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Neointimal hyperplasia (NIH) is a major obstacle to graft patency in the peripheral arteries. A complex interaction of biomechanical factors contribute to NIH development and progression, and although haemodynamic markers such as wall shear stress have been linked to the disease, these have so far been insufficient to fully capture its behaviour. Using a computational model linking computational fluid dynamics (CFD) simulations of blood flow with a biochemical model representing NIH growth mechanisms, we analyse the effect of compliance mismatch, due to the presence of surgical stitches and/or to the change in distensibility between artery and vein graft, on the haemodynamics in the lumen and, subsequently, on NIH progression. The model enabled to simulate NIH at proximal and distal anastomoses of three patient-specific end-to-side saphenous vein grafts under two compliance-mismatch configurations, and a rigid wall case for comparison, obtaining values of stenosis similar to those observed in the computed tomography (CT) scans. The maximum difference in time-averaged wall shear stress between the rigid and compliant models was 3.4 Pa, and differences in estimation of NIH progression were only observed in one patient. The impact of compliance on the haemodynamic-driven development of NIH was small in the patient-specific cases considered., (Copyright © 2019. Published by Elsevier Ltd.)

Agent-based modelling (ABM) offers a framework to realistically couple subcellular signaling pathways to cellular behavior and macroscopic tissue organization. However, these models have been previously inaccessible to many systems biologists due to the difficulties with formulating and simulating multi-scale behavior. In this chapter, a review of the Compucell3D framework is presented along with a general workflow for transitioning from a well-mixed ODE model to an ABM. These techniques are demonstrated through a case study on the simulation of a Notch-Delta Positive Feedback, Lateral Inhibition (PFLI) gene circuit in the intestinal crypts. Specifically, techniques for gene circuit-driven hypothesis formation, geometry construction, selection of simulation parameters, and simulation quantification are presented.

Coloured Petri nets are an excellent choice for exploring large biological models, particularly when there are repetitions of components. Such models can be easily adapted by slight modifications of parameter values related to colours. Similarly, multi-scale models could involve multiple spatial scales in addition to multiple time scales. Thus, they require the full interplay between stochastic as well as deterministic processes. In this paper we take these two aspects into account and present a modelling and simulation approach for multi-scale biochemical networks using Coloured Generalised Hybrid Petri Nets (GHPN C ). GHPN C are a Petri net class that associates colours to Generalised Hybrid Petri Nets (GHPN), which incorporate discrete and continuous places in addition to stochastic and continuous transitions. Moreover, we present two case studies to illustrate typical applications taking advantage of such a Petri net class., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance to therapy since the rescued population is less sensitive to therapy., (Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.)

A new framework for estimation of lumped (for instance, Windkessel) model parameters from uncertain clinical measurements is presented. The ultimate aim is to perform patient-specific haemodynamic analysis. This framework is based on sensitivity analysis tools and the sequential estimation approach of the unscented Kalman filter. Sensitivity analysis and parameter estimation are performed in lumped parameter models, which act as reduced order surrogates of the 3D domain for haemodynamic analysis. While the goal of sensitivity analysis is to assess potential identifiability problems, the unscented Kalman filter estimation leads to parameter estimates based on clinical measurements and modelling assumptions. An application of such analysis and parameter estimation methodology is demonstrated for synthetic and real data. Equality constraints on various physiological parameters are enforced. Since the accuracy of the Windkessel parameter estimates depends on the lumped parameter representativeness, the latter is iteratively improved by running few 3D simulations while simultaneously improving the former. Such a method is applied on a patient-specific aortic coarctation case. Less than 3% and 9% errors between the clinically measured quantities and 3D simulation results for rest and stress are obtained, respectively. Knowledge on how these Windkessel parameters change from rest to stress can thus be learned by such an approach. Lastly, it is demonstrated that the proposed approach is capable of dealing with a wide variety of measurements and cases where the pressure and flow clinical measurements are not taken simultaneously., (Copyright © 2014 John Wiley & Sons, Ltd.)

Mathematical modelling has been used to comprehend the pathology and the assessment of different treatment techniques such as heart failure and left ventricular assist device therapy in the cardiovascular field. In this study, an in-silico model of the heart is developed to understand the effects of idiopathic dilated cardiomyopathy (IDC) as a pathological scenario, with mechanisms described at the cellular, protein and organ levels. This model includes the right and left atria and ventricles, as well as the systemic and pulmonary arteries and veins. First, a multi-scale model of the whole heart is simulated for healthy conditions. Subsequently, the model is modified at its microscopic and macroscopic spatial scale to obtain the characteristics of IDC. The extracellular calcium concentration, the binding affinity of calcium binding proteins and the maximum and minimum elastances have been identified as key parameters across all relevant scales. The modified parameters cause a change in (a) intracellular calcium concentration characterising cellular properties, such as calcium channel currents or the action potential, (b) the proteins being involved in the sliding filament mechanism and the proportion of the attached crossbridges at the protein level, as well as (c) the pressure and volume values at the organ level. This model allows to obtain insight and understanding of the effects of the treatment techniques, from a physiological and biological point of view., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

Architected materials and mechanical metamaterials are known for their unique macroscopic properties and complex behaviour that often defy conventional continuum mechanics. Therefore, in this contribution, a recent multi-scale second-order computational homogenisation method (Dos Santos et al., 2023) is employed to explore these materials under finite strains. The approach combines a second gradient continuum theory at the macro-scale and a representative volume element (RVE) with classical first-order continuum mechanics at the micro-scale. The Method of Multi-scale Virtual Power ensures a consistent scale transition. The predictive capability and applicability of the second-order computational strategy are evaluated through coupled multi-scale numerical simulations. These simulations involve two- and three-dimensional problems, with a strong focus on the development of novel metamaterials, while also accounting for diverse loading conditions, such as tension/compression-induced undulation, bending, and compression-induced torsion. Comparisons with first-order homogenisation and Direct Numerical Simulations validate the approach. Analysis of homogenised consistent tangents reveals valuable insights into macroscopic properties. Overall, the results highlight the capability of the second-order strategy to capture significant phenomena, including second-order deformation modes, coupling deformation mechanisms, and size effects. • A multi-scale second-order homogenisation method is used to explore metamaterials. • A second gradient continuum theory is combined with first-order continuum mechanics. • An assessment is conducted through coupled multi-scale numerical simulations. • Novel metamaterials are investigated for diverse loading conditions. • Higher-order deformation modes, coupling mechanisms and size effects are captured. [ABSTRACT FROM AUTHOR]

Aluminium metal production through electrolytic reduction of alumina in a cryolite bath is a complex, multi-physics, multi-scale process, including magneto-hydrodynamics (MHD), bubble flow, thermal convection, melting and solidification phenomena based on a set of chemical reactions. Through interactions of the different forces applied to the liquid bath combined with the different time and length scales, self-organised fluctuations occur. Moreover, the MHD behaviour causes a complex metal pad profile and a series of surface waves due to the meta-stable condition of the metal/cryolite interface. The large aspect ratio of an industrial cell, with a footprint of 20 by 4 m and at the same time having dimensions approaching just 30 mm of height for the reaction zone, prevents an integrated approach where all relevant physics are included in a single mathematical model of this large degree of freedom system. In order to overcome these challenges, different modelling approaches have been established in ANSYS ® FLUENT ® ; Three models are used to predict details of specific physics: one to predict the electro-magnetic forces and hence the metal pad profile, a second that resolves details of the local bubble dynamics around a single anode and a third for the full cell bath flow. Results from these models are coupled to allow integration of the different phenomena into a full cell alumina distribution model. The current paper outlines each of the approaches and presents how the coupling between them can be realized in a complete framework, aiming to provide new insight into the process. [ABSTRACT FROM AUTHOR]

Aortic dissection is a disease whereby an injury in the wall of the aorta leads to the creation of a true lumen and a false lumen separated by an intimal flap which may contain multiple communicating tears between the lumina. It has a high associated morbidity and mortality, but at present, the timing of surgical intervention for stable type B dissections remains an area of debate. Detailed knowledge of haemodynamics may yield greater insight into the long-term outcomes for dissection patients by providing a greater understanding of pressures, wall shear stress and velocities in and around the dissection. In this paper, we aim to gather further insight into the complex haemodynamics in aortic dissection using medical imaging and computational fluid dynamics modelling. Towards this end, several computer models of the aorta of a patient presenting with an acute Stanford type B dissection were created whereby morphometric parameters related to the dissection septum were altered, such as removal of the septum, and the variation of the number of connecting tears between the lumina. Patient-specific flow data acquired using 2D PC-MRI in the ascending aorta were used to set the inflow boundary condition. Coupled zero-dimensional (Windkessel) models representing the distal vasculature were used to define the outlet boundary conditions and tuned to match 2D PC-MRI flow data acquired in the descending aorta. Haemodynamics in the dissected aorta were compared to those in an equivalent 'healthy aorta', created by virtually removing the intimal flap (septum). Local regions of increased velocity, pressure, wall shear stress and alterations in flow distribution were noted, particularly in the narrow true lumen and around the primary entry tear. The computed flow patterns compared favourably with those obtained using 4D PC-MRI. A lumped-parameter heart model was subsequently used to show that in this case there was an estimated 14 % increase in left ventricular stroke work with the onset of dissection. Finally, the effect of secondary connecting tears (i.e. those excluding the primary entry and exit tears) was also studied, revealing significant haemodynamic changes when no secondary tears are included in the model, particularly in the true lumen where increases in flow over $$+200\,\%$$ and drops in peak pressure of 18 % were observed. [ABSTRACT FROM AUTHOR]

In this paper, we propose the first estimate of some elastic parameters of the relaxed micromorphic model on the basis of real experiments of transmission of longitudinal plane waves across an interface separating a classical Cauchy material (steel plate) and a phononic crystal (steel plate with fluid-filled holes). A procedure is set up in order to identify the parameters of the relaxed micromorphic model by superimposing the experimentally based profile of the reflection coefficient (plotted as function of the wave-frequency) with the analogous profile obtained via numerical simulations. We determine five out of six constitutive parameters which are featured by the relaxed micromorphic model in the isotropic case, plus the determination of the micro-inertia parameter. The sixth elastic parameter, namely the Cosserat couple modulus μc, still remains undetermined, since experiments on transverse incident waves are not yet available. A fundamental result of this paper is the estimate of the non-locality intrinsically associated with the underlying microstructure of the metamaterial. We show that the characteristic length Lc measuring the non-locality of the phononic crystal is of the order of 1/3 of the diameter of its fluidfilled holes. [ABSTRACT FROM AUTHOR]

In this paper we report the extension of an earlier reported DNS method (Deen et al., 2012; Deen and Kuipers, 2013) based on a novel Immersed Boundary Method (IBM) which incorporates the fluid-solid coupling at the level of the discrete field equations. The extended method is used to study coupled mass and heat transport in dense fluid-particle systems where the coupling arises as a consequence of an exothermal chemical reaction proceeding at the exterior surface of the particles. Following a detailed verification (using an independent numerical technique) and validation (using established empirical correlations) we apply our DNS technique to study coupled mass and heat transfer in a dense fluid-particle system. In addition a comparison is made with results obtained from a simple one-dimensional (1D) heterogeneous reactor model which uses empirical closures for the fluid-particle mass and heat transfer coefficients. The main features of the complex transient temperature profiles obtained from our DNS agree quite well with the corresponding profiles obtained from the 1D heterogeneous reactor model. [ABSTRACT FROM AUTHOR]

In-plane centroids of textile composites are simulated as cross-correlated random fields. Each tow position is defined as an average trend quantified from experimental data, added with zero-mean deviations produced as a stochastic field. Realisations of these fields are generated using a framework based on the Karhunen–Loève series expansion that is calibrated with experimental information from prior work. Positional deviations are obtained that are correlated along the tow and between neighbouring tows. The application is a 2/2 twill woven carbon fibre reinforced epoxy consisting of multiple unit cells. Generated in-plane deviations of the warp and weft tows resemble the experimental fluctuations with similar wavelengths. Simulation of thousand specimens demonstrates that the virtual in-plane positions possess the experimental standard deviation and correlation lengths on average. [ABSTRACT FROM AUTHOR]

Abstract: Pore-scale simulations of transport phenomena in foam based catalytic converters are highly desirable due to their intrinsic accuracy in describing the involved physics. Unfortunately, such computations are prohibitively time consuming and costly. Here we combine a detailed pore-scale characterization with a volume average description of an open-cell foam based catalytic converter. The resulting volume averaged model is accurate and more than three orders of magnitude more efficient in terms of computational time, compared to direct pore scale simulations. This makes simulations of the related complex phenomena tractable, providing a highly flexible and powerful tool for parametric studies of open-cell foams. The volume-averaged model is validated with a pore-scale simulation of a full-scale catalytic converter used for automotive exhaust gas treatment. Fast chemistry is assumed and the heat released by the chemical reaction in combination with conjugate heat transfer is considered. We show that the conversion to pressure drop trade-off improves with increasing foam porosity and the heat release of the reaction significantly affects the pressure drop across the reactor. The simulations show non-uniform surface temperatures which are attributed to the non-unity Lewis number of the mass transfer limiting species. The model predictions agree well with experimental measurements of pressure drop and Sherwood number in open-cell foams. [Copyright &y& Elsevier]

The understanding and the prediction of the failure behaviour of materials with pronounced microstructural effects is of crucial importance. This paper presents a novel computational methodology for the handling of fracture on the basis of the microscale behaviour. The basic principles presented here allow the incorporation of an adaptive discretization scheme of the structure as a function of the evolution of strain localization in the underlying microstructure. The proposed quasi-discrete methodology bridges two scales: the scale of the material microstructure, modelled with a continuum type description; and the structural scale, where a discrete description of the material is adopted. The damaging material at the structural scale is divided into unit volumes, called cells, which are represented as a discrete network of points. The scale transition is inspired by computational homogenization techniques; however it does not rely on classical averaging theorems. The structural discrete equilibrium problem is formulated in terms of the underlying fine scale computations. Particular boundary conditions are developed on the scale of the material microstructure to address damage localization problems. The performance of this quasi-discrete method with the enhanced boundary conditions is assessed using different computational test cases. The predictions of the quasi-discrete scheme agree well with reference solutions obtained through direct numerical simulations, both in terms of crack patterns and load versus displacement responses. [ABSTRACT FROM AUTHOR]

Predicting precisely where a crack will develop in a material under stress and exactly when in time catastrophic fracture of the component will occur is one the oldest unsolved mysteries in the design and building of large engineering structures. Where human life depends upon engineering ingenuity, the burden of testing to prove a 'fracture safe design' is immense. For example, when human life depends upon structural integrity as an essential design requirement, it takes ten thousand material test coupons per composite laminate configuration to evaluate an airframe plus loading to ultimate failure tails, wing boxes, and fuselages to achieve a commercial aircraft airworthiness certification. Fitness considerations for long-life implementation of aerospace composites include understanding phenomena such as impact, fatigue, creep, and stress corrosion cracking that affect reliability, life expectancy, and durability of structure. Structural integrity analysis treats the design, the materials used, and figures out how best components and parts can be joined. Furthermore, SI takes into account service duty. However, there are conflicting aims in the complete design process of designing simultaneously for high efficiency and safety assurance throughout an economically viable lifetime with an acceptable level of risk. [ABSTRACT FROM AUTHOR]

An unconventional multi-scale approach is investigated to model interfacial damage and subsequent effects in highly filled particulate composites such as solid propellants. The basic framework by Nadot et al. (2006 Damage modelling framework for viscoelastic particulate composites via a scale transition approach, Journal of Theoretical and Applied Mechanics 44:553–583) is enhanced to deal with damage state and configuration evolution under any loading. Three criteria are formulated at the microscale. The first one concerns the nucleation of new defects, while the other two (for closure and re-opening) monitor the respective proportions of open and closed defects. The formulation exploits the explicit microstructure representation and the knowledge of the local displacement field as a function of local morphology around the interfaces. The multi-scale model is finally implemented through a numerical solving procedure able to deal with successive and/or simultaneous discrete damage events (nucleation/closure/re-opening of defects) depending on the loading path. Numerical illustrations are given for a three-dimensional microstructure containing 351 particles submitted to complex loading sequence involving extension, shear and contraction stages. The results show the ability of the model to estimate damage characteristics (position, orientation within the material) in addition to induced effects at both microscale and macroscale (induced anisotropy, unilateral effects and influence on local fields). [ABSTRACT FROM PUBLISHER]

Abstract: Systems biology is centrally engaged with computational modelling across multiple scales and at many levels of abstraction. Formal modelling, precise and formalised abstraction relationships, and computation also lie at the heart of computer science—and over the past decade a growing number of computer scientists have been bringing their discipline''s core intellectual and computational tools to bear on biology in fascinating new ways. This paper explores some of the apparent points of contact between the two fields, in the context of a multi-disciplinary discussion on conceptual foundations of systems biology. [Copyright &y& Elsevier]

Here we review and extend models on different scales for a comput-ing architecture made from networks of excitable chemical droplets. A system of lipid covered droplets containing reagents of the Belousov-Zhabotinsky (BZ) reaction has been used in our experiments as model system to study the signal transmission dynamics of chemical comput-ers and their modelling. A chemical medium in sub-excitable, excitable or self-exciting (oscillating) regimes supports propagating excitation pulses. These pulses can be used for information coding and process-ing. In the manuscript we review models that can be applied to describe the time evolution of a medium composed of droplets: we discuss a homogeneous differential equation model, a spatially extended par-tial differential equation model and a cellular automaton model of the chemical reaction. Furthermore, wc propose a new high level modelling approach for the droplets, that discretises the chemical states and con-siders stochasticity in the transition functions. We demonstrate how the values of experimentally measured quantities like oscillation periods, diffusion coefficients and wave propagation speeds can be deduced from the lower level models. Furthermore we offer an outlook on the cur-rently ongoing work and the role of the different modelling and simula-tion scopes within. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the on-going research steps aiming at the development of a Method for Multi-scale Modeling and Simulation of Assembly System. The focus lies on the Assembly System Base Model and its integration into the whole method. After motivating the research, the developed method and the conceived model of the assembly system is introduced, by using the proposed methodology. The presented approach aims at the manageability of the systems complexity and the acceleration of optimization and adaption processes. It concludes with a roadmap shaping the next steps and activities. [Copyright &y& Elsevier]

Abstract: A multi-scale modelling approach is employed to investigate the elasto-plastic behaviour of the pure chitosan biological polymer, as well as its composite when it is embedded with a graphene sheet, and a carbon nanotube. The model directly incorporates inter-atomic potentials, describing the energetics of molecular clusters, into a continuum-based computation without any need for a parameter fitting. The coupling of the atomistic and continuum levels is achieved via the adoption of the Cauchy–Born rule which provides a suitable framework for investigating the mechanical behaviour of materials undergoing large deformations. All data on atomic bonding, bond angle, bond torsion, and nonbonding interactions relevant to the molecular clusters are incorporated into the constitutive continuum model. The continuum point within a finite element (FE) mesh is represented by an atomic cluster, referred to as a nanoscopic representative volume element (NRVE). We have introduced a parameter R that represents the ratio of the volume of finite element within which the NRVE is embedded to the volume of the NRVE. It is shown that the variation of R directly affects the results on the stress–strain behaviour of the composite, and that for R ∼1.0, our computed results on the elastic modulus of the simple and composite systems are fair in agreement with the experimental data. [Copyright &y& Elsevier]