1. Project #1: Drug Kinetics in Genetically Modified Mice

2. Model
Initial dose: 𝑋 𝑎 (0)=𝑋 0 ∙𝐹, where 𝐹 is the fraction of drug absorbed.
𝑘 𝑎 𝐾
𝑋 𝑎 𝑋
Absorption compartment: Blood (plasma) compartment:
total drug amount total drug amount
Here 𝑘 𝑎 is absorption rate constant and 𝐾 is drug elimination rate constant.

3. Differential equation model describing drug kinetics has the following solution:
𝑋(𝑡)= 𝑘 𝑎 𝐹 𝑋 0 𝑘 𝑎 −𝐾 exp −𝐾𝑡 −exp(− 𝑘 𝑎 𝑡) .
One can measure the concentration of drug in blood (plasma):
𝐶 𝑡 = 𝑋 𝑡 𝑉 = 𝐹 𝑉 ∙𝑋 0 ∙ 𝑘 𝑎 𝑘 𝑎 −𝐾 exp −𝐾𝑡 − exp − 𝑘 𝑎 𝑡 .
Here 𝑉 is effective distribution volume (not known).

4. Differential equation model describing drug kinetics has the following solution:
𝑋(𝑡)= 𝑘 𝑎 𝐹 𝑋 0 𝑘 𝑎 −𝐾 exp −𝐾𝑡 −exp(− 𝑘 𝑎 𝑡) .
One can measure the concentration of drug in blood (plasma):
𝐶 𝑡 = 𝑋 𝑡 𝑉 = 𝐹 𝑉 ∙𝑋 0 ∙ 𝑘 𝑎 𝑘 𝑎 −𝐾 exp −𝐾𝑡 − exp − 𝑘 𝑎 𝑡 .
Need to estimate: 𝒌 𝒂 , 𝑲, 𝑭/𝑽.

5. Data: Mice A drug concentration in plasma: microgram/ml t=1h t=2h t=4h
initial dose: micrograms
mouse1a
mouse2a
mouse3a
mouse4a
mouse5a
mouse6a
mouse7a
mouse8a
mouse9a
mouse10a

6. Data: Mice B drug concentration in plasma: microgram/ml t=1h t=2h t=4h
initial dose: micrograms
mouse1b
mouse2b
mouse3b
mouse4b
mouse5b
mouse6b
0.6134
mouse7b
mouse8b
mouse9b
mouse10b