Fogliardi R, Di Donfrancesco M, Burattini R
Department of Electronics and Automatica, University of Ancona, Italy.
Am J Physiol. 1996 Dec;271(6 Pt 2):H2661-8. doi: 10.1152/ajpheart.1996.271.6.H2661.
The three-element windkessel model incorporating a constant compliance (model A) was compared with two nonlinear versions of the same model (models B1 and B2) incorporating a pressure-dependent compliance. The aim was to test whether nonlinear elasticity yielded better model behavior in describing ascending aortic pressure-flow relationships and interpreting the physical properties of the arterial system. Exponential and bell-shaped compliance vs. pressure curves were assumed in models B1 and B2, respectively. To test these models, we used measurements of ascending aortic pressure and flow from three dogs under a wide variety of hemodynamic states obtained by administering vasoactive drugs and by pacing the heart. These data involved pressure waves with and without an evident oscillation during diastole. Model parameters were estimated by fitting experimental and model-predicted ascending aortic pressures. Our results indicated that only models A and B1 were identifiable. Fits to ascending aortic pressure obtained from model B1 were significantly better than fits obtained from model A. However, 1) the accuracy of parameter estimates, as judged from parameter estimation error analysis, was better in model A than in model B1, 2) the estimates of characteristic parameters of the compliance vs. pressure relation in model B1 were inconsistent with expected physiological trends of this relation, and 3) model B1 did not improve the approximation of diastolic pressure in the presence of an evident oscillation. We conclude that, even in the presence of better data fit, the nonlinear three-element windkessel cannot be preferred over the traditional linear version of this model.
将包含恒定顺应性的三元风箱模型（模型A）与包含压力依赖性顺应性的同一模型的两个非线性版本（模型B1和B2）进行了比较。目的是测试非线性弹性在描述升主动脉压力-流量关系和解释动脉系统物理特性方面是否产生更好的模型行为。分别在模型B1和B2中假设了指数型和钟形的顺应性与压力曲线。为了测试这些模型，我们使用了三只狗在通过施用血管活性药物和起搏心脏获得的各种血流动力学状态下的升主动脉压力和流量测量值。这些数据涉及舒张期有无明显振荡的压力波。通过拟合实验和模型预测的升主动脉压力来估计模型参数。我们的结果表明只有模型A和B1是可识别的。模型B1对升主动脉压力的拟合明显优于模型A的拟合。然而，1）从参数估计误差分析判断，模型A中参数估计的准确性优于模型B1，2）模型B1中顺应性与压力关系的特征参数估计与该关系的预期生理趋势不一致，3）在存在明显振荡的情况下，模型B1没有改善舒张压的近似值。我们得出结论，即使存在更好的数据拟合，非线性三元风箱模型也不能优于该模型的传统线性版本。
