Viscoelastic finite-element analysis of a lumbar motion segment in combined compression and sagittal flexion. Effect of loading rate.

STUDY DESIGN: A study using a validated viscoelastic finite-element model of a L2-L3 motion segment to identify the load sharing among the passive elements at different loading rates. OBJECTIVE: To enhance understanding concerning the role of the loading rate (i.e., speed of lifting and lowering during manual material handling tasks) on the load sharing and safety margin of spinal structures. SUMMARY OF BACKGROUND DATA: Industrial epidemiologic studies have shown that jobs requiring a higher speed of trunk motion contribute to a higher risk of industrial low back disorders. Consideration of the dynamic loading characteristics, such as lifting at different speeds, requires modeling of the viscoelastic behavior of passive tissues. Detailed systematic analysis of loading rate effects has been lacking in the literature. METHODS: Complex flexion movement was simulated by applying compression and shear loads at the top of the upper vertebra while its sagittal flexion angle was prescribed without constraining any translations. The lower vertebra was fixed at the bottom. The load reached its maximum values of 2000 N compression and 200 N anterior shear while L2 was flexed to 10 degrees of flexion in the three different durations of 0.3, 1, and 3 seconds to represent fast, medium, and slow movements, respectively. The resisted bending moment, gross load-displacement response of the motion segment, forces in facet joints and ligaments, stresses and strains in anulus fibrosus, and intradiscal pressure were compared across different rates. RESULTS: The distribution of stress and strain was markedly affected by the loading rate. The higher loading rate increased the peak intradiscal pressure (12.4%), bending moment (20.7%), total ligament forces (11.4%), posterior longitudinal ligament stress (15.7%), and anulus fiber stress at the posterolateral innermost region (17.9%), despite the 15.4% reduction in their strain. CONCLUSIONS: Consideration of the time-dependent material properties of passive elements is essential to improving understanding of motion segment responses to dynamic loading conditions. Higher loading rate markedly reduces the safety margin of passive spinal elements. When the dynamic tolerance limits of tissues are available, the results provide bases for the guidelines of safe dynamic activities in clinics or industry.

The dynamic response of L(2)/L(3) motion segment in cyclic axial compressive loading.

OBJECTIVE: The dynamic response and load sharing amongst passive elements of an L2-L3 motion segment during axial compressive cyclic loading was investigated. DESIGN: A validated viscoelastic nonlinear finite element model of L2-L3 was used for a detailed stress/strain analysis during axial cyclic loading. BACKGROUND: The repetitive loading of the spine has been implicated as a risk factor in developing low back disorders. However, the quantitative description of injury mechanisms and the internal load sharing have been lacking. METHODS: The applied cyclic axial compressive loading was controlled, peak to peak, from 600 to 1000 N at 0.5 Hz for 15 cycles. The stress/strain and strain energy density of various elements were quantified and the effects of cyclic loading on these parameters were investigated. RESULTS: The axial stiffness of the motion segment decreased, while intradiscal pressure (IDP) and the strain in anulus fibers of the outermost lamella increased. The axial stresses of outer lamellae in the anulus matrix reduced, in contrast to the increased strain at the endplate. CONCLUSIONS: The load sharing amongst the passive elements of the motion segment changed. The response of the motion segment to the same external axial load depends on the history of loading. The anulus fibers in the innermost layer were slack due to compression, hence not at risk of failure. The loss of disc height and increased disc bulge led to higher strain in anulus fibers of outermost layer. In future, more complex loading conditions with a longer duration should be considered.

Three-body segment dynamic model of the human knee.

In this paper, a two-dimensional, three-body segment dynamic model of the human knee is introduced. The model includes tibio-femoral and patello-femoral articulations, and anterior cruciate, posterior cruciate, medial collateral, lateral collateral, and patellar ligaments. It enables one to obtain dynamic response of the knee joint to any one or combination of quadriceps femoris, hamstrings, and gastrocnemius muscle actions, as well as any externally applied forces on the lower leg. A specially developed human knee animation program is utilized in order to fine tune some model parameters. Numerical results are presented for knee extension under the impulsive action of the quadriceps femoris muscle group to simulate a vigorous lower limb activity such as kicking. The model shows that the patella can be subjected to very large transient patello-femoral contact force during a strenuous lower limb activity even under conditions of small knee-flexion angles. The results are discussed and compared with limited data reported in the literature.

Improved dynamic model of the human knee joint and its response to impact loading on the lower leg.

Almost a decade ago, three-dimensional formulation for the dynamic modeling of an articulating human joint was introduced. Two-dimensional version of this formulation was subsequently applied to the knee joint. However, because of the iterative nature of the solution technique, this model cannot handle impact conditions. In this paper, alternative solution methods are introduced which enable investigation of the response of the human knee to impact loading on the lower leg via an anatomically based model. In addition, the classical impact theory is applied to the same model and a closed-form solution is obtained. The shortcomings of the classical impact theory as applied to the impact problem of the knee joint are delineated.

Three-dimensional kinematic modelling of the human shoulder complex--Part I: Physical model and determination of joint sinus cones.

Modelling of the human shoulder complex is essential for the multi-segmented mathematical models as well as design of the shoulder mechanism of anthropometric dummies. In Part I of this paper a three-dimensional kinematic model is proposed by utilizing the concepts of kinematic links, joints, and joint sinuses. By assigning appropriate coordinate systems, parameters required for complete quantitative description of the proposed model are identified. The statistical in-vivo data base established by Engin and Chen (1986) is cast in a form compatible with the model by obtaining a set of unit vectors describing circumductory motion of the upper arm in a torso-fixed coordinate system. This set of unit vectors is then employed in determining the parameters of a composite shoulder complex sinus of a simplified version of the proposed model. Two methods, namely the flexible tolerance and the direct methods, are formulated and tested for the determination of an elliptical cone surface for a given set of generating unit vectors. Numerical results are presented for the apex angles and orientation of the composite joint sinus cone with respect to the anatomical directions.

Three-dimensional kinematic modelling of the human shoulder complex--Part II: Mathematical modelling and solution via optimization.

In this paper, individual joint sinus cones associated with the sternoclavicular, claviscapular, and glenohumeral joints of the three-dimensional kinematic model introduced in Part I for the human shoulder complex are quantitatively determined. First, mathematical description of the humerus orientation with respect to torso is given in terms of eight joint variables. Since the system is a kinematically redundant one, solution for the joint variables satisfying a prescribed humerus orientation is possible only if additional requirements are imposed; and the "minimum joint motion" criterion is introduced for this purpose. Two methods, namely the Lagrange multipliers and flexible tolerance methods, are formulated and tested for the optimization problem. The statistical in-vivo data base for the circumductory motion of the upper arm is employed to determine a set of joint variables via optimization, which are then utilized to establish the sizes and orientations of the elliptical cones for the individual joint sinuses. The results are discussed and compared with those given on the basis of measurements made on cadaveric specimens.

On the biomechanics of human hip complex in vivo--I. Kinematics for determination of the maximal voluntary hip complex sinus.

In recent years, multisegmented mathematical models of the total human body have gained increasing attention in view of the high cost of experiments with human cadavers and/or anthropometric dummies. While these models can simulate very complicated load-motion situations, their effectiveness depends heavily on the proper biomechanical description and modeling of the major articulating joints of the human body. In a research effort to obtain the in vivo biomechanical joint property data suitable for incorporation into these models, the senior author and his associates recently developed a new kinematic and force data collection methodology by means of sonic emitters. By applying and extending this data collection methodology, this paper in Part I presents kinematics for determination of the maximal voluntary hip complex sinus. An overdeterminate number of sonic emitters is utilized and the 'most accurate' three-dimensional kinematic data set is selected by first establishing a selection criterion. Quantitative results obtained from three male subjects are presented in a functional expansion form relative to a locally-defined joint axis system as well as in the form of globographic representation relative to the torso-fixed axis system.

On the biomechanics of human hip complex in vivo--II. Passive resistive properties beyond the hip complex sinus.

In multisegmented mathematical models of the total human body, the resistive force properties of the major articulating joints play a direct and significant role in determining the relative motion between two body segments and in the understanding of injury mechanisms. This paper presents three-dimensional passive resistive properties beyond the maximal voluntary hip complex sinus by applying the kinematic data collection methodology developed in Part I together with a recently developed force data collection technique with sonic emitters (previously reported elsewhere by the senior author and his associates). The same three male subjects as in Part I of this paper were tested. Quantitative results were displayed by establishing the constant resistive force (moment) contours on a modified local joint axis system.

Kinematic and passive resistive properties of human elbow complex.

In recent years, owing to their versatility and reduced cost of operation, multisegmented mathematical models of the total human body have gained increased attention in gross biodynamic motion studies. This, in turn, has stimulated the need for a proper biomechanical data base for the major human articulating joints. The lack of such a database for the humero-elbow complex is the impetus for this study. The total angular range of motion permitted by the complex and the passive resistive properties beyond the full elbow extension were studied. Results obtained on ten normal male subjects were utilized to establish a statistical data base for the humero-elbow complex. Results are also expressed in functional expansion form suitable for incorporation into the existing multisegmented models.

On the biomechanics of human shoulder complex--I. Kinematics for determination of the shoulder complex sinus.

Effectiveness of the multi-segmented total-human-body models to predict realistically live human response depends heavily on the proper biomechanical description and simulation of the major articulating joints of the body. In these models, the most difficult and the least successful modelling of a joint has been the shoulder complex because of the lack of appropriate biomechanical data as well as the anatomical complexity of the region. This paper in Part I presents various aspects of a research program to collect three-dimensional kinematic data for the shoulder complex. A sonic digitizing technique which utilizes an overdeterminate number of sonic emitters on the moving body segment was used for the kinematics analysis. The numerical results are presented for three male subjects for their voluntary shoulder complex sinuses. The results are given in a locally-defined joint axis system as well as in the torso-fixed coordinate system in the form of globographic representation.

On the biomechanics of human shoulder complex--II. Passive resistive properties beyond the shoulder complex sinus.

In multi-segmented total-human-body models the most difficult and the least successful modeling of a major articulating joint has been the shoulder complex because of the lack of appropriate biomechanical data as well as the anatomical complexity of the region. In this paper, quantitative results on the three-dimensional passive resistive properties beyond the voluntary shoulder complex sinus are presented by applying the methodology developed in part I. Constant-restoring-force(moment) contours are established for the shoulder complex and the numerical results are presented for the three subjects tested. In addition, functional expansions are presented for the voluntary and restoring force(moment) contours using spherical coordinates.

Statistical data base for the biomechanical properties of the human shoulder complex--I: Kinematics of the shoulder complex.

In the last two decades, several multi-segmented mathematical models of the total-human-body have appeared in the literature. While these models can handle very sophisticated load-motion situations, their effectiveness depends heavily on the proper biomechanical description and simulation of the major articulating joints of the human body. Among these joints, the most complicated and the least successfully modeled one has been the shoulder complex mainly due to the lack of an appropriate biomechanical data base as well as the anatomical complexity of the shoulder region. In 1984, the senior author and his associates proposed a new kinematic data collection methodology by means of sonic emitters and associated data analysis technique. Based on this data collection methodology, Part I of this paper establishes a statistical data base for the shoulder complex sinus of the male population of ages 18-32. Estimates for the population mean and standard deviation as well as their confidence intervals are presented. The results are expressed in functional expansion form relative to a locally defined joint axis system as well as relative to the torso-fixed coordinate system in the form of globographic representation.

Statistical data base for the biomechanical properties of the human shoulder complex--II: Passive resistive properties beyond the shoulder complex sinus.

In mathematical modeling of multi-segmented articulating total-human-body, there is no doubt that the shoulder complex plays one of the most important roles. However, proper biomechanical passive resistive force data have been lacking in the literature. This paper presents determination of the three-dimensional passive resistive joint properties beyond the maximal voluntary shoulder complex sinus. A functional expansion with two spherical angular variables in the local joint axis system is proposed to fit the overall restoring force (moment) data. A constant restoring force (moment) contour map as well as a three-dimensional perspective view of the results are presented in a new coordinate system defined in this study. Finally, a statistical data base is established by utilizing the statistical analysis procedures discussed in Part I of this paper.

On the damping properties of the shoulder complex.

Effectiveness of the multi-segmented total-human-body models to predict accurately live human response depends heavily on the task of proper biomechanical description and simulation of the articulating joints. Determination of the damping properties in articulating joints is an important part of this task and constitutes the subject of this paper. A new method which is based on the damped oscillations of a body segment is introduced by considering the shoulder complex as an example. The numerical results for the angular damping coefficients at the shoulder complex are presented for forty different orientations of the arm with respect to torso. The angular damping coefficients exhibit a nonlinear behavior as a function of the arm orientation.

Kinematic and force data collection in biomechanics by means of sonic emitters--I: Kinematic data collection methodology.

In this paper, first, the principles of sonic digitizing are presented. Next, a description of quantitative determination of the relative motion between two body segments by utilization of sonic emitters is provided. A new kinematic data collection methodology and data analysis is proposed to check continuously the accuracy of the data collected by means of the sonic emitters. The first part of the paper is terminated by establishment of an accuracy criteria and selection of the most accurate data set and associated error analysis. Quantitative results based upon the kinematic data collection methodology of Part I were obtained for the forced kinematic motion of the human shoulder complex and are presented in Part II.

Kinematic and force data collection in biomechanics by means of sonic emitters--II: Force data collection and application to the human shoulder complex.

In multisegmented mathematical models of the human body the most difficult and the least successful modeling of a major articulating joint has been the shoulder complex because of the lack of appropriate biomechanical data as well as the anatomical complexity of the region. In this paper, quantitative results on the variability of the stiffness of the shoulder complex dependent upon orientation of the upper arm are presented by applying the principles and theory developed in Part I. The paper starts with a description of a multiple-axis force and moment transducer and its utilization with sonic emitters in determining direction as well as location of the general force and moment vectors applied on a body segment. The numerical results which are presented for three subjects are in the form of plots showing the passive resistance of the shoulder complex as functions of drawer displacements of the upper arm along its long bone axis. Exponential and power curve fitting of the numerical results are also provided to establish intra-subject variations and similarities of the behavioral patterns of the axial stiffness characteristics of the human shoulder complex.

Response of a two-dimensional dynamic model of the human knee to the externally applied forces and moments.

This paper is concerned with response of a two-dimensional dynamic model of the human knee to the externally applied forces and moments. The profiles of the articulating surfaces of a normal knee joint are determined from X-ray films and they are represented by polynomials. Ligaments of the joint are modelled as nonlinear elastic springs of realistic stiffness properties. Nonlinear equations of motion, coupled with nonlinear constraint conditions, are solved numerically. Time derivatives are approximated by Newmark difference formulae and the resulting nonlinear algebraic equations are solved employing the Newton-Raphson iteration scheme. Several dynamic loads (force and moment) are applied to the tibia and subsequent motion is investigated. Results for the ligament and contact forces, contact point locations between femur and tibia and the corresponding dynamic orientation of tibia with respect to femur are presented.

Etiology and biomechanics of hernial sac formation.

This paper, to the authors' best knowledge, presents the first attempt on the understanding of the biomechanics of hernial sac formation. First, a brief survey of the selected etiological factors and their related theories on hernia is given. Next, the results of some preliminary tensile tests conducted on normal and sac peritoneum are discussed. The third part of the paper is concerned with a theoretical model which incorporates both material and geometric nonlinearities by considering deformation of circular membrane under internal fluid pressure. The influence of the material properties of the peritoneal sac, its thickness and its initial radius of curvature, as well as the internal fluid pressure on the growth of the sac are illustrated. The existence of a critical value for a non-dimensional parameter is shown and it is proposed that the herniation process can be viewed as a biomechanically unstable phenomenon in the light of the present model.

Effects of oestrogen upon tensile properties of healing fractured avian bone.

The present work considers some of the effects of oestrogen treatment on the biomechanical properties of long bones during the process of osteosynthesis. The influence of the steroid was assessed by determining the tensile strength properties of treated and untreated healing fractured ossa radii. The ultimate tensile strength and modulus of elasticity were determined at one and two week post-fracture induction. In general, oestrogen treatment decelerated healing process of long bones. This was indicated by a significantly reduced ultimate tensile callus strength of oestrogen-treated birds over a two week period post-fracture induction. The same group also exhibited a significant increase in callus cross-sectional area while the elastic moduli of their bones were not significantly different at either one or two weeks post-fracture induction.

Isometric muscle force response of the human lower limb.

This paper deals with isometric muscle force response of the human lower limb when the leg is subjected to various external forces applied on the knee and ankle joints. The major components of the research apparatus are a subject restraint system, a force application device which employs three sonic emitters, and an upper leg cuff with four sonic emitters. The sonic emitters are used to determine the direction and the location of the force application on the lower limb and the orientation of the upper leg with respect to the torso. The numerical results are presented from experiments conducted on three male and three female subjects to determine their isometric muscle resistance against external forces trying to dislodge their lower limbs from several initial configurations. Quantitative results on the isometric muscle force capability of the subjects, when their lower limbs are dislodged from the initial stowed position, are also presented. It is concluded that, although there are intra- and inter-subject variations for the maximum values of the resistive muscle forces of the lower limb, there are some trends in the behavior of their magnitudes. Incorporating the results of the present research into multi-segmented models of the human body should improve the long-time response capabilities of these models so that they can simulate more realistically the biodynamic events which take place when the human body is subjected to high magnitudes of external forces lasting more than a fraction of a second.