# Analysis of ^{82}Rb PET studies

Rubidium is an analogue of potassium, and [^{82}Rb]Rb^{+} is actively transported
into living cells by ion pumps. It is only partially extracted from blood into tissue during one
capillary pass, but can still provide an estimate of tissue
perfusion.
Extraction of Rb^{+} is lower than that of K^{+}
(Sheehan & Renkin, 1972).
The main advantage of [^{82}Rb]Rb^{+} over a diffusible perfusion tracer, such as
[^{15}O]H_{2}O, is that ^{82}Rb can be
produced with a radionuclide generator without access to an on-site cyclotron.

## Myocardial perfusion measurement

Positron emission tomography enables noninvasive quantification of myocardial
perfusion (MBF).
PET tracers that are used for estimation of blood flow include diffusible tracer
[^{15}O]H_{2}O and partially extracted
tracers ^{82}Rb and [^{13}N]ammonia.
During one capillary pass, monovalent potassium analogue ^{82}Rb
([^{82}Rb]Rb^{+}) is only partially extracted by the myocardial cells via the
Na^{+}/K^{+} adenosine triphosphatase pump, and extraction is inversely and
non-linearly proportional to perfusion.
Furthermore, extraction and retention, at a given perfusion level, may be
affected by drugs or severe acidosis, hypoxia, and ischemia.

In ^{82}Rb studies the scanner may be near its saturation limit,
which limits the amount of tracer that can be injected. Together with the short physical halflife,
this leads to a low signal-to-noise ratio. That has to be taken into account, when deciding between
2D and 3D scanning (Votaw & White, 2001).
Model selection can be misguided and analysis may lead to biased results, if PET scanner is
saturated or dead-time correction is not working properly.
The relatively high positron energy of ^{82}Rb leads to relatively poor
image quality and reduced spatial resolution.

Consistent ^{82}Rb administration profile can improve test-retest repeatability,
especially when simplified analyze methods are used
(Klein et al., 2018).

### Analysis methods used in literature

#### Compartment models

Physiological model for ^{82}Rb in myocardium contains three tissue compartments,
capillary space, interstitial space, and intracellular space
(Coxson et al., 1997).
This model, and the reduced model with two tissue compartments (Huang et al., 1989), cannot be applied to noisy
PET data without a priori values for some of the model parameters
(Herrero et al., 1992).
When recovery coefficient and distribution volume of the first tissue compartment were fixed,
good repeatability can be achieved, if the signal-to-noise ratio of PET images is improved using
for example wavelet-based noise reduction protocol
(Lin et al., 2001;
Knešaurek et al., 2009).

The further reduced one-tissue compartment model (Coxson et al., 1995;
Yoshida et al., 1996;
Coxson et al., 1997;
Golanowski et al., 2000;
Lautamäki et al., 2009)
provides results with good reproducibility in rest and hyperemic conditions
(Manabe et al., 2009),
and is therefore better suited for clinical setting.
The result of one or two tissue compartment models (*K _{1}*) is dependent on both
extraction and blood flow, and requires (non-linear) extraction correction, if quantitative flow
estimates are needed (Lortie et al., 2007).
The method was found to be in excellent concordance with [

^{15}O]H

_{2}O method in the MBF range 0.66-4.7 ml/min/g (Prior et al., 2012). Combining the one-compartmental model with clustering enhances the quality of parametric perfusion images (Mohy-ud-Din et al., 2015).

#### Retention model

The simplified retention model (SRM) is basically the same as the
FUR method used for analysis of many tracers,
mainly with irreversible uptake.
In case of [^{82}Rb]Rb^{+} an extraction correction function
(Herrero et al., 1990;
Yoshida et al., 1996;
Renaud et al., 2013) is required
and the result is dependent on the time of imaging the tissue concentration.
Time is usually defined as the time of blood curve peak plus 1.4 min
(Renaud et al., 2013;
Klein et al., 2016).
Scanner and image reconstruction dependent partial volume correction factor
for the myocardial tissue concentration is also used.
Maximum MBF that can be measured with this method is about 2-2.5 ml/(g × min)
(Herrero et al., 1990).

Note that retention model accounts for the efflux from tissue to blood (*k _{2}*)
only by keeping the calculation time as short as possible and by applying nonlinear extraction
correction. Therefore the extraction correction formula is different for different PET scan times
and injection protocols, and is not the same as may be determined for

*K*from compartment models. Klein et al. (2016) reported that SRM was affected more by the tracer infusion protocol than the one tissue compartment model, and proposed using constant-activity-rate infusion instead of bolus administration.

_{1}#### El Fakhri’s approach with factor analysis

El Fakhri et al. (2005) applied
generalized form of least-squares factor analysis of dynamic sequences (GFADS) to generate left
and right ventricular (LV and RV) TACs.
A 1-tissue compartment model was used to estimate the blood flow and extraction dependent parameters
*k _{1}* and

*k*. The contribution from both LV and RV blood to the myocardial activity was taken into account in the model as fitted parameters

_{2}*fiv*and

*riv*. The model was applied to TACs calculated as average of groups of voxels. Voxels were grouped with orthogonal grouping with predetermined number of groups (100).

#### Correction for spillover and partial volume effects

Commonly, the spillover and partial volume effects are
taken into account in compartment models for ^{82}Rb by assuming a geometrical model.

#### Simulations

Herrero et al (1992)
and Meyer et al. (2007)
have published input functions for ^{82}Rb simulation studies.

Coxson et al. (1997) provide compartmental model parameters for simulations.

### Suggested MBF analysis method

Our current suggestion is to apply one-tissue compartment model with geometrical model correction for spillover and partial volume effects. This method is implemented in Carimas™.

To calculate quantitative perfusion values, a nonlinear extraction correction is needed. Parameters for the correction functions may need to be determined for each institute, unless the study protocols are similar. Carimas™ implements the extraction correction function as published in Yoshida et al., 1996 (Nesterov et al., 2014).

### See also:

- MBF using [
^{18}F]Flurpiridaz - MBF using [
^{15}O]H_{2}O - MBF using [
^{13}N]NH_{4}^{+} - Partial volume and spillover effects in cardiac PET

## Renal blood flow measurement

[^{82}Rb]Rb^{+} can be used for measurement of renal blood flow (RBF),
because it is reabsorbed in the tubules of the kidney,
mainly in the cortex, so that the remaining activity in the urine is negligible.
Human studies with ^{82}Rb have been promising
(Tahari et al., 2014).

## Further reading

Chatal J-F, Rouzet F, Haddad F, Bourdeau C, Mathieu C, Le Guludec D.
Story of rubidium-82 and advantages for myocardial perfusion PET imaging.
*Front Med.* 2015; 2:65 doi: 10.3389/fmed.2015.00065.

DeGrado TR, Bergmann SR, Ng CK, Raffel DM. Tracer kinetic modeling in nuclear cardiology.
*J Nucl Cardiol.* 2000; 7: 686-700.

Machac J, Bacharach SL, Bateman TM, Bax JJ, Beanlands R, Bengel F, Bergmann SR, Brunken RC,
Case J, Delbeke D, DiCarli MF, Garcia EV, Goldstein RA, Gropler RJ, Travin M, Patterson R,
Schelbert HR. Positron emission tomography myocardial perfusion and glucose metabolism imaging.
*J Nucl Cardiol.* 2006; 13: e121-e151.

Mohy-ud-Din H, Lodge MA, Rahmim A. Quantitative myocardial perfusion PET parametric imaging at
the voxel-level. *Phys Med Biol.* 2015; 60: 6013-6037. doi:
10.1088/0031-9155/60/15/6013.

Nesterov SV, Deshayes E, Sciagrà R, Settimo L, Declerck JM, Pan X-B, Yoshinaga K, Katoh C,
Slomka PJ, Germano G, Han C, Aalto V, Alessio AM, Ficaro EP, Lee BC, Nekolla SG, Gwet KL,
deKemp RA, Klein R, Dickson J, Case JA, Bateman T, Prior JO, Knuuti J.
Quantification of myocardial blood flow in absolute terms using ^{82}Rb PET imaging:
results of RUBY-10 study. *JACC Cardiovasc Imaging* 2014; 7(11): 1119-1127. doi:
10.1016/j.jcmg.2014.08.003.

Tahari AK, Lee A, Rajaram M, Fukushima K, Lodge MA, Lee BC, Ficaro EP, Nekolla S, Klein R,
deKemp RA, Wahl RL, Bengel FM, Bravo PE. Absolute myocardial flow quantification with
^{82}Rb PET/CT: comparison of different software packages and methods.
*Eur J Nucl Med Mol Imaging* 2014; 41(1): 126-135.

Tags: Perfusion, Myocardium, Kidney, Carimas, MBF

Created at: 2009-03-17

Updated at: 2018-08-14

Written by: Vesa Oikonen, Chunlei Han