Dose Selection for Drug Trials

A model-based approach to identify appropriate starting doses

In 2006, the European Medicines Agency (EMEA) published new guidelines to address the issue of starting dose selection in first-in-human trials. Interestingly, the guidelines recommended that modeling and simulation should play an integral part in the selection process. This example illustrates how simulations can be used to study dose selection.

Download the BioChem library from the System Modeler Modelica Library Store.

Import the library:

In[1]:=

Import["TMDDP.mo","MO"]

Show a diagram of the model:

In[2]:=

diagram=SystemModel"TMDD","Diagram",

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Define a 50mg dose with a 15min infusion time, and plot the first 60 seconds:

In[3]:=

mgDose=50;minInfusionTime=15;dose=Function[t,Piecewise[{{mgDose/minInfusionTime,t<minInfusionTime}},0]];Plot[dose[t],{t,0,60}]

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Simulate for the specified dose:

In[4]:=

simTime=20*60*24;sim50mgDose=SystemModelSimulate["TMDD",{0,simTime},"Inputs"{"dose"dose}];

Plot the dose, the mAb concentration in plasma, and the target concentration in plasma over time:

In[5]:=

plotOptions=

options

;ColumnSystemModelPlotsim50mgDose,{"dose"},

,SystemModelPlotsim50mgDose,{"plasmaCompartment.mAb.c"},

,SystemModelPlotsim50mgDose,{"plasmaCompartment.target.c"},

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The mAb plasma concentration should reach its peak instantly and then decline. The concentration of free target molecules shows the reverse behavior: quickly declining due to mAb-target binding, and then slowly returning to baseline as the mAb concentration decreases.

Plot the target occupancy:

In[6]:=

baselineTargetConc=4.5;targetOccupancy[targetConc_]:=(1-targetConc/baselineTargetConc)*100to50mgDose=targetOccupancy[sim50mgDose[{"plasmaCompartment.target.c"},t]];Plotto50mgDose,{t,0,simTime},

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Simulate different doses to find a dose corresponding to 10% target occupancy:

In[7]:=

mgDoses=Table[10^x,{x,-2,2,0.1}];inputFunction[mgDose_]:=Function[t,Piecewise[{{mgDose/minInfusionTime,t<minInfusionTime}},0]];simDoses=SystemModelSimulate["TMDD",{0,simTime},"Inputs"{"dose"Table[inputFunction[dose],{dose,mgDoses}]}];

Plot mAB concentration in plasma for the different doses:

In[8]:=

SystemModelPlotsimDoses,{"plasmaCompartment.mAb.c"},

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Plot target occupancy for the different doses, highlighting the maximums:

In[9]:=

targetConcDoses=Map[#[{"plasmaCompartment.target.c"},t]&,simDoses];toDoses=targetOccupancy[targetConcDoses];maxTO=Table[FindMaximum[{toSim〚1〛,0≤t≤60*24},{t,180},AccuracyGoal3,PrecisionGoal3],{toSim,toDoses}];PlotEvaluate@toDoses12;;35,{t,0,60*24*3},

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External Links

Dose Selection for Drug Trials Using Wolfram System Modeler and Mathematica

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Contributed by: Jan Brugård

Dose Selection for Drug Trials

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