Numerical modelling of mass transport in an arterial wall with anisotropic transport properties

Coronary artery disease results in blockages or narrowing of the artery lumen. Drug eluting stents (DES) were developed to replace bare metal stents in an effort to combat re-blocking of the diseased artery following treatment. The numerical models developed within this study focus on representing the changing trends of drug delivery from an idealised DES in an arterial wall with an anisotropic ultra-structure. To reduce the computational burden of solving coupled physics problems, a model reduction strategy was adopted. Particular focus has been placed upon adequately modelling the influence of strut compression as there is a paucity of numerical studies that account for changes in transport properties in compressed regions of the arterial wall due to stent deployment. This study developed an idealised numerical modelling framework to account for the changes in the directionally dependent porosity and tortuosities of the arterial wall as a result of radial strut compression. The results show that depending on the degree of strut compression, trends in therapeutic drug delivery within the arterial wall can be either increased or decreased. The study highlights the importance of incorporating compression into numerical models to better represent transport within the arterial wall and suggests an appropriate numerical modelling framework that could be utilised in more realistic patient specific arterial geometries.     

An approach to multiscale modelling with graph grammars

Background and Aims

Functional–structural plant models (FSPMs) simulate biological processes at different spatial scales. Methods exist for multiscale data representation and modification, but the advantages of using multiple scales in the dynamic aspects of FSPMs remain unclear. Results from multiscale models in various other areas of science that share fundamental modelling issues with FSPMs suggest that potential advantages do exist, and this study therefore aims to introduce an approach to multiscale modelling in FSPMs.

Methods

A three-part graph data structure and grammar is revisited, and presented with a conceptual framework for multiscale modelling. The framework is used for identifying roles, categorizing and describing scale-to-scale interactions, thus allowing alternative approaches to model development as opposed to correlation-based modelling at a single scale. Reverse information flow (from macro- to micro-scale) is catered for in the framework. The methods are implemented within the programming language XL.

Key Results

Three example models are implemented using the proposed multiscale graph model and framework. The first illustrates the fundamental usage of the graph data structure and grammar, the second uses probabilistic modelling for organs at the fine scale in order to derive crown growth, and the third combines multiscale plant topology with ozone trends and metabolic network simulations in order to model juvenile beech stands under exposure to a toxic trace gas.

Conclusions

The graph data structure supports data representation and grammar operations at multiple scales. The results demonstrate that multiscale modelling is a viable method in FSPM and an alternative to correlation-based modelling. Advantages and disadvantages of multiscale modelling are illustrated by comparisons with single-scale implementations, leading to motivations for further research in sensitivity analysis and run-time efficiency for these models.     

Modeling the Afferent Dynamics of the Baroreflex Control System

In this study we develop a modeling framework for predicting baroreceptor firing rate as a function of blood pressure. We test models within this framework both quantitatively and qualitatively using data from rats. The models describe three components: arterial wall deformation, stimulation of mechanoreceptors located in the BR nerve-endings, and modulation of the action potential frequency. The three sub-systems are modeled individually following well-established biological principles. The first submodel, predicting arterial wall deformation, uses blood pressure as an input and outputs circumferential strain. The mechanoreceptor stimulation model, uses circumferential strain as an input, predicting receptor deformation as an output. Finally, the neural model takes receptor deformation as an input predicting the BR firing rate as an output. Our results show that nonlinear dependence of firing rate on pressure can be accounted for by taking into account the nonlinear elastic properties of the artery wall. This was observed when testing the models using multiple experiments with a single set of parameters. We find that to model the response to a square pressure stimulus, giving rise to post-excitatory depression, it is necessary to include an integrate-and-fire model, which allows the firing rate to cease when the stimulus falls below a given threshold. We show that our modeling framework in combination with sensitivity analysis and parameter estimation can be used to test and compare models. Finally, we demonstrate that our preferred model can exhibit all known dynamics and that it is advantageous to combine qualitative and quantitative analysis methods.     

A structural constitutive model for collagenous cardiovascular tissues incorporating the angular fiber distribution

Accurate constitutive models are required to gain further insight into the mechanical behavior of cardiovascular tissues. In this study, a structural constitutive framework for cardiovascular tissues is introduced that accounts for the angular distribution of collagen fibers. To demonstrate its capabilities, the model is applied to study the biaxial behavior of the arterial wall and the aortic valve. The pressure-radius relationships of the arterial wall accurately describe experimentally observed sigma-shaped curves. In addition, the nonlinear and anisotropic mechanical properties of the aortic valve can be analyzed with the proposed model. We expect that the current model offers strong possibilities to further investigate the complex mechanical behavior of cardiovascular tissues, including their response to mechanical stimuli.     

Role of physical properties of resistance vessel wall in regulating peripheral blood flow--II. Structural and mechanical behavior

In order to examine the structural and mechanical properties of the vessel wall resistance when subjected to autoregulatory flow control, a mechanical model for the vascular wall was derived from a mathematical model. The mechanical model was an analogue model which connected in series the Maxwell model (elastic modulus: K3) with the parallel elements of Hill's model (elastic modules: K2) and Hooke's elastic model (elastic modulus: K1); it was also mathematically equivalent to the Spring model (see part I). The structural and mechanical properties of the resistance vessel wall were characterized by the three elastic moduli (K1, alpha K2 and K3) [mmHg]. The parameter alpha was a modification factor of the elastic modulus K2 given by the myogenic mechanism. After a numerical analysis of the experimental data given by the mechanical model, we confirmed that the arterial pressure range for autoregulatory flow controls shifted to the upper region with an increase of the elastic modulus K1 and the flow regulation was reduced.     

Impedance-based outflow boundary conditions for human carotid haemodynamics

In this study, we develop structured tree outflow boundary conditions for modelling the human carotid haemodynamics. The model geometry was reconstructed through computerised tomography scan. Unsteady-state computational fluid dynamic analyses were performed under different conditions using a commercial software package ADINA R&D, Inc., (Watertown, MA, USA) in order to assess the impact of the boundary conditions on the flow variables. In particular, the results showed that the peripheral vessels massively impact the pressure while the flow is relatively unaffected. As an example of application of these outflow conditions, an unsteady fluid-structure interaction (FSI) simulation was carried out and the dependence of the wall shear stress (WSS) on the arterial wall compliance in the carotid bifurcation was studied. In particular, a comparison between FSI and rigid-wall models was conducted. Results showed that the WSS distributions were substantially affected by the diameter variation of the arterial wall. In particular, even similar WSS distributions were found for both cases, and differences in the computed WSS values were also found.     

A modelling framework to simulate foliar fungal epidemics using functional–structural plant models

Background and Aims

Sustainable agriculture requires the identification of new, environmentally responsible strategies of crop protection. Modelling of pathosystems can allow a better understanding of the major interactions inside these dynamic systems and may lead to innovative protection strategies. In particular, functional–structural plant models (FSPMs) have been identified as a means to optimize the use of architecture-related traits. A current limitation lies in the inherent complexity of this type of modelling, and thus the purpose of this paper is to provide a framework to both extend and simplify the modelling of pathosystems using FSPMs.

Methods

Different entities and interactions occurring in pathosystems were formalized in a conceptual model. A framework based on these concepts was then implemented within the open-source OpenAlea modelling platform, using the platform''s general strategy of modelling plant–environment interactions and extending it to handle plant interactions with pathogens. New developments include a generic data structure for representing lesions and dispersal units, and a series of generic protocols to communicate with objects representing the canopy and its microenvironment in the OpenAlea platform. Another development is the addition of a library of elementary models involved in pathosystem modelling. Several plant and physical models are already available in OpenAlea and can be combined in models of pathosystems using this framework approach.

Key Results

Two contrasting pathosystems are implemented using the framework and illustrate its generic utility. Simulations demonstrate the framework''s ability to simulate multiscaled interactions within pathosystems, and also show that models are modular components within the framework and can be extended. This is illustrated by testing the impact of canopy architectural traits on fungal dispersal.

Conclusions

This study provides a framework for modelling a large number of pathosystems using FSPMs. This structure can accommodate both previously developed models for individual aspects of pathosystems and new ones. Complex models are deconstructed into separate ‘knowledge sources’ originating from different specialist areas of expertise and these can be shared and reassembled into multidisciplinary models. The framework thus provides a beneficial tool for a potential diverse and dynamic research community.     

A multi-scale mechanobiological model of in-stent restenosis: deciphering the role of matrix metalloproteinase and extracellular matrix changes

Since their first introduction, stents have revolutionised the treatment of atherosclerosis; however, the development of in-stent restenosis still remains the Achilles' heel of stent deployment procedures. Computational modelling can be used as a means to model the biological response of arteries to different stent designs using mechanobiological models, whereby the mechanical environment may be used to dictate the growth and remodelling of vascular cells. Changes occurring within the arterial wall due to stent-induced mechanical injury, specifically changes within the extracellular matrix, have been postulated to be a major cause of activation of vascular smooth muscle cells and the subsequent development of in-stent restenosis. In this study, a mechanistic multi-scale mechanobiological model of in-stent restenosis using finite element models and agent-based modelling is presented, which allows quantitative evaluation of the collagen matrix turnover following stent-induced arterial injury and the subsequent development of in-stent restenosis. The model is specifically used to study the influence of stent deployment diameter and stent strut thickness on the level of in-stent restenosis. The model demonstrates that there exists a direct correlation between the stent deployment diameter and the level of in-stent restenosis. In addition, investigating the influence of stent strut thickness using the mechanobiological model reveals that thicker strut stents induce a higher level of in-stent restenosis due to a higher extent of arterial injury. The presented mechanobiological modelling framework provides a robust platform for testing hypotheses on the mechanisms underlying the development of in-stent restenosis and lends itself for use as a tool for optimisation of the mechanical parameters involved in stent design.     

CESE

Cell electrophysiology simulation environment (CESE) is an integrated environment for performing simulations with a variety of electrophysiological models that have Hodgkin-Huxley and Markovian formulations of ionic currents. CESE is written in Java 2 and is readily portable to a number of operating systems. CESE allows execution of single-cell models and modification and clamping of model parameters, as well as data visualisation and analysis using a consistent interface. Model creation for CESE is facilitated by an object-oriented approach and use of an extensive modelling framework. The Web-based model repository is available. AVAILABILITY: CESE and the Web-based model repository are available at http://cese.sourceforge.net/.     

On a phenomenological model for fatigue effects in skeletal muscles

This work deals with the development and implementation of a new fatigue model for simulating fatigue effects in skeletal muscles. Basic idea of this modelling strategy is an approach that divides the fibres of a muscle into three groups: fibres in the active state, those that are already fatigued and fibres in the resting state. All fibres are able to switch between the different groups by defining adequate rates. In this way a continuous transfer of fibres between those three states has been described. Rooted on an incompressible, hyperelastic constitutive law with transversely isotropic characteristics the fatigue model has been implemented in the framework of the finite element method. Numerical examples are given in order to illustrate the ability of this model. Further, we validate the model by fatigue experiments of the rat soleus muscle. In doing so, it proves that the model is able to predict physiological observations and mechanical test results.     

Fluid–structure interaction analysis of the left coronary artery with variable angulation

The aim of this study is to elucidate the correlation between coronary artery branch angulation, local mechanical and haemodynamic forces at the vicinity of bifurcation. Using a coupled fluid–structure interaction (FSI) modelling approach, five idealized left coronary artery models with various angles ranging from 70° to 110° were developed to investigate the influence of branch angulations. In addition, one CT image-based model was reconstructed to further demonstrate the medical application potential of the proposed FSI coupling method. The results show that the angulation strongly alters its mechanical stress distribution, and the instantaneous wall shear stress distributions are substantially moderated by the arterial wall compliance. As high tensile stress is hypothesized to cause stenosis, the left circumflex side bifurcation shoulder is indicated to induce atherosclerotic changes with a high tendency for wide-angled models.     

Sequential structural and fluid dynamic numerical simulations of a stented bifurcated coronary artery

Despite their success, stenting procedures are still associated to some clinical problems like sub-acute thrombosis and in-stent restenosis. Several clinical studies associate these phenomena to a combination of both structural and hemodynamic alterations caused by stent implantation. Recently, numerical models have been widely used in the literature to investigate stenting procedures but always from either a purely structural or fluid dynamic point of view. The aim of this work is the implementation of sequential structural and fluid dynamic numerical models to provide a better understanding of stenting procedures in coronary bifurcations. In particular, the realistic geometrical configurations obtained with structural simulations were used to create the fluid domains employed within transient fluid dynamic analyses. This sequential approach was applied to investigate the final kissing balloon (FKB) inflation during the provisional side branch technique. Mechanical stresses in the arterial wall and the stent as well as wall shear stresses along the arterial wall were examined before and after the FKB deployment. FKB provoked average mechanical stresses in the arterial wall almost 2.5 times higher with respect to those induced by inflation of the stent in the main branch only. Results also enlightened FKB benefits in terms of improved local blood flow pattern for the side branch access. As a drawback, the FKB generates a larger region of low wall shear stress. In particular, after FKB the percentage of area characterized by wall shear stresses lower than 0.5?Pa was 79.0%, while before the FKB it was 62.3%. For these reasons, a new tapered balloon dedicated to bifurcations was proposed. The inclusion of the modified balloon has reduced the mechanical stresses in the proximal arterial vessel to 40% and the low wall shear stress coverage area to 71.3%. In conclusion, these results show the relevance of the adopted sequential approach to study the wall mechanics and the hemodynamics created by stent deployment.     

Evaluation of accuracy and applicability of protein models: retrospective analysis of biological and biomedical predictions

In order to study protein function and activity structural data is required. Since experimental structures are available for just a small fraction of all known protein sequences, computational methods such as protein modelling can provide useful information. Over the last few decades we have predicted, with homology modelling methods, the structures for numerous proteins. In this study we assess the structural quality and validity of the biological and medical interpretations and predictions made based on the models. All the models had correct scaffolding and were ranked at least as correct or good by numerical evaluators even though the sequence identity with the template was as low as 8%. The biological explanations made based on models were well in line with experimental structures and other experimental studies. Retrospective analysis of homology models indicates the power of protein modelling when made carefully from sequence alignment to model building and refinement. Modelling can be applied to studying and predicting different kinds of biological phenomena and according to our results it can be done so with success.     

A rule-based model of barley morphogenesis, with special respect to shading and gibberellic acid signal transduction

BACKGROUND AND AIMS: Functional-structural plant models (FSPM) constitute a paradigm in plant modelling that combines 3D structural and graphical modelling with the simulation of plant processes. While structural aspects of plant development could so far be represented using rule-based formalisms such as Lindenmayer systems, process models were traditionally written using a procedural code. The faithful representation of structures interacting with functions across scales, however, requires a new modelling formalism. Therefore relational growth grammars (RGG) were developed on the basis of Lindenmayer systems. METHODS: In order to implement and test RGG, a new modelling language, the eXtended L-system language (XL) was created. Models using XL are interpreted by the interactive, Java-based modelling platform GroIMP. Three models, a semi-quantitative gibberellic acid (GA) signal transduction model, and a phytochrome-based shade detection and object avoidance model, both coupled to an existing morphogenetic structural model of barley (Hordeum vulgare L.), serve as examples to demonstrate the versatility and suitability of RGG and XL to represent the interaction of diverse biological processes across hierarchical scales. KEY RESULTS: The dynamics of the concentrations in the signal transduction network could be modelled qualitatively and the phenotypes of GA-response mutants faithfully reproduced. The light model used here was simple to use yet effective enough to carry out local measurement of red:far-red ratios. Suppression of tillering at low red:far-red ratios could be simulated. CONCLUSIONS: The RGG formalism is suitable for implementation of multi-scaled FSPM of plants interacting with their environment via hormonal control. However, their ensuing complexity requires careful design. On the positive side, such an FSPM displays knowledge gaps better thereby guiding future experimental design.     

A General Framework for Longitudinal Data through Marked Point Processes

This paper reviews a general framework for the modelling of longitudinal data with random measurement times based on marked point processes and presents a worked example. We construct a quite general regression models for longitudinal data, which may in particular include censoring that only depend on the past and outside random variation, and dependencies between measurement times and measurements. The modelling also generalises statistical counting process models. We review a non-parametric Nadarya-Watson kernel estimator of the regression function, and a parametric analysis that is based on a conditional least squares (CLS) criterion. The parametric analysis presented, is a conditional version of the generalised estimation equations of LIANG and ZEGER (1986). We conclude that the usual nonparametric and parametric regression modelling can be applied to this general set-up, with some modifications. The presented framework provides an easily implemented and powerful tool for model building for repeated measurements.     

A framework for incorporating 3D hyperelastic vascular wall models in 1D blood flow simulations

We present a novel framework for investigating the role of vascular structure on arterial haemodynamics in large vessels, with a special focus on the human common carotid artery (CCA). The analysis is carried out by adopting a three-dimensional (3D) derived, fibre-reinforced, hyperelastic structural model, which is coupled with an axisymmetric, reduced order model describing blood flow. The vessel transmural pressure and lumen area are related via a Holzapfel–Ogden type of law, and the residual stresses along the thickness and length of the vessel are also accounted for. After a structural characterization of the adopted hyperelastic model, we investigate the link underlying the vascular wall response and blood-flow dynamics by comparing the proposed framework results against a popular tube law. The comparison shows that the behaviour of the model can be captured by the simpler linear surrogate only if a representative value of compliance is applied. Sobol’s multi-variable sensitivity analysis is then carried out in order to identify the extent to which the structural parameters have an impact on the CCA haemodynamics. In this case, the local pulse wave velocity (PWV) is used as index for representing the arterial transmission capacity of blood pressure waveforms. The sensitivity analysis suggests that some geometrical factors, such as the stress-free inner radius and opening angle, play a major role on the system’s haemodynamics. Subsequently, we quantified the differences in haemodynamic variables obtained from different virtual CCAs, tube laws and flow conditions. Although each artery presents a distinct vascular response, the differences obtained across different flow regimes are not significant. As expected, the linear tube law is unable to accurately capture all the haemodynamic features characterizing the current model. The findings from the sensitivity analysis are further confirmed by investigating the axial stretching effect on the CCA fluid dynamics. This factor does not seem to alter the pressure and flow waveforms. On the contrary, it is shown that, for an axially stretched vessel, the vascular wall exhibits an attenuation in absolute distension and an increase in circumferential stress, corroborating the findings of previous studies. This analysis shows that the new model offers a good balance between computational complexity and physics captured, making it an ideal framework for studies aiming to investigate the profound link between vascular mechanobiology and blood flow.

     

The mathematical modelling of cell kinetics in corneal epithelial wound healing

This paper considers the comparison of experimental spatial and temporal data of mitotic rates measured during corneal epithelial wound healing (CEWH) of a rat model with the predictions of a computer modelling framework. We begin by briefly showing that previous models, used in the study of corneal epithelial wound healing speeds, are inadequate for the study of cell kinetics. We proceed to formulate a new modelling framework more suited to such a study. This framework is simulated in its simplest form, and the results from this motivate a new realisation of the modelling framework, including a caricature of age structuring. Finally, a model with a simple representation of juxtacrine signalling is considered. The final model captures many, though not all, of the trends of the experimental data. This paper thus lays a foundation for the modelling of the cell kinetics of corneal epithelial wound healing, and yields valuable insight regarding the important mechanisms a model should consider in order to reproduce the observed experimental trends.     

Cost-Effectiveness of HBV and HCV Screening Strategies – A Systematic Review of Existing Modelling Techniques

Introduction

Studies evaluating the cost-effectiveness of screening for Hepatitis B Virus (HBV) and Hepatitis C Virus (HCV) are generally heterogeneous in terms of risk groups, settings, screening intervention, outcomes and the economic modelling framework. It is therefore difficult to compare cost-effectiveness results between studies. This systematic review aims to summarise and critically assess existing economic models for HBV and HCV in order to identify the main methodological differences in modelling approaches.

Methods

A structured search strategy was developed and a systematic review carried out. A critical assessment of the decision-analytic models was carried out according to the guidelines and framework developed for assessment of decision-analytic models in Health Technology Assessment of health care interventions.

Results

The overall approach to analysing the cost-effectiveness of screening strategies was found to be broadly consistent for HBV and HCV. However, modelling parameters and related structure differed between models, producing different results. More recent publications performed better against a performance matrix, evaluating model components and methodology.

Conclusion

When assessing screening strategies for HBV and HCV infection, the focus should be on more recent studies, which applied the latest treatment regimes, test methods and had better and more complete data on which to base their models. In addition to parameter selection and associated assumptions, careful consideration of dynamic versus static modelling is recommended. Future research may want to focus on these methodological issues. In addition, the ability to evaluate screening strategies for multiple infectious diseases, (HCV and HIV at the same time) might prove important for decision makers.     

Remodelling of the angular collagen fiber distribution in cardiovascular tissues

Understanding collagen fiber remodelling is desired to optimize the mechanical conditioning protocols in tissue-engineering of load-bearing cardiovascular structures. Mathematical models offer strong possibilities to gain insight into the mechanisms and mechanical stimuli involved in these remodelling processes. In this study, a framework is proposed to investigate remodelling of angular collagen fiber distribution in cardiovascular tissues. A structurally based model for collagenous cardiovascular tissues is extended with remodelling laws for the collagen architecture, and the model is subsequently applied to the arterial wall and aortic valve. For the arterial wall, the model predicts the presence of two helically arranged families of collagen fibers. A branching, diverging hammock-type fiber architecture is predicted for the aortic valve. It is expected that the proposed model may be of great potential for the design of improved tissue engineering protocols and may give further insight into the pathophysiology of cardiovascular diseases.