A Finite Element Approach for Skeletal Muscle using a Distributed Moment Model of Contraction

Abstract

The present paper describes a geometrically and physically nonlinear continuum model to study the mechanical behaviour of passive and active skeletal muscle. The contraction is described with a Huxley type model. A Distributed Moments approach is used to convert the Huxley partial differential equation in a set of ordinary differential equations. An isoparametric brick element is developed to solve the field equations numerically. Special arrangements are made to deal with the combination of highly nonlinear effects and the nearly incompressible behaviour of the muscle. For this a Natural Penalty Method (NPM) and an Enhanced Stiffness Method (ESM) are tested. Finally an example of an analysis of a contracting tibialis anterior muscle of a rat is given. The DM-method proved to be an efficient tool in the numerical solution process. The ESM showed the best performance in describing the incompressible behaviour.     

Development of antigenic heterogeneity in the splenic meshwork of severe combined immunodeficient (SCID) mice after reconstitution with T and B lymphocytes

Recently, we produced monoclonal antibodies reacting specifically with the reticular meshwork (RM) of lymphoid tissues, and demonstrated that, in the splenic white pulp of normal mouse, the antigenic heterogeneity of RM was associated with the segregation of the T and B lymphocytes. In the present study, we attempted to visualize further the interaction between splenic RM and T and B lymphocytes transferred into severe combined immunodeficient (SCID) mice. The splenic white pulp of naive SCID mice, containing a few T and B cells, showed little tendency for T-B segregation and antigenic diversity of RM. Transfer of spleen or bone marrow cells from normal mice resulted in complete recovery of lymphocyte populations, showing not only a clear segregation of T and B lymphocytes but also a remarkable antigenic diversity of RM. The same results were obtained following the transfer of spleen or bone marrow cells from the nude mouse. Next, we transferred purified T lymphocytes to one group of SCID mice and B cells to another. In mice given T cells, a few B cells were observed in the white puop; T lymphocytes lodged not only in the inner periarterial lymphatic sheath (PALS) but also in the outer PALS and follicles. In the animals to which B cells were transferred, T cells were few and the homing of B cells occurred only into their proper compartments, such as the outer PALS, follicles and marginal zone, but not in the inner PALS. Thus, B cells can home into their proper compartments of the splenic white pulp independently of T lymphocytes.     

降钙素对骨质疏松大鼠骨密度形态计量学与骨代谢的影响

目的探讨降钙素(密盖息)对骨质疏松大鼠骨密度、骨形态计量学影响以及与血钙、磷、维生素D代谢和生长因子的关系。方法用摘除大鼠双侧卵巢的方式制备骨质疏松模型(OVX),实验动物分为4个组:模型对照组、密盖息治疗组,盐酸雷洛昔芬治疗组,假手术组。应用HOLOGIC第4代双能X线4500W骨密度仪测定大鼠腰椎、股骨上段骨密度值(BMD);以骨形态计量学测股骨骨小梁面积、矿化沉积率;用ELISA法测定血清IGF-1水平和血清25OHVitD浓度以及血淋巴细胞维生素D受体(VDR)含量。结果密盖息治疗组、盐酸雷洛昔芬治疗组均较OVX组腰椎、股骨上段骨密度增高,组间比较差异有显著性(P<0.01)。密盖息治疗组较盐酸雷洛昔芬治疗组股骨上段骨密度增高,两组之间差异有显著性(P<0.01)。密盖息治疗组骨小梁面积明显增加、矿化沉积率增高。密盖息治疗组、盐酸雷洛昔芬治疗组血清IGF-1浓度值、血清25-OHVitD浓度值升高,与OVX组比较差异有显著性(P<0.01)。各组血淋巴细胞VDR含量无明显变化,与OVX组比较差异无显著性(P>0.05)。结论密盖息能够预防腰椎、股骨上段骨密度丢失,使骨小梁面积明显增加、矿化沉积率增高并且血清IGF-1及血清25-OHVitD浓度值升高,但对VDR含量无明显作用。     

Selective Runx2-II deficiency leads to low-turnover osteopenia in adult mice

Runx2 transcribes Runx2-II and Runx2-I isoforms with distinct N-termini. Deletion of both isoforms results in complete arrest of bone development, whereas selective loss of Runx2-II is sufficient to form a grossly intact skeleton with impaired endochondral bone development. To elucidate the role of Runx2-II in osteoblast function in adult mice, we examined heterozygous Runx2-II (Runx2-II(+/-)) and homozygous Runx2-II (Runx2-II(-/-))-deficient mice, which, respectively, lack one or both copies of Runx2-II but intact Runx2-I expression. Compared to wild-type mice, 6-week-old Runx2-II(+/-) had reduced trabecular bone volume (BV/TV%), cortical thickness (Ct.Th), and bone mineral density (BMD), decreased osteoblastic and osteoclastic markers, lower bone formation rates, impaired osteoblast maturation of BMSCs in vitro, and significant reductions in mechanical properties. Homozygous Runx2-II(-/-) mice had a more severe reduction in BMD, BV/TV%, and Ct.Th, and greater suppression of osteoblastic and osteoclastic markers than Runx2-II(+/-) mice. Non-selective Runx2(+/-) mice, which have an equivalent reduction in Runx2 expression due to the lack one copy of Runx2-I and II, however, had an intermediate reduction in BMD. Thus, selective Runx2-II mutation causes diminished osteoblastic function in an adult mouse leading to low-turnover osteopenia and suggest that Runx2-I and II have distinct functions imparted by their different N-termini.     

Trabecular bone fracture healing simulation with finite element analysis and fuzzy logic

Trabecular bone fractures heal through intramembraneous ossification. This process differs from diaphyseal fracture healing in that the trabecular marrow provides a rich vascular supply to the healing bone, there is very little callus formation, woven bone forms directly without a cartilage intermediary, and the woven bone is remodelled to form trabecular bone. Previous studies have used numerical methods to simulate diaphyseal fracture healing or bone remodelling, however not trabecular fracture healing, which involves both tissue differentiation and trabecular formation. The objective of this study was to determine if intramembraneous bone formation and remodelling during trabecular bone fracture healing could be simulated using the same mechanobiological principles as those proposed for diaphyseal fracture healing. Using finite element analysis and the fuzzy logic for diaphyseal healing, the model simulated formation of woven bone in the fracture gap and subsequent remodelling of the bone to form trabecular bone. We also demonstrated that the trabecular structure is dependent on the applied loading conditions. A single model that can simulate bone healing and remodelling may prove to be a useful tool in predicting musculoskeletal tissue differentiation in different vascular and mechanical environments.     

A syndecan-4 binding peptide derived from laminin 5 uses a novel PKCε pathway to induce cross-linked actin network (CLAN) formation in human trabecular meshwork (HTM) cells

In this study, we examined the role(s) of syndecan-4 in regulating the formation of an actin geodesic dome structure called a cross-linked actin network (CLAN) in which syndecan-4 has previously been localized. CLANs have been described in several different cell types, but they have been most widely studied in human trabecular meshwork (HTM) cells where they may play a key role in controlling intraocular pressure by regulating aqueous humor outflow from the eye. In this study we show that a loss of cell surface synedcan-4 significantly reduces CLAN formation in HTM cells. Analysis of HTM cultures treated with or without dexamethasone shows that laminin 5 deposition within the extracellular matrix is increased by glucocorticoid treatment and that a laminin 5-derived, syndecan-4-binding peptide (PEP75), induces CLAN formation in TM cells. This PEP75-induced CLAN formation was inhibited by heparin and the broad spectrum PKC inhibitor Ro-31–7549. In contrast, the more specific PKCα inhibitor Gö 6976 had no effect, thus excluding PKCα as a downstream effector of syndecan-4 signaling. Analysis of PKC isozyme expression showed that HTM cells also expressed both PKCγ and PKCε. Cells treated with a PKCε agonist formed CLANs while a PKCα?γ agonist had no effect. These data suggest that syndecan-4 is essential for CLAN formation in HTM cells and that a novel PKCε-mediated signaling pathway can regulate formation of this unique actin structure.     

MTOR-independent induction of autophagy in trabecular meshwork cells subjected to biaxial stretch

The trabecular meshwork (TM) is part of a complex tissue that controls the exit of aqueous humor from the anterior chamber of the eye, and therefore helps maintaining intraocular pressure (IOP). Because of variations in IOP with changing pressure gradients and fluid movement, the TM and its contained cells undergo morphological deformations, resulting in distention and stretching. It is therefore essential for TM cells to continuously detect and respond to these mechanical forces and adapt their physiology to maintain proper cellular function and protect against mechanical injury. Here we demonstrate the activation of autophagy, a pro-survival pathway responsible for the degradation of long-lived proteins and organelles, in TM cells when subjected to biaxial static stretch (20% elongation), as well as in high-pressure perfused eyes (30 mm Hg). Morphological and biochemical markers for autophagy found in the stretched cells include elevated LC3-II levels, increased autophagic flux, and the presence of autophagic figures in electron micrographs. Furthermore, our results indicate that the stretch-induced autophagy in TM cells occurs in an MTOR- and BAG3-independent manner. We hypothesize that activation of autophagy is part of the physiological response that allows TM cells to cope and adapt to mechanical forces.     

Proteasome inhibition by chronic oxidative stress in human trabecular meshwork cells

The pathophysiologic mechanisms leading to the malfunction of the trabecular meshwork (TM)-Schlemm's canal (SC) outflow pathway in glaucoma are still unclear. We hypothesize that chronic oxidative stress may contribute to the malfunction of the outflow pathway by impairing the intracellular proteasome system of the cells, decreasing the ability of the tissue to modulate outflow resistance. To study the effects of chronic oxidative stress on proteasome function, primary cultures of human TM cells were incubated under 40% oxygen and proteasome activity was analyzed by measuring the accumulation of enhanced green fluorescent protein fused to a PEST motif. Changes in proteasome content, cellular senescence, and cell viability were also monitored. After 10 days of exposure to chronic oxidative stress, TM cells showed a marked decline in proteasome activity that was associated with premature senescence and decreased cell viability. These results suggest that proteasome failure may be involved in glaucoma pathophysiology.     

Dependence of mechanical properties of trabecular bone on plate–rod microstructure determined by individual trabecula segmentation (ITS)

Individual trabecula segmentation (ITS) technique can decompose the trabecular bone network into individual trabecular plates and rods and is capable of quantifying the plate/rod-related microstructural characteristics of trabecular bone. This novel technique has been shown to be able to provide in-depth insights into micromechanics and failure mechanisms of human trabecular bone, as well as to distinguish the fracture status independent of area bone mineral density in clinical applications. However, the plate/rod microstructural parameters from ITS have never been correlated to experimentally determined mechanical properties of human trabecular bone. In this study, on-axis cylindrical trabecular bone samples from human proximal tibia (n=22), vertebral body (n=10), and proximal femur (n=21) were harvested, prepared, scanned using micro computed-tomography (µCT), analyzed with ITS and mechanically tested. Regression analyses showed that the plate bone volume fraction (pBV/TV) and axial bone volume fraction (aBV/TV) calculated by ITS analysis correlated the best with elastic modulus (R²=0.96–0.97) and yield strength (R²=0.95–0.96). Trabecular plate-related microstructural parameters correlated highly with elastic modulus and yield strength, while most rod-related parameters were found inversely and only moderately correlated with the mechanical properties. In addition, ITS analysis also identified that trabecular bone at human femoral neck had the highest trabecular plate-related parameters while the other sites were similar with each other in terms of plate–rod microstructure.     

The role of fabric in the quasi-static compressive mechanical properties of human trabecular bone from various anatomical locations

Osteoporosis leads to an increased risk of bone fracture. While bone density and architecture can be assessed in vivo with increasing accuracy using CT and MRI, their relationship with the critical mechanical properties at various anatomical sites remain unclear. The objective of this study was to quantify the quasi-static compressive mechanical properties of human trabecular bone among different skeletal sites and compare their relationships with bone volume fraction and a measure of microstructural anisotropy called fabric. Over 600 trabecular bone samples from six skeletal sites were assessed by and tested in uniaxial compression. Bone volume fraction correlated positively with elastic modulus, yield stress, ultimate stress, and the relationships depended strongly on skeletal site. The account of fabric improved these correlations substantially, especially when the data of all sites were pooled together, but the fabric–mechanical property relationships remained somewhat distinct among the anatomical sites. The study confirms that, beyond volume fraction, fabric plays an important role in determining the mechanical properties of trabecular bone and should be exploited in mechanical analysis of clinically relevant sites of the human skeleton.