Flores-Gerónimo Joaquín, Keramat Alireza, Alastruey Jordi, Zhang Yuanting
Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong.
Department of Biomedical Engineering, School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK.
Int J Numer Method Biomed Eng. 2024 Dec;40(12):e3867. doi: 10.1002/cnm.3867. Epub 2024 Sep 6.
The Windkessel (WK) model is a simplified mathematical model used to represent the systemic arterial circulation. While the WK model is useful for studying blood flow dynamics, it suffers from inaccuracies or uncertainties that should be considered when using it to make physiological predictions. This paper aims to develop an efficient and easy-to-implement uncertainty quantification method based on a local gradient-based formulation to quantify the uncertainty of the pressure waveform resulting from aleatory uncertainties of the WK parameters and flow waveform. The proposed methodology, tested against Monte Carlo simulations, demonstrates good agreement in estimating blood pressure uncertainties due to uncertain Windkessel parameters, but less agreement considering uncertain blood-flow waveforms. To illustrate our methodology's applicability, we assessed the aortic pressure uncertainty generated by Windkessel parameters-sets from an available in silico database representing healthy adults. The results from the proposed formulation align qualitatively with those in the database and in vivo data. Furthermore, we investigated how changes in the uncertainty of the Windkessel parameters affect the uncertainty of systolic, diastolic, and pulse pressures. We found that peripheral resistance uncertainty produces the most significant change in the systolic and diastolic blood pressure uncertainties. On the other hand, compliance uncertainty considerably modifies the pulse pressure standard deviation. The presented expansion-based method is a tool for efficiently propagating the Windkessel parameters' uncertainty to the pressure waveform. The Windkessel model's clinical use depends on the reliability of the pressure in the presence of input uncertainties, which can be efficiently investigated with the proposed methodology. For instance, in wearable technology that uses sensor data and the Windkessel model to estimate systolic and diastolic blood pressures, it is important to check the confidence level in these calculations to ensure that the pressures accurately reflect the patient's cardiovascular condition.
风箱（WK）模型是一种用于表示体循环动脉系统的简化数学模型。虽然WK模型对于研究血流动力学很有用，但在使用它进行生理预测时，存在一些不准确或不确定的因素需要考虑。本文旨在基于局部梯度公式开发一种高效且易于实现的不确定性量化方法，以量化由于WK参数和血流波形的随机不确定性导致的压力波形的不确定性。所提出的方法与蒙特卡罗模拟进行了对比测试，结果表明，在估计由于风箱参数不确定导致的血压不确定性方面，该方法具有良好的一致性，但在考虑不确定的血流波形时，一致性较差。为了说明我们方法的适用性，我们评估了来自一个代表健康成年人的可用计算机模拟数据库中风箱参数集产生的主动脉压力不确定性。所提出公式的结果在定性上与数据库中的结果以及体内数据一致。此外，我们研究了风箱参数不确定性的变化如何影响收缩压、舒张压和脉压的不确定性。我们发现，外周阻力不确定性在收缩压和舒张压不确定性方面产生的变化最为显著。另一方面，顺应性不确定性会显著改变脉压标准差。所提出的基于展开的方法是一种将风箱参数的不确定性有效地传播到压力波形的工具。风箱模型的临床应用取决于在存在输入不确定性的情况下压力的可靠性，而所提出的方法可以有效地对此进行研究。例如，在使用传感器数据和风箱模型来估计收缩压和舒张压的可穿戴技术中，检查这些计算中的置信水平以确保压力准确反映患者的心血管状况非常重要。
