BMBF Forsys Partner Project: A Systems Biology Approach towards Predictive Cancer Therapy

Transcription

1 ling and ling and BMBF Forsys Partner Project: A Systems Biology Approach towards Predictive Cancer Therapy H. Perfahl, A. Lapin, M. Reuss Germany holger.perfahl@ibvt.uni-stuttgart.de 1

2 ling and Cooperation with H.M. Byrne, M. Owen; Nottingham, UK P.K. Maini; Universtiy of Oxford, UK T. Alarcon; Imperial College London, UK 2

3 Outline ling and

4 ling and Aim of the project: Analyse convection, diffusion and adsorption of drug molecules within tumours Resolve a small tumour section with the following details: 1 Cells / Receptors 2 Extracellular matrix 3 Vascular system / Blood flow 4

5 Modules ling and The different modules are applied to simulate the movement of drugs in the body: Diffusion and convection in the vascular system Extravasation from vascular system Diffusion in the tissue (reflection on ECM) Reaction with receptors 5

6 Tumour subdomain ling and 6

7 Approaches to include a vascular network ling and Real vasculature Virtual vasculature Hybrid vasculature 7

8 - Drug movement ling and Scale Extravasation from vascular system Movement in tissue Receptor-ligand-reaction 8

9 ling and to 9

10 ling and Secretion of VEGF (vascular endothelial growth factor) New vessels emerge Further growth of the tumour 10

11 Work done: Reimplementation from 2D to 3D New random-walk model for vessels and cells Improved vessel adaptation model New anastomosis algorithms FDM and boundary conditions implemented for 3D Application of sparse matrix algorithms Implementation of efficient iterative solvers New modules for analysis and visualisation Interface to include real vascular networks ling and Numerical analysis Long-time runs and stability checks M R Owen, T Alarcon, P K Maini and H M Byrne: and vascular remodelling in normal and cancerous tissues. J. Math. Biol., 58(4-5): (2009) 11

12 ling and 12

13 ling and A multi-scale model is applied to describe angiogenesis: Subcellular level (ODE-model) e.g. cell cycle, protein production (VEGF, p53) Cellular level (CA-model, random walks) Cell-cell interaction, cell movement Biased random walk of new vessels Tissue level Oxygen, VEGF,... (PDE-model) Blood flow Vascular remodelling Mathematical/numerical/computational challenge 13

14 ling and Vessel pruning Haemodynamics Radius Haematocrit New vessels Oxygen VEGF Normal cells - Cell cycle proteins - p53 - VEGF Cancer cells - Cell cycle proteins - p53 - VEGF Endothelial sprouts 14

15 Subcellular model The subcellular model is influenced by the local oxygen concentration, VEGF concentration and cell type. Equations are based on the Thyson-Novak cell-cycle model. We consider the following cell-internal concentrations: p53 p27 cyccdk VEGF Cdh1 nprb ling and Coupled system of nonlinear ordinary differential equations. Cell states: Neutral, proliferating, quiescent, apoptotic 15

16 Cellular automaton model ling and Vessel Normal cell Tumour cell 16

17 Cellular model Probability of sprouting at site i: P s (i) =g(c VEGF ) (1) ling and Random walk of new blood vessels from i to j: P(i j) =f (R ij, c VEGF ), (2) with the resistance R ij and the VEGF concentration c VEGF. Cell movement: Cells move in the direction of high oxygen concentrations ( Grow or go -hypothesis) Normal cell degradation: Cancer cells degrade their environment by decreasing ph Normal cell death 17

18 Tissue layer ling and Diffusive transport of oxygen, c O2 : DΔc O2 = P(c blood O 2 c O2 ) k(φ T,φ H, c O2 ), (3) with the blood oxygen concentration co blood 2, the vessel permeability P and the consumption by cells k(φ T,φ H, c O2 ). φ T is the local volume fraction occupied by tumour cells. φ H is the local volume fraction occupied by normal cells. Diffusive transport of VEGF, c VEGF : DΔc VEGF = Rc VEGF + k VEGF (φ T,φ H ) δc VEGF, (4) with the consumption rate of the vascular system R, VEGF production k VEGF (x) and decay rate δ. 18

19 Vascular system ling and Network analysis: Creation of new vessels by connected sprouts Calculation of pressures and flows Kirchhoff s law Calculation of haematocrit distribution Viscosity Wall-shear stress 19

20 Tissue layer ling and Vessel radius adaptation for i-th vessel: dr i =(S m + S h + S s )R i, (5) dt with S m : Metabolic stimulus (c VEGF, Q, H) S h : Haemodynamic stimulus (WSS, Pressure) S s : Shrinking stimulus Q is the blood flow, H the haematocrit value and the wall-shear stress WSS. 20

21 ling and 21

22 ling and Tumour cells Quiescent tumour cells Vessels Initial tumour nested in initial vessel network Healthy cells are faded out 22

23 ling and Tumour cells Quiescent tumour cells Vessels Tumour degrade environment and spreads Most tumour cells enter quiescence 23

24 ling and Tumour cells Quiescent tumour cells Vessels First tumour cells die Remaining tumour is vascularised and tumour cells 24

25 ling and Tumour cells Quiescent tumour cells Vessels Tumour grows along upper vessel First angio-vessels emerge in lower vessel 25

26 ling and Tumour cells Quiescent tumour cells Vessels First bridging between upper and lower vessel Upper vessel is totally nested in tumour 26

27 ling and Tumour cells Quiescent tumour cells Vessels Tumour invades lower part Tumour is adequately vascularised 27

28 Vascular adaptation ling and 28

29 in real vascular system ling and Tumour cells Quiescent tumour cells Vessel 29

30 in hybrid vascular system ling and Tumour cells Quiescent tumour cells Vessel 30

31 in hybrid vascular system ling and Tumour cells Quiescent tumour cells Vessel 31

32 in hybrid vascular system ling and Tumour cells Quiescent tumour cells Vessel 32

33 Stochastic results ling and Number of tumour cells[ ] Time [h] Number of normal cells [ ] Time [h] Number of vessel cells [ ] Time [h] Mean VEGF [ ] Time [h] 33

34 Averaged results ling and 12 x 104 a) 12 x 104 b) Number of tumour cells [ ] Number of normal cells [ ] Time [h] Time [h] 2 x 104 c) d) Number of vessel cells [ ] Time [h] Mean VEGF [ ] Time [h] 34

35 Targeting strategy (Outlook) ling and Numerical studies: Distribution of drug in the tumour Survivability of tumour cells Drug-receptor kinetics Change of tumour structure Strategies of drug administration 35

36 ling and 36

37 and topics of further research ling and s: Reimplementation of total algorithm from 2D to 3D Improvement of random-walk model Improvement of vessel adaptation model Implementation of hybrid model by including real vasculature Further research: targeting strategies 37

38 ling and End 38