Small Animal Imaging Resource Program @ Johns Hopkins


Coupled Fitting

Introduction: A simplified reference-tissue model (SRTM) is useful for quantifying neuroreceptor binding without arterial blood sampling.  Recently, a noise reduction technique for generating parametric images with SRTM has been described, that uses the fact that the reference region clearance rate (k2r) is a global constant [1].  Since R1 = K1 /K1ris a  parameter of SRTM, constraining k2r  to a single global value ensures that implicitly, the non-specific distribution volume (Ve=K1/k2=K1r /k2r) is also a global constant, which can be seen from the relationship Ver =Ve/K1r =R1/k2=1/k2r .  We have explored a region-of-interest based technique for constraining k2r, for which multiple time-activity curves (TACs) from a single study are fitted simultaneously with Ver coupled across TACs. In addition to preserving the assumption of uniform non-specific binding, this technique reduces the overall number of fitted parameters which may improve the stability of non-linear regression.  We have also implemented this method using more detailed reference-tissue models including a 4-parameter full reference-tissue model (FRTM), as well as a model that assumes two-tissue compartments for the reference region (R2TM).

Methods:  SRTM was applied to PET neuroceptor studies with [11C]MCN5652 (MCN) (nstudies=1),  [11C]DASB (n=1), and [11C]carfentanil (CFN) (n=5). Tissue TACs were generated for a reference region (cerebellum - MCN, DASB), (occipital cortex - CFN), and specific binding regions (MCN (nregions=11), DASB (n=14), and CFN (n=9)). All TACs were fitted simultaneously with coupling of Ver (SRTMC), as well as individually to the SRTM model (SRTMI). For comparison, TACs for MCN and DASB were fit to a 1-tissue blood input model (CM) with no blood volume correction. For CFN, a 2-tissue blood-input model was used. Estimates of f2BP obtained with SRTMC and SRTMI were compared to those obtained with CM. CFN TACS were also fit using FRTM with coupling of  Ver  and k4, where k4 is the receptor dissociation rate, as well as  R2TM with coupling of Ver, ns, and k6, where ns and k6 are non-specific binding parameters for reference-tissue. CFN TACs were also fitted individually to FRTM and R2TM.

Results: For MCN, SRTMI yielded some outliers. With these removed, a plot of SRTMI vs CM gave a regression line of SRTMI=0.70CM+0.21, with correlation r=0.90. With SRTMC, there were no outliers, and the comparison with CM gave a regression line of SRTMC=0.87CM-0.002, with r=0.99.  For DASB, the regression lines were SRTMI=0.99CM+0.09, r=0.98, and SRTMC=1.01CM+0.005, r=1.0. For CFN, both SRTMI and  SRTMC were comparable to CM (r>0.97) for all studies. For FRTM and R2TM, coupled fitting tended to converge more reliably than individual fitting.  However, equivocal results were obtained in that coupled fitting did not necessarily give f2BP estimates that were in better agreement with CM, and particularly for R2TM, coupled fitting often worsened the agreement.

Conclusion: When used with reference-tissue models, simultaneous modeling of multiple TACs with parameter coupling can be used to enforce the assumption of uniform non-specific binding. By reducing the total number of fitted parameters, parameter coupling also tends to stabilize the regression procedure, which may possibly enable the application of more complex models. The present results suggest that coupled fitting may improve parameter estimation in some cases, but more thorough evaluation is needed to better understand the potential benefits of parameter coupling.


[1] Y Wu and RE Carson ; J Cereb Blood Flow Metab  22   1440 - 1452 (2002)