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# Quantification of Myocardial Blood Flow via dynamic PET

Dynamic positron emission tomography (PET) allows for noninvasive examination of physiological processes. Radioactive water (H215O) 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

$J_{\{\mathcal{A},\mathcal{T},\mathcal{V}\}}(t) = F \cdot C_{\{\mathcal{A},\mathcal{T},\mathcal{V}\}}(t).$

Then, we can derive the following ordinary differential equation

with $\inline \lambda = {C_\mathcal{T}}/{C_\mathcal{V}}$ being the partition coefficient, which is assumed to be constant due to the high diffusibility of the tracer. By using the the initial condition $\inline C_\mathcal{T}(0) = 0$ we receive

$C_\mathcal{T} = F \int_0^t C_\mathcal{A}(\tau)\text{e}^{-\frac{F}{\lambda}(t-\tau)}d\tau.$

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.
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