Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue

The mechanical behavior of most biological soft tissue is nonlinear viscoelastic rather than elastic. Many of the models previously proposed for soft tissue involve ad hoc systems of springs and dashpots or require measurement of time-dependent constitutive coefficient functions. The model proposed here is a system of evolution differential equations, which are determined by the long-term behavior of the material as represented by an energy function of the type used for elasticity. The necessary empirical data is time independent and therefore easier to obtain. These evolution equations, which represent non-equilibrium, transient responses such as creep, stress relaxation, or variable loading, are derived from a maximum energy dissipation principle, which supplements the second law of thermodynamics. The evolution model can represent both creep and stress relaxation, depending on the choice of control variables, because of the assumption that a unique long-term manifold exists for both processes. It succeeds, with one set of material constants, in reproducing the loading-unloading hysteresis for soft tissue. The models are thermodynamically consistent so that, given data, they may be extended to the temperature-dependent behavior of biological tissue, such as the change in temperature during uniaxial loading. The Holzapfel et al. three-dimensional two-layer elastic model for healthy artery tissue is shown to generate evolution equations by this construction for biaxial loading of a flat specimen. A simplified version of the Shah-Humphrey model for the elastodynamical behavior of a saccular aneurysm is extended to viscoelastic behavior.     

Modeling of human reactions to whole-body vibration

A computer-automated approach for studying the human body vibration is presented. This includes vertical, horizontal, and torsional vibration. The procedure used is based on Finite Segment Modeling (FSM) of the human body, thus treating it as a mechanical structure. Kane's equations as developed by Huston et al. are used to formulate the governing equations of motion. The connective tissues are modeled by springs and dampers. In addition, the paper presents the transient response of different parts of the body due to a sinusoidal forcing function as well as an impulse function applied to the lower torso in the vertical direction.     

A computer-based biomechanical analysis of the three-dimensional motion of cementless hip prostheses.

A computer-based mathematical technique was developed to measure and completely describe the migration and micromotion of a femoral hip prosthesis relative to the femur. This technique utilized the mechanics of rigid-body motion analysis and apparatus of seven linear displacement transducers to measure and describe the complete three-dimensional motion of the prosthesis during cyclic loading. Computer acquisition of the data and custom analysis software allowed one to calculate the magnitude and direction of the motion of any point of interest on the prostheses from information about the motion of two points on the device. The data were also used to replay the tests using a computer animation technique, which allowed a magnified view of the three-dimensional motion of the prosthesis. This paper describes the mathematical development of the rigid-body motion analysis, the experimental method and apparatus for data collection, the technique used to animate the motion, the sources of error and the effect of the assumptions (rigid bodies) on the results. Selected results of individual test runs of uncemented and cemented prostheses are presented to demonstrate the efficacy of the method. The combined effect of the vibration and electrical noise resulted in a resolution of the system of about 3-5 microns motion for each transducer. Deformation effects appear to contribute about 3-15 microns to the measurement error. This measurement and analysis technique is a very sensitive and powerful means of assessing the effects of different design parameters on the migration and micromotion of total joint prostheses and can be applied to any other case (knee, dental implant) where three-dimensional relative motion between two bodies is important.     

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.     

Blood flow: Theory,effective viscosity and effects of particle distribution

A study is made of blood flow by assuming that the blood constitutes a suspension of cells in plasma instead of a simple homogeneous fluid. A macroscopic theory governing the motion of plasma in a plasma-cell system is derived from the local volume averaging method for a system without mass transfer between the phases, and its characteristic length is much larger than the size of the cells. The equations governing the motion of the local averaged fluid quantities include one additional term in the equation of motion and two additional terms in the energy equation. These terms represent, respectively, the force exerted upon the fluid by the particles, and the rate of heat transfer and work kone upon the fluid by the particles. The theory is applied to obtain the effective viscosity as the explicit function of the volume concentration of the cells by assuming that the cells behave like rigid spherical particles with slip-collision, and the plasma is an compressible Newtonian fluid. Comparison with existing experimental results shows a good agreement. The theory is also used to obtain the effects of cell distribution upon the overall effective viscosity in a circular tube. The quantitative result shows that there is a decrease in overall effective viscosity as the concentration of cells increases toward the center of the tube, and the overall effective viscosity is smaller than the flow with evenly distributed cells.     

Three-Dimensional Flow of an Oldroyd-B Nanofluid towards Stretching Surface with Heat Generation/Absorption

This article addresses the steady three-dimensional flow of an Oldroyd-B nanofluid over a bidirectional stretching surface with heat generation/absorption effects. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are then solved analytically by using the homotpy analysis method (HAM). Graphically results are presented and discussed for various parameters, namely, Deborah numbers and , heat generation/absorption parameter Prandtl parameter , Brownian motion parameters, thermophoresis parameter and Lewis number . We have seen that the increasing values of the Brownian motion parameter and thermophoresis parameter leads to an increase in the temperature field and thermal boundary layer thickness while the opposite behavior is observed for concentration field and concentration boundary layer thickness. To see the validity of the present work, the numerical results are compared with the analytical solutions obtained by Homotopy analysis method and noted an excellent agreement for the limiting cases.     

Three-dimensional static modeling of the lumbar spine

This paper presents three-dimensional static modeling of the human lumbar spine to be used in the formation of anatomically-correct movement patterns for a fully cable-actuated robotic lumbar spine which can mimic in vivo human lumbar spine movements to provide better hands-on training for medical students. The mathematical model incorporates five lumbar vertebrae between the first lumbar vertebra and the sacrum, with dimensions of an average adult human spine. The vertebrae are connected to each other by elastic elements, torsional springs and a spherical joint located at the inferoposterior corner in the mid-sagittal plane of the vertebral body. Elastic elements represent the ligaments that surround the facet joints and the torsional springs represent the collective effect of intervertebral disc which plays a major role in balancing torsional load during upper body motion and the remaining ligaments that support the spinal column. The elastic elements and torsional springs are considered to be nonlinear. The nonlinear stiffness constants for six motion types were solved using a multiobjective optimization technique. The quantitative comparison between the angles of rotations predicted by the proposed model and in the experimental data confirmed that the model yields angles of rotation close to the experimental data. The main contribution is that the new model can be used for all motions while the experimental data was only obtained at discrete measurement points.     

Head trauma--a parametric dynamic study

A mathematical elastodynamic model, Baseline I, consisting of eleven degrees of freedom and describing the human skull, brain, spinal cord, neck, arms and torso as a system of discrete masses, linear translational and torsional springs has been developed. Forced response solutions to the governing equations of motion, which contain selected nonlinear terms, are carried out on the IBM 7094 computer. A parametric study of the effects of location and force-time history of a blow to the head and variations in.neck stiffness was conducted. The significance of these perturbations is determined by comparison with selected response measures.     

An explicit expression for the moment in multibody systems.

The equations of motion are formulated for a set of interacting rigid bodies. An explicit formulation could be derived for the total moment of the forces on such a system. This is applied to (1) the intersegmental moment in a multisegment rigid-body model, and (2) the interpretation of the 'centre of pressure' as defined in the studies of human posture.     

Methodological and technological implications of quantitative human movement analysis in long term space flights

In the frame of the 179-days EUROMIR '95 space mission, two in-flight experiments foresaw the analysis of three-dimensional human movements in microgravity. For this aim, a space qualified opto-electronic motion analyser based on passive markers was installed onboard the MIR Space Station. The paper describes the experimental procedures designed in order to face technical and operational limitations imposed by the critical environment of the orbital module. The reliability of the performed analysis is discussed, focusing two related aspects: accuracy in three-dimensional marker localisation and data comparability among different experimental sessions. The effect of the critical experimental set-up and of TV cameras optical distortions is evaluated on in-flight acquired data, by performing an analysis on Euclidean distance conservation on rigid bodies. An optimisation method for the recovering of a unique reference frame throughout the whole mission is described. Results highlight the potentiality that opto-electronics and close-range photogrammetry have for automatic motion analysis onboard orbital modules. The discussion of the obtained results provides general suggestions for the implementation of experimental human movement analysis in critical environments, based on the suitable trade-off between external constraints and achievable analysis reliability.     

A model for studies of mechanical interactions between the human spine and rib cage

A three-dimensional mathematical model useful for studies of the mechanics of the human skeletal thorax is described. To construct this model, rib cage elements are incorporated into a previously reported model of the thoracolumbar spine. The vertebrae and bony portions of the ribs and sternum are idealized as rigid bodies. The behavior of the discs, ligaments and costal cartilages are modelled by deformable elements. Appropriate geometric and stiffness property data are assigned to the elements of the model. In constructing the model, it was found that the mechanical response of the costo-vertebral joint is strongly influenced by articulation geometry. Although rigid bodies were used to model calcified portions of the ribs, the model predicted rib cage deformations in close agreement with those measured experimentally. These studies indicate that the rigid body motion of calcified portions of the rib makes a major contribution to the deformation of the rib cage in response to certain types of loadings. Quantitative results are also reported on the roles the rib cage plays in bending responses of the spine, the lateral stability of the spine, and the production and correction of several scoliotic deformities.     

The computation of structure from fixed-axis motion: rigid structures

We show that three distinct orthographic views of three points in a rigid configuration are compatibel with at most 64 interpretations of the three-dimensional structure and motion of the points. If, in addition, one assumes that the three points spin about a fixed axis over the three views, then with probability one there is a unique three-dimensional interpretation (plus a reflection). Moreover the probability of false targets is zero. In the special case that the axis of rotation is parallel to the image plane three views of the three points are sufficient to obtain at most two interpretations (plus reflections)-unless one assumes the angular velocity about the axis is constant, in which case three views of two points are sufficient to determine a unique interpretation. Closed form solutions are obtained for each of these cases. The systems of equations studied here are in each case overconstraining (i.e. there are more independent equations than unknowns) and are amenable to solution by nonlinear programming. These two properties make possible the construction of noise insensitive algorithms for computer vision systems. Our uniqueness proofs employ the Principle of upper semicontinuity, a principle which underlies a general mathematical framework for the analysis of solutions to overconstraining systems of equations.     

Peristaltic biofluids flow through vertical porous human vessels using third-grade non-Newtonian fluids model

In this paper, the heat and flow characteristic of third-grade non-Newtonian biofluids flow through a vertical porous human vessel due to peristaltic wall motion are studied. The third-grade model can describe shear thinning (or shear thickening) and normal stress differences, which is acceptable for biofluids modeling. In order to solve the governing equations, the assumption of long-wavelength approximation is utilized. This hypothesis emphasizes that the wavelength of the peristaltic wall motion is large in comparison with the radius of the human vessel, which is widely acceptable in biological investigations. The analytical perturbation method is employed to solve the governing equations. Consequently, analytical expressions for the velocity profile, shear stress, temperature field, and biofluid flow rate are obtained. In addition, the effects of the governing parameters such as the third-grade non-Newtonian parameter, Grashof Number, Eckert number, and porosity, on the results are examined.     

A theory on the determination of 3D motion and 3D structure from features

The present paper proposes a mathematical theory and a method of recognition of both the 3D structure and the motion of a moving object from its monocular image. Initially, characteristic features are extracted from the 2D perspective image of the object. Because motion of the object induces a change in its 2D perspective image, it also induces a change in the features which depends on the 3D structure and the velocity of the object. This suggests the possibility of detecting the 3D structure and the motion directly from the features and their changing rate, without the need for calculating optical flows. An analysis is made of the relation between the 3D rigid motion of a surface element and the change in local linear features. From this relation, a method is proposed for calculating the velocity of and the normal to the surface element without considering any correspondence of points. An optical flow can also be calculated by this method. Two simple computer simulations are provided.     

An evaluation of three-dimensional diarthrodial joint contact using penetration data and the finite element method

We have developed an approximate method for simulating the three-dimensional contact of soft biphasic tissues in diarthrodial joints under physiological loading. Input to the method includes: (i) kinematic information describing an in vitro joint articulation, measured while the cartilage is deformed under physiological loads, (ii) geometric properties for the relaxed (undeformed) cartilage layers, obtained for the analyses in this study via stereophotogrammetry, and (iii) material parameters for the biphasic constitutive relations used to represent cartilage. Solid models of the relaxed tissue layers are assembled in physiological positions, resulting in a mathematical overlap of the cartilage layers. The overlap distribution is quantified and converted via the biphasic governing equations into applied traction boundary conditions for both the solid and fluid phases for each of the contacting layers. Linear, biphasic, three-dimensional, finite element analysis is performed using the contact boundary conditions derived for each of the contacting layers. The method is found to produce results consistent with the continuity requirements of biphasic contact. Comparison with results from independent, biphasic contact analyses of axisymmetric problems shows that the method slightly underestimates the contact area, leading to an overestimation of the total traction, but yields a good approximation to elastic stress and solid phase displacement.     

Precision and accuracy of bone landmarks in characterizing hand and wrist position

Characterization of the motion of the hand and wrist requires reference to the underlying bones which, for three-dimensional analyses, are assumed to be rigid bodies. Stereoradiogrammetric techniques involving the identification of prominent bone landmarks have been used as the standard against which surface markers used for in vivo testing have been evaluated. The precision and accuracy with which the 3D positions of bone landmarks in the hand and wrist could be determined was evaluated in a small inter-observer and inter-cadaver study and compared to the precision and accuracy with which implanted lead markers could be located. A subset of landmarks suitable for evaluating wrist and metacarpal-phalangeal joint motion was identified; the mean precison for identifying these points was better than 1.1 mm in all hand positions with a mean inter-observer accuracy of 2.3 mm. These values show that the average uncertainty in locating bone landmarks is at best roughly twice that for implanted markers.     

Human cortical regions involved in extracting depth from motion

We used functional magnetic resonance imaging (fMRI) to investigate brain regions involved in extracting three-dimensional structure from motion. A factorial design included two-dimensional and three-dimensional structures undergoing rigid and nonrigid motions. As predicted from monkey data, the human homolog of MT/V5 was significantly more active when subjects viewed three-dimensional (as opposed to two-dimensional) displays, irrespective of their rigidity. Human MT/V5+ (hMT/V5+) is part of a network with right hemisphere dominance involved in extracting depth from motion, including a lateral occipital region, five sites along the intraparietal sulcus (IPS), and two ventral occipital regions. Control experiments confirmed that this pattern of activation is most strongly correlated with perceived three-dimensional structure, in as much as it arises from motion and cannot be attributed to numerous two-dimensional image properties or to saliency.