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rumenGP implements a collection of nonlinear models for describing cumulative gas production during in vitro rumen fermentation.
This vignette summarizes:
Throughout this vignette:
\[ V(t) \]
represents cumulative gas production at time:
\[ t \]
\[ V(t) = A \left( 1 - b e^{-kt} \right) \]
| Parameter | Description |
|---|---|
| A | Asymptotic gas production |
| b | Integration constant |
| k | Fractional rate constant |
\[ V(t) = VF + b \left( 1-e^{-kt} \right) \]
| Parameter | Description |
|---|---|
| VF | Initial gas volume (intercept) |
| b | Fermentable fraction |
| k | Fractional rate constant |
\[ V(t) = V_f \left( 1-e^{-kt} \right) \]
| Parameter | Description |
|---|---|
| Vf | Asymptotic gas production |
| k | Fractional rate constant |
\[ V(t) = V_f \left( 1-e^{-k(t-\lambda)} \right) \]
| Parameter | Description |
|---|---|
| Vf | Asymptotic gas production |
| k | Fractional rate constant |
| λ | Lag time |
\[ V(t) = A \exp \left[ - \exp \left( \frac{\mu e}{A} (\lambda-t) + 1 \right) \right] \]
| Parameter | Description |
|---|---|
| A | Asymptotic gas production |
| μ | Maximum gas production rate |
| λ | Lag time |
\[ V(t) = \frac{A} { 1+\exp \left[ 2+ 4k(\lambda-t) \right] } \]
| Parameter | Description |
|---|---|
| A | Asymptotic gas production |
| k | Fractional rate constant |
| λ | Lag time |
\[ V(t) = A \left[ 1 - \exp \left( -k(t-\lambda) - d \left( \sqrt{t+0.001} - \sqrt{\lambda+0.001} \right) \right) \right] \]
| Parameter | Description |
|---|---|
| A | Asymptotic gas production |
| k | Fractional rate constant |
| d | Shape parameter |
| λ | Lag time |
\[ V(t) = \frac{ A \left( 1-e^{-kt} \right) } { 1+\exp \left[ \ln\left(\frac{1}{d}\right)-kt \right] } \]
| Parameter | Description |
|---|---|
| A | Asymptotic gas production |
| k | Fractional rate constant |
| d | Shape parameter |
\[ V(t) = \frac{ A \left( 1-e^{-k(t-\lambda)} \right) } { 1+\exp \left[ \ln\left(\frac{1}{d}\right) - k(t-\lambda) \right] } \]
| Parameter | Description |
|---|---|
| A | Asymptotic gas production |
| k | Fractional rate constant |
| d | Shape parameter |
| λ | Lag time |
\[ V(t) = A \frac{t^{c}} { t^{c}+K^{c} } \]
| Parameter | Description |
|---|---|
| A | Asymptotic gas production |
| K | Half-time parameter |
| c | Shape parameter |
\[ V(t) = \frac{VF} { 1+\left(\frac{b}{t}\right)^k } \]
| Parameter | Description |
|---|---|
| VF | Asymptotic gas production |
| b | Half-time parameter |
| k | Shape parameter |
\[ V(t) = \frac{V_{1F}} { 1+\exp \left[ 2-4k_1(t-\lambda) \right] } + \frac{V_{2F}} { 1+\exp \left[ 2-4k_2(t-\lambda) \right] } \]
| Parameter | Description |
|---|---|
| V1F | Gas volume from rapidly fermentable fraction |
| V2F | Gas volume from slowly fermentable fraction |
| k1 | Rate constant of rapid fraction |
| k2 | Rate constant of slow fraction |
| λ | Lag time |
The Groot and generalized Michaelis-Menten models are mathematically equivalent.
Parameter correspondence:
\[ VF = A \]
\[ b = K \]
\[ k = c \]
Both formulations produce identical fitted values and model diagnostics when convergence is achieved.
Researchers may select either model according to the terminology commonly used in their field.
A practical progression is:
Use when:
Use when:
Use when:
Use when:
rumenGP provides a diverse collection of nonlinear kinetic models ranging from simple exponential equations to flexible multi-pool formulations.
Model choice should be guided by:
Researchers are encouraged to compare multiple models before selecting a final representation of fermentation kinetics.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.