Orthotropic active strain models for the numerical simulation of cardiac biomechanics

An active strain formulation for orthotropic constitutive laws arising in cardiac mechanics modeling is introduced and studied. The passive mechanical properties of the tissue are described by the Holzapfel-Ogden relation. In the active strain formulation, the Euler-Lagrange equations for minimizing the total energy are written in terms of active and passive deformation factors, where the active part is assumed to depend, at the cell level, on the electrodynamics and on the specific orientation of the cardiac cells. The well-posedness of the linear system derived from a generic Newton iteration of the original problem is analyzed and different mechanical activation functions are considered. In addition, the active strain formulation is compared with the classical active stress formulation from both numerical and modeling perspectives. Taylor-Hood and MINI finite elements are employed to discretize the mechanical problem. The results of several numerical experiments show that the proposed formulation is mathematically consistent and is able to represent the main key features of the phenomenon, while allowing savings in computational costs.

Prediction of infant drug exposure through breastfeeding: population PK modeling and simulation of fluoxetine

BACKGROUND: Risks of significant infant drug exposurethrough breastmilk are poorly defined for many drugs, and largescalepopulation data are lacking. We used population pharmacokinetics(PK) modeling to predict fluoxetine exposure levels ofinfants via mother's milk in a simulated population of 1000 motherinfantpairs.METHODS: Using our original data on fluoxetine PK of 25breastfeeding women, a population PK model was developed withNONMEM and parameters, including milk concentrations, wereestimated. An exponential distribution model was used to account forindividual variation. Simulation random and distribution-constrainedassignment of doses, dosing time, feeding intervals and milk volumewas conducted to generate 1000 mother-infant pairs with characteristicssuch as the steady-state serum concentrations (Css) and infantdose relative to the maternal weight-adjusted dose (relative infantdose: RID). Full bioavailability and a conservative point estimate of1-month-old infant CYP2D6 activity to be 20% of the adult value(adjusted by weigth) according to a recent study, were assumed forinfant Css calculations.RESULTS: A linear 2-compartment model was selected as thebest model. Derived parameters, including milk-to-plasma ratios(mean: 0.66; SD: 0.34; range, 0 - 1.1) were consistent with the valuesreported in the literature. The estimated RID was below 10% in >95%of infants. The model predicted median infant-mother Css ratio was0.096 (range 0.035 - 0.25); literature reported mean was 0.07 (range0-0.59). Moreover, the predicted incidence of infant-mother Css ratioof >0.2 was less than 1%.CONCLUSION: Our in silico model prediction is consistent withclinical observations, suggesting that substantial systemic fluoxetineexposure in infants through human milk is rare, but further analysisshould include active metabolites. Our approach may be valid forother drugs. [supported by CIHR and Swiss National Science Foundation(SNSF)]

A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid-solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently bench-marked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

Historical contingency affects signaling strategies and competitive abilities in evolving populations of simulated robots.

One of the key innovations during the evolution of life on earth has been the emergence of efficient communication systems, yet little is known about the causes and consequences of the great diversity within and between species. By conducting experimental evolution in 20 independently evolving populations of cooperatively foraging simulated robots, we found that historical contingency in the occurrence order of novel phenotypic traits resulted in the emergence of two distinct communication strategies. The more complex foraging strategy was less efficient than the simpler strategy. However, when the 20 populations were placed in competition with each other, the populations with the more complex strategy outperformed the populations with the less complex strategy. These results demonstrate a tradeoff between communication efficiency and robustness and suggest that stochastic events have important effects on signal evolution and the outcome of competition between distinct populations.

Direct simulation of interface dynamics: linking capillary pressure, interfacial area and surface energy

We perform direct numerical simulations of drainage by solving Navier- Stokes equations in the pore space and employing the Volume Of Fluid (VOF) method to track the evolution of the fluid-fluid interface. After demonstrating that the method is able to deal with large viscosity contrasts and to model the transition from stable flow to viscous fingering, we focus on the definition of macroscopic capillary pressure. When the fluids are at rest, the difference between inlet and outlet pressures and the difference between the intrinsic phase average pressure coincide with the capillary pressure. However, when the fluids are in motion these quantities are dominated by viscous forces. In this case, only a definition based on the variation of the interfacial energy provides an accurate measure of the macroscopic capillary pressure and allows separating the viscous from the capillary pressure components.

Brownian dynamics simulation of DNA condensation.

DNA condensation observed in vitro with the addition of polyvalent counterions is due to intermolecular attractive forces. We introduce a quantitative model of these forces in a Brownian dynamics simulation in addition to a standard mean-field Poisson-Boltzmann repulsion. The comparison of a theoretical value of the effective diameter calculated from the second virial coefficient in cylindrical geometry with some experimental results allows a quantitative evaluation of the one-parameter attractive potential. We show afterward that with a sufficient concentration of divalent salt (typically approximately 20 mM MgCl(2)), supercoiled DNA adopts a collapsed form where opposing segments of interwound regions present zones of lateral contact. However, under the same conditions the same plasmid without torsional stress does not collapse. The condensed molecules present coexisting open and collapsed plectonemic regions. Furthermore, simulations show that circular DNA in 50% methanol solutions with 20 mM MgCl(2) aggregates without the requirement of torsional energy. This confirms known experimental results. Finally, a simulated DNA molecule confined in a box of variable size also presents some local collapsed zones in 20 mM MgCl(2) above a critical concentration of the DNA. Conformational entropy reduction obtained either by supercoiling or by confinement seems thus to play a crucial role in all forms of condensation of DNA.

Numerical simulation of ambient seismic wavefield modification caused by pore-fluid effects in an oil reservoir

We have modeled numerically the seismic response of a poroelastic inclusion with properties applicable to an oil reservoir that interacts with an ambient wavefield. The model includes wave-induced fluid flow caused by pressure differences between mesoscopic-scale (i.e., in the order of centimeters to meters) heterogeneities. We used a viscoelastic approximation on the macroscopic scale to implement the attenuation and dispersion resulting from this mesoscopic-scale theory in numerical simulations of wave propagation on the kilometer scale. This upscaling method includes finite-element modeling of wave-induced fluid flow to determine effective seismic properties of the poroelastic media, such as attenuation of P- and S-waves. The fitted, equivalent, viscoelastic behavior is implemented in finite-difference wave propagation simulations. With this two-stage process, we model numerically the quasi-poroelastic wave-propagation on the kilometer scale and study the impact of fluid properties and fluid saturation on the modeled seismic amplitudes. In particular, we addressed the question of whether poroelastic effects within an oil reservoir may be a plausible explanation for low-frequency ambient wavefield modifications observed at oil fields in recent years. Our results indicate that ambient wavefield modification is expected to occur for oil reservoirs exhibiting high attenuation. Whether or not such modifications can be detected in surface recordings, however, will depend on acquisition design and noise mitigation processing as well as site-specific conditions, such as the geologic complexity of the subsurface, the nature of the ambient wavefield, and the amount of surface noise.

Method to assess and optimise dependability of complex macro-systems: application to a railway signalling system

Achieving a high degree of dependability in complex macro-systems is challenging. Because of the large number of components and numerous independent teams involved, an overview of the global system performance is usually lacking to support both design and operation adequately. A functional failure mode, effects and criticality analysis (FMECA) approach is proposed to address the dependability optimisation of large and complex systems. The basic inductive model FMECA has been enriched to include considerations such as operational procedures, alarm systems. environmental and human factors, as well as operation in degraded mode. Its implementation on a commercial software tool allows an active linking between the functional layers of the system and facilitates data processing and retrieval, which enables to contribute actively to the system optimisation. The proposed methodology has been applied to optimise dependability in a railway signalling system. Signalling systems are typical example of large complex systems made of multiple hierarchical layers. The proposed approach appears appropriate to assess the global risk- and availability-level of the system as well as to identify its vulnerabilities. This enriched-FMECA approach enables to overcome some of the limitations and pitfalls previously reported with classical FMECA approaches.

Resting-brain functional connectivity predicted by analytic measures of network communication.

The complex relationship between structural and functional connectivity, as measured by noninvasive imaging of the human brain, poses many unresolved challenges and open questions. Here, we apply analytic measures of network communication to the structural connectivity of the human brain and explore the capacity of these measures to predict resting-state functional connectivity across three independently acquired datasets. We focus on the layout of shortest paths across the network and on two communication measures-search information and path transitivity-which account for how these paths are embedded in the rest of the network. Search information is an existing measure of information needed to access or trace shortest paths; we introduce path transitivity to measure the density of local detours along the shortest path. We find that both search information and path transitivity predict the strength of functional connectivity among both connected and unconnected node pairs. They do so at levels that match or significantly exceed path length measures, Euclidean distance, as well as computational models of neural dynamics. This capacity suggests that dynamic couplings due to interactions among neural elements in brain networks are substantially influenced by the broader network context adjacent to the shortest communication pathways.

Numerical simulation of gel electrophoresis of DNA knots in weak and strong electric fields.

Gel electrophoresis allows one to separate knotted DNA (nicked circular) of equal length according to the knot type. At low electric fields, complex knots, being more compact, drift faster than simpler knots. Recent experiments have shown that the drift velocity dependence on the knot type is inverted when changing from low to high electric fields. We present a computer simulation on a lattice of a closed, knotted, charged DNA chain drifting in an external electric field in a topologically restricted medium. Using a Monte Carlo algorithm, the dependence of the electrophoretic migration of the DNA molecules on the knot type and on the electric field intensity is investigated. The results are in qualitative and quantitative agreement with electrophoretic experiments done under conditions of low and high electric fields.

Prediction of Infant Drug Exposure Through Breastfeeding: Population PK Modeling and Simulation of Fluoxetine Exposure.

The likelihood of significant exposure to drugs in infants through breast milk is poorly defined, given the difficulties of conducting pharmacokinetics (PK) studies. Using fluoxetine (FX) as an example, we conducted a proof-of-principle study applying population PK (popPK) modeling and simulation to estimate drug exposure in infants through breast milk. We simulated data for 1,000 mother-infant pairs, assuming conservatively that the FX clearance in an infant is 20% of the allometrically adjusted value in adults. The model-generated estimate of the milk-to-plasma ratio for FX (mean: 0.59) was consistent with those reported in other studies. The median infant-to-mother ratio of FX steady-state plasma concentrations predicted by the simulation was 8.5%. Although the disposition of the active metabolite, norfluoxetine, could not be modeled, popPK-informed simulation may be valid for other drugs, particularly those without active metabolites, thereby providing a practical alternative to conventional PK studies for exposure risk assessment in this population.

Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework

The multiscale finite-volume (MSFV) method is designed to reduce the computational cost of elliptic and parabolic problems with highly heterogeneous anisotropic coefficients. The reduction is achieved by splitting the original global problem into a set of local problems (with approximate local boundary conditions) coupled by a coarse global problem. It has been shown recently that the numerical errors in MSFV results can be reduced systematically with an iterative procedure that provides a conservative velocity field after any iteration step. The iterative MSFV (i-MSFV) method can be obtained with an improved (smoothed) multiscale solution to enhance the localization conditions, with a Krylov subspace method [e.g., the generalized-minimal-residual (GMRES) algorithm] preconditioned by the MSFV system, or with a combination of both. In a multiphase-flow system, a balance between accuracy and computational efficiency should be achieved by finding a minimum number of i-MSFV iterations (on pressure), which is necessary to achieve the desired accuracy in the saturation solution. In this work, we extend the i-MSFV method to sequential implicit simulation of time-dependent problems. To control the error of the coupled saturation/pressure system, we analyze the transport error caused by an approximate velocity field. We then propose an error-control strategy on the basis of the residual of the pressure equation. At the beginning of simulation, the pressure solution is iterated until a specified accuracy is achieved. To minimize the number of iterations in a multiphase-flow problem, the solution at the previous timestep is used to improve the localization assumption at the current timestep. Additional iterations are used only when the residual becomes larger than a specified threshold value. Numerical results show that only a few iterations on average are necessary to improve the MSFV results significantly, even for very challenging problems. Therefore, the proposed adaptive strategy yields efficient and accurate simulation of multiphase flow in heterogeneous porous media.

Monte Carlo simulation of a whole-body counter using IGOR phantoms.

Whole-body counting is a technique of choice for assessing the intake of gamma-emitting radionuclides. An appropriate calibration is necessary, which is done either by experimental measurement or by Monte Carlo (MC) calculation. The aim of this work was to validate a MC model for calibrating whole-body counters (WBCs) by comparing the results of computations with measurements performed on an anthropomorphic phantom and to investigate the effect of a change in phantom's position on the WBC counting sensitivity. GEANT MC code was used for the calculations, and an IGOR phantom loaded with several types of radionuclides was used for the experimental measurements. The results show a reasonable agreement between measurements and MC computation. A 1-cm error in phantom positioning changes the activity estimation by >2%. Considering that a 5-cm deviation of the positioning of the phantom may occur in a realistic counting scenario, this implies that the uncertainty of the activity measured by a WBC is ∼10-20%.

Simulation of interface dynamics across pore discontinuities

We study the dynamics of a water-oil meniscus moving from a smaller to a larger pore. The process is characterised by an abrupt change in the configuration, yielding a sudden energy release. A theoretic study for static conditions provides analytical solutions of the surface energy content of the system. Although the configuration after the sudden energy release is energetically more convenient, an energy barrier must be overcome before the process can happen spontaneously. The energy barrier depends on the system geometry and on the flow parameters. The analytical results are compared to numerical simulations that solve the full Navier-Stokes equation in the pore space and employ the Volume Of Fluid (VOF) method to track the evolution of the interface. First, the numerical simulations of a quasi-static process are validated by comparison with the analytical solutions for a static meniscus, then numerical simulations with varying injection velocity are used to investigate dynamic effects on the configuration change. During the sudden energy jump the system exhibits an oscillatory behaviour. Extension to more complex geometries might elucidate the mechanisms leading to a dynamic capillary pressure and to bifurcations in final distributions of fluid phases in porous