心臟乃包含多成員共同協調工作以達成心律及血氧、養份傳輸至全身之複雜動力學系統。在急速電刺激下，心臟會出現因失穩而產生如交替心律、心動過速及心律不整之豐富動力行為。本論文將呈現我們在體外大鼠全心臟分析心室顫抖數據及抑制交替心律上的成果。我們對體外全心臟在Langendorff系統以急速電刺激引發心室顫抖並同時測量右心房及左心室之電訊號。我們以新穎之非線性分析時間序列方法發現心室顫抖自行復元之先兆，有高達八至九成的成功預測率，並了解其機制。我們以微干擾回饋控制來抑制交替心律之幅度，提出非線性疊代函數理論模型及離子通道模型以理解其機制並以體外大鼠全心臟實驗驗證其詳細之動力學。其控制機制仍源於其微細混沌吸引子之行為，有別於傳統之回饋控制方法與概念。

Heart is a complex dynamical system that contains many components worked
rhythmically in a coordinated manner to produce rhythmic activity for effectively
pumping blood, feeding activities of the whole living body with nutrition and
oxygen. Under fast electrical pacing, heart shows rich dynamical behaviors due
to its instability, such as alternans, tachycardia and fibrillation. In this thesis, we
will present our works in data analysis of ventricular fibrillation and suppressing of
cardiac alternans by alternating-period-feedback stimulations of a whole isolated
rat heart.
Ventricular fibrillation (VF)is an extremely serious arrhythmia which is known to
be the major cause of sudden cardiac death, and thus the research to understand
its mechanism as well as clinical treatments is very important. In our study, VF
in isolated hearts perfused in the Langendorff system is induced by fast electrical
pacing. Electrical signals from right atrium (a site very closed to sinoatrial node)
and left ventricle are recorded simultaneously. We find that when there is strong
component of ventricular signal detected in the atria one during VF, the induced
VF is usually not self-terminating. Quantitative criteria for the prediction ofself-
terminating VF are proposed based on the analysis of bivariate time series (atrial
and ventricular signals)bythe cross-wavelet and cross-Fourier power spectra meth-
ods. The success rate of our prediction is about 80-90%. Our findings suggest that
a heart under VF can recover its sinus rhythm only when the sinoatrial node of
the heart is not under strong influence of the VF from its ventricle.
Alternans response, comprising a sequence of alternating long and short action
potential durations or strong and weak contractions in the heart tissue, seen dur-
ing rapid periodic pacing can lead to conduction block resulting in potentially
fatal cardiac failure. A method of pacing with feedback control is proposed to
reduce the alternans and therefore the probability of subsequent cardiac failure.
The reduction is achieved by feedback control using small perturbations of con-
stant magnitude to the original alternans-generating pacing period T, viz., using
sequences of two periods of T+ǫ and T−ǫ, with ǫ ≪ T. This scheme for alternans
suppression is demonstrated experimentally in isolated whole heart experiments
and further confirmed and investigated in detail by simulations of an iterated map
and also ion-channel based models of cardiac myocytes. The mechanism of the
success of our method is explored by nonlinear dynamic analysis of the cardiac
restitution model: the controlled state is confined in a very small region of chaotic attractor in the phase space, resulting in extremely diminished variation in action
potential durations. This is in contrary to the traditional knowledge in control
of dynamical systems that chaos should be avoided. Most of our theoretical pre-
dictions are well verified experimentally in isolated heart rats. Our method is
much more robust to noise than previous alternans reduction methods based on
fixed point stabilization and should be more efficient in terms of experimental
implementation, and thus for potential clinical treatment for arrhythmia.

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