Guillermo Marshall

A generalized Riemann problem for quasi-one-dimensional gas flows

A generalization of the Riemann problem for gas dynamical flows influenced by curved geometry, such as flows in a variable-area duct, is solved. For this generalized Riemann problem the initial data consist of a pair of steady-state solutions separated by a jump discontinuity. The solution of the generalized Riemann problem is used as a basis for a random choice method in which steady-state solutions are used as an Ansatz to approximate the spatial variation of the solution between grid points. For nearly steady flow in a Laval nozzle, where this Ansatz is appropriate, this generalized random choice method gives greatly improved results.

Structural and kinetic molecular dynamics study of electroporation in cholesterol-containing bilayers.

We present a numerical study of pore formation in lipid bilayers containing cholesterol (Chol) and subjected to a transverse electric field. Molecular dynamics simulations of 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine (DOPC) membranes reveal the formation of a pore when an electric field of 325 mV/nm is applied. The minimum electric field needed for membrane permeabilization strongly increases with the addition of cholesterol above 10 mol %, reaching 750 mV/nm for 40 mol % Chol. Analysis of simulations of DOPC/Chol bilayers suggests this is caused by a substantial increment of membrane cohesion. Simulations also show that pore formation kinetics is much slower at high Chol contents.

When the Optimal Is Not the Best: Parameter Estimation in Complex Biological Models

Background The vast computational resources that became available during the past decade enabled the development and simulation of increasingly complex mathematical models of cancer growth. These models typically involve many free parameters whose determination is a substantial obstacle to model development. Direct measurement of biochemical parameters in vivo is often difficult and sometimes impracticable, while fitting them under data-poor conditions may result in biologically implausible values. Results We discuss different methodological approaches to estimate parameters in complex biological models. We make use of the high computational power of the Blue Gene technology to perform an extensive study of the parameter space in a model of avascular tumor growth. We explicitly show that the landscape of the cost function used to optimize the model to the data has a very rugged surface in parameter space. This cost function has many local minima with unrealistic solutions, including the global minimum corresponding to the best fit. Conclusions The case studied in this paper shows one example in which model parameters that optimally fit the data are not necessarily the best ones from a biological point of view. To avoid force-fitting a model to a dataset, we propose that the best model parameters should be found by choosing, among suboptimal parameters, those that match criteria other than the ones used to fit the model. We also conclude that the model, data and optimization approach form a new complex system and point to the need of a theory that addresses this problem more generally.

The Role of pH Fronts in Reversible Electroporation

We present experimental measurements and theoretical predictions of ion transport in agar gels during reversible electroporation (ECT) for conditions typical to many clinical studies found in the literature, revealing the presence of pH fronts emerging from both electrodes. These results suggest that pH fronts are immediate and substantial. Since they might give rise to tissue necrosis, an unwanted condition in clinical applications of ECT as well as in irreversible electroporation (IRE) and in electrogenetherapy (EGT), it is important to quantify their extent and evolution. Here, a tracking technique is used to follow the space-time evolution of these pH fronts. It is found that they scale in time as , characteristic of a predominantly diffusive process. Comparing ECT pH fronts with those arising in electrotherapy (EChT), another treatment applying constant electric fields whose main goal is tissue necrosis, a striking result is observed: anodic acidification is larger in ECT than in EChT, suggesting that tissue necrosis could also be greater. Ways to minimize these adverse effects in ECT are suggested.

Viscosity Effects in Thin-Layer Electrodeposition

We present experimental results and a theoretical macroscopic model on the effects of viscosity in thin-layer electrochemical growth. The viscosity was changed through glycerol additions; simultaneous use was made of optical and schlieren techniques for tracking concentration and convective fronts, while pH indicators were used for migratory fronts. The theoretical model describes diffusive, migratory, and convective ion transport in a fluid subject to an electric field, The equations are written in terms of dimensionless quantities, in particular, the Migration, Peclet, Poisson, Reynolds, and electrical Grashof numbers, which are found to depend on viscosity, Experiments reveal that with increasing viscosity, convection decreases, concentration profiles are less pronounced, while electric resistance and voltage increase. Concentration and convective fronts slow down with viscosity, but their time scaling follows the Same law as for solutions without glycerol, only differing by a constant. Moreover, under constant electrical current, an increase in viscosity yields slower deposit front velocities, a more uniform deposit with smaller separation between branches, i.e., a change in morphology from more separated compact trees to a more dense, fractal-like structure.

The Role of Ph Fronts in Tissue Electroporation Based Treatments

Treatments based on electroporation (EP) induce the formation of pores in cell membranes due to the application of pulsed electric fields. We present experimental evidence of the existence of pH fronts emerging from both electrodes during treatments based on tissue EP, for conditions found in many studies, and that these fronts are immediate and substantial. pH fronts are indirectly measured through the evanescence time (ET), defined as the time required for the tissue buffer to neutralize them. The ET was measured through a pH indicator imaged at a series of time intervals using a four-cluster hard fuzzy-c-means algorithm to segment pixels corresponding to the pH indicator at every frame. The ET was calculated as the time during which the number of pixels was 10% of those in the initial frame. While in EP-based treatments such as reversible (ECT) and irreversible electroporation (IRE) the ET is very short (though enough to cause minor injuries) due to electric pulse characteristics and biological buffers present in the tissue, in gene electrotransfer (GET), ET is much longer, enough to denaturate plasmids and produce cell damage. When any of the electric pulse parameters is doubled or tripled the ET grows and, remarkably, when any of the pulse parameters in GET is halved, the ET drops significantly. Reducing pH fronts has relevant implications for GET treatment efficiency, due to a substantial reduction of plasmid damage and cell loss.

Ion transport and deposit growth in spatially coupled bipolar electrochemistry

In spatially coupled bipolar electrochemistry, electrodissolution and electrodeposition processes in an applied electric field are exploited to create directional growth of copper deposits between two copper discs, not physically linked to an external voltage source. Here, we study the electric field in the whole cell through theoretical modeling, and ion transport in the interdisc region using optical and particle image velocimetry techniques. Their combined effect on incubation time and deposit morphology is assessed. Both the electric field and ion transport in the interdisc region are crucial factors in the characteristics of the interconnection. The model simulations reveal that the electric field is almost an order of magnitude larger in the region between discs as compared with the mean field value. Measurements and simulations show that the incubation time scales linearly with the inverse of the electric field, an indication that in this period, migration is the dominant transport mode. Experiments reveal that after branching develops, convection plays a relevant role as well, the contact growing linearly in time, with a change of the time/length slope at half the interdisc gap.

Front tracking in thin-layer electrodeposition

We present an experimental and theoretical study of front interaction during the growth of patterns in thin-layer electrochemical deposition. Simultaneous schlieren and particle image velocimetry techniques are used to follow front development of concentration fields and convection rolls in gravitoconvection prevailing flows. A theoretical model describing full front nonlinear interaction taking into account diffusive, migratory and convective motion of ions in a viscous fluid subject to an electric field is presented. The equations are written in terms of a set of dimensionless numbers showing the significance of the gravity Grashof number in a gravitoconvection prevailing regime. Our experiments reveal that concentration and gravity driven convection fronts which develop near the electrodes coincide and that the two evolve together. Prior to the appearance of rough growth, cathodic and anodic concentration and convective fronts are parallel to the electrodes. After branching develops, the cathodic front...

A macroscopic model for growth pattern formation of ramified copper electrodeposits

Abstract This is a first attempt to construct a macroscopic model for the description of growth pattern formation in copper electrodeposits. The theoretical model is formulated as a Stefan-like problem consisting in the Nernst-Planck equations for the concentration of the solute, coupled to an equation for the electric potential and the Navier-Stokes equations for the solvent, with a moving boundary. A discrete version of these equations in a DBM scheme with a random moving boundary constitutes the computational model. Preliminary numerical results show that, with a proper variation of the relevant control parameters, the model proposed is able to describe from fractal to dense branch morphology and, in particular, the interplay of the electroconvective, migration and diffusive motion of the ions near the growing tips.

The role of additional pulses in electropermeabilization protocols.

Electropermeabilization (EP) based protocols such as those applied in medicine, food processing or environmental management, are well established and widely used. The applied voltage, as well as tissue electric conductivity, are of utmost importance for assessing final electropermeabilized area and thus EP effectiveness. Experimental results from literature report that, under certain EP protocols, consecutive pulses increase tissue electric conductivity and even the permeabilization amount. Here we introduce a theoretical model that takes into account this effect in the application of an EP-based protocol, and its validation with experimental measurements. The theoretical model describes the electric field distribution by a nonlinear Laplace equation with a variable conductivity coefficient depending on the electric field, the temperature and the quantity of pulses, and the Pennes Bioheat equation for temperature variations. In the experiments, a vegetable tissue model (potato slice) is used for measuring electric currents and tissue electropermeabilized area in different EP protocols. Experimental measurements show that, during sequential pulses and keeping constant the applied voltage, the electric current density and the blackened (electropermeabilized) area increase. This behavior can only be attributed to a rise in the electric conductivity due to a higher number of pulses. Accordingly, we present a theoretical modeling of an EP protocol that predicts correctly the increment in the electric current density observed experimentally during the addition of pulses. The model also demonstrates that the electric current increase is due to a rise in the electric conductivity, in turn induced by temperature and pulse number, with no significant changes in the electric field distribution. The EP model introduced, based on a novel formulation of the electric conductivity, leads to a more realistic description of the EP phenomenon, hopefully providing more accurate predictions of treatment outcomes.