Modeling endothelial glycocalyx and its interaction with blood flow

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1 Modeling endothelial glycocalyx and its interaction with blood flow Sofia Biagi PhD under the joint supervision of DdR Chaouqi Misbah LIPhy, Grenoble Prof. Francesco Sciortino Università Sapienza, Roma

2 Introduction BLOOD CIRCULATION MODEL one-kind particles in a simple newtonian liquid 1/11

3 Introduction BLOOD CIRCULATION MODEL one-kind particles in a simple newtonian liquid & geometry, elasticity of vessels, morphology of the endothelial surface layer 1/11

4 Introduction BLOOD CIRCULATION MODEL one-kind particles in a simple newtonian liquid & geometry, elasticity of vessels, morphology of the endothelial surface layer 1/11

5 Introduction in vivo in vitro For example: A. R. Pries, T. W. Secomb, Circ. Res. (1990) 2/11

6 Introduction Van den Berg, Vink, Spaan, Circ. Res. 92, 592 (2003) in vivo in vitro For example: A. R. Pries, T. W. Secomb, Circ. Res. (1990) GLYCOCALYX sweet shield Polymer brush, constituted by macromolecules (proteoglycans, hyaluronan, glycoproteins, ) attached to the endothelium 2/11

7 Introduction RELEVANCE: 3/11

8 Introduction RELEVANCE: glycocalyx lack or reduction!!! diseases e.g.: plaque formation in atherosclerosis M. Nieuwdorp et al., Curr. Opin. Lipid. 16, 507 (2005) 3/11

9 Introduction RELEVANCE: glycocalyx lack or reduction!!! diseases e.g.: plaque formation in atherosclerosis M. Nieuwdorp et al., Curr. Opin. Lipid. 16, 507 (2005) understanding polymer brush dynamics under flow e.g.: recent experiments on artificial polymer brushes in Grenoble L. Lanotte et al., Langmuir (2012)??? 3/11

10 OUTLINE 1. Choice of the numerical method 2. Polymer brush at equilibrium 3. Polymer brush under flow 4/11

11 OUTLINE 1. Choice of the numerical method 2. Polymer brush at equilibrium 3. Polymer brush under flow 4/11

12 Choice of the numerical method SIMPLE LIQUID AND LINEAR GRAFTED CHAINS 5/11

13 Choice of the numerical method SIMPLE LIQUID AND LINEAR GRAFTED CHAINS courtesy of L. Rovigatti DISSIPATIVE PARTICLE DYNAMICS (DPD) (coarse-graining of Molecular Dynamics) 5/11

14 Choice of the numerical method SIMPLE LIQUID AND LINEAR GRAFTED CHAINS courtesy of L. Rovigatti DISSIPATIVE PARTICLE DYNAMICS (DPD) (coarse-graining of Molecular Dynamics) hydrodynamic interactions explicit solvent 5/11

15 OUTLINE 1. Choice of the numerical method 2. Polymer brush at equilibrium 3. Polymer brush under flow 4/11

16 ρ Polymer brush at equilibrium At equilibrium conformational entropy excluded volume Milner et al., Macromolecules (1988) Deng et al., J. Fluid Mech. (2012) brush density profiles ρ(z) z varying the chain length n at same grafting density σ graft varying the grafting density σ graft at same chain length n (σ graft = 1.5) (n = 16) 6/11

17 ρ Polymer brush at equilibrium At equilibrium conformational entropy excluded volume Milner et al., Macromolecules (1988) Deng et al., J. Fluid Mech. (2012) brush density profiles ρ(z) z varying the chain length n at same grafting density σ graft varying the grafting density σ graft at same chain length n (σ graft = 1.5) (n = 16) the higher the volume fraction, the more step-like the density profile 6/11

18 OUTLINE 1. Choice of the numerical method 2. Polymer brush at equilibrium 3. Polymer brush under flow 4/11

19 Polymer brush under flow Under flow ( σ graft = 1.5 ) tilting compression (h b h eq )/h eq Wi < R ee x > ~Wi 0.76 (h b h eq )/h eq ~Wi 1.5 7/11

20 Polymer brush under flow Under flow ( σ graft = 1.5 ) tilting compression (h b h eq )/h eq Wi < R ee x > ~Wi 0.76 (h b h eq )/h eq ~Wi 1.5 no consensus on theories -even on the fact that the brush should swell or compress 7/11

21 Polymer brush under flow flow inversions 8/11

22 Polymer brush under flow flow inversions /11

23 Polymer brush under flow 45 9/11

24 Polymer brush under flow /11

25 Polymer brush under flow /11

26 Polymer brush under flow /11

27 Polymer brush under flow /11

28 Polymer brush under flow /11

29 Polymer brush under flow /11

30 Polymer brush under flow /11

31 Considerations which is the actual dynamics of those chains? 10/11

32 Considerations which is the actual dynamics of those chains? stretching - elongation - recoiling M. Müller and C. Pastorino, EPL (2008) Léonforte et al., Cond. Matt. (2011) 10/11

33 Considerations which is the actual dynamics of those chains? stretching - elongation - recoiling M. Müller and C. Pastorino, EPL (2008) Léonforte et al., Cond. Matt. (2011) different concavities well-separated Wi ranges /11

34 Considerations which is the actual dynamics of those chains? stretching - elongation - recoiling M. Müller and C. Pastorino, EPL (2008) Léonforte et al., Cond. Matt. (2011) different concavities well-separated Wi ranges but more than one explication 10/11

35 Considerations NOISE ENTROPY HYDRODYNAMIC SHEAR FENE no periodicity in the cyclic motion collective effects? Wi correlation between velocity and position of monomers periodicity resonance? collective effects? 11/11

36 Next steps: Explanation for the scaling behaviors Polydisperse brush Interaction with solid particles Interaction with RBCs 11/11

37 Next steps: Explanation for the scaling behaviors Polydisperse brush Interaction with solid particles Interaction with RBCs Thank you 11/11