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At least 289 records · Page 16Linked to original sources
PubMed2006

Fast simulation of solid tumors thermal ablation treatments with a 3D reaction diffusion model.

An efficient computational method for near real-time simulation of thermal ablation of tumors via radio frequencies is proposed. Model simulations of the temperature field in a 3D portion of tissue containing the tumoral mass for different patterns of source heating can be used to design the ablation procedure. The availability of a very efficient computational scheme makes it possible to update the predicted outcome of the procedure in real time. In the algorithms proposed here a discretization in space of the governing equations is followed by an adaptive time integration based on implicit multistep formulas. A modification of the ode15s MATLAB function which uses Krylov space iterative methods for the solution of the linear systems arising at each integration step makes it possible to perform the simulations on standard desktop for much finer grids than using the built-in ode15s. The proposed algorithm can be applied to a wide class of nonlinear parabolic differential equations.

Algorithms↗
PubMed2006

Evidence of meniscus interface transport in dip-pen nanolithography: An annular diffusion model.

Ring shaped dots were patterned with mercaptohexadecanoic acid ink by dip-pen nanolithography. These dots have an ink-free inner core surrounded by an inked annular region, making them different from the filled dots usually obtained. This suggests a different transport mechanism than the current hypothesis of bulk water meniscus transport. A meniscus interface ink transport model is proposed, and its general applicability is demonstrated by predicting the patterned dot radii of chemically diverse inks.

Journal Article↗
PubMed1983

Diffusion model of intergroup selection, with special reference to evolution of an altruistic character.

Assume a diploid species consisting of an infinite number of competing demes, each having N(e) reproducing members and in which mating is at random. Then consider a locus at which a pair of alleles A and A' are segregating, where A' is the "altruistic allele," which has selective disadvantage s' relative to A with respect to individual selection, but which is beneficial for a deme in competition with other demes; namely, a deme having A' with frequency x has the advantage c(x - x) relative to the average deme, where c is a positive constant and x is the average of x over the species. Let varphi = varphi(x;t) be the distribution function of x among demes in the species at time t. Then, we have partial differentialvarphi/ partial differentialt = L(varphi) + c(x - x)varphi, where L is the Kolmogorov forward differential operator commonly used in population genetics [i.e., L = (1/2) ( partial differential(2)/ partial differentialx(2))V(deltax) - ( partial differential/ partial differentialx)M(deltax)], and M(deltax) and V(deltax) stand for the mean and variance of the change in x per generation within demes. As to migration, assume Wright's island model and denote by m the migration rate per deme per generation. By investigating the steady state, in which mutation, migration, random drift, and intra- and interdeme selection balance each other, it is shown that the index D = c/m - 4N(e)s' serves as a good indicator for predicting which of the two forces (i.e., group selection or individual selection) prevails; if D > 0, the altruistic allele predominates, but if D < 0, it becomes rare and cannot be established in the species.

Journal Article↗
PubMed2002

Reaction-diffusion model for the growth of avascular tumor.

A nutrient-limited model for avascular cancer growth including cell proliferation, motility, and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are characterized by its gyration radius, total number of cancer cells, and number of cells on tumor periphery. These very distinct morphological patterns follow Gompertz growth curves, but exhibit different scaling laws for their surfaces. Also, the simulated tumors incorporate a spatial structure composed of a central necrotic core, an inner rim of quiescent cells and a narrow outer shell of proliferating cells in agreement with biological data. Finally, our results indicate that the competition for nutrients among normal and cancer cells may be a determining factor in generating papillary tumor morphology.

Animals↗
PubMed2003

Large-scale emergent properties of an autocatalytic reaction-diffusion model subject to noise.

The nonequilibrium dynamic fluctuations of a stochastic version of the Gray-Scott (GS) model are studied analytically in leading order in perturbation theory by means of the dynamic renormalization group. There is an attracting stable fixed point at one-loop order, and the asymptotic scaling of the correlation functions is predicted for both spatial and temporally correlated noise sources. New effective three-body reaction terms, not present in the original GS model, are induced by the combined interplay of the fluctuations and nonlinearities.

Journal Article↗
PubMed2004

Hydrodynamic limit of multichain driven diffusive models.

A class of models, generalizing asymmetric exclusion process for many parallel interacting channels, is proposed. We couple the models with boundary reservoirs, study boundary-driven phase transitions, and show that usually taken hydrodynamic description fails. The adequate hydrodynamic limit is then derived. We support our findings with Monte Carlo simulations of the original stochastic system.

Journal Article↗