主动脉压力感受器编码血压信号的新机制
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摘要
压力感受器如何感受血压变化是感觉神经生理学的一个重要问题。神经生理学已经建立压力感受器通过调节动作电位频率进而感受静态和动态压力的基本概念：神经脉冲发放平均频率编码了外界刺激的强度,脉冲发放的频率数正比于刺激的强度值。由于感受器神经末梢的解剖结构非常微小,目前还不能直接通过实验观察其感受电位。随着神经科学、非线性科学、信息技术和计算机技术的交叉融合,已经形成了以理论和实验结合的神经动力学研究方向。利用非线性动力学的概念,可以对生命中复杂的神经放电模式、模式分岔(转迁)规律进行研究,为认识复杂多变的神经放电节律,揭示神经动态放电和动态外界信息之间的关系,探讨动态放电如何编码动态外界信号的机制。
本文采用理论与实验相结合的研究方法,研究主动脉弓压力感受器编码动脉血压信号这个具体的编码环节的生物物理机制和生理学意义。通过对家兔和大鼠动脉压力感受器动态、静态血压变化作用下,神经单纤维放电模式及其转迁规律的研究。实验发现了感受器的5种活动状态：2类静息(分别对应低压阈值和高压阈值)和3类放电行为。放电行为是由血压变化过程中跨越两个阈值产生的。对应动态血压,跨越低压阈值,感受器在收缩压放电；跨越高压阈值,感受器表现为在收缩压放电的反常簇放电；位于两个阈值之间,持续放电。对应静压力,跨越低压阈值,感受器on-off放电；跨越高压阈值,感受器on-off放电或整数倍放电；位于阈值之间,周期一放电并随压力增加频率加快。实验静压力下出现了on-off放电和整数倍放电等非周期放电模式,模型仿真了这类结果,提示它们分别对应跨越超临界Hopf分岔和亚临界Hopf分岔的动力学行为。神经动力学的应用,为理解实验现象的机理提供了有力的理论依据。
主要结果有
1.实验获得了随动态平均血压变化的感受器神经单纤维的放电模式转迁规律。随着平均压力升高,感受器神经单纤维放电依次经历低压静息->收缩压放电->连续放电->舒张压放电的“反常簇放电”->高压静息。识别了感受器神经单纤维的5种活动状态：3种放电和2种静息。在多例标本发现了新的“反常簇放电”现象,并认识到“反常簇放电”存在于高压力区间,其机理是“去极化阻滞”。
2.实验观察了静压力下感受器神经单纤维放电模式的转迁规律。随着静压力升高,感受器神经单纤维放电依次经历了低压静息->on-off放电->持续周期一放电->on-off放电或者整数倍放电->高压静息。和动态平均血压下的转迁规律类似,感受器的2种静息分别对应了低压和高压阈值。其中非周期的on-off放电和整数倍放电,提示在跨越阈值时,感受器放电遵循动力学的Hopf分岔机制。进而利用神经动力学的分岔理论可以解释感受器编码血压信号的机理。
3.构建了基于血压压力感受器感知血压过程的生物写实数学模型。该模型利用不同的函数,对应血管区、感受器区和编码区,分别仿真了血管壁的机械形变、感受器局部电位产生和编码区动作电位产生,进而构成完整的感受器数学模型。调节与实验相一致的参数变化,研究了该数学模型在静压力和动态血压变化下的放电模式及其转迁规律。
4.数学模型仿真结果揭示了放电节律的转迁规律的机制。随着静压力的增加,确定性模型会表现出静息、连续放电、静息的转迁历程。考虑噪声因素的作用,静压力增加时,放电节律会表现出静息、on-off放电、连续均匀放电、整数倍放电、静息的转迁历程,与实验中静压力增加的现象一致。在动压力作用下,随着平均压力的增加,放电会经历静息、血压峰值放电谷值不放电、连续放电、血压峰值不放电血压谷值放电、静息的历程,与实验一致。
5.对数学模型进行分析,随着静压力的增加,从静息变到放电对应亚临界Hopf分岔,从连续放电再到静息是超临界Hopf分岔。静压力下的on-off放电和整数倍放电是噪声分别在超临界和亚临界Hopf点附件诱发的随机节律。而“反常簇放电”是由于在动压力作用下电活动行为因为血压压力在跨越Hopf分岔点引起的：血压峰值处于静息而血压谷值时处于放电引起的。这就从理论上解释了这些新节律的产生的动力学机制。。
上述结果表明,血压信号的改变会引起感受器兴奋性的变化,也就是去极化电流的动态变化。使得压力感受器的放电节律在以去极化电流作为分岔参数的放电节律静态分岔结构中,在平均血压对应的位置附近按照血压信号的时间历程“动态游走”,形成动态放电节律；动态放电节律的时间历程与血压信号的时间动态历程有较好的对应。利用非线性动力学分岔理论不仅从理论上揭示了血压信号引起感受器神经放电的机理,而且可以在包含放电频率在内的多个层面上,在理论层次上建立动态血压信号与相应动态放电之间的联系,进一步认识了感受器的编码机制。
How blood pressures are encoded by baroreceptors is of fundamental importance in neuroscience. Baroreceptors are stretch-sensitive neural terminals which response to static and dynamic arterial blood pressure variations by evoking action potentials at the connected nerve fibers. It is well established in neurophysiology that baroreceptors and their sensory nerves represent the level of blood pressure by means of action potential frequency. The intensity of external signal is believed encoded in the mean frequency of firing trains, and the frequency of impulse is positively correlated to external stimulus density. Since the size of baroreceptor terminals are very small, it is still difficult to directly observe the relation between receptor potential and firing frequency on the nerve fibers. Combining techniques from neuroscience, nonlinear dynamics, information and computer science, it is possible to study the coding mechanisms of barorceptors. In the present study, we investigated the firing pattern and pattern transition (bifurcation) regularities by single unit recording on depression nerves in rat and rabbit. We formulated a mathematical model of barorecepotr and simulated the coding processes. The results provided a basis for a deeper understanding of complex and variable firing rhythm, identification of the relationship between dynamic firing rhythm and dynamic external signal. The dynamic coding processes were emphasized in the research and discussion. The study also gives a new viewpoint and method to theoretically study the neural firing rhythm and neural coding mechanism.
In the present study, using methods of nonlinear dynamics as well as physiological experiments, the biophysical mechanism and physiological significance of the encoding of blood pressure by aortic arch baroreceptor was studied. The aortic arch baroreceptor from both rats and rabbits were chosen as experimental models. The neural firing and aortic blood pressure were recorded simultaneously. The biological relevant theoretical model was formed by considering transformation of blood vessel, generation of receptor potential, initiation of action potential. The theoretical model was analyzed theoretically, and the experimental results were compared with the numeric simulation. The theoretical analysis could reproduce the present experimental results and was used to guide future experiment. On the other hand, the experimental results verified the theoretical analysis.
The main results are as follows.
1, In experiments, we observed that the firing pattern changed with dynamic variation. When the average level of blood pressure was increased from a relatively lower level, the firing pattern of depression fibers changed from resting, to firing within systolic period, to continuous firing, to firing within diastolic period, and finally to resting caused by depolarization block at a relatively high blood pressure level. Five different firing patterns were identified, including three firing states and two resting states. The "paradoxical firing pattern" observed at high ranged of blood pressure was explained by mechanism of "depolarization block".
2, We formulated an realistic mathematical model based on the transduction process. Multiple compartments were employed to represent blood vessel, receptor region, and the coding region to, respectively, simulate the transformation, receptor potential generation, and action potential initiation. By adjusting the same parameters as used in experiments, the experimental results were reproduced successfully.
3, The simulation revealed mechanisms underpinning firing patterns transition. When the static blood pressure was increased, the deterministic form of the formulated model exhibited transition from polarized resting, to tonic firing, and to depolarized resting behaviors. With consideration of biological fluctuation, the stochastic form of the model exhibited resting, on-off firing, tonic firing, integer multiple firing, and depolarized resting.
Under driven of dynamic blood pressure, the stochastic model generated resting, firing within systolic period, tonic firing, firing within diastolic period, and depolarized resting with respect to increase of blood pressure. The process reproduced the experiment successfully.
4. In analysis of the mathematical mode, it was revealed that increase of static pressure induced subcritical Hopf bifurcation and caused firing, induced supercritical Hopf bifurcation and caused transition from firing to depolarized resting. The on-off and integer multiple firing were induced by dynamic noise at the bifurcation points, and the bifurcation from firing state to depolarized resting generated "paradoxical firing". This mechanism also explains the firing appeared within the diastolic period and the resting within the systolic period.
This new finding implies the existence of working range for single baroreceptors as well as the possibility of population encoding of blood pressure information by all baroreceptors as a whole. In the cases of other sensations like audition, the working range of single receptors is limited and the complete sensory range is formed by the collaboration in receptor populations. Our results imply that baroreceptors may also have to'collaborate' under certain blood pressure to encode the information of blood pressure. The validity of this implication should be further investigate
The above results indicate that blood pressure dynamically modulates the barareceptor to experience transition on the basis of the bifurcation structure of the model, and the structure is readily produced with the deterministic model by using static blood pressure as the bifurcation parameter. In the case of dynamic changes of blood pressure, the receptor system is driven to evolve on the bifurcation and thus generates divers firing patterns, including the "paradoxical firing".
With help of nonlinear dynamics of bifurcation theories, the encoding of blood pressure changes by baroreceptors can be deeply revealed. The mechanism explains relationships between dynamic properties of blood pressure and temporal rhythms of the firing trains on single depression nerve fibers, including firing pattern dynamic and firing frequency. Further investigations may formulate quantitative theories for encoding by the baroreceptors.
本文采用理论与实验相结合的研究方法,研究主动脉弓压力感受器编码动脉血压信号这个具体的编码环节的生物物理机制和生理学意义。通过对家兔和大鼠动脉压力感受器动态、静态血压变化作用下,神经单纤维放电模式及其转迁规律的研究。实验发现了感受器的5种活动状态：2类静息(分别对应低压阈值和高压阈值)和3类放电行为。放电行为是由血压变化过程中跨越两个阈值产生的。对应动态血压,跨越低压阈值,感受器在收缩压放电；跨越高压阈值,感受器表现为在收缩压放电的反常簇放电；位于两个阈值之间,持续放电。对应静压力,跨越低压阈值,感受器on-off放电；跨越高压阈值,感受器on-off放电或整数倍放电；位于阈值之间,周期一放电并随压力增加频率加快。实验静压力下出现了on-off放电和整数倍放电等非周期放电模式,模型仿真了这类结果,提示它们分别对应跨越超临界Hopf分岔和亚临界Hopf分岔的动力学行为。神经动力学的应用,为理解实验现象的机理提供了有力的理论依据。
主要结果有
1.实验获得了随动态平均血压变化的感受器神经单纤维的放电模式转迁规律。随着平均压力升高,感受器神经单纤维放电依次经历低压静息->收缩压放电->连续放电->舒张压放电的“反常簇放电”->高压静息。识别了感受器神经单纤维的5种活动状态：3种放电和2种静息。在多例标本发现了新的“反常簇放电”现象,并认识到“反常簇放电”存在于高压力区间,其机理是“去极化阻滞”。
2.实验观察了静压力下感受器神经单纤维放电模式的转迁规律。随着静压力升高,感受器神经单纤维放电依次经历了低压静息->on-off放电->持续周期一放电->on-off放电或者整数倍放电->高压静息。和动态平均血压下的转迁规律类似,感受器的2种静息分别对应了低压和高压阈值。其中非周期的on-off放电和整数倍放电,提示在跨越阈值时,感受器放电遵循动力学的Hopf分岔机制。进而利用神经动力学的分岔理论可以解释感受器编码血压信号的机理。
3.构建了基于血压压力感受器感知血压过程的生物写实数学模型。该模型利用不同的函数,对应血管区、感受器区和编码区,分别仿真了血管壁的机械形变、感受器局部电位产生和编码区动作电位产生,进而构成完整的感受器数学模型。调节与实验相一致的参数变化,研究了该数学模型在静压力和动态血压变化下的放电模式及其转迁规律。
4.数学模型仿真结果揭示了放电节律的转迁规律的机制。随着静压力的增加,确定性模型会表现出静息、连续放电、静息的转迁历程。考虑噪声因素的作用,静压力增加时,放电节律会表现出静息、on-off放电、连续均匀放电、整数倍放电、静息的转迁历程,与实验中静压力增加的现象一致。在动压力作用下,随着平均压力的增加,放电会经历静息、血压峰值放电谷值不放电、连续放电、血压峰值不放电血压谷值放电、静息的历程,与实验一致。
5.对数学模型进行分析,随着静压力的增加,从静息变到放电对应亚临界Hopf分岔,从连续放电再到静息是超临界Hopf分岔。静压力下的on-off放电和整数倍放电是噪声分别在超临界和亚临界Hopf点附件诱发的随机节律。而“反常簇放电”是由于在动压力作用下电活动行为因为血压压力在跨越Hopf分岔点引起的：血压峰值处于静息而血压谷值时处于放电引起的。这就从理论上解释了这些新节律的产生的动力学机制。。
上述结果表明,血压信号的改变会引起感受器兴奋性的变化,也就是去极化电流的动态变化。使得压力感受器的放电节律在以去极化电流作为分岔参数的放电节律静态分岔结构中,在平均血压对应的位置附近按照血压信号的时间历程“动态游走”,形成动态放电节律；动态放电节律的时间历程与血压信号的时间动态历程有较好的对应。利用非线性动力学分岔理论不仅从理论上揭示了血压信号引起感受器神经放电的机理,而且可以在包含放电频率在内的多个层面上,在理论层次上建立动态血压信号与相应动态放电之间的联系,进一步认识了感受器的编码机制。
How blood pressures are encoded by baroreceptors is of fundamental importance in neuroscience. Baroreceptors are stretch-sensitive neural terminals which response to static and dynamic arterial blood pressure variations by evoking action potentials at the connected nerve fibers. It is well established in neurophysiology that baroreceptors and their sensory nerves represent the level of blood pressure by means of action potential frequency. The intensity of external signal is believed encoded in the mean frequency of firing trains, and the frequency of impulse is positively correlated to external stimulus density. Since the size of baroreceptor terminals are very small, it is still difficult to directly observe the relation between receptor potential and firing frequency on the nerve fibers. Combining techniques from neuroscience, nonlinear dynamics, information and computer science, it is possible to study the coding mechanisms of barorceptors. In the present study, we investigated the firing pattern and pattern transition (bifurcation) regularities by single unit recording on depression nerves in rat and rabbit. We formulated a mathematical model of barorecepotr and simulated the coding processes. The results provided a basis for a deeper understanding of complex and variable firing rhythm, identification of the relationship between dynamic firing rhythm and dynamic external signal. The dynamic coding processes were emphasized in the research and discussion. The study also gives a new viewpoint and method to theoretically study the neural firing rhythm and neural coding mechanism.
In the present study, using methods of nonlinear dynamics as well as physiological experiments, the biophysical mechanism and physiological significance of the encoding of blood pressure by aortic arch baroreceptor was studied. The aortic arch baroreceptor from both rats and rabbits were chosen as experimental models. The neural firing and aortic blood pressure were recorded simultaneously. The biological relevant theoretical model was formed by considering transformation of blood vessel, generation of receptor potential, initiation of action potential. The theoretical model was analyzed theoretically, and the experimental results were compared with the numeric simulation. The theoretical analysis could reproduce the present experimental results and was used to guide future experiment. On the other hand, the experimental results verified the theoretical analysis.
The main results are as follows.
1, In experiments, we observed that the firing pattern changed with dynamic variation. When the average level of blood pressure was increased from a relatively lower level, the firing pattern of depression fibers changed from resting, to firing within systolic period, to continuous firing, to firing within diastolic period, and finally to resting caused by depolarization block at a relatively high blood pressure level. Five different firing patterns were identified, including three firing states and two resting states. The "paradoxical firing pattern" observed at high ranged of blood pressure was explained by mechanism of "depolarization block".
2, We formulated an realistic mathematical model based on the transduction process. Multiple compartments were employed to represent blood vessel, receptor region, and the coding region to, respectively, simulate the transformation, receptor potential generation, and action potential initiation. By adjusting the same parameters as used in experiments, the experimental results were reproduced successfully.
3, The simulation revealed mechanisms underpinning firing patterns transition. When the static blood pressure was increased, the deterministic form of the formulated model exhibited transition from polarized resting, to tonic firing, and to depolarized resting behaviors. With consideration of biological fluctuation, the stochastic form of the model exhibited resting, on-off firing, tonic firing, integer multiple firing, and depolarized resting.
Under driven of dynamic blood pressure, the stochastic model generated resting, firing within systolic period, tonic firing, firing within diastolic period, and depolarized resting with respect to increase of blood pressure. The process reproduced the experiment successfully.
4. In analysis of the mathematical mode, it was revealed that increase of static pressure induced subcritical Hopf bifurcation and caused firing, induced supercritical Hopf bifurcation and caused transition from firing to depolarized resting. The on-off and integer multiple firing were induced by dynamic noise at the bifurcation points, and the bifurcation from firing state to depolarized resting generated "paradoxical firing". This mechanism also explains the firing appeared within the diastolic period and the resting within the systolic period.
This new finding implies the existence of working range for single baroreceptors as well as the possibility of population encoding of blood pressure information by all baroreceptors as a whole. In the cases of other sensations like audition, the working range of single receptors is limited and the complete sensory range is formed by the collaboration in receptor populations. Our results imply that baroreceptors may also have to'collaborate' under certain blood pressure to encode the information of blood pressure. The validity of this implication should be further investigate
The above results indicate that blood pressure dynamically modulates the barareceptor to experience transition on the basis of the bifurcation structure of the model, and the structure is readily produced with the deterministic model by using static blood pressure as the bifurcation parameter. In the case of dynamic changes of blood pressure, the receptor system is driven to evolve on the bifurcation and thus generates divers firing patterns, including the "paradoxical firing".
With help of nonlinear dynamics of bifurcation theories, the encoding of blood pressure changes by baroreceptors can be deeply revealed. The mechanism explains relationships between dynamic properties of blood pressure and temporal rhythms of the firing trains on single depression nerve fibers, including firing pattern dynamic and firing frequency. Further investigations may formulate quantitative theories for encoding by the baroreceptors.
引文
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27. Heymans, C., Reflexogenic areas of the cardiovascular system. Perspect Biol Med, 1960.3:p.409-17.
28. McCubbin, J.W., J.H. Green, and I.H. Page, Baroceptor function in chronic renal hypertension. Circ Res,1956.4(2):p.205-10.
29. Kunze, D.L. and A.M. Brown, Sodium sensitivity of baroreceptors. Reflex effects on blood pressure and fluid volume in the cat. Circ Res,1978.42(5):p.714-20.
30. Saum, W.R., S. Ayachi, and A.M. Brown, Actions of sodium and potassium ions on baroreceptors of normotensive and spontaneously hypertensive rats. Circ Res,1977. 41(6):p.768-74.
31. Kunze, D.L., W.R. Saum, and A.M. Brown, Sodium sensitivity of baroreceptors mediates reflex changes of blood pressure and urine flow. Nature,1977.267(5606):p. 75-8.
32. Folgering, J.H., et al., Molecular basis of the mammalian pressure-sensitive ion channels:focus on vascular mechanotransduction. Prog Biophys Mol Biol,2008. 97(2-3):p.180-95.
33. Kamm, R.D. and M.R. Kaazempur-Mofrad, On the molecular basis for mechanotransduction. Mech Chem Biosyst,2004.1(3):p.201-9.
34. Sullivan, M.J., et al., Non-Voltage-Gated Ca2+ Influx Through Mechanosensitive Ion Channels in Aortic Baroreceptor Neurons. Circ Res,1997.80(6):p.861-867.
35. Naruse, K. and M. Sokabe, Involvement of Stretch-Activated Ion Channels in Ca-2+ Mobilization to Mechanical Stretch in Endothelial-Cells. American Journal of Physiology,1993.264(4):p. C1037-C1044.
36. Morris, C.E., Mechanosensitive ion channels. J Membr Biol,1990.113(2):p. 93-107.
37. Drummond, H.A., et al., A molecular component of the arterial baroreceptor mechanotransducer. Neuron,1998.21(6):p.1435-41.
38. Li, Z., et al., The prostacyclin analogue carbacyclin inhibits Ca(2+)-activated K+ current in aortic baroreceptor neurones of rats. J Physiol,1997.501 (Pt 2):p. 275-87.
39. Cunningham, J.T., R.E. Wachtel, and F.M. Abboud, Mechanosensitive currents in putative aortic baroreceptor neurons in vitro. J Neurophysiol,1995.73(5):p.2094-8.
40. Mendelowitz, D. and D.L. Kunze, Characterization of calcium currents in aortic baroreceptor neurons. J Neurophysiol,1992.68(2):p.509-17.
41. Kraske, S., et al., Mechanosensitive ion channels in putative aortic baroreceptor neurons. Am J Physiol,1998.275(4 Pt 2):p. H1497-501.
42. Stansfeld, C.E., et al.,4-Aminopyridine and dendrotoxin induce repetitive firing in rat visceral sensory neurones by blocking a slowly inactivating outward current. Neurosci Lett,1986.64(3):p.299-304.
43. Fowler, J.C., W.F. Wonderlin, and D. Weinreich, Prostaglandins block a Ca2+-dependent slow spike afterhyperpolarization independent of effects on Ca2+ influx in visceral afferent neurons. Brain Res,1985.345(2):p.345-9.
44. Awayda, M.S. and M. Subramanyam, Regulation of the epithelial Na+ channel by membrane tension. J Gen Physiol,1998.112(2):p.97-111.
45. Kellenberger, S. and L. Schild, Epithelial sodium channel/degenerin family of ion channels:a variety of functions for a shared structure. Physiol Rev,2002.82(3):p. 735-67.
46. Drummond, H.A., D. Gebremedhin, and D.R. Harder, Degenerin/epithelial Na+ channel proteins:components of a vascular mechanosensor. Hypertension,2004. 44(5):p.643-8.
47. Carattino, M.D., S. Sheng, and T.R. Kleyman, Epithelial Na+ channels are activated by laminar shear stress. J Biol Chem,2004.279(6):p.4120-6.
48. Garcia-Anoveros, J., et al., Transport and localization of the DEG/ENaC ion channel BNaC1alpha to peripheral mechanosensory terminals of dorsal root ganglia neurons. J Neurosci,2001.21(8):p.2678-86.
49. Price, M.P., et al., The mammalian sodium channel BNC1 is required for normal touch sensation. Nature,2000.407(6807):p.1007-11.
50. Desai, B.N. and D.E. Clapham, TRP channels and mice deficient in TRP channels. Pflugers Arch,2005.451(1):p.11-8.
51. Clapham, D.E., et al., International Union of Pharmacology. XLⅢ. Compendium of voltage-gated ion channels:transient receptor potential channels. Pharmacol Rev, 2003.55(4):p.591-6.
52. Christensen, A.P. and D.P. Corey, TRP channels in mechanosensation:direct or indirect activation? Nat Rev Neurosci,2007.8(7):p.510-21.
53. Lin, S.Y. and D.P. Corey,TRP channels in mechanosensation. Curr Opin Neurobiol, 2005.15(3):p.350-7.
54. Corey, D.P., New TRP channels in hearing and mechanosensation. Neuron,2003. 39(4):p.585-8.
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56. Celka, P., A neuronal based baroreceptor model Engineering in Medicine and Biology Society,1996.5:p.1794-1795.
57. Schwaber, J.S., E.B. Graves, and J.F. Paton, Computational modeling of neuronal dynamics for systems analysis:application to neurons of the cardiorespiratory NTS in the rat. Brain Res,1993.604(1-2):p.126-41.
58. Stinnett, H.O. and M.L. Hennes, Model inferences on baroreceptor& sinus wall responses. Biomed Sci Instrum,1991.27:p.105-12.
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63. Arndt, J.O., A. Dorrenhaus, and H. Wiecken, The aortic arch baroreceptor response to static and dynamic stretches in an isolated aorta-depressor nerve preparation of cats in vitro. J Physiol,1975.252(1):p.59-78.
64. Miminoshvili, D.I., Investigation of the function of a single aortic baroreceptor. Bulletin of Experimental Biology and Medicine,1957.43(6):p.651-653.
65. Cowley, A.W., Jr., J.F. Liard, and A.C. Guyton, Role of the Baroreceptor Reflex in Daily Control of Arterial Blood Pressure and Other Variables in Dogs. Circ Res, 1973.32(5):p.564-576.
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69. Yang, M., et al., Characteristics of period adding bifurcation without chaos in firing pattern transitions in an experimental neural pacemaker. NeuroReport,2003. 14(17):p.2153-2157.
70. Gu, H., et al., Experimental observation of the stochastic bursting caused by coherence resonance in a neural pacemaker. NeuroReport,2002.13(13):p. 1657-1660.
71. Ren, W., et al., Different classifications of UPOs in the parametrically different chaotic ISI series of a neural pacemaker. NeuroReport,2001.12(10):p.2121-2124.
72. Gu, H.G., et al., [Application of degree of complexity in heart rate variability analysis during orthostatic (correction of orthosatic) standing]. Space Med Med Eng (Beijing),2001.14(3):p.192-5.
73. Gu, H., et al., Integer multiple spiking in neuronal pacemakers without external periodic stimulation. Physics Letters A,2001.285(1):p.63-68.
74. Gu, H., et al., Integer multiple spiking in neural pacemakers without external periodic stimulation. Phys Lett A,2001.285:p.63-68.
75. Gong, Y., et al., Determining the degree of chaos from analysis of ISI time series in the nervous system:a comparison between correlation dimension and nonlinear forecasting methods. Biol Cybern,1998.78(2):p.159-65.
76. Li, L., et al., A series of bifurcation scenarios in the firing transitions in an experimental neural pacemaker. Int J bifurcation& chaos.14(5):p.1813-1817.
77. Schild, J.H. and D.L. Kunze, Experimental and modeling study of Na+ current heterogeneity in rat nodose neurons and its impact on neuronal discharge. J Neurophysiol,1997.78(6):p.3198-209.
78. FitzHugh, R., Impulses and Physiological States in Theoretical Models of Nerve Membrane.1961. p.445-466.
79.汪云九,神经信息学.高等教育出版社,2006.
80. Wladyka, C.L., et al., The KCNQ/M-current modulates arterial baroreceptor function at the sensory terminal in rats. J Physiol,2008.586(3):p.795-802.
81. Barrett, C.J. and C.P. Bolter, The influence of heart rate on baroreceptor fibre activity in the carotid sinus and aortic depressor nerves of the rabbit. Exp Physiol, 2006.91(5):p.845-852.
82. Fazan, V.P.S., H.C. Salgado, and A.A. Barreira, Aortic depressor nerve unmyelinated fibers in spontaneously hypertensive rats. Am J Physiol Heart Circ Physiol,2001.280(4):p. H1560-1564.
83. Fan, W. and M.C. Andresen, Differential frequency-dependent reflex integration of myelinated and nonmyelinated rat aortic baroreceptors. Am J Physiol,1998.275(2 Pt 2):p. H632-40.
84. Saum, W.R., A.M. Brown, and F.H. Tuley, An electrogenic sodium pump and baroreceptor function in normotensive and spontaneously hypertensive rats. Circ Res, 1976.39(4):p.497-505.
85. Schild, J.H., et al., A-and C-type rat nodose sensory neurons:model interpretations of dynamic discharge characteristics. J Neurophysiol,1994.71(6):p.2338-58.
86. Landgren, S., On the excitation mechanism of the carotid baroceptors. Acta Physiol Scand,1952.26(1)(0001-6772 (Print)):p.1-34.
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88. Feng, B., et al., Theoretical and electrophysiological evidence for axial loading about aortic baroreceptor nerve terminals in rats. Am J Physiol Heart Circ Physiol, 2007.293(6):p. H3659-72.
89. Xavier-Neto, J., E.D. Moreira, and E.M. Krieger, Viscoelastic mechanisms of aortic baroreceptor resetting to hypotension and to hypertension. Am J Physiol,1996. 271(4 Pt 2):p.H1407-15.
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25. Pelletier, C.L., D.L. Clement, and J.T. Shepherd, Comparison of Afferent Activity of Canine Aortic and Sinus Nerves. Circ Res,1972.31(4):p.557-568.
26. Krieger, E.M. and R.F. Marseillan, Aortic Depressor Fibers in the Rat:an Electrophysiological Study. Am J Physiol,1963.205:p.771-4.
27. Heymans, C., Reflexogenic areas of the cardiovascular system. Perspect Biol Med, 1960.3:p.409-17.
28. McCubbin, J.W., J.H. Green, and I.H. Page, Baroceptor function in chronic renal hypertension. Circ Res,1956.4(2):p.205-10.
29. Kunze, D.L. and A.M. Brown, Sodium sensitivity of baroreceptors. Reflex effects on blood pressure and fluid volume in the cat. Circ Res,1978.42(5):p.714-20.
30. Saum, W.R., S. Ayachi, and A.M. Brown, Actions of sodium and potassium ions on baroreceptors of normotensive and spontaneously hypertensive rats. Circ Res,1977. 41(6):p.768-74.
31. Kunze, D.L., W.R. Saum, and A.M. Brown, Sodium sensitivity of baroreceptors mediates reflex changes of blood pressure and urine flow. Nature,1977.267(5606):p. 75-8.
32. Folgering, J.H., et al., Molecular basis of the mammalian pressure-sensitive ion channels:focus on vascular mechanotransduction. Prog Biophys Mol Biol,2008. 97(2-3):p.180-95.
33. Kamm, R.D. and M.R. Kaazempur-Mofrad, On the molecular basis for mechanotransduction. Mech Chem Biosyst,2004.1(3):p.201-9.
34. Sullivan, M.J., et al., Non-Voltage-Gated Ca2+ Influx Through Mechanosensitive Ion Channels in Aortic Baroreceptor Neurons. Circ Res,1997.80(6):p.861-867.
35. Naruse, K. and M. Sokabe, Involvement of Stretch-Activated Ion Channels in Ca-2+ Mobilization to Mechanical Stretch in Endothelial-Cells. American Journal of Physiology,1993.264(4):p. C1037-C1044.
36. Morris, C.E., Mechanosensitive ion channels. J Membr Biol,1990.113(2):p. 93-107.
37. Drummond, H.A., et al., A molecular component of the arterial baroreceptor mechanotransducer. Neuron,1998.21(6):p.1435-41.
38. Li, Z., et al., The prostacyclin analogue carbacyclin inhibits Ca(2+)-activated K+ current in aortic baroreceptor neurones of rats. J Physiol,1997.501 (Pt 2):p. 275-87.
39. Cunningham, J.T., R.E. Wachtel, and F.M. Abboud, Mechanosensitive currents in putative aortic baroreceptor neurons in vitro. J Neurophysiol,1995.73(5):p.2094-8.
40. Mendelowitz, D. and D.L. Kunze, Characterization of calcium currents in aortic baroreceptor neurons. J Neurophysiol,1992.68(2):p.509-17.
41. Kraske, S., et al., Mechanosensitive ion channels in putative aortic baroreceptor neurons. Am J Physiol,1998.275(4 Pt 2):p. H1497-501.
42. Stansfeld, C.E., et al.,4-Aminopyridine and dendrotoxin induce repetitive firing in rat visceral sensory neurones by blocking a slowly inactivating outward current. Neurosci Lett,1986.64(3):p.299-304.
43. Fowler, J.C., W.F. Wonderlin, and D. Weinreich, Prostaglandins block a Ca2+-dependent slow spike afterhyperpolarization independent of effects on Ca2+ influx in visceral afferent neurons. Brain Res,1985.345(2):p.345-9.
44. Awayda, M.S. and M. Subramanyam, Regulation of the epithelial Na+ channel by membrane tension. J Gen Physiol,1998.112(2):p.97-111.
45. Kellenberger, S. and L. Schild, Epithelial sodium channel/degenerin family of ion channels:a variety of functions for a shared structure. Physiol Rev,2002.82(3):p. 735-67.
46. Drummond, H.A., D. Gebremedhin, and D.R. Harder, Degenerin/epithelial Na+ channel proteins:components of a vascular mechanosensor. Hypertension,2004. 44(5):p.643-8.
47. Carattino, M.D., S. Sheng, and T.R. Kleyman, Epithelial Na+ channels are activated by laminar shear stress. J Biol Chem,2004.279(6):p.4120-6.
48. Garcia-Anoveros, J., et al., Transport and localization of the DEG/ENaC ion channel BNaC1alpha to peripheral mechanosensory terminals of dorsal root ganglia neurons. J Neurosci,2001.21(8):p.2678-86.
49. Price, M.P., et al., The mammalian sodium channel BNC1 is required for normal touch sensation. Nature,2000.407(6807):p.1007-11.
50. Desai, B.N. and D.E. Clapham, TRP channels and mice deficient in TRP channels. Pflugers Arch,2005.451(1):p.11-8.
51. Clapham, D.E., et al., International Union of Pharmacology. XLⅢ. Compendium of voltage-gated ion channels:transient receptor potential channels. Pharmacol Rev, 2003.55(4):p.591-6.
52. Christensen, A.P. and D.P. Corey, TRP channels in mechanosensation:direct or indirect activation? Nat Rev Neurosci,2007.8(7):p.510-21.
53. Lin, S.Y. and D.P. Corey,TRP channels in mechanosensation. Curr Opin Neurobiol, 2005.15(3):p.350-7.
54. Corey, D.P., New TRP channels in hearing and mechanosensation. Neuron,2003. 39(4):p.585-8.
55. Kendziorski, C.M., et al., Mapping baroreceptor function to genome:a mathematical modeling approach. Genetics,2002.160(4):p.1687-95.
56. Celka, P., A neuronal based baroreceptor model Engineering in Medicine and Biology Society,1996.5:p.1794-1795.
57. Schwaber, J.S., E.B. Graves, and J.F. Paton, Computational modeling of neuronal dynamics for systems analysis:application to neurons of the cardiorespiratory NTS in the rat. Brain Res,1993.604(1-2):p.126-41.
58. Stinnett, H.O. and M.L. Hennes, Model inferences on baroreceptor& sinus wall responses. Biomed Sci Instrum,1991.27:p.105-12.
59. van Brederode, J.F., et al., Experimental and modeling study of the excitability of carotid sinus baroreceptors. Circ Res,1990.66(6):p.1510-25.
60. Hodgkin, A.L. and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol,1952.117(4):p. 500-44.
61. HODGKIN, A.L. and A. Huxley, A Quantitative Description of Memberane Current and Application to Conduction and Excitation in Nerve. J Phys Lond,1952.117:p. 500-544.
62. Pelletier, C.L. and J.T. Shepherd, Brief Reviews Circulatory Reflexes from Mechanoreceptors in the Cardio-Aortic Area. Circ Res,1973.33(2):p.131-138.
63. Arndt, J.O., A. Dorrenhaus, and H. Wiecken, The aortic arch baroreceptor response to static and dynamic stretches in an isolated aorta-depressor nerve preparation of cats in vitro. J Physiol,1975.252(1):p.59-78.
64. Miminoshvili, D.I., Investigation of the function of a single aortic baroreceptor. Bulletin of Experimental Biology and Medicine,1957.43(6):p.651-653.
65. Cowley, A.W., Jr., J.F. Liard, and A.C. Guyton, Role of the Baroreceptor Reflex in Daily Control of Arterial Blood Pressure and Other Variables in Dogs. Circ Res, 1973.32(5):p.564-576.
66. James, J.E.A., The effects of altering mean pressure, pulse pressure and pulse frequency on the impulse activity in baroreceptor fibres from the aortic arch and right subclavian artery in the rabbit.1971. p.65-88.
67. Yang, M., et al., Understanding of physiological neural firing patterns through dynamical bifurcation machineries. NeuroReport,2006.17(10):p.995-9.
68. Gu, H.G., et al., The chaotic and ASR induced firing patterns in an experimental neural pacemaker. Dynamics of Continuous Discrete and Impulsive Systems-Series B-Applications& Algorithms,2004.11A:p.19-24.
69. Yang, M., et al., Characteristics of period adding bifurcation without chaos in firing pattern transitions in an experimental neural pacemaker. NeuroReport,2003. 14(17):p.2153-2157.
70. Gu, H., et al., Experimental observation of the stochastic bursting caused by coherence resonance in a neural pacemaker. NeuroReport,2002.13(13):p. 1657-1660.
71. Ren, W., et al., Different classifications of UPOs in the parametrically different chaotic ISI series of a neural pacemaker. NeuroReport,2001.12(10):p.2121-2124.
72. Gu, H.G., et al., [Application of degree of complexity in heart rate variability analysis during orthostatic (correction of orthosatic) standing]. Space Med Med Eng (Beijing),2001.14(3):p.192-5.
73. Gu, H., et al., Integer multiple spiking in neuronal pacemakers without external periodic stimulation. Physics Letters A,2001.285(1):p.63-68.
74. Gu, H., et al., Integer multiple spiking in neural pacemakers without external periodic stimulation. Phys Lett A,2001.285:p.63-68.
75. Gong, Y., et al., Determining the degree of chaos from analysis of ISI time series in the nervous system:a comparison between correlation dimension and nonlinear forecasting methods. Biol Cybern,1998.78(2):p.159-65.
76. Li, L., et al., A series of bifurcation scenarios in the firing transitions in an experimental neural pacemaker. Int J bifurcation& chaos.14(5):p.1813-1817.
77. Schild, J.H. and D.L. Kunze, Experimental and modeling study of Na+ current heterogeneity in rat nodose neurons and its impact on neuronal discharge. J Neurophysiol,1997.78(6):p.3198-209.
78. FitzHugh, R., Impulses and Physiological States in Theoretical Models of Nerve Membrane.1961. p.445-466.
79.汪云九,神经信息学.高等教育出版社,2006.
80. Wladyka, C.L., et al., The KCNQ/M-current modulates arterial baroreceptor function at the sensory terminal in rats. J Physiol,2008.586(3):p.795-802.
81. Barrett, C.J. and C.P. Bolter, The influence of heart rate on baroreceptor fibre activity in the carotid sinus and aortic depressor nerves of the rabbit. Exp Physiol, 2006.91(5):p.845-852.
82. Fazan, V.P.S., H.C. Salgado, and A.A. Barreira, Aortic depressor nerve unmyelinated fibers in spontaneously hypertensive rats. Am J Physiol Heart Circ Physiol,2001.280(4):p. H1560-1564.
83. Fan, W. and M.C. Andresen, Differential frequency-dependent reflex integration of myelinated and nonmyelinated rat aortic baroreceptors. Am J Physiol,1998.275(2 Pt 2):p. H632-40.
84. Saum, W.R., A.M. Brown, and F.H. Tuley, An electrogenic sodium pump and baroreceptor function in normotensive and spontaneously hypertensive rats. Circ Res, 1976.39(4):p.497-505.
85. Schild, J.H., et al., A-and C-type rat nodose sensory neurons:model interpretations of dynamic discharge characteristics. J Neurophysiol,1994.71(6):p.2338-58.
86. Landgren, S., On the excitation mechanism of the carotid baroceptors. Acta Physiol Scand,1952.26(1)(0001-6772 (Print)):p.1-34.
87. Connor, J.A., D. Walter, and R. McKown, Neural repetitive firing:modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons. Biophys J,1977.18(1):p.81-102.
88. Feng, B., et al., Theoretical and electrophysiological evidence for axial loading about aortic baroreceptor nerve terminals in rats. Am J Physiol Heart Circ Physiol, 2007.293(6):p. H3659-72.
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