Model maternal and fetal compartments separately as a first

Question

Placental transport of AZT to determine the pharmacokinetic parameters, to assess placental toxicity and to assess distribution of AZT in exposed placental tissues. Using the data given below:

1.)  Model maternal and fetal compartments separately as a first order drug absorption and elimination problem.

Model equation :

C(t, I₀ ,K_a,K_te) = I₀ * (K_a/(K_a-K_te))*(e^-Kte(t) - e^-Ka(t))

2.)    Use Matlab to solve for I₀ ,K_a,K_te using nonlinear regression:

a.)    first using Matlab "fminsearch"

b.)     then using Newton's multivariate method.

Regression equation:

SSE(I₀ ,K_a,K_te) = Σ( Ci - c(t, I₀ ,K_a,K_te))²

Sum of the squares of the error between model and data that is to be minimized

3.)   Plot data along with best-fit model

Maternal Data				Fetal Data
0	0			0	0
1.4	1			0.1	1
4.1	3			0.4	5
4.5	5			0.8	10
3.5	10			1.1	20
3	20			1.2	40
2.75	40			1.4	50
2.65	50			1.35	60
2.4	60			1.6	90
2.2	90			1.7	120
2.15	120			1.9	150
2.1	150			2	180
2.15	180			1.95	210
1.8	210			2.2	240
2	240