Evaluation of residual stresses due to bone callus growth: a computational study

Mechanical environment in callus is determinant for the evolution of bone healing. However, recent mechanobiological computational works have underestimated the effect that growth exerts on the mechanical environment of callus. In the present work, we computationally evaluate the significance of growth-induced stresses, commonly called residual stresses, in callus. We construct a mechanobiological model of a callus in the metatarsus of a sheep in two different stages: one week and four weeks after fracture. The magnitude of stresses generated during callus growth is compared with the magnitude of stresses when only external loads are applied to the callus. We predict that residual stresses are relevant in some areas, mainly located at the periosteal side far from the fracture gap. Therefore, the inclusion of these residual stresses could represent a significant impact on the callus growth and predict a different evolution of biological processes occurring during bone healing.     

Regional distribution of axial strain and circumferential residual strain in the layered rabbit oesophagus

The oesophagus is subjected to large axial strains in vivo and the zero-stress state is not a closed cylinder but an open circular cylindrical sector. The closed cylinder with no external loads applied is called the no-load state and residual strain is the difference in strain between the no-load state and zero-stress state. To understand oesophageal physiology and pathophysiology, it is necessary to know the distribution of axial strain, the zero-stress state, the stress-strain relations of oesophageal tissue, and the changes of these states and relationships due to biological remodeling of the tissue under stress. This study is addressed to such biomechanical properties in normal rabbits. The oesophagi were marked on the surface in vivo, photographed, excised (in vitro state), photographed again, and sectioned into rings (no-load state) in an organ bath containing calcium-free Kreb's solution with dextran and EGTA added. The rings were cut radially to obtain the zero-stress state for the non-separated wall and further dissected to separate the muscle and submucosa layers. Equilibrium was awaited for 30min in each state and the specimens were photographed in no-load and the zero-stress states. The oesophageal length, circumferences, layer thicknesses and areas, and openings angle were measured from the digitised images. The oesophagus shortened axially by 35% after excision. The in vivo axial strain showed a significant variation with the highest values in the mid-oesophagus (p<0.001). Luminal area, circumferences, and wall and layer thicknesses and areas varied in axial direction (in all tests p<0.05). The residual strain was compressive at the mucosal surface and tensile at the serosal surface. The dissection studies demonstrated shear forces between the two layers in the non-separated wall in the no-load and zero-stress states. In conclusion, our data show significant axial variation in passive morphometric and biomechanical properties of the oesophagus. The oesophagus is a layered composite structure with nonlinear and anisotropic mechanical behaviour.     

Semi-automated mitral valve morphometry and computational stress analysis using 3D ultrasound

In vivo human mitral valves (MV) were imaged using real-time 3D transesophageal echocardiography (rt-3DTEE), and volumetric images of the MV at mid-systole were analyzed by user-initialized segmentation and 3D deformable modeling with continuous medial representation, a compact representation of shape. The resulting MV models were loaded with physiologic pressures using finite element analysis (FEA). We present the regional leaflet stress distributions predicted in normal and diseased (regurgitant) MVs. Rt-3DTEE, semi-automated leaflet segmentation, 3D deformable modeling, and FEA modeling of the in vivo human MV is tenable and useful for evaluation of MV pathology.     

A 3D computational simulation of fracture callus formation: influence of the stiffness of the external fixator

The stiffness of the external fixation highly influences the fracture healing pattern. In this work we study this aspect by means of a finite element model of a simple transverse mid-diaphyseal fracture of an ovine metatarsus fixed with a bilateral external fixator. In order to simulate the regenerative process, a previously developed mechanobiological model of bone fracture healing was implemented in three dimensions. This model is able to simulate tissue differentiation, bone regeneration, and callus growth. A physiological load of 500 N was applied and three different stiffnesses of the external fixator were simulated (2300, 1725, and 1150 N/mm). The interfragmentary strain and load sharing mechanism between bone and the external fixator were compared to those recorded in previous experimental works. The effects of the stiffness on the callus shape and tissue distributions in the fracture site were also analyzed. We predicted that a lower stiffness of the fixator delays fracture healing and causes a larger callus, in correspondence to well-documented clinical observations.     

Elastic-plastic finite elements analysis of transient and residual stresses in ceramo-metal restorations

Transient and residual stresses occurring in partially fixed dental prostheses after the firing process can be calculated with elastic or elastic-plastic finite element analyses (FEA). In this study, firstly, the mechanical and thermal properties at various temperatures of the materials used in a porcelain fused metal (PFM) system were obtained by experimental and literature studies. The effects of viscoelastic and viscoplastic behaviours of the dental porcelain at the elevated temperatures were reflected onto its elastic properties. The equivalent heat transfer coefficients were determined experimentally by measuring temperatures and the results were supplied as input to the 3D finite elements analysis. It has been observed that the maximum stresses occur within a short time period after cooling begins and that stresses decrease during the cooling process and remain at a constant value at the end of cooling; these are the thermal residual stresses.     

Dynamic visco-elastic buckling analysis of an in vitro airway model: prediction of circumferential and axial buckling mode numbers

The purpose of the research reported here was to elucidate the mechanism of formation of the various lobes observed in asthmatic airways by both theoretical and experimental analysis employing an in vitro airway model. The rationale is that the elucidated mechanism will facilitate the development of new diagnostic methods and treatment regimens for asthma. Lobe formation was analyzed on the basis of an assumption of cross-sectional buckling of the airway. Here, we propose a dynamic visco-elastic buckling model analysis of the airway for the prediction of circumferential and axial buckling mode numbers. The calculated circumferential buckling mode numbers were in reasonably good agreement with those measured in the dynamic buckling experiment using the in vitro airway model. The calculated axial buckling mode numbers were in qualitative agreement with those observed in the experiment. The non-dimensional parameters related to the remodeling and the consequent pathologies occurring in asthmatic airways were also shown, and the influence of changes in the non-dimensional parameters on the circumferential and axial buckling mode numbers was also calculated. The circumferential and axial buckling mode numbers decreased due to thickening and stiffening of the basement membrane. Thickening of the tissues surrounding the basement membrane and the increase in the mucus secreted in the airway lumen were modeled as an increase in the added mass on the basement membrane. The results of calculation showed that the circumferential and axial buckling mode numbers increased because of the thickening of the surrounding tissues and the increase in mucus secretion. We suggest that it may be possible to diagnose the severity of asthma by using the results of the calculation of the changes in the buckling mode numbers caused by the changes in the strength of the remodeling. The physiological reality of the in vitro airway model reported here is discussed using the non-dimensional parameters.     

Molecular modeling of the axial and circumferential elastic moduli of tubulin

Microtubules play a number of important mechanical roles in almost all cell types in nearly all major phylogenetic trees. We have used a molecular mechanics approach to perform tensile tests on individual tubulin monomers and determined values for the axial and circumferential moduli for all currently known complete sequences. The axial elastic moduli, in vacuo, were found to be 1.25 GPa and 1.34 GPa for α- and β-bovine tubulin monomers. In the circumferential direction, these moduli were 378 MPa for α- and 460 MPa for β-structures. Using bovine tubulin as a template, 269 homologous tubulin structures were also subjected to simulated tensile loads yielding an average axial elastic modulus of 1.10 ± 0.14 GPa for α-tubulin structures and 1.39 ± 0.68 GPa for β-tubulin. Circumferentially the α- and β-moduli were 936 ± 216 MPa and 658 ± 134 MPa, respectively. Our primary finding is that that the axial elastic modulus of tubulin diminishes as the length of the monomer increases. However, in the circumferential direction, no correlation exists. These predicted anisotropies and scale dependencies may assist in interpreting the macroscale behavior of microtubules during mitosis or cell growth. Additionally, an intergenomic approach to investigating the mechanical properties of proteins may provide a way to elucidate the evolutionary mechanical constraints imposed by nature upon individual subcellular components.     

A negative correlation between human carotid atherosclerotic plaque progression and plaque wall stress: in vivo MRI-based 2D/3D FSI models

It is well accepted that atherosclerosis initiation and progression correlate positively with low and oscillating flow wall shear stresses (FSS). However, this mechanism cannot explain why advanced plaques continue to grow under elevated FSS conditions. In vivo magnetic resonance imaging (MRI)-based 2D/3D multi-component models with fluid-structure interactions (FSI, 3D only) for human carotid atherosclerotic plaques were introduced to quantify correlations between plaque progression measured by wall thickness increase (WTI) and plaque wall (structure) stress (PWS) conditions. A histologically validated multi-contrast MRI protocol was used to acquire multi-year in vivo MRI images. Our results using 2D models (200-700 data points/patient) indicated that 18 out of 21 patients studied showed significant negative correlation between WTI and PWS at time 2 (T2). The 95% confidence interval for the Pearson correlation coefficient is (-0.443,-0.246), p<0.0001. Our 3D FSI model supported the 2D correlation results and further indicated that combining both plaque structure stress and flow shear stress gave better approximation results (PWS, T2: R(2)=0.279; FSS, T1: R(2)=0.276; combining both: R(2)=0.637). These pilot studies suggest that both lower PWS and lower FSS may contribute to continued plaque progression and should be taken into consideration in future investigations of diseases related to atherosclerosis.     

Benzodiazepine-induced hyperphagia: development and assessment of a 3D pharmacophore by computational methods

Benzodiazepine receptor (BDZR) ligands are structurally diverse compounds that bind to specific binding sites on GABA(A) receptors and allosterically modulate the effect of GABA on chloride ion flux. The binding of BDZR ligands to this receptor system results in activity at multiple behavioral endpoints, including anxiolytic, sedative, anticonvulsant, and hyperphagic effects. In the work presented here, a computational procedure developed in our laboratory has been used to obtain a 3D pharmacophore for ligand recognition of the GABA(A)/BDZRs initiating the hyperphagic response. To accomplish this goal, 17 structurally diverse compounds, previously assessed in our laboratory for activity at the hyperphagic endpoint, were used. The result is a four-component 3D pharmacophore. It consists of two proton acceptor atoms, the centroid of an aromatic ring and the centroid of a hydrophobic moiety in a common geometric arrangement in all compounds with activity at this endpoint. This 3D pharmacophore was then assessed and successfully validated using three different tests. First, two BDZR ligands, which were included as negative controls in the set of seventeen compounds used for the pharmacophore development, did not fit the pharmacophore. Second, some benzodiazepine ligands known to have activity at the hyperphagia endpoint, but not included in the pharmacophore development, were used as positive controls and were found to fit the pharmacophore. Finally, using the 3D pharmacophore developed in the present work to search 3D databases, over 50 classical benzodiazepines were found. Among them, were benzodiazepine ligands known to have an effect at the hyperphagic endpoint. In addition, the novel compounds also found in this search are promising therapeutic agents that could beneficially affect feeding behavior.     

Origin of axial prestretch and residual stress in arteries

The structural protein elastin endows large arteries with unique biological functionality and mechanical integrity, hence its disorganization, fragmentation, or degradation can have important consequences on the progression and treatment of vascular diseases. There is, therefore, a need in arterial mechanics to move from materially uniform, phenomenological, constitutive relations for the wall to those that account for separate contributions of the primary structural constituents: elastin, fibrillar collagens, smooth muscle, and amorphous matrix. In this paper, we employ a recently proposed constrained mixture model of the arterial wall and show that prestretched elastin contributes significantly to both the retraction of arteries that is observed upon transection and the opening angle that follows the introduction of a radial cut in an unloaded segment. We also show that the transmural distributions of elastin and collagen, compressive stiffness of collagen, and smooth muscle tone play complementary roles. Axial prestresses and residual stresses in arteries contribute to the homeostatic state of stress in vivo as well as adaptations to perturbed loads, disease, or injury. Understanding better the development of and changes in wall stress due to individual extracellular matrix constituents thus promises to provide considerable clinically important insight into arterial health and disease.     

Nonuniformity of axial and circumferential remodeling of large coronary veins in response to ligation

The pressure-induced remodeling of coronary veins is important in coronary venous retroperfusion. Our hypothesis is that the response of the large coronary veins to pressure overload will depend on the degree of myocardial support. Eleven normal Yorkshire swine from either sex, weighing 31-39 kg, were studied. Five pigs underwent ligation of the left anterior descending (LAD) vein, and six served as sham-operated controls. The ligation of the coronary vein caused an increase in pressure intermediate to arterial and venous values. After 2 wk of ligation, the animals were euthanized and the coronary vessels were perfusion-fixed with glutaraldehyde. The LAD vein was sectioned, and detailed morphometric measurements were made along its length from the point of ligation near the base down to the apex of the heart. The structural remodeling of the vein was circumferentially nonuniform because the vein is partially embedded in the myocardium; it was also axially nonuniform because it is tethered to the myocardium to different degrees along its axial length. The wall area was significantly larger in the experimental group, whereas luminal area in the proximal LAD vein was significantly smaller in the same group compared with sham-operated controls. The wall thickness-to-radius ratio was also significantly larger in the experimental group in proportion to the increase in pressure. The major conclusion of this study is that the response of the vein depends on the local wall stress, which is, in part, determined by the surrounding tissue. Furthermore, the geometric remodeling of the coronary vein restores the circumferential stress to the homeostatic value.     

Alterations in regional vascular geometry produced by theoretical stent implantation influence distributions of wall shear stress: analysis of a curved coronary artery using 3D computational fluid dynamics modeling

Background  

The success of stent implantation in the restoration of blood flow through areas of vascular narrowing is limited by restenosis. Several recent studies have suggested that the local geometric environment created by a deployed stent may influence regional blood flow characteristics and alter distributions of wall shear stress (WSS) after implantation, thereby rendering specific areas of the vessel wall more susceptible to neointimal hyperplasia and restenosis. Stents are most frequently implanted in curved vessels such as the coronary arteries, but most computational studies examining blood flow patterns through stented vessels conducted to date use linear, cylindrical geometric models. It appears highly probable that restenosis occurring after stent implantation in curved arteries also occurs as a consequence of changes in fluid dynamics that are established immediately after stent implantation.     

Effect of residual stress and heterogeneity on circumferential stress in the arterial wall

Quantifying the stress distribution through the arterial wall is essential to studies of arterial growth and disease. Previous studies have shown that both residual stress, as measured by opening angle, and differing material properties for the media-intima and the adventitial layers affect the transmural circumferential stress (sigma theta) distribution. Because a lack of comprehensive data on a single species and artery has led to combinations from multiple sources, this study determined the sensitivity of sigma theta to published variations in both opening angle and layer thickness data. We fit material properties to previously published experimental data for pressure-diameter relations and opening angles of rabbit carotid artery, and predicted sigma theta through the arterial wall at physiologic conditions. Using a one-layer model, the ratio of sigma theta at the internal wall to the mean sigma theta decreased from 2.34 to 0.98 as the opening angle increased from 60 to 130 deg. In a two-layer model using a 95 deg opening angle, mean sigma theta in the adventitia increased (112 percent for 25 percent adventitia) and mean sigma theta in the media decreased (47 percent for 25 percent adventitia). These results suggest that both residual stress and wall layers have important effects on transmural stress distribution. Thus, experimental measurements of loading curves, opening angles, and wall composition from the same species and artery are needed to accurately predict the transmural stress distribution in the arterial wall.     

Effects of parametric manipulation of inter-stimulus similarity on 3D object categorization

To explore the nature of the representation space of 3D objects, we studied human performance in forced-choice categorization of objects composed of four geon-like parts emanating from a common center. Two categories were defined by prototypical objects, distinguished by qualitative properties of their parts (bulging vs waist-like limbs). Subjects were trained to discriminate between the two prototypes (shown briefly, from a number of viewpoints, in stereo) in a 1-interval forced-choice task, until they reached a 90% correct-response performance level. After training, in the first experiment, 11 subjects were tested on shapes obtained by varying the prototypical parameters both orthogonally (ORTHO) and in parallel (PARA) to the line connecting the prototypes in the parameter space. For the eight subjects who performed above chance, the error rate increased with the ORTHO parameter-space displacement between the stimulus and the corresponding prototype; the effect of the PARA displacement was weaker. Thus, the parameter-space location of the stimuli mattered more than the qualitative contrasts, which were always present. To find out whether both prototypes or just the nearest one to the test shape influenced the decision, in the second experiment we varied the similarity between the categories. Specifically, in the test stage trials the distance between the two prototypes could assume one of three values (FAR, INTERMEDIATE, and NEAR). For the 13 subjects who performed above chance, the error rate (on physically identical stimuli) in the NEAR condition was higher than in the other two conditions. The results of the two experiments contradict the prediction of theories that postulate exclusive reliance on qualitative contrasts, and support the notion of a representation space in which distances to more than one reference point or prototype are encoded (Edelman, 1998).     

3D virtual human atria: A computational platform for studying clinical atrial fibrillation

Despite a vast amount of experimental and clinical data on the underlying ionic, cellular and tissue substrates, the mechanisms of common atrial arrhythmias (such as atrial fibrillation, AF) arising from the functional interactions at the whole atria level remain unclear. Computational modelling provides a quantitative framework for integrating such multi-scale data and understanding the arrhythmogenic behaviour that emerges from the collective spatio-temporal dynamics in all parts of the heart. In this study, we have developed a multi-scale hierarchy of biophysically detailed computational models for the human atria - the 3D virtual human atria. Primarily, diffusion tensor MRI reconstruction of the tissue geometry and fibre orientation in the human sinoatrial node (SAN) and surrounding atrial muscle was integrated into the 3D model of the whole atria dissected from the Visible Human dataset. The anatomical models were combined with the heterogeneous atrial action potential (AP) models, and used to simulate the AP conduction in the human atria under various conditions: SAN pacemaking and atrial activation in the normal rhythm, break-down of regular AP wave-fronts during rapid atrial pacing, and the genesis of multiple re-entrant wavelets characteristic of AF. Contributions of different properties of the tissue to mechanisms of the normal rhythm and arrhythmogenesis were investigated. Primarily, the simulations showed that tissue heterogeneity caused the break-down of the normal AP wave-fronts at rapid pacing rates, which initiated a pair of re-entrant spiral waves; and tissue anisotropy resulted in a further break-down of the spiral waves into multiple meandering wavelets characteristic of AF. The 3D virtual atria model itself was incorporated into the torso model to simulate the body surface ECG patterns in the normal and arrhythmic conditions. Therefore, a state-of-the-art computational platform has been developed, which can be used for studying multi-scale electrical phenomena during atrial conduction and AF arrhythmogenesis. Results of such simulations can be directly compared with electrophysiological and endocardial mapping data, as well as clinical ECG recordings. The virtual human atria can provide in-depth insights into 3D excitation propagation processes within atrial walls of a whole heart in vivo, which is beyond the current technical capabilities of experimental or clinical set-ups.     

Regional distribution of layer-specific circumferential residual deformations and opening angles in the porcine aorta

Information on the layer-specific residual deformations of aortic tissue and how these vary throughout the vessel is important for understanding the regionally-varying aortic functions and pathophysiology, but not so much can be found in the literature. Toward this end, porcine aortas were sectioned into eighteen rings, with one ring from each anatomical position radially cut to obtain the zero-stress state for the intact wall and the other ring dissected into intimal-medial and adventitial layers; these rings were then radially cut to reach the zero-stress state for the intima-media and adventitia. Peripheral variations in internal/external circumferences, thickness, and opening angle of the intact wall and its layers were measured through image analysis at the no-load and zero-stress states. Intact wall and layer circumferences at both states significantly declined along the aorta, as did intact wall and intimal-medial but not adventitial thickness. Adventitia exhibited the greatest opening angles, approaching 180 deg all over the aorta. The opening angles of the intima-media and intact wall were quite similar, with the highest values in the ascending aorta, the lowest at the diaphragm, and increasing subsequently. Bending-related residual stretches were released by radial cutting that were compressive internally and tensile externally, displaying distinct axial variation for the intima-media and intact wall, and non-significant variation for the adventitia. Evidence is provided for the release upon layer separation of compressive stretches in the intima-media and of tensile stretches in the adventitia, whose values were smallest in the descending thoracic aorta and highest near the iliac artery bifurcation.     

The influence of computational strategy on prediction of mechanical stress in carotid atherosclerotic plaques: Comparison of 2D structure-only, 3D structure-only,one-way and fully coupled fluid-structure interaction analyses

Background

Compositional and morphological features of carotid atherosclerotic plaques provide complementary information to luminal stenosis in predicting clinical presentations. However, they alone cannot predict cerebrovascular risk. Mechanical stress within the plaque induced by cyclical changes in blood pressure has potential to assess plaque vulnerability. Various modeling strategies have been employed to predict stress, including 2D and 3D structure-only, 3D one-way and fully coupled fluid-structure interaction (FSI) simulations. However, differences in stress predictions using different strategies have not been assessed.

Methods

Maximum principal stress (Stress-P1) within 8 human carotid atherosclerotic plaques was calculated based on geometry reconstructed from in vivo computerized tomography and high resolution, multi-sequence magnetic resonance images. Stress-P1 within the diseased region predicted by 2D and 3D structure-only, and 3D one-way FSI simulations were compared to 3D fully coupled FSI analysis.

Results

Compared to 3D fully coupled FSI, 2D structure-only simulation significantly overestimated stress level (94.1 kPa [65.2, 117.3] vs. 85.5 kPa [64.4, 113.6]; median [inter-quartile range], p=0.0004). However, when slices around the bifurcation region were excluded, stresses predicted by 2D structure-only simulations showed a good correlation (R²=0.69) with values obtained from 3D fully coupled FSI analysis. 3D structure-only model produced a small yet statistically significant stress overestimation compared to 3D fully coupled FSI (86.8 kPa [66.3, 115.8] vs. 85.5 kPa [64.4, 113.6]; p<0.0001). In contrast, one-way FSI underestimated stress compared to 3D fully coupled FSI (78.8 kPa [61.1, 100.4] vs. 85.5 kPa [64.4, 113.7]; p<0.0001).

Conclusions

A 3D structure-only model seems to be a computationally inexpensive yet reasonably accurate approximation for stress within carotid atherosclerotic plaques with mild to moderate luminal stenosis as compared to fully coupled FSI analysis.     

Comprehensive expression analysis of rice phospholipase D gene family during abiotic stresses and development

Phospholipase D is one of the crucial enzymes involved in lipid mediated signaling, triggered during various developmental and physiological processes. Different members of PLD gene family have been known to be induced under different abiotic stresses and during developmental processes in various plant species. In this report, we are presenting a detailed microarray based expression analysis and expression profiles of entire set of PLD genes in rice genome, under three abiotic stresses (salt, cold and drought) and different developmental stages (3-vegetative stages and 11-reproductive stages). Seven and nine PLD genes were identified, which were expressed differentially under abiotic stresses and during reproductive developmental stages, respectively. PLD genes, which were expressed significantly under abiotic stresses exhibited an overlapping expression pattern and were also differentially expressed during developmental stages. Moreover, expression pattern for a set of stress induced genes was validated by real time PCR and it supported the microarray expression data. These findings emphasize the role of PLDs in abiotic stress signaling and development in rice. In addition, expression profiling for duplicated PLD genes revealed a functional divergence between the duplicated genes and signify the role of gene duplication in the evolution of this gene family in rice. This expressional study will provide an important platform in future for the functional characterization of PLDs in crop plants.     

On the interrelationship of permeability and structural parameters of vertebral trabecular bone: a parametric computational study

To characterise the flow of a fluid through a uniform porous medium, the medium may be completely described by its permeability, a measure of flow resistance. Fluid flow in the intertrabecular spaces of cancellous bone has been recognised as an important factor in a number of physical phenomena. In order to investigate the interdependence of permeability, porosity and the structural parameters, we adapted a morphological model and systematically varied its structural parameters. By simulating a viscous Stokes flow regime, we were able to estimate the anisotropic permeability tensor and performed an extensive, stepwise multivariate regression analysis to establish empirical relationships between the morphological parameters and the permeability for the anatomical directions individually. The regression analysis indicated high values of determination coefficients [0.88 < R² < 0.89 (transversal directions) and R² = 0.60 (longitudinal direction), porosity-based prediction and R² = 0.98 for all directions and information presented to the regression model]. We conclude that a pooled set of structural parameters may explain up to 98% of the permeability variability, the regression model predicts permeability values that match experimental data, and a good prediction performance could be achieved by only incorporating the porosity and either the degree of anisotropy (0.89 < R² < 0.91) or the trabecular spacing predictor (0.96 < R² < 0.97). These conclusions imply that trabecular thickness and shape parameters only play a minor role in the determination of vertebral trabecular bone permeability. However, a major limitation of the model is that it reflects an idealisation of the real, regionally varying structure of trabecular bone. Therefore, the goodness-of-fit estimates we are presenting should be considered as an upper bound limitation regarding the prediction performance.