In this example we will show how to model a conditional dosing using the DiscreteCallbacks
. The problem is as follows. The patient has a drug A(t)
in their system. The concentration of the drug is given as C(t)=A(t)/V
for some volume constant V
. At t=4
, the patient goes to the clinic and is checked. If the concentration of the drug in their body is below 4
, then they will receive a new dose.
For our model, we will use the simple decay equation. We will write this in the in-place form to make it easy to extend to more complicated examples:
using DifferentialEquations function f(du,u,p,t) du[1] = -u[1] end u0 = [10.0] const V = 1 prob = ODEProblem(f,u0,(0.0,10.0))
ODEProblem with uType Vector{Float64} and tType Float64. In-place: true timespan: (0.0, 10.0) u0: 1-element Vector{Float64}: 10.0
Let's see what the solution looks like without any events.
sol = solve(prob,Tsit5()) using Plots; gr() plot(sol)
We see that at time t=4
, the patient should receive a dose. Let's code up that event. We need to check at t=4
if the concentration u[1]/4
is <4
, and if so, add 10
to u[1]
. We do this with the following:
condition(u,t,integrator) = t==4 && u[1]/V<4 affect!(integrator) = integrator.u[1] += 10 cb = DiscreteCallback(condition,affect!)
DiffEqBase.DiscreteCallback{typeof(Main.##WeaveSandBox#4067.condition), typ eof(Main.##WeaveSandBox#4067.affect!), typeof(DiffEqBase.INITIALIZE_DEFAULT ), typeof(DiffEqBase.FINALIZE_DEFAULT)}(Main.##WeaveSandBox#4067.condition, Main.##WeaveSandBox#4067.affect!, DiffEqBase.INITIALIZE_DEFAULT, DiffEqBas e.FINALIZE_DEFAULT, Bool[1, 1])
Now we will give this callback to the solver, and tell it to stop at t=4
so that way the condition can be checked:
sol = solve(prob,Tsit5(),tstops=[4.0],callback=cb) using Plots; gr() plot(sol)
Let's show that it actually added 10 instead of setting the value to 10. We could have set the value using affect!(integrator) = integrator.u[1] = 10
println(sol(4.00000)) println(sol(4.000000000001))
[0.18316389222022983] [10.183163892210045]
Now let's model a patient whose decay rate for the drug is lower:
function f(du,u,p,t) du[1] = -u[1]/6 end u0 = [10.0] const V = 1 prob = ODEProblem(f,u0,(0.0,10.0))
ODEProblem with uType Vector{Float64} and tType Float64. In-place: true timespan: (0.0, 10.0) u0: 1-element Vector{Float64}: 10.0
sol = solve(prob,Tsit5()) using Plots; gr() plot(sol)
Under the same criteria, with the same event, this patient will not receive a second dose:
sol = solve(prob,Tsit5(),tstops=[4.0],callback=cb) using Plots; gr() plot(sol)
These tutorials are a part of the SciMLTutorials.jl repository, found at: https://github.com/SciML/SciMLTutorials.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.
To locally run this tutorial, do the following commands:
using SciMLTutorials
SciMLTutorials.weave_file("tutorials/models","02-conditional_dosing.jmd")
Computer Information:
Julia Version 1.6.2
Commit 1b93d53fc4 (2021-07-14 15:36 UTC)
Platform Info:
OS: Linux (x86_64-pc-linux-gnu)
CPU: AMD EPYC 7502 32-Core Processor
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-11.0.1 (ORCJIT, znver2)
Environment:
JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/a6029d3a-f78b-41ea-bc97-28aa57c6c6ea
JULIA_NUM_THREADS = 16
Package Information:
Status `/var/lib/buildkite-agent/builds/1-amdci4-julia-csail-mit-edu/julialang/scimltutorials-dot-jl/tutorials/models/Project.toml`
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