Department of Information Technology, Uppsala University, Uppsala, Sweden.
Front Endocrinol (Lausanne). 2022 Nov 1;13:957993. doi: 10.3389/fendo.2022.957993. eCollection 2022.
This work considers the estimation of impulsive time series pertaining to biomedical systems and, in particular, to endocrine ones. We assume a signal model in the form of the output of a continuous linear time-invariant system driven by a sequence of instantaneous impulses, which concept is utilized here, in particular, for modeling of the male reproductive hormone axis. An estimation method to identify the impulsive sequence and the continuous system dynamics from sampled measurements of the output is proposed. Hinging on thorough mathematical analysis, the method improves upon a previously developed least-squares algorithm by resolving the trade-off between model fit and input sparsity, thus removing the need for manual tuning of user-defined estimation algorithm parameters. Experiments with synthetic data and Markov chain Monte-Carlo estimation demonstrate the viability of the proposed method, but also indicate that measurement noise renders the estimation problem ill-posed, as multiple estimates along a curve in the parameter space yield similar fits to data. The method is furthermore applied to clinical luteinizing hormone data collected from healthy males and, for comparability, one female, with similar results. Comparison between the estimated and theoretical elimination rates, as well as simulation of the estimated models, demonstrate the efficacy of the method. The sensitivity of the impulse distribution to the estimated elimination rates is investigated on a subject-specific data subset, revealing that the input sequence and elimination rate estimates can be interdependent. The dose-dependent effect of a selective gonadotropin releasing hormone receptor antagonist on the frequency and weights of the estimated impulses is also analyzed; a significant impact of the medication on the impulse weights is confirmed. To demonstrate the feasibility of the estimation approach for other hormones with pulsatile secretion, the modeling of cortisol data sets collected from three female adolescents was performed.
这项工作考虑了生物医学系统中脉冲时间序列的估计，特别是内分泌系统。我们假设信号模型为连续线性时不变系统的输出，由一系列瞬时脉冲驱动，该概念特别用于建模男性生殖激素轴。提出了一种从输出的采样测量中识别脉冲序列和连续系统动态的估计方法。基于彻底的数学分析，该方法通过解决模型拟合和输入稀疏之间的权衡来改进先前开发的最小二乘算法，从而无需手动调整用户定义的估计算法参数。合成数据和马尔可夫链蒙特卡罗估计的实验证明了所提出方法的可行性，但也表明测量噪声使估计问题变得不适定，因为参数空间中的曲线多个估计值与数据具有相似的拟合度。该方法还应用于从健康男性和一名女性收集的临床黄体生成素数据，为了可比性，结果相似。对估计模型和理论消除率进行比较，以及对估计模型进行模拟，证明了该方法的有效性。在一个特定于个体的数据集上研究了脉冲分布对估计消除率的敏感性，结果表明输入序列和消除率估计值可能相互依赖。还分析了选择性促性腺激素释放激素受体拮抗剂对估计脉冲频率和权重的剂量依赖性影响，证实了药物对脉冲权重的显著影响。为了证明该估计方法用于其他具有脉冲分泌的激素的可行性，对从三名女性青少年收集的皮质醇数据集进行了建模。
