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PubMed1984

Analysis and design of multiple-beam appliances.

A new approach for the analysis of multiple-beam structures, such as headgear bows, is developed for beams which contain arbitrary curvatures, twists, and material properties. The generalized transfer matrix of a single-beam analysis is converted to a stiffness matrix and inserted into a global matrix which describes the entire system. The effect of inner bow wire size (0.044 inch and 0.051 inch) on the force system is demonstrated. The inner bow with the larger cross section shows only a slight (not clinically significant) reduction in rotational moment and buccal force applied because of its greater ability to resist deformation during the loading process. Small amounts of tooth and/or tube rotations ("play") result in a significant reduction of the crown rotational moment. With increasing rotation of the tube to the inner bow, the high lateral forces and large moments found about the long axis of the teeth are found to reduce. Symmetrical headgears are chosen to illustrate the analysis and to indicate the manner in which this approach may be used to study and design similar orthodontic appliances.

Elasticity↗
PubMed1999

Multijoint muscle regulation mechanisms examined by measured human arm stiffness and EMG signals.

Stiffness properties of the musculo-skeletal system can be controlled by regulating muscle activation and neural feedback gain. To understand the regulation of multijoint stiffness, we examined the relationship between human arm joint stiffness and muscle activation during static force control in the horizontal plane by means of surface electromyographic (EMG) studies. Subjects were asked to produce a specified force in a specified direction without cocontraction or they were asked to keep different cocontractions while producing or not producing an external force. The stiffness components of shoulder, elbow, and their cross-term and the EMG of six related muscles were measured during the tasks. Assuming that the EMG reflects the corresponding muscle stiffness, the joint stiffness was predicted from the EMG by using a two-link six-muscle arm model and a constrained least-square-error regression method. Using the parameters estimated in this regression, single-joint stiffness (diagonal terms of the joint-stiffness matrix) was decomposed successfully into biarticular and monoarticular muscle components. Although biarticular muscles act on both shoulder and elbow, they were found to covary strongly with elbow monoarticular muscles. The preferred force directions of biarticular muscles were biased to the directions of elbow monoarticular muscles. Namely, the elbow joint is regulated by the simultaneous activation of monoarticular and biarticular muscles, whereas the shoulder joint is regulated dominantly by monoarticular muscles. These results suggest that biarticular muscles are innervated mainly to control the elbow joint during static force-regulation tasks. In addition, muscle regulation mechanisms for static force control tasks were found to be quite different from those during movements previously reported. The elbow single-joint stiffness was always higher than cross-joint stiffness (off-diagonal terms of the matrix) in static tasks while elbow single-joint stiffness is reported to be sometimes as small as cross-joint stiffness during movement. That is, during movements, the elbow monoarticular muscles were occasionally not activated when biarticular muscles were activated. In static tasks, however, monoarticular muscle components in single-joint stiffness were increased considerably whenever biarticular muscle components in single- and cross-joint stiffness increased. These observations suggest that biarticular muscles are not simply coupled with the innervation of elbow monoarticular muscles but also are regulated independently according to the required task. During static force-regulation tasks, covariation between biarticular and elbow monoarticular muscles may be required to increase stability and/or controllability or to distribute effort among the appropriate muscles.

Adult↗
PubMed1994

Mechanical properties of canine articular cartilage are significantly altered following transection of the anterior cruciate ligament.

The compressive, tensile, and swelling properties of articular cartilage were studied at two time periods following transection of the anterior cruciate ligament in the knee of greyhound dogs. An experimental protocol was designed to quantify the essential equilibrium and biphasic material properties of cartilage in tension, compression, and shear, as well as the parameters of isometric swelling behavior. All properties were measured at several sites to elicit differences between sites of frequent and less frequent contact. Hydration was determined at each site and was compared with the material properties of cartilage from corresponding sites. There were extensive changes in all compressive, tensile, and swelling properties of cartilage after transection of the anterior cruciate ligament. Twelve weeks after surgery, the intrinsic moduli were reduced significantly in compression (approximately 24% of control values), tension (approximately 64%), and shear (approximately 24%), and the hydraulic permeability was elevated significantly (approximately 48%). Significant increases in hydration (approximately 9%) also were observed, as well as a strong correlation of hydration with hydraulic permeability. The pattern of these changes was not found to differ with site in the joint, but significant differences were observed in the magnitude of change for cartilage from the femoral groove and the femoral condyle. The pattern and extent of changes in the material properties following transection of the anterior cruciate ligament indicate that altered loading of the joint severely compromises the overall mechanical behavior of articular cartilage. The observed loss of matrix stiffness in compression, tension, and shear is associated with increases in the deformation of the solid matrix, a diminished ability to resist swelling, and the increase in hydration observed in this study. The increased swelling and elevated water content were related directly to the increase in hydraulic permeability; this suggests an associated loss of fluid pressurization as the load support mechanism in the degenerated cartilage. Without a successful mechanism for repair, damage to the solid matrix may progress and lead to further degenerative changes in the biochemistry, morphology, and mechanical behavior of articular cartilage.

Animals↗
PubMed1990

Human arm stiffness characteristics during the maintenance of posture.

When the hand is displaced from an equilibrium position, the muscles generate elastic forces to restore the original posture. In a previous study, Mussa-Ivaldi et al. (1985) have measured and characterized the field of elastic forces associated with hand posture in the horizontal plane. Hand stiffness which describes the relation between force and displacement vectors in the vicinity of equilibrium position was measured and graphically represented by an ellipse, characterized by its size, shape and orientation. The results indicated that the shape and orientation of the stiffness ellipse are strongly dependent on arm configuration. At any given hand position, however, the values of these parameters were found to remain invariant among subjects and over time. In this study we investigate the underlying causes for the observed spatial pattern of variation of the hand stiffness ellipse. Mathematically analyzing the relation between hand and joint stiffness matrices, we found that in order to produce the observed spatial variations of the stiffness ellipse, the shoulder stiffness must covary in the workspace with the stiffness component provided by the two-joint muscles. This condition was found to be satisfied by the measured joint stiffness components. Using anatomical data and considering the effects that muscle cross-sections and changes in muscle moment arms have on the joint stiffness matrix, we found that these anatomical factors are not sufficient to account for the observed pattern of variation of joint stiffness in the workspace. To examine whether the coupling between shoulder and two-joint stiffnesses results from the coactivation of muscles contributing to these stiffnesses, EMG signals were recorded from shoulder, elbow and two-joint muscles. Our results indicated that, while some muscle coactivation may indeed exist, it can be found for only some of the muscles and in only part of the workspace.

Arm↗
PubMed2003

Adaptive control of stiffness to stabilize hand position with large loads.

The goal of this work was to investigate stability in relation to the magnitude and direction of forces applied by the hand. The endpoint stiffness and joint stiffness of the arm were measured during a postural task in which subjects exerted up to 30% maximum voluntary force in each of four directions while controlling the position of the hand. All four coefficients of the joint stiffness matrix were found to vary linearly with both elbow and shoulder torque. This contrasts with the results of a previous study, which employed a force control task and concluded that the joint stiffness coefficients varied linearly with either shoulder or elbow torque but not both. Joint stiffness was transformed into endpoint stiffness to compare the effect on stability as endpoint force increased. When the joint stiffness coefficients were modeled as varying with the net torque at only one joint, as in the previous study, we found that hand position became unstable if endpoint force exceeded about 22 N in a specific direction. This did not occur when the joint stiffness coefficients were modeled as varying with the net torque at both joints, as in the present study. Rather, hand position became increasingly more stable as endpoint force increased for all directions of applied force. Our analysis suggests that co-contraction of biarticular muscles was primarily responsible for the increased stability. This clearly demonstrates how the central nervous system can selectively adapt the impedance of the arm in a specific direction to stabilize hand position when the force applied by the hand has a destabilizing effect in that direction.

Adaptation, Physiological↗
PubMed1998

A method to determine the 3-D stiffness of fracture fixation devices and its application to predict inter-fragmentary movement.

Inter-fragmentary movement considerably influences the fracture healing process. Large shear movement delays while moderate axial movement stimulates the healing process. To be able to control the mechanical situation at a fracture site and to achieve optimal bony healing it is essential to understand the relationship between inter-fragmentary movement, bony loading and fixation stiffness. A 6 x 6 stiffness matrix is introduced which completely describes the linear relationship between the 6 inter-fragmentary movements and the resulting bony loading (3 forces and 3 moments). Further, it is illustrated that even in relatively stiff external fixateur constructs simple axial loading of the bony fragments leads to complex inter-fragmentary movement. When the 3-D stiffness description is multiplied by the load state in sheep tibiae, movements similar to those measured in vivo are calculated. The relationship between axial compression and medio-lateral or dorso-ventral shear varies depending on the mounting plane of the external fixateur. The authors conclude that a single value is not sufficient to describe the mechanical relationship between inter-fragmentary movement and bony loading. Only a complete description of fixation stiffness allows prediction of inter-fragmentary movement and differentiation between various configurations of fixation devices and their potential for mechanically promoting bony healing.

Animals↗
PubMed1992

A theoretical model of the knee and ACL: theory and experimental verification.

A three-dimensional mathematical model of the human knee joint was developed to examine the role of single ligaments, such as an anterior cruciate ligament (ACL) graft in ACL reconstruction, on joint motion and tissue forces. The model is linear and valid for small motions about an equilibrium position. The knee joint is modeled as two rigid bodies (the femur and the tibia) interconnected by deformable structures, including the ACL or ACL graft, the cartilage layer, and the remainder of the knee tissues (modeled as a single element). The model was demonstrated for the equilibrium condition of the knee in extension with an anterior tibial force, causing anterior drawer and hyperextension. The knee stiffness matrix for this condition was measured for a human right knee in vitro. Predicted model response was compared with experimental observations. Qualitative agreement was found between model and experiment, validating the model and its assumptions. The model was then used to predict the change in graft and cartilage forces and joint motion of the knee due to an increment of load in the normal joint both after ACL removal and with various altered states simulating ACL reconstructions. Results illustrate the interdependence between loads in the ACL graft, other knee structures, and contact force. Stiffer grafts and smaller maximum unloaded length of the ligament lead to higher graft and contact forces. Changes in cartilage stiffness alter load sharing between ACL graft and other joint tissues.

Anterior Cruciate Ligament↗
PubMed1996

A method for determination of the anisotropic properties of biomembranes.

A methodology was developed for potential determination of the anisotropic properties of biomembranes. This method is based on the theoretical discretization of a continuous membrane used for finite element analysis and the simultaneous measurement of the displacement of nodes on the surface of a membrane. From the given loads and measured nodal displacements, one can assemble the resulting stiffness matrix and approximate the material properties associated with the membrane. Mathematical estimations and computer simulations were performed to determine the perturbation of load and displacement errors on the resulting material properties. The results indicated that the material properties are particularly sensitive to displacement errors. The displacement measurements may require an accuracy of 20 microns for a 4 x 4 cm2 specimen. Significant inaccuracies occur close to the points of load application.

Anisotropy↗
PubMed2026

Rewiring Cellular Context as A Central Mechanism Governing Cancer Stem Cell Survival: Insights from ESC Comparisons.

Cancer stem cells (CSCs) drive tumor initiation, metastasis, and therapy resistance, yet their remarkable persistence remains poorly understood. While CSCs share stemness attributes with embryonic stem cells (ESCs), including self-renewal, transcriptional plasticity, and permissive chromatin, they exhibit a fundamentally divergent regulatory logic that prioritizes survival over developmental fidelity. ESCs maintain globally open chromatin that supports transcriptional hyperactivity but predisposes them to apoptosis under genotoxic stress, whereas CSCs maintain dynamically inducible, permissive chromatin at survival loci while repressing differentiation programs, enabling adaptive stress responses. We advance the hypothesis that CSC persistence emerges not from any single factor, but from the integrative rewiring of signaling cascades (Wnt/β-catenin, Notch, Hedgehog, PI3K/AKT/mTOR), stress-responsive transcription factors (HIFs, NF-κB, STAT3), and core pluripotency networks (OCT4, SOX2, NANOG) within a survival-centric context, reinforced by dynamic chromatin remodeling, inducible super-enhancer landscapes, and microenvironmental cues (hypoxia, inflammation, matrix stiffness). Within this framework, the E2F family serves as a key contextual integrator: in ESCs, constitutive E2F activity triggers p53-mediated apoptosis upon DNA damage, preserving genomic integrity; in CSCs, deregulated E2F activity redirects transcription toward DNA repair, antioxidant defenses, and anti-apoptotic programs. This functional divergence underscores that phenotypic outcome is determined by the broader cellular and epigenetic landscape rather than any single factor. We conclude that CSC persistence is an emergent property of this integrated, survival-centric program, fundamentally distinct from the developmental imperative of ESCs. Effective therapeutic strategies must therefore move beyond targeting individual pathways to dismantle the interconnected regulatory networks that define the CSC survival context, offering a more robust approach to overcome therapy resistance and prevent tumor relapse.

Cancer Stem Cells (CSCs)↗
PubMed1987

Response of a human head/neck/upper-torso replica to dynamic loading--II. Analytical/numerical model.

A three-dimensional lumped-parameter model of the human head/neck/upper-torso was developed to predict its motion for any specified initial conditions and that could also be used to compare with the results of other investigators. This model consists of ten rigid bodies representing the head, cervical vertebrae C1-C7, T1 and T2 combined with the rest of the torso. These rigid bodies were connected by intervertebral joints described by a stiffness matrix relating the force (moment) and translation (rotation). Fifteen pairs of muscles were incorporated in the model, represented by three-point linear elements with nonlinear constitutive relationships obtained from cadaver test results. The calculated response compared favorably with human volunteer data for both flexion and lateral whiplash. However, tests on an inanimate replica of a human indicated greater flexibility than predicted by the corresponding numerical model. The difference is believed to be due to insufficient mass of the muscles incorporated in the structure.

Acceleration↗
PubMed1992

Application of the finite-element method to simulation of damage to the human skull as a consequence of missile impact on a multi-layered composite crash helmet.

Finite-element analysis is a powerful technique which could be applicable to the study of a wide range of circumstances where the frame and/or the vital organs of the body are subjected to extreme loading conditions. This paper reports the results of an exploratory investigation in which the performance of a crash helmet in protecting the skull from an impacting load is modelled. The immediate objective is to show how a typical crash helmet design of glass-reinforced plastic (GRP) outer casing with quasi-foam-like liner can, with a suitable choice of material properties, attenuate the transfer of energy from the impacting mass such that the damage intensity to the skull is minimized. A simplified structure for both helmet and skull shape is adopted and the skull is modelled as being supported on an elastic foundation. The material properties used are representative rather than being accurately matched to experimentally determined ones. Several aspects of the modelling technique are worthy of particular note: the simulation of material anisotropy by means of multiple reinforcement layers with varying orientation, the use of dashpot elements for energy attenuation and the incorporation of multipoint constraint between the skull and the helmet lining to ensure integrity of the model with correct stiffness matrix values and allowing independent monitoring of all stress levels at the mating interface region. The results of the modelling show that the specific limited objectives can be met but also indicate how vitally important information could be obtained from similar but more detailed studies which included representative modelling of the body organs and skeleton.

Anisotropy↗
PubMed2003

Elastic properties of cancellous bone derived from finite element models of parameterized microstructure cells.

Evaluation of constitutive properties of cancellous bone and their relationships to microstructural parameters is a crucial issue in analysis of stresses and strains in bone tissues and simulation of their remodelling. Known limitations of experimental methods as well as of the micro-FE techniques make the analysis and homogenization of 'equivalent' trabecular microstructures an advantageous tool for this task. In this study, parameterized orthotropic constitutive models of cancellous bone are derived from finite element analysis of repeatable microstructure cells. Two cell types are analysed: cube- and prism-based. The models are fully three-dimensional, have realistic curvilinear shapes and are parameterized with three shape parameters. Variation of the parameters allows to imitate most of the typical microstructure patterns observed in real bones, along with variety of intermediate geometries. Finite element models of cells are generated by a special-purpose structured mesh generator for any arbitrary set of shape parameter values. Six static numerical tests are performed for an exhaustive number of parameter value sets (microstructure instances). Multi-point boundary conditions imposed on the models ensure mutual fitting of deformed neighbouring cells. Values of computed stresses allow to determine all coefficients of elastic orthotropic stiffness matrix. Results have a form of tabularized functions of elastic constants versus the shape parameters. Comparison of the results with micro-FE data obtained for a large set of cancellous bone specimens proves a good agreement, though evidently better in the case of the prism-based cell model.

Animals↗
PubMed2002

Anisotropic properties of human tibial cortical bone as measured by nanoindentation.

The purpose of this study was to investigate the effects of elastic anisotropy on nanoindentation measurements in human tibial cortical bone. Nanoindentation was conducted in 12 different directions in three principal planes for both osteonic and interstitial lamellae. The experimental indentation modulus was found to vary with indentation direction and showed obvious anisotropy (one-way analysis of variance test, P < 0.0001). Because experimental indentation modulus in a specific direction is determined by all of the elastic constants of cortical bone, a complex theoretical model is required to analyze the experimental results. A recently developed analysis of indentation for the properties of anisotropic materials was used to quantitatively predict indentation modulus by using the stiffness matrix of human tibial cortical bone, which was obtained from previous ultrasound studies. After allowing for the effects of specimen preparation (dehydrated specimens in nanoindentation tests vs. moist specimens in ultrasound tests) and the structural properties of bone (different microcomponents with different mechanical properties), there were no statistically significant differences between the corrected experimental indentation modulus (Mexp) values and corresponding predicted indentation modulus (Mpre) values (two-tailed unpaired t-test, P > 0.5). The variation of Mpre values was found to exhibit the same trends as the corrected Mexp data. These results show that the effects of anisotropy on nanoindentation measurements can be quantitatively evaluated.

Anisotropy↗
PubMed1999

A new variational shape-from-orientation approach to correcting intensity inhomogeneities in magnetic resonance images.

A new intensity inhomogeneity correction algorithm based on a variational shape-from-orientation formulation is presented. Unlike most previous methods, the proposed algorithm is fully automatic, widely applicable and very efficient. Since no prior classification knowledge about the image is assumed in the proposed algorithm, it can be applied to correct intensity inhomogeneities for a wide variety of medical images. In this paper, a finite-element method is used to model the smooth bias-field function. Orientation constraints for the bias-field function are computed at the nodal locations of the regular discretization grid away from the boundary between different class regions. The selection of reliable orientation constraints is facilitated by the goodness of fit of a first-order polynomial model to the neighborhood of each nodal location. The automatically selected orientation constraints are integrated in a regularization framework, which leads to minimization of a convex and quadratic energy function. This energy minimization is accomplished by solving a linear system with a large, sparse, symmetric and positive semi-definite stiffness matrix. We employ an adaptive preconditioned conjugate-gradient algorithm to solve the linear system very efficiently. Experimental results on a variety of magnetic resonance images are given to demonstrate the effectiveness and efficiency of the proposed algorithm.

Algorithms↗
PubMed1997

Ultrasound critical-angle reflectometry (UCR): a new modality for functional elastometric imaging.

This paper discusses the measurement of velocity in a solid based on the analysis of the amplitude and phase of ultrasound waves reflected by a solid, a technique called ultrasound critical-angle reflectometry (UCR). To this end, the complete formulation of ultrasound wave reflection and refraction from a liquid-solid interface is described. Differences between this formulation and previously published ones are briefly discussed. Based on this analysis it is in particular possible to measure by this technique not only pressure but also, for the first time in such studies, shear wave velocities, an experimentally confirmed result. The measurement of the complete stiffness matrix of a transversely isotropic solid, specifically cortical bone, by applying UCR elastometry to any point on the solid's surface is demonstrated. Finally this method is extended to functional elastometric imaging. The techniques presented in this paper offer new opportunities for applications of UCR imaging to the assessment of bone metabolism, formation and disease and also the analysis of composite materials in general.

Anisotropy↗
PubMed2001

Finite element modeling of transient ultrasonic waves in linear viscoelastic media.

Linear viscoelasticity offers a minimal framework within which to construct a causal model for wave propagation in absorptive media. Viscoelastic media are often described as media with 'fading memory,' that is, the present state of stress is dependent on the present strain and the complete time history of strain convolved with appropriate time-dependent shear and bulk stress relaxation moduli. An axisymmetric, displacement-based finite element method for modeling pulsed ultrasonic waves in linear, homogeneous, and isotropic (LHI) viscoelastic media is developed that does not require storage of the complete time history of displacement at every node. This is accomplished by modeling stress relaxation moduli as discrete or continuous spectra of decaying exponentials and relaxation times. Details of the construction and computation of the time-dependent stiffness matrix are presented. As an application of the finite element method, a finite number of exponentials (amplitudes and relaxation times) are employed to represent a typical model for a continuous relaxation spectrum. It is demonstrated that a small number of discrete exponentials are required to model ultrasonic wave propagation of a typical band-limited pulse in a model material accurately. Previous work has shown this model to be consistent with other analytic models for wave propagation in viscoelastic media [1].

Journal Article↗
PubMed2002

Time-resolved line focus acoustic microscopy of layered anisotropic media: application to composites.

This paper presents theoretical and experimental studies of the time-domain response of line focus acoustic microscopy from a layered anisotropic medium. A method for elastic constant reconstruction from acoustic microscopy signatures also is presented. The microscopy response is complicated by multiple reflections in the layers and by the anisotropic nature of the material. The model is based on a new, stable recursive stiffness matrix algorithm developed for a multilayered anisotropic medium, which is applied to the interpretation of the time-resolved acoustic microscopy signature. Specific examples are given for unidirectional and multidirectional graphite epoxy composites. It is shown that the fluid load has a significant effect on the leaky surface waves in these composites, increasing surface wave speed above that for the slow transverse wave. This results in its absence from the microscopy signature of the surface wave. The theoretical results are compared with experiments carried out using a line focus PVDF transducer developed at National Institute of Standards and Technology (NIST). Time-resolved acoustic microscopy has been applied to the determination of elastic constants of a unidirectional composite or of one lamina in a cross-ply composite. The lateral waves and multiple reflections of bulk waves appearing in the microscopy signatures are used for the elastic properties reconstruction. The reconstruction results are compared to data obtained by the self-reference double-through-transmission ultrasonic bulk wave method.

Journal Article↗
PubMed2000

A bidomain model based BEM-FEM coupling formulation for anisotropic cardiac tissue.

A hybrid boundary element method (BEM)/finite element method (FEM) approach is proposed in order to properly consider the anisotropic properties of the cardiac muscle in the magneto- and electrocardiographic forward problem. Within the anisotropic myocardium a bidomain model based FEM formulation is applied. In the surrounding isotropic volume conductor the BEM is adopted. Coupling is enabled by requesting continuity of the electric potential and the normal of the current density across the boundary of the heart. Here, the BEM part is coupled as an equivalent finite element to the finite element stiffness matrix, thus preserving in part its sparse property. First, continuous convergence of the coupling scheme is shown for a spherical model comparing the computed results to an analytic reference solution. Then, the method is extended to the depolarization phase in a fibrous model of a dog ventricle. A precomputed activation sequence obtained using a fine mesh of the heart was downsampled and used to calculate body surface potentials and extracorporal magnetic fields considering the anisotropic bidomain conductivities. Results are compared to those obtained by neglecting in part or totally (oblique or uniform dipole layer model) anisotropic properties. The relatively large errors computed indicate that the cardiac muscle is one of the major torso inhomogeneities.

Animals↗