fit_ppf - tpcclib 0.8.0 © 2023 by Turku PET Centre

Fits an empirical function to plasma parent (unchanged) tracer
fraction curve (1), where the fractions are between 0 and 1.
Usage: fit_ppf [Options] fractionfile [fitfile]
 -model=<PF | HILL | GCDF | EP | MPF | MHILL>
     Select the function (see descriptions below); default is HILL.
     Use MPF or MHILL to fit functions to 2-3 metabolite fraction curves
     instead of parent fraction curve.
     Sum-of-squares (ordinal least squares, OLS) is minimized by default,
     but optionally, sum of absolute deviations (LAD), or
     sum-of-squares of Akaho distances (orthogonal distances, ODR) 
     can be selected. ODR can be used only with PF and HILL.
     Set the lower limit for delay parameter.
 -mdelay=<separated | joint>
     Delay parameter for each metabolite is fitted separately, or
     all metabolites are assumed to share common delay time (default).
     Parent fraction at time zero is fixed to zero sample, if available.
 -a=<value>, -b=<value>, -c=<value>, ...
     Specified parameter is fixed to given (population mean) value.
     Option -fix0 overrides other options when possible.
     The last data column contains sample weights.
     All weights are set to 1.0 (no weighting)
     Less frequent samples are given more weight.
 -WP=<weight>, -WM1=<weight>, -WM2=<weight>, -WM3=<weight>
     Put additional or less weight to parent and/or metabolite fractions.
     Some fractions are known to exceed 1, not divided by 100.
     Error is returned if MRL check is not passed.
     Fitted and measured TACs are plotted in specified SVG 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.
Fraction datafile must contain at least two columns: sample times (min) and
fractions of parent tracer. Fractions of 1-3 metabolites can be given in
additional columns. Weights column can be given as specified in
DFT format (2) or with option -wc.
Program writes the fit start and end times, nr of points, WSS,
and parameters of the fitted function to the FIT file (3).
Available functions:
PF - extended power function (1,4,5)
  f(x) = {D^(-1/C) + (A*(x-E))^B }^-C , when x>E,
  f(x) = D                            , when x<=E ,
  where 0<A<=1, B>1.5, C>0, 0<D<=1, 0<=E.
  With option -d=1 this is essentially the same function as proposed in (4)
  or with options -b=2 -d=1 -e=0 the same as suggested in (5).
HILL - Extended Hill type function (1,6)
  f(x) = D - {(D-A)(x-E)^B}/{C+(x-E)^B} , when x>E,
  f(x) = D                              , when x<=E ,
  where 0<=A<=D, 1<=B, 0<C, 0<D<=1, 0<=E.
  With options -d=1 -e=0 this is the traditional Hill type function (6)
  f(x) = 1 - {(1-A)x^B}/(C+x^B)
  where C>0<=A<=D, 1<=B, 0<C, 0<D<=1, 0<=E.
GCDF - Inverted Gamma CDF (7)
  f(x) = A{1-B*gcdf(C(x-E),D)}, where 0<A<=1,0<=B<=1,C>0,D>0.
EP - Exponential/Power function based on Mu et al (8)
  f(x) = B*(C*exp(-D*(x-A)^3/(E+(x-A)^2)) + (1-C)*exp(-F*(x-A))), when x>A,
  f(x) = B                                                      , when x<=A ,
MPF - Extended power function is fitted to 1-3 metabolite fractions.
MHILL - Extended Hill type function is fitted to 1-3 metabolite fractions.
1. Fitting the fractions of parent tracer in plasma.
4. Meyer PT, et al. J Cereb Blood Flow Metab. 2004;24(3):323-333.
5. Watabe H, et al. J Cereb Blood Flow Metab 2000;20:899-909.
6. Wu S, et al. J Nucl Med 2007;48:926-931.
7. Naganawa M, et al. J Cereb Blood Flow Metab. 2014;34:1818-1825.
8. Mu L et al. EJNMMI Res. 2020;10:114.
See also: fit2dat, metabcor, avgfract, fitedit, fit_fexp, fith2met, tac2svg
Keywords: input, plasma, modelling, simulation, metabolite correction