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# Bioprocess Engineering - Handling Specific growth rate.

## Bioprocess Engineering - Handling Specific growth rate.

(OP)
Hi Everyone,

I am currently looking for tips or if anyone knows any papers that can help me. I have been researching for a while and cannot seem to find more help in this.

For SGR (specific growth rate of cultured cells):

SGR = ln(X2/X1)/t2-t1

Where X is the biomass (g/L) and t is time in hours.

There have been other calculated parameters such as carbon dioxide production rate (CPR). This rate has been known to grow proportional to X. Therefore as X grows so does CPR and when graphed together they are fairly linear.

As "X2/X1" is mainly a ratio. and X is proportional to CPR. Would "CPR2/CPR1" make a good replacement for this equation to find SGR?

Thank you very much for taking the time to read this!

### RE: Bioprocess Engineering - Handling Specific growth rate.

Given your assumptions that CPR is directly proportional to X and no other factors contribute to SGR, that would be an acceptable mathematical substitution. This can be easily checked by substituting some equation X = m*CPR, for some constant of proportionality (m)... checking the ratio X1/X2, we can quickly recover CPR1/CPR2...

This could work for a quick and dirty calculation, I suspect things are a bit more nuanced.

Seems many people use a multivariate regression including not only CPR, but also oxygen uptake rate (OUR) and base consumption - with growth independent constants.

Even the measured off-gas CPR and OUR must be modified as both can dissolve in the substrate. pH and medium characteristics have been used to refine the mass transfer calculations to dial in actual gas content.

Furthermore, the growth rate doesn't seem to be constant: "In the experiments, the culture was shown to exactly follow a complicated path with considerable jumps in the specific growth rate"...

I think even the measurement process could introduce plenty of error...

https://www.sciencedirect.com/science/article/pii/...

https://www.researchgate.net/publication/11139231_...

### RE: Bioprocess Engineering - Handling Specific growth rate.

(OP)
@onatirec

Thank you so much for the help, it was really handy. According to my values, cumulative CPR seems to be in great correlation with X that X2/X1 is almost equal to CPR2/CPR1.

From the paper, I also see that CPR is directly correlated to dX/dt, or in the case of the paper "Rx(t)". This should mean that cumulative CPR be related to X as instantaneous CPR (or "CPR(t)") is the case that (CPR(t)-CPR(t-1))

I cannot find any papers that state that I am able to replace such values due to their proportionality.

The equation is SGR = ln(X2/X1)/(t2-t1)

I was wondering that it should be possible then to estimate SGR by => SGR = ln (CPR2/CPR1)/(t2/t1)?

Apologies for my confusing confusion.

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