On 01-18-98 William Elliot wrote to John Boone... 
 
        Hello William and thanks for writing, 
  
        [snip] 
  
 WE>  JB> Now, let x be HR1 and y be HR2 and plot the point, 
 WE>  JB> next let x by HR2 and y be HR3 and plot the point, etc.  
 WE>  JB> Said plotting technique results in a distribution on the  
 WE>  JB> x-y plane.  Apparently, the smaller the spread, the more  
 WE>  JB> likely death is to occur.  The trick becomes what spread  
 WE>  JB> is "Ok" and what spread is not.  
 
 WE> Given a function f measured at discrete times t1, t2, ..., 
 WE> ti, ... with ti < ti' where i' = i+1, plot the pairs <  
 WE> f(ti), f(ti') >.  So what's the spread function?  A measure  
  
  The spread function is the thousand dollar question and 
one I am still pondering.  Something, more mathematical, 
"what is the minimum domain of the representation function 
(f(ti),f(ti')) such that the heart shows sufficient chaotic 
behavior?" 
 
 WE> of what?  The function of your example is 60/(Pulse 
 WE> Interval).  Why the reciprocal? 
   
  In response to "Why the reciprocal?"  I assume by this 
why plot (f(ti),f(ti'))?  It was arbitary and gleamed by 
the work of some in "Scientific American" four years ago. 
There are many other ways to represent the data. 
  However, it a reasonable way to represent the data. 
If you look at a -simple- system of degree 2, pendulum 
with moving pivot point, the representation of the 
movement of pendulum as a function of time could be 
done by (P(ti),P(ti')). 
  It seems reasonable to continue the method of 
representation with heart rate.   
 
 WE> Now if the pulse interval is holding steady, the points 
 
  Ah, bingo, in healthy hearts, the pulse interval doesn't 
hold steady, but in fact is "choatic." Reason, the pulse 
interval is a representation of a multiple of excitable 
tissue or cells, in this case, the heart. 
  IOW, the less "choatic" the heart the more unhealthy 
it is.  
 
 WE> will all fall at about the same point.  A -small- spread 
 WE> but a likelihood of death?   
    
  We find that as the plot domain diminishes, the less spread, 
the more unhealthy the heart.  
  
 WE>  WE> uncertainty is frequent companion to diagnosis.  Let me 
 WE>  WE> know if you find any examples.  
 
 WE>  JB> Right, now, I have 5 magazines to read, just got 4 in the mail, 
 
 WE> Any fuzz in any of these magazines? 
 
  Nope, the one I am currently reading, reentrant supraventricular 
tachycardia, fast heart beat. 
  There doesn't seem to be much research in this area, perhaps, 
there doesn't seem to be an awareness or understanding of "fuzzy" 
or fractals. 
 
Take care, 
John 
 
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