Biomedical subjects

Leonard M Sander

Publications and source records attributed to Leonard M Sander.

10 recordsLinked to original sources

PubMed2006

A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment.

Glioblastoma, the most malignant form of brain cancer, is responsible for 23% of primary brain tumors and has extremely poor outcome. Confounding the clinical management of glioblastomas is the extreme local invasiveness of these cancer cells. The mechanisms that govern invasion are poorly understood. To gain insight into glioblastoma invasion, we conducted experiments on the patterns of growth and dispersion of U87 glioblastoma tumor spheroids in a three-dimensional collagen gel. We studied two different cell lines, one with a mutation to the EGFR (U87DeltaEGFR) that is associated with increased malignancy, and one with an endogenous (wild-type) receptor (U87WT). We developed a continuum mathematical model of the dispersion behaviors with the aim of identifying and characterizing discrete cellular mechanisms underlying invasive cell motility. The mathematical model quantitatively reproduces the experimental data, and indicates that the U87WT invasive cells have a stronger directional motility bias away from the spheroid center as well as a faster rate of cell shedding compared to the U87DeltaEGFR cells. The model suggests that differences in tumor cell dispersion may be due to differences in the chemical factors produced by cells, differences in how the two cell lines remodel the gel, or different cell-cell adhesion characteristics.

Brain Neoplasms↗

PubMed2006

Dynamics and pattern formation in invasive tumor growth.

We study the in vitro dynamics of the malignant brain tumor glioblastoma multiforme. The growing tumor consists of a dense proliferating zone and an outer less dense invasive region. Experiments with different types of cells show qualitatively different behavior: one cell line invades in a spherically symmetric manner, but another gives rise to branches. We formulate a model for this sort of growth using two coupled reaction-diffusion equations for the cell and nutrient concentrations. When the ratio of the nutrient and cell diffusion coefficients exceeds some critical value, the plane propagating front becomes unstable with respect to transversal perturbations. The instability threshold and the full phase-plane diagram in the parameter space are determined. The results are in a qualitative agreement with experimental findings for the two types of cells.

Brain Neoplasms↗

PubMed2005

Island, pit, and groove formation in strained heteroepitaxy.

We study the morphological evolution of strained heteroepitaxial films using a kinetic Monte Carlo method in three dimensions. The elastic part of the problem uses a Green's function method. Isolated islands are observed under deposition conditions for deposition rates slow compared with intrinsic surface roughening rates. They are hemispherical and truncated conical for high and low temperature cases, respectively. Annealing of films at high temperature leads to the formation of closely packed islands as in instability theory. At low temperature, pits form via a multistep layer-by-layer nucleation mechanism in contrast to the conventional single-step nucleation process. They subsequently develop into grooves, which are energetically more favorable.

Journal Article↗

PubMed2005

Random walks, diffusion limited aggregation in a wedge, and average conformal maps.

We investigate diffusion-limited aggregation (DLA) in a wedge geometry. Arneodo and collaborators have suggested that the ensemble average of DLA cluster density should be close to the noise-free selected Saffman-Taylor finger. We show that a different, but related, ensemble average, that of the conformal maps associated with random clusters, yields a nontrivial shape which is also not far from the Saffman-Taylor finger. However, we have previously demonstrated that the same average of DLA in a channel geometry is not the Saffman-Taylor finger. This casts doubt on the idea that the average of noisy diffusion-limited growth is governed by a simple transcription of noise-free results.

Cluster Analysis↗

PubMed2004

Growth by random walker sampling and scaling of the dielectric breakdown model.

Random walkers absorbing on a boundary sample the harmonic measure linearly and independently: we discuss how the recurrence times between impacts enable nonlinear moments of the measure to be estimated. From this we derive a technique to simulate dielectric breakdown model growth, which is governed nonlinearly by the harmonic measure. For diffusion-limited aggregation, recurrence times are shown to be accurate and effective in probing the multifractal growth measure in its active region. For the dielectric breakdown model our technique grows large clusters efficiently and we are led to significantly revise earlier exponent estimates. Previous results by two conformal mapping techniques were less converged than expected, and in particular a recent theoretical suggestion of superuniversality is firmly refuted.

Journal Article↗

PubMed2004

Kinetic pinning and biological antifreezes.

Biological antifreezes protect cold-water organisms from freezing. An example is the antifreeze proteins (AFP's) that attach to the surface of ice crystals and arrest growth. The mechanism for growth arrest has not been heretofore understood in a quantitative way. We present a complete theory based on a kinetic model. We use the "stones on a pillow" picture. Our theory of the suppression of the freezing point as a function of the concentration of the AFP is quantitatively accurate. It gives a correct description of the dependence of the freezing point suppression on the geometry of the protein, and might lead to advances in design of synthetic AFP's.

Antifreeze Proteins↗

PubMed2003

Diffusion-limited aggregation in channel geometry.

We performed extensive numerical simulation of diffusion-limited aggregation in two-dimensional channel geometry. Contrary to earlier claims, the measured fractal dimension D=1.712+/-0.002 and its leading correction to scaling are the same as in the radial case. The average cluster, defined as the average conformal map, is similar but not identical to Saffman-Taylor fingers.

Journal Article↗

PubMed2002

Growth patterns of microscopic brain tumors.

Highly malignant brain tumors such as glioblastoma multiforme form complex growth patterns in vitro in which invasive cells organize in tenuous branches. Here, we formulate a chemotaxis model for this sort of growth. A key element controlling the pattern is homotype attraction, i.e., the tendency for invasive cells to follow pathways previously explored. We investigate this in two ways: we show that there is an intrinsic instability in the model, which leads to branch formation. We also give a discrete description for the expansion of the invasive zone, and a continuum model for the nutrient supply. The results indicate that both strong heterotype chemotaxis and strong homotype chemoattraction are required for branch formation within the invasive zone. Our model thus can give a way to assess the importance of the various processes, and a way to explore and analyze transitions between different growth regimes.

Biophysical Phenomena↗

PubMed2002

Competing roughening mechanisms in strained heteroepitaxy: a fast kinetic Monte Carlo study.

We study the morphological evolution of strained heteroepitaxial films using kinetic Monte Carlo simulations in two dimensions. A novel Green's function approach, analogous to boundary integral methods, is used to calculate elastic energies efficiently. We observe island formation at low lattice misfit and high temperature that is consistent with the Asaro-Tiller-Grinfeld instability theory. At high misfit and low temperature, islands or pits form according to the nucleation theory of Tersoff and LeGoues.

Journal Article↗

PubMed2002

Off-lattice noise reduction and the ultimate scaling of diffusion-limited aggregation in two dimensions.

Off-lattice diffusion-limited aggregation (DLA) clusters grown with different levels of noise reduction are found to be consistent with a simple fractal fixed point. Cluster shapes and their ensemble variation exhibit a dominant slowest correction to scaling, and this also accounts for the apparent "multiscaling" in the DLA mass distribution. We interpret the correction to scaling in terms of renormalized noise. The limiting value of this variable is strikingly small and is dominated by fluctuations in cluster shape. Earlier claims of anomalous scaling in DLA were misled by the slow approach to this small fixed point value.

Journal Article↗