Boundary elements and β-spline surface modeling for medical applications

The aim of this paper is to present and discuss an approach based on the integration of the boundary element method (BEM) with β-spline geometric modeling of the different surfaces involved in the external bone remodeling phenomena. The purpose of combining these two techniques is to avoid the jagged edges shapes and thus, to increase the convergence speed of the bone remodeling function. In this study, the external bone remodeling model proposed by Fridez et al. [P. Fridez, L. Rakotomanana, A. Terrier, P.F. Leyvraz, Three dimensional model of bone external adaptation, Comput. Methods Biomech. Biomed. Eng. 2 (1998) 189–196] is used. This model shows the change of the external bone surface remodeling at a boundary point, as a function of the stimulus variable Ψ. This variable is related to the stress tensor and the normal vector to that point. The β-spline surfaces were used because they are simple and reliable to smooth the contour by using the less possible number of geometric constraints. Some numerical examples are presented and discussed in order to show the versatility of the proposed approach.     

Computational simulation of piezo-electrically stimulated bone remodeling surrounding teeth implant

Since the natural ligament responsible for the fixation of teeth in jawbone is destroyed when artificial replacements are implanted, the mechanical stimulation of the bone is reversed. Idea of this research project is the development of active implants which provide additional electrical stimulation for bone adaption. A new electromechanically driven bone remodeling theory will be developed and the osseointegration of bone implants has been simulated by means of bio-active interface theory. The thin bone-implant interface is described by the Drucker-Prager plasticity model. Besides the consistent combination of electromechanical bone remodeling simulation, 3D-finite element model of lower mandible has been reconstructed. As the micromotions at the implant-abutment level are reported to be a major determinant of longterm implant success, the osseointegration process is limited by micromotion threshold. The applicability is indicated on a dental implant in order to optimize new developed techniques for activating implants with piezo-electric coatings. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An algorithm for addressing the real interval eigenvalue problem

In this paper we present an algorithm for approximating the range of the real eigenvalues of interval matrices. Such matrices could be used to model real-life problems, where data sets suffer from bounded variations such as uncertainties (e.g. tolerances on parameters, measurement errors), or to study problems for given states.The algorithm that we propose is a subdivision algorithm that exploits sophisticated techniques from interval analysis. The quality of the computed approximation and the running time of the algorithm depend on a given input accuracy. We also present an efficient C++ implementation and illustrate its efficiency on various data sets. In most of the cases we manage to compute efficiently the exact boundary points (limited by floating point representation).     

A classification rule reduction algorithm based on significance domains

Many rule systems generated from decision trees (like CART, ID3, C4.5, etc.) or from direct counting frequency methods (like Apriori) are usually non-significant or even contradictory. Nevertheless, most papers on this subject demonstrate that important reductions can be made to generate rule sets by searching and removing redundancies and conflicts and simplifying the similarities between them. The objective of this paper is to present an algorithm (RBS: Reduction Based on Significance) for allocating a significance value to each rule in the system so that experts may select the rules that should be considered as preferable and understand the exact degree of correlation between the different rule attributes. Significance is calculated from the antecedent frequency and rule frequency parameters for each rule; if the first one is above the minimal level and rule frequency is in a critical interval, its significance ratio is computed by the algorithm. These critical boundaries are calculated by an incremental method and the rule space is divided according to them. The significance function is defined for these intervals. As with other methods of rule reduction, our approach can also be applied to rule sets generated from decision trees or frequency counting algorithms, in an independent way and after the rule set has been created. Three simulated data sets are used to carry out a computational experiment. Other standard data sets from UCI repository (UCI Machine Learning Repository) and two particular data sets with expert interpretation are used too, in order to obtain a greater consistency. The proposed method offers a more reduced and more easily understandable rule set than the original sets, and highlights the most significant attribute correlations quantifying their influence on consequent attribute.     

Optimization of Euclidean distance threshold in the application of recurrence quantification analysis to heart rate variability studies

An integrated approach is proposed to solve the optimization problem of the Euclidean distance threshold ε in recurrence quantification analysis (RQA), which is increasingly applied in the study of heart rate variability (HRV). In this paper, ε is inversely computed from a given recurrence rate (REC), the percentage of recurrence points. From the inversely computed ε, two other RQA output variables: determinism (DET), the percentage of recurrence points forming diagonal line structures, and laminarity (LAM), the percentage of recurrence points forming vertical and horizontal structures, are computed out as well. The trend of DET, LAM values at different REC levels (DLR trend) is introduced to comprehensively represent the dynamic properties of a time series. Based on the DLR trend, the variation of discrimination power, represented by the average loss (or Bayes risk), of DET and LAM, at different REC values is analyzed. Surrogate techniques are used to generate reliable test data sets for the discrimination evaluation. In particular, the results show that (1) the optimal REC can be much higher than the widely used 1% REC, and (2) after the optimization, the average loss can be reduced compared to 1% REC. It is also demonstrated that the optimal ε depends on the dynamic source and RQA variables, and the DLR trend based ε optimization method can improve RQA discrimination analysis especially for the short term HRV analysis.     

Interactive computer assistance with calculations arising in undergraduate laboratory experiments†

The paper describes an approach to the use of interactive computing to assist students in calculating results from their experimental data in situations where several similar sets of data have to be processed, either by numerical calculation or graphically. The computer programs require the students to show that they understand the calculations by processing one set of data correctly themselves before the remaining sets are computed for them. The detection and diagnosis, by the computer, of students' calculation errors are described. The educational problems and advantages of such an approach are discussed.     

An existence and uniqueness result for a strain-adaptive bone remodeling problem

In this paper we prove an existence and uniqueness result for a strain-adaptive bone remodeling model that couples the displacements and the apparent density (the porosity) of the bone. The rate of this density at a particular location is described as an objective function, which depends on a particular stimulus at that location. Then, a new version of this problem is considered, based on a regularization on the bone remodeling law by using convolution operators. The existence and uniqueness result is proved by applying classical results for nonlinear parabolic differential inclusions, Gronwall’s inequality and the Banach fixed point theorem.     

Influence of the nonlinear matrix material behaviour on the effective properties of textile-reinforced thermoplastics

For a consistent lightweight design the consideration of the nonlinear macroscopic material behaviour of composites, which is amongst others driven by damage and strain-rate effects on the mesoscale, is required. Therefore, a modelling approach using numerical homogenization techniques is applied to predict the effective nonlinear material behaviour of the composite based on the finite element simulation of a representative volume element (RVE). In this RVE suitable constitutive relations account for the material behaviour of each constituents. While the reinforcing glass fibres are assumed to remain linear elastic, a viscoplastic constitutive law is applied to represent the strain-rate dependent, inelastic deformation of the matrix material. In order to analyse the influence of the nonlinear matrix material behaviour on the global mechanical response of the composite, effective stress-strain-curves are computed for different load cases and compared to experimental observations. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A level set approach for the solution of a state-constrained optimal control problem

Summary. State constrained optimal control problems for linear elliptic partial differential equations are considered. The corresponding first order optimality conditions in primal-dual form are analyzed and linked to a free boundary problem resulting in a novel algorithmic approach with the boundary (interface) between the active and inactive sets as optimization variable. The new algorithm is based on the level set methodology. The speed function involved in the level set equation for propagating the interface is computed by utilizing techniques from shape optimization. Encouraging numerical results attained by the new algorithm are reported on.Mathematics Subject Classification (1991): 35R35, 49K20, 49Q10, 65K10Revised version received March 19, 2003     

Memory-efficient Implementation of Riccati Approach for Time-Dependent Optimal Control Problems in ODEs

We consider a time-dependent optimal control problem, where the state evolution is described by an ODE. There is a variety of methods for the treatment of such problems. We prefer to view them as boundary value problems and apply to them the Riccati approach for non-linear BVPs with separated boundary conditions. There are many relationships between multiple shooting techniques, the Riccati approach and the Pantoja method, which describes a computationally efficient stage-wise construction of the Newton direction for the discrete-time optimal control problem. We present an efficient implementation of this approach. Furthermore, the well-known checkpointing approach is extended to a ‘nested checkpointing’ for multiple transversals. Some heuristics are introduced for an efficient construction of nested reversal schedules. We discuss their benefits and compare their results to the optimal schedules computed by exhaustive search techniques. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Online powermanagement optimization of a fuel cell-based hybrid electric powertrain

In this paper an online optimization approach of the powermanagement of a fuel cell-based hybrid electric powertrain system is desribed. Therefore two online optimization algorithms of the powermanagement control parameters are introduced and compared experimentally. The first one deals with parameters rating the performance of the system with respect to efficiency, availability, and lifetime. Using a pre-defined load profile the optimal parameters can be determined for a given powermanagement. The second approach is based on the statistical properties of a predicted and online-updated measured load profile defining the actual load profile characteristics. Depending on this load profile and with the knowledge of the design parameters of the system appropriate adaptive powermanagement parameters are determined. It becomes clear that the performance of the system with respect to the mentioned system properties can be improved by these approaches. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Isotropic continuum damage/repair model for alveolar bone remodeling

Several authors have proposed mechanical models to predict long term tooth movement, considering both the tooth and its surrounding bone tissue as isotropic linear elastic materials coupled to either an adaptative elasticity behavior or an update of the elasticity constants with density evolution. However, tooth movements obtained through orthodontic appliances result from a complex biochemical process of bone structure and density adaptation to its mechanical environment, called bone remodeling. This process is far from linear reversible elasticity. It leads to permanent deformations due to biochemical actions. The proposed biomechanical constitutive law, inspired from Doblaré and García (2002) [30], is based on a elasto-viscoplastic material coupled with Continuum isotropic Damage Mechanics (Doblaré and García (2002) [30] considered only the case of a linear elastic material coupled with damage). The considered damage variable is not actual damage of the tissue but a measure of bone density. The damage evolution law therefore implies a density evolution. It is here formulated as to be used explicitly for alveolar bone, whose remodeling cells are considered to be triggered by the pressure state applied to the bone matrix. A 2D model of a tooth submitted to a tipping movement, is presented. Results show a reliable qualitative prediction of bone density variation around a tooth submitted to orthodontic forces.     

Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data

This work takes advantage of semiparametric modelling which improves significantly in many situations the estimation accuracy of the purely nonparametric approach. Herein for semiparametric estimations of probability mass function (pmf) of count data, and an unknown count regression function (crf), the kernel used is a binomial one and the bandiwdth selection is investigated by developing Bayesian approaches. About the latter, Bayes local and global bandwidth approaches are used to establish data-driven selection procedures in semiparametric framework. From conjugate beta prior distributions of the smoothing parameter and under the squared errors loss function, Bayes estimate for pmf is obtained in closed form. This is not available for the crf which is computed by the Markov Chain Monte Carlo technique. Simulation studies demonstrate that both proposed methods perform better than the classical cross-validation procedures, in particular the smoothing quality and execution times are optimized. All applications are made on real data sets.     

Geometric Analysis and Symbol Calculus: Fourier Transform Magnetic Resonance Imaging and Wavelets

Due to its unequalled advantages, the magnetic resonance imaging (MRI) modality has truly revolutionized the diagnosis and evaluation of pathology. Because many morphological anatomic details that may not be visualized by other high tech imaging methods can now be readily shown by diagnostic MRI, it has already become the standard modality by which all other clinical imaging techniques are measured. The unique quantum physical basis of the MRI modality combined with the imaging capabilities of current computer technology has made this imaging modality a target of interdisciplinary interest for clinicians, physicists, biologists, engineers, and mathematicians. Due to the fact that MRI scanners perform corticomorphic processing, this modality is by far more complex than all the other high tech clinical imaging techniques. The purpose of this paper is to outline a phase coherent wavelet approach to Fourier transform MRI. It is based on distributional harmonic analysis on the Heisenberg nilpotent Lie group G and the associated symplectically invariant symbol calculus of pseudodifferential operators. The contour and contrast resolution of MRI scans which is controlled by symplectic filter bank processing gives the noninvasive MRI modality superiority over X-ray computed tomography (CT) in soft tissue differentiation.     

Studies on Bone Remodeling Theory Based on Microcracks Using Finite Element Computations

The investigation of the microcrack theory supports the research work of understanding the microstructural behaviour of physiological loaded bones. Microcracks in cortical bone are assumed to have a stimulatory effect on osteocytes – the sensor cells for the bone remodeling process. In this contribution an approch to simulate microcrack initiation and propagation inside a 3D anisotropic and inhomogenious FEA model of cortical bone tissue will be shown. The numerical formulations are based on computational continuum damage mechanics. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A “reduce and solve” approach for the multiple-choice multidimensional knapsack problem

The multiple-choice multidimensional knapsack problem (MMKP) is a well-known NP-hard combinatorial optimization problem with a number of important applications. In this paper, we present a “reduce and solve” heuristic approach which combines problem reduction techniques with an Integer Linear Programming (ILP) solver (CPLEX). The key ingredient of the proposed approach is a set of group fixing and variable fixing rules. These fixing rules rely mainly on information from the linear relaxation of the given problem and aim to generate reduced critical subproblem to be solved by the ILP solver. Additional strategies are used to explore the space of the reduced problems. Extensive experimental studies over two sets of 37 MMKP benchmark instances in the literature show that our approach competes favorably with the most recent state-of-the-art algorithms. In particular, for the set of 27 conventional benchmarks, the proposed approach finds an improved best lower bound for 11 instances and as a by-product improves all the previous best upper bounds. For the 10 additional instances with irregular structures, the method improves 7 best known results.     

Clustering reduced interval data using Hausdorff distance

Summary  In the last decade, factorial and clustering techniques have been developed to analyze multidimensional interval data (MIDs). In classic data analysis, PCA and clustering of the most significant components are usually performed to extract cluster structure from data. The clustering of the projected data is then performed, once the noise is filtered out, in a subspace generated by few orthogonal variables. In the framework of interval data analysis, we propose the same strategy. Several computational questions arise from this generalization. First of all, the representation of data onto a factorial subspace: in classic data analysis projected points remain points, but projected MIDs do not remains MIDs. Further, the choice of a distance between the represented data: many distances between points can be computed, few distances between convex sets of points are defined. We here propose optimized techniques for representing data by convex shapes, for computing the Hausdorff distance between convex shapes, based on an L ₂ norm, and for performing a hierarchical clustering of projected data.