Modeling the acute effects of exercise on glucose dynamics in healthy nondiabetic subjects.

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.

Modeling the acute effects of exercise on insulin kinetics in type 1 diabetes.

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 ([Formula: see text]) from subcutaneous tissue, the insulin delivery rate ([Formula: see text]) 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 ([Formula: see text]) and exercising subjects ([Formula: see text])] 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 [Formula: see text] and [Formula: see text], 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.

Closed-loop feedback control and bifurcation analysis of epileptiform activity via optogenetic stimulation in a mathematical model of human cortex.

Optogenetics provides a method of neuron stimulation that has high spatial, temporal, and cell-type specificity. Here we present a model of optogenetic feedback control that targets the inhibitory population, which expresses light-sensitive channelrhodopsin-2 channels, in a mean-field model of undifferentiated cortex that is driven to seizures. The inhibitory population is illuminated with an intensity that is a function of electrode measurements obtained via the cortical model. We test the efficacy of this control method on seizurelike activity observed in two parameter spaces of the cortical model that most closely correspond to seizures observed in patients. We also compare the effect of closed-loop and open-loop control on seizurelike activity using a less-complicated ordinary differential equation model of the undifferentiated cortex in parameter space. Seizurelike activity is successfully suppressed in both parameter planes using optimal illumination intensities less likely to have adverse effects on cortical tissue.

Coupled gel spreading and diffusive transport models describing microbicidal drug delivery.

Gels are a drug delivery platform that is being evaluated for application of active pharmaceutical ingredients, termed microbicides, that act topically against vaginal and rectal mucosal infection by sexually transmitted HIV. Despite success in one Phase IIb trial of a vaginal gel delivering tenofovir, problems of user adherence to designed gel application scheduling have compromised results in two other trials. The microbicides field is responding to this dilemma by expanding behavioral analysis of the determinants of adherence while simultaneously improving the pharmacological, biochemical, and biophysical analyses of the determinants of microbicide drug delivery. The intent is to combine results of these two complementary perspectives on microbicide performance and epidemiological success to create an improved product design paradigm. Central to both user sensory perceptions and preferences, key factors that underlie adherence, and to vaginal gel mucosal drug delivery, that underlies anti-HIV efficacy, are gel properties (e.g. rheology) and volume. The specific engineering problem to be solved here is to develop a model for how gel rheology and volume, interacting with loaded drug concentration, govern the transport of the microbicide drug tenofovir into the vaginal mucosa to its stromal layer. These are factors that can be controlled in microbicide gel design. The analysis here builds upon our current understanding of vaginal gel deployment and drug delivery, incorporating key features of the gel's environment, the vaginal canal, fluid production and subsequent gel dilution, and vaginal wall elasticity. These have not previously been included in the modeling of drug delivery. We consider the microbicide drug tenofovir, which is the drug most completely studied for gels: in vitro, in animal studies in vivo, and in human clinical trials with both vaginal or rectal gel application. Our goal is to contribute to improved biophysical and pharmacological understanding of gel functionality, providing a computational tool that can be used in future vaginal microbicide gel design.

Optogenetic induced epileptiform activity in a model human cortex.

BACKGROUND: Cortical stimulation plays an important role in the study of epileptic seizures. We present a numerical simulation of stimulation using optogenetic channels expressed by excitatory cells in a mean field model of the human cortex. FINDINGS: Depolarising excitatory cells in a patch of model cortex using Channelrhodpsin-2 (ChR2) ion channels, we are able to hyper-excite a normally functioning cortex and mimic seizure activity. The temporal characteristics of optogenetic channels, and the ability to control the frequency of synchronous activity using these properties are also demonstrated. CONCLUSIONS: Optogenetics is a powerful stimulation technique with high spatial, temporal and cell-type specificity, and would be invaluable in studying seizures and other brain disorders and functions.

A probabilistic method for determining cortical dynamics during seizures.

This work presents a probabilistic method for inferring the parameter ranges in a biologically relevant mathematical model of the cortex most likely to be producing seizures observed in an electrocorticogram (ECoG) signal from a human subject. Additionally, this method produces a probabilistic pathway of the temporal evolution of physiological state in the cortex over the course of individual seizures, leveraging a model of the cortex that describes cortical physiology. We describe ways in which these methods and results offer insights into seizure etiology and have the potential to suggest new treatment options. To directly account for the stochastic and noisy nature of the mathematical model and the ECoG signal, we use a probabilistic Bayesian framework to map features of ECoG segments onto a distribution of likelihoods over physiologically-relevant parameter states. A Hidden Markov Model (HMM) is then introduced to incorporate the belief that cortical physiology has both temporal continuity and also a degree of reproducibility between individual seizures. By inspecting the ratio of likelihoods between HMMs run under two possible parameter regions, both of which produce seizures in the model, we determine which physiological parameter regions are more likely to be causing the observed seizures. We show that between individual seizures, there is consistency in these likelihood ratios between hypothesized regions, in the temporal pathways calculated, and in the separation of seizure from non-seizure time segment likelihood maps.

Emergence from general anesthesia and the sleep-manifold.

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.

A probabilistic framework for a physiological representation of dynamically evolving sleep state.

This work presents a probabilistic method for mapping human sleep electroencephalogram (EEG) signals onto a state space based on a biologically plausible mathematical model of the cortex. From a noninvasive EEG signal, this method produces physiologically meaningful pathways of the cortical state over a night of sleep. We propose ways in which these pathways offer insights into sleep-related conditions, functions, and complex pathologies. To address explicitly the noisiness of the EEG signal and the stochastic nature of the mathematical model, we use a probabilistic Bayesian framework to map each EEG epoch to a distribution of likelihoods over all model sleep states. We show that the mapping produced from human data robustly separates rapid eye movement sleep (REM) from slow wave sleep (SWS). A Hidden Markov Model (HMM) is incorporated to improve the path results using the prior knowledge that cortical physiology has temporal continuity.

Open loop optogenetic control of simulated cortical epileptiform activity.

We present a model for the use of open loop optogenetic control to inhibit epileptiform activity in a meso scale model of the human cortex. The meso scale cortical model first developed by Liley et al. (2001) is extended to two dimensions and the nature of the seizure waves is studied. We adapt to the meso scale a 4 state functional model of Channelrhodopsin-2 (ChR2) ion channels. The effects of pulsed and constant illumination on the conductance of these ion channels is presented. The inhibitory cell population is targeted for the application of open loop control. Seizure waves are successfully suppressed and the inherent properties of the optogenetic channels ensures charge balance in the cortex, protecting it from damage.

Mechanical clot damage from cavitation during sonothrombolysis.

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.

Transient swelling, spreading, and drug delivery by a dissolved anti-HIV microbicide-bearing film.

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.

Adaptive control of contrast agent microbubbles for shell parameter identification.

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.

Transient spreading and swelling behavior of a gel deploying an anti-HIV topical microbicide.

Drug delivery of topical microbicidal molecules against HIV offers promise as a modality to prevent sexual transmission of the virus. Success of any microbicide product depends, in an interactive way, upon its drug (the microbicide active pharmaceutical ingredient, API) and its delivery system (e.g. a gel, film or intravaginal ring). There is a widespread agreement that more effective drug delivery vehicles, as well as better APIs, must be developed to improve the efficacy of microbicide products. Non-Newtonian gels are primary microbicide vehicles, but those to date have been created with limited understanding of how their properties govern their spreading and retention in the vagina, which, in turn, govern successful drug delivery. Here, we apply fundamental fluid mechanical and physicochemical transport theory to help better understand how successful microbicide API delivery depends upon properties of a gel and the vaginal environment. We address several critical components of this complex process, including: elastohydrodynamic flow of the bolus of a non-Newtonian fluid; and mass transfer due to inhomogeneous dilution of the gel by vaginal fluid contacting it along a moving boundary (the locally deforming vaginal epithelial surface). Local dilution of gel alters local rheological properties. We evaluated this experimentally, delin-eating the way that constitutive parameters of a shear-thinning gel are modified by dilution. We supplement the Reynolds lubrication equation with a mass conservation equation to model diluting fluid movement across the moving vaginal epithelial surface and into the gel bolus. This is a physicochemically complex phenomenon that is not well understood. We implement a boundary flux model based upon the elevated hydrodynamic pressures in the cells. Results show that this model produces fluxes that lie within the range of mean values that have been reported. Further experimental characterization of the vaginal wall is required for a more precise set of parameters and a more sophisticated theoretical treatment of epithelium.

The effects of inhomogeneous boundary dilution on the coating flow of an anti-HIV microbicide vehicle.

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.

A continuous mapping of sleep states through association of EEG with a mesoscale cortical model.

Here we show that a mathematical model of the human sleep cycle can be used to obtain a detailed description of electroencephalogram (EEG) sleep stages, and we discuss how this analysis may aid in the prediction and prevention of seizures during sleep. The association between EEG data and the cortical model is found via locally linear embedding (LLE), a method of dimensionality reduction. We first show that LLE can distinguish between traditional sleep stages when applied to EEG data. It reliably separates REM and non-REM sleep and maps the EEG data to a low-dimensional output space where the sleep state changes smoothly over time. We also incorporate the concept of strongly connected components and use this as a method of automatic outlier rejection for EEG data. Then, by using LLE on a hybrid data set containing both sleep EEG and signals generated from the mesoscale cortical model, we quantify the relationship between the data and the mathematical model. This enables us to take any sample of sleep EEG data and associate it with a position among the continuous range of sleep states provided by the model; we can thus infer a trajectory of states as the subject sleeps. Lastly, we show that this method gives consistent results for various subjects over a full night of sleep and can be done in real time.

The consequences of yield stress on deployment of a non-Newtonian anti-HIV microbicide gel.

A recent study in South Africa has confirmed, for the first time, that a vaginal gel formulation of the antiretroviral drug Tenofovir, when applied topically, significantly inhibits sexual HIV transmission to women [10]. However the gel for this drug, and anti-HIV microbicide gels in general, have not been designed using full understanding of how gel spreading and retention in the vagina govern successful drug delivery. Elastohydrodynamic lubrication theory can be applied to model such spreading of microbicide gels, which are inherently non-Newtonian [13,15]. A yield stress is emerging as one of the important properties of microbicide gel vehicle deployment, as this may improve retention within the vaginal canal. On the other hand, a yield stress may decrease the initial extent of the coating flow. Here, we first explain a certain yield stress paradox observed generally in many lubrication flows. Four conditions are determined, via scaling analysis, which mitigate the inconsistency in the use of lubrication theory to analyze the specific problem of elastic wall squeezing flow of yield stress fluid. Parameters characterizing these conditions are obtained experimentally for a test gel. Using them, it is shown that the lubrication approximation may be applied to the elastic wall-squeezing problem for this gel.

Increasing the effectiveness of vaginal microbicides: a biophysical framework to rethink behavioral acceptability.

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.

Impact of a compound droplet on a flat surface: A model for single cell epitaxy.

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.

A model of feedback control for the charge-balanced suppression of epileptic seizures.

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.