monoexponential: Monoexponential function

In mnirs: Muscle Near-Infrared Spectroscopy Processing and Analysis

Monoexponential function

Description

Calculate a 3- or 4-parameter monoexponential curve. Model family fit by analyse_kinetics() with method = "monoexponential", and by stats::nls() via the self-starting wrapper SSmonoexponential().

Usage

monoexponential(t, A, B, tau, 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.
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

• 3-parameter: A + (B - A) * (1 - exp(-t / tau))

• 4-parameter: A + (B - A) * (1 - exp(-pmax(t - TD, 0) / tau))

Clamping the shifted time at zero holds the curve flat at the baseline A until the response onset at t = TD.

Derived quantities

The rate constant k is the reciprocal of tau (k = 1 / tau) in reciprocal units of t (e.g. sec^-1). The mean response time is the time sum MRT = TD + tau, and the half-response time is HRT = TD + tau * log(2).

Value

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

See Also

analyse_kinetics(), SSmonoexponential(), exponential_drift(), biexponential(), response_time(), peak_slope()

Examples

## create an exponential curve with random noise
set.seed(13)
t <- 1:60
x <- monoexponential(t, A = 10, B = 100, tau = 8, TD = 15) +
    rnorm(length(t), 0, 3)
data <- data.frame(t, x)

## 4-parameter fit with the self-starting wrapper
model <- nls(x ~ SSmonoexponential(t, A, B, tau, TD), data = data)
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.