Pant Sanjay, Corsini Chiara, Baker Catriona, Hsia Tain-Yen, Pennati Giancarlo, Vignon-Clementel Irene E
Inria Paris & Sorbonne Universités UPMC Paris 6, Laboratoire Jacques-Louis Lions, Paris, France.
Laboratory of Biological Structure Mechanics, Department of Chemistry, Materials and Chemical Engineering 'Giulio Natta', Politecnico di Milano, Milan, Italy.
J R Soc Interface. 2017 Jan;14(126). doi: 10.1098/rsif.2016.0513.
Inverse problems in cardiovascular modelling have become increasingly important to assess each patient individually. These problems entail estimation of patient-specific model parameters from uncertain measurements acquired in the clinic. In recent years, the method of data assimilation, especially the unscented Kalman filter, has gained popularity to address computational efficiency and uncertainty consideration in such problems. This work highlights and presents solutions to several challenges of this method pertinent to models of cardiovascular haemodynamics. These include methods to (i) avoid ill-conditioning of the covariance matrix, (ii) handle a variety of measurement types, (iii) include a variety of prior knowledge in the method, and (iv) incorporate measurements acquired at different heart rates, a common situation in the clinic where the patient state differs according to the clinical situation. Results are presented for two patient-specific cases of congenital heart disease. To illustrate and validate data assimilation with measurements at different heart rates, the results are presented on a synthetic dataset and on a patient-specific case with heart valve regurgitation. It is shown that the new method significantly improves the agreement between model predictions and measurements. The developed methods can be readily applied to other pathophysiologies and extended to dynamical systems which exhibit different responses under different sets of known parameters or different sets of inputs (such as forcing/excitation frequencies).
在心血管建模中，反问题对于个体患者评估变得越来越重要。这些问题需要根据在临床中获取的不确定测量值来估计患者特定的模型参数。近年来，数据同化方法，尤其是无迹卡尔曼滤波器，在解决此类问题的计算效率和不确定性考虑方面受到了广泛关注。这项工作突出并提出了解决该方法在心血管血流动力学模型中面临的几个挑战的方案。这些挑战包括：（i）避免协方差矩阵的病态；（ii）处理各种测量类型；（iii）在方法中纳入各种先验知识；（iv）纳入在不同心率下获取的测量值，这在临床中是常见情况，即患者状态会根据临床情况而有所不同。给出了两个先天性心脏病患者特定病例的结果。为了用不同心率下的测量值说明和验证数据同化，结果展示在一个合成数据集和一个有心脏瓣膜反流的患者特定病例上。结果表明，新方法显著提高了模型预测与测量值之间的一致性。所开发的方法可以很容易地应用于其他病理生理学情况，并扩展到在不同已知参数集或不同输入集（如强迫/激励频率）下表现出不同响应的动态系统。
