Quantification of regional myocardial blood flow estimation with three-dimensional dynamic rubidium-82 PET and modified spillover correction model

Abstract

Purpose

Myocardial blood flow (MBF) estimation with ⁸²Rubidium (⁸²Rb) positron emission tomography (PET) is technically difficult because of the high spillover between regions of interest, especially due to the long positron range. We sought to develop a new algorithm to reduce the spillover in image-derived blood activity curves, using non-uniform weighted least-squares fitting.

Methods

Fourteen volunteers underwent imaging with both 3-dimensional (3D) ⁸²Rb and ¹⁵O-water PET at rest and during pharmacological stress. Whole left ventricular (LV) ⁸²Rb MBF was estimated using a one-compartment model, including a myocardium-to-blood spillover correction to estimate the corresponding blood input function Ca(t)^whole. Regional K1 values were calculated using this uniform global input function, which simplifies equations and enables robust estimation of MBF. To assess the robustness of the modified algorithm, inter-operator repeatability of 3D ⁸²Rb MBF was compared with a previously established method.

Results

Whole LV correlation of ⁸²Rb MBF with ¹⁵O-water MBF was better (P < .01) with the modified spillover correction method (r = 0.92 vs r = 0.60). The modified method also yielded significantly improved inter-operator repeatability of regional MBF quantification (r = 0.89) versus the established method (r = 0.82) (P < .01).

Conclusion

A uniform global input function can suppress LV spillover into the image-derived blood input function, resulting in improved precision for MBF quantification with 3D ⁸²Rb PET.

Appendix

¹⁵O-Water Model

The myocardium was modeled as a partial-volume mixture of arterial blood Ca(t) and tissue Ct(t) activity concentrations as in Eq. 1 (see below) where PTF denoted perfusable tissue fraction, VA is the fractional arterial blood volume, and ρ is the density of tissue (1.04 g/ml).

$$ {\text{R}}\left( t \right) = {\text{PTF}} \cdot \rho \cdot {\text{Ct}}\left( {\text{t}} \right) + {\text{VA}} \cdot {\text{Ca}}\left( {\text{t}} \right) $$

(1)

The change in tissue activity concentration was modeled using the 1-tissue compartment model in Eq. 2 (see below) where F denotes blood flow in mL/minute/g. The parameter ρ is the partition coefficient of water in the myocardium and is equal to 0.91.

$$ {\text{dCt}}\left( t \right) / {\text{d}}t = F \cdot {\text{Ca}}\left( t \right)-(F/\rho) \cdot {\text{Ct}}\left( t \right) $$

(2)

In the LV blood cavity, activity concentration was modeled as a partial-volume mixture of β = 85% arterial blood and (1 - β = 15%) myocardial tissue as shown in Eq. 3.

$$ {\text{LV}}\left( {\text{t}} \right) = \beta \cdot {\text{Ca}}\left( {\text{t}} \right) + ( 1- \beta ) \cdot \rho \cdot {\text{Ct}}\left( {\text{t}} \right) $$

(3)

Equations 1, 2, and 3 were solved with a nonlinear least-squares analysis to estimate PTF, VA, and F, which was used as the estimate of MBF.

⁸²Rb Models

Established method

The measured tissue TAC in each myocardial ROI, R(t), during the entire scan length was estimated using Eq. 1. The change in tissue activity concentration was modeled using the one-tissue compartment model

$$ {\text{dCt}}\left( {\text{t}} \right) /{\text{dt}} = K1 \cdot {\text{Ca}}\left( {\text{t}} \right) -k2 \cdot {\text{Ct}}\left( {\text{t}} \right) $$

(4)

where K1 (mL/minute/g) is the uptake rate from blood into the tissue and k2 (/minute) is the washout rate from myocardial tissue into the blood Ca(t) (Bq/mL). Radioactivity in the LV blood pool was calculated using Eq. 3 with β = 85%.

The parameters PTF, VA, K1, and k2 were derived by nonlinear least-squares minimization using Eqs. 1, 3, and 4, where PTF represents the tissue fraction in the LV myocardium ROI.

Thus, the spillover-corrected pure blood Ca(t) for each segment was estimated. Conversion from K1 to MBF was estimated with the modified Renkin-Crone model1,27 as shown in Eq. 5.

$$ K1 = {\text{MBF}}\left[ { 1- 0.86 {\text{ exp }}\left( { -0.543/{\text{MBF}}} \right)} \right] $$

(5)

Modified or dual-spillover method

Regional myocardial ROI data, R(t), were then analyzed using Eqs. 6 and 7.

$$ {\text{R}}\left( {\text{t}} \right) = {\text{PTF}} \cdot \rho \cdot {\text{Ct}}\left( {\text{t}} \right) + {\text{VA}} \cdot {\text{Ca}}^{\text{whole}} \left( {\text{t}} \right) $$

(6)

$$ {\text{dCt}}\left( {\text{t}} \right) /{\text{ dt }} = K1 \cdot {\text{Ca}}^{\text{whole}} \left( {\text{t}} \right) -k2 \cdot {\text{Ct}}\left( {\text{t}} \right) $$

(7)

The regional myocardial ROI curve and left ventricular ROI blood curve (R(t) and LV(t), respectively) were sampled from the dynamic image as in the established conventional method and were assumed to be a linear combination of the uniform blood Ca^whole(t) and myocardium Ct(t) as in Eqs. 1 and 3. In addition, the relationship between Ca^whole(t) and Ct(t) was defined by the one-tissue-compartment model as in Eq. 7.

The parameters PTF, VA, K1, and k2 were simultaneously estimated by minimizing the weighted error (ε) as shown in Eq. 8 between the measured curve R(t) and the model in Eq. 6. The error was weighted by the blood activity concentration Ca^whole(t) to enforce strict tolerance in the curve fitting during the timeframes corresponding to high radioactivity in the blood.

$$ \varepsilon = \Upsigma [{\text{Ca}}^{\text{whole}} \left( {\text{t}} \right) \cdot ({\text{PTF}} \cdot \rho \cdot {\text{Ct}}\left( {\text{t}} \right) + {\text{VA}} \cdot {\text{Ca}}^{\text{whole}} \left( {\text{t}} \right) - {\text{R}}\left( {\text{t}} \right))]^{ 2} $$

(8)

K1 values were converted into MBF using the Renkin-Crone extraction function as in Eq. 5.3

The estimated MBF values from the established uniform and modified weighted methods were compared against MBF values estimated from the corresponding ¹⁵O-water images.