A nonlinear variational method for improved quantification of myocardial blood flow using dynamic H215O PET

H2¹⁵O as a PET-tracer offers the opportunity to examine perfusion of blood into tissue non-invasively (cf. [1]). It features a short radioactive half-life (≈ 2 min.) and therefore adds a smaller radiation exposure to the patient in comparison to other tracers. The disadvantages arising from the short radioactive half-life are noisy, low-resolution reconstructions. Previous algorithms first reconstruct images from each dynamic H2¹⁵O dataset independently, e.g. via the standard EM-algorithm (cf. [2]) or FBP. Hence, temporal correlation is neglected. The myocardial blood flow (MBF) and other important parameters, like tissue fraction, arterial and venous spillover effects are computed subsequently from these reconstructed images. Our new method interprets the direct computation of parameters as a nonlinear inverse problem. This implies the need for inversion of a nonlinear operator G(p) (with p denoting the parameters to compute), but allows to skip the process of generating noisy images. The process is schematically described in Figure 1. Therefore, our method takes into account the temporal correlation between the datasets, and not the correlation between noisy, low resolution images. The problem is transferred to a nonlinear parameter identification problem. Furthermore, regularization can be added to each parameter independently, assuring meaningful results.