Calculation of the Heart Rate:A mathematical Analysis!!!

In ECG if we want calculate what is the heart rate then we follow the following formulas

If Rythm  is Regular, then,

HR=300/Number of Large square from one R to another R wave

or, 1500/Number of small square frome one R to another R

But question is from where is 300 no is coming,or 1500 number is coming.And also why we are considering number if the squares of two R-R interval.

Let see,

According to ECG Convention we know that,

In 1 second  ECG paper runs 25 mm বা 25 small square or 5 large square.......... ( 1)

So we can write

 To run 5 large square time requires  =1 second

To run 5 large square time requires = 1/5 or  0.2 second

So 1 Large square= 0.2 second .........(2)

Now, Between the two R,if we go from one another then number of the beat is=1....... ...(3) 

Assume that From one to another R the distance that is R-R interval is= "a"large squares.                                          

Now,  1‌ large square= 0.2 second

         So, " a" large square= a×0.2 seconds

Now According to equation (3)

 In a×0.2 second   number of Beat = 1

   If we multiply both side by 300 then 

In a×0.2×300 second number of the beat = 300‌ 

Or, In 60 second number of the  Beat হয় =300/a

 

So, 

In 1 minute number of the  Beat = 300/a ..(4)

Now we no that In 1 minute the number of the beat is Heart rate

So, Heart rate= 300/ Numbers of the lrage square in R-R interval   ( "a"= number of large square between R-R interval)      

 

 In the same way we can proof that,

HR= 1500/ R-R interval এ number of small square.

If Rythm is not regular then how we can count the heart rate,

We know that In  1 minute or in 60 seconds the number of  QRS Complex or R wave  R is heart rate Heart rate.But it is difficult to measure this numbers in 1second from ECG.

‌So if we take less seconds and then if we calculate the beats in 60seconds then that will be  easier.

For example If we consider  3 second then we will multiply the number of R wave within this time by 20 and the product will be heart.

   

Now let prove we calculate it.

Assume that in  "x" second  number of R wave is "d"

According to equation (1) 

In 1 second an ECG paper runs  5 large squares,

So in  "x"  second  an ECG paper will run = 5x large square. ......... (5)

Now in in  5x large square the number of  R wave (here it is "d') should be multiplied with such a number that  the product of the number and "x" will be 60. (Because in 60 second or in 1minute the number of R wave is the heart rate.) Assume the number is "c" 

So, we can write, x•c=60    ............ (6)

                              Or, x=60/c............(7)

‌ 

Again in  x second number of beat is beat= d 

So,in  60 second number of beat = d*60/x 

So in  1 minute number of  beat= (d*60)/(60/c)   ( Because according to equation (7), x= 60/c)

                                   

So in  1 minute number of the beat  beat = d*c 

So Heart ratet=d*c/minute

So now finish with an example

In 3 seconds (x=6) or In  30 large square  (5*x=5*6=30) if number of R wave is 5 (d=5) then it should be multiplied by ( c= 60/x=60/3=20) then the heart rate will be  100 beats/minute (d*c=5*20=100)

This is all about for today

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