Measurement of a spinal motion segment stiffness matrix.

The six-degrees-of-freedom elastic behavior of spinal motion segments can be approximated by a stiffness matrix. A method is described to measure this stiffness matrix directly with the motion segment held under physiological conditions of axial preload and in an isotonic fluid bath by measuring the forces and moments associated with each of the six orthogonal translations and rotations. The stiffness matrix was obtained from the load-displacement measurements by linear least squares assuming a symmetric matrix. Results from a pig lumbar spinal motion segment in an isotonic bath, with and without a 500 N axial preload, showed a large stiffening effect with axial preload.

Refinement of elastic, poroelastic, and osmotic tissue properties of intervertebral disks to analyze behavior in compression.

Intervertebral disks support compressive forces because of their elastic stiffness as well as the fluid pressures resulting from poroelasticity and the osmotic (swelling) effects. Analytical methods can quantify the relative contributions, but only if correct material properties are used. To identify appropriate tissue properties, an experimental study and finite element analytical simulation of poroelastic and osmotic behavior of intervertebral disks were combined to refine published values of disk and endplate properties to optimize model fit to experimental data. Experimentally, nine human intervertebral disks with adjacent hemi-vertebrae were immersed sequentially in saline baths having concentrations of 0.015, 0.15, and 1.5 M and the loss of compressive force at constant height (force relaxation) was recorded over several hours after equilibration to a 300-N compressive force. Amplitude and time constant terms in exponential force-time curve-fits for experimental and finite element analytical simulations were compared. These experiments and finite element analyses provided data dependent on poroelastic and osmotic properties of the disk tissues. The sensitivities of the model to alterations in tissue material properties were used to obtain refined values of five key material parameters. The relaxation of the force in the three bath concentrations was exponential in form, expressed as mean compressive force loss of 48.7, 55.0, and 140 N, respectively, with time constants of 1.73, 2.78, and 3.40 h. This behavior was analytically well represented by a model having poroelastic and osmotic tissue properties with published tissue properties adjusted by multiplying factors between 0.55 and 2.6. Force relaxation and time constants from the analytical simulations were most sensitive to values of fixed charge density and endplate porosity.

Limitation of finite element analysis of poroelastic behavior of biological tissues undergoing rapid loading.

The finite element method is used in biomechanics to provide numerical solutions to simulations of structures having complex geometry and spatially differing material properties. Time-varying load deformation behaviors can result from solid viscoelasticity as well as viscous fluid flow through porous materials. Finite element poroelastic analysis of rapidly loaded slow-draining materials may be ill-conditioned, but this problem is not widely known in the biomechanics field. It appears as instabilities in the calculation of interstitial fluid pressures, especially near boundaries and between different materials. Accurate solutions can require impractical compromises between mesh size and time steps. This article investigates the constraints imposed by this problem on tissues representative of the intervertebral disc, subjected to moderate physiological rates of deformation. Two test cylindrical structures were found to require over 10(4) linear displacement-constant pressure elements to avoid serious oscillations in calculated fluid pressure. Fewer Taylor-Hood (quadratic displacement-linear pressure elements) were required, but with complementary increases in computational costs. The Vermeer-Verruijt criterion for 1D mesh size provided guidelines for 3D mesh sizes for given time steps. Pressure instabilities may impose limitations on the use of the finite element method for simulating fluid transport behaviors of biological soft tissues at moderately rapid physiological loading rates.

Spatially resolved streaming potentials of human intervertebral disk motion segments under dynamic axial compression.

Intervertebral disk degeneration results in alterations in the mechanical, chemical, and electrical properties of the disk tissue. The purpose of this study is to record spatially resolved streaming potential measurements across intervertebral disks exposed to cyclic compressive loading. We hypothesize that the streaming potential profile across the disk will vary with radial position and frequency and is proportional to applied load amplitude, according to the presumed fluid-solid relative velocity and measured glycosaminoglycan content. Needle electrodes were fabricated using a linear array of AgAgCl micro-electrodes and inserted into human motion segments in the midline from anterior to posterior. They were connected to an amplifier to measure electrode potentials relative to the saline bath ground. Motion segments were loaded in axial compression under a preload of 500 N, sinusoidal amplitudes of +/-200 N and +/-400 N, and frequencies of 0.01 Hz, 0.1 Hz, and 1 Hz. Streaming potential data were normalized by applied force amplitude, and also compared with paired experimental measurements of glycosaminoglycans in each disk. Normalized streaming potentials varied significantly with sagittal position and there was a significant location difference at the different frequencies. Normalized streaming potential was largest in the central nucleus region at frequencies of 0.1 Hz and 1.0 Hz with values of approximately 3.5 microVN. Under 0.01 Hz loading, normalized streaming potential was largest in the outer annulus regions with a maximum value of 3.0 microVN. Correlations between streaming potential and glycosaminoglycan content were significant, with R(2) ranging from 0.5 to 0.8. Phasic relationships between applied force and electrical potential did not differ significantly by disk region or frequency, although the largest phase angles were observed at the outermost electrodes. Normalized streaming potentials were associated with glycosaminoglycan content, fluid, and ion transport. Results suggested that at higher frequencies the transport of water and ions in the central nucleus region may be larger, while at lower frequencies there is enhanced transport near the periphery of the annulus. This study provides data that will be helpful to validate multiphasic models of the disk.

Influence of fixed charge density magnitude and distribution on the intervertebral disc: applications of a poroelastic and chemical electric (PEACE) model.

A 3-dimensional formulation for a poroelastic and chemical electric (PEACE) model is presented and applied to an intervertebral disc slice in a 1-dimensional validation problem and a 2-dimensional plane stress problem. The model was used to investigate the influence of fixed charge density magnitude and distribution on this slice of disc material. Results indicated that the mechanical, chemical, and electrical behaviors were all strongly influenced by the amount as well as the distribution of fixed charges in the matrix. Without any other changes in material properties, alterations in the fixed charge density (proteoglycan content) from a healthy to a degenerated distribution will cause an increase in solid matrix stresses and can affect whether the tissue imbibes or exudes fluid under different loading conditions. Disc tissue with a degenerated fixed charge density distribution exhibited greater solid matrix stresses and decreased streaming potential, all of which have implications for disc nutrition, disc biomechanics, and tissue remodeling. It was also seen that application of an electrical potential across the disc can induce fluid transport.