Huang reduced growth model

HuangRM function to fit the Huang reduced growth model to a reduced microbial growth curve. Returns the model parameters estimated according to data collected in microbial growth experiments.

Usage

HuangRM(t, Y0, MUmax, lag)

Arguments

t

is a numeric vector indicating the time of the experiment

Y0

is the natural logarithm of the initial microbial concentration (ln(N0)) at time=0

MUmax

is the maximum specific growth rate given in time units

lag

is the duration of the lag phase in time units

Value

A numeric vector with the fitted values

Details

Model's inputs are:

t: time, assuming time zero as the beginning of the experiment.

Y(t): the natural logarithm of the microbial concentration (ln(N(t))) measured at time t.

Users should make sure that the microbial concentration input is entered in natural logarithm, Y(t) = ln(N(t)).

References

Huang L (2008). “Growth Kinetics of Listeria monocytogenes in Broth and Beef Frankfurters-Determination of Lag Phase Duration and Exponential Growth Rate under Isothermal Conditions.” Journal of Food Science, 73(5), E235-E242. doi:10.1111/j.1750-3841.2008.00785.x .

Author

Vasco Cadavez, vcadavez@ipb.pt & Ursula Gonzales-Barron, ubarron@ipb.pt

Examples

## Example: Huang reduced model
library(gslnls)
data(growthred) # simulated data set.
initial_values <- list(Y0 = 0, MUmax = 1.7, lag = 5) # define the initial values
fit <- gsl_nls(lnN ~ HuangRM(Time, Y0, MUmax, lag),
  data = growthred,
  start = initial_values
)
summary(fit)
#> 
#> Formula: lnN ~ HuangRM(Time, Y0, MUmax, lag)
#> 
#> Parameters:
#>       Estimate Std. Error t value Pr(>|t|)    
#> Y0     0.04513    0.22979   0.196    0.851    
#> MUmax  1.83842    0.04777  38.485 2.06e-08 ***
#> lag    5.03914    0.22005  22.900 4.54e-07 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.3959 on 6 degrees of freedom
#> 
#> Number of iterations to convergence: 7 
#> Achieved convergence tolerance: 0
#>