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Linear quadratic: Y is number dead

Linear quadratic: Y is number dead

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Linear quadratic: Y is number dead

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Introduction

Mammalian cell death after exposure to radiation after a dose D of radiation often follows the linear-quadratic model.

Step by step

Create an XY table. Enter radiation doses into X and number of dead cells into Y.  After entering data, click Analyze, choose nonlinear regression, choose the panel of linear-quadratic equations, and choose Linear quadratic: Y is number of cells dead.

Consider constraining Y0, the number of cells alive when X=0, to a constant value.

Model

 Y = Y0 * [1.0 - exp(-1*(A*X + B*X^2))]

Interpret the parameters

X: Dose of radiation

Y: Number of cells surviving

A: Coefficient for linear killing

B: Coefficient for quadratic killing

Y0: Number of cells alive when X=0.