Sélard Eric, Shirazi-Adl A, Urban Jill P G
Department of Mechanical Engineering, Ecole Polytechnique, Station centre-ville, Montreal, Quebec, Canada H3C 3A7.
Spine (Phila Pa 1976). 2003 Sep 1;28(17):1945-53; discussion 1953. doi: 10.1097/01.BRS.0000087210.93541.23.
The diffusion of small nutrients in the intervertebral human disc was examined using a finite element model.
To investigate nutrient transport into the disc using a numerical approach.
The intervertebral disc is the largest avascular tissue in the body. Nutrients necessary for cellular survival diffuse from the blood supply around the disc margins to the cells. Limited analytical studies have been performed and compared with measurements. However, the studies have only considered supply through the center of the nucleus and have only examined single solutes. A more sophisticated model is required to investigate the solute supply.
An axisymmetric finite element model has been created to study the transport of three solutes, i.e., oxygen, glucose, and lactate, using nonlinear consumption-concentration and production-concentration rates. For each of them, data for the consumption/production rate, diffusivity, and concentration in the blood were taken from experimental measurements and used in the model. The effect of varying disc height, exchange area with the blood supply, solute consumption rates, and diffusivities was investigated.
The model predicted that concentrations of oxygen and glucose, which are consumed by cells, fell towards the disc center. Concentration levels decreased with a decrease in fractional exchange area and diffusivity, or with an increase in disc height and consumption rate. In contrast, the concentration of lactate, produced by the cells, was highest in the center and fell towards the disc-blood vessel interface. The absolute values of concentrations were in agreement with available measurements in vivo and those computed by few available analytical models, indicating the reliability of the finite element simulations.
Finite element methods can be used to predict concentration gradients of solutes throughout the disc in relation to changes in disc and endplate morphology, disc properties, and cellular activities. This study provides a foundation for investigating the effect of load-induced changes or effects of changes in cellular metabolism on disc nutritional supply.
使用有限元模型研究人体椎间盘内小营养物质的扩散。
采用数值方法研究营养物质向椎间盘内的转运。
椎间盘是人体最大的无血管组织。细胞存活所需的营养物质从椎间盘边缘周围的血液供应处扩散至细胞。已开展的有限分析研究并与测量结果进行了比较。然而，这些研究仅考虑了通过髓核中心的供应，且仅研究了单一溶质。需要一个更复杂的模型来研究溶质供应情况。
创建了一个轴对称有限元模型，以研究三种溶质（即氧气、葡萄糖和乳酸）的转运，使用非线性消耗 - 浓度和生成 - 浓度速率。对于每种溶质，消耗/生成速率、扩散系数和血液中浓度的数据均取自实验测量值并用于模型。研究了椎间盘高度变化、与血液供应的交换面积、溶质消耗速率和扩散系数的影响。
该模型预测，被细胞消耗的氧气和葡萄糖浓度向椎间盘中心下降。浓度水平随着分数交换面积和扩散系数的降低，或随着椎间盘高度和消耗速率的增加而降低。相比之下，细胞产生的乳酸浓度在中心最高，向椎间盘 - 血管界面下降。浓度的绝对值与体内现有测量值以及少数可用分析模型计算的值一致，表明有限元模拟的可靠性。
有限元方法可用于预测整个椎间盘中溶质的浓度梯度，这些梯度与椎间盘和终板形态、椎间盘特性及细胞活动的变化有关。本研究为研究负荷引起的变化或细胞代谢变化对椎间盘营养供应的影响提供了基础。
