Using Three-Dimensional Lorenz Scatter Plots to Detect Patients with Atrioventricular Node Double Path Caused by Interpolated Ventricular Premature Systoles: A Case Study

A series of related electrophysiology phenomena can be caused by the occurrence of interpolated ventricular premature contraction.In our recent three-dimensional Lorenz R-R scatter plot research,we found that atrioventricular node double path caused by interpolated ventricular premature contraction imprints a specifi c pattern on three-dimensional Lorenz plots generated from 24-hour Holter recordings.We found two independent subclusters separated from the interpolated premature beat precluster,the interpolated premature beat cluster,and the interpolated premature beat postcluster,respectively.Combined with use of the trajectory tracking function and the leap phenomenon,our results reveal the presence of the atrioventricular node double conduction path.

Timed RR-interval Scatter Plots and Reverse Technology

Lorenz-RR scatter plot has an obvious shortcoming in that it does not indicate the time when the scatter point happens.On the Lorenz RR scatter plot,one cannot know the time during which the cardiac rhythms take place.Since occurrence of cardiac rhythms is time-related,time should be introduced to such plots.In this study,time was used as abscissa and RR interval(the time interval between the previous RR wave and the R wave)as the ordinate and time was compressed into a visually observable length,and thereby a timed RR-interval scatter plot,or t-RR scatter plot,for short,was developed.On t-RR scatter plot,the patterns were band-shaped or were of linear type.On the t-RR plot,the sinus rhythm presented bands of various widths,with the spiculate or burred upper and lower boundaries,having diurnal variation.Premature beats showed separate layers(“stratification”),the layer number corresponding the number of RR-intervals.With simple premature beats,the layers were clearly separated.With parasystole rhythm,the upper and lower bands or layers might become thicker.With arial premature beats,the space or distance between layers varied.Ventricular premature beats presented equal space or distance between layers.With tachycardia,the lower layer became a“solid”layer.With atrial fibration,the“stratification”disappeared,presenting thicker or widened layers or bands,with neat lower boundary.With atrial flutter,the layers went parallel,with the layers being evenly separated or some distances being exact multiples of others.The second degree atrioventricular block displayed two layers,the lower and upper bands being equally away from the X-axis,presenting a straight line(pacing at a fixed rate)or a thicker or wider bands,with a neat upper boundary(the lowest pacing rate).When the scatter plot presented uncharacteristic patterns or had some scattered points,which rendered diagnosis difficult,a reverse technology could be used.Briefly,upon selection of scattered points,they were subjected to computerization,by regression,to reveal the piece of electrocardiogram(ECG)containing an R wave(QRS complex).Then ECG was analyzed to diagnose the cardiac rhythms.In conclusion,t-RR is a novel methodology which helps us understand heart rhythms from a new perspective.

Parameter Sensitivity and Qualitative Analysis of Dynamics of Ovarian Tumor Growth Model with Treatment Strategy

In this paper, we are interested to find the most sensitive parameter, local and global stability of ovarian tumor growth model. For sensitivity analysis, we use Latin Hypercube Sampling (LHS) method to generate sample points and Partial Rank Correlation Coefficient (PRCC) method, uses those sample points to find out which parameters are important for the model. Based on our findings, we suggest some treatment strategies. We investigate the sensitivity of the parameters for tumor volume, y, cell nutrient density, Q and maximum tumor size, ymax. We also use Scatter Plot method using LHS samples to show the consistency of the results obtained by using PRCC. Moreover, we discuss the qualitative analysis of ovarian tumor growth model investigating the local and global stability.