Tumour Growth Modelling and Computational Simulation Ana Leal 2 , Joana Louren¸ co 2 , Tom´ as Cruz 1 1 Mestrado Integrado em Engenharia F´ ısica Tecnol´ ogica 2 Mestrado Integrado em Engenharia Biom´ edica Instituto Superior T´ ecnico May 30, 2012 Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Index I. State of the art. II. Principles of tumour growth simulation Biological principles concerning tumour growth Biophysical principles concerning tumour growth Mathematical models for tumour growth III. Case Study IV. Final Remarks. V. References. Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
State of the art To better understand tumour growth mechanisms, researchers are applying mathematical models to predict tumour behaviour, for example, it’s aggressiveness or it’s susceptibility to chemotherapy. Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
State of the art To better understand tumour growth mechanisms, researchers are applying mathematical models to predict tumour behaviour, for example, it’s aggressiveness or it’s susceptibility to chemotherapy. In Cancer Research (2009), Bearer E. L. et al., created a model that links the behaviour of cancer cells and their surrounding to tumour growth, shape and treatment response. They conclude that tumour growth and invasion are not only explained by genomic and molecular events, but can be predictable processes that obey physical laws. Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
State of the art Frieboes, H. B. et al. (2009), created a model to predict a patient’s response to a particular drug with a basic model representing the tumour as a sphere-like structure. Sophisticated multiphase tumour simulators, capable of simulating vascularized tumour growth in 3D, have the potential to predict cancer behaviour. Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Biological principles concerning tumour growth Tumour is characterized by an abnormal cell proliferation. Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Biological principles concerning tumour growth Tumour is characterized by an abnormal cell proliferation. There are two types of tumours: Benign Malignant - Cancer Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Biological principles concerning tumour growth Tumour is characterized by an abnormal cell proliferation. There are two types of tumours: Benign Malignant - Cancer Invasion of other tissues - METASTASIS Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Biological principles concerning tumour growth Tumour is characterized by an abnormal cell proliferation. There are two types of tumours: Benign Malignant - Cancer Invasion of other tissues - METASTASIS Multicellular spheroid Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Biological principles concerning tumour growth Carcinogenesis: Process through which cancer is generated. Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Biological principles concerning tumour growth Carcinogenesis: Process through which cancer is generated. Phases Initiation Promotion Progression Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Biological principles concerning tumour growth Carcinogenesis: Process through which cancer is generated. Phases Initiation Promotion Activation of Oncogene Progression Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Biophysical principles concerning tumour growth The mechanical properties of the cell can be altered by biochemical processes, invasion of foreign organisms or disease development. Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Biophysical principles concerning tumour growth The mechanical properties of the cell can be altered by biochemical processes, invasion of foreign organisms or disease development. Mechanic deformation characteristics are determined by the cytoskeleton. Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Biophysical principles concerning tumour growth The mechanical properties of the cell can be altered by biochemical processes, invasion of foreign organisms or disease development. Mechanic deformation characteristics are determined by the cytoskeleton. The physics of adhesion between biological cells influences cancer cell motility, invasion and metastasis. Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Biophysical principles concerning tumour growth The mechanical properties of the cell can be altered by biochemical processes, invasion of foreign organisms or disease development. Mechanic deformation characteristics are determined by the cytoskeleton. The physics of adhesion between biological cells influences cancer cell motility, invasion and metastasis. The ECM plays an important role in tumour growth and shape. Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Mathematical models for tumour growth Types of models Continuum Models Discrete Models Figure: Example discrete model. Figure: Example continuum model. Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Mathematical models for tumour growth Oxygen/nutrient consumption Continuity Equation ∂ n i ∂ t + ∇ � Γ i + S i ( � r , t ) − L i ( � r , t ) = 0 Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Mathematical models for tumour growth Oxygen/nutrient consumption Fick’s Law Continuity Equation Γ i = − D i ∇ n i ∂ n i ∂ t + ∇ � Γ i + S i ( � r , t ) − L i ( � r , t ) = 0 Γ i = ± µ i n i � E − D i ∇ n i Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Mathematical models for tumour growth Oxygen/nutrient consumption Fick’s Law Continuity Equation Γ i = − D i ∇ n i ∂ n i ∂ t + ∇ � Γ i + S i ( � r , t ) − L i ( � r , t ) = 0 Γ i = ± µ i n i � E − D i ∇ n i General equation that describe uncharged substances behaviour ∂ n i ∂ t − D i ∇ 2 n i + S i ( � r , t ) − L i ( � r , t ) = 0 Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Mathematical models for tumour growth Cell behaviour as a function of the diffusion of substances Each substance in the extracellular medium has its movement described by one of the equations previously shown; Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Mathematical models for tumour growth Cell behaviour as a function of the diffusion of substances Each substance in the extracellular medium has its movement described by one of the equations previously shown; Function that outputs the probability of the behaviour depending on the concentration of the relevant substances; Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Mathematical models for tumour growth Cell behaviour as a function of the diffusion of substances Each substance in the extracellular medium has its movement described by one of the equations previously shown; Function that outputs the probability of the behaviour depending on the concentration of the relevant substances; These relation functions are very dependent on experimental parameters Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Mathematical models for tumour growth Cell behaviour as a function of the diffusion of substances Each substance in the extracellular medium has its movement described by one of the equations previously shown; Function that outputs the probability of the behaviour depending on the concentration of the relevant substances; These relation functions are very dependent on experimental parameters Example � 2 � n P death = e − σ nd Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
Mathematical models for tumour growth Cell movement and proliferation Cell population as an incompressible fluid Single cell movement ∂ Φ i ∂ t + ∇ � ( u i Φ i ) = ∇ � ( D i ∇ Φ i ) + λ i − µ i n i � d � r i � d t = � u i � � n i Figure: Illustration based Figure: Schematic representation of an invading on a discrete model. carcinoma. Ana Leal, Joana Louren¸ co, Tom´ as Cruz Tumour Growth Modelling and Computational Simulation
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