Endplate Permeability Regulates Nutrient Supply and Cell Population in Intervertebral Discs: A Cell Viability Model Study

INTRODUCTION The cells of the largest avascular tissues, the discs of the spinal column, responsible for making and maintaining the extracellular matrix, are supplied with essential nutrients by diffusion from the blood supply through mainly the cartilaginous endplates (CEP) and disc tissue. As disc cells use oxygen and glucose and produce lactic acid, concentration gradients develop depending on the balance between the rate of transport on one hand and cell population and activity on the other. Decrease in transport rate or increase in cellular activity may lead to conditions where nutrient concentrations fall too low to support viable cells; indeed cell culture analogs of the disc have demonstrated that the viable cell population density is limited by nutritional constraints [1]. Calcification of the CEP seen in aging, scoliosis and degenerate discs, limits penetration of nutrients into the disc and removal of metabolic wastes from it [2]. The present computational study aims for the first time to investigate the effect of gradual blockage of CEP on nutrient supply and on cell population by introducing novel cell viabilitynutritional demand relationships that govern cell activity and population. METHODS A uniaxial model of an in vitro cell culture study [1] is initially investigated to validate the cell viability-nutritional demand relations. In accordance with the diffusion chamber used in measurements, a 26mm long model of an agarose gel embedding bovine nucleus cells at 2, 4, 8 and 16 million cells/ml was supplied at both ends with 21% oxygen and 5 mM glucose at pH 7.4. Subsequently, an axisymmetric model of a lumbar disc [3] with distinct regions (CEP, nucleus, inner/outer annuli) and properties was used. Initial cell density in annulus varied linearly along the radius from 4 million cells/ml in the nucleus to 16 million cells/ml at the outer periphery. The nonlinear equations governing the diffusion of oxygen and lactate were coupled via tissue pH which varied depending on the lactate concentration [4]. Consumption/production rates of species were evaluated based on the cell density in each region. The ratio between lactate production and glucose consumption was taken as 2.0 [4]. Supply and uptake sources were taken at the outer annulus periphery and CEP. The effects on metabolite concentrations and cell population of gradual reduction in endplate permeability (exchange area) were investigated by varying the diffusivities at both CEPs from 100% (fully permeable) to as low as 1%. The program COMSOL was used for these coupled nonlinear analyses. The effect of nutrient supply on cell viability was introduced by initiating cell death at values of 0.5 mM for glucose, 3 kPa for oxygen and 6.8 for pH. All cells died as these values reached as low as of 0.2 mM, 0 kPa and 6.4, respectively. Analyses were repeated till a convergent solution in which the cell population was in equilibrium with available solute concentrations according to the foregoing viability relations. RESULTS Cell viability profiles in the diffusion chamber agreed with measurements and demonstrated increase in cell death at higher cell densities and further away from the supply sources (Fig. 1a). The viable distance from supply sources with a minimum cell survivorship of 95% diminished with cell density (Fig. 1b). In the disc model, the critical zone with minimum oxygen and glucose concentrations and maximum lactic acid occurred in the nucleus at disc mid-height. Solute concentrations were markedly influenced by changes in the CEP exchange area (Fig. 2). Without any constitutive equations governing cell viability (cases with “wo”), glucose concentrations fell to negative values when the CEP diffusivity dropped below ~25%. Inclusion of the cell viability-nutrient supply relations, however, automatically resolved such unrealistic conditions by regulating cell populations in the affected areas. Cell death was initiated as CEP permeability <30% and occurred primarily in the nucleus (Fig. 3 and Table 1). Foregoing results were obtained with the viability-demand criterion for the glucose with/without pH level. Inclusion of the oxygen criterion, however, increased the cell death at all regions and CEP exchange areas (results not presented). DISCUSSION This was a novel attempt to incorporate cell death into diffusionreaction model of nutrient transport into the intervertebral disc; cell viability-nutrient supply relationships were considered to regulate cell population. In agreement with earlier in vitro studies [1], predictions demonstrated that concentrations of nutrients have profound effects on cell population. Cells remained alive at very low densities but died away from the nutrient supply when the cell density increased. In the current work, results were presented that considered the regulation of cell population only by glucose concentration and pH level. Consideration of oxygen concentration had a more severe effect on cell population. Glucose has, however, been recognized as the critical nutrient as the disc cells could survive for days even in absence of oxygen [1]. The CEP in human discs plays a significant role by controlling solute transport in and out of the discs and hence by governing gradients of nutrients within the disc. We found that as the exchange area across the CEP fell below 30% with consequent fall in nutrient concentrations at the disc centre in particular, disc cell death increased in an exponential manner. The nucleus centre being farthest away from supply sources was the area most affected (Fig. 3). Hence, the viable cell population of the disc was governed by CEP exchange area. Such mechanisms are likely to operate in vivo; nutrition shortfall because of drop in CEP exchange area and increase in disc height are possible causes of the disappearance of notochordal cells in the growing human disc [5]. Perturbations in transport across the CEPs because of ageing, fractures and degeneration or increases in cellular nutritional demands as a result of growth factor treatment could all adversely influence the viability of disc cells and, hence, the intervertebral disc function. ACKNOWELEDGEMENT: Supported by the NSERC-Canada and the EU FP7 (grant agreement no. HEALTH-F2-2008-201626). REFERENCES: [1] Horner and Urban, Spine 26:2543-9, 2001 [2] Rajasekaran et al, JMRI 25:410-8, 2007 [3] Mokhbi-Soukane et al, J Biomech 40:2645–54, 2007 [4] Bibby et al, Spine 30:487-96, 2005 [5] Guehring et al, Arthritis & Rheumatism 60:1026-34, 2009. Table 1. Cell death at different disc regions as % of initial population CEPs permeability NP CEPs IA OA Total 1% 82 36 2 29 5% 69 2 19 10% 41 11 15% 22 6 20% 11 3