An explicitly multi-component arterial gas embolus dissolves much more slowly than its one-component approximation.

We worked out the growth and dissolution rates of an arterial gas embolism (AGE), to illustrate the evolution over time of its size and composition, and the time required for its total dissolution. We did this for a variety of breathing gases including air, pure oxygen, Nitrox and Heliox (each over a range of oxygen mole fractions), in order to assess how the breathing gas influenced the evolution of the AGE. The calculations were done by numerically integrating the underlying rate equations for explicitly multi-component AGEs, that contained a minimum of three (water, carbon dioxide and oxygen) and a maximum of five components (water, carbon dioxide, oxygen, nitrogen and helium). The rate equations were straight-forward extensions of those for a one-component gas bubble. They were derived by using the Young-Laplace equation and Dalton's law for the pressure in the AGE, the Laplace equation for the dissolved solute concentration gradients in solution, Henry's law for gas solubilities, and Fick's law for diffusion rates across the AGE/arterial blood interface. We found that the 1-component approximation, under which the contents of the AGE are approximated by its dominant component, greatly overestimates the dissolution rate and underestimates the total dissolution time of an AGE. This is because the 1-component approximation manifestly precludes equilibration between the AGE and arterial blood of the inspired volatile solutes (O2, N2, He) in arterial blood. Our calculations uncovered an important practical result, namely that the administration of Heliox, as an adjunct to recompression therapy for treating a suspected N2-rich AGE must be done with care. While Helium is useful for preventing nitrogen narcosis which can arise in aggressive recompression therapy wherein the N2 partial pressure can be quite high (e.g.∼5 atm), it also temporarily expands the AGE, beyond the expansion arising from the use of Oxygen-rich Nitrox. For less aggressive recompression therapy wherein nitrogen narcosis is not a significant concern, Oxygen-rich Nitrox is to be preferred, both because it does not temporarily expand the AGE as much as Heliox, and because it is much cheaper and more conservation-minded.

Laser Spot Detection Based on Reaction Diffusion.

Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.

Thermodynamic stability in elastic systems: Hard spheres embedded in a finite spherical elastic solid.

We determined the total system elastic Helmholtz free energy, under the constraints of constant temperature and volume, for systems comprised of one or more perfectly bonded hard spherical inclusions (i.e. "hard spheres") embedded in a finite spherical elastic solid. Dirichlet boundary conditions were applied both at the surface(s) of the hard spheres, and at the outer surface of the elastic solid. The boundary conditions at the surface of the spheres were used to describe the rigid displacements of the spheres, relative to their initial location(s) in the unstressed initial state. These displacements, together with the initial positions, provided the final shape of the strained elastic solid. The boundary conditions at the outer surface of the elastic medium were used to ensure constancy of the system volume. We determined the strain and stress tensors numerically, using a method that combines the Neuber-Papkovich spherical harmonic decomposition, the Schwartz alternating method, and Least-squares for determining the spherical harmonic expansion coefficients. The total system elastic Helmholtz free energy was determined by numerically integrating the elastic Helmholtz free energy density over the volume of the elastic solid, either by a quadrature, or a Monte Carlo method, or both. Depending on the initial position of the hard sphere(s) (or equivalently, the shape of the un-deformed stress-free elastic solid), and the displacements, either stationary or non-stationary Helmholtz free energy minima were found. The non-stationary minima, which involved the hard spheres nearly in contact with one another, corresponded to lower Helmholtz free energies, than did the stationary minima, for which the hard spheres were further away from one another.

Decompression sickness in breath-hold diving, and its probable connection to the growth and dissolution of small arterial gas emboli.

We solved the Laplace equation for the radius of an arterial gas embolism (AGE), during and after breath-hold diving. We used a simple three-region diffusion model for the AGE, and applied our results to two types of breath-hold dives: single, very deep competitive-level dives and repetitive shallower breath-hold dives similar to those carried out by indigenous commercial pearl divers in the South Pacific. Because of the effect of surface tension, AGEs tend to dissolve in arterial blood when arteries remote from supersaturated tissue. However if, before fully dissolving, they reach the capillary beds that perfuse the brain and the inner ear, they may become inflated with inert gas that is transferred into them from these contiguous temporarily supersaturated tissues. By using simple kinetic models of cerebral and inner ear tissue, the nitrogen tissue partial pressures during and after the dive(s) were determined. These were used to theoretically calculate AGE growth and dissolution curves for AGEs lodged in capillaries of the brain and inner ear. From these curves it was found that both cerebral and inner ear decompression sickness are expected to occur occasionally in single competitive-level dives. It was also determined from these curves that for the commercial repetitive dives considered, the duration of the surface interval (the time interval separating individual repetitive dives from one another) was a key determinant, as to whether inner ear and/or cerebral decompression sickness arose. Our predictions both for single competitive-level and repetitive commercial breath-hold diving were consistent with what is known about the incidence of cerebral and inner ear decompression sickness in these forms of diving.

Gas bubble dynamics in soft materials.

Epstein and Plesset's seminal work on the rate of gas bubble dissolution and growth in a simple liquid is generalized to render it applicable to a gas bubble embedded in a soft elastic solid. Both the underlying diffusion equation and the expression for the gas bubble pressure were modified to allow for the non-zero shear modulus of the medium. The extension of the diffusion equation results in a trivial shift (by an additive constant) in the value of the diffusion coefficient, and does not change the form of the rate equations. But the use of a generalized Young-Laplace equation for the bubble pressure resulted in significant differences on the dynamics of bubble dissolution and growth, relative to an inviscid liquid medium. Depending on whether the salient parameters (solute concentration, initial bubble radius, surface tension, and shear modulus) lead to bubble growth or dissolution, the effect of allowing for a non-zero shear modulus in the generalized Young-Laplace equation is to speed up the rate of bubble growth, or to reduce the rate of bubble dissolution, respectively. The relation to previous work on visco-elastic materials is discussed, as is the connection of this work to the problem of Decompression Sickness (specifically, "the bends"). Examples of tissues to which our expressions can be applied are provided. Also, a new phenomenon is predicted whereby, for some parameter values, a bubble can be metastable and persist for long times, or it may grow, when embedded in a homogeneous under-saturated soft elastic medium.

The lifetimes of small arterial gas emboli, and their possible connection to Inner Ear Decompression Sickness.

We solved both the Diffusion and Laplace equations which predicted very similar results for the problem of a dissolving small gas bubble suspended in a liquid medium. These bubbles dissolved both because of surface tension and solute concentration effects. We focused on predicting bubble lifetimes ("td"), and dissolution dynamics - radius vs time (R vs t) for these contracting bubbles. We also presented a direct comparison of the predicted results, obtained by applying either Dirichlet or Neumann boundary conditions, to the bubble/medium interface. To the best of our knowledge, this is the first direct comparison that has ever been published on the application of these different boundary conditions to a moving gas/liquid boundary. We found that the results obtained by applying either Dirichlet or Neumann boundary conditions were very similar for small, short-lived bubbles (R0<25 µ,td<40s), but diverged considerably for larger, longer-lived bubbles. We applied our expressions to the timely problem of Inner Ear Decompression Sickness, where we found that our predictions were consistent with much of what is known about this condition.

Flow-mediated coupling on projectiles falling within a superlight granular medium.

Interesting collective motion emerges when several heavy intruder disks fall in a loose packed, quasi-two-dimensional granular bed of extremely light grains [F. Pacheco-Vázquez and J. C. Ruiz-Suárez, Nat. Commun. 1, 123 (2010)]. In particular, when two disks impact side by side, they initially repel and then they attract each other until they finally stop. Here we perform experiments and discrete-element soft-particle simulations to determine the range of action and the origin of these attractive and repulsive flow-mediated forces. We find that (1) the drag force on the disks fluctuate with a characteristic length linked to force chains that build up and break; (2) the repulsive force is present when the separation of the intruder disks is less than 6 times the size of the grains of the granular bed, which is the size of an aperture that allows a continuous discharge flow from a container; (3) the attractive force has a range of action between 5 and 6 times the size of the intruder disks; and (4) attraction exists only when intruders move faster than 1 m/s. These results suggest that repulsion originates from jamming of grains between intruders, and it supports the idea that attraction could be due to a "granular pressure" drop in the region between intruders caused by a high flow velocity of grains: a Bernoulli-like effect. However, our results do not rule out other mechanisms of interaction, like fluctuation-induced forces.

Infinite penetration of a projectile into a granular medium.

An object falling in a fluid reaches a terminal velocity when the drag force and its weight are balanced. Contrastingly, an object impacting into a granular medium rapidly dissipates all its energy and comes to rest always at a shallow depth. Here we study, experimentally and theoretically, the penetration dynamics of a projectile in a very long silo filled with expanded polystyrene particles. We discovered that, above a critical mass, the projectile reaches a terminal velocity and, therefore, an endless penetration.