心肌细胞团搏动整数倍节律的非线性动力学机制

利用心肌细胞耦合模型研究心肌整数倍节律的动力学机理。确定性模型仿真揭示了心肌细胞团同步搏动加周期分岔的节律变化规律;随机模型仿真发现在加周期分岔序列中分岔点附近会出现整数倍节律,其中,0-1整数倍节律产生于从静息到周期1的Hopf分岔点附近,1-2整数倍节律产生于周期1和周期2极限环间的加周期分岔点附近;对系统相空间轨道的分析进一步揭示出整数倍节律是由系统运动在相邻的两个轨道之间随机跃迁形成的。上述分析结果不仅阐明了心肌整数倍节律的机理,并且揭示了各种整数倍节律与加周期分岔序列中相邻节律的内在联系,为重新认识心律变化的规律开辟了新的途径。     

心肌单细胞兴奋模式转迁规律和转迁过程中延迟后去极化、早后去极化的生成

实验观察了培养心肌单细胞自发性兴奋节律的不同模式以及兴奋模式的转迁规律。结果表明,单细胞在正常灌流条件下可处于不同的兴奋状态,产生不同的兴奋节律,包括延迟后去极化、早后去极化现象。不同的兴奋模式在膜电流改变条件下可规律地相互转迁。随外向电流的逐渐减弱、内向电流的逐渐加强,同一细胞顺序历经“极化”静息状态、含延迟后去极化电位的节律、连续兴奋节律、含早后去极化电位的节律和“去极化”静息状态的兴奋节律动态转迁过程,形成心肌单细胞自发兴奋的哗律谱系”。其中延迟后去极化节律介于“极化”静息状态和连续放电节律之间,是连续放电节律向“极化”静息过渡的一种表现形式。而早后去极化节律则介于连续放电节律和“去极化”静息状态之间,是连续放电向“去极化”静息过渡的一种表现形式。哗律谱系”的概念在延迟后去极化、早后去极化现象和正常节律之间建立了内在联系。     

神经放电加周期分岔中由随机自共振引起一类新节律

当改变实验性神经起步点细胞外[Ca^2 ]时,放电节律表现出从周期1节律转换为周期4节律的加周期分岔序列。其中,周期n节律转换为周期n 1节律的过程中(n=1,2,3)存在一种新的具有交替特征的节律,该新节律为周期n簇与周期n 1簇放电的交替,并且周期n 1簇的时间间隔序列呈现出整数倍特征。确定性神经放电理论模型(chay模型)只能模拟周期n节律直接到周期n 1节律的加周期分岔序列;而随机chay模型可以模拟实验中的加周期分岔过程和新节律。进一步,新节律被确认是经随机自共振机制产生的。这不仅解释了实验现象,也将随机自共振的产生区间从以前认识到的Hopf分岔点附近扩大到加周期分岔点附近,同时扩大了噪声在神经放电和神经编码中起重要作用的参数区间。     

交流外电场下映射神经元放电节律的分析

神经元不同的放电节律承载着不同的刺激信息。文章基于神经元映射模型,研究低频交流电场对神经元放电节律的影响。在外部刺激下映射模型表现出丰富的放电模式,包括周期簇放电、周期峰放电、交替放电和混沌放电。神经元对刺激频率和振幅的变化极为敏感,随着频率的增大,放电节律表现出从簇放电到峰放电和混沌放电的反向加周期分岔序列;在周期节律转迁过程中存在一种新的交替节律,其放电序列为两种周期放电模式的交替,峰峰间期序列具有整数倍特征。外电场的频率影响细胞内、外离子振荡周期,导致神经元放电与刺激信号同步,对放电节律的影响更为明显。研究结果揭示了交流外电场对神经元放电节律的作用规律,有助于探寻外电场对生物神经系统兴奋性的影响和神经系统疾病的致病机理。     

神经起步点产生的一种新型簇放电节律———阵发周期1节律

实验中发现了神经起步点产生的一种新型的簇放电节律－－阵发周期1节律。其特征如下：连续周期1放电与休止期（quiescence）轮流出现;非周期性,连续放电持续期、连续放电次数以及休止期有较大变异性;位于周期1节律和静息状态之间。具有较长周期的伪单色噪声激励的FHN（FizHugh-Nagumo）模型可以产生类似的阵发周期1节律。模型和实验中的阵发周期1节律的统计特征、变化规律和所处的参数区间相类似。这表明：阵发周期1节律是由与伪单色噪声类似的长时程振荡激励引起的。     

由三态跃迁机制产生的两种神经放电节律

在实验性神经起步点自发放电中,发现了两种三态跃迁节律,其特征为静息、周期n及周期n+1(n=1,2)簇放电随机交替出现。应用随机Chay模型数值仿真,分别得到了与实验模型中相似的两种三态跃迁节律,这两种节律都是在两个紧邻的分岔点附近,由噪声驱动而产生的。理论分析提示,当神经元系统接近从静息经分岔到放电的临界状态,且从静息到周期n的分岔点,与从周期n到周期n+1的分岔点非常接近时,在噪声的作用下,系统运动会在静息、周期n和周期n+1三种状态之间随机跃迁,从而形成了这种三态跃迁节律。基于这种三态跃迁放电的随机共振,还有待进一步深入研究。     

心肌细胞自发性搏动节律的分岔和混沌现象

心脏的节律是复杂的、非线性的;其节律复杂性的起源是多层次的。实验观察了心肌细胞自发性搏动节律的模式,以及改变细胞间耦合强度时节律的转化规律。表明在以正常灌流液灌流状态下,心肌细胞表现为多种不同的节律模式,可以是周期的,也可以是非周期的。当细胞间耦合强度下降时,心肌细胞节律发生转化,并经倍周期分岔进入混沌节律。实验结果有助于更好地理解心脏节律复杂性的起源。     

神经自发整数倍峰放电节律的随机性和确定性模式的比较

为进一步区分神经自发整数倍峰放电节律的随机性和确定性模式的动力学性质,详细研究了实验神经起步点、随机理论模型(Chay模型)和确定性理论模型(Wang模型)产生的3种整数倍峰放电节律及其变化规律。结果发现,实验和随机模型经随机自共振产生的整数倍峰放电节律具有相同的统计性质(峰峰间期越大,出现的频度越低,约呈指数递减)和变化规律,与确定性Wang模型产生的整数倍节律明显不同。这提示,呈指数衰减分布的整数倍峰放电节律是经随机自共振产生的,是确定性因素和随机因素共同作用的结果。     

实验性神经起步点自发放电的分叉和整数倍节律

在实验性神经起步点发现了放电峰峰间期序列随细胞外[Ca^2 ]变化产生的加周期分叉和整数倍节律。并用确定性Chay模型和随机Chay模型进行数值模拟。从模拟实验结果的角度看,加周期分叉过程遵从Chay模型决定的确定性机制,随机因素对其有影响但影响较小;而在相应的参数区间,整数倍节律则是在随机因素驱动下产生,是随机共振现象,是由确定性机制和随机因素共同作用的结果。这表明,实验性神经起步点放电节律的分叉和随机共振现象的出现是必然的,受确定性机制和随机因素共同影响。但在不同参数区间,随机因素对神经放电节律的作用不同。     

实验性神经起步点产生的整数倍簇放电节律

随机Hindmarsh-Rose模型中产生簇（bursting)放电节律是神经放电中存在随机自共振的一个重要理论证据,但是,该簇放电节律在实验中一直没有被发现。在实验性神经起步点细胞外[Ca^2 ]([Ca^2 ]o)低于周期1节律的[Ca^2 ]o时,发现了一种簇放电节律。其簇簇间期（inter-burst intervals,IBIs)呈现出与随机自共振引起的整数倍峰放电（interger multiple spiking)节律的峰峰间期类似的整数倍特征。随机Hindmarsh-Rose模型中产生的簇（bursting)放电节律也表现出类似的特征。结果验证了随机自共振簇放电的存在性,揭示该簇放电节律的统计特征。此外,该簇放电节律的参数区间以及其与整数倍峰放电节律的区别被揭示,簇放电节律的[Ca^2 ]o低于峰放电律的[Ca^2 ]o。     

心肌单细胞兴奋模式转迁的非线性动力学机理

利用Moms-Lecar模型研究实验观察到的培养心肌单细胞自发性兴奋模式转迁规律的动力学机理,确定性模型仿真,揭示了心肌单细胞随参数由“极化”静息经规则节律到“去极化”静息的节律变化规律。随机因素扰动下的模型仿真发现在分岔序列中的分岔点附近会出现含延迟后去极化电位、旱后去极化电位的节律模式,其中,延迟后去极化节律产生于从“极化”静息到规则节律的分岔点附近,而旱后去极化节律产生于从规则节律到“去极化”静息的分岔点附近。这表明含延迟后去极化电位的节律和含旱后去极化电位的节律是系统在自动兴奋和静息之间的分岔点附近由于参数的随机扰动而产生的。     

Effect of change in levels of motor activity and innervation on basic and secondary rhythms of rat heart rate and respiration in ontogenesis

Changes in the heart basic rhythm, its rhythmical variations on periodograms, and level of spontaneos motor activity were studied on offspring of white rats from newborn to 3-week age at transition from the state of active wakefulness to narcosis as well as under conditions of blockade of M-cholinoreceptors with atropine. It is shown that the endogenous rhythmical activity can be regulated not only by a change in frequency of basic rhythms, but also by action on all parameters and properties of their rhythmical variations and secondary rhythms. The changes in power of the heart secondary rhythms exceed considerably the frequency oscillations of basic rhythms during blockade of cholinergic innervation or a change in the motor activity level that affects both the basic rhythm circulation and respiration and their variations--secondary rhythms. The atropine blockade of M-cholinoreceptors at the studied ages changes the heart beating rhythm within the limits of 10% of bradicardia in newborns to tachycardia in the 3-week old animals. At the same time, power of the cardiac rhythm secondary oscillations changes several times. These data indicate that the cholinergic mechanisms play the key role in formation of the secondary rhythms and their correlation with motor activity.     

Quantitative tests of a dual circalunidian clock model for tidal rhythmicity in the sand beach isopod Cirolana cookii

In constant conditions (constant darkness [DD], 20°C), the sand beach isopod Cirolana cookii exhibits spontaneous rhythmic swimming activity with an average free-running period of 12.5h. The rhythms are seen as temporal adaptations to a complex intertidal environment. These results support a dual circalunidian clock model for tidal rhythms in which two components of the rhythm have characteristic periods and active phase lengths and are hypothesized to be controlled by separate circalunidian clocks. A quantitative model successfully simulates many of the properties of endogenous swimming rhythms of C. cookii, including free-running behavior, entrainment, and phase-response curves (PRCs). (Chronobiology International 17 (1), 29-41, 2000)     

Circadian rhythms of melatonin in European starlings exposed to different lighting conditions: relationship with locomotor and feeding rhythms

In passerine birds, the periodic secretion of melatonin by the pineal organ represents an important component of the pacemaker that controls overt circadian functions. The daily phase of low melatonin secretion generally coincides with the phase of intense activity, but the precise relationship between the melatonin and the behavioral rhythms has not been studied. Therefore, we investigated in European starlings (Sturnus vulgaris) (1) the temporal relationship between the circadian plasma melatonin rhythm and the rhythms in locomotor activity and feeding; (2) the persistence of the melatonin rhythm in constant conditions; and (3) the effects of light intensity on synchronized and free-running melatonin and behavioral rhythms. There was a marked rhythm in plasma melatonin with high levels at night and/or the inactive phase of the behavioral cycles in almost all birds. Like the behavioral rhythms, the melatonin rhythm persisted for at least 50 days in constant dim light. In the synchronized state, higher daytime light intensity resulted in more tightly synchronized rhythms and a delayed melatonin peak. While all three rhythms usually assumed a rather constant phase relationship to each other, in one bird the two behavioral rhythms dissociated from each other. In this case, the melatonin rhythm retained the appropriate phase relationship with the feeding rhythm. Accepted: 10 December 1999     

Alpha-Frequency Rhythms Desynchronize over Long Cortical Distances: A Modeling Study

Neocortical networks of excitatory and inhibitory neurons can display alpha()-frequency rhythms when an animal is in a resting or unfocused state. Unlike some - and -frequency rhythms, experimental observations in cats have shown that these -frequency rhythms need not synchronize over long cortical distances. Here, we develop a network model of synaptically coupled excitatory and inhibitory cells to study this asynchrony. The cells of the local circuit are modeled on the neurons found in layer V of the neocortex where -frequency rhythms are thought to originate. Cortical distance is represented by a pair of local circuits coupled with a delay in synaptic propagation. Mathematical analysis of this model reveals that the h and T currents present in layer V pyramidal (excitatory) cells not only produce and regulate the -frequency rhythm but also lead to the occurrence of spatial asynchrony. In particular, these inward currents cause excitation and inhibition to have nonintuitive effects in the network, with excitation delaying and inhibition advancing the firing time of cells; these reversed effects create the asynchrony. Moreover, increased excitatory to excitatory connections can lead to further desynchronization. However, the local rhythms have the property that, in the absence of excitatory to excitatory connections, if the participating cells are brought close to synchrony (for example, by common input), they will remain close to synchrony for a substantial time.     

A Minimal Model for the Respiratory Sinus Arrhythmia

The cardiac and respiratory rhythms in humans are known to be coupled by several mechanisms. In particular, the first rhythm is deeply modulated by the second. In this report we propose a simple operational model for heart rate variability which, taking such modulation into account, reproduces the main features of some experimental sequences of RR intervals recorded from healthy subjects in the resting condition. Also, peer analysis of the model performance allows us to answer the question whether the observed behaviour should be ascribed to phase synchronisation of the heart beating to the respiratory rhythm. Lastly, the changes of the model activity brought about by changing its relevant parameters are analysed and discussed     

Rhythms of high-grade block in an ionic model of a strand of regionally ischemic ventricular muscle

Electrical alternans, a beat-to-beat alternation in the electrocardiogram or electrogram, is frequently seen during the first few minutes of acute myocardial ischemia, and is often immediately followed by malignant cardiac arrhythmias such as ventricular tachycardia and ventricular fibrillation. As ischemia progresses, higher-order periodic rhythms (e.g., period-4) can replace the period-2 alternans rhythm. This is also seen in modelling work on a two-dimensional (2-D) sheet of regionally ischemic ventricular muscle. In addition, in the experimental work, ventricular arrhythmias are overwhelmingly seen only after the higher-order rhythms arise. We investigate an ionic model of a strand of ischemic ventricular muscle, constructed as a 3-cm-long 1-D cable with a centrally located 1-cm-long segment exposed to an elevated extracellular potassium concentration ([K(+)](o)). As [K(+)](o) is raised in this "ischemic segment" to represent one major effect of ongoing ischemia, the sequence of rhythms {1:1-->2:2 (alternans)-->2:1} is seen. With further increase in [K(+)](o), one sees higher-order periodic 2N:M rhythms {2:1-->4:2-->4:1-->6:2-->6:1-->8:2-->8:1}. In a 2N:M cycle, only M of the 2N action potentials generated at the proximal end of the cable successfully traverse the ischemic segment, with the remaining ones being blocked within the ischemic segment. Finally, there is a transition to complete block {8:1-->2:0-->1:0} (in an n:0 rhythm, all action potentials die out within the ischemic segment). Changing the length of the ischemic segment results in different rhythms and transitions being seen: e.g., when the ischemic segment is 2 cm long, the period-6 rhythms are not seen; when it is 0.5 cm long, there is a 3:1 rhythm interposed between the 2:1 and 1:0 rhythms. We discuss the relevance of our results to the experimental observations on the higher-order rhythms that presage reentrant ischemic ventricular arrhythmias.