# Partial volume and spillover effects in cardiac PET

## Analytical method

Henze et al. (1983) suggested an analytical method to correct for the spillover and recovery fractions in the studies of cardiac muscle. The method was validated by Herrero et al. (1988). The method needs the cardiac dimensions: myocardial wall thickness and cavity diameter, which may not always be available. The method also assumes 10% vascular space in tissue, which is also corrected.

This correction can be applied to the regional data before modelling, for example by using heartcor. It will also be included in Carimas™. However, with the improved image resolution of the modern PET scanners, this method provides little or no benefit, since it does not account for the beating of the heart or respiratory motion.

In studies of small animals the corrections may still be needed. Mu et al. (2013) proposed using nonnegative matrix factorization for retrieving input function from LV cavity of mouse FDG studies.

## Geometrical model

The spillover and partial volume effects are taken into account in compartment models by assuming a geometrical model (Hutchins et al., 1990) and based on that

, where CPET(t) is the measured myocardial PET concentration as a function of time, CLV(t) is the measured concentration in the middle of left ventricular cavity, representing also true arterial concentration, and (1-FLV) is regional recovery coefficient (between 0 and 1). This method is easy to implement, but it ignores the partial volume effect on the outer side of myocardial wall (Hutchins et al., 1992).

This method is included in compartmental models in Carimas™.

More general approach is to assume that there are two independent spillover factors, from cavity blood to myocardial muscle, and from muscle into the cavity. The spillover factors can be fitted together with compartment model parameters, but for instance in the case of FDG additional blood samples are needed for scaling the blood curve derived from the LV cavity (Feng et al., 1996; Li et al., 1998).

## Model for [15O]H2O

Iida et al., 1988, 1991, and 1992) proposed a model for quantification of myocardial blood flow (MBF) with [15O]H2O and PET, where the recovery coefficients in both myocardial and LV regions and the spillover fractions from blood to myocardium and from myocardium to blood were included in the model parameters. Model equations are given in http://www.turkupetcentre.net/reports/tpcmod0005.pdf.

This model is applied in Carimas™, and can be applied to the regional TAC data by using fitmbf.

### Simulation

A very simple simulation of the effects of scanner resolution and heart beating can demonstrate the performance of the MBF model. Measurement noise is not simulated here. All software are available in our web pages, with source codes (except Carimas™). We will start with an arterial blood time-activity curve (BTAC), based on actual [15O]H2O PET studies, and available in radiowater.zip. BTAC is corrected for decay to zero time. BTAC is calculated from mathematical function parameters at 1 s intervals, and then moved 30 s forward in time to simulate the time delay with these commands:

fit2dat -c=0,600,1 radiowater.fit radiowater.dat
tactime -nogap radiowater.dat 30 radiowater.tac


Myocardial tissue time-activity curve (TTAC) is then simulated using the one-tissue compartmental model for [15O]H2O, setting blood flow inside perfusable tissue volume to 100 mL/(min×100 mL), partition coefficient of water to 0.91 mL/mL, extraction coefficient to 1, vascular volume to 10%, and arterial fraction of that to 50%:

b2t_h2o -nosub -fpt radiowater.tac 100 0.91 1 10 50 myocardium.tac


TTAC and BTAC are then combined into one file, and 1×30, 6×5, 3×10, 4×15, and 6×30 s PET time frames are simulated:

tacadd -ovr temp.tac myocardium.tac
tacadd temp.tac radiowater.tac
simframe -sec temp.tac frames.dat mbfsim.tac


Simple dynamic 2D PET image (100 × 100 pixels), representing myocardial left ventriculum (LV), is then simulated with 50 mm LV cavity diameter, 10 mm myocardial thickness, and 1×1 mm image pixel size, assuming no movement and resolution effects, and no radioactivity around the LV:

simimyoc -fwhm=0 -diameter=50 -thickness=10 -diamin=1 -dim=100 -pxlsize=1 mbfsim.tac mbfsim1.v


Figure 1. BTAC and simulated myocardial TTAC, and simulated PET image frames, with myocardial TTAC surrounding the BTAC, representing the left myocardial cavity.

During PET study the heart is beating, and during one cycle heart muscle diameter is decreasing and muscle thickness increasing during systole, with decreasing LV cavity volume; during diastole the changes are reversed. Even during the shortest PET time frame (5 s) the heart goes through at least 5 cycles, leading to blurred PET image. In this simulation we assume that the minimum LV cavity diameter is 60% of the maximum diameter (0.6×50 mm = 30 mm). Changes in volumes are divided into 12 phases (Fig. 2) with realistic time fractions. The effect of heart beating is simulated with command:

simimyoc -fwhm=0 -diameter=50 -thickness=10 -diamin=0.6 -dim=100 -pxlsize=1 mbfsim.tac mbfsim2.v


Figure 2. Simulated LV volume changes from time frame 9, and simulated PET image frames, including the effect of heart beating.

The spatial resolution in PET image should also be simulated. Here we assume that FWHM is 10 mm, and simulate a 3D PET image (100 × 100 &times 100 pixels):

simimyoc -3D -fwhm=10 -diameter=50 -thickness=10 -diamin=0.6 -dim=100 -pxlsize=1 mbfsim.tac mbfsim3.v


Figure 3. Simulated PET image frames, including the effects image resolution and heart beating from a middle image plane, and all image planes of 3D simulation from time frame 9.

Next we open the simulated dynamic image in Carimas, and draw ROIs representing the LV cavity (model input), and myocardial muscle ROIs:

Figure 4. Screenshots from Carimas showing the ROIs and ROI TACs.

Due to the heart beating and relatively poor image resolution the myocardial TACs are far from the true ones (Fig 5), but these will be accounted for in the MBF model. LV cavity TAC is close to the true BTAC, because small ROI was drawn in the middle of the cavity.

Figure 5. The plot on the left compares the true BTAC and TTAC used in simulation (dots) and the TACs from cavity and myocardial ROIs drawn to the simulated dynamic image. The plot on the right shows the MBF model fitted TACs.

Myocardial perfusion calculation can be performed in Carimas, but here we will estimate the model parameters using a separate program fitmbf and TACs saved from Carimas in file mbfsim_carimas.dft:

fitmbf mbfsim_carimas.dft 0.95 lvcav whole mbfsim.res


The fitted TACs are shown in figure 5. MBF model fitting provides results:

Region        MBF         PTF     Vb
# Units:      ml/(min*ml) ml/ml   ml/ml
whole-muscle  0.9944      0.7177  0.1097
roi1          0.9939      0.6216  0.1368
roi2          0.9939      0.6978  0.1833
roi3          0.9826      0.5560  0.0500


MBF estimates from all myocardial ROIs are close to the correct perfusion value; 1 mL/(min×mL) equals 100 mL/(min×100 mL). Perfusable tissue volume (PTF) and blood volume (Vb) are estimated as separate parameters, and ROI placement affects mostly these parameters. Note that if myocardial ROI would contain scar tissue, it would also increase PTF, but not decrease the perfusion estimate.

Additional error sources in the actual PET scans include statistical noise in the emission and transmission acquisition, movement (especially breathing), which also affects attenuation correction, and scatter correction problems.

## References:

Feng D, Li X, Huang S-C. A new double modeling approach for dynamic cardiac PET studies using noise and spillover contaminated LV measurements. IEEE Trans Biomed Eng. 1996; 43(3): 319-327. doi: 10.1109/10.486290.

Henze E, Huang S-C, Ratib O, Hoffman E, Phelps ME, Schelbert HR. Measurements of regional tissue and blood-pool radiotracer concentrations from serial tomographic images of the heart. J Nucl Med. 1983; 24: 987-996.

Herrero P, Markham J, Myears DW, Weinheimer CJ, Bergmann SR. Measurement of myocardial blood flow with positron emission tomography: correction for count spillover and partial volume effects. Math Comput Modeling 1988; 11: 807-812. doi: 10.1016/0895-7177(88)90605-X.

Hutchins GD, Schwaiger M, Rosenspire KC, Krivokapich J, Schelbert H, Kuhl DE. Noninvasive quantification of regional myocardial blood flow in the human heart using N-13 ammonia and dynamic positron emission tomographic imaging. J Am Coll Cardiol. 1990; 15(5): 1032-1042. doi: 10.1016/0735-1097(90)90237-J.

Hutchins GD, Caraher JM, Raylman RR. A region of interest strategy for minimizing resolution distortions in quantitative myocardial PET studies. J Nucl Med. 1992; 33: 1243-1250. PMID: 1597746.

Iida H, Rhodes CG, de Silva R, Yamamoto Y, Araujo LI, Maseri A, Jones T. Myocardial tissue fraction - correction for partial volume effects and measure of tissue viability. J Nucl Med. 1991; 32: 2169-2175. PMID: 1941156.

Iida H, Rhodes CG, de Silva R, Araujo LI, Bloomfield P, Lammertsma AA, Jones T. Use of the left ventricular time-activity curve as a noninvasive input function in dynamic oxygen-15-water positron emission tomography. J Nucl Med. 1992; 33: 1669-1677. PMID: 1517842.

Oikonen V. Model equations for myocardial perfusion studies with [15O]H2O PET. http://www.turkupetcentre.net/reports/tpcmod0005.pdf

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Updated at: 2019-01-02
Created at: 2012-02-29
Written by: Chunlei Han, Vesa Oikonen