# 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) = 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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