Bayesian calibration, validation, and uncertainty quantification of diffuse interface models of tumor growth
From MaRDI portal
Publication:2435073
DOI10.1007/s00285-012-0595-9zbMath1280.35163OpenAlexW1986775347WikidataQ51311686 ScholiaQ51311686MaRDI QIDQ2435073
Andrea Hawkins-Daarud, J. Tinsley Oden, Kristoffer G. Van Der Zee, Serge Prudhomme
Publication date: 3 February 2014
Published in: Journal of Mathematical Biology (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00285-012-0595-9
Bayesian inference (62F15) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) PDEs with randomness, stochastic partial differential equations (35R60)
Related Items
Mathematical modeling of therapeutic neural stem cell migration in mouse brain with and without brain tumors, Image inversion and uncertainty quantification for constitutive laws of pattern formation, Optimal control of treatment time in a diffuse interface model of tumor growth, Strong well-posedness and inverse identification problem of a non-local phase field tumour model with degenerate mobilities, Data partition methodology for validation of predictive models, Well-posedness for a class of phase-field systems modeling prostate cancer growth with fractional operators and general nonlinearities, Phase-field model and its splitting numerical scheme for tissue growth, Bayesian calibration, validation and uncertainty quantification for predictive modelling of tumour growth: a tutorial, Adaptive selection and validation of models of complex systems in the presence of uncertainty, Analysis of a diffuse interface model of multispecies tumor growth, Weak and stationary solutions to a Cahn-Hilliard-Brinkman model with singular potentials and source terms, Evaluation of innate and adaptive immune system interactions in the tumor microenvironment via a 3D continuum model, Bayesian operator inference for data-driven reduced-order modeling, On a diffuse interface model of tumour growth, Vanishing viscosities and error estimate for a Cahn-Hilliard type phase field system related to tumor growth, From short-range repulsion to Hele-Shaw problem in a model of tumor growth, Bayesian model calibration for diblock copolymer thin film self-assembly using power spectrum of microscopy data and machine learning surrogate, Optimal treatment for a phase field system of Cahn-Hilliard type modeling tumor growth by asymptotic scheme, Image-Driven Biophysical Tumor Growth Model Calibration, Residual-based error corrector operator to enhance accuracy and reliability of neural operator surrogates of nonlinear variational boundary-value problems, On a non-isothermal Cahn-Hilliard model for tumor growth, Asymptotic analysis of a tumor growth model with fractional operators, Simulation of the phase field Cahn-Hilliard and tumor growth models via a numerical scheme: element-free Galerkin method, Penalisation of long treatment time and optimal control of a tumour growth model of Cahn-Hilliard type with singular potential, A tutorial review of mathematical techniques for quantifying tumor heterogeneity, Optimal control of a phase field system modelling tumor growth with chemotaxis and singular potentials, A Cahn–Hilliard–Darcy model for tumour growth with chemotaxis and active transport, The stochastic viscous Cahn-Hilliard equation: well-posedness, regularity and vanishing viscosity limit, Models, measurement and inference in epithelial tissue dynamics, Optimality conditions for an extended tumor growth model with double obstacle potential via deep quench approach, Selection and validation of predictive models of radiation effects on tumor growth based on noninvasive imaging data, Full-scale, three-dimensional simulation of early-stage tumor growth: the onset of malignancy, Bayesian Parameter Identification in Cahn--Hilliard Models for Biological Growth, Selection, calibration, and validation of models of tumor growth, PDE-constrained optimization in medical image analysis, On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport, Parameter identification via optimal control for a Cahn-Hilliard-chemotaxis system with a variable mobility, Where did the tumor start? An inverse solver with sparse localization for tumor growth models, Formal asymptotic limit of a diffuse-interface tumor-growth model
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the mechanics of a growing tumor
- Unconditionally stable finite difference, nonlinear multigrid simulation of the Cahn-Hilliard-Hele-Shaw system of equations
- A systematic approach to model validation based on Bayesian updates and prediction related rejection criteria
- The thermodynamics of elastic materials with heat conduction and viscosity
- Mathematical models for phase change problems. Proceedings of the European workshop held at Óbidos, Portugal, October 1-3, 1988
- Continuous and discrete mathematical models of tumor-induced angiogenesis
- On Latin hypercube sampling
- The role of growth factors in avascular tumour growth
- Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis
- Statistical and computational inverse problems.
- Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method
- Modelling the growth of solid tumours and incorporating a method for their classification using nonlinear elasticity theory
- An \(L^ \infty\) bound for solutions of the Cahn-Hilliard equation
- Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching
- GENERAL DIFFUSE-INTERFACE THEORIES AND AN APPROACH TO PREDICTIVE TUMOR GROWTH MODELING
- An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
- Random field finite elements
- Bayesian Measures of Model Complexity and Fit
- Inverse Problem Theory and Methods for Model Parameter Estimation
- ON THE CLOSURE OF MASS BALANCE MODELS FOR TUMOR GROWTH
- Modelling solid tumour growth using the theory of mixtures
- On the Cahn–Hilliard Equation with Degenerate Mobility
- A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues I: A General Formulation
- On Information and Sufficiency
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data