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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_at_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
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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

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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
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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 !)

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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
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OUR MODEL. I specific problem
The problem tumor growth depends upon the
intrinsic neoplastic properties, the host
properties and the action of drugs
Cellular growth is controlled by nutrients
availability
Regulation of cells behavior according to the
environment.
Apoptosis is regulated by adhesion properties
which are modulated by pressure constraints on
the neoplasm
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OUR MODEL. II biological mechanisms
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OUR MODEL. III hypotheses
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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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SIMULATIONS AND VALIDATION. I - AVASCULAR PHASE
Spherical shape Necrotic core Latency at a radius
of about 200 mm
Gompertzian growth law
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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).
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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)

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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)
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SIMULATIONS AND VALIDATION III - ANGIOGENESIS
INHIBITION
Angiogenesis may be inhibited when the affinity
of EC for TAFs 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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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)
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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
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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
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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