusion of an injected drug (simulation by E. Mottola and M. Trucco).
Lecture 4 - Growth of a monolayer of cells. Lecture 4 - Growth of a monolayer of cells. Colors indicate the concentration of available nutrient. Dark cells are undergoing necrosis. Lecture 4 - Section of a tumor cord. Green cells are tumour cells, yellow cells are tumor cells in hypoxia, white cells are host cells (simulations by G. Mersi). Lecture 4 - Growth of a tumor cord along a capillary (simulations by G. Mersi).
Lecture 5 - Growth of two colonies of WiDr cell lines which differ in their motility. Evolution of the cell volume ratios. and the one on the right the growth rate (more info). Lecture 5 - Growth of two colonies of WiDr cell lines which differ in their motility. Evolution of the cell the growth rates (more info). Lecture 5 - Simulation of the same problem by an individual cell based model (by J. Galle). Lecture 5 - Simulation of the growth of a monolayer to confluence. Here duplication stops because of contact inhibition.
Lecture 5 - Simulation of the growth of a monolayer to confluence. Here the orange clone is not inhibited by the contact with the other cells. Lecture 7 - Magnitude of the computed shear stress for a T24 cell line shown in terms of a color map (more info). Lecture 7 - Motion of an ensemble of cells attracted to the right by a chemoattractant in an heterogeneous environment (denser region in the center) (more info). Lecture 7 - Motion of an ensemble of cells attracted to the right by a chemoattractant in an anisotropic environment (fibers aligned along x in the center) (more info).
Lecture 8 - First moments of the formation of a capillary network by 125 cells/mm2 of human microvascular endothelial cells plated on Matrigel. (more info). Contact me for a longer version (too big to be put on the web). Lecture 8 - Simulation of the formation of a capillary network by human microvascular endothelial cells at an initial density of 200 cells/mm2. Lecture 8 - Simulation of the formation of a capillary network by human microvascular endothelial cells at an initial density of 400 cells/mm2. Lecture 8 - Effect of the interaction with the Matrigel on the process of formation of the capillary network by vasculogenesis.
Lecture 9 - Angiogenesis without haptotaxis. Angiogenic growth factors are produced on the right edge of the domain. Simulation by students of the course on the basis of the model by A. Anderson and M. Chaplain, Bull. Math. Biol., 60(5):857-899 (1998). Lecture 9 - Angiogenesis with haptotaxis. Angiogenic growth factors are produced on the right edge of the domain. Simulation by students of the course on the basis of the model by A. Anderson and M. Chaplain, Bull. Math. Biol., 60(5):857-899 (1998). Lecture 9 - Angiogenesis without haptotaxis. Angiogenic growth factors are produced at the center of the right edge, mimicking a tumor positioned there. Simulation by students of the course on the basis of the model by A. Anderson and M. Chaplain, Bull. Math. Biol., 60(5):857-899 (1998).
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