Multiscale modelling of the circulatory system: a preliminary analysis

In this paper we show how numerical solutions of human cardiovascular system may be devised by coupling models having different physical dimensions. One of the aspects of circulatory system is indeed its multiscale nature. Local flow features may have a global effect on circulation. For instance, a stenosis caused by an atherosclerotic plaque may change the overall characteristic of the vessels involved, and consequently have significant influence on the flow in the whole system. Hence, it lays the interest to set up a numerical device that could represent accurately both local and systemic features. For that, it is needed to couple different model scales. From lumped models (which are traditionally described by means of an electrical network analog) to local models based on 2D or 3D Navier-Stokes equations, passing through intermediate 1D models. In this paper, the different assumptions underlying these models, some mathematical issues related to their coupling and preliminary numerical results are presented. Received: 30 April 1999 / Accepted: 17 June 1999     

Analysis of Iterative Methods for Solving a Ginzburg-Landau Equation

Very recently we have proposed to use a complex Ginzburg-Landau equation for high contrast inpainting, to restore higher dimensional (volumetric) data (which has applications in frame interpolation), improving sparsely sampled data and to fill in fragmentary surfaces. In this paper we review digital inpainting algorithms and compare their performance with a Ginzburg-Landau inpainting model. For the solution of the Ginzburg-Landau equation we compare the performance of several numerical algorithms. A stability and convergence analysis is given and the consequences for applications to digital inpainting are discussed.First online version published in June, 2005     

Ten challenges in modeling bibliographic data for bibliometric analysis

The complexity and variety of bibliographic data is growing, and efforts to define new methodologies and techniques for bibliometric analysis are intensifying. In this complex scenario, one of the most crucial issues is the quality of data and the capability of bibliometric analysis to cope with multiple data dimensions. Although the problem of enforcing a multidimensional approach to the analysis and management of bibliographic data is not new, a reference design pattern and a specific conceptual model for multidimensional analysis of bibliographic data are still missing. In this paper, we discuss ten of the most relevant challenges for bibliometric analysis when dealing with multidimensional data, and we propose a reference data model that, according to different goals, can help analysis designers and bibliographic experts in working with large collections of bibliographic data.     

A multiscale analysis of growth and diffusion dynamics in biological materials

We study a growing biological tissue as an open biphasic mixture whose phases undergo exchange interactions. We assume that both the solid- and fluid-phase are composed of several constituents allowed to be transferred from one phase to the other. Because of growth and exchange, or transfer, source terms must be accounted for in balance laws. We relate the source terms which are relevant for our purposes with thermodynamic quantities defined at the pore scale of the tissue. This procedure, carried out through the Theory of Homogenization, aims to give growth a pore scale justification. Particular attention is given to the exploitation of the Clausius-Duhem inequality and the kinematics of growth. Since the mixture under investigation has to satisfy restrictions, we provide a modified Clausius-Duhem inequality that, following Liu’s theorem, accounts for constraints through the Lagrange multiplier technique. Constraints, and related Lagrange multipliers, are also introduced in the definition of Helmholtz free energy densities in order to include constitutive laws for solid- and fluid-phase mass densities less strict than incompressibility. We perform an analysis of our constrained Clausius-Duhem inequality in the neighborhood of thermodynamic equilibrium. This enables us to obtain Onsager relations that generalize some results found in the literature about a thermodynamically consistent procedure for determining an evolution law for growth and mass transfer. We show that the driving mechanism for mass transfer and growth is related to a generalized Eshelby-like tensor, which accounts for chemical potential. Effective stiffness tensor is derived by means of the self-consistent effective field method using the analogy with Levin’s method of effective thermal expansion.     

An Allen–Cahn approach to the remodelling of fibre-reinforced anisotropic materials

We propose a theory of remodelling in fibre-reinforced biological tissues, in which the fibre orientation follows a given probability density. The latter is characterised by variance and mean angle. We claim that the fibres may change their orientation in time, thereby triggering a remodelling process that can be described by the spatiotemporal evolution of the mean angle. This is determined by solving a balance of external and internal generalised forces. We assign the latter ones by establishing a constitutive theory capable of resolving the spatial variability of the fibre mean angle and featuring a free energy density of the Allen–Cahn type. Through numerical simulations, we compare the predictions of our model with the results of another model available in the literature. Finally, we interpret the evolution of the mean angle as the consequence of a symmetry breaking that occurs in the tissue both spontaneously and due to the coupling between remodelling and deformation.     

Effects of parathyroid hormone and serum calcium on the phenotype and function of mononuclear cells in patients with primary hyperparathyroidism

The University of Pennsylvania Smell Identification Test (UPSIT) and a smell ability questionnaire were administered to 167 Japanese volunteers ranging in age from 20 to 59 years. Of these subjects, 80 also received the T&T olfactometer threshold test. Of the latter subjects, 36 were patients tested before endoscopic nasal surgery for sinusitis and polyposis. The patients exhibited decreased smell function, as measured by the T&T olfactometer, the UPSIT, and a 30-item version of the UPSIT in which the 10 least familiar items were removed (ps < 0.001). Spearman correlations ranging from 0.53 to 0.70 were found between (i) scores on the 30- and 40-item UPSITs and (ii) the T&T detection and recognition threshold values. Significant correlations were found between scores on the smell ability questionnaire and the olfactory test measures (UPSIT30 r = 0.56; UPSIT40 r = 0.58; T&T detection r = 0.56; T&T recognition r = 0.69, p < 0.001), indicating that subjects are relatively accurate in assessing their olfactory ability. This study suggests that the 30 and 40-item UPSITs correlate well with measures derived from the T&T olfactometer, and that all three tests are sensitive to the smell loss of Japanese sinusitis/polyposis patients.     

Angioscopic predictors of early adverse outcome after coronary angioplasty in patients with unstable angina and non-Q-wave myocardial infarction

BACKGROUND: Clinical and angiographic criteria have a limited ability to predict adverse outcome in patients with unstable angina who are undergoing percutaneous transluminal coronary angioplasty (PTCA). We investigated whether the use of angioscopy can improve prediction of early adverse outcome after PTCA. METHODS AND RESULTS: Angioscopic characterization of the culprit lesion was performed before PTCA in 32 patients with unstable angina and 10 with non-Q-wave infarction. Seven patients (17%) had an adverse outcome (myocardial infarction, repeat PTCA, or need for coronary artery bypass graft surgery) within 24 hours after PTCA. Six of 18 patients with a yellow culprit lesion had an adverse outcome compared with 1 of 24 in whom the culprit lesion was white (P = .03). Six of 20 patients with plaque disruption suffered an adverse outcome compared with 1 of 22 with nondisrupted plaques (P = .04). Six of 17 patients with intraluminal thrombus had an adverse outcome, whereas only 1 of 25 patients without thrombus suffered an adverse outcome (P = .01). Yellow color, disruption, and thrombus at the culprit lesion site were associated with an eightfold increase in risk of adverse outcome after PTCA. The prediction of PTCA outcome based on characteristics of the plaque that were identifiable by angioscopy was superior to that estimated by the use of angiographic variables. CONCLUSIONS: In patients with unstable angina and non-Q-wave infarction, angioscopic features of disruption, yellow color, or thrombus at the culprit lesion site can identify patients at high risk of early adverse outcome after PTCA. Angioscopy was superior to angiography for prediction of PTCA outcome.