Computation of coupled diffusion of oxygen, glucose and lactic acid in an intervertebral disc.

The present numerical study aims to investigate the disc nutrition and factors affecting it by evaluating the concentrations of oxygen, glucose and lactic acid in the disc while accounting for the coupling between these species via the pH level in the tissue and the nonlinear concentration-consumption (for glucose and oxygen) and concentration-production (for lactate) relations. The effects of changes in the endplate exchange area (EA) adjacent to the nucleus or the inner annulus for the transport of nutrients and in the disc geometry as well as tissue diffusivities under static compression loading on species concentrations are also studied. Moreover, alterations in solute diffusion following a central endplate fracture are investigated. An axisymmetric geometry with four distinct regions is considered. Supply sources are assumed at the outer annulus periphery and disc endplates. Coupling between different solutes, pH level, endplate disruptions (calcifications and fractures) and mechanical loads substantially influenced the distribution of nutrients throughout the disc as well as the magnitude and location of critical concentrations; maximum for the lactic acid and minimum for oxygen and glucose. In cases with loss of endplate permeability and/or disruptions therein, as well as changes in geometry and fall in diffusivity associated with fluid expression, the nutrient concentrations could fall to levels inadequate to maintain cellular activity or viability, thus initiating or accelerating disc degeneration.

[1]  V. Duance,et al.  Biology of the Intervertebral Disc , 2002 .

[2]  S Holm,et al.  Nutrition of the intervertebral disc: effect of fluid flow on solute transport. , 1982, Clinical orthopaedics and related research.

[3]  E C Teo,et al.  Poroelastic Analysis of Lumbar Spinal Stability in Combined Compression and Anterior Shear , 2004, Journal of spinal disorders & techniques.

[4]  Andrzej Przybyla,et al.  Outer annulus tears have less effect than endplate fracture on stress distributions inside intervertebral discs: relevance to disc degeneration. , 2006, Clinical biomechanics.

[5]  S. Roberts,et al.  The cartilage end‐plate and intervertebral disc in scoliosis: Calcification and other sequelae , 1993, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[6]  S Holm,et al.  Nutrition of the intervertebral disk. An in vivo study of solute transport. , 1977, Clinical orthopaedics and related research.

[7]  A. Ejeskär,et al.  Oxygen tension measurements in the intervertebral disc. A methodological and experimental study. , 1979, Upsala journal of medical sciences.

[8]  B. Peng,et al.  [The relationship between cartilage end-plate calcification and disc degeneration: an experimental study]. , 1999, Zhonghua wai ke za zhi [Chinese journal of surgery].

[9]  A. Nachemson,et al.  Carbohydrate metabolism and concentration profiles of solutes in the canine lumbar intervertebral disc. , 1982, Acta physiologica Scandinavica.

[10]  Adams Ma,et al.  Prolapsed Intervertebral Disc: A Hyperflexion Injury , 1982 .

[11]  T. Shibata,et al.  Morphologic Differences of the Vascular Buds in the Vertebral Endplate: Scanning Electron Microscopic Study , 1996, Spine.

[12]  J. Urban,et al.  The measurement of fixed charged density in the intervertebral disc , 1979 .

[13]  O. Perey,et al.  Fracture of the vertebral end-plate in the lumbar spine; an experimental biochemical investigation. , 1957, Acta orthopaedica Scandinavica. Supplementum.

[14]  S Holm,et al.  Nutrition of the intervertebral disc: solute transport and metabolism. , 1981, Connective tissue research.

[15]  C. Hamanishi,et al.  Schmorl's nodes on magnetic resonance imaging. Their incidence and clinical relevance. , 1994, Spine.

[16]  B. Grignon,et al.  The structure of the cartilaginous end-plates in elder people , 2000, Surgical and Radiologic Anatomy.

[17]  J. Urban,et al.  Evidence for a negative Pasteur effect in articular cartilage. , 1997, The Biochemical journal.

[18]  S. Bibby,et al.  Effect of nutrient deprivation on the viability of intervertebral disc cells , 2004, European Spine Journal.

[19]  N. Eie.  Load capacity of the low back. , 1966, Journal of the Oslo city hospitals.

[20]  J. Urban,et al.  Effects of low oxygen concentrations and metabolic inhibitors on proteoglycan and protein synthesis rates in the intervertebral disc , 1999, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[21]  J. Zerwekh,et al.  Biochemical changes associated with the symptomatic human intervertebral disk. , 1993, Clinical orthopaedics and related research.

[22]  N. Boos,et al.  The Course of Macroscopic Degeneration in the Human Lumbar Intervertebral Disc , 2006, Spine.

[23]  Keita Ito,et al.  2004 Young Investigator Award Winner: Vertebral Endplate Marrow Contact Channel Occlusions and Intervertebral Disc Degeneration , 2005, Spine.

[24]  A. Nachemson,et al.  In vitro diffusion of dye through the end-plates and the annulus fibrosus of human lumbar inter-vertebral discs. , 1970, Acta orthopaedica Scandinavica.

[25]  Keita Ito,et al.  Fluid flow and convective transport of solutes within the intervertebral disc. , 2004, Journal of biomechanics.

[26]  A. Shirazi-Adl,et al.  Finite–Element Simulation of Changes in the Fluid Content of Human Lumbar Discs: Mechanical and Clinical Implications , 1992, Spine.

[27]  A R Hargens,et al.  Intervertebral disc nutrition. Diffusion versus convection. , 1986, Clinical orthopaedics and related research.

[28]  H. Junghanns,et al.  The human spine in health and disease , 1971 .

[29]  A. Nachemson,et al.  Factors involved in the nutrition of the human lumbar intervertebral disc: cellularity and diffusion of glucose in vitro. , 1975, Journal of anatomy.

[30]  R. Benn,et al.  Vertebral end-plate lesions (Schmorl's nodes) in the dorsolumbar spine. , 1976, Annals of the rheumatic diseases.

[31]  A Shirazi-Adl,et al.  On the fibre composite material models of disc annulus--comparison of predicted stresses. , 1989, Journal of biomechanics.

[32]  K. Huebner.  The finite element method for engineers , 1975 .

[33]  S. Rajasekaran,et al.  ISSLS Prize Winner: A Study of Diffusion in Human Lumbar Discs: A Serial Magnetic Resonance Imaging Study Documenting the Influence of the Endplate on Diffusion in Normal and Degenerate Discs , 2004, Spine.

[34]  S. A. Shirazi-Adl,et al.  Nutrient supply and intervertebral disc metabolism. , 2006, The Journal of bone and joint surgery. American volume.

[35]  Robert Roaf,et al.  A STUDY OF THE MECHANICS OF SPINAL INJURIES , 1960 .

[36]  Christoph Weiler,et al.  Classification of Age-Related Changes in Lumbar Intervertebral Discs: 2002 Volvo Award in Basic Science , 2002, Spine.

[37]  Rolander Sd,et al.  Deformation and fracture of the lumbar vertebral end plate. , 1975 .

[38]  S. Bibby,et al.  Cell Viability in Scoliotic Discs in Relation to Disc Deformity and Nutrient Levels , 2002, Spine.

[39]  R. Cailliet,et al.  Vertebral End-Plate Changes With Aging of Human Vertebrae , 1982, Spine.

[40]  Ruth M Ripley,et al.  Metabolism of the Intervertebral Disc: Effects of Low Levels of Oxygen, Glucose, and pH on Rates of Energy Metabolism of Bovine Nucleus Pulposus Cells , 2005, Spine.

[41]  G. Andersson.  Epidemiological features of chronic low-back pain , 1999, The Lancet.

[42]  S. Ullberg,et al.  Uptake of S35 in the intervertebral discs after injection of S35-sulphate. An autoradiographic study. , 1960, Acta orthopaedica Scandinavica.

[43]  A Shirazi-Adl,et al.  Analysis of nonlinear coupled diffusion of oxygen and lactic acid in intervertebral discs. , 2005, Journal of biomechanical engineering.

[44]  M. Adams,et al.  Internal Intervertebral Disc Mechanics as Revealed by Stress Profilometry , 1992, Spine.

[45]  F. Hartmann,et al.  Biomechanical behavior of human intervertebral discs subjected to long lasting axial loading. , 1984, Biorheology.

[46]  S. Holm,et al.  Factors Influencing Oxygen Concentration Gradients in the Intervertebral Disc: A Theoretical Analysis , 1991, Spine.

[47]  A Shirazi-Adl,et al.  Poroelastic creep response analysis of a lumbar motion segment in compression. , 1996, Journal of biomechanics.

[48]  J. Urban,et al.  The role of the physicochemical environment in determining disc cell behaviour. , 2002, Biochemical Society transactions.

[49]  C. Peter Winlove,et al.  Oxygen and Lactate Concentrations Measured in Vivo in the Intervertebral Discs of Patients With Scoliosis and Back Pain , 1998, Spine.

[50]  S. Roberts,et al.  Transport Properties of the Human Cartilage Endplate in Relation to Its Composition and Calcification , 1996, Spine.

[51]  P Brinckmann,et al.  Injury of the Annulus Fibrosus and Disc Protrusions: An In Vitro Investigation on Human Lumbar Discs , 1986, Spine.

[52]  P. Farrell,et al.  Estimation of the permeability of cellulosic membranes from solute dimensions and diffusivities. , 1973, Journal of biomedical materials research.

[53]  T. Brown,et al.  Some mechanical tests on the lumbosacral spine with particular reference to the intervertebral discs; a preliminary report. , 1957, The Journal of bone and joint surgery. American volume.

[54]  S. Roberts,et al.  Biochemical and Structural Properties of the Cartilage End-Plate and its Relation to the Intervertebral Disc , 1989, Spine.

[55]  G. de Vahl Davis,et al.  The Method of the False Transient for the Solution of Coupled Elliptic Equations , 1973 .

[56]  A Shirazi-Adl,et al.  Finite Element Study of Nutrient Diffusion in the Human Intervertebral Disc , 2003, Spine.

[57]  M. Jayson,et al.  The Lumbar Spine and Back Pain , 1993 .

[58]  S. Roberts,et al.  Proteoglycan synthesis in the intervertebral disk nucleus: the role of extracellular osmolality. , 1997, The American journal of physiology.

[59]  Keita Ito,et al.  Correlation of radiographic and MRI parameters to morphological and biochemical assessment of intervertebral disc degeneration , 2005, European Spine Journal.