Detection of an Irregular (Human) Heart Beat using a math model


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6 days ago by
      

'Typical' Readback pulse                   'Defective' Readback pulse

We are seeking High School & College math teachers that may be interested in the following problem: Detection of an Irregular (Human) Heart Beat by Curve Fitting data sets to some math models; e.g. a Lorentz Series.  This type problem would be of great help for many future Engineering & Science students in industry. Do you know of any HS teachers that might be interested in teaching such?  If so, please forward a copy of this message and attached file to them.

Thanks, Phil
PS: A computer disc drive mfg. company had a problem similar to this irregular heart beat problem, 1985.  The disc drive model consisted of 3 modified Lorentz functions.  The model was tried on 200 drives; 199 drives agreed with a small standard deviation.  But, the last drive showed a -major- defective drive.  Thus solving a mfg. problem with a least-square curve fit.  So, it can be done ... try it!
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Want to help solve world (math) problems?
      =====================

Here is a typical cycle ... Problem to Solution
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  • Find a Math model for a -regular- or normal cycle; i.e. a Lorentzian, sinusoidal, or whatever series.  If your model has 'n' components and works for both -regular- and -irregular- cycles you hit the jackpot!  Your 'n' value must always be the same.  Other values in a math model are called Parameters and their values will vary with each data set.
  • Build Pulse train: add 'i' -regular- cycles together separated by Tmin and add 1, 2, or 'j' -irregular- cycles in order to build your problem.  Next, find or build a 'black box' that can detect when a cycle is -irregular-.
  • Find or develop a 'pill' or 'black box' that will stop these -irregular- cycles from occurring.

Learn Curve Fitting for Industrial Applications
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  With the Lorentz (function) where y = 1/(1+x*x), one can fit data to a wide variety of data.  There is a Windows App called CurvFit that has an option of a Lorentzian or Modified Lorentzian series; Sine & Damped Sine; and other series.  Please download, install, and run some of its demo files.  It's free and includes source files for modifying CurvFit as you like.

  If it looks okay to you, then find some example data sets to fit on the web.  For example, I used Google to search for "one-cycle heartbeat data -apple".  When you find a one-cycle data set, build a math model using my CurvFit app.  A heart-beat math model may help other researchers discover what's wrong with a heart, or, other disease.

  Would your students like to help find solutions to medical diseases/problems?  Ask them to find a math model for one-cycle heart-beat data set problem using my CurvFit app.  Suggest forwarding top 5 (or so) CurvFit input files with the files named after the creators or any 'username'; e.g. JimS (for Jim S...) or ElsaB (for Elsa B...).  Link all of them with the same fileType of YYY (?).  Be sure students add their 'notes' below the "20. >> Keep notes below" line.  They should also point out any unusual things that happen during a CurvFit run with their input (file) problem.  Also a good place to put references; e.g. Data set came from the Oil Refinery field; or, Bob Jones provided this data set from the magnetic disc drive field.  (Adding the YYY fileType may help websites locate these problem-solutions, in the future.)

  Add a write-up of a paragraph or two, stating the names of students that were involved in this exercise?  I would then add your statement to my CurvFit app's manual file or ReadMe.txt files for future (free) downloads.  Hope this would encourage your students.

  How about asking your students to ask their parents, grandparents, & friends if they have a data set that may help R & D folks solve their problems?  The more folks involved the more excitement for the students.

  Math folks:
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Develop a math model of a regular one-cycle heartbeat.  Try using a Lorentzian or Modified Lorentzian series.  Download the (free) CurvFit app for more insight.

  R & D folks:
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Build a pulse train of regular cycle heart-beats and 1 or 2 or ??? irregular cycles.  Build/develop a 'black box' what can detect irregular cycles.

  Chemistry folks:
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Find/develop a 'pill' or 'black box' that will stop future irregular cycles.

  Irregular cycle problem solved!
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