Istituto Nazionale di Fisica della Materia

1. Istituto Nazionale di Fisica della Materia Dip.to di Fisica MODELING AND COMPUTER SIMULATIONS: TOOLS TO SUPPORT EXPERIMENTAL RESEARCH IN BIOPHYSICS APPLICATIONS TO TUMOR GROWTH M.Scalerandi, P.P.Delsanto, M.Griffa INFM - Dip. Fisica, Politecnico di Torino, Italy e-mail: marco.scalerandi@infm.polito.it Also with: G.P.Pescarmona, Università di Torino, Italy C.A.Condat, University of Puerto Rico at Mayaguetz, US M.Magnano, Ospedale Umberto I, Torino, Italy B.Capogrosso Sansone, University of Massachusets, US

2. Istituto Nazionale di Fisica della Materia Dip.to di Fisica GOALS of MODELING Support in the interpretation of data Optimization of experiments Predictive power • Prediction of the evolution of a tumor “in vivo” (???) • Suggest new experiments • Preliminary validation and formulation of hypotheses

3. Istituto Nazionale di Fisica della Materia Dip.to di Fisica MODELING Formulation of a problem into mathematical terms (equations), which allows to obtain predictions • Ingredients • basic knowledge (biological, physical, biochemical, etc. • phenomenology (in vivo and in vitro observations) • hypotheses (to bridge the gap !) Simplification: impossible to describe entirely the real system (mathematical complexity)  Specific problem identification Validation: rejection or acceptance of the hypotheses through comparison with data  Design of new experiments

4. Istituto Nazionale di Fisica della Materia Dip.to di Fisica COMPUTER SIMULATIONS The tool to obtain predictions from the model • computers are capable to solve a problem regardless of the mathematical difficulty • computers are fast (parallel computing) and cheaper than real experiments • computers may describe the spatio-temporal evolution of a given system • nevertheless the computational time may increase dramatically with the complexity of the problem (keep it simple to avoid computational complexity !)

5. ! ! ! Selection of few mechanisms (eventually aggregation of biological properties into a single mechanism) Additional hypotheses No problem to restart! Simulations Failure Comparison with data Istituto Nazionale di Fisica della Materia MODELING AND COMPUTER SIMULATIONS Determination of the problem Restriction of the field of validity New mechanisms Math. inconsistency • prediction of new results not yet observed: suggest new experiments • confirmation of biological assumptions • optimization of existing experiments • performing experiments not feasible in reality (e.g. prediction of the growth outcome without any therapy in a patient) • application to a different problem Different hypotheses

6. Radiotherapy, chemiotherapy, etc. ! ! ! Regulation of apoptotic inhibition Antiangiogenetic therapies Istituto Nazionale di Fisica della Materia Dip.to di Fisica OUR MODEL. I specific problem The problem: tumor growth depends upon the intrinsic neoplastic properties, the host properties and the action of drugs Regulation of cells behavior according to the environment. Cellular growth is controlled by nutrients availability Apoptosis is regulated by adhesion properties which are modulated by pressure constraints on the neoplasm

7. CELLS • Absorption (energy storing) • Metabolism (energy consumption) • Mitosis, necrosis and apoptosis (depending on the absorbed signals) • Adhesion, metastasis and invasion (diffusion) Emission • SIGNALS • Growth factors, nutrients, tumor angiogenetic factors, apoptosis inhibitors • “Fast” diffusion Inhibition or activation Istituto Nazionale di Fisica della Materia Dip.to di Fisica ENVIRONMENT OUR MODEL. II biological mechanisms

8. Istituto Nazionale di Fisica della Materia Dip.to di Fisica OUR MODEL. III hypotheses

9. Istituto Nazionale di Fisica della Materia Dip.to di Fisica PARAMETERS Important task in modeling is the choice of reasonable values for the large number of parameters (which increases dramatically with the problem complexity: parameter space complexity): a) parameters with a biological (physical) interpretation experimentally measured  estimate, at least, the order of magnitude b) parameters with a biological interpretation, difficult to measure or never measured  suggest experiments or indirect measurements b) parameters with a purely mathematical meaning  used to fit the data

10. Dip.to di Fisica SIMULATIONS AND VALIDATION. I - AVASCULAR PHASE Spherical shape Necrotic core Latency at a radius of about 200 mm Gompertzian growth law

11. Dip.to di Fisica SIMULATIONS AND VALIDATION. I - AVASCULAR PHASE The cord grows around the vessel and reaches an equilibrium “dynamical” state A necrotic core is formed at the front of the neoplasm The cord radius increases when the nutrient consumption decreases The cord radius (calculated from the volume) oscillates between 50 and 130 mm, in agreement with in-vivo data Experimental data from J. V. Moore, H. A. Hopkins, and W. B. Looney, Eur. J. Cancer Clin. Oncol. 19, 73 (1984).

12. B B D A C A C B D A C Istituto Nazionale di Fisica della Materia Dip.to di Fisica SIMULATIONS AND VALIDATION II - CT SCANS COMPARISON WITH CLINICAL DATA ! Temporal sequence Numerical Results CTScan Clinical data: Dr. M.Magnano Head and Neck Division Ospedale Umberto I Torino, Italy • identification of features which might help a better prediction of the tumor margins (optimization) • prediction of the tumor evolution without intervention (not feasible experiment)

13. Cancer cells (no angiogenesis) Cancer cells Vessels T =2000 T=10000 T=20000 Istituto Nazionale di Fisica della Materia T=25000 SIMULATIONS AND VALIDATION III - ANGIOGENESIS MORPHOLOGY • latency in the avascular phase • directional vessels growth • correct profile of the capillaries distribution • infiltration of the vascular system inside the tumor mass For experimental data, see e.g. M.I. Koukourakis et al., Cancer Res. 60, 3088 (2000)

14. t = 20000 t t = 50000 t z = 1 t = 70000 t t = 20000 t z = 0.4 t = 20000 t t = 180000 t z = 0.1 Istituto Nazionale di Fisica della Materia Dip.to di Fisica t = 20000 t t = 180000 t z = 10 SIMULATIONS AND VALIDATION III - ANGIOGENESIS INHIBITION Angiogenesis may be inhibited when the affinity of EC for TAF’s is reduced (e.g. by inhibiting VEGFR2) Experimentally observed For experimental data see e.g. R. Cao et al., Proc. Natl. Acad. Sci. USA 96, 5728 (1999) Surprisingly angiogenesis is also inhibited when affinity is increased. For experimental evidence see e.g. H.H.chen et al., Pharmacology 71, 1 (2004)

15. (a) (b) Istituto Nazionale di Fisica della Materia Dip.to di Fisica SIMULATIONS AND VALIDATION III - ANGIOGENESIS VEGFR2-inhibition Slight stimulation of VEGF receptor 2 Simulation Experiment X Action of a monoclonal antibody (2C3) inhibiting VEGFR2 Experimentally has been observed a reduction up to 70% of the VEGF affinity a a function of the drug dose Exp. data from Brekken et al., Cancer Research 60, 5117 (2000)

16. SIMULATIONS AND VALIDATION IV - ROLE OF THE ENVIRONMENT RIGIDITY Multicellular spheroids growth in a matrix with different percentuals of diluted agarose • different agar concentrations are simulated using different rigidities of the matrix • comparison of the average diameter of the spheroids (in equilibrium conditions) between numerical and experimental data at different concentrations Experimental data from G.Helmlinger et al., Nature Biotechnology 15 (1997) 778

17. SIMULATIONS AND VALIDATION IV - ROLE OF THE ENVIRONMENT RIGIDITY Cellular density (Variation with respect to the 0% agar matrix) Mitosis rate (Variation with respect to the 0% agar matrix) N.B. both in experiments and simulations the final pressure on the spheroids is independent from the agar concentration Experimental data from G.Helmlinger et al., Nature Biotechnology 15 (1997) 778

18. Istituto Nazionale di Fisica della Materia Dip.to di Fisica CONCLUSIONS • Modeling and simulations = simplified version of a specific real problem • Hypotheses must always be introduced • A validation through comparison with experimental data and application of the model to novel problems is needed • suggest new experiments and new questions • optimize existing experiments (in particular for therapies) • validate preliminary hypotheses