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. The coefficient of variation (v), characterizing heterogeneity, was modeled as a function of the number of segments (n), characterizing spatial resolution of the measurement, using two independent pairs of mutually dependent parameters: the first pair describes v as a power function of n, and the second pair adds a correction for n small. n was varied by joining equal numbers of neighboring segments. Local similarity of the perfusion was characterized by the correlation between the perfusions of neighboring segments. Genesis of the perfusion distribution was modeled by repeated asymmetric subdivision of the perfusion into a volume among two equal subvolumes. These analyses were applied to study the differences between 16 syndrome X patients and 16 age- and sex-matched healthy volunteers using 13N-ammonia parametric PET perfusion data with a spatial resolution of 480 segments. The heterogeneity of patients is higher for the whole range of spatial resolutions considered (2 < or = n < or = 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 is a formal description of the patchy nature of the perfusion distribution. When comparing values of v, these should be based on the same value of n. The model makes it possible to calculate v for all values of n < or = 480. Mean perfusion together with the two pairs of parameters are necessary and sufficient to describe all aspects of the perfusion distribution. For n small, heterogeneity estimation is less reliable. Patients have a higher heterogeneity because their perfusion distribution is more asymmetrical from the third to the seventh generation of subdivision (8 < or = n < or = 128). Therefore, a spatial resolution of n > or = 128 is recommended for parametric imaging of perfusion with PET. Patients have only a very slightly more patchy distribution than volunteers. The differences in perfusion between areas with low perfusion and areas with high perfusion is larger in patients.