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. 2015 Feb;35(2):304-11.
doi: 10.1038/jcbfm.2014.202. Epub 2014 Nov 26.

The simplified reference tissue model: model assumption violations and their impact on binding potential

Cristian A Salinas  1 , Graham E Searle  2 , Roger N Gunn  3
Affiliations

The simplified reference tissue model: model assumption violations and their impact on binding potential

Cristian A Salinas et al. J Cereb Blood Flow Metab. 2015 Feb.

Abstract

Reference tissue models have gained significant traction over the last two decades as the methods of choice for the quantification of brain positron emission tomography data because they balance quantitative accuracy with less invasive procedures. The principal advantage is the elimination of the need to perform arterial cannulation of the subject to measure blood and metabolite concentrations for input function generation. In particular, the simplified reference tissue model (SRTM) has been widely adopted as it uses a simplified model configuration with only three parameters that typically produces good fits to the kinetic data and a stable parameter estimation process. However, the model's simplicity and its ability to generate good fits to the data, even when the model assumptions are not met, can lead to misplaced confidence in binding potential (BPND) estimates. Computer simulation were used to study the bias introduced in BPND estimates as a consequence of violating each of the four core SRTM model assumptions. Violation of each model assumption led to bias in BPND (both over and underestimation). Careful assessment of the bias in SRTM BPND should be performed for new tracers and applications so that an appropriate decision about its applicability can be made.

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Figures

Figure 1
Figure 1
Summary of simplified reference tissue model (SRTM) citations from the publications of Lammertsma and Hume and Gunn et al demonstrating increasing uptake and use of SRTM. Citation source Scopus, Elsevier (www.scopus.com).
Figure 2
Figure 2
Simplified reference tissue model (SRTM) model configuration (A) and violation of model assumptions (B–E): (A) SRTM, (B) displaceable signal in the reference tissue, (C) two tissue compartment model in the target and/or reference tissues, (D) whole blood contribution to target and reference regions, and (E) differences in nonspecific binding between target and reference regions.
Figure 3
Figure 3
Bias in simplified reference tissue model (SRTM) binding potential estimates when specific binding is present in the reference region. The theoretical bias derived from equation 2 (dashed line) lies exactly underneath the simulation results (solid line).
Figure 4
Figure 4
Simplified reference tissue model (SRTM) binding potential bias for different model topologies. (A) Noiseless simulations. The upper left plot represents the nonviolated topology of the SRTM where the true value of binding potential is always correctly estimated (0% bias). In all other cases, the magnitude and direction (overestimation or underestimation) of the biases depends on the value of the true binding potential. (B) Noisy simulations across a wide range of kinetics. The mean absolute SRTM binding potential bias (hot map value) is displayed as a function of the model order metric (MOM) in the target (y-axis) and reference (x-axis) regions. Both x axis and y axis MOM values range from one tissue compartment (1TC) model kinetics up to a clear requirement for a 2TC model representation of the time activity curves.
Figure 5
Figure 5
Bias introduced in the simplified reference tissue model (SRTM) estimates of binding potential because of a nonnegligible blood volume contribution. Solid lines represent the simulation results. Dashed lines represent the theoretical bias from equation 4. Only when VB is zero are non-biased estimates of binding potential obtained.
Figure 6
Figure 6
Bias introduced in simplified reference tissue model (SRTM) binding potential estimates because of differences in nondisplaceable binding in the target and references regions. Solid lines represent the simulation results. Dashed lines represent the theoretical bias derived from equation 5. Only when VND is the same in the target and reference regions (PND=1) are nonbiased estimates of binding potential obtained.
Figure 7
Figure 7
Bias in pseudo reference tissue model (PRTM) estimates of binding potential for different model topologies. The solid line in each plots represent the biased simplified reference tissue model (SRTM) estimate of binding potential because of the uncorrected presence of specific binding in the reference region. The dashed line is the bias for PRTM. When one tissue compartment (1TC) is present in both reference and target regions, PRTM is able to provide an unbiased estimate of binding potential, but for more complex model configurations a bias (either positive or negative) is nearly always present.
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