model initial increase in response for inhibitory drug

hi all,

I have a question please,

I am trying to model the glucose as it changes with anti-diabetic drug but the initial measurement of glucose was taken on fasting but then the patient might started eating and that is why even after the administration of anti-diabetic medication, there was an increase in the glucose and after about 2 hours it started going down. I tried the turnover inhibitory models and the transduction model but these model don’t capture the initial increase in the glucose so I am not sure how can I account for that? (I also tried adding sin or cosin to account for the rhythm of the glucose fluctuation but that doesn’t seem to be helpful

these are the codes I used

test(){

deriv(Aa = - Ka * Aa)

deriv(A1 = Ka * Aa - Cl * C)

dosepoint(Aa)

C = A1 / V

sequence{Ez=E0; E1=E0; E2=E0; E3=E0}

cycle= 10

Kin_mean=39

Kin=Kin_mean + amplt * Kin_mean * sin((2*3.14/cycle) * (t-T0))

deriv(Ez = Kin * (E0 -Ez))

deriv(E1 = (1/Tau) * (Ez * (1 - Emax * C^gam / (C^gam + EC50^gam)) - E1))

deriv(E2 = (1/Tau) * (E1-E2))

deriv(E3 = (1/Tau) * (E2-E3))

error(EEps = 0.1)

observe(EObs = E3 * exp(EEps))

fixef(Ka(freeze) = c(, 0.286517, ))

fixef(V(freeze) = c(, 216719, ))

fixef(Cl(freeze) = c(, 24349.2, ))

fixef(Emax = c(, 4.5, ))

fixef(EC50 = c(, 4, ))

fixef(Tau = c(, 2, ))

fixef(E0 = c(, 100, ))

fixef(gam = c(, 2, ))

fixef(amplt = c(, 0.71, ))

fixef(T0= c(, 1, ))

ranef(diag( nEmax, nEC50n, nE0, nTau, ngam) = c( 0.017685303, 1, 1,1,1))

}

not sure what would be a good strategy to model the initial increase in glucose due to glucose intake.

thank you very much

Omamah

what kind of design and data you have ?

you might want to try a more mechanistic model :

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6063744/
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5658280/

it is observational prospective study where the glucose and the anti-diabetic medication concentration is collected together as the patient walk in the clinic in his regular visit . the collection time is from predose, 1 , 2 ,4 ,6 and some 8 hours. because this is observational study this is the maximum time scale we could go for. the issue is that the first sampling of glucose is as fasting condition but then they can eat (there is no control over that because of the risk of hypoglycemia for the patients). so the curve looks as the initial drug concentration increases the glucose is also increasing then the glucose start going down.

I will check the papers that you have attached. I appreciate it very much!