Mathematical models can provide useful insights explaining behavior observed in experimental data; however, rigorous analysis is needed to select a subset of model parameters that can be informed by available data. Here we present a method to estimate an identifiable set of parameters based on baseline left ventricular pressure and volume time series data. From this identifiable subset, we then select, based on current understanding of cardiovascular control, parameters that vary in time in response to blood withdrawal, and estimate these parameters over a series of blood withdrawals. These time-varying parameters are first estimated using piecewise linear splines minimizing the mean squared error between measured and computed left ventricular pressure and volume data over four consecutive blood withdrawals. As a final step, the trends in these splines are fit with empirical functional expressions selected to describe cardiovascular regulation during blood withdrawal. Our analysis at baseline found parameters representing timing of cardiac contraction, systemic vascular resistance, and cardiac contractility to be identifiable. Of these parameters, vascular resistance and cardiac contractility were varied in time. Data used for this study were measured in a control Sprague-Dawley rat. To our knowledge, this is the first study to analyze the response to multiple blood withdrawals both experimentally and theoretically, as most previous studies focus on analyzing the response to one large blood withdrawal. Results show that during each blood withdrawal both systemic vascular resistance and contractility decrease acutely and partially recover, and they decrease chronically across the series of blood withdrawals.

中文翻译：

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应对多种出血的心血管调节：分析和参数估计。

数学模型可以提供有用的见解，解释实验数据中观察到的行为。但是，需要进行严格的分析以选择可以由可用数据告知的模型参数的子集。在这里，我们提出了一种基于基线左心室压力和体积时间序列数据来估计可识别参数集的方法。然后，根据当前对心血管控制的认识，从这个可识别的子集中选择随抽血而变化的参数，并估算一系列抽血的参数。首先使用分段线性样条估计这些随时间变化的参数，这些样条最小化在连续四次抽血时测量和计算的左心室压力和体积数据之间的均方误差。最后一步 这些样条曲线的趋势与选择用来描述抽血期间心血管调节的经验功能表达相吻合。我们在基线时的分析发现，可以确定代表心脏收缩时机，全身血管阻力和心脏收缩力的参数。在这些参数中，血管阻力和心脏收缩力随时间变化。本研究使用的数据在对照组Sprague-Dawley大鼠中进行测量。据我们所知，这是第一项在实验和理论上分析对多次采血的反应的研究，因为大多数先前的研究集中在分析对一次大采血的反应。结果显示，在每次抽血期间，全身血管阻力和收缩力均会急剧下降并部分恢复，