Appendix 1
Patlak analysis can be derived from a two-compartment model that describes the one-way transfer of contrast material from the intravascular space to the extravascular space, i.e. there is no significant backflow during the examination time. At any time point, the tissue concentration of contrast material is equivalent to the sum of the intravascular and extravascular concentrations of contrast material as denoted by the following equation: where C(t) is the concentration of contrast material within the tissue, CBV is the cerebral blood volume, C A(t) is the concentration of contrast material in blood (the arterial input function AIF) and K Trans is the volume transfer constant [29]; ∆t describes the time it takes the input function to travel to the tissue voxel; ∆t is determined automatically by cross correlation analysis of the AIF with the voxel TAC separately for every voxel.
Dividing the equation by C A(t) produces the linear relationship
By fitting a straight line to the data points, K Trans can be derived from the slope of this line and CBV from the intercept.
K Trans describes the portion of blood flow F that is extracted into the extravascular space, i.e. K Trans = E ∙ F, with the extraction fraction E (EK1), which is defined as
PS is the permeability–surface area product and Hct the haematocrit value.
Note that we define K Trans with respect to whole blood flow, while in MR perfusion imaging it is typically defined with respect to plasma flow: K Trans = K Trans(MRI)/(1 − Hct).
From these relationships it can be derived that for tumours which are well perfused, K Trans(1 − Hct) is approximately equal to PS.

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