Mathematical Modeling and Simulations Supporting Medicine and Biology
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1 Mathematical Modeling and Simulations Supporting Medicine and Biology Luigi Preziosi Politecnico di Torino calvino.polito.it/~preziosi
2 Mathematical Modeling and Simulations Supporting Medicine and Biology Mathematics is Biology's Next Microscope, Only Better; Biology is Mathematics Next Physics, Only Better J.E. Cohen, PLoS Biol 2, e439 (2004) Although living systems obey the laws of physics and chemistry, the notion of function or purpose differentiate biology from other natural sciences Hartwell, Hopfield, Leibner, Murray, Nature 402, c47-c52 (1999)
3 From mathematics to medicine Phenomenological observation Independent variables Dependent variables Parameters Deduction of the mathematical model Qualitative analysis No Simulation of known cases Experimental validation Yes Simulation of unknown cases and new phenomena Dipartimento di Matematica
4 From medicine to mathematics Tissue growth (growth) Tissue remodelling (tissue engineering) Tissue activation (cell, muscles, heart)
5 An example: Vascular network formation Stimulation Proliferation Migration Organisation Short version of the movie at: v22/n8/suppinfo/ as1.html
6 Assumptions Cells move on the Matrigel surface and do not duplicate The cell population can be described by a continuous distribution of density n and velocity v Cells release chemical mediators (c) Cells are accelerated by gradients of soluble mediators Original at and slowed down by friction For low densities (early stages) the cell population can be modelled as a fluid of non directly interacting particles showing a certain degree of persistence in their motion Tightly packed cells respond to compression Original at Dipartimento di Matematica
7
8 Mathematical Model Gamba, Ambrosi, Serini, Giraudo, Preziosi, Bussolino, Phys. Rev. Letters, 90, (2003) n = 200 cells/mm2 ξ = (α τ)1/2~ mm α ~ 10-7 cm2/s τ ~ 103 s ~ 20 min a ~.02 mm
9 Exogenous chemorepellent new characteristic length action range of chemorepellent Parameters used give: l' = 0.31mm In dimensionless form: l'* = l'* 0.27
10 A comparison on the state-of-the-art 20nM 1h 50nM 1h 20nM 6h 50nM 6h 20nM 24h resistenti Kepler Decoding human genome He inherited a huge quantity of very precise data from Tycho Brahe on the position of the planets. The main problem was to organise the data and understand their meaning Enormous quantity of data to be organized Understand their meaning
11 A comparison on the state-of-the-art Kepler He inherited a huge quantity of very precise data from Tycho Brahe on the position of the planets. The main problem was to organise the data and give them a sense??. Newton Copernico He explained Kepler laws assuming that there is a force of gravity depending on 1/r2. He proposed a revolutionary structure of the solar system
12 20nM 1h 50nM 1h 20nM 6h 50nM 6h 20nM 24h resistenti Mathematics and Genomics Medical needs Organizing huge sets of data (statistics) Understand the past (inverse problem) Foresee the future (direct problem) Optimizing, controlling and personalizing therapies (control problem) Rosso = genes expressed more by tumour cells after the treatment Verde = genes expressed more by tumour cells before the treatment Yellow = genes equally expressed in the two situations
13 Mathematics and proteomics
14 Protein networks ErbB2/neu Tyorsine Kinase Receptor Amplificata nel 25% dei tumori al seno cmyc/ Lymphome de Burkitt
15 Protein networks
16 Nested models in PDE Sub-cellular level
17 Nested models in IBM Sub-cellular level
18 Cellular Potts model for vasculogenesis
19 Cellular Potts model for vasculogenesis
20 Cellular Potts model for vasculogenesis M. Scianna, L. Munaron & L.P., Prog. Biophys. Mol. Biol. (2011) Dipartimento di Matematica
21 Cellular Potts model for vasculogenesis
22 Cellular Potts model for vasculogenesis
23 Invasion of ovary cancer cells
24 Invasion of ovary cancer cells Top view Side view C. Giverso, M. Scianna, L.P., N. Lo Buono & A. Funaro Math. Model. Nat. Phenom. 5 (2010)
25 Rigid nucleus in microchannels (J. Guch) Rolli et al. PlosOne, 5, e8726 (2010)
26 Deformable nucleus in microchannels (J. Guch)
27 Influence of nucleus rigidity
28 Continuous Criterium for Invasion Giverso & L.P., Biomech. Model. Mechanobiol.
29 Elastic solid
30 Invasion of Ovary Cancer Cells
31
32 Invasion of Ovary Cancer Cells Dipartimento di Matematica
33 Mathematics and connectomics Human brain project
Modelling cell motion: From microscopic to macroscopic scale. Luigi Preziosi Luigi.preziosi@polito.it calvino.polito.it/~preziosi
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