Computational models to predict stenosis growth in carotid arteries: which is the role of boundary conditions?

This work addresses the problem of prescribing proper boundary conditions at the artificial boundaries that separate the vascular district from the remaining part of the circulatory system. A multiscale (MS) approach is used where the Navier-Stokes equations for the district of interest are coupled to a non-linear system of ordinary differential equations which describe the circulatory system. This technique is applied to three 3D models of a carotid bifurcation with increasing stenosis resembling three phases of a plaque growth. The results of the MS simulations are compared to those obtained by two stand-alone models. The MS shows a great flexibility in numerically predicting the haemodynamic changes due to the presence of a stenosis. Nonetheless, the results are not significantly different from a stand-alone approach where flows derived by the MS without stenosis are imposed. This is a consequence of the dominant role played by the outside districts with respect to the stenosis resistance.     

Multiscale modelling as a tool to prescribe realistic boundary conditions for the study of surgical procedures

This work was motivated by the problems of analysing detailed 3D models of vascular districts with complex anatomy. It suggests an approach to prescribing realistic boundary conditions to use in order to obtain information on local as well as global haemodynamics. A method was developed which simultaneously solves Navier-Stokes equations for local information and a non-linear system of ordinary differential equations for global information. This is based on the principle that an anatomically detailed 3D model of a cardiovascular district can be achieved by using the finite element method. In turn the finite element method requires a specific boundary condition set. The approach outlined in this work is to include the system of ordinary differential equations in the boundary condition set. Such a multiscale approach was first applied to two controls: (i) a 3D model of a straight tube in a simple hydraulic network and (ii) a 3D model of a straight coronary vessel in a lumped-parameter model of the cardiovascular system. The results obtained are very close to the solutions available for the pipe geometry. This paper also presents preliminary results from the application of the methodology to a particular haemodynamic problem: namely the fluid dynamics of a systemic-to-pulmonary shunt in paediatric cardiac surgery.     

Mechanical properties of the coronary vasculature: indirect evaluation.

Information on the mechanical properties of the coronary vascular bed can be obtained indirectly by modelling the vascular system. This indirect approach, unlike 'in vitro' measurements, allows to take into account the vasomotor conditions of the circulatory district as well as the effect of the surrounding embedding tissue on the vascular performance. An experimental manoeuvre of sudden occlusion and subsequent release of the thoracic descendent aorta on 5 anaesthetized dogs with open pericardium induces a step-like variation in the coronary perfusion pressure and the occurrence of oscillations in the mean coronary flow. Such a behaviour can be described using a second-order model ('windkessel'+inductance, which takes into account blood inertia in the large vessels). The value of the coefficients entering the equations have been obtained with a 'best-fit' procedure (minimum of the chi-squared variable) on the haemodynamical data. Coefficient variations are in agreement with the direct estimation of the myocardial compliance and volume, measured by Ultrasound Echocardiographic imaging (4-chamber projection mode).     

Phenomenological and molecular-level Petri net modeling and simulation of long-term potentiation

Petri net-based modeling methods have been used in many research projects to represent biological systems. Among these, the hybrid functional Petri net (HFPN) was developed especially for biological modeling in order to provide biologists with a more intuitive Petri net-based method. In the literature, HFPNs are used to represent kinetic models at the molecular level. We present two models of long-term potentiation previously represented by differential equations which we have transformed into HFPN models: a phenomenological synapse model and a molecular-level model of the CaMKII regulation pathway. Through simulation, we obtained results similar to those of previous studies using these models. Our results open the way to a new type of modeling for systems biology where HFPNs are used to combine different levels of abstraction within one model. This approach can be useful in fully modeling a system at the molecular level when kinetic data is missing or when a full study of a system at the molecular level it is not within the scope of the research.     

Cleaning of raw peptide MS/MS spectra: improved protein identification following deconvolution of multiply charged peaks, isotope clusters, and removal of background noise

The dominant ions in MS/MS spectra of peptides, which have been fragmented by low-energy CID, are often b-, y-ions and their derivatives resulting from the cleavage of the peptide bonds. However, MS/MS spectra typically contain many more peaks. These can result not only from isotope variants and multiply charged replicates of the peptide fragmentation products but also from unknown fragmentation pathways, sample-specific or systematic chemical contaminations or from noise generated by the electronic detection system. The presence of this background complicates spectrum interpretation. Besides dramatically prolonged computation time, it can lead to incorrect protein identification, especially in the case of de novo sequencing algorithms. Here, we present an algorithm for detection and transformation of multiply charged peaks into singly charged monoisotopic peaks, removal of heavy isotope replicates, and random noise. A quantitative criterion for the recognition of some noninterpretable spectra has been derived as a byproduct. The approach is based on numerical spectral analysis and signal detection methods. The algorithm has been implemented in a stand-alone computer program called MS Cleaner that can be obtained from the authors upon request.     

Model reduction using a posteriori analysis

Mathematical models in biology and physiology are often represented by large systems of non-linear ordinary differential equations. In many cases, an observed behaviour may be written as a linear functional of the solution of this system of equations. A technique is presented in this study for automatically identifying key terms in the system of equations that are responsible for a given linear functional of the solution. This technique is underpinned by ideas drawn from a posteriori error analysis. This concept has been used in finite element analysis to identify regions of the computational domain and components of the solution where a fine computational mesh should be used to ensure accuracy of the numerical solution. We use this concept to identify regions of the computational domain and components of the solution where accurate representation of the mathematical model is required for accuracy of the functional of interest. The technique presented is demonstrated by application to a model problem, and then to automatically deduce known results from a cell-level cardiac electrophysiology model.     

Mechanisms Explaining Transitions between Tonic and Phasic Firing in Neuronal Populations as Predicted by a Low Dimensional Firing Rate Model

Several firing patterns experimentally observed in neural populations have been successfully correlated to animal behavior. Population bursting, hereby regarded as a period of high firing rate followed by a period of quiescence, is typically observed in groups of neurons during behavior. Biophysical membrane-potential models of single cell bursting involve at least three equations. Extending such models to study the collective behavior of neural populations involves thousands of equations and can be very expensive computationally. For this reason, low dimensional population models that capture biophysical aspects of networks are needed. The present paper uses a firing-rate model to study mechanisms that trigger and stop transitions between tonic and phasic population firing. These mechanisms are captured through a two-dimensional system, which can potentially be extended to include interactions between different areas of the nervous system with a small number of equations. The typical behavior of midbrain dopaminergic neurons in the rodent is used as an example to illustrate and interpret our results. The model presented here can be used as a building block to study interactions between networks of neurons. This theoretical approach may help contextualize and understand the factors involved in regulating burst firing in populations and how it may modulate distinct aspects of behavior.     

Numerical simulation of steady turbulent flow through trileaflet aortic heart valves—I. Computational scheme and methodology

A numerical simulation model and technique are described to simulate steady turbulent blood flow through trileaflet tissue valves of varying degrees of stenosis. The aortic trileaflet tissue valve design was chosen as the subject of this study, since it is the only popular valve in current clinical use which is approximately axisymmetric. An axisymmetric geometry is computationally more convenient since it involves only two dimensional equations. The geometry and dimensions of the aorta were designed from angiographic studies and measurements made from cadavers. The valve dimensions were obtained from tissue leaflet photography studies conducted on tissue bioprostheses of varying degrees of stenosis. The nonrectangular nature of this valve necessitated the use of a body conforming grid. Thompson's method coupled with a Chimera grid system was chosen for this purpose. The Chimera grid was used to avoid a grid with highly skewed cells. Turbulence was simulated by using the k- model with the wall function method. This decision was made after comparing the k- model's performance with that of lower order models, and after considering the increased computer time requirements and decreased stability of more complex models, such as the Reynolds stress model. The results of the study which are very encouraging and compare favorably with in vitro experimental data, are described in Part II of the paper.     

The identification of transport parameters from truncated physiological tracer curves

The primary data curves from the injection of tracers into the circulation are often obscured by the appearance of a recirculation hump. Previous techniques for parameter identification in the presence of such a complication have been extended from compartmental models to include circulatory models consisting of partial differential equations of the Taylor dispersion and Turner capacitance types. A comparative analysis of the efficiency of parameter identification by several computational strategies is presented.     

Rule-Based Model of Vein Graft Remodeling

When vein segments are implanted into the arterial system for use in arterial bypass grafting, adaptation to the higher pressure and flow of the arterial system is accomplished thorough wall thickening and expansion. These early remodeling events have been found to be closely coupled to the local hemodynamic forces, such as shear stress and wall tension, and are believed to be the foundation for later vein graft failure. To further our mechanistic understanding of the cellular and extracellular interactions that lead to global changes in tissue architecture, a rule-based modeling method is developed through the application of basic rules of behaviors for these molecular and cellular activities. In the current method, smooth muscle cell (SMC), extracellular matrix (ECM), and monocytes are selected as the three components that occupy the elements of a grid system that comprise the developing vein graft intima. The probabilities of the cellular behaviors are developed based on data extracted from in vivo experiments. At each time step, the various probabilities are computed and applied to the SMC and ECM elements to determine their next physical state and behavior. One- and two-dimensional models are developed to test and validate the computational approach. The importance of monocyte infiltration, and the associated effect in augmenting extracellular matrix deposition, was evaluated and found to be an important component in model development. Final model validation is performed using an independent set of experiments, where model predictions of intimal growth are evaluated against experimental data obtained from the complex geometry and shear stress patterns offered by a mid-graft focal stenosis, where simulation results show good agreements with the experimental data.     

On Bivariate Cumulative Damage Models With Application

Bivariate cumulative damage models are proposed where the responses given the damages are independent random variables. The bivariate damage process can be either bivariate Poisson or bivariate gamma. A bivariate continuous cumulative damage model is investigated in which the responses given the damages have gamma distributions. In this case evaluation of the joint density function and bivariate tail probability function is facilitated by expanding the gamma distributions of the conditional responses by Laguerre polynomials. This approach also leads to evaluation of associated survival models. Moments and estimating equations are discussed. In addition, a bivariate discrete cumulative damage model is investigated in which the responses given the damages have a distribution chosen from a class that includes the negative binomial, the Neyman Type‐A, the Polya‐Aeppli, and the Lagrangian Poisson. Probabilities are obtained from recursive formulas which do not involve cancellation error as all quantities are non‐negative. Moments and estimating equations are presented for these models also. The continuous and the discrete models are applied to describe the rise of systolic and diastolic blood pressure with age.     

Influence of arterial wall compliance on the pressure drop across coronary artery stenoses under hyperemic flow condition

Hemodynamic endpoints such as flow and pressure drop are often measured during angioplasty procedures to determine the functional severity of a coronary artery stenosis. There is a lack of knowledge regarding the influence of compliance of the arterial wall-stenosis on the pressure drop under hyperemic flows across coronary lesions. This study evaluates the influence in flow and pressure drop caused by variation in arterial-stenosis compliance for a wide range of stenosis severities. The flow and pressure drop were evaluated for three different severities of stenosis and tested for limiting scenarios of compliant models. The Mooney-Rivlin model defined the non-linear material properties of the arterial wall and the plaque regions. The non-Newtonian Carreau model was used to model the blood flow viscosity. The fluid (blood)-structure (arterial wall) interaction equations were solved numerically using the finite element method. Irrespective of the stenosis severity, the compliant models produced a lower pressure drop than the rigid artery due to compliance of the plaque region. A wide variation in the pressure drop was observed between different compliant models for significant (90% area occlusion) stenosis with 41.0, 32.1, and 29.8 mmHg for the rigid artery, compliant artery with calcified plaque, and compliant artery with smooth muscle cell proliferation, respectively. When compared with the rigid artery for significant stenosis the pressure drop decreased by 27.7% and 37.6% for the calcified plaque and for the smooth muscle cell proliferation case, respectively. These significant variations in pressure drop for the higher stenosis may lead to misinterpretation and misdiagnosis of the stenosis severity.     

Consistent micro, macro and state-based population modelling

A population system can be modelled using a micro model focusing on the individual entities, a macro model where the entities are aggregated into compartments, or a state-based model where each possible discrete state in which the system can exist is represented. However, the concepts, building blocks, procedural mechanisms and the time handling for these approaches are very different. For the results and conclusions from studies based on micro, macro and state-based models to be consistent (contradiction-free), a number of modelling issues must be understood and appropriate modelling procedures be applied. This paper presents a uniform approach to micro, macro and state-based population modelling so that these different types of models produce consistent results and conclusions. In particular, we demonstrate the procedures (distribution, attribute and combinatorial expansions) necessary to keep these three types of models consistent. We also show that the different time handling methods usually used in micro, macro and state-based models can be regarded as different integration methods that can be applied to any of these modelling categories. The result is free choice in selecting the modelling approach and the time handling method most appropriate for the study without distorting the results and conclusions.     

Bayesian deconvolution analysis of pulsatile hormone concentration profiles

Many hormones are secreted into the circulatory system in a pulsatile manner and are cleared exponentially. The most common method of analyzing these systems is to deconvolve the hormone concentration into a secretion function and a clearance function. Accurate estimation of the model parameters depends on the number and location of the secretion pulses. To date, deconvolution analysis assumes the number and approximate location of these pulses are known a priori. In this article, we present a novel Bayesian approach to deconvolution that jointly models the number of pulses along with all other model parameters. Our method stochastically searches for the secretion pulses. This is accomplished by viewing the set of parameters that define the pulses as a point process. Pulses are determined by a birth-death process which is embedded in Markov chain Monte Carlo algorithm. This idea originated with Stephens (2000, Annals of Statistics 28, 40-74) in the context of finite mixture model density estimation, where the number of mixture components is unknown. There are several advantages that our model enjoys over the traditional frequentist approaches. These advantages are highlighted with four datasets consisting of serum concentration levels of luteinizing hormone obtained from ovariectomized ewes.     

Kinematic analysis of over-determinate biomechanical systems

In this paper, we introduce a new general method for kinematic analysis of rigid multi body systems subject to holonomic constraints. The method extends the standard analysis of kinematically determinate rigid multi body systems to the over-determinate case. This is accomplished by introducing a constrained optimisation problem with the objective function given as a function of the set of system equations that are allowed to be violated while the remaining equations define the feasible set. We show that exact velocity and acceleration analysis can also be performed by solving linear sets of equations, originating from differentiation of the Karush-Kuhn-Tucker optimality conditions. The method is applied to the analysis of an 18 degrees-of-freedom gait model where the kinematical drivers are prescribed with data from a motion capture experiment. The results show that significant differences are obtained between applying standard kinematic analysis or minimising the least-square errors on the two fully equivalent 3D gait models with only the way the experimental data is processed being different.     

Differential expression analysis of Escherichia coli proteins using a novel software for relative quantitation of LC-MS/MS data

The study of changes in protein levels between samples derived from cells representing different biological conditions is a key to the understanding of cellular function. There are two main methods available that allow both for global scanning for significantly varying proteins and targeted profiling of proteins of interest. One method is based on 2-D gel electrophoresis and image analysis of labelled proteins. The other method is based on LC-MS/MS analysis of either unlabelled peptides or peptides derived from isotopically labelled proteins or peptides. In this study, the non-labelling approach was used involving a new software, DeCyder MS Differential Analysis Software (DeCyder MS) intended for automated detection and relative quantitation of unlabelled peptides in LC-MS/MS data.Total protein extracts of E. coli strains expressing varying levels of dihydrofolate reductase and integron integrase were digested with trypsin and analyzed using a nanoscale liquid chromatography system, Ettan MDLC, online connected to an LTQTM linear ion-trap mass spectrometer fitted with a nanospray interface. Acquired MS data were subjected to DeCyder MS analysis where 2-D representations of the peptide patterns from individual LC-MS/MS analyses were matched and compared.This approach to unlabelled quantitative analysis of the E. coli proteome resulted in relative protein abundances that were in good agreement with results obtained from traditional methods for measuring protein levels.     

基于智能体模型的青岛市林地生态格局评价与优化

设计并在GIS平台上开发了基于智能体的生态格局评价模型,以青岛市及周边地区林地为研究对象,分析不同林地空间格局及生态网络保护框架对于物种生存与扩散的影响.结果表明,与现状相比,不同等级的生态网络框架对物种种群数量与物种迁移都有明显提升,且等级越高的生态网络框架提升作用越明显.然而仅仅依靠生态网络框架不足以使研究区域林地系统形成功能上的相互连通,因此,在分析研究区域现状土地利用格局基础上,提出与湿地系统结合,在胶州湾周围及大沽河干流地区增加林地的空间布局.通过模型模拟分析,发现优化后的林地空间格局结合生态网络框架能有效提升林地之间的物种扩散.基于模拟结果,为研究区林地生态格局构建提出如下建议:(1)保证现有的规模较大的林地不被破坏;(2)青岛市中部湿地系统可以作为新增林地的理想区域;(3)生态网络框架可作为青岛市建立城市组团间生态间隔的空间参考.     

Quantifying Burial,the Transport of Matter from the Lake Biosphere to the Geosphere

Burial is one of the most fundamental processes in contexts of massbalance calculations for substances (such as nutrients, organics, metals and radionuclides) in lakes. Substances can leave a lake by two processes, outflow, i.e., the transport to a downstream system, and burial, i.e., the transport by sedimentation from the lake biosphere to the geosphere. This work gives for the first time, to there best of the author's knowledge, a review on the factors and processes regulating burial and presents a general model for burial. This approach accounts for bottom dynamic conditions (i.e., where areas of fine sediment erosion, transport and accumulation prevail), sedimentation, bioturbation, mineralisation, and the depth and age of the bioactive sediment layer. This approach has been critically tested with very good results for radiocesium, radiostrontium, many metals, calcium from liming and phosphorus, but it has not been presented before in a comprehensive way. This model for burial is meant to be used in massbalance models based on ordinary differential equations (i.e., box models) in contexts where burial is not a target y‐variable but a necessary model variable (an x‐variable). This means that there are also specific demands on this approach, e.g., it must be based on readily accessible driving variables so that it is not too difficult to use the model in practice within the context of an overall lake model. The factors influencing burial, e.g., the deposition of materials and the depth of the bioactive sediment layer, are also needed in calculations of sediment concentrations and to determine amounts of substances or pollutants in sediments. To carry out such calculations, one also needs information on sediment bulk density, water content and organic content. This paper also presents new empirical models for such calculations to be used in the new model for burial.     

A network model of successive partitioning-limited solute diffusion through the stratum corneum

As the most exposed point of contact with the external environment, the skin is an important barrier to many chemical exposures, including medications, potentially toxic chemicals and cosmetics. Traditional dermal absorption models treat the stratum corneum lipids as a homogenous medium through which solutes diffuse according to Fick's first law of diffusion. This approach does not explain non-linear absorption and irregular distribution patterns within the stratum corneum lipids as observed in experimental data. A network model, based on successive partitioning-limited solute diffusion through the stratum corneum, where the lipid structure is represented by a large, sparse, and regular network where nodes have variable characteristics, offers an alternative, efficient, and flexible approach to dermal absorption modeling that simulates non-linear absorption data patterns. Four model versions are presented: two linear models, which have unlimited node capacities, and two non-linear models, which have limited node capacities. The non-linear model outputs produce absorption to dose relationships that can be best characterized quantitatively by using power equations, similar to the equations used to describe non-linear experimental data.