Sarcomere length organization as a design for cooperative function amongst all lumbar spine muscles

The functional design of spine muscles in part dictates their role in moving, loading, and stabilizing the lumbar spine. There have been numerous studies that have examined the isolated properties of these individual muscles. Understanding how these muscles interact and work together, necessary for the prediction of muscle function, spine loading, and stability, is lacking. The objective of this study was to measure sarcomere lengths of lumbar muscles in a neutral cadaveric position and predict the sarcomere operating ranges of these muscles throughout full ranges of spine movements. Sarcomere lengths of seven lumbar muscles in each of seven cadaveric donors were measured using laser diffraction. Using published anatomical coordinate data, superior muscle attachment sites were rotated about each intervertebral joint and the total change in muscle length was used to predict sarcomere length operating ranges. The extensor muscles had short sarcomere lengths in a neutral spine posture and there were no statistically significant differences between extensor muscles. The quadratus lumborum was the only muscle with sarcomere lengths that were optimal for force production in a neutral spine position, and the psoas muscles had the longest lengths in this position. During modeled flexion the extensor, quadratus lumborum, and intertransversarii muscles lengthened so that all muscles operated in the approximate same location on the descending limb of the force-length relationship. The intrinsic properties of lumbar muscles are designed to complement each other. The extensor muscles are all designed to produce maximum force in a mid-flexed posture, and all muscles are designed to operate at similar locations of the force-length relationship at full spine flexion.     

A multisegmental cross-bridge kinetics model of the myofibril

Striated muscle is a mechanical system that develops force and generates power in serving vital activities in the body. Striated muscle is a complex biological system; a single mammalian muscle fibre contains up to hundred or even more myofibrils in parallel connected via an inter-myofibril filament network. In one single myofibril thousands of sarcomeres are lined up as a series of linear motors. We recently demonstrated that half-sarcomeres (hS) in a single myofibril operate non-uniformly. We outline a mathematical framework based on cross-bridge kinetics for the simulation of the force response and length change of individual hS in a myofibril. The model describes the muscle myofibril in contraction experiments under various conditions. The myofibril is modeled as a multisegmental mechanical system of hS models, which have active and viscoelastic properties. In the first approach, a two-state cross-bridge formalism relates the hS force to the chemical kinetics of ATP hydrolysis, as first described by Huxley [1957. Muscle structure and theories of contraction. Prog. Biophys. Mol. Biol. 7, 255-318]. Two possible types of biological variability are introduced and modeled. Numerical simulations of a myofibril composed of four to eight hS show a non-uniform hS length distribution and complex internal dynamics upon activation. We demonstrate that the steady-state approximation holds only in restricted time zones during activation. Simulations of myofibril contraction experiments that reproduce the classic steady-state force-length and force-velocity relationships, strictly constrained or “clamped” in either end-held isometric or isotonic contraction conditions, reveal a small but conspicuous effect of hS dynamics on force.     

Diastolic ventricular aspiration: a mechanism supporting the rapid filling phase of the human ventricles

During the rapid filling phase of the heart cycle, the internal volumes of the two ventricular cavities approximately double, while the intraventricular pressures rise typically only by an amount of less than 1 kPa. Such a small pressure increase cannot be the sole driving mechanism for the large inflow of blood associated with ventricular expansion during this period. Instead, the rapid filling phase is to be interpreted as being mediated primarily by the heart recoiling elastically from its contracted state, causing blood to be aspirated rapidly into the ventricles. In order to study the role of this mechanism, elastic finite element (FE) simulations of ventricular expansion were performed, taking into account the large deformations occurring during this period and the effective compressibility of the myocardium due to intramural fluid flow. Thereby, a realistic three-dimensional geometry derived from magnetic resonance imaging (MRI) measurements of both human ventricles was used. To validate our FE analyses, the results were compared with published measurements relating to the rapid filling phase of the human left ventricle. Our study shows that, under normal physiological conditions, ventricular aspiration plays a key role in the ventricular filling process.     

A finite element study relating to the rapid filling phase of the human ventricles

During the rapid diastolic filling phase at rest, the ventricles of the human heart double approximately in volume. In order to investigate whether the ventricular filling pressures measured under physiological conditions can give rise to such an extensive augmentation in ventricular volumes, a finite element model of the human right and left ventricles has been developed, taking into account the nonlinear mechanical behavior and effective compressibility of the myocardial tissue. The results were compared with the filling phase of the human left ventricle as extrapolated from measurements documented in the literature. We arrived at the conclusion that the ventricular pressures measured during the rapid filling phase cannot be the sole cause of the rise of the observed ventricular volumes. We rather advocate the assumption that further dilating mechanisms might be part of ventricular activity thus heralding a multiple function of the ventricular muscle body. A further result indicates that under normal conditions the influence of the viscoelasticity of the tissue should not be disregarded in ventricular mechanics.     

Influence of viscosity on myocardium mechanical activity: a mathematical model

We have previously proposed and validated a mathematical model of myocardium contraction-relaxation cycle based on current knowledge of regulatory role of Ca2+ and cross-bridge kinetics in cardiac cell. That model did not include viscous elements. Here we propose a modification of the model, in which two viscous elements are added, one in parallel to the contractile element, and one more in parallel to the series elastic element. The modified model allowed us to simulate and explain some subtle experimental data on relaxation velocity in isotonic twitches and on a mismatch between the time course of sarcomere shortening/lengthening and the time course of active force generation in isometric twitches. Model results were compared with experimental data obtained from 28 rat LV papillary muscles contracting and relaxing against various loads. Additional model analysis suggested contribution of viscosity to main inotropic and lusitropic characteristics of myocardium performance.     

A study of the viscoelastic effect in a bone remodeling model

The present paper addresses the following question can a simple regulatory bone remodeling model predict effects of viscosity on the trabecular morphology? For that, we propose an extension of a previous bone remodeling model by taking into account the viscosity properties of the tissue. Zener’s law is used to describe the mechanical behavior of the bone and a specific law of the apparent bone density rate is proposed. Based on stability analysis, numerical simulations are then performed to investigate the viscosity role on simulations of the bone remodeling process. We show that the viscous contribution affects the evolution of the apparent bone density, by slowing down the adaptation process, which seems to be confirmed by simulations with real data obtained from rat tibia.     

3D finite element model of the diabetic neuropathic foot: A gait analysis driven approach

Diabetic foot is an invalidating complication of diabetes that can lead to foot ulcers. Three-dimensional (3D) finite element analysis (FEA) allows characterizing the loads developed in the different anatomical structures of the foot in dynamic conditions. The aim of this study was to develop a subject specific 3D foot FE model (FEM) of a diabetic neuropathic (DNS) and a healthy (HS) subject, whose subject specificity can be found in term of foot geometry and boundary conditions. Kinematics, kinetics and plantar pressure (PP) data were extracted from the gait analysis trials of the two subjects with this purpose. The FEM were developed segmenting bones, cartilage and skin from MRI and drawing a horizontal plate as ground support. Materials properties were adopted from previous literature. FE simulations were run with the kinematics and kinetics data of four different phases of the stance phase of gait (heel strike, loading response, midstance and push off). FEMs were then driven by group gait data of 10 neuropathic and 10 healthy subjects. Model validation focused on agreement between FEM-simulated and experimental PP.     

Strains at the myotendinous junction predicted by a micromechanical model

The goal of this work was to create a finite element micromechanical model of the myotendinous junction (MTJ) to examine how the structure and mechanics of the MTJ affect the local micro-scale strains experienced by muscle fibers. We validated the model through comparisons with histological longitudinal sections of muscles fixed in slack and stretched positions. The model predicted deformations of the A-bands within the fiber near the MTJ that were similar to those measured from the histological sections. We then used the model to predict the dependence of local fiber strains on activation and the mechanical properties of the endomysium. The model predicted that peak micro-scale strains increase with activation and as the compliance of the endomysium decreases. Analysis of the models revealed that, in passive stretch, local fiber strains are governed by the difference of the mechanical properties between the fibers and the endomysium. In active stretch, strain distributions are governed by the difference in cross-sectional area along the length of the tapered region of the fiber near the MTJ. The endomysium provides passive resistance that balances the active forces and prevents the tapered region of the fiber from undergoing excessive strain. These model predictions lead to the following hypotheses: (i) the increased likelihood of injury during active lengthening of muscle fibers may be due to the increase in peak strain with activation and (ii) endomysium may play a role in protecting fibers from injury by reducing the strains within the fiber at the MTJ.     

3D non-linear analysis of the acetabular construct following impaction grafting

The study investigates the short-term behaviour of the acetabular construct following revision hip arthroplasty, carried out using the Slooff–Ling impaction grafting technique; using 3D finite element analyses. An elasto-plastic material model is used to describe the constitutive behaviour of morsellised cortico-cancellous bone (MCB) graft, since it has been shown that MCB undergoes significant plastic deformation under normal physiological loads. Based on previous experimental studies carried out by the authors and others, MCB is modelled using non-linear elasticity and Drucker Prager Cap (DPC) plasticity. Loading associated with walking, sitting down, and standing up is applied to the acetabular cup through a femoral head using smooth sliding surfaces. The analyses yield distinctive patterns of migration and rotation due to different activities. These are found to be similar to those observed in the clinical setting.     

Sensitivity of stress and strain calculations to passive material parameters in cardiac mechanical models using unloaded geometries

Cardiac stress (load) and strain (stretch) are widely studied indicators of cardiac function and outcome, but are difficult or impossible to directly measure in relation to the cardiac microstructure. An alternative approach is to estimate these states using computer methods and image-based measurements, but this still requires knowledge of the tissue material properties and the unloaded state, both of which are difficult to determine. In this work, we tested the sensitivity of these two interdependent unknowns (reference geometry and material parameters) on stress and strain calculations in cardiac tissue. Our study used a finite element model of the human ventricle, with a hyperelastic passive material model, and was driven by a cell model mediated active contraction. We evaluated 21 different published parameter sets for the five parameters of the passive material model, and for each set we optimised the corresponding unloaded geometry and contractility parameter to model a single pressure-volume loop. The resulting mechanics were compared, and calculated systolic stresses were largely insensitive to the chosen parameter set when an unloading algorithm was used. Meanwhile, material strain calculations varied substantially depending on the choice of material parameters. These results indicate that determining the correct material and unloaded configuration may be highly important to understand strain driven processes, but less so for calculating stress estimates.     

The ultrastructure of pinealocytes in the pig

Summary Pinealocytes of female pigs were studied electron-microscopically and compared with those of other mammals. A prominent Golgi apparatus forming dense-cored vesicles was widely dispersed in the cytoplasm of the cell body. A very characteristic feature of the pig pinealocytes was the presence of membrane-bounded bodies showing wide variations in internal structure. Possible roles of the dense-cored vesicles and membrane-bounded bodies in secretory processes of pinealocytes are discussed.     

A novel methodology for generating 3D finite element models of the hip from 2D radiographs

Finite element (FE) modelling has been proposed as a tool for estimating fracture risk and patient-specific FE models are commonly based on computed tomography (CT). Here, we present a novel method to automatically create personalised 3D models from standard 2D hip radiographs. A set of geometrical parameters of the femur were determined from seven a–p hip radiographs and compared to the 3D femoral shape obtained from CT as training material; the error in reconstructing the 3D model from the 2D radiographs was assessed. Using the geometry parameters as the input, the 3D shape of another 21 femora was built and meshed, separating a cortical and trabecular compartment. The material properties were derived from the homogeneity index assessed by texture analysis of the radiographs, with focus on the principal tensile and compressive trabecular systems. The ability of these FE models to predict failure load as determined by experimental biomechanical testing was evaluated and compared to the predictive ability of DXA. The average reconstruction error of the 3D models was 1.77 mm (±1.17 mm), with the error being smallest in the femoral head and neck, and greatest in the trochanter. The correlation of the FE predicted failure load with the experimental failure load was r²=64% for the reconstruction FE model, which was significantly better (p<0.05) than that for DXA (r²=24%). This novel method for automatically constructing a patient-specific 3D finite element model from standard 2D radiographs shows encouraging results in estimating patient-specific failure loads.     

Mechanical performance of endodontic restorations with prefabricated posts: sensitivity analysis of parameters with a 3D finite element model

Many studies have investigated the effect of different parameters of the endodontically restored tooth on its final strength, using in vitro tests and model simulations. However, the differences in the experimental set-up or modelling conditions and the limited number of parameters studied in each case prevent us from obtaining clear conclusions about the relative importance of each parameter. In this study, a validated 3D biomechanical model of the restored tooth was used for an exhaustive sensitivity analysis. The individual influence of 20 different parameters on the mechanical performance of an endodontic restoration with prefabricated posts was studied. The results bring up the remarkable importance of the loading angle on the final restoration strength. Flexural loads are more critical than compressive or tensile loads. Young's modulus of the post and its length and diameter are the most influential parameters for strength, whereas other parameters such as ferrule geometry or core and crown characteristics are less significant.     

Using 3D finite element models verified the importance of callus material and microstructure in biomechanics restoration during bone defect repair

Background: There is lack of further observations on the microstructure and material property of callus during bone defect healing and the relationships between callus properties and the mechanical strength. Methods: Femur bone defect model was created in rabbits and harvested CT data to reconstruct finite element models at 1 and 2 months. Three types of assumed finite element models were compared to study the callus properties, which assumed the material elastic property as heterogeneous (R-model), homogenous (H-model) or did not change from 1 to 2 months (U-model). Results: The apparent elastic moduli increased at 2 months (from 355.58 ± 132.67 to 1139.30 ± 967.43 MPa) in R-models. But there was no significant difference in apparent elastic moduli between R-models (355.58 ± 132.67 and 1139.30 ± 967.43 MPa) and H-models (344.79 ± 138.73 and 1001.52 ± 692.12 MPa) in 1 and 2 months. A significant difference of apparent elastic moduli was found between the R-model (1139.30 ± 967.43 MPa) and U-model group (207.15 ± 64.60 MPa) in 2 months. Conclusions: This study showed that the callus structure stability remodeled overtime to achieve a more effective structure, while the material quality of callus tissue is a very important factor for callus strength. At the meantime, this study showed an evidence that the material heterogeneity maybe not as important as it is in bone fracture model.     

Prenatal appearance of a short nucleosomal DNA repeat length in neurons of the guinea pig cerebral cortex

The organization of chromatin in neurons of the cerebral cortex of the guinea pig brain was analyzed by digesting isolated nuclei with micrococcal nuclease. During development, cortical neurons were observed to undergo an alteration in chromatin structure which results in an atypically short nucleosomal DNA repeat length of 164 bp. This change in chromatin organization occurs postnatally in certain mammals but in the guinea pig it takes place prior to birth between days 32 and 44 of fetal development. This suggests that the appearance of the short nucleosomal DNA repeat length in cortical neurons correlates to a particular stage of differentiation of cortical neurons rather than to the event of birth.     

Purification of reconstitutively active α-oxoglutarate carrier from pig heart mitochondria

The α-oxoglutarate carrier from pig heart mitochondria has been solubilized with Triton X-114 and purified by chromatography on hydroxyapatite and celite in the presence of cardiolipin. When applied to SDS gel electrophoresis, the purified protein consists of only a single protein band with an apparent M_r of 31.5 kDa. It corresponds to band 4 of the five protein bands previously identified in the hydroxyapatite pass-through of Triton X-114 solubilized heart mitochondria (Bisaccia, F. and Palmieri, F. (1984) Biochim. Biophys. Acta 766, 386–394). When reconstituted into liposomes the α-oxoglutarate transport protein catalyzes a phthalonate-sensitive α-oxoglutarate / α-oxoglutarate exchange. It is purified 250-fold with a recovery of 62% and a protein yield of 0.1% with respect to the mitochondrial extract. The properties of the reconstituted carrier, i.e., the requirements for a counteranion, the substrate specificity and the inhibitor sensitivity, are similar to those described for α-oxoglutarate transport in mitochondria.     

Maxillary expansion treatment using bone anchors: development and validation of a 3D finite element model

Objective: Develop a finite element (FE) model of a skull to perform biomechanical studies of maxillary expansion using bone anchors (BA).

Materials and methods: A skull model was developed and assigned material properties based on Hounsfield unit (HU) values of cone-beam computerized tomography (CBCT) images. A 3 mm diameter cylindrical BA was modelled and inserted in the palatal bone. A 4 mm transverse displacement was applied on the anchor. An evaluation on the effect on local stresses of BA implantation inclination angle was performed.

Results: Proper displacement results and strain–stress trends for the expansion process were present. Stress distribution patterns were similar as reported in the literature. No significant difference between BA inclination angles was found.

Conclusion: This work leads to a better understanding and prediction of craniofacial and maxillary bone remodelling during ME with BA treatments and is a first step towards the development of patient specific treatments.