arXiv subjects

John Lowengrub

Publications and source records attributed to John Lowengrub.

At least 19 recordsLinked to original sources

arXiv2026

A phase-field model for viscoelastic compressible tumor growth

It is well known that growing tumors generate and respond to stress in their local microenvironment. Tissue re-arrangements can relax these mechanical stresses and make the tissue more fluid-like. Further, intricate coupling between mechanotransduction and biochemical signaling leads to complex patterns of growth. To predict the outcomes of these nonlinear interactions, we develop a phase-field model to simulate tumors growing into a surrounding medium taking into account their elastic and viscous properties as well as their compressibilities. We couple continuum modeling of the viscoelastic mechanics to the concentration of a diffusible growth-promoting nutrient in a mass conservative way. The phase-field method is a stable and flexible way to describe the dynamics of arbitrarily shaped tumors. We demonstrate convergence of the phase-field model to a sharp interface model in radially symmetric geometries and can observe progression to stationary tumors. However, our results show that these stationary symmetric tumors are subject to symmetry-breaking instabilities in 2D and 3D driven by two primary mechanisms: (i) elastic buckling instabiliies due to differential growth induced by the nutrient gradient and (ii) instabilities generated by apoptosis-related volumetric loss. Further, tissue fluidity and compressibility can lead to changes in tumor topologies. Our modeling framework provides a robust methodology for investigating how tissue mechanics and growth factor signaling influence the progression and invasive potential of solid tumors.

cond-mat.soft↗

arXiv2026

An Efficient Constant-Coefficient MSAV Scheme for Computing Vesicle Growth and Shrinkage

We present a fast, unconditionally energy-stable numerical scheme for simulating vesicle deformation under osmotic pressure using a phase-field approach. The model couples an Allen-Cahn equation for the biomembrane interface with a variable-mobility Cahn-Hilliard equation governing mass exchange across the membrane. Classical approaches, including nonlinear multigrid and Multiple Scalar Auxiliary Variable (MSAV) methods, require iterative solution of variable-coefficient systems at each time step, resulting in substantial computational cost. We introduce a constant-coefficient MSAV (CC-MSAV) scheme that incorporates stabilization directly into the Cahn-Hilliard evolution equation rather than the chemical potential. This reformulation yields fully decoupled constant-coefficient elliptic problems solvable via fast discrete cosine transform (DCT), eliminating iterative solvers entirely. The method achieves O(N^2 log N) complexity per time step while preserving unconditional energy stability and discrete mass conservation. Numerical experiments verify second-order temporal and spatial accuracy, mass conservation to relative errors below 5 x 10^-11, and close agreement with nonlinear multigrid benchmarks. On grids with N >= 2048, CC-MSAV achieves 6-15x overall speedup compared to classical MSAV with optimized preconditioning, while the dominant Cahn-Hilliard subsystem is accelerated by up to two orders of magnitude. These efficiency gains, achieved without sacrificing accuracy, make CC-MSAV particularly well suited for large-scale simulations of vesicle dynamics.

math.NA↗

arXiv2025

Membrane Heterogeneity Driven Dynamics of Multicomponent Vesicles in Shear Flow

Despite their significance in biology and materials science, the dynamics of multicomponent vesicles under shear flow remain poorly understood because of their nonlinear and strongly coupled nature, especially regarding the role of membrane heterogeneity in driving nonequilibrium behavior. Here we present a thermodynamically consistent phase-field model, which is validated against experiments, for the quantitative investigation of these dynamics. While prior research has primarily focused on viscosity or bending rigidity contrasts, we demonstrate that surface tension heterogeneity can also trigger swinging and tumbling in vesicles under shear. Additionally, our systematic phase diagram reveals three previously unreported dynamical regimes arising from the interplay between bending rigidity heterogeneity and shear flow. Overall, our model provides a robust framework for understanding multicomponent vesicle dynamics, with findings offering new physical insights and design principles for tunable vesicle-based carriers.

cond-mat.soft↗

arXiv2024

Chemomechanical regulation of growing tissues from a thermodynamically-consistent framework and its application to tumor spheroid growth

It is widely recognized that reciprocal interactions between cells and their microenvironment, via mechanical forces and biochemical signaling pathways, regulate cell behaviors during normal development, homeostasis and disease progression such as cancer. However, it is still not well understood how complex patterns of tissue growth emerge. Here, we propose a framework for the chemomechanical regulation of growth based on thermodynamics of continua and growth-elasticity to predict growth patterns. Combining the elastic and chemical energies, we use an energy variational approach to derive a novel formulation that incorporates an energy-dissipating stress relaxation and biochemomechanical regulation of the volumetric growth rate. We validate the model using experimental data from growth of tumor spheroids in confined environments. We also investigate the influence of model parameters, including tissue rearrangement rate, tissue compressibility, strength of mechanical feedback and external mechanical stimuli, on the growth patterns of tumor spheroids.

physics.bio-ph↗

arXiv2022

The Liver Tumor Segmentation Benchmark (LiTS)

In this work, we report the set-up and results of the Liver Tumor Segmentation Benchmark (LiTS), which was organized in conjunction with the IEEE International Symposium on Biomedical Imaging (ISBI) 2017 and the International Conferences on Medical Image Computing and Computer-Assisted Intervention (MICCAI) 2017 and 2018. The image dataset is diverse and contains primary and secondary tumors with varied sizes and appearances with various lesion-to-background levels (hyper-/hypo-dense), created in collaboration with seven hospitals and research institutions. Seventy-five submitted liver and liver tumor segmentation algorithms were trained on a set of 131 computed tomography (CT) volumes and were tested on 70 unseen test images acquired from different patients. We found that not a single algorithm performed best for both liver and liver tumors in the three events. The best liver segmentation algorithm achieved a Dice score of 0.963, whereas, for tumor segmentation, the best algorithms achieved Dices scores of 0.674 (ISBI 2017), 0.702 (MICCAI 2017), and 0.739 (MICCAI 2018). Retrospectively, we performed additional analysis on liver tumor detection and revealed that not all top-performing segmentation algorithms worked well for tumor detection. The best liver tumor detection method achieved a lesion-wise recall of 0.458 (ISBI 2017), 0.515 (MICCAI 2017), and 0.554 (MICCAI 2018), indicating the need for further research. LiTS remains an active benchmark and resource for research, e.g., contributing the liver-related segmentation tasks in \url{http://medicaldecathlon.com/}. In addition, both data and online evaluation are accessible via \url{www.lits-challenge.com}.

cs.CV↗

arXiv2022

Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis

In this paper, we develop a sharp interface tumor growth model in two dimensions to study the effect of both the intratumoral structure using a controlled necrotic core and the extratumoral nutrient supply from vasculature on tumor morphology. We first show that our model extends the benchmark results in the literature using linear stability analysis. Then we solve this generalized model numerically using a spectrally accurate boundary integral method in an evolving annular domain, not only with a Robin boundary condition on the outer boundary for the nutrient field which models tumor vasculature, but also with a static boundary condition on the inner boundary for pressure field which models the control of tumor necrosis. The discretized linear systems for both pressure and nutrient fields are shown to be well-conditioned through tracing GMRES iteration numbers. Our nonlinear simulations reveal the stabilizing effects of angiogenesis and the destabilizing ones of chemotaxis and necrosis in the development of tumor morphological instabilities if the necrotic core is fixed in a circular shape. When the necrotic core is controlled in a non-circular shape, the stabilizing effects of proliferation and the destabilizing ones of apoptosis are observed. Finally, the values of the nutrient concentration with its fluxes and the pressure level with its normal derivatives, which are solved accurately at the boundaries, help us to characterize the corresponding tumor morphology and the level of the biophysical quantities on interfaces required in keeping various shapes of the necrotic region of the tumor. Interestingly, we notice that when the necrotic region is fixed in a 3-fold non-circular shape, even if the initial shape of the tumor is circular, the tumor will evolve into a shape corresponding to the 3-fold symmetry of the shape of the fixed necrotic region.

math.NA↗

arXiv2022

Numerical study on viscous fingering using electric fields in a Hele-Shaw cell

We investigate the nonlinear dynamics of a moving interface in a Hele-Shaw cell subject to an in-plane applied electric field. We develop a spectrally accurate boundary integral method where a coupled integral equation system is formulated. Although the stiffness due to the high order spatial derivatives can be removed, the long-time simulation is still expensive since the evolving velocity of the interface drops dramatically as the interface expands. We remove this physically imposed stiffness by employing a rescaling scheme, which accelerates the slow dynamics and reduces the computational cost. Our nonlinear results reveal that positive currents restrain finger ramification and promote overall stabilization of patterns. On the other hand, negative currents make the interface more unstable and lead to the formation of thin tail structures connecting the fingers and a small inner region. When no flux is injected, and a negative current is utilized, the interface tends to approach the origin and break up into several drops. We investigate the temporal evolution of the smallest distance between the interface and the origin and find that it obeys an algebraic law $\displaystyle (t_*-t)^b$, where $t_*$ is the estimated pinch-off time.

physics.flu-dyn↗

arXiv2021

Electrically-controlled self-similar evolution of viscous fingering patterns in radial Hele-Shaw flows

Time-dependent injection strategies are commonly employed to control the number of viscous fingers emerging at the interface separating two fluids during radial displacement in Hele-Shaw flows. Here we demonstrate theoretically that such a usual controlling method is significantly improved by taking advantage of an electro-osmotic flow generated by applying an external electric field. More specifically, under the coupled action of time-varying electric currents and injection rates, we design a strategy capable of controlling not only the number of fingers emerging at the interface but also when (and if) the self-similar evolution occurs. In addition, the level of instability of the $n$-fold fingered patterns can also be tuned. This improved control over the interfacial features cannot be realized by the sole consideration of a time-varying injection rate. Perturbative second-order mode-coupling analysis and boundary integral simulations confirm that the validity and effectiveness of the controlling protocol go beyond the linear regime.

physics.flu-dyn↗

arXiv2021

Sharp-interface problem of the Ohta-Kawasaki model for symmetric diblock copolymers

The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding sharp-interface limit using matched asymptotic expansions, and show that the limiting process leads to a Hele-Shaw type moving interface problem. The numerical treatment of the sharp-interface limit is more complicated due to the stiffness of the equations. To address this problem, we present a boundary integral formulation corresponding to a sharp interface limit of the Ohta-Kawasaki model. Starting with the governing equations defined on separate phase domains, we develop boundary integral equations valid for multi-connected domains in a 2D plane. For numerical simplicity we assume our problem is driven by a uniform Dirichlet condition on a circular far-field boundary. The integral formulation of the problem involves both double- and single-layer potentials due to the modified boundary condition. In particular, our formulation allows one to compute the nonlinear dynamics of a non-equilibrium system and pattern formation of an equilibrating system. Numerical tests on an evolving slightly perturbed circular interface (separating the two phases) are in excellent agreement with the linear analysis, demonstrating that the method is stable, efficient and spectrally accurate in space.

math.NA↗

arXiv2020

A multi-scale model of virus pandemic: Heterogeneous interactive entities in a globally connected world

This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an aggressive virus, specifically the so-called \textit{SARS--CoV--2 Severe Acute Respiratory Syndrome, corona virus n.2}. The study is developed within a multiscale framework accounting for the interaction of different spatial scales, from the small scale of the virus itself and cells, to the large scale of individuals and further up to the collective behaviour of populations. An interdisciplinary vision is developed thanks to the contributions of epidemiologists, immunologists and economists as well as those of mathematical modellers. The first part of the contents is devoted to understanding the complex features of the system and to the design of a modelling rationale. The modelling approach is treated in the second part of the paper by showing both how the virus propagates into infected individuals, successfully and not successfully recovered, and also the spatial patterns, which are subsequently studied by kinetic and lattice models. The third part reports the contribution of research in the fields of virology, epidemiology, immune competition, and economy focused also on social behaviours. Finally, a critical analysis is proposed looking ahead to research perspectives.

q-bio.PE↗

arXiv2020

Nonlinear limiting dynamics of a shrinking interface in a Hele-Shaw cell

The flow in a Hele-Shaw cell with a time-increasing gap poses a unique shrinking interface problem. When the upper plate of the cell is lifted perpendicularly at a prescribed speed, the exterior less viscous fluid penetrates the interior more viscous fluid, which generates complex, time-dependent interfacial patterns through the Saffman-Taylor instability. The pattern formation process sensitively depends on the lifting speed and is still not fully understood. For some lifting speeds, such as linear or exponential speed, the instability is transient and the interface eventually shrinks as a circle. However, linear stability analysis suggests there exist shape invariant shrinking patterns if the gap $b(t)$ is increased more rapidly: $\displaystyle b(t)=\left(1-\frac{7}{2}τ\mathcal{C} t\right)^{-{2}/{7}}$, where $τ$ is the surface tension and $\mathcal{C}$ is a function of the interface perturbation mode $k$. Here, we use a spectrally accurate boundary integral method together with an efficient time adaptive rescaling scheme, which for the first time makes it possible to explore the nonlinear limiting dynamical behavior of a vanishing interface. When the gap is increased at a constant rate, our numerical results quantitatively agree with experimental observations (Nase et al., Phys. Fluids, vol. 23, 2011, pp. 123101). When we use the shape invariant gap $b(t)$, our nonlinear results reveal the existence of $k$-fold dominant, one-dimensional, web-like networks, where the fractal dimension is reduced to almost one at late times. We conclude by constructing a morphology diagram for pattern selection that relates the dominant mode $k$ of the vanishing interface and the control parameter $\mathcal{C}$.

physics.flu-dyn↗

arXiv2020

Complex Far-Field Geometries Determine the Stability of Solid Tumor Growth with Chemotaxis

In this paper, we develop a sharp interface tumor growth model to study the effect of the tumor microenvironment using a complex far-field geometry that mimics a heterogeneous distribution of vasculature. Together with different nutrient uptake rates inside and outside the tumor, this introduces variability in spatial diffusion gradients. Linear stability analysis suggests that the uptake rate in the tumor microenvironment, together with chemotaxis, may induce unstable growth, especially when the nutrient gradients are large. We investigate the fully nonlinear dynamics using a spectrally accurate boundary integral method. Our nonlinear simulations reveal that vascular heterogeneity plays an important role in the development of morphological instabilities that range from fingering and chain-like morphologies to compact, plate-like shapes in two-dimensions.

math.NA↗

arXiv2019

Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries

The diffuse-domain, or smoothed boundary, method is an attractive approach for solving partial differential equations in complex geometries because of its simplicity and flexibility. In this method the complex geometry is embedded into a larger, regular domain. The original PDE is reformulated using a smoothed characteristic function of the complex domain and source terms are introduced to approximate the boundary conditions. The reformulated equation, which is independent of the dimension and domain geometry, can be solved by standard numerical methods and the same solver can be used for any domain geometry. A challenge is making the method higher-order accurate. For Dirichlet boundary conditions, which we focus on here, current implementations demonstrate a wide range in their accuracy but generally the methods yield at best first order accuracy in $ε$, the parameter that characterizes the width of the region over which the characteristic function is smoothed. Typically, $ε\propto h$, the grid size. Here, we analyze the diffuse-domain PDEs using matched asymptotic expansions and explain the observed behaviors. Our analysis also identifies simple modifications to the diffuse-domain PDEs that yield higher-order accuracy in $ε$, e.g., $O(ε^2)$ in the $L^2$ norm and $O(ε^p)$ with $1.5\le p\le 2$ in the $L^{\infty}$ norm. Our analytic results are confirmed numerically in stationary and moving domains where the level set method is used to capture the dynamics of the domain boundary and to construct the smoothed characteristic function.

math.NA↗

arXiv2019

Modeling the vertical growth of van der Waals stacked 2D materials using the diffuse domain method

Vertically-stacked monolayers of graphene and other atomically-thin 2D materials have attracted considerable research interest because of their potential in fabricating materials with specifically-designed properties. Chemical vapor deposition has proved to be an efficient and scalable fabrication method. However, a lack of mechanistic understanding has hampered efforts to control the fabrication process beyond empirical trial-and-error approaches. In this paper, we develop a general multiscale Burton-Cabrera-Frank (BCF) type model of the vertical growth of 2D materials to predict the necessary growth conditions for vertical versus in-plane (monolayer) growth of arbitrarily-shaped layers. This extends previous work where we developed such a model assuming the layers were fully-faceted (Ye et al., ACS Nano, 11, 12780-12788, 2017). To solve the model numerically, we reformulate the system using the phase-field/diffuse domain method that enables the equations to be solved in a fixed regular domain. We use a second-order accurate, adaptive finite-difference/nonlinear multigrid algorithm to discretize and solve the discrete system. We investigate the effect of parameters, including the van der Waals interaction energies between the layers, the kinetic attachment rates, the edge-energies and the deposition flux, on layer growth and morphologies. While the conditions that favor vertical growth generally follow an analytic thermodynamic criterion we derived for circular layers, the layer boundaries may develop significant curvature during growth, consistent with experimental observations. Our approach provides a mechanistic framework for controlling and optimizing the growth multilayered 2D materials.

physics.comp-ph↗

arXiv2017

Non-stiff methods for Airy flow and the modified Korteweg-de Vries equation

In this paper, we implement non-stiff interface tracking methods for the evolution of 2-D curves that follow Airy flow, a curvature-dependent dispersive geometric evolution law. The curvature of the curve satisfies the modified Korteweg-de Vries equation, a dispersive non-linear soliton equation. We present a fully discrete space-time analysis of the equations (proof of convergence) and numerical evidence that confirms the accuracy, convergence, efficiency, and stability of the methods.

math.NA↗

arXiv2017

Automated Unsupervised Segmentation of Liver Lesions in CT scans via Cahn-Hilliard Phase Separation

The segmentation of liver lesions is crucial for detection, diagnosis and monitoring progression of liver cancer. However, design of accurate automated methods remains challenging due to high noise in CT scans, low contrast between liver and lesions, as well as large lesion variability. We propose a 3D automatic, unsupervised method for liver lesions segmentation using a phase separation approach. It is assumed that liver is a mixture of two phases: healthy liver and lesions, represented by different image intensities polluted by noise. The Cahn-Hilliard equation is used to remove the noise and separate the mixture into two distinct phases with well-defined interfaces. This simplifies the lesion detection and segmentation task drastically and enables to segment liver lesions by thresholding the Cahn-Hilliard solution. The method was tested on 3Dircadb and LITS dataset.

cs.CV↗

arXiv2017

Mass Conservative and Energy Stable Finite Difference Methods for the Quasi-incompressible Navier-Stokes-Cahn-Hilliard system: Primitive Variable and Projection-Type Schemes

In this paper we describe two fully mass conservative, energy stable, finite difference methods on a staggered grid for the quasi-incompressible Navier-Stokes-Cahn-Hilliard (q-NSCH) system governing a binary incompressible fluid flow with variable density and viscosity. Both methods, namely the primitive method (finite difference method in the primitive variable formulation) and the projection method (finite difference method in a projection-type formulation), are so designed that the mass of the binary fluid is preserved, and the energy of the system equations is always non-increasing in time at the fully discrete level. We also present an efficient, practical nonlinear multigrid method - comprised of a standard FAS method for the Cahn-Hilliard equation, and a method based on the Vanka-type smoothing strategy for the Navier-Stokes equation - for solving these equations. We test the scheme in the context of Capillary Waves, rising droplets and Rayleigh-Taylor instability. Quantitative comparisons are made with existing analytical solutions or previous numerical results that validate the accuracy of our numerical schemes. Moreover, in all cases, mass of the single component and the binary fluid was conserved up to 10 to -8 and energy decreases in time.

math.NA↗

arXiv2016

Dynamics of a multicomponent vesicle in shear flow

We study the fully nonlinear, nonlocal dynamics of two-dimensional multicomponent vesicles in a shear flow with matched viscosity of the inner and outer fluids. Using a nonstiff, pseudo-spectral boundary integral method, we investigate dynamical patterns induced by inhomogeneous bending for a two phase system. Numerical results reveal that there exist novel phase-treading and tumbling mechanisms that cannot be observed for a homogeneous vesicle. In particular, unlike the well-known steady tank-treading dynamics characterized by a fixed inclination angle, here the phase-treading mechanism leads to unsteady periodic dynamics with an oscillatory inclination angle. When the average phase concentration is around 1/2, we observe tumbling dynamics even for very low shear rate, and the excess length required for tumbling is significantly smaller than the value for the single phase case. We summarize our results in phase diagrams in terms of the excess length, shear rate, and concentration of the soft phase. These findings go beyond the well known dynamical regimes of a homogeneous vesicle and highlight the level of complexity of vesicle dynamics in a fluid due to heterogeneous material properties.

cond-mat.soft↗