I have been using a semi-physiologic model reported by Hendrickx (CPT, 2018) to investigate lung and plasma PK. The Hendrickx model as published has worked well for the datasets I have been using. For the next stage of work I would like to simulate the effects of dissolution in the lung. There is a published model (Franek F, 2018) that I have incorporated into the Hendrickx model. Output from the simulation demonstrated an effect of dissolution on the lung curve. Nevertheless, the lung output was insenstive to changes in the amount of drug delivered to the lung. I have detailed the model text below, that in blue reflects the changes I made incorporating the lung dissolution model. Has the rate (dissolution) been correctly applied to the lung dosing point A2?
test(){
dose
dosepoint(A2,rate=Fd) # Lung deposited dose in shallow lung, compartment 2 (Table S4)
dosepoint(Aa,bioavail=F) # Portion of inhaled dose ending up in gastro-intestinal tract
Fd = (1- exp(-(t/t63)^b))
differential equations describing rate of change for the amounts over time in each of the 5 compartments
Aa = amount in GI tract
deriv(Aa = -ka*Aa)
A1 = amount in plasma
deriv(A1 = (kaAa)+(C2fu2CLD12)+(C4uCLD14)-(C1CL)-(C1fu1CLD12)-(C1fu1*CLD14))
A2 = amount in ‘shallow’ lung
deriv(A2 = (K32A3)+(CLD12fu1C1)-(C2fu2CLD12)-(C2fu2*CLD23))
A3 = amount in ’deep’ lung
deriv(A3 = (fu2CLD23C2)-(K32*A3))
A4 = amount in ‘shallow’ tissue (without lung)
deriv(A4 = (K32A5)+(CLD14fu1C1)-(C4uCLD14)-(C4u*CLD45))
A5 = amount in ’deep’ tissue (without lung)
deriv(A5 = (CLD45C4u)-(K32A5))
initial values residual error standard deviations
#error(CEps = 0.1)# st. dev residual error connected to plasma concentrations
#error(LEps = 0.1)# st. dev. residual error connected to lung concentrations
concentration terms
C1=A1/V1# total plasma concentrations, compartment 1
C2=A2/V2# total concentration in ‘shallow’ lung, compartment 2
C4u=A4*fu4_V4# unbound concentration in ‘shallow’ tissue (without lung), compartment 4
Clung = (A2+A3)/V2 # total lung concentrations
residual error model
#observe(LObs= Clung *(1 + LEps)) # proportional residual error on total lung concentrations
#observe(CObs=C1 *(1 + CEps))# proprotional residual error on total plasma concentrations
parameters
stparm(K32 = tvK32)# fractional distribution rate constant from ‘deep’ to ‘shallow’ lung
stparm(CLD23 = tvCLD23)# unbound distributional clearance from ‘shallow’ to ‘deep’ lung
stparm(CLD45 = tvCLD45)# unbound distributional clearance from ‘shallow’ to ‘deep’ tissue
stparm(CLD12 = tvCLD12)# unbound distributional clearance between ‘shallow’ lung and #plasma
stparm(CLD14 = tvCLD14)# unbound distributional clearance between plasma and ‘shallow’ #tissue (without lung)
stparm(CL = tvCL)# elimination clearance from total plasma
stparm(V1 = tvV1)# volume of plasma compartment
stparm(V2 = tvV2)# volume of ’shallow’ lung compartment
stparm(fu1 = tvfu1)# unbound fraction in plasma
stparm(fu2 = tvfu2)# unbound fraction in ’shallow’ lung compartment
stparm(fu4_V4 = tvfu4_V4)# ratio unbound fraction and volume in ’shallow’ tissue (without #lung)
stparm(F=tvF)# bioavailability from GI tract
stparm(ka=tvka)# first order absorption rate constant
stparm(t63=tvt63)# dissolution parameter
stparm(b=tvb) #dissolution parameter
fixed parameter and constants for simulation
fixef(tvK32 = c(,1.84,))
fixef(tvCLD23 = c(,3895,))
fixef(tvCLD45 (freeze) = c(,4391,))value
fixef(tvCLD12 (freeze) = c(,22327,))
fixef(tvCLD14 (freeze) = c(,4327,))
fixef(tvCL (freeze) = c(,200,))
fixef(tvV1 (freeze) = c(,46,))
fixef(tvV2 (freeze)= c(,14,))
fixef(tvfu1 (freeze) = c(,0.07,))
fixef(tvfu2 (freeze) = c(,0.03,))
fixef(tvfu4_V4 (freeze)= c(,0.0000442,))
fixef(tvF (freeze)= c(,0.98,))# constant
fixef(tvka (freeze)= c (,0.94,))# constant
fixef(tvt63 (freeze)= c (,2.6,))# constant
fixef(tvb (freeze)= c (,1.2,))# constant
}
