Topological optimization in hip prosthesis design

With particular interest on total hip arthroplasty (THA), optimization of orthopedic prostheses is employed in this work to minimize the probability of implant failure or maximize prosthesis reliability. This goal is often identified with the reduction of stress concentrations at the interface between bone and these devices. However, aseptic loosening of the implant is mainly influenced by bone resorption phenomena revealed in some regions of the femur when a prosthesis is introduced. As a consequence, bone resorption appears due to stress shielding, that is to say the decrease of the stress level in the implanted femur caused by the significant load carrying of the prosthesis due to its higher stiffness. A maximum stiffness topological optimization-based (TO) strategy is utilized for non-linear static finite element (FE) analyses of the femur–implant assembly, with the goal of reducing stress shielding in the femur and to furnish guidelines for re-designing hip prostheses. This is accomplished by employing an extreme accuracy for both the three-dimensional reconstruction of the femur geometry and the material properties maps assigned as explicit functions of the local densities.     

Determination of kinetic parameters from chemical relaxation data discrimination between coupled two-step binding reactions differing in stoichiometry

The chemical relaxation times of two different two-step equilibrium reactions, characterized by a 1:1 binding process followed by a subsequent rearrangement step and a stepwise 1:2 binding reaction, are analyzed for the purpose of qualitative model discrimination and quantitative determination of kinetic parameters. The equations describing the dependences of the two reciprocal relaxation times on suitable concentrations are given for both models in the general case as well as for four different limiting situations which are characterized by well separated relaxation times. The conditions corresponding to the limiting cases are expressed in terms of strong, weak and no coupling between the two partial equilibrium steps involved in both models. The coupling strength depends on the rate constants as well as on the total concentrations of the reactants. Criteria to discriminate between these two reaction models under defined limiting conditions are developed. In the general case, the product of both reciprocal relaxation times can be used to distinguish both models. If only one relaxation time can be resolved experimentally, it is possible under conditions described to determine only a reduced set of individual rate constants for most of the limiting cases considered. If both relaxation times are observed, all rate constants are determinable in the general case as well as in most of the limiting cases discussed.     

Inverse finite element characterization of the human myometrium derived from uniaxial compression experiments / Von einaxialen Druckversuchen hergeleitete inverse Finite-Elemente-Charakterisierung des menschlichen Myometriums

Abstract The low strain-rate behavior of the human myometrium under compression was determined. To this end, uniaxial, unconstrained compression experiments were conducted on a total of 25 samples from three excised human uteri at strain rates between 0.001 s(-1) and 0.008 s(-1). A three-dimensional finite element model of each sample was created and used together with an optimization algorithm to find material parameters in an inverse estimation process. Friction and shape irregularities of samples were incorporated in the models. The uterine specimens in compression were modeled as viscoelastic, non-linear, nearly incompressible and isotropic continua. Simulations of uniaxial, frictionless compressions of an idealized cuboid were used to compare the resulting material parameters among each other. The intra- and inter-subject variability in stiffness of specimens was found to be large and to cover such a wide range that the effect of anisotropy which is of minor influence under compressive deformations in the first place could be neglected. Material parameters for a viscoelastic model based on a decoupled, reduced quadratic strain-energy function were presented for the uterine samples representing a median stiffness.     

Introducing mesoscopic information into constitutive equations for arterial walls

We propose a new elastic constitutive law for arterial tissue in which the limiting polymeric chain extensibility of both collagen and elastin fibres is accounted for. The elastic strain-energy function is separated additively into two parts: an isotropic contribution associated with the matrix (incorporating the elastin fibre network) and an anisotropic one associated with the collagen fibres. Information on the limiting extensibility in each case provides some mesoscopic input into the model. The (logarithm-based) model is compared with the Fung-Demiray exponential model and certain other recently proposed models. Some aspects of the elastic response under extension and inflation of a thin-walled circular cylindrical tube (the artery) are then examined and compared with the corresponding response of a rubber-like tube. We point out that our model, when both isotropic and anisotropic terms are included, can be developed to accommodate changing mechanical properties associated with degradation of the elastin and collagen by considering the material constants that define the limit of chain extensibility to evolve in time.     

A new device to control mechanical environment in bone defect healing in rats

Mechanical conditions have a significant influence on the biological processes of bone healing. Small animal models that allow controlling the mechanical environment of fracture and bone defect healing are needed. The aim of this study was to develop a new animal model that allows to reliably control the mechanical environment in fracture and bone defect healing in rats using different implant materials. An external fixator was designed and mounted in vitro to rat femurs using four Kirschner-wires (titanium (T) or steel (S)) of 1.2mm diameter. The specimens were distracted to a gap of 1.5mm. Axial and torsional stiffness of the device was tested increasing the offset (distance between bone and fixator crossbar) from 5 to 15mm. In vivo performance (well-being, infection, breaking of wires and bone healing) was evaluated in four groups of 24 Sprague-Dawley rats varying in offset (7.5 and 15mm) and implant material (S/T) over 6 weeks. Torsional and axial stiffness were higher in steel compared to titanium setups. A decrease in all configurations was observed by increasing the offset. The offset 7.5mm showed a significantly higher torsional (S: p<0.01, T: p<0.001) and axial in vitro stiffness (S: p<0.001, T: p<0.001) compared to 15mm offset of the fixator. Although in vitro designed to be different in mechanical stiffness, no difference was found between the groups regarding complication rate. The overall-complication rate was 5.2%. In conclusion, we were able to establish a small animal model for bone defect healing which allows modeling the mechanical conditions at the defect site in a defined manner.     

Growth models of cultures with two liquid phases. II. Pure substrate in dispersed phase

Mathematical models which can be used to describe batch frowth in fermentations with two liquid phases are developed for systems in which the growth limiting substrate is the dispersed liquid phase. Three special cases are considered assuming pure substrate in the dispersed phase and a decreasing interfacial area due to substrate consumption. In the first, it is assumed that all growth occurs at the surface of the dispersed phase. In the second and third growth occurs at the interface and in the continuous phase. The second case assumes substrate equilibrium between the two phases while the third assumes substrate consumption in the continuous phase is limited by rate of substrate transport to that phase. Since the amount of growth at the interface and substrate transport to the continuous phase depend on the interfacial area, two limiting cases for the decrease of interfacial area with substrate consumption are also considered in this investigation. The first and third models are compared with available experimental data.     

A pragmatic approach to understand peripheral artery lumen surface stiffness due to plaque heterogeneity

The goal of this study was to develop a pragmatic approach to build patient-specific models of the peripheral artery that are aware of plaque inhomogeneity. Patient-specific models using element-specific material definition (to understand the role of plaque composition) and homogeneous material definition (to understand the role of artery diameter and thickness) were automatically built from intravascular ultrasound images of three artery segments classified with low, average, and high calcification. The element-specific material models had average surface stiffness values of 0.0735, 0.0826, and 0.0973?MPa/mm, whereas the homogeneous material models had average surface stiffness values of 0.1392, 0.1276, and 0.1922?MPa/mm for low, average, and high calcification, respectively. Localization of peak lumen stiffness and differences in patient-specific average surface stiffness for homogeneous and element-specific models suggest the role of plaque composition on surface stiffness in addition to local arterial diameter and thickness.     

The biomechanics of human femurs in axial and torsional loading: comparison of finite element analysis, human cadaveric femurs, and synthetic femurs

To assess the performance of femoral orthopedic implants, they are often attached to cadaveric femurs, and biomechanical testing is performed. To identify areas of high stress, stress shielding, and to facilitate implant redesign, these tests are often accompanied by finite element (FE) models of the bone/implant system. However, cadaveric bone suffers from wide specimen to specimen variability both in terms of bone geometry and mechanical properties, making it virtually impossible for experimental results to be reproduced. An alternative approach is to utilize synthetic femurs of standardized geometry, having material behavior approximating that of human bone, but with very small specimen to specimen variability. This approach allows for repeatable experimental results and a standard geometry for use in accompanying FE models. While the synthetic bones appear to be of appropriate geometry to simulate bone mechanical behavior, it has not, however, been established what bone quality they most resemble, i.e., osteoporotic or osteopenic versus healthy bone. Furthermore, it is also of interest to determine whether FE models of synthetic bones, with appropriate adjustments in input material properties or geometric size, could be used to simulate the mechanical behavior of a wider range of bone quality and size. To shed light on these questions, the axial and torsional stiffness of cadaveric femurs were compared to those measured on synthetic femurs. A FE model, previously validated by the authors to represent the geometry of a synthetic femur, was then used with a range of input material properties and change in geometric size, to establish whether cadaveric results could be simulated. Axial and torsional stiffnesses and rigidities were measured for 25 human cadaveric femurs (simulating poor bone stock) and three synthetic "third generation composite" femurs (3GCF) (simulating normal healthy bone stock) in the midstance orientation. The measured results were compared, under identical loading conditions, to those predicted by a previously validated three-dimensional finite element model of the 3GCF at a variety of Young's modulus values. A smaller FE model of the 3GCF was also created to examine the effects of a simple change in bone size. The 3GCF was found to be significantly stiffer (2.3 times in torsional loading, 1.7 times in axial loading) than the presently utilized cadaveric samples. Nevertheless, the FE model was able to successfully simulate both the behavior of the 3GCF, and a wide range of cadaveric bone data scatter by an appropriate adjustment of Young's modulus or geometric size. The synthetic femur had a significantly higher stiffness than the cadaveric bone samples. The finite element model provided a good estimate of upper and lower bounds for the axial and torsional stiffness of human femurs because it was effective at reproducing the geometric properties of a femur. Cadaveric bone experiments can be used to calibrate FE models' input material properties so that bones of varying quality can be simulated.     

石墨化炭/ 炭复合材料+ 羟基磷灰石涂层(C/C+HA) 复合骨植入材料研究

目的:通过建立兔股骨缺损的动物实验模型,对采用等温化学气相沉积法和等离子喷涂技术所制备的石墨化炭/炭复合材料+羟基磷灰石涂层(C/C+HA)复合骨植入材料进行骨植入实验的的生物相容性进行评价,探索该复合材料作为植入机体骨组织的可行性依据.方法:采用骨科钻在实验动物股骨髁上钻孔的方法建立骨缺损的动物实验模型,将待研究比较的实验材料分别植入实验动物的股骨髁内,持续观察8周,在术后第2、4、8周时应用X线照片、组织学染色和扫描电镜技术,分别观察所研究材料在机体内对骨缺损愈合及其对机体的影响,进行组间比较和相关性分析.结果:石墨化炭/炭复合材料+羟基磷灰石涂层(C/C+HA)复合骨植入材料的骨植入实验生物相容性良好,材料与骨组织结合牢固,界面中成骨细胞生长明显,且炭颗粒脱落现象少,未见炎症细胞浸润.植入动物体内的材料在植入期未引起机体局部的炎症浸润反应且表面脱落的碳颗粒在机体组织中也未引起局部严重的炎症反应.在实验动物植入材料后的连续8周观察期中,组织学观察显示:表面涂有HA的炭/炭复合材料对骨组织形态改建上表现良好,其与骨组织接界处所形成的纤维结缔组织膜层厚度明显比未涂HA的材料要小,与骨组织结合更为紧密和牢固;碳颗粒出现脱落游离的现象明显减少.结论:在炭/炭复合材料表面涂以HA生物涂层对骨的形态改建和促进骨小梁生长等方面具有良好的作用,是一种具有发展潜力的骨修复材料.     

The Concept of Monophyly: A Speculative Essay

The concept of monophyly is central to much of modern biology. Despite many efforts over many years, important questions remain unanswered that relate both to the concept itself and to its various applications. This essay focuses primarily on four of these: i) Is it possible to define monophyly operationally, specifically with respect to both the structures of genomes and at the levels of the highest phylogenetic categories (kingdoms, phyla, classes)? ii) May the mosaic and chimeric structures of genomes be sufficiently important factors in phylogeny that situations exist in which the concept may not be applicable? iii) In the history of life on earth were there important groups of organisms that probably had polyphyletic, rather than monophyletic, origins? iv) Does the near universal search for monophyletic origins of clades lead, on occasion, to both undesirable narrowing of acceptable options for development of evolutionary scenarios and sometimes actual omission from consideration of less conventional types of both data and modes of thought, possibly at the expense of biological understanding? Three sections in the essay consider possible answers to these questions: i) A reassessment is made of major features of both the concept and some of its applications. Recent research results make it seem improbable that there could have been single basal forms for many of the highest categories of evolutionary differentiation (kingdoms, phyla, classes). The universal tree of life probably had many roots. Facts contributing to this perception include the phylogenetically widespread occurrences of: horizontal transfers of plasmids, viral genomes, and transposons; multiple genomic duplications; the existence and properties of large numbers of gene families and protein families; multiple symbioses; broad-scale hybridizations; and multiple homoplasys. Next, justifications are reassessed for the application of monophyletic frameworks to two major evolutionary developments usually interpreted as having been monophyletic: ii) the origins of life; and iii) the origins of the vertebrate tetrapods. For both cases polyphyletic hypotheses are suggested as more probable than monophyletic hypotheses. Major conclusions are, as answers to the four questions posed above: probably not, yes, yes, and yes.     

TiO2 nanotubes for bone regeneration

Nanostructured materials are believed to play a fundamental role in orthopedic research because bone itself has a structural hierarchy at the first level in the nanometer regime. Here, we report on titanium oxide (TiO(2)) surface nanostructures utilized for orthopedic implant considerations. Specifically, the effects of TiO(2) nanotube surfaces for bone regeneration will be discussed. This unique 3D tube shaped nanostructure created by electrochemical anodization has profound effects on osteogenic cells and is stimulating new avenues for orthopedic material surface designs. There is a growing body of data elucidating the benefits of using TiO(2) nanotubes for enhanced orthopedic implant surfaces. The current trends discussed within foreshadow the great potential of TiO(2) nanotubes for clinical use.     

Design and mathematical description of differential contactors used in extractive fermentations

The performance of differential contactors for use in extractive fermentation is complicated by the effects of product formation in the contactor. When product formation is significant, approximate analytical solutions are presented for the performance of the contactor for two limiting cases: high and low substrate concentrations. When products are formed at a constant rate, there is a minimum raffinate solute concentration that can be obtained, in contrast to the behavior of a column in the absence of product formation. General equations describing the behavior of the system for product formation with backmixing in both phases are presented. The case of a stripping factor not equal to unity is considered.     

Interrogating the effect of enzyme kinetics on metabolism using differentiable constraint-based models

Metabolic models are typically characterized by a large number of parameters. Traditionally, metabolic control analysis is applied to differential equation-based models to investigate the sensitivity of predictions to parameters. A corresponding theory for constraint-based models is lacking, due to their formulation as optimization problems. Here, we show that optimal solutions of optimization problems can be efficiently differentiated using constrained optimization duality and implicit differentiation. We use this to calculate the sensitivities of predicted reaction fluxes and enzyme concentrations to turnover numbers in an enzyme-constrained metabolic model of Escherichia coli. The sensitivities quantitatively identify rate limiting enzymes and are mathematically precise, unlike current finite difference based approaches used for sensitivity analysis. Further, efficient differentiation of constraint-based models unlocks the ability to use gradient information for parameter estimation. We demonstrate this by improving, genome-wide, the state-of-the-art turnover number estimates for E. coli. Finally, we show that this technique can be generalized to arbitrarily complex models. By differentiating the optimal solution of a model incorporating both thermodynamic and kinetic rate equations, the effect of metabolite concentrations on biomass growth can be elucidated. We benchmark these metabolite sensitivities against a large experimental gene knockdown study, and find good alignment between the predicted sensitivities and in vivo metabolome changes. In sum, we demonstrate several applications of differentiating optimal solutions of constraint-based metabolic models, and show how it connects to classic metabolic control analysis.     

Large deformation analysis of some basic problems in biophysics

This study is concerned with the application of a possible form of a strain-energy function suitable for soft biological tissues. Two problems considered here are related to simultaneous extension and inflation of cylindrical arteries, and inflation of the left ventricle under a given internal pressure. The values of the material constants are obtained via comparison of theoretical results with experimental findings. Some details concerning the wall stresses and the elastic stiffness are also given in the paper. For each case, it is seen that experiment and theory are in good agreement.     

Mechanical analysis of a rodent segmental bone defect model: The effects of internal fixation and implant stiffness on load transfer

Segmental bone defect animal models are often used for evaluating the bone regeneration performance of bone substituting biomaterials. Since bone regeneration is dependent on mechanical loading, it is important to determine mechanical load transfer after stabilization of the defect and to study the effects of biomaterial stiffness on the transmitted load. In this study, we assess the mechanical load transmitted over a 6 mm femur defect that is stabilized with an internal PEEK fixation plate. Subsequently, three types of selective laser melted porous titanium implants with different stiffness values were used to graft the defect (five specimens per group). In one additional group, the defect was left empty. Micro strain gauges were used to measure strain values at four different locations of the fixation plate during external loading on the femoral head. The load sharing between the fixation plate and titanium implant was highly variable with standard deviations of measured strain values between 31 and 93% of the mean values. As a consequence, no significant differences were measured between the forces transmitted through the titanium implants with different elastic moduli. Only some non-significant trends were observed in the mean strain values that, consistent with the results of a previous finite element study, implied the force transmitted through the implant increases with the implant stiffness. The applied internal fixation method does not standardize mechanical loading over the defect to enable detecting small differences in bone regeneration performances of bone substituting biomaterials. In conclusion, the fixation method requires further optimization to reduce the effects of the operative procedure and make the mechanical loading more consistent and improve the overall sensitivity of this rat femur defect model.     

A 3D finite element model of an implanted scapula: importance of a multiparametric validation using experimental data

In order to help to understand the loosening phenomenon around gleno?d prostheses, a 3D finite element model of a previously tested implanted scapula has been developed. The construction of the model was done using CT scans of the tested scapula. Different bone material properties were tested and shell elements or 8 nodes hexaedric elements were used to model the cortical bone. Surface contact elements were introduced on one hand between the bone and the lower part of the plate of the implant, and on the other, between the loading metallic ball and the upper surface of the implant. The results of the model were compared with those issued from in vitro experiments carried out on the same scapula. The evaluation of the model was done for nine cases of loading of 500 N distributed on the implant, in terms of strains (principal strains of six spots around peripheral cortex of the gleno?d) and displacement of four points positioned on the implant. The best configuration of the model presented here, fits with experiments for most of the strains (difference lower than 150microdef) but it seems to be still too stiff (mainly in the lower part). Nevertheless, we want, in this paper, to underline the importance of doing a multiparametric validation for such a model. Indeed, some models can give correct results for one case of loading but bad results for another kind of loading, some others can give good results for one kind of compared parameters (like strains for instance) but bad results for the other one (like displacements).     

Increased osteoblast cell density on nanostructured PLGA-coated nanostructured titanium for orthopedic applications

There are more than 30,000 orthopedic implant revision surgeries necessary each year in part due to poor implant fixation with juxtaposed bone. A further emphasis on the current problems associated with insufficient bone implant performance is the fact that many patients are receiving hip implants earlier in life, remaining active older, and that the human lifespan is continuously increasing. Collectively, it is clear that there is a strong clinical need to improve implant performance through proper, prolonged fixation. For these reasons, the objective of the present in vitro study was to improve the performance of titanium (Ti), one of the most popular orthopedic implant materials. Accordingly, the proliferative response of osteoblasts (bone-forming cells) on novel nanostructured Ti/PLGA (poly-lactic-co-glycolic acid) composites was examined. This study showed that nano-topography can be easily applied to Ti (through anodization) and porous PLGA (through NaOH chemical etching) to enhance osteoblast cell proliferation which may lead to better orthopedic implant performance. This straight forward application of nano-topography on current bone implant materials represents a new direction in the design of enhanced biomaterials for the orthopedic industry.     

Coating with a Modular Bone Morphogenetic Peptide Promotes Healing of a Bone-Implant Gap in an Ovine Model

Despite the potential for growth factor delivery strategies to promote orthopedic implant healing, there is a need for growth factor delivery methods that are controllable and amenable to clinical translation. We have developed a modular bone growth factor, herein termed “modular bone morphogenetic peptide (mBMP)”, which was designed to efficiently bind to the surface of orthopedic implants and also stimulate new bone formation. The purpose of this study was to coat a hydroxyapatite-titanium implant with mBMP and evaluate bone healing across a bone-implant gap in the sheep femoral condyle. The mBMP molecules efficiently bound to a hydroxyapatite-titanium implant and 64% of the initially bound mBMP molecules were released in a sustained manner over 28 days. The results demonstrated that the mBMP-coated implant group had significantly more mineralized bone filling in the implant-bone gap than the control group in C-arm computed tomography (DynaCT) scanning (25% more), histological (35% more) and microradiographic images (50% more). Push-out stiffness of the mBMP group was nearly 40% greater than that of control group whereas peak force did not show a significant difference. The results of this study demonstrated that mBMP coated on a hydroxyapatite-titanium implant stimulates new bone formation and may be useful to improve implant fixation in total joint arthroplasty applications.     

Determination of material models for arterial walls from uniaxial extension tests and histological structure

An approach is proposed that allows the determination of material models from uniaxial tests and histostructural data including fiber orientation of the tissue. A combination of neo-Hookean and Fung-type strain-energy functions is utilized, and inequality constraints imposed on the constitutive parameters are derived providing strict local convexity and preferred fiber orientations. It is shown how the Fung-type model gets a pseudo-structural aspect inherent in the phenomenological model; a correlation between the fiber structure and the parameters of the Fung-type model is explicitly provided. In order to apply the proposed approach, quasi-static uniaxial extension tests of preconditioned prepared strips from the intima, media and adventitia of a human aorta with non-atherosclerotic intimal thickening are acquired in axial and circumferential directions; structural information from histological analyses for each aortic tissue are documented. Data reveal a remarkable thickness, load-bearing capacity and stiffness of the intimal samples in comparison with the media and adventitia. Constitutive parameters for each aortic tissue layer are determined by solving the constrained problem using a penalty function method; a new approach for the estimation of appropriate start values is proposed. Finally, the predictivity and efficacy of the material models is shown by comparing model data with data from the uniaxial extension tests and histological image analyses.     

Foraging-area size and food density: Some predictive models

It has been observed that when food increases in density along an environmental gradient, the size of foraging areas used by desert ant colonies decreases. Factors that could cause this inverse relationship are explored. Four models of ant foraging are developed and presented in the form of equations for calculating net foraging energy as a function of size of the foraging area. These are used to predict the optimal sizes of foraging areas under conditions of different food densities. Only one of the models predicts an inverse relationship between density of food and size of foraging area when food is the limiting factor in colony reproduction. In this model, the foraging areas of adjacent colonies are assumed to be overlapping and the number of foragers assigned to each square meter of the foraging area is constant, regardless of food density or distance from the nest entrance. Tests for distinguishing among the four models, as well as for determining whether colonies are or are not food limited, are discussed.