Spectral analysis (SA) in PET

In comparison to compartmental models, SA has only few presumptions. Like compartmental models, SA describes the kinetics of the radiopharmaceutical using homogeneous compartments, but there is no need to know the number of compartments; SA can instead be used to estimate the number of compartments. Therefore SA can be used for selecting or validating a compartmental model. SA has also been applied in determination of time delay (Hinz and Turkheimer, 2006), in discriminating brain grey and white matter uptake on voxel-level analysis (Heurling et al., 2015), and for analysis of heterogeneous tissue data (Veronese et al., 2018).

Impulse response function (IRF)

IRF represents the tissue tracer concentration curve that would be measured (with PET) after an ideal instantaneous bolus injection. In spectral analysis IRF is assumed to be the sum of M+1 (0, ..., M) exponential functions:

, where αj≥0, β0=0, and βj≥0.

Simulation of tissue curve

In practice, the input function to the tissue is far from ideal bolus. Spectral analysis requires arterial blood sampling to get the radiotracer concentration in arterial plasma, CP(t), used as the input function. Tissue curve, CT(t), can be computed (simulated) by convolution between h(t) and CP(t):

Estimation of the spectrum

First a fixed list of βj values is defined, with a range starting from zero (β0=0). Since input function CP(t) is measured, we can calculate a table of basis functions for each βj,

, to replace the nonlinear part in equation 2. Non-negative least-squares (NNLS) method can then be used to solve the αj values, minimizing the weighted residuals sum of squares (WRSS) between the simulated tissue curve and measured tissue curve, CPET(t):

, where N is the number of PET time frames, and wi are the weights of the time frames. Negative αj values would be non-physiological, and NNLS method is therefore suitable for estimating αj.

The estimated αj values can be called the spectrum of the regional tissue TAC, and the structure of the model (number of compartments, reversibility and irreversibility) can be derived from the spectrum.

NNLS method is fast to compute, but SA as such should still not be applied to pixel-by-pixel calculations because of its sensitivity to noise.


Spectral analysis is applicable to analysis of PET data when the radiopharmaceutical has a radioactive metabolite which is transported into tissue, and the plasma input curves of both parent tracer and radioactive metabolite are measured and incorporated in the model (thus the name dual-input or double-input) (Tomasi et al., 2012).

See also:


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Updated at: 2019-11-22
Created at: 2014-05-07
Written by: Vesa Oikonen