Strain Energy Density Changes Research Articles

Insight to motor clutch model for sensing of ECM residual strain

The mechanical microenvironment strongly affects cell state and decisions. Cell mechanosensing has been described by a molecular clutch which gets progressively engaged depending upon the stiffness of the extracellular material. Through the actuation of pulling forces exerted by actin fibres on the mechanosensitive talin-integrin molecular complex, cells sense and react to the stiffness of their surroundings. However, whether the truly cell mechanosensing is regulated by the pure elastic stiffness or by the strain energy density of the ECM is still debated. Here we report that the cell response to change of strain energy density out of loading induced deformation (purely elastic) can be accounted for by including, within the same frame of the molecular clutch model, the residual strain/stress to which the ECM could be subjected before establishing any interaction with the molecular clutches. To include the contribution of residual stresses, an additional spring orthogonal to the ones already present in the original clutch model has been introduced; this spring takes memory of the ECM strain energy when axially deformed before any interaction with cell molecular clutches can occur. To evaluate the influence of strain on the optimum number of clutches, the model has been implemented with different levels of strain. Results suggest that cells undergo a reinforcement process, stiffening the cytoskeleton in response to the ECM stress/strain energy.

Changes in strain energy density in the temporomandibular joint disk after sagittal split ramus osteotomy using acomputed tomography-based finite element model.

We evaluated the changes in the strain energy density (SED) in the temporomandibular joint (TMJ) disk after sagittal split ramus osteotomy (SSRO) at three time points. Afinite element model (FEM) based on real patient-based computed tomography (CT) data was used to examine the effect of SSRO on the TMJ. Measurements of the condylar position and angulation in CT images and FEM analyses were performed for 17patients scheduled to undergo SSROs at the following time points: before surgery, immediately after surgery, and 1year after surgery. SED on the entire disk was calculated at each of the three time points using FEM. Furthermore, the relationship between individual SED values and the corresponding condylar position was also evaluated. No significant change was observed in the condylar position at the three time points. The FEM analysis showed that SED was the highest and lowest immediately after and 1year after surgery, respectively. Apossible SED distribution imbalance between the left and right joints was improved 1year after SSRO. Concerning the effect of fossa morphometry and condylar position, wide and deep glenoid fossae and amore posterior condylar position tended to show lower SED. SED in the articular disk temporarily increased after surgery and significantly decreased 1year after surgery compared with that before surgery. SSRO generally improved the imbalance between the left and right joints. Thus, SSRO, which improves maxillofacial morphology, may also improve components of temporomandibular disorders.

Biomechanical Effects of Pedicle Screw Positioning on the Surgical Segment in Models After Oblique Lumbar Interbody Fusion: An in-silico Study

BackgroundBilateral pedicle screw (BPS) is the “gold standard” of fixation methods for patients with lumbar interbody fusion. Biomechanical deterioration initially triggers complications in the surgical segment. Studies proved that BPS positions and trajectory changes affect the local biomechanical environment. However, no study illustrates the biomechanical effect of insertional screw positions’ change on the surgical segment.MethodsOblique lumbar interbody fusion (OLIF) with different BPS insertional positions has been simulated in a well-validated lumbo-sacral model. Fixation stability and stress responses on the surgical segment were evaluated under identical loading conditions.ResultsThere is no clear variation tendency for the risk of BPS failure and the change of strain energy density of the grafted bone. However, shifting the insertional screw position close to the surgical segment will increase the range of motions (ROM) in the surgical segment and lead to stress concentration of bony structures, especially in the caudal side of the surgical segment.ConclusionAdjusting the insertional position of BPS close to the surgical segment in OLIF models will lead to stress concentration of bony structures and surgical segmental instability. Therefore, reducing BPS’s fixation length was not recommended, which may increase the risk of segmental instability, non-union, and cage subsidence.

Structural analysis of hollow versus solid-stemmed shoulder implants of proximal humeri with different bone qualities.

Stress shielding of the proximal humerus following total shoulder arthroplasty (TSA) can promote unfavorable bone remodeling, especially for osteoporotic patients. The objective of this finite element (FE) study was to determine if a hollow, rather than solid, titanium stem can mitigate this effect for healthy, osteopenic, and osteoporotic bone. Using a population-based model of the humerus, representative average healthy, osteopenic, and osteoporotic humerus FE models were created. For each model, changes in bone and implant stresses following TSA were evaluated for different loading scenarios and compared between solid versus hollow-stemmed implants. For cortical bone, using an implant decreased von Mises stress with respect to intact values up to 34.4%, with a more pronounced effect at more proximal slices. In the most proximal slice, based on changes in strain energy density, hollow-stemmed implants outperformed solid-stemmed ones through reducing cortical bone volume with resorption potential by 11.7% ± 2.1% (p = .01). For cortical bone in this slice, the percentage of bone with resorption potential for the osteoporotic bone was greater than the healthy bone by 8.0% ± 1.4% using the hollow-stemmed implant (p = .04). These results suggest a small improvement in bone-implant mechanics using hollow-stemmed humeral implants and indicate osteoporosis could exacerbate stress shielding to some extent. The hollow stems maintained adequate strength and using even thinner walls may further reduce stress shielding. After further developing these models, future studies could yield optimized implant designs tuned for varying bone qualities.

Impact of surgical alignment, tray material, PCL condition, and patient anatomy on tibial strains after TKA

Bone remodeling after total knee arthroplasty is regulated by the changes in strain energy density (SED), however, the critical parameters influencing post-operative SED distributions are not fully understood. This study aimed to investigate the impact of surgical alignment, tray material properties, posterior cruciate ligament (PCL) balance, tray posterior slope, and patient anatomy on SED distributions in the proximal tibia.Finite element models of two tibiae (different anatomy) with configurations of two implant materials, two surgical alignments, two posterior slopes, and two PCL conditions were developed. The models were tested under the peak loading conditions during gait, deep knee bending, and stair descent. For each configuration, the contact forces and locations and soft-tissue loads of interest were taken into consideration. SED in the proximal tibia was predicted and the changes in strain distributions were compared for each of the factors studied.Tibial anatomy had the most impact on the proximal bone SED distributions, followed by PCL balancing, surgical alignment, and posterior slope. In addition, the thickness of the remaining cortical wall after implantation was also a significant consideration when evaluating tibial anatomy. The resulting SED changes for alignment, posterior slope, and PCL factors were mainly due to the differences in joint and soft-tissue loading conditions. A lower modulus tray material did result in changes in the post-operative strain state, however, these were almost negligible compared to that seen for the other factors.

A mathematical biomechanical model for bone remodeling integrated with a radial point interpolating meshless method

Bone remodeling is a highly complex process, in which bone cells interact and regulate bone's apparent density as a response to several external and internal stimuli. In this work, this process is numerically described using a novel 2D biomechanical model. Some of the new features in this model are (i) the mathematical parameters used to determine bone's apparent density and cellular density; (ii) an automatic boundary recognition step to spatially control bone remodeling and (iii) an approach to mimic the mechanical transduction to osteoclasts and osteoblasts. Moreover, this model is combined with a meshless approach – the Radial Point Interpolation Method (RPIM). The use of RPIM is an asset for this application, especially in the construction of the boundary maps. This work studies bone's adaptation to a certain loading regime through bone resorption. The signaling pathways of bone cells are dependent on the level of strain energy density (SED) in bone. So, when SED changes, bone cells' functioning is affected, causing also changes on bone's apparent density. With this model, bone is able to achieve an equilibrium state, optimizing its structure to withstand the applied loads. Results suggest that this model has the potential to provide high quality solutions while being a simpler alternative to more complex bone remodeling models in the literature.

Finite element model of load adaptive remodelling induced by orthodontic forces

Many hypotheses have been formulated to explain orthodontic tooth movement. However, none of them can satisfactorily explain how small static orthodontic forces can induce bone remodelling. Our hypothesis assumes that small orthodontic forces do not lead to bone remodelling response directly, but rather indirectly by offsetting the tooth, leading to changes in bone loading during chewing that far exceed the changes caused by the orthodontic force alone. We developed a finite element model of a tooth with the periodontal ligament and the surrounding bone, and calculated the changes in strain energy density caused by the chewing force alone, the orthodontic force alone, and the combined action of the chewing and orthodontic forces. The results (average strain energy density 0.0005–0.01 kPa) demonstrate that the orthodontic loading alone does not produce strain energy density values in a range that is expected to induce remodelling (0.016–1.6 kPa). However, when the chewing and orthodontic forces are applied together, the highest values for the average strain energy density (0.02–0.99 kPa) as well as large changes in the bone tissue strain energy density (31.19–166.65%) are obtained. We conclude that the proposed hypothesis can indeed explain the observed bone remodelling that agrees with Wolff's law.

Influence of collars on the primary stability of cementless femoral stems: A finite element study using a diverse patient cohort

For cementless femoral stems, there is debate as to whether a collar enhances primary stability and load transfer compared to collarless designs. Finite Element (FE) analysis has the potential to compare stem designs within the same cohort, allowing for subtle performance differences to be identified, if present. Subject-specific FE models of intact and implanted femora were run for a diverse cohort (21 males, 20 females; BMI 16.4-41.2 kg/m2 , age 50-80 yrs). Collared and collarless versions of Corail® (DePuy Synthes, Warsaw, IN) were sized and positioned using an automated algorithm that aligns the femoral/stem axes, preserves the head-center location, and maximizes metaphyseal fit. Joint contact and muscle forces simulating peak forces in level gait and stair climbing and were scaled to the body mass and applied to each subject. Three failure scenarios were assessed: Potential for peri-prosthetic fibrous tissue formation (stem micromotion), potential for peri-prosthetic bone damage (equivalent strains), and calcar bone remodeling (changes in strain-energy density). Comparisons were performed using paired t-tests. Only subtle differences were found (mean 90th percentile micromotion: Collared = 86 µm, collarless = 92.5 µm, mean 90th percentile interface strains: Collared = 733 µϵ, collarless = 767 µϵ, and similar remodeling stimuli were predicted). The slight differences observed were small in comparison with the inter-patient variability. Statement of clinical significance: Our results suggest that the presence/absence of a collar is unlikely to substantially alter the bone-implant biomechanics nor the initial mechanical environment. Hence, a collar is likely to have minimal clinical impact. Analysis using different femoral stem designs is recommended before generalising these findings. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:1185-1195, 2018.

歪みエネルギー密度を用いた海溝型地震の長期予測——千島海溝及び日本海溝を例に——

The long-term forecasts of interplate earthquakes are usually given using their average occurrence intervals. In this paper, I propose a new simple forecast method; first, the accumulation rate of strain energy density is estimated on the assumption that the accumulated and released strain energies balance in a large area for a long period; second, the secular change of strain energy density is calculated in each place; finally, the earthquake occurrence probabilities within 10, 30, and 50 years are calculated using a simple relation between the earthquake occurrence rate and strain energy density. The proposed method was applied to the Kuril Trench and the Japan Trench with the earthquake data of Utsu catalogue and the database of the Japan Meteorological Agency from 1885 to 2010. The forecasts obtained are similar to those given by the Headquarters for Earthquake Research Promotion for all the regions except the region off Shikotan Island.

Predicting bone remodeling around tissue- and bone-level dental implants used in reduced bone width

The objective of this study was to predict time-dependent bone remodeling around tissue- and bone-level dental implants used in patients with reduced bone width. The remodeling of bone around titanium tissue-level, and titanium and titanium–zirconium alloy bone-level implants was studied under 100N oblique load for one month by implementing the Stanford theory into three-dimensional finite element models. Maximum principal stress, minimum principal stress, and strain energy density in peri-implant bone and displacement in x- and y- axes of the implant were evaluated. Maximum and minimum principal stresses around tissue-level implant were higher than bone-level implants and both bone-level implants experienced comparable stresses. Total strain energy density in bone around titanium implants slightly decreased during the first two weeks of loading followed by a recovery, and the titanium–zirconium implant showed minor changes in the axial plane. Total strain energy density changes in the loading and contralateral sides were higher in tissue-level implant than other implants in the cortical bone at the horizontal plane. The displacement values of the implants were almost constant over time. Tissue-level implants were associated with higher stresses than bone-level implants. The time-dependent biomechanical outcome of titanium–zirconium alloy bone-level implant was comparable to the titanium implant.

Biomechanical Comparison of 2 Proximally Coated Femoral Stems: Effects of Stem Length and Surface Finish

Proximally hydroxyapatite-coated stems have performed well clinically but produced moderate proximal stress shielding and midstem cancellous condensation. Stem modification (stem shortening and distal tip polishing) has resulted in greater incidence of thigh pain. We performed a retrospective finite element analysis of the effects of stem length and surface finish to determine if midstem fixation could be avoided and the results could relate to the clinical outcomes. The modified short stem not only produced moderately less proximal bone resorption but also exhibited greater instability with 40% to 94% greater bone-implant relative motion at the stem tip. Bone formation potential at the transition between the coated and uncoated regions of both stems was observed based on changes in strain energy density. These findings are consistent with previous radiographic and clinical comparisons of short- and long-stem designs. Increased pain incidence for short-stem patients may be related to decreased implant instability and increased interface relative motion.

Elastomers - An Engineering Material

Abstract Elastomers are engineering materials. Defined as nonlinear viscoelastic solids; applications are normally deformations under twenty five (25) percent. Conventional engineering values of shear modulus G and Young's modulus E can be determined in this relatively linear section of the stress-strain relationships. The viscoelastic description indicates a time/temperature relation response. Treloar notes that G is both the shear modulus value and the elastic constant. The high bulk modulus allows us to assume E=3G thus we have several approaches to develop G and utilize the equation G=NκT=ρRT/Mc, (hereby ρ is density, R gas constant, Mc average chain molecular weight, T temperature Kelvin). This allows us to monitor aging by changes in Mc that occur due to network aging. The aging process will be monitored by strain energy density changes, compressive stress-relaxation (CSR) and dynamic mechanical rheologic testing (DMRT)

Crack Length Estimation for Large Deformable Non-Linear Elastic Materials

A method to measure the crack length in rubbery materials is described. Through dimensional analysis and experiments, an equation is derived to give the crack length as a function of the change of strain energy density in a region remote from the crack. The function is provided in a form of separated terms of loading and material, the validity of which is experimentally proved using separation parameters.

Deformation and thermodynamic response for a crack dislocation model of brittle fracture

Concepts from dislocation and microcrack models are used to define idealized attributes describing the tip region of a crack. The attributes characterize both geometry and deformation; and this identifies a material defect species called a crack dislocation. With the attributes as variables, a scalar density function for each crack dislocation species can be defined. The crack dislocation is different from the common edge or screw species because it creates a new surface area as well as a displacement discontinuity as it propagates through a crystalline lattice. To model the discontinuities, a relative deformation functional is developed which depends on the crack dislocation density function. Since the crack dislocations are the only material defects assumed to contribute deformation discontinuities, the model is for brittle fracture only. The thermodynamic response uses primarily the methodology established by Gibbs. The existence of an internal energy functional is assumed. The methodology results in a definition for a thermodynamic potential for crack dislocation kinetics, a generalization of the Griffith crack propagation concept, and a local measure for the surface strain energy density changes on the crack dislocation line. The equilibrium thermodynamic potential for crack dislocation kinetics introduces a thermodynamic concept to demarcate crack dislocation density transitions from stationary to non-stationary; hence, it provides an incipient fracture criterion that has a thermodynamic basis. For nonequilibrium thermodynamics, the Onsager formalism is used to model the rates and fluxes of the thermodynamic functions.