Cells as strain-cued automata.

We argue in favor of representing living cells as automata and review demonstrations that autonomous cells can form patterns by responding to local variations in the strain fields that arise from their individual or collective motions. An autonomous cell's response to strain stimuli is assumed to be effected by internally-generated, internally-powered forces, which generally move the cell in directions other than those implied by external energy gradients. Evidence of cells acting as strain-cued automata have been inferred from patterns observed in nature and from experiments conducted in vitro. Simulations that mimic particular cases of pattern forming share the idealization that cells are assumed to pass information among themselves solely via mechanical boundary conditions, i.e., the tractions and displacements present at their membranes. This assumption opens three mechanisms for pattern formation in large cell populations: wavelike behavior, kinematic feedback in cell motility that can lead to sliding and rotational patterns, and directed migration during invasions. Wavelike behavior among ameloblast cells during amelogenesis (the formation of dental enamel) has been inferred from enamel microstructure, while strain waves in populations of epithelial cells have been observed in vitro. One hypothesized kinematic feedback mechanism, "enhanced shear motility", accounts successfully for the spontaneous formation of layered patterns during amelogenesis in the mouse incisor. Directed migration is exemplified by a theory of invader cells that sense and respond to the strains they themselves create in the host population as they invade it: analysis shows that the strain fields contain positional information that could aid the formation of cell network structures, stabilizing the slender geometry of branches and helping govern the frequency of branch bifurcation and branch coalescence (the formation of closed networks). In simulations of pattern formation in homogeneous populations and network formation by invaders, morphological outcomes are governed by the ratio of the rates of two competing time dependent processes, one a migration velocity and the other a relaxation velocity related to the propagation of strain information. Relaxation velocities are approximately constant for different species and organs, whereas cell migration rates vary by three orders of magnitude. We conjecture that developmental processes use rapid cell migration to achieve certain outcomes, and slow migration to achieve others. We infer from analysis of host relaxation during network formation that a transition exists in the mechanical response of a host cell from animate to inanimate behavior when its strain changes at a rate that exceeds 10-4-10-3s-1. The transition has previously been observed in experiments conducted in vitro.

Tensile testing of materials at high temperatures above 1700 °C with in situ synchrotron X-ray micro-tomography.

A compact ultrahigh temperature tensile testing instrument has been designed and fabricated for in situ x-ray micro-tomography using synchrotron radiation at the Advanced Light Source, Lawrence Berkeley National Laboratory. It allows for real time x-ray micro-tomographic imaging of test materials under mechanical load at temperatures up to 2300 °C in controlled environments (vacuum or controlled gas flow). Sample heating is by six infrared halogen lamps with ellipsoidal reflectors arranged in a confocal configuration, which generates an approximately spherical zone of high heat flux approximately 5 mm in diameter. Samples are held between grips connected to a motorized stage that loads the samples in tension or compression with forces up to 2.2 kN. The heating chamber and loading system are water-cooled for thermal stability. The entire instrument is mounted on a rotation stage that allows stepwise recording of radiographs over an angular range of 180°. A thin circumferential (360°) aluminum window in the wall of the heating chamber allows the x-rays to pass through the chamber and the sample over the full angular range. The performance of the instrument has been demonstrated by characterizing the evolution of 3D damage mechanisms in ceramic composite materials under tensile loading at 1750 °C.

How the tooth got its stripes: patterning via strain-cued motility.

We hypothesize that a population of migrating cells can form patterns when changes in local strains owing to relative cell motions induce changes in cell motility. That the mechanism originates in competing rates of motion distinguishes it from mechanisms involving strain energy gradients, e.g. those generated by surface energy effects or eigenstrains among cells, and diffusion-reaction mechanisms involving chemical signalling factors. The theory is tested by its ability to reproduce the morphological characteristics of enamel in the mouse incisor. Dental enamel is formed during amelogenesis by a population of ameloblasts that move about laterally within an expanding curved sheet, subject to continuously evolving spatial and temporal gradients in strain. Discrete-cell simulations of this process compute the changing strain environment of all cells and predict cell trajectories by invoking simple rules for the motion of an individual cell in response to its strain environment. The rules balance a tendency for cells to enhance relative sliding motion against a tendency to maintain uniform cell-cell separation. The simulations account for observed waviness in the enamel microstructure, the speed and shape of the 'commencement front' that separates domains of migrating secretory-stage ameloblasts from those that are not yet migrating, the initiation and sustainment of layered, fracture-resistant decussation patterns (cross-plied microstructure) and the transition from decussating inner enamel to non-decussating outer enamel. All these characteristics can be correctly predicted with the use of a single scalar adjustable parameter.

Real-time quantitative imaging of failure events in materials under load at temperatures above 1,600 °C.

Ceramic matrix composites are the emerging material of choice for structures that will see temperatures above ~1,500 °C in hostile environments, as for example in next-generation gas turbines and hypersonic-flight applications. The safe operation of applications depends on how small cracks forming inside the material are restrained by its microstructure. As with natural tissue such as bone and seashells, the tailored microstructural complexity of ceramic matrix composites imparts them with mechanical toughness, which is essential to avoiding failure. Yet gathering three-dimensional observations of damage evolution in extreme environments has been a challenge. Using synchrotron X-ray computed microtomography, we have fully resolved sequences of microcrack damage as cracks grow under load at temperatures up to 1,750 °C. Our observations are key ingredients for the high-fidelity simulations used to compute failure risks under extreme operating conditions.

Enhanced cell viability via strain stimulus and fluid flow in magnetically actuated scaffolds.

A novel magnetically actuated scaffold was used to explore the effects of strain stimulus on the proliferation and spatial distribution of smooth muscle cells and improve cell viability in the scaffold interior by pumping nutrients throughout the structure. Magnetically actuable scaffolds were fabricated in a tube shape by winding electrospun sheets of a biodegradable polymer modified with magnetic Fe(2)O(3) nanoparticles. Prior to rolling, the sheets were seeded with smooth muscle cells and wound into tubes with diameter 5.2 mm and wall thickness 0.2 mm. The tubular scaffolds were actuated by a magnetic field to induce a cyclic crimping deformation, which applies strain stimulus to the cells and pumps nutrient fluid through the porous tube walls. Comparison with non-actuated controls shows that magnetic actuation increases the total cell count throughout the scaffold after 14 days of incubation. Furthermore, whereas cell density as a function of position through the tube wall thickness showed a minimum in the mid-interior in the controls after 14 days due to cell starvation, the actuated scaffolds displayed a maximum cell density. Comparison of cell distributions with the expected spatial variations in strain amplitude and nutrient flux implies that both strain stimulus and nutrient pumping are significant factors in cell proliferation.

A strain-cue hypothesis for biological network formation.

The direction of migration of a cell invading a host population is assumed to be controlled by the magnitude of the strains in the host medium (cells plus extracellular matrix) that arise as the host medium deforms to accommodate the invader. The single assumption that invaders are cued by strains external to themselves is sufficient to generate network structures. The strain induced by a line of invaders is greatest at the extremity of the line and thus the strain field breaks symmetry, stabilizing branch formation. The strain cue also triggers sprouting from existing branches, with no further model assumption. Network characteristics depend primarily on the ratio of the rate of advance of the invaders to the rate of relaxation of the host cells after their initial deformation. Intra-cell mechanisms that govern these two rates control network morphology. The strain field that cues an individual invader is a collective response of the combined cell populations, involving the nearest 100 cells, to order of magnitude, to any invader. The mechanism does not rely on the pre-existence of the entire host medium prior to invasion; the host cells need only maintain a layer several cells thick around each invader. Consistent with recent experiments, networks result only from a strain cue that is based on strain magnitudes. Spatial strain gradients do not break symmetry and therefore cannot stabilize branch formation. The theory recreates most of the geometrical features of the nervous network in the mouse gut when the most influential adjustable parameter takes a value consistent with one inferred from human and mouse amelogenesis. Because of similarity in the guiding local strain fields, strain cues could also be a participating factor in the formation of vascular networks.

Fracture length scales in human cortical bone: the necessity of nonlinear fracture models.

Recently published data for fracture in human humeral cortical bone are analyzed using cohesive-zone models to deal with the nonlinear processes of material failure. Such models represent the nonlinear deformation processes involved in fracture by cohesive tractions exerted by the failing material along a fracture process zone, rather than attributing all damage to a process occurring at a single point, as in conventional linear-elastic fracture mechanics (LEFM). The relationship between the tractions and the net displacement discontinuity across the process zone is hypothesized to be a material property for bone. To test this hypothesis, the cohesive law was evaluated by analyzing published load vs. load-point displacement data from one laboratory; the calibrated law was then used to predict similar data taken for a different source of bone using a different specimen geometry in a different laboratory. Further model calculations are presented to illustrate more general characteristics of the nonlinear fracture of bone and to demonstrate in particular that LEFM is not internally consistent for all cases of interest. For example, the fracture toughness of bone deduced via LEFM from test data is not necessarily a material constant, but will take different values for different crack lengths and test configurations. LEFM is valid when the crack is much longer than a certain length scale, representative of the length of the process zone in the cohesive model, which for human cortical bone ranges from 3 to 10mm. Since naturally occurring bones and the specimens used to test them are not much larger than this dimension for most relevant orientations, it is apparent that only nonlinear fracture models can give an internally consistent account of their fracture. The cohesive law is thus a more complete representation of the mechanics of material failure than the single-parameter fracture toughness and may therefore provide a superior measure of bone quality. The analysis of fracture data also requires proper representation of the approximately orthotropic elasticity of the bone specimen; if the specimen is incorrectly assumed to be isotropic, the initial measured compliance cannot be reproduced to within a factor of four and the fracture toughness deduced from the measured work of fracture will be overestimated by approximately 30%.