laplace-kinetics

A Laplace library of parametric nonlinear functions for pharmacokinetics, dose-response modeling, and growth/decay processes — ready to import into any .laplace model with namespaced calls (kinetics::function_name(...)).

Like all Laplace libraries, kinetics compiles down to plain, readable Stan functions. Nothing about how you use it hides what actually ends up in your .stan file.

What's included

Dose-response / pharmacology (dose_response.laplacelib)

Parametric functions for dose-response modeling, pharmacological effect and inhibition models, receptor binding and cooperativity, and biological assay calibration.

Function	Description
emax(E0, Emax, x, EC50)	Parametric Emax dose-response: $E_0 + \frac{E_{\max}x}{EC_{50}+x}$
sigmoid_emax(E0, Emax, x, EC50, h)	Sigmoid Emax / Hill: $E_0 + \frac{E_{\max}x^h}{EC_{50}^h+x^h}$
four_pl(d, a, x, b, c)	Four-parameter logistic: $d + \frac{a-d}{1+(x/c)^b}$
imax(E0, Imax, x, IC50)	Parametric Imax inhibitory response: $E_0 - \frac{I_{\max}x}{IC_{50}+x}$
inhibitory_emax(E0, Imax, x, IC50, h)	Sigmoid inhibitory Emax: $E_0 - \frac{I_{\max}x^h}{IC_{50}^h+x^h}$
logistic_dose_response(L, U, x, k, xo)	Logistic dose-response: $L + \frac{U-L}{1+\exp[-k(x-x_0)]}$
hill(x, n, K)	Hill equation for binding/cooperativity: $\frac{x^n}{K^n+x^n}$

Growth and decay (growth_decay.laplacelib)

Functions for biological/population growth, pharmacokinetic elimination, decay processes, organismal growth, and multi-phase exponential processes.

Function	Description
exponential_growth(A, k, x)	Exponential growth: $Ae^{kx}$
exponential_decay(A, k, x)	Exponential decay: $Ae^{-kx}$
logistic_growth(K, A, r, x)	Logistic growth: $\frac{K}{1+Ae^{-rx}}$
gompertz(A, B, k, x)	Gompertz growth: $Ae^{-Be^{-kx}}$
von_bertalanffy(Linf, B, k, t)	Von Bertalanffy growth: $L_{\infty}(1-Be^{-kt})^3$
biexponential(A, B, k1, k2, t)	Biexponential decay: $Ae^{-k_1t} + Be^{-k_2t}$

Pharmacokinetics (pharmacokinetics.laplacelib)

Closed-form deterministic functions for one- and two-compartment PK models, IV bolus and infusion, first-order absorption, extravascular dosing, and Bateman kinetics.

Function	Description
one_comp_iv_bolus(D, V, k, t)	One-compartment IV bolus: $\frac{D}{V}e^{-kt}$
one_comp_iv_infusion(R0, V, k, t)	One-compartment IV infusion: $\frac{R_0}{Vk}(1-e^{-kt})$
one_comp_iv_post_infusion(R0, V, k, T, t)	One-compartment IV post-infusion: $\frac{R_0}{Vk}(1-e^{-kT})e^{-k(t-T)}$
two_comp_iv_bolus(A, B, alpha, beta, t)	Two-compartment IV bolus: $Ae^{-\alpha t} + Be^{-\beta t}$
bateman(F, D, V, ka, k, t)	Bateman function (first-order absorption + elimination): $\frac{FDk_a}{V(k_a-k)}(e^{-kt}-e^{-k_at})$
first_order_absorption(D, ka, t)	First-order absorption: $De^{-k_at}$

Installation

kinetics is distributed as a git-hosted Laplace library — there's no published registry entry yet, so it's added by pointing laplace (or cmdlaplacer, if you're working from R) directly at the repository.

Via the laplace CLI

From inside a Laplace project (a directory with its own laplace.toml):

laplace add kinetics --git https://github.com/mlatinov/laplace-kinetics --tag 0.1.0

Via R (cmdlaplacer)

library(cmdlaplacer)

laplace_install_git(
  "kinetics",
  "https://github.com/mlatinov/laplace-kinetics",
  tag = "0.1.0"
)

Either way, this pins the dependency in your project's laplace.toml/laplace.lock at tag 0.1.0. Check the releases for newer tags as they become available.

Usage

Import the library and call its functions with the kinetics:: namespace prefix:

library {
    kinetics;
}

model {
    mu = kinetics::emax(E0, Emax, x, EC50);
    // ...
}

License

See LICENSE.