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We analyze a nonlinear integral equation for calculating free‐surface divergence that was proposed by Szeri (2017, https://doi.org/10.1002/2016JC012312). When given the temperature and heat flux at a free surface, the surface divergence can be calculated through a nonlinear singular Volterra‐type integral equation. The two given functions in the integral equation satisfy auxiliary conditions through a higher dimensional partial differential equation. We prove the existence and uniqueness of the solution of the integral equation. We also prove the local linear convergence of the corresponding Picard iteration method for solving the integral equation when the surface heat flux is a real‐analytic function of time. The rate of convergence is derived explicitly, which depends on the function of surface heat flux. Numerical examples are provided to validate the convergence performance. [ABSTRACT FROM AUTHOR]

To shed light on how acute exercise affects blood glucose (BG) concentrations in nondiabetic subjects, we develop a physiological pharmacokinetic/pharmacodynamic model of postprandial glucose dynamics during exercise. We unify several concepts of exercise physiology to derive a multiscale model that includes three important effects of exercise on glucose dynamics: increased endogenous glucose production (EGP), increased glucose uptake in skeletal muscle (SM), and increased glucose delivery to SM by capillary recruitment (i.e. an increase in surface area and blood flow in capillary beds). We compare simulations to experimental observations taken in two cohorts of healthy nondiabetic subjects (resting subjects (n = 12) and exercising subjects (n = 12)) who were each given a mixed-meal tolerance test. Metabolic tracers were used to quantify the glucose flux. Simulations reasonably agree with postprandial measurements of BG concentration and EGP during exercise. Exercise-induced capillary recruitment is predicted to increase glucose transport to SM by 100%, causing hypoglycemia. When recruitment is blunted, as in those with capillary dysfunction, the opposite occurs and higher than expected BG levels are predicted. Model simulations show how three important exercise-induced phenomena interact, impacting BG concentrations. This model describes nondiabetic subjects, but it is a first step to a model that describes glucose dynamics during exercise in those with type 1 diabetes (T1D). Clinicians and engineers can use the insights gained from the model simulations to better understand the connection between exercise and glucose dynamics and ultimately help patients with T1D make more informed insulin dosing decisions around exercise. [ABSTRACT FROM AUTHOR]

Our objective is to develop a physiology-based model of insulin kinetics to understand how exercise alters insulin concentrations in those with type 1 diabetes (T1D). We reveal the relationship between the insulin absorption rate (kaI) from subcutaneous tissue, the insulin delivery rate (kdI) to skeletal muscle, and two physiological parameters that characterize the tissue: the perfusion rate (Q) and the capillary permeability surface area (PS), both of which increase during exercise because of capillary recruitment. We compare model predictions to experimental observations from two pump-wearing T1D cohorts [resting subjects (n=17) and exercising subjects (n=12)] who were each given a mixed-meal tolerance test and a bolus of insulin. Using independently measured values of Q and PS from literature, the model predicts that during exercise insulin concentration increases by 30% in plasma and by 60% in skeletal muscle. Predictions reasonably agree with experimental observations from the two cohorts, without the need for parameter estimation by curve fitting. The insulin kinetics model suggests that the increase in surface area associated with exercise-induced capillary recruitment significantly increases kaI and kdI, which explains why insulin concentrations in plasma and skeletal muscle increase during exercise, ultimately enhancing insulin-dependent glucose uptake. Preventing hypoglycemia is of paramount importance in determining the proper insulin dose during exercise. The presented model provides mechanistic insight into how exercise affects insulin kinetics, which could be useful in guiding the design of decision support systems and artificial pancreas control algorithms. [ABSTRACT FROM AUTHOR]

The electroencephalogram (EEG) during the re-establishment of consciousness after general anesthesia and surgery varies starkly between patients. Can the EEG during this emergence period provide a means of estimating the underlying biological processes underpinning the return of consciousness? Can we use a model to infer these biological processes from the EEG patterns? A frontal EEG was recorded from 84 patients. Ten patients were chosen for state-space analysis. Five showed archetypal emergences; which consisted of a progressive decrease in alpha power and increase peak alpha frequency before return of responsiveness. The five non-archetypal emergences showed almost no spectral EEG changes (even as the volatile general anesthetic decreased) and then an abrupt return of responsiveness. We used Bayesian methods to estimate the likelihood of an EEG pattern corresponding to the position of the patient on a 2-dimensional manifold in a state space of excitatory connection strength vs. change in intrinsic resting neuronal membrane conductivity.We could thus visualize the trajectory of each patient in the state-space during their emergence period. The patients who followed an archetypal emergence displayed a very consistent pattern; consisting of progressive increase in conductivity, and a temporary period of increased connection strength before return of responsiveness. The non-archetypal emergence trajectories remained fixed in a region of phase space characterized by a relatively high conductivity and low connection strength throughout emergence. This unexpected progressive increase in conductivity during archetypal emergence may be due to an abating of the surgical stimulus during this period. Periods of high connection strength could represent forays into dissociated consciousness, but the model suggests all patients reposition near the fold in the state space to take advantage of bi-stable cortical dynamics before transitioning to consciousness. [ABSTRACT FROM AUTHOR]

A correction to this paper has been published: https://doi.org/10.1007/s10928-021-09766-9 [ABSTRACT FROM AUTHOR]

Recent studies have shown that high intensity focused ultrasound (HIFU) accelerates thrombolysis for ischemic stroke. Although the mechanisms are not fully understood, cavitation is thought to play an important role. The goal of this paper is to investigate the potential for cavitation to cause mechanical damage to a blood clot. The amount of damage to the fiber network caused by a single bubble expansion and collapse is estimated by two independent approaches: One based on the stretch of individual fibers and the other based on the energy available to break individual fibers. The two methods yield consistent results. The energy method is extended to the more important scenario of a bubble outside a blood clot that collapses asymmetrically creating an impinging jet. This leads to significantly more damage compared to a bubble embedded within the clot structure. Finally, as an example of how one can apply the theory, a simulation of the propagation of HIFU waves through model calvaria of varying density is explored. The maximum amount of energy available to cause damage to a blood clot increases as the density of the calvaria decreases. [ABSTRACT FROM AUTHOR]

An adaptive controller design is proposed and simulated for parameter identification and oscillation control in microbubble systems. Lyapunov's direct method and a Lyapunov-like analysis are used to show stability and convergence of trajectory tracking and parameter adaptation. The method allows for the determination of microbubble contrast agent shell thickness or material parameters in a nondestructive manner. [ABSTRACT FROM AUTHOR]

A recent study in South Africa has confirmed, for the first time, that a vaginal gel formulation of the antiretroviral drug Tenofovir, when topically applied, significantly inhibits sexual HIV transmission to women [Karim et al., Science 329, 1168 (2010)]. However, the gel for this drug and anti-HIV microbicide gels in general have not been designed using an understanding of how gel spreading and retention in the vagina govern successful drug delivery. Elastohydrodynamic lubrication theory can be applied to model spreading of microbicide gels [Szeri et al., Phys. Fluids 20, 083101 (2008)]. This should incorporate the full rheological behavior of a gel, including how rheological properties change due to contact with, and dilution by, ambient vaginal fluids. Here, we extend our initial analysis, incorporating the effects of gel dilution due to contact with vaginal fluid produced at the gel-tissue interface. Our original model is supplemented with a convective-diffusive transport equation to characterize water transport into the gel and, thus, local gel dilution. The problem is solved using a multi-step scheme in a moving domain. The association between local dilution of gel and rheological properties is obtained experimentally, delineating the way constitutive parameters of a shear-thinning gel are modified by dilution. Results show that dilution accelerates the coating flow by creating a slippery region near the vaginal wall akin to a dilution boundary layer, especially if the boundary flux exceeds a certain value. On the other hand, if the diffusion coefficient of boundary fluid is increased, the slippery region diminishes in extent and the overall rate of gel spreading decreases. [ABSTRACT FROM AUTHOR]

Background: Microbicide candidates delivered via gel vehicles are intended to coat the vaginal epithelium after application. The coating process depends on intrinsic biophysical properties of the gel texture, which restricts the potential choices for an effective product: the gel first must be physically synthesizable, then acceptable to the user, and finally applied in a manner promoting timely adequate coating, so that the user adherence is optimized. We present a conceptual framework anchoring microbicide behavioral acceptability within the fulfillment of the product biophysical requirements. Methods: We conducted a semi-qualitative/quantitative study targeting women aged 18-55 in Northern California to assess user preferences for microbicide gel attributes. Attributes included: (i) the wait time between application and intercourse, (ii) the gel texture and (iii) the trade-off between wait time and gel texture. Wait times were assessed using a mathematical model determining coating rates depending upon the gel's physical attributes. Results: 71 women participated. Results suggest that women would independently prefer a gel spreading rapidly, in 2 to 15 minutes (P<0.0001), as well as one that is thick or slippery (P<0.02). Clearly, thick gels do not spread rapidly; hence the motivation to study the trade-off. When asked the same question 'constrained' by the biophysical reality, women indicated no significant preference for a particular gel thickness (and therefore waiting time) (P>0.10) for use with a steady partner, a preference for a watery gel spreading rapidly rather than one having intermediate properties for use with a casual partner (P = 0.024). Conclusions: Biophysical constraints alter women's preferences regarding acceptable microbicide attributes. Product developers should offer a range of formulations in order to address all preferences. We designed a conceptual framework to rethink behavioral acceptability in terms of biophysical requirements that can help improve adherence in microbicide use ultimately enhancing microbicide effectiveness. [ABSTRACT FROM AUTHOR]

The impact and spreading of a compound viscous droplet on a flat surface are studied computationally using a front-tracking method as a model for the single cell epitaxy. This is a technology developed to create two-dimensional and three-dimensional tissue constructs cell by cell by printing cell-encapsulating droplets precisely on a substrate using an existing ink-jet printing method. The success of cell printing mainly depends on the cell viability during the printing process, which requires a deeper understanding of the impact dynamics of encapsulated cells onto a solid surface. The present study is a first step in developing a model for deposition of cell-encapsulating droplets. The inner droplet representing the cell, the encapsulating droplet, and the ambient fluid are all assumed to be Newtonian. Simulations are performed for a range of dimensionless parameters to probe the deformation and rate of deformation of the encapsulated cell, which are both hypothesized to be related to cell damage. The deformation of the inner droplet consistently increases: as the Reynolds number increases; as the diameter ratio of the encapsulating droplet to the cell decreases; as the ratio of surface tensions of the air-solution interface to the solution-cell interface increases; as the viscosity ratio of the cell to encapsulating droplet decreases; or as the equilibrium contact angle decreases. It is observed that maximum deformation for a range of Weber numbers has (at least) one local minimum at We=2. Thereafter, the effects of cell deformation on viability are estimated by employing a correlation based on the experimental data of compression of cells between parallel plates. These results provide insight into achieving optimal parameter ranges for maximal cell viability during cell printing. [ABSTRACT FROM AUTHOR]

Experimental work on mixing in microfluidic devices has been of growing importance in recent years. Interest in probing reaction kinetics faster than the minute or hour time scale has intensified research in designing microchannel devices that would allow the reactants to be mixed on a time scale faster than that of the reaction. Particular attention has been paid to the design of microchannels in order to enhance the advection phenomena in these devices. Ultimately, in vitro studies of biological reactions can now be performed in conditions that reflect their native intracellular environments. Liau et al. (Anal. Chem., vol. 77, 2005, p. 7618) have demonstrated a droplet-based microfluidic mixer that induces improved chaotic mixing of crowded solutions in milliseconds due to protrusions ('bumps') on the microchannel walls. Liau et al. (2005) have shown it to be possible to mix rapidly plugs of highly concentrated protein solutions such as bovine hemoglobin and bovine serum albumin. The present work concerns an analysis of the underlying mechanisms of shear stress transfer at liquid-liquid interfaces and associated enhanced mixing arising from the protrusions along the channel walls. The role of non-Newtonian rheology and surfactants is also considered within the mixing framework developed by Aref, Ottino and Wiggins in several publications. Specifically, we show that proportional thinning of the carrier fluid lubrication layer at the bumps leads to greater advection velocities within the plugs, which enhances mixing. When the fluid within the plugs is Newtonian, mixing will be enhanced by the bumps if they are sufficiently close to one another. Changing either the rheology of the fluid within the plugs (from Newtonian to non-Newtonian) or modifying the mechanics of the carrier fluid-plug interface (by populating it with insoluble surfactants) alters the mixing enhancement. [ABSTRACT FROM AUTHOR]

Here we present several refinements to a model of feedback control for the suppression of epileptic seizures. We utilize a stochastic partial differential equation (SPDE) model of the human cortex. First, we verify the strong convergence of numerical solutions to this model, paying special attention to the sharp spatial changes that occur at electrode edges. This allows us to choose appropriate step sizes for our simulations; because the spatial step size must be small relative to the size of an electrode in order to resolve its electrical behavior, we are able to include a more detailed electrode profile in the simulation. Then, based on evidence that the mean soma potential is not the variable most closely related to the measurement of a cortical surface electrode, we develop a new model for this. The model is based on the currents flowing in the cortex and is used for a simulation of feedback control. The simulation utilizes a new control algorithm incorporating the total integral of the applied electrical potential. Not only does this succeed in suppressing the seizure-like oscillations, but it guarantees that the applied signal will be charge-balanced and therefore unlikely to cause cortical damage. [ABSTRACT FROM AUTHOR]

Currently, commercial ion traps used for mass spectrometry are controlled in an open-loop manner with sinusoidally varying inputs. In this paper, we discuss the possible advantages of adding nonlinear feedback control to this system and demonstrate them through numerical simulations. Using sliding-mode control, we find that we can have a particle fall onto a trapping surface of our choosing, despite, the presence of uncertainty in the system. In addition, when used in an open-loop fashion, the sliding-mode input creates stable attractors in the phase space. This shows that nonsinusoidal periodic inputs can effectively trap a group of particles. When an adaptive component is added to the closed-loop sliding-mode controller, we see that a simulated particle of unknown mass and charge can be successfully trapped and driven onto a desired surface. In addition, if that trajectory satisfies the persistent-excitation condition, then the controller can attain perfect estimation of the unknown parameters, thus measuring the particle mass and charge without ejecting it from the trap. These simulation results suggest a number of interesting experiments. [ABSTRACT FROM AUTHOR]

Nested invariant 3-tori surrounding a torus braid of elliptic type are found to exist in a model of a fluid flow with quasiperiodic forcing. The Hamiltonian describing the system is given by the superposition of two steady stream functions, one with an elliptic fixed point and the other with a coincident hyperbolic fixed point. The superposition, modulated by two incommensurate frequencies, yields an elliptic torus braid at the location of the fixed point. The system is suspended in a four-dimensional phase space (two space and two phase directions). To analyze this system we define two three-dimensional, global, Poincaré sections of the flow. The coherent structures (cross-sections of nested 2 tori) are found each to have a fractal dimensional of two, in each Poincaré cross-section. This framework has applications to tidal and other mixing problems of geophysical interest. [ABSTRACT FROM AUTHOR]

In [Spears et al., 2005] it was demonstrated that insight into the geometry and topology of attractors for nonlinear oscillators driven by n incommensurate frequencies may be obtained from the study of n Poincaré maps defined on global cross-sections. The attractors take the form of stable torus braids. Here, attention is focused on saddle-type torus braids in similar systems. Transverse intersections of stable and unstable manifolds are computed using the phase slice method, along with the application of the crossover map. This neatly maps from one global Poincaré section to another. As such, it can be used to compute lobe intersection geometries in the remaining n - 1 Poincaré sections after doing so by the phase slice method in the first. [ABSTRACT FROM AUTHOR]

Elastohydrodynamic lubrication over soft substrates is of importance in a number of biomedical problems: From lubrication of the eye surface by the tear film, to lubrication of joints by synovial fluid, to lubrication between the pleural surfaces that protect the lungs and other organs. Such flows are also important for the drug delivery functions of vehicles for anti-HIV topical microbicides. These are intended to inhibit transmission into vulnerable mucosa, e.g., in the vagina. First generation prototype microbicides have gel vehicles, which spread after insertion and coat luminal surfaces. Effectiveness derives from potency of the active ingredients and completeness and durability of coating. Delivery vehicle rheology, luminal biomechanical properties, and the force due to gravity influence the coating mechanics. We develop a framework for understanding the relative importance of boundary squeezing and body forces on the extent and speed of the coating that results. A single dimensionless number, independent of viscosity, characterizes the relative influences of squeezing and gravitational acceleration on the shape of spreading in the Newtonian case. A second scale, involving viscosity, determines the spreading rate. In the case of a shear-thinning fluid, the Carreau number also plays a role. Numerical solutions were developed for a range of the dimensionless parameter and compared well with asymptotic theory in the limited case where such results can be obtained. Results were interpreted with respect to trade-offs between wall elasticity, longitudinal forces, bolus viscosity, and bolus volume. These provide initial insights of practical value for formulators of gel delivery vehicles for anti-HIV microbicidal formulations. [ABSTRACT FROM AUTHOR]

The problem of a single acoustically driven bubble translating unsteadily in a fluid is considered. The investigation of the translation equation identifies the inverse Reynolds number as a small perturbation parameter. The objective is to obtain a closed-form, leading order solution for the translation of the bubble, assuming nonlinear radial oscillations and a pressure field as the forcing term. In a second part, the periodic attractor of the Rayleigh–Plesset equation serves as basis for an optimal acoustic forcing designed to achieve maximized bubble translation over one dimensionless period. At near-resonant or super-resonant driving frequencies, it seems one cannot improve much on sinusoidal forcing. However at moderate acoustic intensity and sub-resonant frequencies, acoustic wave forms that enhance bubble collapse lead to displacement many times larger than the case of purely sinusoidal forcing. The survey covers a wide spectrum of driving ratios and bubble diameters including those relevant to biomedical applications. Shape stability issues are considered. Together, these results suggest new ways to predict some of the direct and indirect effects of the acoustic radiation force in applications such as targeted drug delivery, selective bubble driving, and accumulation. [ABSTRACT FROM AUTHOR]

The light emission from a converging shock wave was investigated experimentally. Results show that the shape of the shock wave close to the center of convergence has a large influence on the amount of emitted light. It was found that a symmetrical polygonal shock front produced more light than an asymmetrical shape. The light emission appears as the shock wave collapses. The full width at half maximum of the light pulse is about 200 ns for all geometrical shapes. It was also found that argon as a test gas produces more light than air. Numerical simulations showed good agreement with experimental results regarding the shape of the shock and the flow field behind the shock. The temperature field from the numerical simulations was investigated and shows that the triple points behind the shock front are hot spots that increase the temperature at the center as they arrive there. [ABSTRACT FROM AUTHOR]

A method to characterize shock wave lithotripters by examining the potential for cavitation associated with the lithotripter shock wave (LSW) has been developed. The method uses the maximum radius achieved by a bubble subjected to a LSW as a representation of the cavitation potential for that region in the lithotripter. It is found that the maximum radius is determined by the work done on a bubble by the LSW. The method is used to characterize two reflectors: an ellipsoidal reflector and an ellipsoidal reflector with an insert. The results show that the use of an insert reduced the -6 dB volume (with respect to peak positive pressure) from 1.6 to 0.4 cm3, the -6 dB volume (with respect to peak negative pressure) from 14.5 to 8.3 cm3, and reduced the volume characterized by high cavitation potential (i.e., regions characterized by bubbles with radii larger than 429 μm) from 103 to 26 cm3. Thus, the insert is an effective way to localize the potentially damaging effects of shock wave lithotripsy, and suggests an approach to optimize the shape of the reflector. [ABSTRACT FROM AUTHOR]

Three synchronization measures are applied to scalp electroencephalogram (EEG) data collected from 20 patients diagnosed to have either: (1) no dementia, (2) mild cognitive impairment (MCI), or (3) Alzheimer's disease (AD). We apply the three synchronization measures — the phase synchronization, and two measures of nonlinear interdependency — to the data collected from awake patients resting with eyes closed. We show that the synchronization in potential between electrodes near the left and right occipital lobes provides a statistically significant discriminant between the healthy and AD subjects, and the MCI and AD subjects. None of the three measures appears able to distinguish between the healthy and MCI subjects, although MCI subjects show synchronization values intermediate between healthy subjects (with high synchronization values) and AD subjects (with low synchronization values) on average. [ABSTRACT FROM AUTHOR]

Acoustically driven bubbles can develop shape instabilities and, if forced sufficiently strongly, distort greatly and break up. Perturbation theory provides some insight as to how these nonspherical shape modes grow initially but loses validity for large deformations. To validate the perturbation theory, we use a numerical model based on the boundary integral method capable of simulating nonspherical, axisymmetric bubbles subject to acoustic driving. The results show that the perturbation theory compares well with numerical simulations in predicting bubble breakup and stability. Thereafter, we compare the peak temperatures and pressures of spherical to nonspherical bubble collapses by forcing them with standing waves and traveling waves, respectively. This comparison is made in parameter ranges of relevance to both single bubble sonoluminescence and multibubble sonoluminescence and sonochemistry. At moderate forcing, spherical and nonspherical collapses achieve similar peak temperatures and pressures but, as the forcing is increased, spherical collapses become much more intense. The reduced temperature of nonspherical collapses at high forcing is due to residual kinetic energy of a liquid jet that pierces the bubble near the time of minimum volume. This is clarified by a calculation of the (gas) thermal equivalent of this liquid kinetic energy. [ABSTRACT FROM AUTHOR]

A microbubble in a sound wave oscillates in volume and translates unsteadily. The two motions are coupled. In large-scale simulations of the structure of bubble clouds driven by acoustic fields, it has been of significant convenience to decouple volume oscillations and translation, as an approximation. The errors of this decoupling approximation were considered in an earlier presentation [A. J. Reddy and A. J. Szeri, J. Acoust. Soc. Am. 112, 1346–1352 (2002)], in the parameter range of interest in medical ultrasound. In this work, the approximation is reexamined for a much broader range of driving frequencies and bubble sizes. Solving the equation of motion for linearly oscillating bubbles, it is found that even for weak acoustic forcing, the translation speed obtained with the decoupling approximation can be in error as much as 30% relative to the translation speed in the full equations. The error depends on the bubble size, the driving frequency, and the liquid properties. The results are presented in a form convenient for applications. The principal utility of the analysis is for bubbles in microgravity, or in normal gravity driven by a soundfield with a horizontal wave-number vector. [ABSTRACT FROM AUTHOR]

We consider a sequence of topological torus bifurcations (TTBs) in a nonlinear, quasiperiodic Mathieu equation. The sequence of TTBs and an ensuing transition to chaos are observed by computing the principal Lyapunov exponent over a range of the bifurcation parameter. We also consider the effect of the sequence on the power spectrum before and after the transition to chaos. We then describe the topology of the set of knotted tori that are present before the transition to chaos. Following the transition, solutions evolve on strange attractors that have the topology of fractal braids in Poincaré sections. We examine the topology of fractal braids and the dynamics of solutions that evolve on them. We end with a brief discussion of the number of TTBs in the cascade that leads to chaos. [ABSTRACT FROM AUTHOR]

A quantitative approximation of the conical surface potential from measured scalp surface potential data is developed. The derivation is based on a local Taylor series expansion (TSE) in the surface normal coordinate. Analytical and numerical results for the four shell spherical head model show that the TSE method improves the spatial deblurring of the surface Laplacian method. The inclusion of the biharmonic term, the extension to other geometries, and the application to electrocorticogram measurements are discussed. [ABSTRACT FROM AUTHOR]

A model is developed for the response of a micromachined, rotary gyroscope subject to a general input motion. The governing equations are formulated for weakly nonlinear oscillations of the rotor, suspended above the moving substrate via elastic beams. The method of multiple scales is used to separate the slow and fast responses. This approach allows quick computation of the long-term behavior of the rotor without the need to integrate over fast oscillations. The power of the model to evince cross-coupling errors is demonstrated through examples. [ABSTRACT FROM AUTHOR]

The very high speed of collapse of cavitation bubbles is responsible for a number of phenomena of interest in science and engineering: Luminescence, sonochemistry, cavitation damage, ultrasonic cleaning, etc. Strongly forced bubbles may collapse with such violence that the relatively slow processes of diffusion of the heat of compression and of excess vapor to the bubble wall are obviated. This leads to an approximately adiabatic system with nearly constant mass during the final stages of extreme collapses, accompanied by the evolution of sharp thermal and compositional boundary layers on either side of the interface. It is shown that the boundary layers, which are involved in the determination of the interfacial temperature through the balance of sensible and latent heats, may profitably be described mathematically through integral equations. This complements well the boundary integral solution of the fluid dynamics, which has been the basis of much progress in the field. [ABSTRACT FROM AUTHOR]

The second harmonic radiation of acoustically driven bubbles is a useful discriminant for their presence in clinical ultrasound applications. It is useful because the scatter from a bubble at a frequency different from the driving can have a contrast-to-tissue ratio better than at the drive frequency. In this work a technique is developed to optimize the scattering from a microbubble at a frequency different from the driving. This is accomplished by adjusting the relative phase and amplitudes of the components of a dual-frequency incident ultrasound wave form. The investigation is focused primarily on the example of dual-mode driving at frequencies of 1 MHz and 3 MHz, with the scattering optimized at 2 MHz. Bubble radii of primary interest are 0.5 to 2 µm and driving amplitudes to 0.5 atm. Bubbles in this size range are sensitive to modulation of driving. It is shown that an optimal forcing scheme can increase the target response eightfold or more. This suggests new applications in imaging and in bubble detection. [ABSTRACT FROM AUTHOR]

Pressure gradients drive the motion of microbubbles relative to liquids in which they are suspended. Examples include the hydrostatic pressure due to a gravitational field, and the pressure gradients in a sound field, useful for acoustic levitation. In this paper, the equations describing the coupled dynamics of radial oscillation and translation of a microbubble are given. The formulation is based on a recently derived expression for the hydrodynamic force on a bubble of changing size in an incompressible liquid [J. Magnaudet and D. Legendre, Phys. Fluids 10, 550-556 (1998)]. The complex interaction between radial and translation dynamics is best understood by examination of the added momentum associated with the liquid motion caused by the moving bubble. Translation is maximized when the bubble collapses violently. The new theory for coupled collapse and translation dynamics is compared to past experiments and to previous theories for decoupled translation dynamics. Special attention is paid to bubbles of relevance in biomedical applications. © 2002 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

In a classical paper Plesset has determined conditions under which a bubble changing in volume maintains a spherical shape. The stability analysis was further developed by Prosperetti to include the effects of liquid viscosity on the evolving shape modes. In the present work the theory is further modified to include the changing density of the bubble contents. The latter is found to be important in violent collapses where the densities of the gas and vapor within a bubble may approach densities of the liquid outside. This exerts a stabilizing influence on the Rayleigh-Taylor mechanism of shape instability of spherical bubbles. A comparison with experimental data shows good agreement with the new theory; the Rayleigh-Taylor instability does provide an extinction threshold for violently collapsing bubbles. It is also explained why earlier works did not produce a slope in the RayleighTaylor stability curve that conforms with that of the present work. [ABSTRACT FROM AUTHOR]

In this paper the problem of shape stability is considered, for a bubble with time-dependent radius, translating unsteadily in a flow. This situation can be brought about, for example, by forcing with an acoustic traveling wave. The equation governing translation was derived in a previous work [Reddy and Szeri (unpublished)]. Here, the equations governing the amplitudes of shape modes are derived using domain perturbation theory, following a classical paper by Plesset. Contrary perhaps to intuition, results show that driving at the natural frequency of volume oscillations is not necessarily the ideal forcing to engender a shape instability. Moreover, severe radial oscillations can have a stabilizing effect on shape oscillations. The results suggest the possibility of destroying bubbles selectively by size. [ABSTRACT FROM AUTHOR]

Direct measurements of individual bubble oscillations in lithotripsy fields have been performed using light-scattering techniques. Studies were performed with bubble clouds in gassy water as well as single levitated bubbles in degassed water. There is direct evidence that the bubble survives the inertial collapse, rebounding several times before breaking up. Bubble dynamics calculations agree well with the observations, provided that vapor trapping (a reduction in condensation during bubble collapse) is included. Furthermore, the afterbounces are dominated by vapor diffusion, not gas diffusion. Vapor trapping is important in limiting the collapse strength of bubbles, and in sonochemical activity. [ABSTRACT FROM AUTHOR]

Recently developed techniques of Wiggins [SIAM J. Appl. Math. 48, 262 (1988)] are used to study the onset of chaotic oscillations and explosive growth of a spherical bubble in an otherwise quiescent, incompressible fluid. It is shown that bubbles forced with a quasiperiodic background pressure can respond chaotically and grow explosively at lower amplitudes of the primary component of the forcing than bubbles forced with a single frequency. The means of extension of these results to an arbitrary, but finite, number of forcing frequencies is presented. [ABSTRACT FROM AUTHOR]

Considers the formation of spherically symmetric shocks converging on the center of a spherical bubble driven by a strong acoustic field. Role of the shocks in producing rapid compression and heating that give rise to brief flash of light known as sonoluminescence; Launching of an inwardly-traveling compression wave.

Explores the dynamical behavior of suspensions of rod-like particles in unsteady elementary flows. Orientational distribution of a Brownian suspension in a closed flow; Protocols that are most effective at achieving various degrees of anisotropy of the suspension within the class of flows under consideration.

Features a model for the gas dynamics within a bubble at conditions that lead to the phenomenon of sonoluminescence. Navier-Stokes equations with variable properties; Momentum and energy equations in the liquid; Calculations for bubbles of argon, helium, and xenon in liquid water.

An explanation is provided for the influence of relatively small changes in liquid temperature on the hot spot within a sonoluminescence bubble. This influence derives from a change in the (stable) equilibrium mass of the bubble due to a variation of the gas solubility in the liquid with temperature. If the acoustic drive amplitude is held constant, a change in the liquid temperature has a large or small effect depending on the variability of the solubility with temperature. For a gas like xenon, which has rapidly decreasing solubility in water with increasing temperature, a decrease in water temperature shifts the stable mass exchange equilibrium to a smaller bubble size. This increases the ratio of maximum to minimum bubble radius over an acoustic cycle, resulting in a much higher hot spot temperature. In contrast helium has very little variation of solubility with temperature near room temperature; therefore the hot spot temperature is relatively insensitive to variations in the liquid temperature outside a helium bubble. © 1998 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

An abstract of the article "Interpretation of seizure evolution pathways via a mean-field cortical model," by Vera M. Dadok, Andrew J. Szeri, Heidi Kirsch, Jamie Sleigh, and Beth Lopour is presented.

Introduction There is a complex relationship between sleep and the onset of epileptic seizures. Current methods of sleep scoring divide data into discrete stages, but a continuous model may provide more insight into this phenomenon. This would not only allow a more detailed analysis of the sleep leading up to the seizure, but it would give us greater predictive power regarding impending transitions. Continuous models of the human sleep cycle already exist; however, it is very difficult to connect these models to actual EEG sleep data. Here we present a possible solution to this problem using a technique called locally linear embedding (LLE). Method LLE is a method for discovering the structure of highdimensional data by projecting it to a lower-dimensional manifold. It accomplishes this by characterizing the local structure around each data point (based on its "nearest neighbors") and then computing a nonlinear re-mapping of the data that optimally preserves that local structure. Here we apply the LLE algorithm to both human EEG data recorded during sleep and simulated EEG data from a continuous mathematical model of the sleep cycle. The data starts in a 7-dimensional feature space based on power in three frequency bands and several statistical measures; we then project each one into a 2-D space and compare the resulting structures. Results First, we look at the result of running the LLE algorithm on sleep EEG data gathered from epileptic patients undergoing surgical evaluation at the UC San Francisco Epilepsy Center. The projection into 2-D space reveals three overlapping lines, each one associated with different EEG characteristics. Next, we examine the effect of applying LLE to data generated by a mathematical model of the sleep cycle. Again, we see distinct clusters of points based on the properties of the input data. The two sets of LLE results can then be directly compared; this allows us to take an EEG data point and find its analogous point in the projection of the simulated data, thereby determining its position in the sleep cycle. Summary These results represent the first steps toward connecting EEG sleep data to a continuous mathematical model of the human sleep cycle. This type of analysis not only provides a more detailed picture of sleep stages and the transitions between them, but it may also have implications for the prediction of epileptic seizures. [ABSTRACT FROM AUTHOR]

There is a widespread agreement that more effective drug delivery vehicles with more alternatives, as well as better active pharmaceutical ingredients (APIs), must be developed to improve the efficacy of microbicide products. For instance, in tropical regions, films are more appropriate than gels due to better stability of drugs at extremes of moisture and temperature. Here, we apply fundamental fluid mechanical and physicochemical transport theory to help better understand how successful microbicide API delivery depends upon properties of a film and the human reproductive tract environment. Several critical components of successful drug delivery are addressed. Among these are: elastohydrodynamic flow of a dissolved non-Newtonian film; mass transfer due to inhomogeneous dilution of the film by vaginal fluid contacting it along a moving boundary (the locally deforming vaginal epithelial surface); and drug absorption by the epithelium. Local rheological properties of the film are dependent on local volume fraction of the vaginal fluid. We evaluated this experimentally, delineating the way that constitutive parameters of a shear-thinning dissolved film are modified by dilution. To develop the mathematical model, we integrate the Reynolds lubrication equation with a mass conservation equation to model diluting fluid movement across the moving vaginal epithelial surface and into the film. This is a complex physicochemical phenomenon that is not well understood. We explore time- and space-varying boundary flux model based upon osmotic gradients. Results show that the model produces fluxes that are comparable to experimental data. Further experimental characterization of the vaginal wall is required for a more precise set of parameters and a more sophisticated theoretical treatment of epithelium. [ABSTRACT FROM AUTHOR]

An abstract of the article "What can be learned from high-resolution sleep data using ECoG," by Vera M. Dadok, Andrew J. Szeri, Heidi Kirsch, Jamie Sleigh, Rochelle Zak, and Beth Lopour is presented.

In this paper, a theoretical framework is developed for the mechanics of kidney stones with an isotropic, random microstructure—such as those comprised of cystine or struvite. The approach is based on a micromechanical description of kidney stones comprised of crystals in a binding matrix. Stress concentration functions are developed to determine load sharing of the particle phase and the binding matrix phase. As an illustration of the theory, the fatigue of kidney stones subject to shock wave lithotripsy is considered. Stress concentration functions are used to construct fatigue life estimates for each phase, as a function of the volume fraction and of the mechanical properties of the constituents, as well as the loading from SWL. The failure of the binding matrix is determined explicitly in a model for the accumulation of distributed damage. Also considered is the amount of material damaged in a representative non-spherical collapse of a cavitation bubble near the stone surface. The theory can be used to assess the importance of microscale heterogeneity on the comminution of renal calculi and to estimate the number of cycles to failure in terms of measurable material properties. [ABSTRACT FROM AUTHOR]

We consider dilute suspensions that have a microstructure that may be characterized by an axial state vector. Examples include axisymmetric particles, line elements of the fluid itself, or, as an approximation, droplets of fluid or polymer molecules. Past studies, in which sufficient conditions for stretch or coherent orientation of the microstructure are obtained for steady flows with homogeneous velocity gradient tensors are shown not to apply to the general situation. Instead, a careful analysis of the microdynamical equations reveals that stretching and orientation of the microstructure by the flow must be analyzed over a time interval. Using techniques from the theory of dynamical systems, a quantitative measure is developed to determine orientations and/or stretched lengths of the microstructure, that are robust and attractive to nearby states. This leads to a strong flow criterion for unsteady flows with inhomogeneous velocity gradient tensors in which the effects of history dependence are apparent. A particular model system is treated in the case of general two-dimensional flow. The sensitivity of the results to changes in the modeling assumptions is investigated. [ABSTRACT FROM AUTHOR]