Influence of Fixed Charge Density Magnitude and Distribution on the Intervertebral Disc: Applications of a Poroelastic and Chemical Electric (PEACE) Model

[+] Author and Article Information
James C. Iatridis

Dept. of Mechanical Engineering, University of Vermont, Burlington, VT 05405-0084

Jeffrey P. Laible

Dept. of Civil & Environmental Engineering, University of Vermont, Burlington, VT 05405-0084

Martin H. Krag

Dept. of Orthopaedics and Rehabilitation, and Vermont Back Research Center, University of Vermont, Burlington, VT 05405-0084

J Biomech Eng 125(1), 12-24 (Feb 14, 2003) (13 pages) doi:10.1115/1.1537190 History: Received April 01, 2001; Revised August 01, 2002; Online February 14, 2003
Copyright © 2003 by ASME
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Frymoyer,  J. W., and Cats-Baril,  W. L., 1991, “An Overview of Incidences and Costs of Low Back Care,” Orthop. Clin. North Am., 22, pp. 263–271.
Rutlow,  I. M., 1986, “Orthopaedic Operations in the United States 1979–1983,” J. Bone Jt. Surg., 68A, pp. 716–719.
Antoniou,  J., Steffen,  T., Nelson,  F., Winterbottom,  N., Hollander,  A., Poole,  R. A., Aebi,  M., and Alini,  M., 1996, “The Human Lumbar Disc: Evidence for Changes in the Biosynthesis and Denaturation of the Extracellular Matrix with Growth, Maturation, Ageing, and Degeneration,” J. Clin. Invest., 98, pp. 996–1003.
Lyons,  G., Eisenstein,  S., and Sweet,  M., 1981, “Biochemical Changes in Intervertebral Disc Degeneration,” Biochim. Biophys. Acta, 673, pp. 443–453.
Urban, J. P. G., and Holm, S. H., 1986, “Intervertebral Disc Nutrition as Related to Spinal Movements and Fusion,” Tissue Nutrition and Viability, Edited by AR Hargens, New York, NY, Springer-Verlag, pp. 101–119.
Iatridis,  J. C., Setton,  L. A., Foster,  R. J., Rawlins,  B. A., Weidenbaum,  M., and Mow,  V. C., 1998, “Degeneration Affects the Anisotropic and Nonlinear Behaviors of Human Anulus Fibrosus in Compression,” J. Biomech., 31, pp. 535–544.
Nachemson,  A., 1960, “Lumbar Intradiscal Pressure,” Acta Orthop. Scand. Suppl., 43, pp. 1–104.
Panjabi,  M., Brown,  M., Lindahl,  S., Irstam,  L., and Hermens,  M., 1988, “Intrinsic Disc Pressure as a Measure of Integrity of the Lumbar Spine,” Spine, 13, pp. 913–917.
Urban,  J. P. G., and McMullin,  J. F., 1988, “Swelling Pressure of the Lumbar Intervertebral Discs: Influence of Age, Spinal Level, Composition, and Degeneration,” Spine, 13, 179–187.
Gu,  W. Y., Mao,  X. G., Rawlins,  B. A., Iatridis,  J. C., Foster,  R. J., Sun,  D. N., Weidenbaum,  M., and Mow,  V. C., 1999, “Streaming Potential of Human Lumbar Anulus Fibrosus is Anisotropic and Affected by Disc Degeneration,” J. Biomech., 32, pp. 1177–1182.
Gu,  W. Y., Mao,  X. G., Foster,  R. J., Weidenbaum,  M., Mow,  V. C., and Rawlins,  B. A., 1999, “The Anisotropic Hydraulic Permeability of Human Lumbar Anulus Fibrosus. Influence of Age, Degeneration, Direction, and Water Content,” Spine, 24, pp. 2449–2455.
Frank,  E. H., and Grodzinsky,  A. J., 1987, “Cartilage Electromechanics. I. Electrokinetic Transduction and the Effect of Electrolyte pH and Ionic Strength,” J. Biomech., 20, pp. 615–627.
Frank,  E. H., and Grodzinsky,  A. J., 1987, “Cartilage Electromechanics. II. A Continuum Model of Cartilage Electrokinetics and Correlation with Experiments,” J. Biomech., 20, pp. 629–639.
Gu,  W. Y., Lai,  W. M., and Mow,  V. C., 1993, “Transport of Fluid and Ions Through a Porous-permeable Charged-hydrated Tissue and Streaming Potential Data on Normal Bovine Articular Cartilage,” J. Biomech., 26, pp. 709–723.
Lai,  W. M., Hou,  J. S., and Mow,  V. C., 1991, “A Triphasic Theory for the Swelling and Deformation Behavior of Articular Cartilage,” ASME J. Biomech. Eng., 113, pp. 245–258.
Maroudas, A., 1979, “Physicochemical Properties of Articular Cartilage,” Adult Articular Cartilage, Edited by Freeman MAR, Kent, U.K., Pitman Medical, pp. 215–290.
Urban,  J. P. G., Maroudas,  A., Bayliss,  M. T., and Dillon,  J., 1979, “Swelling Pressures of Proteoglycans at the Concentrations Found in Cartilaginous Tissues,” Biorheology, 16, pp. 447–464.
Argoubi,  M., and Shirazi-Adl,  A., 1996, “Poroelastic Creep Response Analysis of a Lumbar Motion Segment in Compression,” J. Biomech., 29, pp. 1331–1339.
Best,  B. A., Guilak,  F., Setton,  L. A., Zhu,  W., Saed-Nejad,  F., Radcliffe,  A., Weidenbaum,  M., and Mow,  V. C., 1994, “Compressive Mechanical Properties of the Human Annulus Fibrosus and Their Relationship to Biochemical Composition,” Spine, 19, pp. 212–221.
Frijns,  A. J. H., Huyghe,  J. M., and Janssen,  J. D., 1997, “A Validation of the Quadriphasic Mixture Theory for Intervertebral Disc Tissue,” Int. J. Eng. Sci., 35, pp. 1419–1429.
Laible,  J. P., Pflaster,  D., Krag,  M. H., Simon,  B. R., and Haugh,  L. D., 1993, “A Poroelastic-swelling Finite Element Model with Application to the Intervertebral Disc,” Spine, 18, pp. 659–670.
Laible,  J. P., Pflaster,  D., Simon,  B. R., Krag,  M. H., Pope,  M. H., and Haugh,  L. D., 1994, “A Dynamic Material Parameter Estimation Procedure for Soft Tissue Using a Poroelastic Finite Element Model,” ASME J. Biomech. Eng., 116, pp. 19–29.
Simon,  B. R., Wu,  J. S., Carlton,  M. W., Evans,  J. H., and Kazarian,  L. E., 1985, “Structural Models for Human Spinal Motion Segments Based on a Poroelastic View of the Intervertebral Disc,” ASME J. Biomech. Eng., 107, pp. 327–335.
Snijders,  H., Huyghe,  J. M., and Janssen,  J. D., 1995, “Triphasic Finite Element Model for Swelling of Porous Media,” Int. J. Numer. Methods Fluids, 20, pp. 1039–1046.
Iatridis,  J. C., Setton,  L. A., Weidenbaum,  M., and Mow,  V. C., 1997, “Alterations in the Mechanical Behavior of the Human Lumbar Nucleus Pulposus with Degeneration and Aging,” J. Orthop. Res., 15, pp. 318–322.
Biot,  M. A., 1962, “Mechanics of Deformation and Acoustic Propagation in Porous Media,” J. Appl. Phys., 33, pp. 1482–1498.
Biot,  M. A., 1972, “Theory of Finite Deformation of Porous Soils,” Indiana Univ. Math. J., 21, pp. 597–620.
Simon,  B. R., 1992, “Multi-phase Poroelastic Finite Element Models for Soft Tissue Structures,” Appl. Mech. Rev., 45, pp. 191–219.
Simon,  B. R., Laible,  J. P., Pflaster,  D., Yuan,  Y., and Krag,  M., 1996, “A Poroelastic Finite Element Formulation Including Transport Swelling in Soft Tissue Structures,” ASME J. Biomech. Eng., 118, pp. 1–9.
Sun,  D. N., Gu,  W. Y., Guo,  X. E., Lai,  W. M., and Mow,  V. C., 1999, “A Mixed Finite Element Formulation of Triphasic Mechano-electrochemical Theory for Charged, Hydrated Biological Soft Tissues,” Int. J. Numer. Methods Eng., 45, pp. 1375–1402.
Huyghe,  J. M., and Janssen,  J. D., 1997, “Quadriphasic Mechanics of Swelling Incompressible Porous Media,” Int. J. Eng. Sci., 35, pp. 793–802.
Drost,  M. R., Willems,  P., Snijders,  H., Huyghe,  J. M., Janssen,  J. D., and Huson,  A., 1995, “Confined Compression of Canine Annulus Fibrosus Under Chemical and Mechanical Loads,” ASME J. Biomech. Eng., 117, pp. 390–396.
Urban,  J. P. G., Holm,  S., Maroudas,  A., and Nachemson,  A., 1982, “Nutrition of the Intervertebral Disc: Effect of Fluid Flow on Solute Transport,” Clin. Orthop. Relat. Res., 170, pp. 296–302.
Keller,  T., Spengler,  D., and Hansson,  T., 1987, “Mechanical Behavior of the Human Lumbar Spine. I. Creep Analysis During Static Compressive Loading,” J. Orthop. Res., 5, pp. 467–478.
Holm,  S., Maroudas,  A., Urban,  J. P. G., Selstam,  G., and Nachemson,  A., 1981, “Nutrition of the Intervertebral Disc: Solute Transport and Metabolism,” Connect. Tissue Res., 8, pp. 101–119.
Elliott,  D. M., and Setton,  L. A., 2001, “Anisotropic and Inhomogeneous Tensile Behavior of the Human Anulus Fibrosus: Experimental Measurement and Material Model Predictions,” ASME J. Biomech. Eng., 23, pp. 256–263.
Acaroglu,  E., Iatridis,  J. C., Setton,  L. A., Foster,  R., Mow,  V. C., and Weidenbaum,  M., 1995, “Degeneration and Aging Affect the Tensile Behavior of Human Lumbar Annulus Fibrosus,” Spine, 20, pp. 2690–2701.
Galante,  J., 1967, “Tensile Properties of the Human Lumbar Anulus Fibrosus,” Acta Orthop. Scand., 100, pp. 68–82.
Kraemer,  J., Kolditz,  D., and Gowin,  R., 1985, “Water and Electrolyte Content of Human Intervertebral Discs Under Variable Load,” Spine, 10, pp. 69–71.
Krag,  M., Seroussi,  R., Wilder,  D., and Pope,  M., 1987, “Internal Displacement Distribution from in Vitro Loading of Human Thoracic and Lumbar Spinal Motion Segments: Experimental Results and Theoretical Predictions,” Spine, 12, pp. 1001–1007.


Grahic Jump Location
Electric potential fields for (a) healthy and (b) degenerate disc slices subjected to swelling and compression loading immediately after the compressive load was applied.
Grahic Jump Location
Electric potential field with applied potential difference across the right side of the disc slice with (a) healthy and (b) degenerate fixed charge density distribution. For the healthy disc the two potentials at A and B are 0 and −10.75 mV, respectively. For the degenerate disc the two potentials at A and B are 0 and −6.3 mV, respectively.
Grahic Jump Location
Fluid (a, b) and solid (c, d) stress distributions for disc slices with healthy and degenerate fixed charge density distributions at equilibrium under compressive loading of −200,000 N/m2 . The fluid stress is equivalent to the negative of the pressure.
Grahic Jump Location
Effect of applied electrical potential on water transport (dw/dt) for (a) healthy and (b) degenerated disc slices.
Grahic Jump Location
Experimental results (circles, from Drost et al. 1995) and simulation of the PEACE model (curves a,b,c) for a 1 dimensional confined compression study of canine annulus under chemical and mechanical loading. Displacement of anulus fibrosus specimens (d=4 mm diameter, h=1 mm thick) was measured while the NaCl bath concentration c* and load P were varied in 3 stages: 1) Conditioning, c*=0.6 M,P=0.08 MPa, 2) Swelling, c*=0.2 M,P=0.08 MPa and 3) Consolidation, c*=0.2 M,P=0.20 MPa. Curves a, b and c show the PEACE simulation at h=1 mm, 0.5 mm and 0.25 mm, respectively.
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Mesh for plane stress analysis of intervertebral disc slice. The numbers of three nodes are given for reference to the time histories of the loading and fluid flow.
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Fixed charge density distribution for healthy and degenerate intervertebral discs in the sagittal plane. The experimental data was digitized from Urban & Holm, 1986. The healthy and degenerate fixed charge distribution (a) were used to generate a 2-dimensional cF field over our finite element mesh for healthy (b) and degenerate (c) discs. The constant equivalent healthy fixed charge distribution cequivF was taken as the average fixed charge density over the surface of the healthy disc and can be seen as the horizontal plane in (b).
Grahic Jump Location
Time history for the change in water content (-zeta) of the disc slice during the swelling phase and with creep loading for healthy (a) and degenerate (b) discs. The location of nodes 120, 104, and 92 are given in Fig. 2.
Grahic Jump Location
Water displacement vectors for disc slices with (a) healthy fixed charge density (cF), (b) degenerate cF, and (c) constant equivalent healthy cF. All plots are at the same scale with the maximum fluid displacement vector of wmax=0.005 m.
Grahic Jump Location
Change in water content (−ζ) for disc slices with (a) healthy, (b) degenerate, and (c) constant healthy equivalent fixed charge density distributions. Change in water content is measured after both swelling and compression stages of the experiment.




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