# Fitting the blood-to-plasma or plasma-to-blood ratios (draft)

## 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 usually 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 tracers, 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.

### 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 fraction curve for other purposes, e.g. for drawing graphs.

## See also:

## References

Bloomfield PS, Selvaraj S, Veronese M, Rizzo G, Bertoldo A, Owen DR,
Bloomfield MA, Bonoldi I, Kalk N, Turkheimer F, McGuire P, de Paola V, Howes OD.
Microglial activity in people at ultra high risk of psychosis and in
schizophrenia: An [^{11}C]PBR28 PET brain imaging study.
*Am J Psychiatry* 2016; 173(1): 44-52.

Edison P, Brooks DJ, Turkheimer FE, Archer HA, Hinz R. Strategies for the
generation of parametric images of [^{11}C]PIB with plasma input
functions considering discriminations and reproducibility.
*NeuroImage* 2009; 48: 329-338.

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

Created at: 2016-04-06

Updated at: 2016-04-06

Written by: Vesa Oikonen