Personalized predictions of Glioblastoma infiltration: Mathematical models, Physics-Informed Neural Networks and multimodal scans.
Medical Image Anal., 2025
PIEZO1 regulates leader cell formation and cellular coordination during collective keratinocyte migration.
PLoS Comput. Biol., 2024
BiLO: Bilevel Local Operator Learning for PDE inverse problems.
CoRR, 2024
Sharp-interface problem of the Ohta-Kawasaki model for symmetric diblock copolymers.
J. Comput. Phys., May, 2023
Individualizing Glioma Radiotherapy Planning by Optimization of a Data and Physics Informed Discrete Loss.
CoRR, 2023
Correction: Stress generation, relaxation and size control in confined tumor growth.
PLoS Comput. Biol., 2022
Spatial dynamics of feedback and feedforward regulation in cell lineages.
PLoS Comput. Biol., 2022
Mathematical modeling of cancer immunotherapy for personalized clinical translation.
Nat. Comput. Sci., 2022
Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis.
J. Comput. Phys., 2022
Second order approximation for a quasi-incompressible Navier-Stokes Cahn-Hilliard system of two-phase flows with variable density.
J. Comput. Phys., 2022
Phase field modeling and computation of vesicle growth or shrinkage.
CoRR, 2022
Numerical study on viscous fingering using electric fields in a Hele-Shaw cell.
CoRR, 2022
Corrections to "A multiscale Agent-Based Model of Ductal Carcinoma in Situ".
IEEE Trans. Biomed. Eng., 2021
Stress generation, relaxation and size control in confined tumor growth.
PLoS Comput. Biol., 2021
A Multiscale Agent-Based Model of Ductal Carcinoma In Situ.
IEEE Trans. Biomed. Eng., 2020
Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries.
J. Comput. Phys., 2020
Personalized Radiotherapy Design for Glioblastoma: Integrating Mathematical Tumor Models, Multimodal Scans, and Bayesian Inference.
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IEEE Trans. Medical Imaging, 2019
Hydrodynamics of transient cell-cell contact: The role of membrane permeability and active protrusion length.
PLoS Comput. Biol., 2019
Efficient simulation of thermally fluctuating biopolymers immersed in fluids on 1-micron, 1-second scales.
J. Comput. Phys., 2019
Morphological stability of an elastic tumor-host interface.
J. Comput. Appl. Math., 2019
Complex far-field geometries determine the stability of solid tumor growth with chemotaxis.
CoRR, 2019
Boundary integral methods for dispersive equations, Airy flow and the modified Korteweg de Vries equation.
Adv. Comput. Math., 2019
Computation of a Shrinking Interface in a Hele-Shaw Cell.
SIAM J. Sci. Comput., 2018
A Uniquely Solvable, Energy Stable Numerical Scheme for the Functionalized Cahn-Hilliard Equation and Its Convergence Analysis.
J. Sci. Comput., 2018
A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-cartesian grids.
J. Comput. Phys., 2018
Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization.
J. Comput. Phys., 2018
Personalized Radiotherapy Planning for Glioma Using Multimodal Bayesian Model Calibration.
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CoRR, 2018
Multiscale Modeling of Glioblastoma Suggests that the Partial Disruption of Vessel/Cancer Stem Cell Crosstalk Can Promote Tumor Regression Without Increasing Invasiveness.
IEEE Trans. Biomed. Eng., 2017
Automated Unsupervised Segmentation of Liver Lesions in CT scans via Cahn-Hilliard Phase Separation.
CoRR, 2017
Feedback, Lineages and Self-Organizing Morphogenesis.
PLoS Comput. Biol., 2016
Numerical simulation of endocytosis: Viscous flow driven by membranes with non-uniformly distributed curvature-inducing molecules.
J. Comput. Phys., 2016
An energy stable, hexagonal finite difference scheme for the 2D phase field crystal amplitude equations.
J. Comput. Phys., 2016
Collective Properties of a Transcription Initiation Model Under Varying Environment.
J. Comput. Biol., 2016
Nonlinear simulations of elastic fingering in a Hele-Shaw cell.
J. Comput. Appl. Math., 2016
An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension.
Adv. Comput. Math., 2016
POPE: post optimization posterior evaluation of likelihood free models.
BMC Bioinform., 2015
A numerical method for the quasi-incompressible Cahn-Hilliard-Navier-Stokes equations for variable density flows with a discrete energy law.
J. Comput. Phys., 2014
Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations.
J. Comput. Phys., 2014
Diffuse interface models of locally inextensible vesicles in a viscous fluid.
J. Comput. Phys., 2014
Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation.
SIAM J. Numer. Anal., 2013
Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation.
J. Comput. Phys., 2013
Modeling an Elastic Fingering Instability in a Reactive Hele-Shaw Flow.
SIAM J. Appl. Math., 2012
Predicting simulation parameters of biological systems using a Gaussian process model.
Stat. Anal. Data Min., 2012
A level-set continuum method for two-phase flows with insoluble surfactant.
J. Comput. Phys., 2012
An adaptive multigrid algorithm for simulating solid tumor growth using mixture models.
Math. Comput. Model., 2011
A diffuse-interface method for two-phase flows with soluble surfactants.
J. Comput. Phys., 2011
A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion.
J. Comput. Phys., 2011
Dynamics of multicomponent vesicles in a viscous fluid.
J. Comput. Phys., 2010
An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation.
SIAM J. Numer. Anal., 2009
Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation.
J. Comput. Phys., 2009
A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth.
J. Sci. Comput., 2008
Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method.
J. Comput. Phys., 2007
A rescaling scheme with application to the long-time simulation of viscous fingering in a Hele-Shaw cell.
J. Comput. Phys., 2007
An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids.
J. Comput. Phys., 2006
A level-set method for interfacial flows with surfactant.
J. Comput. Phys., 2006
An improved geometry-aware curvature discretization for level set methods: Application to tumor growth.
J. Comput. Phys., 2006
Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering.
Math. Comput., 1999
High-Order and Efficient Methods for the Vorticity Formulation of the Euler Equations.
SIAM J. Sci. Comput., 1993
The Convergence of an Exact Desingularization for Vortex Methods.
SIAM J. Sci. Comput., 1993