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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)

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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) = &#931;( 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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