John Lowengrub

Bio: John Lowengrub is an academic researcher from University of California, Irvine. The author has contributed to research in topics: Nonlinear system & Multigrid method. The author has an hindex of 58, co-authored 241 publications receiving 13368 citations. Previous affiliations of John Lowengrub include Courant Institute of Mathematical Sciences & University of Minnesota.

Quasi–incompressible Cahn–Hilliard fluids and topological transitions

Abstract: One of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe this type of phenomena. Following some previous work in this area, we suggest a physically motivated regularization of the Euler equations which allows topological transitions to occur smoothly. In this model, the sharp interface is replaced by a narrow transition layer across which the fluids may mix. The model describes a flow of a binary mixture, and the internal structure of the interface is determined by both diffusion and motion. An advantage of our regularization is that it automatically yields a continuous description of surface tension, which can play an important role in topological transitions. An additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the Euler (or Navier–Stokes) and the Cahn–Hilliard equations. The model takes into account weak non–locality (dispersion) associated with an internal length scale and localized dissipation due to mixing. The non–locality introduces a dimensional surface energy; dissipation is added to handle the loss of regularity of solutions to the sharp interface equations and to provide a mechanism for topological changes. In particular, we study a non–trivial limit when both components are incompressible, the pressure is kinematic but the velocity field is non–solenoidal (quasi–incompressibility). To demonstrate the effects of quasi–incompressibility, we analyse the linear stage of spinodal decomposition in one dimension. We show that when the densities of the fluids are not perfectly matched, the evolution of the concentration field causes fluid motion even if the fluids are inviscid. In the limit of infinitely thin and well–separated interfacial layers, an appropriately scaled quasi–incompressible Euler–Cahn–Hilliard system converges to the classical sharp interface model. In order to investigate the behaviour of the model outside the range of parameters where the sharp interface approximation is sufficient, we consider a simple example of a change of topology and show that the model permits the transition to occur without an associated singularity.

Nonlinear modelling of cancer: Bridging the gap between cells and tumours

Abstract: Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis.

The Liver Tumor Segmentation Benchmark (LiTS)

Abstract: In this work, we report the set-up and results of the Liver Tumor Segmentation Benchmark (LITS) organized in conjunction with the IEEE International Symposium on Biomedical Imaging (ISBI) 2016 and International Conference On Medical Image Computing Computer Assisted Intervention (MICCAI) 2017. Twenty four valid state-of-the-art liver and liver tumor segmentation algorithms were applied to a set of 131 computed tomography (CT) volumes with different types of tumor contrast levels (hyper-/hypo-intense), abnormalities in tissues (metastasectomie) size and varying amount of lesions. The submitted algorithms have been tested on 70 undisclosed volumes. The dataset is created in collaboration with seven hospitals and research institutions and manually reviewed by independent three radiologists. We found that not a single algorithm performed best for liver and tumors. The best liver segmentation algorithm achieved a Dice score of 0.96(MICCAI) whereas for tumor segmentation the best algorithm evaluated at 0.67(ISBI) and 0.70(MICCAI). The LITS image data and manual annotations continue to be publicly available through an online evaluation system as an ongoing benchmarking resource.

Methods in Enzymology.

Abstract: I read this book the same weekend that the Packers took on the Rams, and the experience of the latter event, obviously, colored my judgment. Although I abhor anything that smacks of being a handbook (like, \"How to Earn a Merit Badge in Neurosurgery\") because too many volumes in biomedical science already evince a boyscout-like approach, I must confess that parts of this volume are fast, scholarly, and significant, with certain reservations. I like parts of this well-illustrated book because Dr. Sj6strand, without so stating, develops certain subjects on technique in relation to the acquisition of judgment and sophistication. And this is important! So, given that the author (like all of us) is somewhat deficient in some areas, and biased in others, the book is still valuable if the uninitiated reader swallows it in a general fashion, realizing full well that what will be required from the reader is a modulation to fit his vision, propreception, adaptation and response, and the kind of problem he is undertaking. A major deficiency of this book is revealed by comparison of its use of physics and of chemistry to provide understanding and background for the application of high resolution electron microscopy to problems in biology. Since the volume is keyed to high resolution electron microscopy, which is a sophisticated form of structural analysis, but really morphology in a modern guise, the physical and mechanical background of The instrument and its ancillary tools are simply and well presented. The potential use of chemical or cytochemical information as it relates to biological fine structure , however, is quite deficient. I wonder when even sophisticated morphol-ogists will consider fixation a reaction and not a technique; only then will the fundamentals become self-evident and predictable and this sine qua flon will become less mystical. Staining reactions (the most inadequate chapter) ought to be something more than a technique to selectively enhance contrast of morphological elements; it ought to give the structural addresses of some of the chemical residents of cell components. Is it pertinent that auto-radiography gets singled out for more complete coverage than other significant aspects of cytochemistry by a high resolution microscopist, when it has a built-in minimal error of 1,000 A in standard practice? I don't mean to blind-side (in strict football terminology) Dr. Sj6strand's efforts for what is \"routinely used in our laboratory\"; what is done is usually well done. It's just that …

Evolution of nanoporosity in dealloying

Abstract: Dealloying is a common corrosion process during which an alloy is 'parted' by the selective dissolution of the most electrochemically active of its elements. This process results in the formation of a nanoporous sponge composed almost entirely of the more noble alloy constituents. Although considerable attention has been devoted to the morphological aspects of the dealloying process, its underlying physical mechanism has remained unclear. Here we propose a continuum model that is fully consistent with experiments and theoretical simulations of alloy dissolution, and demonstrate that nanoporosity in metals is due to an intrinsic dynamical pattern formation process. That is, pores form because the more noble atoms are chemically driven to aggregate into two-dimensional clusters by a phase separation process (spinodal decomposition) at the solid-electrolyte interface, and the surface area continuously increases owing to etching. Together, these processes evolve porosity with a characteristic length scale predicted by our continuum model. We expect that chemically tailored nanoporous gold made by dealloying Ag-Au should be suitable for sensor applications, particularly in a biomaterials context.

Phase-Field Models for Microstructure Evolution

Abstract: ■ Abstract The phase-field method has recently emerged as a powerful computational approach to modeling and predicting mesoscale morphological and microstructure evolution in materials. It describes a microstructure using a set of conserved and nonconserved field variables that are continuous across the interfacial regions. The temporal and spatial evolution of the field variables is governed by the Cahn-Hilliard nonlinear diffusion equation and the Allen-Cahn relaxation equation. With the fundamental thermodynamic and kinetic information as the input, the phase-field method is able to predict the evolution of arbitrary morphologies and complex microstructures without explicitly tracking the positions of interfaces. This paper briefly reviews the recent advances in developing phase-field models for various materials processes including solidification, solid-state structural phase transformations, grain growth and coarsening, domain evolution in thin films, pattern formation on surfaces, dislocation microstructures, crack propagation, and electromigration.