# Quantification of Myocardial Blood Flow via dynamic PET

Dynamic positron emission tomography (PET) allows for noninvasive examination of physiological processes. Radioactive water (H

_{2}

^{15}O) as a PET-tracer is the preferred candidate for examining myocardial bloodflow because of its short half-time, resulting in a low radiation burden to the patient, and its high diffusibility. Unfortunately, the short half-time leads to noisy, low-resolution reconstructions.

## The common approach

The common approach for myocardial blood flow quantification is to reconstruct images for each temporal dataset independently via the standard expectation-maximization-algorithm or filtered backprojection and to compute the parameters from images like the one above. However, the temporal correlation between the datasets is neglected in this approach.## Model-based approach

Rather than using the correlation between noisy, low resolution images we want to use the temporal correlation inherent in the datasets. This can be achieved by building up a nonlinear physiological model depending on physiological parameters (e.g. perfusion) and solving the respective parameter identification problem. As another advantage, regularization can be added to each parameter in-dependently to ensure meaningful results.## Kinetic Modeling

To model physiological processes, like the perfusion of blood in the myocardium, one often uses so called compartment models. In our case, we use a one-tissue compartment model which has been extended to terms of flow.In the figure above, C is denoting the tracer concentration and J the tracer flux, with the subscripts A,T and V referring to 'artery', 'tissue' and 'vene' respectively, while F is denoting the blood flow rate. Note that the tracer flux is defined by

Then, we can derive the following ordinary differential equation

with being the partition coefficient, which is assumed to be constant due to the high diffusibility of the tracer. By using the the initial condition we receive

Adding a tissue fraction term R and a spillover term S to correct for the low spatial resolution of the PET scanner and for heart motion, we end up with the following model operator, that we incorporate into our reconstruction process,

## Results

The model-based approach improves the reconstructions as one can see in the images below.

**PET Images.**

*Left:*Simple EM reconstruction with gaussian smoothing.

*Right:*Model-based reconstruction with gaussian smoothing.

## References:

- M. Benning, T. Kösters, F. Wübbeling, K. Schäfers and M. Burger.
*A Nonlinear Variational Method for Improved Quantification of Myocardial Blood Flow Using Dynamic H215O PET*, IEEE Nuclear Science Symposium Conference Record, November 2008 - G. T. Gullberg, B. W. Reutter, A. Sitek, J. S. Maltz and T. F. Budinger.
*Dynamic single photon emission computed tomography - basic principles and cardiac applications*, Phys. Med. Biol. 55:R111-R191, 2010. - A. J. Reader, J. C. Matthews, F. C. Sureau, C. Comtat, R. Trébossen and I. Buvat.
*Fully 4D image reconstruction by estimation of an input function and spectral coefficients*, IEEE Nuclear Science Symposium Conference Record, pages 3260-3267, 2007. - A. Sawatzky, C. Brune, F. Wübbeling, T. Kösters, F.Schäfers and M. Burger.
*Accurate EM-TV Algorithm in PET with low SNR*, IEEE Nuclear Science Symposium Conference Board, pages 5133-5137, 2008. - M. N. Wernick and J. N. Aarsvold.
*Emission Tomography: The Fundamentals of PET and SPECT*, Elsevier Academic Press, 2004.