From: <HIDDEN>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Bacterial specific growth rate calculation.
Date: Wed, 14 Mar 2012 08:11:12 +0000 (UTC)
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"smith" wrote in message <jjpg8m$gej$>...
> I need to calculate the bacterial specific growth rate for a batch process i.e I want to calculate the maximum growth rate at exponential growing condition. I have to calculate for a large set of varied cases.
> In the plot of log of biomass versus time,I have been taking the mean of slopes at each point (x2-x1)/(t2-t1) from time t=0 to the end of exponential growth phase. This method is not accurate,gives a reduced growth rate. For each case one has to take the mean of the slopes those are at higher range and exclude the lower values of slope.
> Is there any other way to get this?
- - - - - - - - - -
  If your time intervals are all equal you could get a second order approximation to the derivative using matlab's 'gradient' function.

  With unequal intervals you can use the formula

 (x2-x1)/(t2-t1)*(t3-t2)/(t3-t1) + (x3-x2)/(t3-t2)*(t2-t1)/(t3-t1)

as a second order approximation to the derivative at (t2,x2) with (t1,x1) and (t3,x3) as points on either side.  Second order approximation here means the slope of a parabola at (t2,x2) which runs through all three points.

  Both methods assume that your plotted data is relatively noise-free.

Roger Stafford