A MATHEMATICAL-MODEL FOR THE HETEROGENEITY OF MYOCARDIAL PERFUSION USING NITROGEN-13-AMMONIA

Heterogeneity of left ventricular myocardial perfusion is an important clinical characteristic. Different aspects of this heterogeneity were analyzed. Methods: The coefficient of variation (v), characterizing h eterogeneity, was modeled as a function of the number of segments (n), characterizing spatial resolution of the measurement, using two indep endent pairs of mutually dependent parameters: the first pair describe s v as a power function of n, and the second pair adds a correction fo r n small. n was Varied by joining equal numbers of neighboring segmen ts. Local similarity of the perfusion was characterized by the correla tion between the perfusions of neighboring segments, Genesis of the pe rfusion distribution was modeled by repeated asymmetric subdivision of the perfusion into a volume among two equal subvolumes. These analyse s were applied to study the differences between 16 syndrome X patients and 16 age- and sex-matched healthy volunteers using N-13-ammonia par ametric PET perfusion data with a spatial resolution of 480 segments. Results: The heterogeneity of patients is higher for the whole range o f spatial resolutions considered (2 less than or equal to n less than or equal to 480; for n = 480, v = 0.22 +/- 0.03 and 0.18 +/- 0.02; p < 0.005). This is because the first pair of parameters differs between patients and volunteers (p < 0.005), whereas the second pair does not (p > 0.1), For both groups of subjects there is a significant positive local correlation for distances up to 30 segments. This correlation i s a formal description of the patchy nature of the perfusion distribut ion. Conclusion: When comparing values of v, these should be based on the same value of n. The model makes it possible to calculate v for al l values of n 480. Mean perfusion together with the two pairs of param eters are necessary and sufficient to describe all aspects of the perf usion distribution. For n small, heterogeneity estimation is less reli able. Patients have a higher heterogeneity because their perfusion dis tribution is more asymmetrical from the third to the seventh generatio n of subdivision (8 less than or equal to n less than or equal to 128) . Therefore, a spatial resolution of n greater than or equal to 128 is recommended for parametric imaging of perfusion with PET. Patients ha ve only a very slightly more patchy distribution than volunteers. The differences in perfusion between areas with low perfusion and areas wi th high perfusion is larger in patients.