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.