Fitting function to TAC

Example: fitting pharmacokinetic one-compartment model

Farmacokinetic one-compartment model

At any time t the drug concentration in plasma, CP(t), can be computed from the drug dose, the clearance, and the volume of distribution (VD):

Example: fitting Patlak plot data

Patlak plot typically starts with a rapid increase, which then stabilizes into a linear phase, and Ki is estimated as the slope of line fitted to the linear phase. All of the Patlak plot data can be fitted using a function that describes an exponential approach to a straight line (Cunningham & Lammerstma, 1989):

Fits to Patlak plots

Figure. Examples of Patlak plots that could be fitted using the function that describes an exponential approach to a straight line.

See also:


Bevington PR, Robinson DK: Data Reduction and Error Analysis for the Physical Sciences, 3rd ed. McGraw-Hill Education, 2003. ISBN13: 9780072472271.

Cunningham VJ, Lammertsma AA. Kinetic modelling of L-[18F]-fluorodopa uptake for PET studies in man. In: Positron Emission Tomography in Clinical Research and Clinical Diagnosis: Tracer Modelling and Radioreceptors, edited by C Beckers et al., 1989, 81-89.

Motulsky HJ, Ransnas LA. Fitting curves to data using nonlinear regression: a practical and nonmathematical review. FASEB J. 1987; 1: 365-374.

Muzic RF Jr, Christian BT. Evaluation of objective functions for estimation of kinetic parameters. Med Phys. 2006; 33(2): 342-353.

Sederholm K. Globaali optimointi positroniemissiotomografia-kuvantamiseen liittyvässä mallintamisessa. Pro gradu, 2003.

Yaqub M, Boellaard R, Kropholler MA, Lammertsma AA. Optimization algorithms and weighting factors for analysis of dynamic PET studies. Phys Med Biol. 2006; 51: 4217-4232.

Yaqub M, Boellaard R, Kropholler MA, Lubberink M, Lammertsma AA. Simulated annealing in pharmacokinetic modeling of PET neuroreceptor studies: accuracy and precision compared with other optimization algorithms. Nuclear Science Symposium Conference Record, 2004 IEEE. 5: 3222-3225. doi: 10.1109/NSSMIC.2004.1466368.


Created at: 2014-01-28
Updated at: 2018-12-07
Written by: Vesa Oikonen