# Fitting the blood-to-plasma or plasma-to-blood ratios

## Why to fit the ratio curves?

The plasma must be separated from blood, and the radioactivity and mass of both plasma and blood samples (or the precipitant left in the tube after most of plasma is removed) must be measured. Radioactivity measurement is hampered by the fast decay of radioactivity, especially with C-11 labeled tracers. Fitting of a mathematical function to the fraction curves reduces variation and enables interpolation and extrapolation of the ratio curve, for the conversion of blood TAC to plasma.

Individually fitted ratios can be applied in the conversion of blood TAC to plasma using taccalc, but often a population mean curve is determined and implemented in programs b2plasma and p2blood.

## How to fit the ratio curves?

### Functions

The plasma-to-blood and blood-to-plasma ratio curves can be very different for different radiotracers, and therefore a suitable function must first be selected.

Edison et al (2009)
used extended Hill (sigmoidal) function for fitting
[^{11}C]PIB plasma-to-blood ratios, and
Bloomfield et al (2016) applied it to
[^{11}C]PBR28:

, where *p _{1}* < 0. Similar function was used to fit blood-to-plasma ratio
curves by Tarkia et al (2012):

Exponential or two-exponential function with constant term has sometimes been used for fitting plasma-to-blood or blood-to-plasma ratio curves (Lee et al., 2008; Wu et al., 2016).

### Models

Time-dependent plasma-to-blood ratio can also be described using compartmental models.
For instance, Lee et al (2008) proposed
a simple model for [^{18}F]FDG rat studies.

### Software

Applications fit_bpr and fit_sigm may be useful in fitting functions to blood-to-plasma or RBC-to-plasma ratio data.

### Function parameters

Function parameters are saved into specific fit file format, which are ASCII text files.

Program fit2dat can be used to calculate the fitted ratio curve for other purposes, e.g. for drawing graphs.

## See also:

- Blood to plasma conversion
- Plotting curves
- Blood sampling
- Processing input data
- Fitting PET input curves

## References

Lee J-S, Su K-H, Lin J-C, Chuang Y-T, Chueh H-S, Liu R-S, Wang S-J, Chen J-C.
A novel blood-cell-two-compartment model for transferring a whole blood time activity curve to
plasma in rodents. *Comput Methods Programs Biomed.* 2008; 92(3): 299-304.
doi: 10.1016/j.cmpb.2008.02.006.

Tags: Input function, Blood, Plasma, RBC, Fitting

Updated at: 2018-12-18

Created at: 2016-04-06

Written by: Vesa Oikonen