Implementing multiphysics models in FEniCS: Viscoelastic flows, poroelasticity, and tumor growth

[1]  Matthew W. Scroggs,et al.  Basix: a runtime finite element basis evaluation library , 2022, J. Open Source Softw..

[2]  Garth N. Wells,et al.  Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes , 2021, ACM Trans. Math. Softw..

[3]  Guillermo Lorenzo,et al.  Integrating Quantitative Assays with Biologically Based Mathematical Modeling for Predictive Oncology , 2020, iScience.

[4]  D. Garcia-Gonzalez,et al.  Magneto-diffusion-viscohyperelasticity for magneto-active hydrogels: Rate dependences across time scales , 2020 .

[5]  Jeffery Allen,et al.  A generalized poroelastic model using FEniCS with insights into the Noordbergum effect , 2020, Comput. Geosci..

[6]  Michael Hinczewski,et al.  The 2019 mathematical oncology roadmap , 2019, Physical biology.

[7]  Christos Davatzikos,et al.  Advancing The Cancer Genome Atlas glioma MRI collections with expert segmentation labels and radiomic features , 2017, Scientific Data.

[8]  T E Yankeelov,et al.  Selection, calibration, and validation of models of tumor growth. , 2016, Mathematical models & methods in applied sciences : M3AS.

[9]  M. Davis.  Glioblastoma: Overview of Disease and Treatment. , 2016, Clinical journal of oncology nursing.

[10]  G. Genin,et al.  Multi-scale Modeling in Clinical Oncology: Opportunities and Barriers to Success , 2016, Annals of Biomedical Engineering.

[11]  Anders Logg,et al.  Solving PDEs in Python , 2016 .

[12]  Brian B. Avants,et al.  The Multimodal Brain Tumor Image Segmentation Benchmark (BRATS) , 2015, IEEE Transactions on Medical Imaging.

[13]  Thomas E Yankeelov,et al.  Toward a science of tumor forecasting for clinical oncology. , 2015, Cancer research.

[14]  J. Tinsley Oden,et al.  Analysis and numerical solution of stochastic phase‐field models of tumor growth , 2015 .

[15]  Ernesto A. B. F. Lima,et al.  A hybrid ten-species phase-field model of tumor growth , 2014 .

[16]  H. Fathallah-Shaykh,et al.  A Multilayer Grow-or-Go Model for GBM: Effects of Invasive Cells and Anti-Angiogenesis on Growth , 2014, Bulletin of mathematical biology.

[17]  T. Phillips,et al.  Spectral/hp element methods for plane Newtonian extrudate swell , 2014, 1408.5167.

[18]  K. Urbańska,et al.  Glioblastoma multiforme – an overview , 2014, Contemporary oncology.

[19]  Anders Logg,et al.  Unified form language: A domain-specific language for weak formulations of partial differential equations , 2012, TOMS.

[20]  Thomas E Yankeelov,et al.  Clinically Relevant Modeling of Tumor Growth and Treatment Response , 2013, Science Translational Medicine.

[21]  K. R. Swanson,et al.  From Patient-Specific Mathematical Neuro-Oncology to Precision Medicine , 2013, Front. Oncol..

[22]  David A. Ham,et al.  Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs , 2012, SIAM J. Sci. Comput..

[23]  C. Rycroft,et al.  Reference map technique for finite-strain elasticity and fluid-solid interaction , 2012 .

[24]  Hui Wu,et al.  Designing nanostructured Si anodes for high energy lithium ion batteries , 2012 .

[25]  G. Georgiou,et al.  A study of various factors affecting Newtonian extrudate swell , 2012 .

[26]  Anders Logg,et al.  Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book , 2012 .

[27]  Anders Logg,et al.  FFC: the FEniCS Form Compiler , 2012 .

[28]  Robert C. Kirby,et al.  FIAT: numerical construction of finite element basis functions , 2012 .

[29]  Anders Logg,et al.  DOLFIN: a C++/Python Finite Element Library , 2012 .

[30]  C. Kruchko,et al.  CBTRUS statistical report: primary brain and central nervous system tumors diagnosed in the United States in 2005-2009. , 2012, Neuro-oncology.

[31]  Garth N. Wells,et al.  Optimizations for quadrature representations of finite element tensors through automated code generation , 2011, TOMS.

[32]  Anders Logg,et al.  DOLFIN: Automated finite element computing , 2010, TOMS.

[33]  Xiangrong Li,et al.  Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching , 2009, Journal of mathematical biology.

[34]  H. Frieboes,et al.  Three-dimensional multispecies nonlinear tumor growth--I Model and numerical method. , 2008, Journal of theoretical biology.

[35]  Kristin R. Swanson,et al.  Quantifying glioma cell growth and invasion in vitro , 2008, Math. Comput. Model..

[36]  B. Scheithauer,et al.  The 2007 WHO classification of tumours of the central nervous system , 2007, Acta Neuropathologica.

[37]  Gunilla Kreiss,et al.  A conservative level set method for two phase flow II , 2005, J. Comput. Phys..

[38]  Anders Logg,et al.  A compiler for variational forms , 2006, TOMS.

[39]  Martin J. van den Bent,et al.  Radiotherapy plus concomitant and adjuvant temozolomide for glioblastoma. , 2005, The New England journal of medicine.

[40]  Robert C. Kirby,et al.  Algorithm 839: FIAT, a new paradigm for computing finite element basis functions , 2004, TOMS.

[41]  A. Tsoularis,et al.  Analysis of logistic growth models. , 2002, Mathematical biosciences.

[42]  Noel J. Walkington,et al.  Digital Object Identifier (DOI) 10.1007/s002050100158 An Eulerian Description of Fluids Containing Visco-Elastic Particles , 2022 .

[43]  Hua-Shu Dou,et al.  Viscoelastic flow past a cylinder: drag coefficient , 1999 .

[44]  N. Phan-Thien,et al.  The flow of an Oldroyd-B fluid past a cylinder in a channel: adaptive viscosity vorticity (DAVSS-ω) formulation , 1999 .

[45]  N. Phan-Thien,et al.  Galerkin/least-square finite-element methods for steady viscoelastic flows , 1999 .

[46]  G. Georgiou,et al.  Converged solutions of the Newtonian extrudate-swell problem , 1999 .

[47]  Robert C. Armstrong,et al.  Viscoelastic flow of polymer solutions around a periodic, linear array of cylinders: comparisons of predictions for microstructure and flow fields , 1998 .

[48]  Hua-Shu Dou,et al.  Parallelisation of an unstructured finite volume code with PVM: viscoelastic flow around a cylinder , 1998 .

[49]  Alan C. Evans,et al.  BrainWeb: Online Interface to a 3D MRI Simulated Brain Database , 1997 .

[50]  N. Phan-Thien,et al.  An adaptive viscoelastic stress splitting scheme and its applications: AVSS/SI and AVSS/SUPG , 1996 .

[51]  A. McCulloch,et al.  Stress-dependent finite growth in soft elastic tissues. , 1994, Journal of biomechanics.

[52]  A. Cheng,et al.  Fundamentals of Poroelasticity , 1993 .

[53]  Phillip Colella,et al.  A higher-order Godunov method for modeling finite deformation in elastic-plastic solids , 1991 .

[54]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[55]  N. Phan-Thien,et al.  A boundary element investigation of extrudate swell , 1985 .

[56]  R. Tanner,et al.  Finite element and boundary element methods for extrusion computations , 1984 .

[57]  R. Keunings,et al.  Finite-element Analysis of Die Swell of a Highly Elastic Fluid , 1982 .

[58]  R. Tanner,et al.  Finite element solution of viscous jet flows with surface tension , 1978 .

[59]  J. Rice,et al.  Some basic stress diffusion solutions for fluid‐saturated elastic porous media with compressible constituents , 1976 .

[60]  M. Biot.  General Theory of Three‐Dimensional Consolidation , 1941 .