420 



8. INHIBITOR DISTRIBUTION IN LIVING ORGANISMS 



This drug is acetylated in the tissues and both forms are excreted through 

 the kidneys. This situation may be represented as: 



L 





I. 



(8-19) 



where Ij is the inhibitor within the body, I^ is the excreted inhibitor, I,„ 

 is the metaboHc product, and !„;<, is tlie excreted metaboKc product. It may 

 be pointed out that either I, or I,„ may be the active inhibitory form, or 

 that both may participate in the inhibition to varying extents. The follow- 

 ing differential equations may be written: 



dt 



{kr + h) (I,) 



= k,aj 



= k,{h) 



(8-20) 

 (8-21) 

 (8-22) 

 (8-23) 



If we set ki -\- k^ = k (representing the over-all rate of removal of the inhi- 

 bitor from the body) and let / be the fraction of the inhibitor that is ex- 

 creted unchanged: 



dt 



djle 



dt 



= - A'(I,) 

 ^fkih) 



(8-24) 



(8-25) 



Expressions for the concentrations of the forms of the inhibitor and the 

 amounts excreted may be obtained by integration and combination of 

 these equations. 



(I,) = axe-''' 



(U =/(I,)o[l -e~^'] 

 kAlX 



(IJ 

 (I..) 



(I,Jo + 



kAlX 



k - k. 



(8-26) 

 (8-27) 



(8-28) 



1 



k - k_ ^ 



^l«^2(lt)o 



k 



[k{lj, - A%(I,Jo + ^i(I.)o] [1 - 



[1 - 6-*='] 



-kot^ 



(8-29) 



'4^ 



