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Cerebral vasospasm, a prolonged constriction of cerebral arteries, is the first cause of morbidity and mortality for patients who survive hospitalisation after aneurysmal subarachnoid haemorrhage. The recent finding that stent-retrievers can successfully treat the disease has challenged the viewpoint that damage to the extracellular matrix is necessary. We apply a 3D finite element rate-based constrained mixture model (rb-CMM) to simulate vasospasm, remodelling and treatment with stents. The artery is modelled as a thick-walled fibre-reinforced constrained mixture subject to physiological pressure and axial stretch. The model accounts for distributions of collagen fibre homeostatic stretches, VSMC active response, remodelling and damage. After simulating vasospasm and subsequent remodelling of the artery to a new homeostatic state, we simulate treatment with commonly available stent-retrievers. We perform a parameter study to examine how arterial diameter and thickness affect the success of stent treatment. The model predictions on the pressure required to mechanically resolve the constriction are consistent with stent-retrievers. In agreement with clinical observations, our model predicts that stent-retrievers tend to be effective in arteries of up to 3mm diameter, but fail in larger ones. Variations in arterial wall thickness significantly affect stent pressure requirements. We have developed a novel rb-CMM that accounts for VSMC active response, remodelling and damage. Consistently with clinical observations, simulations predict that stent-retrievers can mechanically resolve vasospasm. Moreover, accounting for a patient's arterial properties is important for predicting likelihood of stent success. This in silico tool has the potential to support clinical decision-making and guide the development and evaluation of dedicated stents for personalised treatment of vasospasm., Comment: 32 pages, 10 figures

Parametric reduced-order modelling often serves as a surrogate method for hemodynamics simulations to improve the computational efficiency in many-query scenarios or to perform real-time simulations. However, the snapshots of the method require to be collected from the same discretisation, which is a straightforward process for physical parameters, but becomes challenging for geometrical problems, especially for those domains featuring unparameterised and unique shapes, e.g. patient-specific geometries. In this work, a data-driven surrogate model is proposed for the efficient prediction of blood flow simulations on similar but distinct domains. The proposed surrogate model leverages group surface registration to parameterise those shapes and formulates corresponding hemodynamics information into geometry-informed snapshots by the diffeomorphisms constructed between a reference domain and original domains. A non-intrusive reduced-order model for geometrical parameters is subsequently constructed using proper orthogonal decomposition, and a radial basis function interpolator is trained for predicting the reduced coefficients of the reduced-order model based on compressed geometrical parameters of the shape. Two examples of blood flowing through a stenosis and a bifurcation are presented and analysed. The proposed surrogate model demonstrates its accuracy and efficiency in hemodynamics prediction and shows its potential application toward real-time simulation or uncertainty quantification for complex patient-specific scenarios.

In-Stent Restenosis is a recurrence of coronary artery narrowing due to vascular injury caused by balloon dilation and stent placement. It may lead to the relapse of angina symptoms or to an acute coronary syndrome. An uncertainty quantification of a model for In-Stent Restenosis with four uncertain parameters (endothelium regeneration time, the threshold strain for smooth muscle cells bond breaking, blood flow velocity and the percentage of fenestration in the internal elastic lamina) is presented. Two quantities of interest were studied, namely the average cross-sectional area and the maximum relative area loss in a vessel. Due to the computational intensity of the model and the number of evaluations required in the uncertainty quantification, a surrogate model, based on Gaussian process regression with proper orthogonal decomposition, was developed which subsequently replaced the original In-Stent Restenosis model in the uncertainty quantification. A detailed analysis of the uncertainty propagation and sensitivity analysis is presented. Around 11% and 16% of uncertainty are observed on the average cross-sectional area and maximum relative area loss respectively, and the uncertainty estimates show that a higher fenestration mainly determines uncertainty in the neointimal growth at the initial stage of the process. On the other hand, the uncertainty in blood flow velocity and endothelium regeneration time mainly determine the uncertainty in the quantities of interest at the later, clinically relevant stages of the restenosis process. The uncertainty in the threshold strain is relatively small compared to the other uncertain parameters.

Uncertainty estimations are presented of the response of a multiscale in-stent restenosis model, as obtained by both non-intrusive and semi-intrusive uncertainty quantification. The in-stent restenosis model is a fully coupled multiscale simulation of post-stenting tissue growth, in which the most costly submodel is the blood flow simulation. Surrogate modeling for non-intrusive uncertainty quantification takes the whole model as a black-box and maps directly from the three uncertain inputs to the quantity of interest, the neointimal area. The corresponding uncertain estimates matched the results from quasi-Monte Carlo simulations well. In the semi-intrusive uncertainty quantification, the most expensive submodel is replaced with a surrogate model. We developed a surrogate model for the blood flow simulation by using a convolutional neural network. The semi-intrusive method with the new surrogate model offered efficient estimates of uncertainty and sensitivity while keeping relatively high accuracy. It outperformed the result obtained with earlier surrogate models. It also achieved the estimates comparable to the non-intrusive method with similar efficiency. Presented results on uncertainty propagation with non-intrusive and semi-intrusive metamodeling methods allow us to draw some conclusions on the advantages and limitations of these methods.

Shear thickening of particle suspensions is characterized by a transition between lubricated and frictional contacts between the particles. Using 3D numerical simulations, we study how the inter-particle friction coefficient influences the effective macroscopic friction coefficient and hence the microstructure and rheology of dense shear thickening suspensions. We propose expressions for effective friction coefficient in terms of distance to jamming for varying shear stresses and particle friction coefficient values. We find effective friction coefficient to be rather insensitive to interparticle friction, which is perhaps surprising but agrees with recent theory and experiments.

In this paper, the sensitivity analysis of a single scale model is employed in order to reduce the input dimensionality of the related multiscale model, in this way, improving the efficiency of its uncertainty estimation. The approach is illustrated with two examples: a reaction model and the standard Ornstein-Uhlenbeck process. Additionally, a counterexample shows that an uncertain input should not be excluded from uncertainty quantification without estimating the response sensitivity to this parameter. In particular, an analysis of the function defining the relation between single scale components is required to understand whether single scale sensitivity analysis can be used to reduce the dimensionality of the overall multiscale model input space.

A family of semi-intrusive uncertainty propagation (UP) methods for multiscale models is introduced. The methods are semi-intrusive in the sense that inspection of the model is limited up to the level of the single scale systems, and viewing these single scale components as black-boxes. The goal is to estimate uncertainty in the result of multiscale models at a reduced amount of time as compared to black-box Monte Carlo (MC). In the resulting semi-intrusive MC method, the required number of samples of an expensive single scale model is minimized in order to reduce the execution time for the overall UP. In the metamodeling approach, the expensive model component is replaced completely by a computationally much cheaper surrogate model. These semi-intrusive algorithms have been tested on two case studies based on reaction-diffusion dynamics. The results demonstrate that the proposed semi-intrusive methods can result in a significant reduction of the computational time for multiscale UP, while still computing accurately the estimates of uncertainties. The semi-intrusive methods can, therefore, be a valid alternative, when uncertainties of a multiscale model cannot be estimated by the black-box MC methods in a feasible amount of time.

In dynamical systems, local interactions between dynamical units generate correlations which are stored and transmitted throughout the system, generating the macroscopic behavior. However a framework to quantify and study this at the microscopic scale is missing. Here we propose an 'information processing' framework based on Shannon mutual information quantities between the initial and future states. We apply it to the 256 elementary cellular automata (ECA), which are the simplest possible dynamical systems exhibiting behaviors ranging from simple to complex. Our main finding for ECA is that only a few features are needed for full predictability and that the 'information integration' (synergy) feature is always most predictive. Finally we apply the formalism to foreign exchange (FX) and interest-rate swap (IRS) time series data and find that the 2008 financial crisis marks a sudden and sustained regime shift (FX and EUR IRS) resembling tipping point behavior. The USD IRS market exhibits instead a slow and steady progression which appears consistent with the hypothesis that this market is (part of) the driving force behind the crisis. Our work suggests that the proposed framework is a promising way of predicting emergent complex systemic behaviors in terms of the local information processing of units.

We expect that multiscale simulations will be one of the main high performance computing workloads in the exascale era. We propose multiscale computing patterns as a generic vehicle to realise load balanced, fault tolerant and energy aware high performance multiscale computing. Multiscale computing patterns should lead to a separation of concerns, whereby application developers can compose multiscale models and execute multiscale simulations, while pattern software realises optimized, fault tolerant and energy aware multiscale computing. We introduce three multiscale computing patterns, present an example of the extreme scaling pattern, and discuss our vision of how this may shape multiscale computing in the exascale era.

The Fisher-Rao metric from Information Geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of Information Geometry to study more general phase transitions in complex systems. However, it is unclear whether the Fisher-Rao metric does indeed detect these more general transitions, especially in the absence of a statistical model. In this paper we study the transitions between patterns in the Gray-Scott reaction-diffusion model using Fisher information. We describe the system by a probability density function that represents the size distribution of blobs in the patterns and compute its Fisher information with respect to changing the two rate parameters of the underlying model. We estimate the distribution non-parametrically so that we do not assume any statistical model. The resulting Fisher map can be interpreted as a phase-map of the different patterns. Lines with high Fisher information can be considered as boundaries between regions of parameter space where patterns with similar characteristics appear. These lines of high Fisher information can be interpreted as phase transitions between complex patterns., Comment: 13 pages, 8 figures

The Fisher Information matrix is a widely used measure for applications ranging from statistical inference, information geometry, experiment design, to the study of criticality in biological systems. Yet there is no commonly accepted non-parametric algorithm to estimate it from real data. In this rapid communication we show how to accurately estimate the Fisher information in a nonparametric way. We also develop a numerical procedure to minimize the errors by choosing the interval of the finite difference scheme necessary to compute the derivatives in the definition of the Fisher information. Our method uses the recently published "Density Estimation using Field Theory" algorithm to compute the probability density functions for continuous densities. We use the Fisher information of the normal distribution to validate our method and as an example we compute the temperature component of the Fisher Information Matrix in the two dimensional Ising model and show that it obeys the expected relation to the heat capacity and therefore peaks at the phase transition at the correct critical temperature., Comment: 6 pages, 5 figures

We present the Multiscale Coupling Library and Environment: MUSCLE 2. This multiscale component-based execution environment has a simple to use Java, C++, C, Python and Fortran API, compatible with MPI, OpenMP and threading codes. We demonstrate its local and distributed computing capabilities and compare its performance to MUSCLE 1, file copy, MPI, MPWide, and GridFTP. The local throughput of MPI is about two times higher, so very tightly coupled code should use MPI as a single submodel of MUSCLE 2; the distributed performance of GridFTP is lower, especially for small messages. We test the performance of a canal system model with MUSCLE 2, where it introduces an overhead as small as 5% compared to MPI., Comment: 18 pages, 22 figures, submitted to journal

Multiscale simulations are essential in the biomedical domain to accurately model human physiology. We present a modular approach for designing, constructing and executing multiscale simulations on a wide range of resources, from desktops to petascale supercomputers, including combinations of these. Our work features two multiscale applications, in-stent restenosis and cerebrovascular bloodflow, which combine multiple existing single-scale applications to create a multiscale simulation. These applications can be efficiently coupled, deployed and executed on computers up to the largest (peta) scale, incurring a coupling overhead of 1 to 10% of the total execution time., Comment: accepted by Interface Focus. 17 pages, 2 figures, 4 tables

Light scattering patterns (LSP) of blood platelets were theoretically and experimentally analyzed. We used spicular spheroids as a model for the platelets with pseudopodia. The discrete dipole approximation was employed to simulate light scattering from an individual spicular spheroid constructed from a homogeneous oblate spheroid and 14 rectilinear parallelepipeds rising from the cell centre. These parallelepipeds have a weak effect on the LSP over the measured angular range. Therefore, a homogeneous oblate spheroid was taken as a simplified optical model for platelets. Using the T-matrix method, we computed the LSP over a range of volumes, aspect ratios and refractive indices. Measured LSPs of individual platelets were compared one by one with the theoretical set and the best fit was taken to characterize the measured platelets, resulting in distributions of volume, aspect ratio and refractive index., Comment: 10 pages, 6 figures

Elastic light scattering by mature red blood cells (RBCs) was theoretically and experimentally analyzed with the discrete dipole approximation (DDA) and the scanning flow cytometry (SFC), respectively. SFC permits measurement of angular dependence of light-scattering intensity (indicatrix) of single particles. A mature RBC is modeled as a biconcave disk in DDA simulations of light scattering. We have studied the effect of RBC orientation related to the direction of the incident light upon the indicatrix. Numerical calculations of indicatrices for several aspect ratios and volumes of RBC have been carried out. Comparison of the simulated indicatrices and indicatrices measured by SFC showed good agreement, validating the biconcave disk model for a mature RBC. We simulated the light-scattering output signals from the SFC with the DDA for RBCs modeled as a disk-sphere and as an oblate spheroid. The biconcave disk, the disk-sphere, and the oblate spheroid models have been compared for two orientations, i.e. face-on and rim-on incidence. Only the oblate spheroid model for rim-on incidence gives results similar to the rigorous biconcave disk model., Comment: 13 pages, 9 figures

We present a review of the discrete dipole approximation (DDA), which is a general method to simulate light scattering by arbitrarily shaped particles. We put the method in historical context and discuss recent developments, taking the viewpoint of a general framework based on the integral equations for the electric field. We review both the theory of the DDA and its numerical aspects, the latter being of critical importance for any practical application of the method. Finally, the position of the DDA among other methods of light scattering simulation is shown and possible future developments are discussed., Comment: 36 pages, 1 figure; added several corrections according to the published erratum except for Eq.(5) (it was correct in the original paper)

In this manuscript we investigate the capabilities of the Discrete Dipole Approximation (DDA) to simulate scattering from particles that are much larger than the wavelength of the incident light, and describe an optimized publicly available DDA computer program that processes the large number of dipoles required for such simulations. Numerical simulations of light scattering by spheres with size parameters x up to 160 and 40 for refractive index m=1.05 and 2 respectively are presented and compared with exact results of the Mie theory. Errors of both integral and angle-resolved scattering quantities generally increase with m and show no systematic dependence on x. Computational times increase steeply with both x and m, reaching values of more than 2 weeks on a cluster of 64 processors. The main distinctive feature of the computer program is the ability to parallelize a single DDA simulation over a cluster of computers, which allows it to simulate light scattering by very large particles, like the ones that are considered in this manuscript. Current limitations and possible ways for improvement are discussed., Comment: 13 pages, 10 figures

We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many different discretizations. The quality of the extrapolation improves with refining discretization reaching extraordinary performance especially for cubically shaped particles. A two order of magnitude decrease of error was demonstrated. We also propose estimates of the extrapolation error, which were proven to be reliable. Finally we propose a simple method to directly separate shape and discretization errors and illustrated this for one test case., Comment: 17 pages, 8 figures

We performed a rigorous theoretical convergence analysis of the discrete dipole approximation (DDA). We prove that errors in any measured quantity are bounded by a sum of a linear and quadratic term in the size of a dipole d, when the latter is in the range of DDA applicability. Moreover, the linear term is significantly smaller for cubically than for non-cubically shaped scatterers. Therefore, for small d errors for cubically shaped particles are much smaller than for non-cubically shaped. The relative importance of the linear term decreases with increasing size, hence convergence of DDA for large enough scatterers is quadratic in the common range of d. Extensive numerical simulations were carried out for a wide range of d. Finally we discuss a number of new developments in DDA and their consequences for convergence., Comment: 23 pages, 5 figures; added several corrections according to the published erratum except for Eq.(6) (it was correct in the original paper) and with additional correction in Eq.(96) [$\bar{\mathbf{G}}(...)\mathbf{P}_i^s -\bar{\mathbf{G}}^s(...)\mathbf{P}_i^p$ instead of $(\bar{\mathbf{G}}(...) - \bar{\mathbf{G}}^s(...))\mathbf{P}_i^s$]