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Multiscale analysis of heart rate dynamics: entropy and time irreversibility measures. 心率动力学的多尺度分析:熵和时间不可逆性测量。
Pub Date : 2008-06-01 DOI: 10.1007/s10558-007-9049-1
Madalena D Costa, Chung-Kang Peng, Ary L Goldberger

Cardiovascular signals are largely analyzed using traditional time and frequency domain measures. However, such measures fail to account for important properties related to multiscale organization and non-equilibrium dynamics. The complementary role of conventional signal analysis methods and emerging multiscale techniques, is, therefore, an important frontier area of investigation. The key finding of this presentation is that two recently developed multiscale computational tools--multiscale entropy and multiscale time irreversibility--are able to extract information from cardiac interbeat interval time series not contained in traditional methods based on mean, variance or Fourier spectrum (two-point correlation) techniques. These new methods, with careful attention to their limitations, may be useful in diagnostics, risk stratification and detection of toxicity of cardiac drugs.

心血管信号的分析主要采用传统的时域和频域方法。然而,这些措施不能解释与多尺度组织和非平衡动力学有关的重要性质。因此,传统的信号分析方法和新兴的多尺度技术的互补作用是一个重要的前沿研究领域。本报告的关键发现是,最近开发的两种多尺度计算工具——多尺度熵和多尺度时间不可逆性——能够从基于均值、方差或傅立叶谱(2点相关)技术的传统方法中提取心脏搏动间隔时间序列中不包含的信息。这些新方法在谨慎注意其局限性的情况下,可能在心脏药物的诊断、风险分层和毒性检测方面有用。
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引用次数: 285
Modeling heart rate regulation--part I: sit-to-stand versus head-up tilt. 心率调节模型——第一部分:坐立对抗平头倾斜。
Pub Date : 2008-06-01 DOI: 10.1007/s10558-007-9050-8
Mette S Olufsen, April V Alston, Hien T Tran, Johnny T Ottesen, Vera Novak

In this study we describe a model predicting heart rate regulation during postural change from sitting to standing and during head-up tilt in five healthy elderly adults. The model uses blood pressure as an input to predict baroreflex firing-rate, which in turn is used to predict efferent parasympathetic and sympathetic outflows. The model also includes the combined effects of vestibular and central command stimulation of muscle sympathetic nerve activity, which is increased at the onset of postural change. Concentrations of acetylcholine and noradrenaline, predicted as functions of sympathetic and parasympathetic outflow, are then used to estimate the heart rate response. Dynamics of the heart rate and the baroreflex firing rate are modeled using a system of coupled ordinary delay differential equations with 17 parameters. We have derived sensitivity equations and ranked sensitivities of all parameters with respect to all state variables in our model. Using this model we show that during head-up tilt, the baseline firing-rate is larger than during sit-to-stand and that the combined effect of vestibular and central command stimulation of muscle sympathetic nerve activity is less pronounced during head-up tilt than during sit-to-stand.

在这项研究中,我们描述了一个模型预测心率调节从坐到站的姿势变化和头向上倾斜在五名健康老年人。该模型使用血压作为输入来预测气压反射放电速率,进而用于预测副交感神经和交感神经的输出。该模型还包括前庭和中枢指令刺激肌肉交感神经活动的联合效应,这种刺激在姿势改变开始时增加。乙酰胆碱和去甲肾上腺素的浓度被预测为交感神经和副交感神经流出的功能,然后被用来估计心率反应。采用17个参数的耦合常延迟微分方程系统对心率和气压反射射率的动力学进行了建模。我们推导了灵敏度方程,并对模型中所有状态变量的所有参数的灵敏度进行了排序。利用该模型,我们发现,在平头倾斜时,基线射击率比坐立时大,前庭和中枢指令刺激肌肉交感神经活动的联合效应在平头倾斜时比坐立时不那么明显。
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引用次数: 40
Statistical considerations and techniques for understanding physiological data, modeling, and treatments. 理解生理数据、建模和治疗的统计学考虑和技术。
Pub Date : 2008-06-01 DOI: 10.1007/s10558-007-9052-6
Ben G Fitzpatrick

Comparing models with data always forces us to deal with uncertainty. This uncertainty may take many different forms and involve multiple scales of resolution in the model and in the experiment. In this paper, we discuss issues surrounding the development of deterministic dynamic models of mean behavior and the associated statistical models of the difference between model and experiment. We touch on a variety of topics, including basic exploratory data analysis, confidence bounds and model reduction hypothesis tests. Tools ranging from nonlinear regression to time series to Bayesian decision theory are presented.

将模型与数据进行比较总是迫使我们处理不确定性。这种不确定性可以采取许多不同的形式,并在模型和实验中涉及多个分辨率尺度。在本文中,我们讨论了围绕平均行为的确定性动态模型和模型与实验之间差异的相关统计模型的发展问题。我们涉及各种主题,包括基本的探索性数据分析,置信界限和模型简化假设检验。介绍了从非线性回归到时间序列到贝叶斯决策理论的各种工具。
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引用次数: 1
Modeling heart rate regulation--part II: parameter identification and analysis. 心率调节建模——第二部分:参数辨识与分析。
Pub Date : 2008-06-01 DOI: 10.1007/s10558-007-9048-2
K R Fowler, G A Gray, M S Olufsen

In part I of this study we introduced a 17-parameter model that can predict heart rate regulation during postural change from sitting to standing. In this subsequent study, we focus on the 17 model parameters needed to adequately represent the observed heart rate response. In part I and in previous work (Olufsen et al. 2006), we estimated the 17 model parameters by minimizing the least squares error between computed and measured values of the heart rate using the Nelder-Mead method (a simplex algorithm). In this study, we compare the Nelder-Mead optimization method to two sampling methods: the implicit filtering method and a genetic algorithm. We show that these off-the-shelf optimization methods can work in conjunction with the heart rate model and provide reasonable parameter estimates with little algorithm tuning. In addition, we make use of the thousands of points sampled by the optimizers in the course of the minimization to perform an overall analysis of the model itself. Our findings show that the resulting least-squares problem has multiple local minima and that the non-linear-least squares error can vary over two orders of magnitude due to the complex interaction between the model parameters, even when provided with reasonable bound constraints.

在本研究的第一部分中,我们介绍了一个17参数模型,可以预测从坐姿到站立姿势变化期间的心率调节。在接下来的研究中,我们重点关注17个模型参数,以充分代表观察到的心率反应。在第一部分和之前的工作(Olufsen et al. 2006)中,我们使用Nelder-Mead方法(一种单纯形算法)通过最小化计算值和测量值之间的最小二乘误差来估计17个模型参数。在本研究中,我们将Nelder-Mead优化方法与两种采样方法:隐式滤波方法和遗传算法进行了比较。我们表明,这些现成的优化方法可以与心率模型结合使用,并提供合理的参数估计,只需很少的算法调整。此外,我们利用优化器在最小化过程中采样的数千个点来对模型本身进行全面分析。我们的研究结果表明,所得到的最小二乘问题具有多个局部极小值,并且即使提供了合理的边界约束,由于模型参数之间复杂的相互作用,非线性最小二乘误差也可以变化两个数量级以上。
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引用次数: 11
Sensitivity analysis and model assessment: mathematical models for arterial blood flow and blood pressure. 敏感性分析和模型评估:动脉血流和血压的数学模型。
Pub Date : 2008-06-01 DOI: 10.1007/s10558-007-9047-3
Laura M Ellwein, Hien T Tran, Cheryl Zapata, Vera Novak, Mette S Olufsen

The complexity of mathematical models describing the cardiovascular system has grown in recent years to more accurately account for physiological dynamics. To aid in model validation and design, classical deterministic sensitivity analysis is performed on the cardiovascular model first presented by Olufsen, Tran, Ottesen, Ellwein, Lipsitz and Novak (J Appl Physiol 99(4):1523-1537, 2005). This model uses 11 differential state equations with 52 parameters to predict arterial blood flow and blood pressure. The relative sensitivity solutions of the model state equations with respect to each of the parameters is calculated and a sensitivity ranking is created for each parameter. Parameters are separated into two groups: sensitive and insensitive parameters. Small changes in sensitive parameters have a large effect on the model solution while changes in insensitive parameters have a negligible effect. This analysis was successfully used to reduce the effective parameter space by more than half and the computation time by two thirds. Additionally, a simpler model was designed that retained the necessary features of the original model but with two-thirds of the state equations and half of the model parameters.

近年来,为了更准确地解释生理动力学,描述心血管系统的数学模型变得越来越复杂。为了帮助模型验证和设计,对Olufsen, Tran, Ottesen, Ellwein, Lipsitz和Novak首先提出的心血管模型进行了经典的确定性敏感性分析(应用物理学报99(4):1523- 1537,2005)。该模型使用11个微分状态方程和52个参数来预测动脉血流和血压。计算了模型状态方程对各参数的相对灵敏度解,并对各参数进行了灵敏度排序。参数分为敏感参数和不敏感参数两组。敏感参数的微小变化对模型解的影响很大,而不敏感参数的变化对模型解的影响可以忽略不计。该方法使有效参数空间缩短了一半以上,计算时间缩短了三分之二。此外,设计了一个更简单的模型,保留了原模型的必要特征,但具有三分之二的状态方程和一半的模型参数。
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引用次数: 88
Arterial baroreflexes and cardiovascular modeling. 动脉压力反射和心血管模型。
Pub Date : 2008-03-01 DOI: 10.1007/s10558-007-9042-8
Dwain L Eckberg

Many cardiovascular models involve prediction of changes that occur when a subject is perturbed in some way, to move from one state to another. A successful, predictive model should involve at least two elements: First, the model should include some index of the intensity of the perturbation that elicits the response; effective responses should, in some fashion, be linearly or nonlinearity related to perturbations. Second, the model should factor in subjects' abilities to meet the challenges posed by the perturbations. This review indicates that these two basic components of a successful model may be difficult to incorporate. In the simple case of passive upright tilt, blood pressure measurements may not accurately indicate the stimulus, because blood pressure reductions are reversed by rapidly occurring reflex blood pressure increases. Since not all subject populations respond identically to hemodynamic challenges, it also may be important to characterize baroreflex responsiveness, and include such a term in a model. Although vagal and sympathetic baroreflex responses to stereotyped challenges can be measured accurately, recent research points to extraordinary variability of baroreflex responsiveness. The complexities discussed in this review should be considered, whether they are, or even can be incorporated into cardiovascular models.

许多心血管模型都涉及到当受试者受到某种方式的干扰,从一种状态转移到另一种状态时发生的变化的预测。一个成功的预测模型应该至少包含两个要素:首先,模型应该包含引起响应的扰动强度的一些指数;在某种程度上,有效的响应应该与扰动呈线性或非线性关系。其次,该模型应考虑受试者应对扰动带来的挑战的能力。这一审查表明,一个成功模式的这两个基本组成部分可能很难结合起来。在被动直立倾斜的简单情况下,血压测量可能不能准确地指示刺激,因为血压下降被快速发生的反射性血压升高所逆转。由于并非所有受试者群体对血流动力学挑战的反应都相同,因此表征气压反射反应性并将其包含在模型中可能也很重要。尽管迷走神经和交感神经对刻板印象挑战的压力反射反应可以精确测量,但最近的研究指出压力反射反应的异常可变性。本综述中讨论的复杂性应该被考虑,无论它们是否,甚至是否可以被纳入心血管模型。
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引用次数: 17
Modeling of autonomic control in sleep-disordered breathing. 睡眠呼吸障碍的自律神经控制模型。
Pub Date : 2008-03-01 DOI: 10.1007/s10558-007-9041-9
Michael C K Khoo

There is ample evidence to support the notion that chronic exposure to repetitive episodes of interrupted breathing during sleep can lead to systemic hypertension, heart failure, myocardial infarction and stroke. Recent studies have suggested that abnormal autonomic control may be the common factor linking sleep-disordered breathing (SDB) to these cardiovascular diseases. We have developed a closed-loop minimal model that enables the delineation of the major physiological mechanisms responsible for changes in autonomic system function in SDB, and also forms the basis for a noninvasive technique that enables the early detection of cardiovascular control abnormalities. The model is "minimal" in the sense that all its parameters can be estimated through analysis of the data measured noninvasively from a single experimental procedure. Parameter estimation is enhanced by broadening the frequency content of the subject's ventilatory pattern, either through voluntary control of breathing or involuntary control using ventilator assistance. Although the original form of the model is linear and time-invariant, extensions of the model include the incorporation of nonlinear dynamics in the autonomic control of heart rate, and allowing the transfer functions of the model components to assume time-varying characteristics. The various versions of the model have been applied to different populations of subjects with SDB under different conditions (e.g. supine wakefulness, orthostatic stress, sleep). Our cumulative findings suggest that the minimal model approach provides a more sensitive means of detecting abnormalities in autonomic cardiovascular control in SDB, compared to univariate analysis of heart rate variability or blood pressure variability.

有大量证据表明,长期在睡眠中反复出现呼吸中断会导致全身性高血压、心力衰竭、心肌梗塞和中风。最近的研究表明,自律神经控制异常可能是睡眠呼吸紊乱(SDB)与这些心血管疾病相关的共同因素。我们开发了一个闭环最小模型,该模型能够确定导致 SDB 自主呼吸系统功能变化的主要生理机制,并为早期检测心血管控制异常的无创技术奠定了基础。该模型是 "最小 "的,因为其所有参数都可以通过分析从单一实验过程中测得的无创数据进行估算。通过自愿控制呼吸或使用呼吸机辅助进行非自愿控制,拓宽受试者通气模式的频率内容,可以增强参数估计。虽然模型的原始形式是线性和时间不变的,但模型的扩展包括在心率的自主控制中加入非线性动力学,并允许模型各组成部分的传递函数具有时变特性。该模型的不同版本已应用于不同条件下(如仰卧清醒、正压应激、睡眠)的 SDB 受试者群体。我们的累积研究结果表明,与心率变异性或血压变异性的单变量分析相比,最小模型方法能更灵敏地检测出 SDB 患者的自律神经心血管控制异常。
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引用次数: 0
Variability in cardiovascular control: the baroreflex reconsidered. 心血管控制的变异性:重新考虑气压反射。
Pub Date : 2008-03-01 DOI: 10.1007/s10558-007-9046-4
John M Karemaker, Karel H Wesseling

Although blood pressure control is often viewed as a paradigmatic example of a "homeostatic" biological control system, blood pressure levels can fluctuate considerably over shorter and longer time scales. In modern signal analysis, coherence between heart rate and blood pressure variability is used to estimate baroreflex gain. However, the shorter the measurement period, the more variability this gain factor reveals. We review evidence that this variability is not due to the technique used for the estimation, but may be an intrinsic property of the circulatory control mechanisms. The baroreflex is reviewed from its evolutionary origin, starting in fishes as a reflex mechanism to protect the gills from excessively high pressures by slowing the heart via the (parasympathetic) vagus nerve. Baroreflex inhibition of cardiovascular sympathetic nervous outflow is a later development; the maximally possible extent of sympathetic activity probably being set in the central nervous system by mechanisms other than blood pressure per se. In the sympathetic outflow tract not only baroreflex inhibition but also as yet unidentified, stochastic mechanisms decide to pass or not pass on the sympathetic activity to the periphery. In this short essay, the "noisiness" of the baroreflex as nervous control system is stressed. This property is observed in all elements of the reflex, even at the--supposedly--most basic relation between afferent receptor nerve input and efferent--vagus--nerve output signal.

虽然血压控制通常被视为“体内平衡”生物控制系统的典型例子,但血压水平在较短和较长的时间尺度上波动很大。在现代信号分析中,心率和血压变异性之间的一致性用于估计压力反射增益。然而,测量周期越短,该增益因子显示的可变性越大。我们审查的证据表明,这种可变性不是由于用于估计的技术,但可能是循环控制机制的内在特性。压力反射从其进化起源开始,在鱼类中作为一种反射机制,通过(副交感)迷走神经减缓心脏的速度,保护鳃免受过高的压力。心血管交感神经流出的压力反射抑制是后来的发展;交感神经活动的最大可能程度可能是由中枢神经系统的机制设定的,而不是血压本身。在交感神经流出道中,除了压力反射抑制外,还有一些未知的随机机制决定交感神经活动是否传递到外周。在这篇短文中,强调了压力反射作为神经控制系统的“噪声”。这种特性在反射的所有元素中都可以观察到,甚至在传入受体神经输入和传出-迷走-神经输出信号之间最基本的关系中也是如此。
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引用次数: 57
Receding horizon controller for the baroreceptor loop in a model for the cardiovascular system. 心血管系统模型中压力感受器回路的后退水平控制器。
Pub Date : 2008-03-01 DOI: 10.1007/s10558-007-9043-7
Mark Mutsaers, Mostafa Bachar, Jerry Batzel, Franz Kappel, Stefan Volkwein

In this article, we discuss the design and implementation of a receding horizon control (RHC) which will be used to represent the control for the baroreceptor loop in the human cardiovascular system (CVS). This control will be applied to a model of the CVS developed in a previous work by Kappel and Peer. In that earlier work, a linear quadratic control strategy (LQR) was implemented to represent this baroreflex control which was designed to stabilize the system under an ergometric workload. The RHC approach will be examined as an alternate to the LQR implementation. The control parameters in the cost functional of the RHC will be estimated using the same experimental data as was used in the LQR study. The results of the RHQ implementation will be compared with the LQR implementation.

在本文中,我们讨论了一个后退水平控制(RHC)的设计和实现,它将被用来代表人类心血管系统(CVS)中压力受体回路的控制。该控件将应用于Kappel和Peer在之前的工作中开发的CVS模型。在早期的工作中,实现了线性二次控制策略(LQR)来表示这种压力反射控制,旨在稳定系统在几何负荷下的稳定性。RHC方法将作为LQR实现的替代方法进行研究。RHC成本函数中的控制参数将使用与LQR研究中使用的相同的实验数据进行估计。RHQ实现的结果将与LQR实现的结果进行比较。
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引用次数: 9
Nonlinear assessment of cerebral autoregulation from spontaneous blood pressure and cerebral blood flow fluctuations. 自发性血压和脑血流波动对脑自动调节的非线性评价。
Pub Date : 2008-03-01 DOI: 10.1007/s10558-007-9045-5
Kun Hu, C K Peng, Marek Czosnyka, Peng Zhao, Vera Novak

Cerebral autoregulation (CA) is an most important mechanism responsible for the relatively constant blood flow supply to brain when cerebral perfusion pressure varies. Its assessment in nonacute cases has been relied on the quantification of the relationship between noninvasive beat-to-beat blood pressure (BP) and blood flow velocity (BFV). To overcome the nonstationary nature of physiological signals such as BP and BFV, a computational method called multimodal pressure-flow (MMPF) analysis was recently developed to study the nonlinear BP-BFV relationship during the Valsalva maneuver (VM). The present study aimed to determine (i) whether this method can estimate autoregulation from spontaneous BP and BFV fluctuations during baseline rest conditions; (ii) whether there is any difference between the MMPF measures of autoregulation based on intra-arterial BP (ABP) and based on cerebral perfusion pressure (CPP); and (iii) whether the MMPF method provides reproducible and reliable measure for noninvasive assessment of autoregulation. To achieve these aims, we analyzed data from existing databases including: (i) ABP and BFV of 12 healthy control, 10 hypertensive, and 10 stroke subjects during baseline resting conditions and during the Valsalva maneuver, and (ii) ABP, CPP, and BFV of 30 patients with traumatic brain injury (TBI) who were being paralyzed, sedated, and ventilated. We showed that autoregulation in healthy control subjects can be characterized by specific phase shifts between BP and BFV oscillations during the Valsalva maneuver, and the BP-BFV phase shifts were reduced in hypertensive and stroke subjects (P < 0.01), indicating impaired autoregulation. Similar results were found during baseline condition from spontaneous BP and BFV oscillations. The BP-BFV phase shifts obtained during baseline and during VM were highly correlated (R > 0.8, P < 0.0001), showing no statistical difference (paired-t test P > 0.47). In TBI patients there were strong correlations between phases of ABP and CPP oscillations (R = 0.99, P < 0.0001) and, thus, between ABP-BFV and CPP-BFV phase shifts (P < 0.0001, R = 0.76). By repeating the MMPF 4 times on data of TBI subjects, each time on a selected cycle of spontaneous BP and BFV oscillations, we showed that MMPF had better reproducibility than traditional autoregulation index. These results indicate that the MMPF method, based on instantaneous phase relationships between cerebral blood flow velocity and peripheral blood pressure, has better performance than the traditional standard method, and can reliably assess cerebral autoregulation dynamics from ambulatory blood pressure and cerebral blood flow during supine rest conditions.

脑自动调节(Cerebral autoregulation, CA)是脑灌注压变化时脑供血相对稳定的重要机制。其在非急性病例中的评估依赖于无创搏动血压(BP)和血流速度(BFV)之间关系的量化。为了克服BP和BFV等生理信号的非平稳性,最近发展了一种称为多模态压力-流量(MMPF)分析的计算方法来研究Valsalva机动(VM)过程中BP-BFV的非线性关系。本研究旨在确定(i)该方法是否可以估计基线休息条件下自发BP和BFV波动的自动调节;(ii)基于动脉内血压(ABP)和基于脑灌注压(CPP)的MMPF自动调节测量是否有差异;(iii) MMPF方法是否为自动调节的无创评估提供了可重复和可靠的测量方法。为了实现这些目标,我们分析了现有数据库中的数据,包括:(i) 12名健康对照者、10名高血压患者和10名中风患者在基线静息条件和Valsalva操作期间的ABP和BFV,以及(ii) 30名创伤性脑损伤(TBI)患者在瘫痪、镇静和通气状态下的ABP、CPP和BFV。我们发现,健康对照者在Valsalva动作过程中BP和BFV之间的相移可以表征自身调节,高血压和脑卒中患者BP-BFV相移减少(P < 0.01),表明自身调节受损。在基线条件下,自发的BP和BFV振荡也发现了类似的结果。基线和VM期间BP-BFV相移高度相关(R > 0.8, P < 0.0001),差异无统计学意义(配对t检验P > 0.47)。在TBI患者中,ABP与CPP振荡的相位之间存在很强的相关性(R = 0.99, P < 0.0001),因此ABP- bfv与CPP- bfv相移之间存在很强的相关性(P < 0.0001, R = 0.76)。通过在脑外伤患者的数据上重复MMPF 4次,每次选择一个自发BP和BFV振荡周期,我们发现MMPF比传统的自动调节指数具有更好的再现性。上述结果表明,基于脑血流速度与外周血压瞬时相位关系的MMPF方法比传统标准方法具有更好的性能,可以可靠地从动态血压和脑血流来评估仰卧休息状态下的脑自调节动力学。
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引用次数: 72
期刊
Cardiovascular Engineering (dordrecht, Netherlands)
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