Tumor Growth - Nautilus - Universidade de Coimbra
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Transcript Tumor Growth - Nautilus - Universidade de Coimbra
The Physics in Biology
Modeling Tumor Growth and Angiogenesis
Rui Travasso
Centro de Física Computacional
Universidade de Coimbra
Physics Today
Mass
galaxy
1040
black hole
Sun
1031
1030
Earth
1024
Man
G. Relativity
?
Classical Mech.
Material Properties
Superconductivity
Superfluidity
Turbulence
Chaos
Life
Consciousness
Social Relations
100
Number of Particles
dust
10-12
DNA
10-21
atoms
10-27
electrons
10-31
Quantum Mech.
Physics in Biology
Physics is needed
Physical processes entangled with biology
Tumor growth
Embryonic development
Consciousness
Interdisciplinary subject
Physics
Biology
Mathematics
Chemistry
Informatics
Simple Systems
Liquid membranes
Canham-Helfrish energy
Minimization of energy provided surface and volume constant
Curvature Energy Relevant
Influence of changing c0
Constant: pearling instability
Gradient: tube formation
So?
Simple models present rich behavior
Biologically relevant
Mechanical effects are important in
cell behaviour
Red blood cells change mechanical
properties if patient has malaria
Organization of endothelial cells
through mechanical adhesion
But
Insight is important but not sufficient
Interdisciplinary study is essential for advance of field
Cancer and Physics
Physics important in developing
imaging tools for detection and
following tumor growth
but recently...
Physics may be important for
understanding tumor growth
Physics meets Biology meets Chemistry
Mechanical interactions, viscoelastic
dynamics, protein diffusion, chemical
reactions, gene regulatory networks,
population dynamics, evolution
Physics World, June 2010
Crescimento de Tumores - Mutações
Fase 1: Mutações genéticas
Genes que regulam processos essenciais
Ciclo celular Reprodução descontrolada
Sistemas de reparação do DNA e de proteínas
Perda de mecanismo de morte programada
Crescimento de Tumores - Tecido
Fase 2: Interacção com o tecido celular
Células cancerígenas inibem células imunitárias
Ou recrutam células imunitárias
(que recrutam vasos sanguíneos)
Sobrevivem em condições adversas
(ambiente ácido e baixos níveis de oxigénio)
Célula Tumoral
Célula do sist.
imunitário
Crescimento de Tumores - Caderinas
Fase 3: “Cadherin switch”
Células interagem com vizinhas através
de proteínas da membrana
Caderinas
Mutação deste mecanismo pode levar
a altas taxas de proliferação mesmo
quando densidade celular alta.
Crescimento de Tumores - Esferóides
Fase 4: Células cancerígenas ganham forma: Esferóide
Difusão macroscópica de células
Formação de zonas necróticas
Tumor com diâmetro 1-2 mm
Necroticas
Quiescentes
Proliferativas
Alta Pressão
Zona Necrótica
Reprodução
Descontrolada
Células Saudáveis
Crescimento de Tumores - Angiogénese
Tumor necessita nutrientes para crescer
Busca activa de nutrientes
Fase 5: “Angiogenic switch”
Segregação de proteínas
que promovem formação
de novos vasos sanguíneos
Rede vascular aberrante
M. D. Anderson Cancer Center, Univ. of Texas
Crescimento de Tumores - Metástase
Fase 6: Metástase
Células cancerígenas entram na
circulação sanguínea
Invasão de regiões saudáveis
Pulmão
Fígado
Alguns Tópicos sobre Tumores
Reprodução desregulada de células cancerínenas
Grande diversidade de material genético das células
Maior adaptabilidade
Tumor vive num ambiente que lhe é extremamente hostil
A destruição do hospitaleiro é uma vitória da adaptação.
Infelizmente isso significa a morte do tumor também
Vasos saguíneos frágeis
O tumor sangra
Angiogénesis contínua
O tumor é uma ferida que não sara
Understanding Tumors Through Modeling
Effect of pressure inside tumors in affecting circulation
Vessel collapse
Tumor surface instabilities as a function of limitations in
transport of nutrients
May lead to phenotypic alterations
Balance between cell-cell adhesion
and nutrient delivery
Tumor adaptability and tumor
stem cells
Guide treatment
Use of modeling as a tool for predicting patient-specific evolution
and treatment of tumors
Tumor Modeling
Many models
Review article:
Nonlinearity, 23, R1 (2010)
578 references
Each paper introduces
different model for a
specific application
Classification of models
Discrete: Cellular automata, Agent based, ...
Continuous: Multiphase, Interface focused, ...
Discrete Models
Focus on individual cells
Mutations
Contact forces
Cell division
Movement and growth
Gene regulatory networks
Shirinifard et al, PLoS One, 4, e7190
Advantage
Some parameters may be obtained from single cell experiments
Limitations
Challenging to simulate millions of cells
Large number of parameters (which ones are controlling factors?)
Continuous Models
Interface focused
Map tumor surface behavior to existing interface models
In general do not include biological details
Multiphase modeling
From mixture theory
Consider different components
Conservation laws (mass, momentum)
Constitutive relations specific
for each component
Thermodynamic consistency
Possibility of including biological processes
Fewer parameters than discrete methods
Preziosi et al, J.Math.Biol., 58, 625
Phase-Field Models
Approach to moving boundary problems
Phases associated with value of
Interface implies f = 0
Diffuse interface
Original problem obtained
when e → 0
f
f= 1
Dynamics of
Phase 1
e
f= -1
f
Phase 2
f
Can be derived from a free energy F[f,e]
f 1
f
F
Non-conserved order parameter: Allen-Cahn equation
t
f
f
F
Conserved order parameter: Cahn-Hilliard equation
2
t
f
-1
Examples
Canham-Helfrisch energy
Dendritic growth
Phase separation of elastic phases
Phase-field model in tumor growth
Travasso, Castro, Oliveira, Phil. Mag. (2011)
Example of Multiphase and Phase-Field
A multiphase model Cristini et al, J.Math.Biol., 58, 723 (2009)
Mass balance for each
component
Momentum conservation
Constitutive
Relations
Incompressibility
Example of Multiphase and Phase-Field
Formation of ramified structures
More dramatic at low proliferation rate
Fingering occurs at zero chemotaxis
Instability driven by non-linear mobility
Cristini et al, J.Math.Biol.,
58, 723 (2009)
Therefore...
Phase-Field is focused at the interface
Link between phase-field and multiphase
Further reduction of parameters
Variability of existing phase-field models
lead to possibility of direct application
in tumor growth
Able to answer questions on the evolution
of tumor size
BUT...
Do not include competing populations of
tumor cells or mutations
Hybrid models are a possible solution
Tumor Growth - Competition - Evolution
Deregulated proliferation
Mutations
Darwin selection
Acid
Metabolism and migration
Anaerobic matabolism
2 ATP instead of 36
No need of Oxygen
Produces acid
Helps migration
Prevailing phenotype
Acid resistant
Gerlee, Anderson, J Theor Biol 2007
Tumor Growth - Angiogenesis Switch - Vascular Phase
The tumor promotes the
development of nearby
vessels to have oxygen
Challenging simulations
Chaplain et al, Annu Rev Biomed Eng 2006
Many parameters
Cell based
Continuous
Hybrid
MackLin et al, J Math Biol 2009
Angiogenesis
Sprouting of new blood vessels from existing ones
Relevant in varied situations
Morphogenesis
Gerhardt et al, Cell (2003)
Inflammation
Wound healing
Neoplasms
Diabetic Retinopathy
For tumors
Altered vessel network
Lee et al, Cell (2007)
Dense, no hierarchical structure
Capillaries are fragile, permeable, with variable diameter
Capillary network carries both nutrients and drugs
Two types of cells
Tip cells are special
Have filopodia
Follow gradients of VEGF
Produce MMPs which degrade ECM
Construct path
Do not proliferate
Gerhardt et al, Cell (2003)
Stalk cells
Proliferation regulated by VEGF
Not diggers
Follow tip cell created pathway
Gerhardt et al, Cell (2003)
Angiogenesis in a Nutshell
Capillaries are constituted by
Endothelial cells
Endothelial cells
Pericites, smooth muscle cells…
Pericites, muscle cells
VEGF weakens capillary wall
Endothelial cells may divide
VEGF
Cells follow VEGF gradient
The first cell is activated and opens way in ECM
Cells organize to form lumen
Meyer et al, Am.J.Path. (1997)
Blood flows when capillaries form loops
Blood reorganizes network
The Model
Two equations
Diffusion: concentration of VEGF, T
Phase-Field: order parameter dynamics
The penetration length of
T inside the capillary
is given by D
t f f Tf(f)
2
Tip cell
f 2 f 4 e 2
2
F
Ginzburg-Landau
free energyradius
Characteristic
Rc 2 4 2 f dr
Perfect Notchsignaling
F
f f 3 e 2 2f
Chemical
potential
Introduced when
f T > Tc
D T
Velocity: v t
f f
Cahn-Hilliard dynamics
f = 1 inside capillary
f = -1 outside capillary
T
t
tension
f regulates
thematerial
proliferation
and
Surface
driven, bulk
conservation
Df the chemotaxis
Simulation
Starting configuration
Capillary
Cells in hypoxia
Capillary close to tissue
in hypoxia
Concentration of VEGF at
hypoxic cells constant
Blood vessel network emerge
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QuickTime™ and a
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Proliferation
Low Proliferation
High Proliferation
Higher proliferation rate leads to thicker and ramified vessels
Chemotaxis Response
Low Chemotaxis
High Chemotaxis
Higher tip cell velocity leads to thinner and more ramified vessels
VEGF Prodution
Gerhardt et al.,
Develop. Biol. (2003)
Low VEGF
High VEGF
Higher production of VEGF leads to more vessels but not thicker
vessels
Matrix Metalloproteinase
MMPs implementation:
bound to matrix if cMMP high
cMMP high in a radius RMMP
of tumor cell
Diffusion in function of Th
low cMMP
D
high cMMP
Th
Formation of thick vessels
Thin vessel merging
MMP-9 Overexpressed MMP-9 Inhibition
Heavy VEGF isoforms get
Rodriguez-Manzaneque et al, PNAS (2001)
Insight is important but not sufficient
Taxa de proliferação
Dependente do meio (VEGF, Ang-2)? Como?
Propriedades dos tecidos
Tecido como meio viscoelástico
Permeabilidade e elasticidade dos vasos
Metabolismo das células
Possibilidade de respiração anaeróbia? Em que circunstâncias?
Influencia do meio ácido na viabilidade das células
Transporte de proteínas
Reacções químicas
As células tumorais são de diferentes tipos
Dinâmica de populações
Evolução
Interdisciplinaridade
A Física poderá ajudar, mas como um elemento de um esforço
interdisciplinar
Integração de técnicas e métodos de diferentes disciplinas
Simulação
medição exp.
de parâmetros
Lab in vitro
novas hipóteses
e experiências
• Morfogénese
• Tumores
• Pólipos
• Retinopatia
observações
clínicas
termos relevantes
in vivo
Lab in vivo
previsões de
crescimento
vascular
acompanhamento
clínico individualizado
Dados Clínicos
Conclusion
High Pressure
Physics required to tackle problems in Biology
New insights
New therapies
Interdisciplinary context
Modeling tumor growth
Variety of modeling techniques
Gerhardt et al, Cell (2003)
Hybrid models are able to integrate in a continuous description
cell based processes essential in tumor growth and angiogenesis
Hybrid model for angiogenesis with phase-field component
Proliferation rate and matrix dependent tip cell velocity regulate
capillary network morphology
High production VEGF levels lead to increased vessel density
Bio-avaibility of VEGF determines network
A Pretty One
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are needed to see this picture.