exponential_drift: Exponential-drift function

In mnirs: Muscle Near-Infrared Spectroscopy Processing and Analysis

Exponential-drift function

Description

Calculate a two-phase curve: a fast monoexponential() primary response plus a slow linear secondary drift beginning near the primary asymptote. Model family fit by analyse_kinetics() with method = "exponential_drift", and by stats::nls() via the self-starting wrapper SSexponential_drift().

Usage

exponential_drift(t, A, B, tau, slope_B, drift_fraction, TD = NULL)

Arguments

t	A numeric vector of the predictor variable (time).
A	A numeric parameter for the starting baseline of the response variable.
B	A numeric parameter for the ending asymptote of the response variable.
tau	A numeric parameter for the time constant (\tau) of the exponential response, in units of the predictor variable t.
slope_B	A numeric parameter for the linear drift rate dx/dt of the secondary phase, in response units per unit of the predictor variable t.
drift_fraction	A numeric fraction of the primary amplitude B - A in ⁠(0.5, 1)⁠ at which the linear drift begins, where the primary response reaches A + drift_fraction * (B - A).
TD	A numeric parameter for the time delay before the onset of the exponential response, in units of the predictor variable t. If NULL (default), a 3-parameter model without time delay is used.

Details

Model equations

• 5-parameter: A + (B - A) * (1 - exp(-t / tau)) + slope_B * pmax(t + tau * log(1 - drift_fraction), 0)

• 6-parameter: A + (B - A) * (1 - exp(-pmax(t - TD, 0) / tau)) + slope_B * pmax(t - TD + tau * log(1 - drift_fraction), 0)

A, B, tau, and TD are as for monoexponential(). The drift onset is not a free estimate: the secondary drift is exactly zero before TD - tau * log(1 - drift_fraction) (TD = 0 when absent), and drift_fraction = 0.95 places the onset at TD + 3 * tau.

The excursion point texc is where the drift rate overtakes the decaying primary rate, ⁠TD + tau * log(|B - A| / (|slope_B| * tau))⁠, floored at the drift onset.

Value

A numeric vector of predicted values the same length as the predictor variable t.

See Also

analyse_kinetics(), SSexponential_drift(), monoexponential(), biexponential(), sigmoidal_drift()

Examples

## create an exponential curve with late linear drift and random noise
set.seed(13)
t <- 1:180
x <- exponential_drift(
    t, A = 10, B = 100, tau = 12,
    slope_B = -0.5, drift_fraction = 0.95, TD = 15
) + rnorm(length(t), 0, 2)
data <- data.frame(t, x)

## the drift onset fraction is held constant in the formula
model <- nls(
    x ~ SSexponential_drift(
        t, A, B, tau, slope_B, drift_fraction = 0.95, TD
    ),
    data = data,
    algorithm = "port",
    lower = c(-Inf, -Inf, 0, -Inf, 0),
    control = nls.control(warnOnly = TRUE)
)
summary(model)

y <- predict(model, data)


    if (requireNamespace("ggplot2", quietly = TRUE)) {
        ggplot2::ggplot(data, ggplot2::aes(t, x)) +
            theme_mnirs() +
            ggplot2::geom_point() +
            ggplot2::geom_line(ggplot2::aes(y = y))
    }

mnirs documentation built on Sept. 13, 2026, 1:06 a.m.