FastPKSim.jl

This package implements a fast simulator of the two and three compartment pharmacokinetic (PK) model.

Two compartment model

The two compartment model is described by the following differential equations

$$ \dfrac{dx_1}{dt} = - (k_{10} + k_{12}) x_1 + k_{21} x_2 \dfrac{1}{V_1} u $$

$$ \dfrac{dx_2}{dt} = k_{12} x_1 - k_{21} x_2 $$

where

• $x_i(t)$ is the ith state
• $k_{ij}$ is the transfer rate from compartment $j$ to $i$.
• $u(t)$ is the input
• $V_1$ is the central compartment volume.

You can call the simulator using pk2sim! and the function modifies the input vector y. For speedup, use Float32 values for your inputs.

    pk2sim!(y, θ, u, v, hs, youts)
Fast simulation of the three compartment mammillary PK model.

The parameter vector θ has the following structure
`θ = [k10, k12, k21, V1]`
# Arguments:
- `y`: Preallocated output vector of size length(youts)
- `θ`: Parameter vector, see above.
- `u`: Infusion rate vector of size length(hs)
- `v`: Bolus dose vector of size length(hs)
- `hs`: Step size, should have the size of [diff(time) diff(time)[end]] where time is the matching time vector to u, v
- `youts`: Indices for output observations, corresponding to times in hs

Updates `y` with simulated output `x_1` at time instances `youts`.

Three compartment model

The three compartment model is described by the following differential equations

$$ \dfrac{dx_1}{dt} = - (k_{10} + k_{12} + k_{13}) x_1 + k_{21} x_2 + k_{31} x_3 + \dfrac{1}{V_1} u $$

$$ \dfrac{dx_2}{dt} = k_{12} x_1 - k_{21} x_2 $$

$$ \dfrac{dx_3}{dt} = k_{13} x_1 - k_{31} x_3, $$

where

• $x_i(t)$ is the ith state
• $k_{ij}$ is the transfer rate from compartment $j$ to $i$.
• $u(t)$ is the input
• $V_1$ is the central compartment volume.

You can call the simulator using pk3sim! and the function modifies the input vector y. For speedup, use Float32 values for your inputs.

    pk3sim!(y, θ, u, v, hs, youts)
Fast simulation of the three compartment mammillary PK model.

The parameter vector θ has the following structure
`θ = [k10, k12, k13, k21, k31, V1]`
# Arguments: see pk2sim!

Installation

To install, in the Julia REPL:

using Pkg; Pkg.add(url="https://github.com/wahlquisty/FastPKSim.jl")

Example

The following example simulates the three compartment PK model using FastPKSim.jl. We will simulate a patient model with parameter values $\theta$ with constant infusions and boluses as inputs.

using FastPKSim, Plots

θ = [1.f0,2.f0,3.f0,4.f0,5.f0,6.f0] # Parameter values, k10, k12, k13, k21, k31, V1

nu = 50 # length of input
u = [1.1f0*ones(Float32,10) ; 0.1f0*ones(Float32,nu-10)] # Infusion rates
v = [2.0f0*ones(Float32,10) ;0.0f0*ones(Float32,nu-10)  ] # Bolus doses

time = 0.f0:1.f0:nu
hs = diff(time)

youts = [2, 3, 6, 7, 9, 13, 16, 27, 46, 47] # observation times, matching time vector

y = zeros(length(youts)) # Create output vector
pk3sim!(y, θ, u, v, hs, youts) # Simulate model

plot(time[youts], y, xlabel="time", ylabel="y", label="")