Experimental validation of a nonlinear μ FE model based on cohesive-frictional plasticity for trabecular bone

Trabecular bone is a porous mineralized tissue playing a major load bearing role in the human body. Prediction of age-related and disease-related fractures and the behavior of bone implant systems needs a thorough understanding of its structure-mechanical property relationships, which can be obtained using microcomputed tomography-based finite element modeling. In this study, a nonlinear model for trabecular bone as a cohesive-frictional material was implemented in a large-scale computational framework and validated by comparison of μFE simulations with experimental tests in uniaxial tension and compression. A good correspondence of stiffness and yield points between simulations and experiments was found for a wide range of bone volume fraction and degree of anisotropy in both tension and compression using a non-calibrated, average set of material parameters. These results demonstrate the ability of the model to capture the effects leading to failure of bone for three anatomical sites and several donors, which may be used to determine the apparent behavior of trabecular bone and its evolution with age, disease, and treatment in the future.

A nonlinear QCT-based finite element model validation study for the human femur tested in two configurations in vitro

Purpose Femoral fracture is a common medical problem in osteoporotic individuals. Bone mineral density (BMD) is the gold standard measure to evaluate fracture risk in vivo. Quantitative computed tomography (QCT)-based homogenized voxel finite element (hvFE) models have been proved to be more accurate predictors of femoral strength than BMD by adding geometrical and material properties. The aim of this study was to evaluate the ability of hvFE models in predicting femoral stiffness, strength and failure location for a large number of pairs of human femora tested in two different loading scenarios. Methods Thirty-six pairs of femora were scanned with QCT and total proximal BMD and BMC were evaluated. For each pair, one femur was positioned in one-legged stance configuration (STANCE) and the other in a sideways configuration (SIDE). Nonlinear hvFE models were generated from QCT images by reproducing the same loading configurations imposed in the experiments. For experiments and models, the structural properties (stiffness and ultimate load), the failure location and the motion of the femoral head were computed and compared. Results In both configurations, hvFE models predicted both stiffness (R2=0.82 for STANCE and R2=0.74 for SIDE) and femoral ultimate load (R2=0.80 for STANCE and R2=0.85 for SIDE) better than BMD and BMC. Moreover, the models predicted qualitatively well the failure location (66% of cases) and the motion of the femoral head. Conclusions The subject specific QCT-based nonlinear hvFE model cannot only predict femoral apparent mechanical properties better than densitometric measures, but can additionally provide useful qualitative information about failure location.

Risk of severe asthma episodes predicted from fluctuation analysis of airway function

Asthma is an increasing health problem worldwide, but the long-term temporal pattern of clinical symptoms is not understood and predicting asthma episodes is not generally possible. We analyse the time series of peak expiratory flows, a standard measurement of airway function that has been assessed twice daily in a large asthmatic population during a long-term crossover clinical trial. Here we introduce an approach to predict the risk of worsening airflow obstruction by calculating the conditional probability that, given the current airway condition, a severe obstruction will occur within 30 days. We find that, compared with a placebo, a regular long-acting bronchodilator (salmeterol) that is widely used to improve asthma control decreases the risk of airway obstruction. Unexpectedly, however, a regular short-acting beta2-agonist bronchodilator (albuterol) increases this risk. Furthermore, we find that the time series of peak expiratory flows show long-range correlations that change significantly with disease severity, approaching a random process with increased variability in the most severe cases. Using a nonlinear stochastic model, we show that both the increased variability and the loss of correlations augment the risk of unstable airway function. The characterization of fluctuations in airway function provides a quantitative basis for objective risk prediction of asthma episodes and for evaluating the effectiveness of therapy.

Genetic variation and demographic history of the Haplochromis laparogramma group of Lake Victoria-An analysis based on SINEs and mitochondrial DNA

More than 500 endemic haplochromine cichlid species inhabit Lake Victoria. This striking species diversity is a classical example of recent explosive adaptive radiation thought to have happened within the last similar to 15,000 years. In this study, we examined the population structure and historical demography of 3 pelagic haplochromine cichlid species that resemble in morphology and have similar niche, Haplochromis (Yssichromis) laparogramma, Haplochromis (Y.) pyrrhocephalus, and Haplochromis (Y.) sp. "glaucocephalus". We investigated the sequences of the mitochondrial DNA control region and the insertion patterns of short interspersed elements (SINEs) of 759 individuals. We show that sympatric forms are genetically differentiated in 4 of 6 cases, but we also found apparent weakening of the genetic differentiation in areas with turbid water. We estimated the timings of population expansion and species divergence to coincide with the refilling of the lake at the Pleistocene/Holocene boundary. We also found that estimates can be altered significantly by the choice of the shape of the molecular clock. If we employ the nonlinear clock model of evolutionary rates in which the rates are higher towards the recent, the population expansion was dated at around the event of desiccation of the lake ca. 17,000 YBP. Thus, we succeeded in clarifying the species and population structure of closely related Lake Victoria cichlids and in showing the importance of applying appropriate clock calibrations in elucidating recent evolutionary events. (C) 2009 Elsevier B.V. All rights reserved.

Finite element analysis predicts experimental failure patterns in vertebral bodies loaded via intervertebral discs up to large deformation

Vertebral compression fracture is a common medical problem in osteoporotic individuals. The quantitative computed tomography (QCT)-based finite element (FE) method may be used to predict vertebral strength in vivo, but needs to be validated with experimental tests. The aim of this study was to validate a nonlinear anatomy specific QCT-based FE model by using a novel testing setup. Thirty-seven human thoracolumbar vertebral bone slices were prepared by removing cortical endplates and posterior elements. The slices were scanned with QCT and the volumetric bone mineral density (vBMD) was computed with the standard clinical approach. A novel experimental setup was designed to induce a realistic failure in the vertebral slices in vitro. Rotation of the loading plate was allowed by means of a ball joint. To minimize device compliance, the specimen deformation was measured directly on the loading plate with three sensors. A nonlinear FE model was generated from the calibrated QCT images and computed vertebral stiffness and strength were compared to those measured during the experiments. In agreement with clinical observations, most of the vertebrae underwent an anterior wedge-shape fracture. As expected, the FE method predicted both stiffness and strength better than vBMD (R2 improved from 0.27 to 0.49 and from 0.34 to 0.79, respectively). Despite the lack of fitting parameters, the linear regression of the FE prediction for strength was close to the 1:1 relation (slope and intercept close to one (0.86 kN) and to zero (0.72 kN), respectively). In conclusion, a nonlinear FE model was successfully validated through a novel experimental technique for generating wedge-shape fractures in human thoracolumbar vertebrae.

Nonlinear three-dimensional noise filter with low-dose CT angiography: effect on the detection of small high-contrast objects in a phantom model

To study the effect of a nonlinear noise filter on the detection of simulated endoleaks in a phantom with 80- and 100-kVp multidetector computed tomographic (CT) angiography.

An insulin infusion advisory system based on autotuning nonlinear model-predictive control

This paper aims at the development and evaluation of a personalized insulin infusion advisory system (IIAS), able to provide real-time estimations of the appropriate insulin infusion rate for type 1 diabetes mellitus (T1DM) patients using continuous glucose monitors and insulin pumps. The system is based on a nonlinear model-predictive controller (NMPC) that uses a personalized glucose-insulin metabolism model, consisting of two compartmental models and a recurrent neural network. The model takes as input patient's information regarding meal intake, glucose measurements, and insulin infusion rates, and provides glucose predictions. The predictions are fed to the NMPC, in order for the latter to estimate the optimum insulin infusion rates. An algorithm based on fuzzy logic has been developed for the on-line adaptation of the NMPC control parameters. The IIAS has been in silico evaluated using an appropriate simulation environment (UVa T1DM simulator). The IIAS was able to handle various meal profiles, fasting conditions, interpatient variability, intraday variation in physiological parameters, and errors in meal amount estimations.

Loop formulation of the supersymmetric nonlinear O(N) sigma model

We derive the fermion loop formulation for the supersymmetric nonlinear O(N) sigma model by performing a hopping expansion using Wilson fermions. In this formulation the fermionic contribution to the partition function becomes a sum over all possible closed non-oriented fermion loop configurations. The interaction between the bosonic and fermionic degrees of freedom is encoded in the constraints arising from the supersymmetry and induces flavour changing fermion loops. For N ≥ 3 this leads to fermion loops which are no longer self-avoiding and hence to a potential sign problem. Since we use Wilson fermions the bare mass needs to be tuned to the chiral point. For N = 2 we determine the critical point and present boson and fermion masses in the critical regime.

Uniform approach to linear and nonlinear interrelation patterns in multivariate time series

Currently, a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series. Whereas the former are by definition insensitive to nonlinear effects, the latter detect both nonlinear and linear interrelation. In the present contribution we employ a uniform surrogate-based approach, which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation. The bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation. To demonstrate applicability of the approach to multivariate real-world time series we investigate resting state functional magnetic resonance imaging (rsfMRI) data of two healthy subjects as well as intracranial electroencephalograms (iEEG) of two epilepsy patients with focal onset seizures. The main findings are that for our rsfMRI data interrelations can be described by linear cross-correlation. Rejection of the null hypothesis of linear iEEG interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures.

Mechanisms of intrinsic beating variability in cardiac cell cultures and model pacemaker networks

Heart rate variability (HRV) exhibits fluctuations characterized by a power law behavior of its power spectrum. The interpretation of this nonlinear HRV behavior, resulting from interactions between extracardiac regulatory mechanisms, could be clinically useful. However, the involvement of intrinsic variations of pacemaker rate in HRV has scarcely been investigated. We examined beating variability in spontaneously active incubating cultures of neonatal rat ventricular myocytes using microelectrode arrays. In networks of mathematical model pacemaker cells, we evaluated the variability induced by the stochastic gating of transmembrane currents and of calcium release channels and by the dynamic turnover of ion channels. In the cultures, spontaneous activity originated from a mobile focus. Both the beat-to-beat movement of the focus and beat rate variability exhibited a power law behavior. In the model networks, stochastic fluctuations in transmembrane currents and stochastic gating of calcium release channels did not reproduce the spatiotemporal patterns observed in vitro. In contrast, long-term correlations produced by the turnover of ion channels induced variability patterns with a power law behavior similar to those observed experimentally. Therefore, phenomena leading to long-term correlated variations in pacemaker cellular function may, in conjunction with extracardiac regulatory mechanisms, contribute to the nonlinear characteristics of HRV.

Analysis of nonlinear gain-induced effects on short-pulse amplification in doped fibers by use of an extended power equation

Optical pulse amplification in doped fibers is studied using an extended power transport equation for the coupled pulse spectral components. This equation includes the effects of gain saturation, gain dispersion, fiber dispersion, fiber nonlinearity, and amplified spontaneous emission. The new model is employed to study nonlinear gain-induced effects on the spectrotemporal characteristics of amplified subpicosecond pulses, in both the anomalous and the normal dispersion regimes.

An anisotropic elastic-viscoplastic damage model for bone tissue

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain D(κ) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

A cardiovascular mathematical model of graded head-up tilt

A lumped parameter model of the cardiovascular system has been developed and optimized using experimental data obtained from 13 healthy subjects during graded head-up tilt (HUT) from the supine position to [Formula: see text]. The model includes descriptions of the left and right heart, direct ventricular interaction through the septum and pericardium, the systemic and pulmonary circulations, nonlinear pressure volume relationship of the lower body compartment, arterial and cardiopulmonary baroreceptors, as well as autoregulatory mechanisms. A number of important features, including the separate effects of arterial and cardiopulmonary baroreflexes, and autoregulation in the lower body, as well as diastolic ventricular interaction through the pericardium have been included and tested for their significance. Furthermore, the individual effect of parameter associated with heart failure, including LV and RV contractility, baseline systemic vascular resistance, pulmonary vascular resistance, total blood volume, LV diastolic stiffness and reflex gain on HUT response have also been investigated. Our fitted model compares favorably with our experimental measurements and published literature at a range of tilt angles, in terms of both global and regional hemodynamic variables. Compared to the normal condition, a simulated congestive heart failure condition produced a blunted response to HUT with regards to the percentage changes in cardiac output, stroke volume, end diastolic volume and effector response (i.e., heart contractility, venous unstressed volume, systemic vascular resistance and heart rate) with progressive tilting.

Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.