Angiogenesis and the regeneration and. What can we learn from computers?

Transcription

1 Angiogenesis and the regeneration and engineering ee g of bone What can we learn from computers? Hans Van Oosterwyck Biomechanics and Engineering Design K.U.Leuven, Belgium

2 Clinical problem Non-healing bone fractures (delayed or non-unions) Large bone defects: Trauma Infection Tumor 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 2

3 Clinical problem Importance of mechanics (mechanical stability) after stabilisation (Prof. J. Lammens, UZ Pellenberg) 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 3

4 Mechanoregulation models (Lacroix & Prendergast, J Biomech 2002) (Carter et al, Clin Orthop Rel Res 1998) 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers

5 Clinical problem Importance of vascularisation (angiogenesis): no vessels, no bone (clinical) reality may be more complex (Reed et al., J Oth Orthop Res 2002) 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 5

6 Clinical problem What is needed to induce bone regeneration in a nonhealing environment? Can we speed up the healing of large bone defects (by means of a tissue engineering approach)? (Clemens van Blitterswijk) 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers

7 Our questions Can computational models be used to increase our understanding of bone regeneration (in particular non- healing cases)? Can computational models be used to predict the (clinical) outcome of bone regeneration and engineering therapies? angiogenesis should be essential ingredient of such models! 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 7

8 Bioregulation model (Geris et al, J Theor Biol 2008) 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 8

9 Bioregulation model Coupled, non-linear PDE system of taxis-diffusionreaction type c 8 migr = Dmigr migr migr fi i + f0 migr t i = 1 ( c) c c ( c) c ( c, c) c = D Δ c + g( cmigr, c) t Change in Migration of cells and concentration/density growth factors over time Reaction terms (differentiation, decay, matrix production) 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 9

10 Bioregulation model functions that account for growth factor or ECM dependent rates: Chondrogenic differentiation rate cc = Fc 2 m t Y 2 g c F2 = H g + growth factor concentration 2 c Chondrogenic growth factor production rate g t E c = E c = gc c gc c gc 3 3 Hgc gc Kgc m ifferentiation rate F di grow wth factor production rate G g m x growth total factor ECM concentration density October, 2010 Modelling angiogenesis: joining cells, maths and computers 10

11 Mechanobioregulation model (Geris et al, Phil Trans Royal Soc A 2009, Biomech Modelling Mechanobiol 2010) 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 11

12 Fracture healing Standardised rodent femoral fracture model (Harrison et al, J Orthop Trauma 2003) periosteal callus 3 endosteal callus 2 intercortical callus 4 cortex 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 12

13 Fracture healing Bone formation (day 0-35) (Geris et al, J Theor Biol 2008) 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 13

14 Fracture healing Improved prediction of tissue fractions: periosteal callus tissue fraction [%] [days post fracture] (Bailon-Plaza 4) & van der Meulen 2001) (Geris et al 2008) 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 14

15 Fracture healing what did we learn? Computational model can predict the spatial and temporal evolution of normal fracture healing Results on tissue fractions are in qualitative agreement with in vivo data 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 15

16 Atrophic nonunion Rat model of atrophic nonunion (Reed et al, J Bone Joint Surgery Br, 2003): Stripping of periosteum Scraping of intramedullary canal Representation in mathematical model: (Geris et al., PloS Comp Biol 2010) 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 16

17 Atrophic nonunion Prediction of callus tissue fractions: Good qualitative agreement Simulated healing slightly faster for control ( healing ) group 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 17

18 Atrophic nonunion Model limitations: Time course of revascularisation only partially captured: 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 18

19 Atrophic nonunion Model limitations: Interpretation of growth factor concentrations: 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 19

20 Treatment of atrophic nonunion Injection of bone marrow cells at week 3: 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 20

21 Treatment of atrophic nonunion Prediction of callus tissue fractions: Good qualitative agreement: 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 21

22 Treatment of atrophic nonunion Effect of location of injection: 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 22

23 Atrophic nonunion what did we learn? Model, originally developed for normal healing, can qualitatively predict occurence of atrophic nonunion and the outcome of cellular therapy (without tuning the parameters!) Model can help in interpreting experimental results: Effect of cell injection site Model limitations: Vascularisation and growth factor dynamics not well captured 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 23

24 Mechanobioregulation model 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 24

25 Mechanobioregulation model Fluid flow mediated model parameters Rates of Baseline value Stimulated value Case 1 Endothelial cell proliferation A v Blood vessel synthesis P vs 1e-6 2e-6 Blood vessel degradation κ v 4e6 1e6 Vascular growth factor production by chondrocytes E gc 0.5e-3 1e-3 Case 2 Osteoblasts proliferation A b Endothelial cell proliferation A v Mesenchymal stem cell differentiation into osteoblasts Y Bone synthesis P bs 1 2 Chondrocyte replacement Y October, 2010 Modelling angiogenesis: joining cells, maths and computers 25

26 Overload-induced nonunion Only angiogenesis dependent on fluid flow (case 1) normal load (2x BW) overload (8x BW) (Geris et al., Biomech Modelling Mechanbiol 2010) 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 26

27 Overload-induced nonunion Angiogenesis, intramembraneous and endochondral ossification dependent on fluid flow (case 2) normal load (2x BW) overload (8x BW) 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 27

28 Treatment of overload-induced nonunion 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 28

29 Overload-induced nonunion what did we learn? Model can be used to test hypotheses with respect to: (mechanoregulation) mechanisms Therapeutic strategies for (overload-induced) nonunion Use computational models to run in silico experiments prior to real experiments 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 29

30 Are we happy now? Generic growth factors: How to discriminate / validate? Stem cells and mature cells : How to discriminate / validate? Angiogenesis: Discrete, instead of continuous phase 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 30

31 Hybrid bone regeneration model Growth of blood vessels: v t (Sun et al., Bull Math Biol 2005) Branching Anastomosis 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 31 31

32 Hybrid bone regeneration model 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 32

33 Hybrid bone regeneration model 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 33

34 Hybrid bone regeneration model Vascular network Bone matrix density Cartilage matrix density Fibrous matrix density day October, 2010 Modelling angiogenesis: joining cells, maths and computers 34

35 Hybrid bone regeneration model - benefits Improved description of angiogenesis Interaction between angiogenesis, oxygen concentration and other biological processes: angiogenic growth factor synthesis osteogenic differentiation endochondral replacement 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 35

36 Acknowledgements Lies Geris (she did all the work!) Funding resources: Research Council of K.U.Leuven Research Foundation Flanders (FWO Vlaanderen) Collaboration: Dr. C. Maes, Prof. G. Carmeliet (Dept. Experimental Medicine, K.U.Leuven, Belgium) Prof. A. Goodship (Royal Veterinary College London, UK) Dr. A. Reed, Prof. H. Simpson (Univ. of Oxford, Edinburgh Univ., UK) Dr. A. Gerisch, Prof. R. Weiner (MLU Halle-Wittenberg, Germany) 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 36

37 References L. Geris, A. Gerisch, J. Vander Sloten, R. Weiner, H. Van Oosterwyck, Angiogenesis in bone fracture healing: a bioregulatory model, Journal of Theoretical Biology 2008;251: L. Geris, AAC A.A.C. Reed, J. Vander Sloten, A.H.R.W. AHRW Simpson, H. Van Oosterwyck (2009), Occurrence and Treatment of Bone Atrophic Non- Unions Investigated by an Integrative Approach, PLoS Computational Biology 2010; 6(9): 1-11, e , doi: /journal.pcbi L. Geris, J. Vander Sloten, H. Van Oosterwyck, Connecting biology and mechanics in fracture healing: an integrated mathematical modeling framework for the study of nonunions, Biomechanics and Modelling in Mechanobiology 2010 (DOI /s ) V. Peiffer, A. Gerisch, D. Vandepitte, H. Van Oosterwyck, L. Geris, A hybrid bioregulatory model of angiogenesis during bone fracture healing, Biomechanics i and Modelling in Mechanobiology 2010 (Epub ahead of print) 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 37

38 4-8 October, 2010 Modelling angiogenesis: joining cells, maths and computers 38