Reducing complexity and unidentifiability when modelling human atrial cells

Mathematical models of a cellular action potential in cardiac modelling have become increasingly complex, particularly in gating kinetics which control the opening and closing of individual ion channel currents. As cardiac models advance towards use in personalised medicine to inform clinical decision- making, it is critical to understand the uncertainty hidden in parameter estimates from their calibration to experimental data. This study applies approximate Bayesian computation to re-calibrate the gating kinetics of four ion channels in two existing human atrial cell models to their original datasets, providing a measure of uncertainty from the parameter posterior distributions. Two approaches are investigated to reduce the uncertainty present: firstly to re-calibrate the models to a more complete ‘unified’ dataset and, secondly, the use of a standardised formulation with fewer parameters to constrain. The study shows that the use of more complete datasets does not eliminate uncertainty present in parameter estimates. The standardised model, particularly for the fast sodium current, shows reduced residuals from experimental data alongside lower parameter uncertainty and improved performance. Methods All database files are the raw output from a pyABC calibration using the ion-channel-ABC Python library, as described in the corresponding research paper. Jupyter notebooks are available at the ion-channel-ABC (https://github.com/charleshouston/ion-channel-ABC) within the human-atrial folder describing how each database file was generated and how to analyse the results within.心脏建模领域中，细胞动作电位的数学模型日趋复杂，在调控单个离子通道电流启闭的门控动力学（gating kinetics）方面尤为突出。随着心脏模型逐步向辅助临床决策的个性化医疗（personalised medicine）应用演进，理解其通过实验数据校准得到的参数估计中潜藏的不确定性，已成为至关重要的研究课题。本研究采用近似贝叶斯计算（approximate Bayesian computation），对两类已有的人心房细胞模型中的4个离子通道的门控动力学进行重新校准，使其适配原始数据集，并基于参数后验分布（posterior distributions）量化不确定性。 本研究探究了两种降低现有不确定性的路径：其一为将模型重新校准至更完整的「统一」数据集；其二为采用参数更少、更易于约束的标准化公式（standardised formulation）。研究结果显示，采用更完整的数据集并无法消除参数估计中存在的不确定性。而标准化模型——尤其是针对快钠电流（fast sodium current）的模型——不仅与实验数据的残差（residuals）更低，同时参数不确定性更小，模型性能也得到了显著提升。 研究方法 所有数据库文件均为使用ion-channel-ABC Python库开展pyABC校准的原始输出，相关细节参见对应研究论文。 可在ion-channel-ABC项目的human-atrial文件夹（链接：https://github.com/charleshouston/ion-channel-ABC）中获取Jupyter笔记本（Jupyter notebook），其中详述了各数据库文件的生成流程，以及如何在其中开展结果分析。