1. 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
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
Istituto Nazionale
di Fisica della Materia
Dip.to di Fisica

2. Support in the interpretation of data
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
Istituto Nazionale
di Fisica della Materia
Dip.to di Fisica

3. 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
Istituto Nazionale
di Fisica della Materia
Dip.to di Fisica

4. di Fisica della Materia
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 !)
Istituto Nazionale
di Fisica della Materia
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5. MODELING AND COMPUTER SIMULATIONS
Determination of the problem
Selection of few mechanisms (eventually aggregation of biological properties into a single mechanism)
Failure
Additional hypotheses
Restriction of the field of validity !
New mechanisms
No problem to restart! !
Math. inconsistency
Simulations
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
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di Fisica della Materia
Comparison with data !

6. OUR MODEL. I specific problem
The problem: tumor growth depends upon the intrinsic neoplastic properties, the host properties and the action of drugs
Radiotherapy,
chemiotherapy, etc. !
Regulation of cells behavior according to the environment.
Cellular growth
is controlled by nutrients availability
Antiangiogenetic
therapies ! !
Regulation of
apoptotic inhibition
Apoptosis is regulated by adhesion properties which are modulated by pressure constraints on the neoplasm
Istituto Nazionale
di Fisica della Materia
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7. OUR MODEL. II biological mechanisms
Inhibition or activation
CELLS
Absorption (energy storing)
Metabolism (energy consumption)
Mitosis, necrosis and apoptosis
(depending on the absorbed signals)
Adhesion, metastasis and invasion
(diffusion)
SIGNALS
Growth factors, nutrients, tumor angiogenetic factors, apoptosis inhibitors
“Fast” diffusion
ENVIRONMENT
Emission
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di Fisica della Materia
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8. OUR MODEL. III hypotheses
Istituto Nazionale
di Fisica della Materia
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9. di Fisica della Materia
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
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di Fisica della Materia
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10. SIMULATIONS AND VALIDATION.
I - AVASCULAR PHASE
Spherical shape
Necrotic core
Latency at a radius of about 200 mm
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Gompertzian growth law

11. 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
Dip.to di Fisica
Experimental data from J. V. Moore, H. A. Hopkins, and W. B. Looney, Eur. J. Cancer Clin. Oncol. 19, 73 (1984).

12. SIMULATIONS AND VALIDATION
II - CT SCANS
COMPARISON WITH CLINICAL DATA !
Temporal sequence
Numerical Results
CTScan A B C A B C D
Clinical data:
Dr. M.Magnano
Head and Neck Division
Ospedale Umberto I
Torino, Italy
Istituto Nazionale
di Fisica della Materia
identification of features which might help a better prediction of the tumor margins (optimization)
prediction of the tumor evolution without intervention (not feasible experiment)
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13. di Fisica della Materia
SIMULATIONS AND VALIDATION
III - ANGIOGENESIS MORPHOLOGY
T =2000
T=10000
T=20000
T=25000
Cancer cells
(no angiogenesis)
Vessels
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)
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di Fisica della Materia

14. di Fisica della Materia
SIMULATIONS AND VALIDATION
III - ANGIOGENESIS INHIBITION
z = 0.1
t = t
t = t
z = 10
t = t
z = 0.4
t = t
z = 1
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)
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di Fisica della Materia
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15. SIMULATIONS AND VALIDATION III - ANGIOGENESIS VEGFR2-inhibition
Slight stimulation of VEGF receptor 2
(a)
(b)
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
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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. (Variation with respect to the 0% agar matrix)
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. di Fisica della Materia
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
Istituto Nazionale
di Fisica della Materia
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