Reduced Order Modeling for Real-Time Stent Deformation Simulations of Transcatheter Aortic Valve Prostheses

Computational modeling can be a critical tool to predict deployment behavior for transcatheter aortic valve replacement (TAVR) in patients with aortic stenosis. However, due to the mechanical complexity of the aortic valve and the multiphysics nature of the problem, described by partial differential equations (PDEs), traditional finite element (FE) modeling of TAVR deployment is computationally expensive. In this preliminary study, a PDEs-based reduced order modeling (ROM) framework is introduced for rapidly simulating structural deformation of the Medtronic Evolut R valve stent frame. Using fifteen probing points from an Evolut model with parametrized loads enforced, 105 FE simulations were performed in the so-called offline phase, creating a snapshot library. The library was used in the online phase of the ROM for a new set of applied loads via the proper orthogonal decomposition-Galerkin (POD-Galerkin) approach. Simulations of small radial deformations of the Evolut stent frame were performed and compared to full order model (FOM) solutions. Linear elastic and hyperelastic constitutive models in steady and unsteady regimes were implemented within the ROM. Since the original POD-Galerkin method is formulated for linear problems, specific methods for the nonlinear terms in the hyperelastic case were employed, namely, the Discrete Empirical Interpolation Method. The ROM solutions were in strong agreement with the FOM in all numerical experiments, with a speed-up of at least 92% in CPU Time. This framework serves as a first step toward real-time predictive models for TAVR deployment simulations.

Harris hawks optimization algorithm for model order reduction of interconnected wind turbines

This paper illustrates the investigation of higher-scale interconnected wind turbine to realize its analytical design and simulation performance in terms of reduced order model. The present research is aimed to visualize the efficacy of the propounded harris hawks optimization (HHO) approach for different reduced order transfer functions with reference to model order reduction studies. Compared to the higher-scale model, the applied methodology aims to obtain better results in terms of steadiness and computational effort. Moreover, to realize a higher-dimensional power system, the implementation of the HHO may proffer more effectiveness and robustness as opposed to the state-of-the-art optimization techniques. The applied methodology aims to obtain better results in terms of stability and computational effort. Furthermore, to realize a higher dimensional system, implementation of the HHO may offer more effectiveness and robustness as opposed to the state-of-the-art optimization techniques.

A technique for non-intrusive greedy piecewise-rational model reduction of frequency response problems over wide frequency bands

In the field of model order reduction for frequency response problems, the minimal rational interpolation (MRI) method has been shown to be quite effective. However, in some cases, numerical instabilities may arise when applying MRI to build a surrogate model over a large frequency range, spanning several orders of magnitude. We propose a strategy to overcome these instabilities, replacing an unstable global MRI surrogate with a union of stable local rational models. The partitioning of the frequency range into local frequency sub-ranges is performed automatically and adaptively, and is complemented by a (greedy) adaptive selection of the sampled frequencies over each sub-range. We verify the effectiveness of our proposed method with two numerical examples.

Model order reduction of flow based on a modular geometrical approximation of blood vessels

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier-Stokes equations. Our algorithm is based on an approximated domain-decomposition of the target geometry into a number of subdomains obtained from the parametrized deformation of geometrical building blocks (e.g., straight tubes and model bifurcations). On each of these building blocks, we build a set of spectral functions by Proper Orthogonal Decomposition of a large number of snapshots of finite element solutions (offline phase). The global solution of the Navier-Stokes equations on a target geometry is then found by coupling linear combinations of these local basis functions by means of spectral Lagrange multipliers (online phase). Being that the number of reduced degrees of freedom is considerably smaller than their finite element counterpart, this approach allows us to significantly decrease the size of the linear system to be solved in each iteration of the Newton-Raphson algorithm. We achieve large speedups with respect to the full order simulation (in our numerical experiments, the gain is at least of one order of magnitude and grows inversely with respect to the reduced basis size), whilst still retaining satisfactory accuracy for most cardiovascular simulations.

A Practical Step-by-Step Guide for Quantifying Retroactivity in Gene Networks

One of the fundamental properties of engineered large-scale complex systems is modularity. In synthetic biology, genetic parts exhibit context-dependent behavior. Here, we describe and quantify a major source of such behavior: retroactivity. In particular, we provide a step-by-step guide for characterizing retroactivity to restore the modular description of genetic modules. Additionally, we also discuss how retroactivity can be leveraged to quantify and maximize robustness to perturbations due to interconnection of genetic modules.

The influence of model order reduction on the computed fractional flow reserve using parameterized coronary geometries

Computational fluid dynamics (CFD) models combined with patient-specific imaging data are used to non-invasively predict functional significance of coronary lesions. This approach to predict the fractional flow reserve (FFR) is shown to have a high diagnostic accuracy when comparing against invasively measured FFR. However, one of the main drawbacks is the high computational effort needed for preprocessing and computations. Hence, uncertainty quantification may become unfeasible. Reduction of complexity is desirable, computationally inexpensive models with high diagnostic accuracy are preferred. We present a parametric comparison study for three types of CFD models (2D axisymmetric, Semi-3D and 3D) in which we study the impact of model reduction on three models on the predicted FFR. In total 200 coronary geometries were generated for seven geometrical characteristics e.g. stenosis severity, stenosis length and vessel curvature. The effect of time-averaged flow was investigated using unsteady, mean steady and a root mean square (RMS) steady flow. The 3D unsteady model was regarded as reference model. Results show that when using an unsteady or RMS flow, predicted FFR hardly varies between models contrary to using average flows. The 2D model with RMS flow has a high diagnostic accuracy (0.99), reduces computational time by a factor 162,000 and the introduced model error is well below the clinical relevant differences. Stenosis severity, length, curvature and tapering cause most discrepancies when using a lower order model. An uncertainty analysis showed that this can be explained by the low variability that is caused by variations in stenosis asymmetry.

Understanding and reducing complex systems pharmacology models based on a novel input-response index

A growing understanding of complex processes in biology has led to large-scale mechanistic models of pharmacologically relevant processes. These models are increasingly used to study the response of the system to a given input or stimulus, e.g., after drug administration. Understanding the input-response relationship, however, is often a challenging task due to the complexity of the interactions between its constituents as well as the size of the models. An approach that quantifies the importance of the different constituents for a given input-output relationship and allows to reduce the dynamics to its essential features is therefore highly desirable. In this article, we present a novel state- and time-dependent quantity called the input-response index that quantifies the importance of state variables for a given input-response relationship at a particular time. It is based on the concept of time-bounded controllability and observability, and defined with respect to a reference dynamics. In application to the brown snake venom-fibrinogen (Fg) network, the input-response indices give insight into the coordinated action of specific coagulation factors and about those factors that contribute only little to the response. We demonstrate how the indices can be used to reduce large-scale models in a two-step procedure: (i) elimination of states whose dynamics have only minor impact on the input-response relationship, and (ii) proper lumping of the remaining (lower order) model. In application to the brown snake venom-fibrinogen network, this resulted in a reduction from 62 to 8 state variables in the first step, and a further reduction to 5 state variables in the second step. We further illustrate that the sequence, in which a recursive algorithm eliminates and/or lumps state variables, has an impact on the final reduced model. The input-response indices are particularly suited to determine an informed sequence, since they are based on the dynamics of the original system. In summary, the novel measure of importance provides a powerful tool for analysing the complex dynamics of large-scale systems and a means for very efficient model order reduction of nonlinear systems.

On the use of absolute interface coordinates in the floating frame of reference formulation for flexible multibody dynamics

In this work a new formulation for flexible multibody systems is presented based on the floating frame formulation. In this method, the absolute interface coordinates are used as degrees of freedom. To this end, a coordinate transformation is established from the absolute floating frame coordinates and the local interface coordinates to the absolute interface coordinates. This is done by assuming linear theory of elasticity for a body's local elastic deformation and by using the Craig-Bampton interface modes as local shape functions. In order to put this new method into perspective, relevant relations between inertial frame, corotational frame and floating frame formulations are explained. As such, this work provides a clear overview of how these three well-known and apparently different flexible multibody methods are related. An advantage of the method presented in this work is that the resulting equations of motion are of the differential rather than the differential-algebraic type. At the same time, it is possible to use well-developed model order reduction techniques on the flexible bodies locally. Hence, the method can be employed to construct superelements from arbitrarily shaped three dimensional elastic bodies, which can be used in a flexible multibody dynamics simulation. The method is validated by simulating the static and dynamic behavior of a number of flexible systems.

Order reduction and efficient implementation of nonlinear nonlocal cochlear response models

The cochlea is an indispensable preliminary processing stage in auditory perception that employs mechanical frequency-tuning and electrical transduction of incoming sound waves. Cochlear mechanical responses are shown to exhibit active nonlinear spatiotemporal response dynamics (e.g., otoacoustic emission). To model such phenomena, it is often necessary to incorporate cochlear fluid-membrane interactions. This results in both excessively high-order model formulations and computationally intensive solutions that limit their practical use in simulating the model and analyzing its response even for simple single-tone inputs. In order to address these limitations, the current work employs a control-theoretic framework to reformulate a nonlinear two-dimensional cochlear model into discrete state space models that are of considerably lower order (factor of 8) and are computationally much simpler (factor of 25). It is shown that the reformulated models enjoy sparse matrix structures which permit efficient numerical manipulations. Furthermore, the spatially discretized models are linearized and simplified using balanced transformation techniques to result in lower-order (nonlinear) realizations derived from the dominant Hankel singular values of the system dynamics. Accuracy and efficiency of the reduced-order reformulations are demonstrated under the response to two fixed tones, sweeping tones and, more generally, a brief speech signal. The corresponding responses are compared to those produced by the original model in both frequency and spatiotemporal domains. Although carried out on a specific instance of cochlear models, the introduced framework of control-theoretic model reduction could be applied to a wide class of models that address the micro- and macro-mechanical properties of the cochlea.

Predicting muscle fatigue: a response surface approximation based on proper generalized decomposition technique

A novel technique is proposed to predict force reduction in skeletal muscle due to fatigue under the influence of electrical stimulus parameters and muscle physiological characteristics. Twelve New Zealand white rabbits were divided in four groups ([Formula: see text]) to obtain the active force evolution of in vitro Extensor Digitorum Longus muscles for an hour of repeated contractions under different electrical stimulation patterns. Left and right muscles were tested, and a total of 24 samples were used to construct a response surface based in the proper generalized decomposition. After the response surface development, one additional rabbit was used to check the predictive potential of the technique. This multidimensional surface takes into account not only the decay of the maximum repeated peak force, but also the shape evolution of each contraction, muscle weight, electrical input signal and stimulation protocol. This new approach of the fatigue simulation challenge allows to predict, inside the multispace surface generated, the muscle response considering other stimulation patterns, different tissue weight, etc.

Automatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimization

In this paper, we present new reliable model order reduction strategies for computational micromechanics. The difficulties rely mainly upon the high dimensionality of the parameter space represented by any load path applied onto the representative volume element. We take special care of the challenge of selecting an exhaustive snapshot set. This is treated by first using a random sampling of energy dissipating load paths and then in a more advanced way using Bayesian optimization associated with an interlocked division of the parameter space. Results show that we can insure the selection of an exhaustive snapshot set from which a reliable reduced-order model can be built.

Homogenization of locally resonant acoustic metamaterials towards an emergent enriched continuum

This contribution presents a novel homogenization technique for modeling heterogeneous materials with micro-inertia effects such as locally resonant acoustic metamaterials. Linear elastodynamics is used to model the micro and macro scale problems and an extended first order Computational Homogenization framework is used to establish the coupling. Craig Bampton Mode Synthesis is then applied to solve and eliminate the microscale problem, resulting in a compact closed form description of the microdynamics that accurately captures the Local Resonance phenomena. The resulting equations represent an enriched continuum in which additional kinematic degrees of freedom emerge to account for Local Resonance effects which would otherwise be absent in a classical continuum. Such an approach retains the accuracy and robustness offered by a standard Computational Homogenization implementation, whereby the problem and the computational time are reduced to the on-line solution of one scale only.

A simplification of Cobelli's glucose-insulin model for type 1 diabetes mellitus and its FPGA implementation

Cobelli's glucose-insulin model is the only computer simulator of glucose-insulin interactions accepted by Food Drug Administration as a substitute to animal trials. However, it consists of multiple differential equations that make it hard to be implemented on a hardware platform. In this investigation, the Cobelli's model is simplified by Padé approximant method and implemented on a field-programmable gate array-based platform as a hardware model for predicting glucose changes in subjects with type 1 diabetes mellitus. Compared with the original Cobelli's model, the implemented hardware model provides a nearly perfect approximation in predicting glucose changes with rather small root-mean-square errors and maximum errors. The RMSE results for 30 subjects show that the method for simplifying and implementing Cobelli's model has good robustness and applicability. The successful hardware implementation of Cobelli's model will promote a wider adoption of this model that can substitute animal trials, provide fast and reliable glucose and insulin estimation, and ultimately assist the further development of an artificial pancreas system.

Intelligent modified internal model control for speed control of nonlinear uncertain heavy duty vehicles

The objective of this paper is to control the speed of heavy duty vehicle (HDV) through angular position of throttle valve. Modified internal model control (IMC) schemes with fuzzy supervisor as an adaptive tuning are proposed to control the speed of HDV. Internal model (IM) plays a key role in design of various IMC structures with robust and adaptive features. The motivation to design an IM is to produce nearly stable performance as of the system itself. Clustering algorithm and Hankel approximation based model order reduction techniques are used for the design of suitable IM. The time domain performance specifications such as overshoot, settling time, rise time and integral error performance indices such as the integral of the absolute error and the integral of the square of error are taken into consideration for performance analysis of HDV for various uncertainties.