Mathematical Models for FDG Kinetics in Cancer: A Review

Compartmental analysis is the mathematical framework for the modelling of tracer kinetics in dynamical Positron Emission Tomography. This paper provides a review of how compartmental models are constructed and numerically optimized. Specific focus is given on the identifiability and sensitivity issues and on the impact of complex physiological conditions on the mathematical properties of the models.

Parametric Mapping for TSPO PET Imaging with Spectral Analysis Impulsive Response Function

Purpose The aim of this study was to investigate the use of spectral analysis (SA) for voxel-wise analysis of TSPO PET imaging studies. TSPO PET quantification is methodologically complicated by the heterogeneity of TSPO expression and its cell-dependent modulation during neuroinflammatory response. Compartmental models to account for this complexity exist, but they are unreliable at the high noise typical of voxel data. On the contrary, SA is noise-robust for parametric mapping and provides useful information about tracer kinetics with a free compartmental structure. Procedures SA impulse response function (IRF) calculated at 90 min after tracer injection was used as main parameter of interest in 3 independent PET imaging studies to investigate its sensitivity to (1) a TSPO genetic polymorphism (rs6971) known to affect tracer binding in a cross-sectional analysis of healthy controls scanned with [11C]PBR28 PET; (2) TSPO density with [11C]PBR28 in a competitive blocking study with a TSPO blocker, XBD173; and (3) the higher affinity of a second radiotracer for TSPO, by using data from a head-to-head comparison between [11C]PBR28 and [11C]ER176 scans. Results SA-IRF produced parametric maps of visually good quality. These were sensitive to TSPO genotype (mean relative difference between high- and mixed-affinity binders = 25 %) and TSPO availability (mean signal displacement after 90 mg oral administration of XBD173 = 39 %). Regional averages of voxel-wise IRF estimates were strongly associated with regional total distribution volume (VT) estimated with a 2-tissue compartmental model with vascular compartment (Pearson’s r = 0.86 ± 0.11) but less strongly with standard 2TCM-VT (Pearson’s r = 0.76 ± 0.32). Finally, SA-IRF estimates for [11C]ER176 were significantly higher than [11C]PBR28 ones, consistent with the higher amount of specific binding of the former tracer. Conclusions SA-IRF can be used for voxel-wise quantification of TSPO PET data because it generates high-quality parametric maps, it is sensitive to TSPO availability and genotype, and it accounts for the complexity of TSPO tracer kinetics with no additional assumptions.

Differential equation methods for simulation of GFP kinetics in non–steady state experiments

Genetically encoded fluorescent proteins, combined with fluorescence microscopy, are widely used in cell biology to collect kinetic data on intracellular trafficking. Methods for extraction of quantitative information from these data are based on the mathematics of diffusion and tracer kinetics. Current methods, although useful and powerful, depend on the assumption that the cellular system being studied is in a steady state, that is, the assumption that all the molecular concentrations and fluxes are constant for the duration of the experiment. Here, we derive new tracer kinetic analytical methods for non–steady state biological systems by constructing mechanistic nonlinear differential equation models of the underlying cell biological processes and linking them to a separate set of differential equations governing the kinetics of the fluorescent tracer. Linking the two sets of equations is based on a new application of the fundamental tracer principle of indistinguishability and, unlike current methods, supports correct dependence of tracer kinetics on cellular dynamics. This approach thus provides a general mathematical framework for applications of GFP fluorescence microscopy (including photobleaching [FRAP, FLIP] and photoactivation to frequently encountered experimental protocols involving physiological or pharmacological perturbations (e.g., growth factors, neurotransmitters, acute knockouts, inhibitors, hormones, cytokines, and metabolites) that initiate mechanistically informative intracellular transients. When a new steady state is achieved, these methods automatically reduce to classical steady state tracer kinetic analysis.