Determination of Elastic Modulus in Mouse Bones Using a Nondestructive Micro-Indentation Technique Using Reference Point Indentation.

The determination of the elastic modulus of bone is important in studying the response of bone to loading and is determined using a destructive three-point bending method. Reference point indentation (RPI), with one cycle of indentation, offers a nondestructive alternative to determine the elastic modulus. While the elastic modulus could be determined using a nondestructive procedure for ex vivo experiments, for in vivo testing, the three-point bending technique may not be practical and hence RPI is viewed as a potential alternative and explored in this study. Using the RPI measurements, total indentation distance (TID), creep indentation distance, indentation force, and the unloading slope, we have developed a numerical analysis procedure using the Oliver-Pharr (O/P) method to estimate the indentation elastic modulus. Two methods were used to determine the area function: (1) Oliver-Pharr (O/P-based on a numerical procedure) and (2) geometric (based on the calculation of the projected area of indentation). The indentation moduli of polymethyl methacrylate (PMMA) calculated by the O/P (3.49-3.68 GPa) and geometric (3.33-3.49 GPa) methods were similar to values in literature (3.5-4 GPa). In a study using femurs from C57Bl/6 mice of different ages and genders, the three-point bending modulus was lower than the indentation modulus. In femurs from 4 to 5 months old TOPGAL mice, we found that the indentation modulus from the geometric (5.61 ± 1.25 GPa) and O/P (5.53 ± 1.27 GPa) methods was higher than the three-point bending modulus (5.28 ± 0.34 GPa). In females, the indentation modulus from the geometric (7.45 ± 0.86 GPa) and O/P (7.46 ± 0.92 GPa) methods was also higher than the three-point bending modulus (7.33 ± 1.13 GPa). We can conclude from this study that the RPI determined values are relatively close to three-point bending values.

Role of biomechanical forces in hyperfiltration-mediated glomerular injury in congenital anomalies of the kidney and urinary tract.

Congenital anomalies of the kidney and urinary tract (CAKUT) including solitary kidney constitute the main cause of progressive chronic kidney disease (CKD) in children. Children born with CAKUT develop signs of CKD only during adolescence and do not respond to renin-angiotensin-aldosterone system blockers. Early cellular changes underlying CKD progression to end-stage renal disease by early adulthood are not well understood. The mechanism of maladaptive hyperfiltration that occurs from loss of functional nephrons, including solitary kidney, is not clear. We re-examine the phenomenon of hyperfiltration in the context of biomechanical forces with special reference to glomerular podocytes. Capillary stretch exerts tensile stress on podocytes through the glomerular basement membrane. The flow of ultrafiltrate over the cell surface directly causes fluid flow shear stress (FFSS) on podocytes. FFSS on the podocyte surface increases 1.5- to 2-fold in animal models of solitary kidney and its effect on podocytes is a subject of ongoing research. Podocytes (i) are mechanosensitive to tensile and shear forces, (ii) use prostaglandin E2, angiotensin-II or nitric oxide for mechanoperception and (iii) use specific signaling pathways for mechanotransduction. We discuss (i) the nature of and differences in cellular responses to biomechanical forces, (ii) methods to study biomechanical forces and (iii) effects of biomechanical forces on podocytes and glomeruli. Future studies on FFSS will likely identify novel targets for strategies for early intervention to complement and strengthen the current regimen for treating children with CAKUT.

Biomechanical Comparison of 2 Methods of Intramedullary K-Wire Fixation of Transverse Metacarpal Shaft Fractures.

PURPOSE: To determine the relative importance of intramedullary wire (IMW) diameter and IMW number in conferring stability to a metacarpal fracture fixation construct. Our research hypothesis was that the stiffness of IMW fixation for metacarpal shaft fractures using a single 1.6-mm-diameter (0.062-in) wire would be greater than three 0.8-mm-diameter (0.031-in) wires. METHODS: Our study compared the biomechanical stiffness between one 1.6-mm K-wire and three 0.8-mm K-wires in a composite, fourth-generation, biomechanical metacarpal construct under cantilever testing to treat transverse metacarpal shaft fractures. Six composite bone-wire constructs were tested in each group using constant-rate, nondestructive testing. Stiffness (load/displacement) was measured for each construct. RESULTS: All constructs demonstrated a linear load-displacement relationship. Wires were all tested in their elastic zone. The mean stiffness of the 1-wire construct was 3.20 N/mm and the mean stiffness of the 3-wire construct was 0.76 N/mm. These differences were statistically significant with a large effect size. CONCLUSIONS: The stiffness of IMW fixation for metacarpal shaft fractures using a single 1.6-mm-diameter wire was significantly greater than using three 0.8-mm-diameter wires. CLINICAL RELEVANCE: When IMW fixation is clinically indicated for the treatment of metacarpal fractures, the increased stiffness of a single large-diameter construct provides more stability in the plane of finger flexion-extension.

Fracture resistance and failure pattern of endodontically treated maxillary premolars restored with transfixed glass fiber post: an in vitro and finite element analysis.

The aims of the study were to determine the effect of different types of endodontic sealers and the presence of a horizontal glass fiber post (HGFP) on the fracture resistance and fracture pattern of mesio-occluso-distal (MOD) restored upper premolars and to analyze the stress distribution. Sixty extracted upper premolars received root canal treatment (RCT) and a MOD cavity preparation. All MOD cavities were restored with the same composite resin (CR). The 60 teeth were divided randomly into 6 groups (n = 10); Group1= AH Plus sealer; Group 2= TotalFill BC sealer; Group 3= BioRoot RCS sealer; Group 4= AH plus sealer + HGFP; Group 5= TotalFill BC sealer + HGFP; and, Group 6= Bio Root RCS sealer + HGFP. All specimens were thermocycled and subjected to cyclic loading. Next, the specimens were subjected to a static load using a universal testing machine. Data were analyzed using two-way ANOVA. Two micro-CTs of the same upper premolar, one without the HGFP and later one with HGFP inserted were made and used to create two finite element (FE) models. For the fracture resistance, two-way ANOVA revealed significant differences for the effect of HGFP (p = 0.029), but no differences for the effect of root canal sealer type (p = 0.561). The HGFP groups showed higher restorable fracture compared to groups without HGFP (p = 0.013). Finite element analysis showed that the inclusion of HGFP reduces stress concentration at the occlusal interface and cervical region. Therefore, it can be concluded that HGFP significantly increased the fracture resistance of endodontically treated upper premolars with MOD cavities and reduced the risk for non-restorable fractures. The FE analysis supports the mechanical test results.

Application of multivariate spectral analyses in micro-Raman imaging to unveil structural/chemical features of the adhesive/dentin interface.

This study presents the application of multivariate analyses to analyze micro-Raman spectral imaging data in reference to the adhesive/dentin interface as well as comparison with univariate analysis. The univariate statistical methods, such as mapping of specific functional group peak intensities, do not always detect functional group positions and quantities due to peak overlapping. A comprehensive chemical analysis of the adhesive/dentin interface, along with the multivariate statistical methods, principal component analysis, and fuzzy c-means clustering, is studied. Compared to univariate analysis, multivariate methods present the entire hyperspectral information from the specimen in a concise and uncorrelated way. Apart from the ease with which information can be extracted and presented, multivariate methods also highlight minute and often important variations in the spectra that are difficult to observe using univariate methods. The results show for the first time the clear chemical and structural classifications in the adhesive/dentin interface at successively greater resolutions.

Nano finite element modeling of the mechanical behavior of biocomposites using multi-scale (virtual internal bond) material models.

It is evident that biocomposites, specifically mineralized Type-I collagen fibrils, have strong mechanical properties, such as a desirable combination of elastic modulus, fracture toughness, and fracture strength. The mineral Hydroxyapatite [Hap] by itself is stiffer, and it is not clear whether a collagen fiber by itself has a lower breaking strength than the mineralized fiber. Hence, the objective of this paper is to develop, outline, apply, and demonstrate issues involving a new nano explicit finite element based framework, by which the mechanical behavior of mineralized collagen fibrils and their constituents can be studied. A multi-scale virtual internal bond model is used to model the material behavior and failure of such biocomposites. In this research two models have been studied. The first model attempts to illustrate the hypothesis that materials are less sensitive to flaws at nanoscale and the second model studies the mechanical behavior of a nano sized dahlite mineral crystal commonly found in collagen fibril. Two important implementation characteristics have been introduced and illustrated, namely that scaled properties can be used at the micro and nano length scales along with scaled dimensions and secondly the loading time can be appropriately scaled without the loading becoming a dynamic loading.

Comparison of strain measurement in the mouse forearm using subject-specific finite element models, strain gaging, and digital image correlation.

Mechanical loading in bone leads to the activation of bone-forming pathways that are most likely associated with a minimum strain threshold being experienced by the osteocyte. To investigate the correlation between cellular response and mechanical stimuli, researchers must develop accurate ways to measure/compute strain both externally on the bone surface and internally at the osteocyte level. This study investigates the use of finite element (FE) models to compute bone surface strains on the mouse forearm. Strains from three FE models were compared to data collected experimentally through strain gaging and digital image correlation (DIC). Each FE model was assigned subject-specific bone properties and consisted of one-dimensional springs representing the interosseous membrane. After three-point bending was performed on the ulnae and radii, moment of inertia was determined from microCT analysis of the bone region between the supports and then used along with standard beam analyses to calculate the Young's modulus. Non-contact strain measurements from DIC were determined to be more suitable for validating numerical results than experimental data obtained through conventional strain gaging. When comparing strain responses in the three ulnae, we observed a 3-14% difference between numerical and DIC strains while the strain gage values were 37-56% lower than numerical values. This study demonstrates a computational approach for capturing bone surface strains in the mouse forearm. Ultimately, strains from these macroscale models can be used as inputs for microscale and nanoscale FE models designed to analyze strains directly in the osteocyte lacunae.

The interrelationship of microstructure and hardness of human coronal dentin using reference point indentation technique and micro-Raman spectroscopy.

OBJECTIVES: The aim of this paper is to determine the interrelationship between the microstructure - in terms of chemical composition and crystallinity - to the microhardness of coronal dentin. METHODS: Dentin microhardness was tested by a novel reference point indenter and compared to the traditional Knoop hardness method. Micro-Raman spectroscopy was used to determine the chemical composition and crystallinity of dentin. RESULTS: From the occlusal groove to the border of the coronal pulp chamber, dentin hardness decreased from superficial dentin (SD) to deep dentin (DD). Mineral/organic matrix ratios (phosphate/CH and phosphate/amide I) also decreased from SD to DD; however, this change was significant (P<0.05) in the phosphate/amide I ratio only. The phosphate/carbonate ratio decreased significantly by varying position from SD to DD. The degree of the crystallinity, as measured by the full width at half maximum (FWHM) of the peak at 960cm-1, decreased significantly going from superficial to deep dentin. SIGNIFICANCE: For the first time, the interrelationship between the microstructure and the mechanical properties of coronal dentin was determined by using the novel reference point indentation technique and micro-Raman spectroscopy. We hypothesize that the decrease in hardness from superficial to deep dentin can potentially be explained by decreased mineral content and increased carbonate content, which is also associated with decreased crystallinity. Collectively, there is a positive association between dentin hardness and mineral content and a negative association between dentin hardness and carbonate content.

Stress analysis of irradiated human tooth enamel using finite element methods.

The objectives of this project were to use finite element methods to determine how changes in the elastic modulus due to oral cancer therapeutic radiation alter the distribution of mechanical stresses in teeth and to determine if observed failures in irradiated teeth correlate with changes in mechanical stresses. A thin slice section finite element (FE) model was constructed from micro CT sections of a molar tooth using MIMICS and 3-Matic software. This model divides the tooth into three enamel regions, the dentin-enamel junction (DEJ) and dentin. The enamel elastic modulus was determined in each region using nano indentation for three experimental groups namely - control (non-radiated), in vitro irradiated (simulated radiotherapy following tooth extraction) and in vivo irradiated (extracted subsequent to oral cancer patient radiotherapy) teeth. Physiological loads were applied to the tooth models at the buccal and lingual cusp regions for all three groups (control, in vitro and in vivo). The principal tensile stress and the maximum shear stress were used to compare the results from different groups since it has been observed in previous studies that delamination of enamel from the underlying dentin was one of the major reasons for the failure of teeth following therapeutic radiation. From the FE data, we observed an increase in the principal tensile stress within the inner enamel region of in vivo irradiated teeth (9.97 ± 1.32 MPa) as compared to control/non-irradiated teeth (8.44 ± 1.57 MPa). Our model predicts that failure occurs at the inner enamel/DEJ interface due to extremely high tensile and maximum shear stresses in in vivo irradiated teeth which could be a cause of enamel delamination due to radiotherapy.

Non-contact strain measurement in the mouse forearm loading model using digital image correlation (DIC).

This study investigates the use of a non-contact method known as digital image correlation (DIC) to measure strains in the mouse forearm during axial compressive loading. A two camera system was adapted to analyze the medial and lateral forearm displacements simultaneously, and the derived DIC strain measurements were compared to strain gage readings from both the ulna and radius. Factors such as region-of-interest (ROI) location, lens magnification, noise, and out-of-plane motion were examined to determine their influence on the DIC strain measurements. We confirmed that our DIC system can differentiate ROI locations since it detected higher average strains in the ulna compared to the radius and detected compressive strains on medial bone surfaces vs. tensile strains on lateral bone surfaces. Interestingly, the DIC method also captured heterogeneity in surface strain fields which are not detectable by strain gage based methods. A separate analysis of the noise intrinsic to the DIC system also revealed that the noise constituted less than 4.5% of all DIC strain measurements. Furthermore, finite element (FE) simulations of the forearm showed that out-of-plane motion was not a significant factor that influenced DIC measurements. Finally, we observed that average DIC strain measurements can be up to 1.5-2 times greater than average strain gage readings on the medial bone surfaces. These findings suggest that strain experienced in the mouse forearm model by loading is better captured through DIC as opposed to strain gages, which as a result of being glued to the bone surface artificially stiffen the bone and lead to an underestimation of the strain response.

A preliminary three-dimensional finite element analysis of mandibular implant overdentures.

A treatment protocol that may lead to reduced mandibular posterior residual ridge resorption in patients with overdentures retained and supported by two interforaminal implants was investigated. The treatment included the addition of short implants in the posterior edentulous mandible for the presumed purpose of favorable provision of mechanical load stimulus to alveolar bone. Three-dimensional finite element analysis was used to model cited effective strains that may stimulate bone remodeling in two selected models. Based on this laboratory study, the addition of posterior short implants has a favorable effect in maintaining bone mass under implant retained overdentures.

Experimental and finite element analysis of dynamic loading of the mouse forearm.

Bone formation is reported to initiate in osteocytes by mechanotransduction due to dynamic loading of bone. The first step towards this is to characterize the dynamic strain fields in the overall bone. Here, the previously developed mouse forearm ulna-radius model, subjected to static loading, has been further enhanced by incorporating a loading cap and applying a cyclic dynamic load to more closely approximate experimental biological conditions. This study also incorporates data obtained from strain gauging both the ulna and radius simultaneously. Based on separate experiments, the elastic modulus of the ulna and radius were determined to be 13.8 and 9.9 GPa, respectively. Another novel aspect of the numerical model is the inclusion of the interosseous membrane in the FE model with membrane stiffness ranging from 5-15 N/mm that have been found to give strain values closer to that from the experiments. Interestingly, the inclusion of the interosseous membrane helped to equalize the peak strain magnitudes in the ulna and radius (∼1800 at 2 N load and ∼3200 at 3.5 N), which was also observed experimentally. This model represents a significant advance towards being able to simulate through FE analysis the strain fields generated in vivo upon mechanical loading of the mouse forearm.

A multibody knee model with discrete cartilage prediction of tibio-femoral contact mechanics.

Combining musculoskeletal simulations with anatomical joint models capable of predicting cartilage contact mechanics would provide a valuable tool for studying the relationships between muscle force and cartilage loading. As a step towards producing multibody musculoskeletal models that include representation of cartilage tissue mechanics, this research developed a subject-specific multibody knee model that represented the tibia plateau cartilage as discrete rigid bodies that interacted with the femur through deformable contacts. Parameters for the compliant contact law were derived using three methods: (1) simplified Hertzian contact theory, (2) simplified elastic foundation contact theory and (3) parameter optimisation from a finite element (FE) solution. The contact parameters and contact friction were evaluated during a simulated walk in a virtual dynamic knee simulator, and the resulting kinematics were compared with measured in vitro kinematics. The effects on predicted contact pressures and cartilage-bone interface shear forces during the simulated walk were also evaluated. The compliant contact stiffness parameters had a statistically significant effect on predicted contact pressures as well as all tibio-femoral motions except flexion-extension. The contact friction was not statistically significant to contact pressures, but was statistically significant to medial-lateral translation and all rotations except flexion-extension. The magnitude of kinematic differences between model formulations was relatively small, but contact pressure predictions were sensitive to model formulation. The developed multibody knee model was computationally efficient and had a computation time 283 times faster than a FE simulation using the same geometries and boundary conditions.

A data-driven surrogate model to connect scales between multi-domain biomechanics simulations.

A data driven surrogate was developed to bridge the gap between finite element and multibody modeling and to expand the information available from a rigid multibody cartilage simulation. An indentation experiment performed on canine stifle cartilage was modeled in both paradigms with acceptable accuracy and the data were used to create the surrogate. Neural networks were found to adequately approximate the von Mises stress calculated by the finite element model based on force values provided from the multibody model with a correlation coefficient over 0.96.

Load/strain distribution between ulna and radius in the mouse forearm compression loading model.

Finite element analysis (FEA) of the mouse forearm compression loading model is used to relate strain distributions with downstream changes in bone formation and responses of bone cells. The objective of this study was to develop two FEA models - the first one with the traditional ulna only and the second one in which both the ulna and radius are included, in order to examine the effect of the inclusion of the radius on the strain distributions in the ulna. The entire mouse forearm was scanned using microCT and images were converted into FEA tetrahedral meshes using a suite of software programs. The performance of both linear and quadratic tetrahedral elements and coarse and fine meshes were studied. A load of 2N was applied to the ulna/radius model and a 1.3N load (based on previous investigations of load sharing between the ulna and radius in rats) was applied to the ulna only model for subsequent simulations. The results showed differences in the cross sectional strain distributions and magnitude within the ulna for the combined ulna/radius model versus the ulna only model. The maximal strain in the combined model occurred about 4mm toward the distal end from the ulna mid-shaft in both models. Results from the FEA model simulations were also compared to experimentally determined strain values. We conclude that inclusion of the radius in FE models to predict strains during in vivo forearm loading increases the magnitude of the estimated ulna strains compared to those predicted from a model of the ulna alone but the distribution was similar. This has important ramifications for future studies to understand strain thresholds needed to activate bone cell responses to mechanical loading.

A subject specific multibody model of the knee with menisci.

The menisci of the knee play an important role in joint function and our understanding of knee mechanics and tissue interactions can be enhanced through computational models of the tibio-menisco-femoral structure. Several finite element models of the knee that include meniscus-cartilage contact exist, but these models are typically limited to simplified boundary conditions. Movement simulation and musculoskeletal modeling can predict muscle forces, but are typically performed using the multibody method with simplified representation of joint structures. This study develops a subject specific computational model of the knee with menisci that can be incorporated into neuromusculoskeletal models within a multibody framework. Meniscus geometries from a 78-year-old female right cadaver knee were divided into 61 discrete elements (29 medial and 32 lateral) that were connected through 6x6 stiffness matrices. An optimization and design of experiments approach was used to determine parameters for the 6x6 stiffness matrices such that the force-displacement relationship of the meniscus matched that of a linearly elastic transversely isotropic finite element model for the same cadaver knee. Similarly, parameters for compliant contact models of tibio-menisco-femoral articulations were derived from finite element solutions. As a final step, a multibody knee model was developed and placed within a dynamic knee simulator model and the tibio-femoral and patello-femoral kinematics compared to an identically loaded cadaver knee. RMS errors between finite element displacement and multibody displacement after parameter optimization were 0.017 mm for the lateral meniscus and 0.051 mm for the medial meniscus. RMS errors between model predicted and experimental cadaver kinematics during a walk cycle were less than 11 mm translation and less than 7 degrees orientation. A small improvement in kinematics, compared to experimental measurements, was seen when the menisci were included versus a model without the menisci. With the menisci the predicted tibio-femoral contact force was significantly reduced on the lateral side (937 N peak force versus 633 N peak force), but no significant reduction was seen on the medial side.