Computational model of the dual action of PTH - Application to a rat model of osteoporosis.

This paper presents a pharmacokinetic/pharmacodynamic (PK/PD) model of the action of PTH(1-34) on bone modelling and remodelling, developed for quantitatively investigating the dose- and administration pattern-dependency of the bone tissue response to this drug. Firstly, a PK model of PTH(1-34) was developed, accounting for administration via subcutaneous injections. Subsequently, the PK model was coupled to a (mechanistic) bone cell population model of bone modelling and remodelling, taking into account the effects of PTH(1-34) on the differentiation of lining cells into active osteoblasts, on the apoptosis of active osteoblasts, and on proliferation of osteoblast precursors, as well as on the key regulatory pathways of bone cell activities.

Early-Age Evolution of Strength, Stiffness, and Non-Aging Creep of Concretes: Experimental Characterization and Correlation Analysis.

Six different concretes are characterized during material ages between 1 and 28 days. Standard tests regarding strength and stiffness are performed 1, 3, 7, 14, and 28 days after production. Innovative three-minute-long creep tests are repeated hourly during material ages between one and seven days.

X-ray physics-based CT-to-composition conversion applied to a tissue engineering scaffold, enabling multiscale simulation of its elastic behavior.

Nowadays, the assessment of the mechanical competence of tissue engineering scaffolds based on computer simulations is a well-accepted technology. Typically, such simulations are performed by means of the Finite Element (FE) method, with the underlying structural model being created based on micro-computed tomography (microCT). Here, this analysis modality is applied to a new, ternary composite, consisting of PHBV, i.

Modal analysis of nanoindentation data, confirming that reduced bone turnover may cause increased tissue mineralization/elasticity.

It is widely believed that the activities of bone cells at the tissue scale not only govern the size of the vascular pore spaces (and hence, the amount of bone tissue available for actually carrying the loads), but also the characteristics of the extracellular bone matrix itself. In this context, increased mechanical stimulation (in mediolateral regions of human femora, as compared to anteroposterior regions) may lead to increased bone turnover, lower bone matrix mineralization, and therefore lower tissue modulus. On the other hand, resorption-only processes (in endosteal versus periosteal regions) may have the opposite effect.

Fermentation of Saccharomyces cerevisiae - Combining kinetic modeling and optimization techniques points out avenues to effective process design.

A combined experimental/theoretical approach is presented, for improving the predictability of Saccharomyces cerevisiae fermentations. In particular, a mathematical model was developed explicitly taking into account the main mechanisms of the fermentation process, allowing for continuous computation of key process variables, including the biomass concentration and the respiratory quotient (RQ). For model calibration and experimental validation, batch and fed-batch fermentations were carried out.

Creep and cracking of concrete hinges: insight from centric and eccentric compression experiments.

Existing design guidelines for concrete hinges consider bending-induced tensile cracking, but the structural behavior is oversimplified to be time-independent. This is the motivation to study creep and bending-induced tensile cracking of initially monolithic concrete hinges systematically. Material tests on plain concrete specimens and structural tests on marginally reinforced concrete hinges are performed.

A mathematical multiscale model of bone remodeling, accounting for pore space-specific mechanosensation.

While bone tissue is a hierarchically organized material, mathematical formulations of bone remodeling are often defined on the level of a millimeter-sized representative volume element (RVE), "smeared" over all types of bone microstructures seen at lower observation scales. Thus, there is no explicit consideration of the fact that the biological cells and biochemical factors driving bone remodeling are actually located in differently sized pore spaces: active osteoblasts and osteoclasts can be found in the vascular pores, whereas the lacunar pores host osteocytes - bone cells originating from former osteoblasts which were then "buried" in newly deposited extracellular bone matrix. We here propose a mathematical description which considers size and shape of the pore spaces where the biological and biochemical events take place.

Multiscale Mathematical Modeling in Dental Tissue Engineering: Toward Computer-Aided Design of a Regenerative System Based on Hydroxyapatite Granules, Focussing on Early and Mid-Term Stiffness Recovery.

We here explore for the very first time how an advanced multiscale mathematical modeling approach may support the design of a provenly successful tissue engineering concept for mandibular bone. The latter employs double-porous, potentially cracked, single millimeter-sized granules packed into an overall conglomerate-type scaffold material, which is then gradually penetrated and partially replaced by newly grown bone tissue. During this process, the newly developing scaffold-bone compound needs to attain the stiffness of mandibular bone under normal physiological conditions.

Patient-specific fracture risk assessment of vertebrae: A multiscale approach coupling X-ray physics and continuum micromechanics.

While in clinical settings, bone mineral density measured by computed tomography (CT) remains the key indicator for bone fracture risk, there is an ongoing quest for more engineering mechanics-based approaches for safety analyses of the skeleton. This calls for determination of suitable material properties from respective CT data, where the traditional approach consists of regression analyses between attenuation-related grey values and mechanical properties. We here present a physics-oriented approach, considering that elasticity and strength of bone tissue originate from the material microstructure and the mechanical properties of its elementary components.

X-ray physics- and bone composition-based estimation of thickness characteristics from clinical mandibular radiographs.

In dentistry, clinical radiographs (also called X-ray images) reflect the intensity loss of an X-ray when being transmitted through the mandibular objects, and this loss is quantified in terms of grey values. While such images are standardly used for pathology detection by the experienced dentist, we here present a new method for getting more quantitative information out of such 2D radiographs, "extending" them into the third dimension. This "extension" requires consistent combination of X-ray physics (namely, X-ray intensity loss quantification along paths orthogonal to the panoramic clinical image and X-ray attenuation averaging for composite materials) with anatomically known upper and lower limits of vascular porosities in cortical and trabecular bone compartments.

A multiscale mechanobiological model of bone remodelling predicts site-specific bone loss in the femur during osteoporosis and mechanical disuse.

We propose a multiscale mechanobiological model of bone remodelling to investigate the site-specific evolution of bone volume fraction across the midshaft of a femur. The model includes hormonal regulation and biochemical coupling of bone cell populations, the influence of the microstructure on bone turnover rate, and mechanical adaptation of the tissue. Both microscopic and tissue-scale stress/strain states of the tissue are calculated from macroscopic loads by a combination of beam theory and micromechanical homogenisation.

Poromicromechanics reveals that physiological bone strains induce osteocyte-stimulating lacunar pressure.

Mechanical loads which are macroscopically acting onto bony organs, are known to influence the activities of biological cells located in the pore spaces of bone, in particular so the signaling and production processes mediated by osteocytes. The exact mechanisms by which osteocytes are actually able to "feel" the mechanical loading and changes thereof, has been the subject of numerous studies, and, while several hypotheses have been brought forth over time, this topic has remained a matter of debate. Relaxation times reported in a recent experimental study of Gardinier et al.

Assessment of solutions from the consistently linearized eigenproblem by means of finite difference approximations.

The consistently linearized eigenproblem (CLE) plays an important role in stability analysis of structures. Solution of the CLE requires computation of the tangent stiffness matrix [Formula: see text] and of its first derivative with respect to a dimensionless load parameter , denoted as [Formula: see text]. In this paper, three approaches of computation of [Formula: see text] are discussed.

Extracellular bone matrix exhibits hardening elastoplasticity and more than double cortical strength: Evidence from homogeneous compression of non-tapered single micron-sized pillars welded to a rigid substrate.

We here report an improved experimental technique for the determination of Young׳s modulus and uniaxial strength of extracellular bone matrix at the single micrometer scale, giving direct access to the (homogeneous) deformation (or strain) states of the tested samples and to the corresponding mechanically recoverable energy, called potential or elastic energy. Therefore, a new protocol for Focused Ion Beam milling of prismatic non-tapered micropillars, and attaching them to a rigid substrate, was developed. Uniaxial strength turns out as at least twice that measured macroscopically, and respective ultimate stresses are preceded by hardening elastoplastic states, already at very low load levels.

Micro-poro-elasticity of baghdadite-based bone tissue engineering scaffolds: a unifying approach based on ultrasonics, nanoindentation, and homogenization theory.

Microstructure-elasticity relations for bone tissue engineering scaffolds are key to rational biomaterial design. As a contribution thereto, we here report comprehensive length measuring, weighing, and ultrasonic tests at 0.1MHz frequency, on porous baghdadite (Ca3ZrSi2O9) scaffolds.

Is trabecular bone permeability governed by molecular ordering-induced fluid viscosity gain? Arguments from re-evaluation of experimental data in the framework of homogenization theory.

It is generally agreed on that trabecular bone permeability, a physiologically important quantity, is governed by the material׳s (vascular or intertrabecular) porosity as well as by the viscosity of the pore-filling fluids. Still, there is less agreement on how these two key factors govern bone permeability. In order to shed more light onto this somewhat open issue, we here develop a random homogenization scheme for upscaling Poiseuille flow in the vascular porosity, up to Darcy-type permeability of the overall porous medium "trabecular bone".

Ultrasonic elasticity determination of 45S5 Bioglass(®)-based scaffolds: influence of polymer coating and crosslinking treatment.

Highly porous 45S5 Bioglass(®)-based scaffolds with interconnected pore structure are promising candidates for bone tissue engineering due to their bioactivity, biocompatibility, osteogenic and angiogenic effects. In the present study, to ensure the mechanical competence of the 45S5 Bioglass(®)-based scaffolds, their stiffness was adjusted by applying polymer coatings and further crosslinking treatment. A non-destructive ultrasonic technique was used to determine the stiffness of the scaffolds.

The role of endplate poromechanical properties on the nutrient availability in the intervertebral disc.

Objective: To investigate the relevance of the human vertebral endplate poromechanics on the fluid and metabolic transport from and to the intervertebral disc (IVD) based on educated estimations of the poromechanical parameter values of the bony endplate (BEP).

Methods: 50 micro-models of different BEP samples were generated from μCTs of lumbar vertebrae and allowed direct determination of porosity values. Permeability values were calculated by using the micro-models, through the simulation of permeation via computational fluid dynamics.

A multiscale analytical approach for bone remodeling simulations: linking scales from collagen to trabeculae.

Bone is a dynamic and hierarchical porous material whose spatial and temporal mechanical properties can vary considerably due to differences in its microstructure and due to remodeling. Hence, a multiscale analytical approach, which combines bone structural information at multiple scales to the remodeling cellular activities, could form an efficient, accurate and beneficial framework for the prognosis of changes in bone properties due to, e.g.

A multiscale poromicromechanical approach to wave propagation and attenuation in bone.

Ultrasonics is an important diagnostic tool for bone diseases, as it allows for non-invasive assessment of bone tissue quality through mass density-elasticity relationships. The latter are, however, quite complex for fluid-filled porous media, which motivates us to develop a rigorous multiscale poromicrodynamics approach valid across the great variety of different bone tissues. Multiscale momentum and mass balance, as well as kinematics of a hierarchical double porous medium, together with Darcy's law for fluid flow and micro-poro-elasticity for the solid phase of bone, give access to the so-called dispersion relation, linking the complex wave numbers to corresponding wave frequencies.

Structure-function relationships in hardwood--insight from micromechanical modelling.

A micromechanical model is presented that predicts the stiffness of wood tissues in their three principal anatomical directions, across various hardwood species. The wood polymers cellulose, hemicellulose, and lignin, common to all wood tissues, serve as the starting point. In seven homogenisation steps, the stiffnesses of these polymers are linked to the macroscopic stiffness.

Mathematical modeling of postmenopausal osteoporosis and its treatment by the anti-catabolic drug denosumab.

Denosumab, a fully human monoclonal antibody, has been approved for the treatment of postmenopausal osteoporosis. The therapeutic effect of denosumab rests on its ability to inhibit osteoclast differentiation. Here, we present a computational approach on the basis of coupling a pharmacokinetics model of denosumab with a pharmacodynamics model for quantifying the effect of denosumab on bone remodeling.

Intravoxel bone micromechanics for microCT-based finite element simulations.

While micro-FE simulations have become a standard tool in computational biomechanics, the choice of appropriate material properties is still a relevant topic, typically involving empirical grey value-to-elastic modulus relations. We here derive the voxel-specific volume fractions of mineral, collagen, and water, from tissue-independent bilinear relations between mineral and collagen content in extracellular bone tissue (J. Theor.

Mathematical conditions for and physical meaning of a maximum of the determinant of [Formula: see text] in the prebuckling regime.

It is shown that the determinant of the tangent stiffness matrix has a maximum in the prebuckling regime if and only if the determinant of a specific linear combination of the first and the third derivative of this matrix with respect to a dimensionless load factor vanishes. The mathematical tool for this proof is the so-called consistently linearized eigenproblem in the frame of the Finite Element Method. The physical meaning of the mentioned maximum is the one of a minimum of the percentage bending energy of the total strain energy.