fit_o2bl - tpcclib 0.8.0 © 2023 by Turku PET Centre

Non-linear fitting of compartmental model for whole body production of
labelled water during [O-15]O2 bolus PET studies.
Co(t) and Cw(t) represent the concentrations of [O-15]O2 and [O-15]H2O in
arterial blood, respectively, and Ct(t) represents the whole body tissue
compartment for [O-15]H2O.
The model is based on the following articles:
1. Huang S-C et al. Modelling approach for separating blood time-activity
   curves in positron emission tomographic studies.
   Phys Med Biol. 1991;36(6):749-761.
2. Iida H et al. Modelling approach to eliminate the need to separate
   arterial plasma in oxygen-15 inhalation positron emission tomography.
   J Nucl Med. 1993;34:1333-1340.
3. Kudomi N et al. A physiologic model for recirculation water correction
   in CMRO2 assessment with 15O2 inhalation PET.
   J Cereb Blood Flow Metab. 2009;29(2):355-364.
    ______        ______        ______   
   |      |  k1  |      |  k3  |      |  
   |  Co  | ---> |  Cw  | ---> |  Ct  |  
   |      |      |      | <--- |      |  
   |______|      |______|  k4  |______|  
The corresponding differential equations are:             
    dCw(t)/dt = k1*Cb(t-delay) - (k1+k3)*Cw(t) + k4*Ct(t) 
    dCt(t)/dt = k3*Cw(t) - k4*Ct(t)                       
, where Cb(t)=Co(t)+Cw(t)                                 
If k4 is assumed to zero, then:
    dCw(t)/dt = k1*Cb(t-delay) - (k1+k3)*Cw(t)
Total arterial blood curve Cb(t), and Cw(t) are required for the fitting.
TAC files must be corrected for physical decay.
Cw(t) can be calculated from measured arterial plasma curve Ca(t), because
oxygen concentration in plasma is negligible, by multiplying it with
[O-15]H2O blood-to-plasma ratio, for example using program o2_p2w.
The estimated model parameters, or population averages, can then be used to
calculate the [O-15]O2 and [O-15]H2O blood curves using program o2metab.
Usage: fit_o2bl [Options] cbtacfile cwtacfile resultfile
     Select the model: with k4 the full model is fitted (default);
     with k3 it is assumed that k4=0.
     Time delay is fitted in both models by default.
     Constrain delay time to specified value (sec); fitted by default.
     Constrain k3 to specified value (1/sec); fitted by default.
     Constrain k3/k4 to specified value (unitless); fitted by default.
 -w1 All weights are set to 1.0 (no weighting); by default, weights in
     data file are used, if available.
     Weight by sampling interval.
     Fitted and measured TACs are plotted in specified SVG file.
     Fitted Cw(t) TAC is written in specified TAC file.
 -h, --help
     Display usage information on standard output and exit.
 -v, --version
     Display version and compile information on standard output and exit.
 -d[n], --debug[=n], --verbose[=n]
     Set the level (n) of debugging messages and listings.
 -q, --quiet
     Suppress displaying normal results on standard output.
 -s, --silent
     Suppress displaying anything except errors.
Results can be saved in RES, IFT, or HTML format.
File will contain the parameters k1, k1+k3, and delay (model k3), or, 
k1, k3, k3/k4, and delay (model k4).
See also: o2metab, o2_p2w, sim_o2bl, fit_mo2, b2t_mo2
Keywords: input, oxygen, blood, metabolite correction