On 01-22-98 William Elliot wrote to John Boone... 
 
        Hello William and thanks for writing, 
  
 WE>  JB> For example if the time for one beat to the next beat is  
 WE>  JB> .5 seconds, P-P interval is .5 seconds, the persons heart  
 WE>  JB> rate is 120 beats per minute, (60/.5).  
 
 WE> I see, since the P-P interval is less than one the 
 WE> reciprocal transformation exaggerates the spread.  As the  
 
   Yes and more familar for most physicians. 
  
 WE> critical focus is zero spread, this data transform is more 
 WE> accurate than the simple: 
 
 WE>  JB> I am interested in Heart rate, however, one could just measure 
 WE>  JB> the P-P interval variability as well.  
   
 WE>  JB> IAE, make up some heart rates and plot it on a x-y  
 WE>  JB> graph, here are some realistic ones.  HR1=80, HR2=75, HR3=70,  
 WE>  JB> HR4=85, HR5=90, HR6=72, HR7=65, HR8=75, ....  
 WE>  JB> Point 1 is (80,75), point 2 (75,70), point 3 (70,85),  
 WE>  JB> point 4 (85,90), etc.  
 
 WE>   7 8 9 
 WE> 7  2 
 WE>     1 
 WE> 8  
 WE>   3 
 WE> 9    4 
 
 WE> Hm, it's doing more than just checking the deviation of distance(HRi' 
 WE> - HRi) 
 WE> i' = i+1.  It's checking meander.  How conceptually does  
 
  You got it. 
  
 WE> this compare with the deviation of the data set HRi? 
 
  Not sure what you what you mean by this question. 
  
 WE> There's some sort of smoothing going on? 
   
        [snip] 
  
 WE>  JB> Think of a simple pendulum with the pivot point fixed.  
 WE>  JB> Now move the pivot point horizontal say with a certain  
 WE>  JB> omega, frequency.   
  
 WE> Oh a simple one dimensional oscillation?  The amplitude 
 
   Oscillation within a plane (x,y).  The plot (x,y) is the 
path of the pendulum, the thing at the end of the string. 
If the pendulum swings with frequency, sf, whose pivot point 
moves along a line -segment- with frequency, hf, the pendulum's 
path at certain hf become chaotic.  
 
 WE> would slowly diminish.  As the pendulum approached center 
 WE> the spread area would approach zero.  No? 
   
 WE>  WE> Hm, what about fibrillation and other erratic heart  
 
 WE>  JB> Hard one for me to answer, in particular. But I can 
 WE>  JB> answer ventricular fibrillantion, VF.   VF does not plot  
 WE>  JB> out "choatic", interesting no.  
 
 WE> Is this quiescence during or before a VF attack. 
   
  Before, hence, the reasoning for wanting to explore it. 
  
 WE>  JB> Of interesting note, if one looks at EEG, electro-encephalo 
 WE>  JB> graph, activity, brain activity, the plot becomes very  
 WE>  JB> non-chaotic just before a seizure, interesting no.  
 
 WE> Hm, going back to the example of the pendulum, something is 
 WE> coming to a standstill.  Now consider a moving marble  
 
  Yep, and that "something" (coming to a standstill) is 
variability. 
  
 WE> moving around a shallow funnel.  It's spread approaches 
 WE> zero as it nears the center and if there's a big enuf hole  
 WE> in the center ... 
   
 WE>  WE> Plot domain?  The smallest rectangle with sides parallel to  
 WE>  WE> the axis that contains all the plotted points.  
 
 WE>  JB> Yep, the plot, even though choatic, is constrained within 
 WE>  JB> limits on the x,y plane.      
 
 WE> My think tank has sprung a leak. -) 
    
  Ah, at least with the pendulum example, the plot (x,y) of 
the pendulum although chaotic is within certain bounds. 
 
 WE> WE> I've heard it rumored some years ago that medical students 
 WE> WE> are mathematical shy.  Is that so?  Are you in medicine or   
 WE> WE> biology?  Are you considering a fuzzy thesis or research  
 
 WE> JB> Some are, some are not.  I was once a medical student. 
 WE> JB> Medicine.  
 WE> JB> Research while working leaving little time for research.   
 
 WE> So you're a mathematical literate doctor that would like to 
 WE> do research except for lacking funds? 
 
  Yep.  BTW, thanks for sending me your thoughts on 
logical qualifiers.  I printed it out so that I could read it 
and no, I didn't try to save it to a file .  
 
Take care, 
John 
 
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