A new ghost cell/level set method for moving boundary problems:application to tumor growth

In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth

Broad-scale patterns of body size in squamate reptiles of Europe and North America

Aim To document geographical interspecific patterns of body size of European and North American squamate reptile assemblages and explore the relationship between body size patterns and environmental gradients. Location North America and western Europe. Methods We processed distribution maps for native species of squamate reptiles to document interspecific spatial variation of body size at a grain size of 110 x 110 km. We also examined seven environmental variables linked to four hypotheses possibly influencing body size gradients. We used simple and multiple regression, evaluated using information theory, to identify the set of models best supported by the data. Results Europe is characterized by clear latitudinal trends in body size, whereas geographical variation in body size in North America is complex. There is a consistent association of mean body size with measures of ambient energy in both regions, although lizards increase in size northwards whereas snakes show the opposite pattern. Our best models accounted for almost 60% of the variation in body size of lizards and snakes within Europe, but the proportions of variance explained in North America were less than 20%. Main conclusions Although body size influences the energy balance of thermoregulating ectotherms, inconsistent biogeographical patterns and contrasting associations with energy in lizards and snakes suggest that no single mechanism can explain variation of reptile body size in the northern temperate zone

The Effect of Impact Damage on the Room-Temperature Fatigue Behavior of γ-TiAl

The relationship between impact damage and the fatigue behavior of γ-TiAl has been examined. Axial fatigue specimens fabricated from cast Ti-47.9Al-2.0Cr-1.9Nb (to be referred to as 48-2-2) and Ti-47.3Al-2.2Nb-0.5Mn-0.4W-0.4Mo-0.23Si (to be referred to as WMS) alloys were damaged by impact under controlled conditions with a 60 deg wedge-shaped indenter to simulate assembly-related damage in low-pressure turbine blades. The level of damage produced was quantified and found to correlate well with the peak load of the impact event. The WMS alloy exhibited a greater resistance to impact damage due to its higher yield strength and lamellar microstructure. A measure of the ambient-temperature fatigue failure stress in the alloys was obtained by standard fatigue testing employing a step-loading approach. The failure stress of the WMS alloy was greater than that of the 48-2-2 alloy in the undamaged state. The relationship between impact damage and failure stress was examined using a threshold-based approach. These studies indicate that, for damage levels below a transitional flaw size, the failure stress is near that for undamaged specimens. At damage levels greater than the transitional flaw size, the failure stress can be adequately approximated using the threshold stress-intensity range (ΔKTH ) from long-crack growth testing. Fractographic studies were performed to investigate impact damage and crack-advance mechanisms, which match those observed in other alloys tested at room temperature