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The Physics in Biology Modeling Tumor Growth and Angiogenesis Rui Travasso Centro de Física Computacional Universidade de Coimbra.

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Apresentação em tema: "The Physics in Biology Modeling Tumor Growth and Angiogenesis Rui Travasso Centro de Física Computacional Universidade de Coimbra."— Transcrição da apresentação:

1 The Physics in Biology Modeling Tumor Growth and Angiogenesis Rui Travasso Centro de Física Computacional Universidade de Coimbra

2 Physics Today electrons atoms DNA dust Man Earth Sun black hole galaxy Mass Number of Particles ? Material Properties Superconductivity Superfluidity Turbulence Chaos Life Consciousness Social Relations G. Relativity Quantum Mech. Classical Mech.

3 Physics in Biology Physics is needed Physical processes entangled with biology Tumor growth Embryonic development Consciousness Interdisciplinary subject Physics Biology Mathematics Chemistry Informatics

4 Simple Systems Liquid membranes Canham-Helfrish energy Minimization of energy provided surface and volume constant

5 Curvature Energy Relevant Influence of changing c 0 Constant: pearling instability Gradient: tube formation

6 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

7 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

8 Crescimento de Tumores - Mutações Fase 1: Muta ç ões gen é ticas Genes que regulam processos essenciais Ciclo celular Reprodu ç ão descontrolada Sistemas de repara ç ão do DNA e de prote í nas Perda de mecanismo de morte programada

9 Crescimento de Tumores - Tecido Fase 2: Interacção com o tecido celular C é lulas cancer í genas inibem c é lulas imunit á rias Ou recrutam c é lulas imunit á rias (que recrutam vasos sangu í neos) Sobrevivem em condi ç ões adversas (ambiente á cido e baixos n í veis de oxig é nio) C é lula Tumoral C é lula do sist. imunit á rio

10 Crescimento de Tumores - Caderinas Fase 3: Cadherin switch C é lulas interagem com vizinhas atrav é s de prote í nas da membrana Caderinas Muta ç ão deste mecanismo pode levar a altas taxas de prolifera ç ão mesmo quando densidade celular alta.

11 Crescimento de Tumores - Esfer ó ides Fase 4: C é lulas cancer í genas ganham forma: Esfer ó ide Difusão macrosc ó pica de c é lulas Forma ç ão de zonas necr ó ticas Tumor com diâmetro 1-2 mm Zona Necr ó tica Reprodução Descontrolada C é lulas Saud á veis Necroticas Quiescentes Proliferativas Alta Pressão

12 Crescimento de Tumores - Angiog é nese Tumor necessita nutrientes para crescer Busca activa de nutrientes Fase 5: Angiogenic switch Segregação de prote í nas que promovem forma ç ão de novos vasos sangu í neos Rede vascular aberrante M. D. Anderson Cancer Center, Univ. of Texas

13 Crescimento de Tumores - Met á stase Fase 6: Met á stase C é lulas cancer í genas entram na circula ç ão sangu í nea Invasão de regiões saud á veis Pulmão F í gado

14 Alguns T ó picos sobre Tumores Reprodu ç ão desregulada de c é lulas cancer í nenas Grande diversidade de material gen é tico das c é lulas Maior adaptabilidade Tumor vive num ambiente que lhe é extremamente hostil A destrui ç ão do hospitaleiro é uma vit ó ria da adapta ç ão. Infelizmente isso significa a morte do tumor tamb é m Vasos sagu í neos fr á geis O tumor sangra Angiog é nesis cont í nua O tumor é uma ferida que não sara

15 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

16 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,...

17 Discrete Models Focus on individual cells Mutations Contact forces Cell division Movement and growth Gene regulatory networks 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?) Shirinifard et al, PLoS One, 4, e7190

18 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

19 Approach to moving boundary problems Phases associated with value of Interface implies = 0 Diffuse interface Original problem obtained when 0 Dynamics of Can be derived from a free energy F[, ] Non-conserved order parameter: Allen-Cahn equation Conserved order parameter: Cahn-Hilliard equation Phase-Field Models Phase 1 Phase 2 = -1 = 1 f 1

20 Examples Canham-Helfrisch energy Phase separation of elastic phases Dendritic growth Phase-field model in tumor growth Travasso, Castro, Oliveira, Phil. Mag. (2011)

21 Example of Multiphase and Phase-Field A multiphase model Cristini et al, J.Math.Biol., 58, 723 (2009) Mass balance for each component Incompressibility Momentum conservation Constitutive Relations

22 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)

23 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

24 Tumor Growth - Competition - Evolution Deregulated proliferation Mutations Darwin selection 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 Acid

25 Tumor Growth - Angiogenesis Switch - Vascular Phase The tumor promotes the development of nearby vessels to have oxygen Challenging simulations Many parameters Cell based Continuous Hybrid MackLin et al, J Math Biol 2009 Chaplain et al, Annu Rev Biomed Eng 2006

26 Angiogenesis Sprouting of new blood vessels from existing ones Relevant in varied situations Morphogenesis Inflammation Wound healing Neoplasms Diabetic Retinopathy For tumors Altered vessel network Dense, no hierarchical structure Capillaries are fragile, permeable, with variable diameter Capillary network carries both nutrients and drugs Gerhardt et al, Cell (2003) Lee et al, Cell (2007)

27 Two types of cells Tip cells are special Have filopodia Follow gradients of VEGF Produce MMPs which degrade ECM Construct path Do not proliferate Stalk cells Proliferation regulated by VEGF Not diggers Follow tip cell created pathway Gerhardt et al, Cell (2003) Agent Based Component Phase-field Component

28 Angiogenesis in a Nutshell Capillaries are constituted by Endothelial cells Pericites, muscle cells Endothelial cells Pericites, smooth muscle cells… VEGF VEGF weakens capillary wall Endothelial cells may divide Cells follow VEGF gradient The first cell is activated and opens way in ECM Cells organize to form lumen Blood flows when capillaries form loops Blood reorganizes network Meyer et al, Am.J.Path. (1997)

29 The Model The penetration length of T inside the capillary is given by D = 1 inside capillary = -1 outside capillary T Two equations Diffusion: concentration of VEGF, T Phase-Field: order parameter dynamics Tip cell Characteristic radius R c Perfect Notch signaling Introduced when T > T c Velocity: regulates the proliferation and D the chemotaxis Ginzburg-Landau free energy Chemical potential Cahn-Hilliard dynamics Surface tension driven, bulk material conservation

30 Simulation Starting configuration Capillary close to tissue in hypoxia Concentration of VEGF at hypoxic cells constant Capillary Cells in hypoxia Blood vessel network emerge

31 Proliferation Higher proliferation rate leads to thicker and ramified vessels Low ProliferationHigh Proliferation

32 Chemotaxis Response Higher tip cell velocity leads to thinner and more ramified vessels Low ChemotaxisHigh Chemotaxis

33 VEGF Prodution Higher production of VEGF leads to more vessels but not thicker vessels Gerhardt et al., Develop. Biol. (2003) Low VEGFHigh VEGF

34 Matrix Metalloproteinase MMPs implementation: Heavy VEGF isoforms get bound to matrix if c MMP high c MMP high in a radius R MMP of tumor cell Diffusion in function of T h Formation of thick vessels Thin vessel merging Rodriguez-Manzaneque et al, PNAS (2001) MMP-9 Inhibition MMP-9 Overexpressed ThTh D high c MMP low c MMP

35 Insight is important but not sufficient Taxa de proliferação Dependente do meio (VEGF, Ang-2)? Como? Propriedades dos tecidos Tecido como meio viscoel á stico Permeabilidade e elasticidade dos vasos Metabolismo das c é lulas Possibilidade de respiração anaer ó bia? Em que circunstâncias? Influencia do meio á cido na viabilidade das c é lulas Transporte de prote í nas Reacções qu í micas As c é lulas tumorais são de diferentes tipos Dinâmica de popula ç ões Evolução

36 Interdisciplinaridade Simulação Morfog é nese Tumores P ó lipos Retinopatia Lab in vitroLab in vivo Dados Cl í nicos medição exp. de parâmetros novas hip ó teses e experiências previsões de crescimento vascular termos relevantes in vivo acompanhamento cl í nico individualizado observações cl í nicas A F í sica poder á ajudar, mas como um elemento de um esfor ç o interdisciplinar Integra ç ão de t é cnicas e m é todos de diferentes disciplinas

37 Physics required to tackle problems in Biology New insights New therapies Interdisciplinary context Modeling tumor growth Variety of modeling techniques 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 Conclusion Gerhardt et al, Cell (2003) High Pressure

38 A Pretty One


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