Aniort Julien, Chupin Laurent, Cîndea Nicolae
Service de nephrologie, dialyse et tranplantation rénale. Centre Hospitalier Universitaire Gabriel Montpied, Clermont-Ferrand, France.
Université Clermont Auvergne, Laboratoire de Mathématiques Blaise Pascal CNRS-UMR, Aubière Cedex, France.
Math Med Biol. 2018 Mar 16;35(suppl_1):87-120. doi: 10.1093/imammb/dqx013.
Calcium has two important roles in haemodialysis. It participates in the activation of blood coagulation and calcium intakes have a major impact on patient mineral and bone metabolism. The aim of this article is to propose a mathematical model for calcium ions concentration in a dialyzer during haemodialysis using a citrate dialysate. The model is composed of two elements. The first describes the flows of blood and dialysate in a dialyzer fibre. It was obtained by asymptotic analysis and takes into account the anisotropy of the fibres forming a dialyzer. Newtonian and non-Newtonian blood rheologies were tested. The second part of the model predicts the evolution of the concentration of five chemical species present in these fluids. The fluid velocity field drives the convective part of a convection-reaction-diffusion system that models the exchange of free and complexed calcium. We performed several numerical experiments to calculate the free calcium concentration in the blood in a dialyzer using dialysates with or without citrate. The choice of blood rheology had little effect on the fluid velocity field. Our model predicts that only a citrate based dialysate without calcium can decrease free calcium concentration at the blood membrane interface low enough to inhibit blood coagulation. Moreover for a given calcium dialysate concentration, adding citrate to the dialysate decreases total calcium concentration in the blood at the dialyzer outlet. This decrease of the calcium concentration can be compensated by infusing in the dialyzed blood a quantity of calcium computed from the model.
钙在血液透析中具有两个重要作用。它参与血液凝固的激活，并且钙的摄入量对患者的矿物质和骨代谢有重大影响。本文的目的是提出一种使用柠檬酸盐透析液的血液透析过程中透析器内钙离子浓度的数学模型。该模型由两个部分组成。第一部分描述了透析器纤维内血液和透析液的流动。它是通过渐近分析得到的，并考虑了构成透析器的纤维的各向异性。对牛顿和非牛顿血液流变学进行了测试。模型的第二部分预测了这些流体中存在的五种化学物质浓度的变化。流体速度场驱动了一个对流 - 反应 - 扩散系统的对流部分，该系统模拟了游离钙和络合钙的交换。我们进行了几个数值实验，以计算使用含或不含柠檬酸盐的透析液时透析器内血液中的游离钙浓度。血液流变学的选择对流体速度场影响很小。我们的模型预测，只有不含钙的基于柠檬酸盐的透析液才能将血膜界面处的游离钙浓度降低到足以抑制血液凝固的程度。此外，对于给定的钙透析液浓度，向透析液中添加柠檬酸盐会降低透析器出口处血液中的总钙浓度。钙浓度的这种降低可以通过向透析后的血液中注入根据模型计算出的一定量的钙来补偿。
