A unidimensional diffusion model applied to uremic toxin kinetics in haemodiafiltration treatments.

IF 0.8 4区 数学 Q4 BIOLOGY Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2019-06-13 DOI:10.1093/imammb/dqy008
Miquel Gomez, Francisco Maduell
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引用次数: 0

Abstract

Kinetic modelling in haemodialysis is usually based upon the resolution of volume-defined compartment models. The interaction among these compartments is described by purely diffusive processes. In this paper we present an alternative kinetic model for uremic toxins in post-dilutional haemodiafiltration treatments by means of a unidimensional diffusion equation. A wide range of solutes such as urea, creatinine, $\beta _{2}$-microglobulin, myoglobin and prolactin were studied by imposing appropriate boundary and initial conditions in a virtual [0,1] domain. The diffusivity along the domain and the extraction rate at the dialyser are the kinetic parameters which were fitted by least-squares for every studied solute. The accuracy of the presented volumeless model as well as the behavior of the proposed kinetic parameters could be an alternative to the compartment description for a variety of molecular weight uremic toxins undergoing different treatment configurations.

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一维扩散模型应用于血液滤过处理中的尿毒症毒素动力学。
血液透析的动力学建模通常是基于体积定义的室模型的分辨率。这些隔室之间的相互作用用纯粹的扩散过程来描述。本文用一维扩散方程提出了稀释后血液滤过处理中尿毒症毒素的另一种动力学模型。通过在虚[0,1]结构域中施加适当的边界和初始条件,研究了尿素、肌酐、β _{2}$-微球蛋白、肌红蛋白和泌乳素等多种溶质。对所研究的溶质,用最小二乘拟合得到沿区域扩散率和在透析器上的萃取速率的动力学参数。所提出的无体积模型的准确性以及所提出的动力学参数的行为可以替代对各种分子量尿毒症毒素进行不同处理配置的隔室描述。
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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