Nonlinear regression of pharmacokinetic model using matlab

Question

Question:

Nonlinear regression of pharmacokinetic model using Matlab

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 ,Ka,Kte 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