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Nonlinear regression of pharmacokinetic model using Matlab

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All I can tell you is that we are supposed to use a multidimensional extension of Taylor's theorem to approx. the variation of f(x) in the neighborhood of an initial guess, x^(k) where f'(x^(k)) is the Jacobian system of equations.

I have the equation J^k * deltax^k = -f(x^k) for the system of linear equations

(See attached file for full problem description with proper symbols)

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 ,Ka,Kte) = I0 * (Ka/(Ka-Kte))*(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 ,Ka,Kte) = Σ( Ci - c(t, I0 ,Ka,Kte))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

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Thank you for the explanations

The attached file azt.zip (I hope you can extract the files from it) contains 5 files collected in a directory azt:

mother.tab and fetus.tab contain the measurement points from your original file

models.m calculates a model for given ...

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