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A Mathematical Model for the Heterogeneity of Myocardial Perfusion Using Nitrogen-13-Ammonia

Deportment of Cardiology and PET Center, University Hospital Groningen, Groningen; Laboratory for Physiology, Institute for Cardiovascular Research, Free University, Amsterdam; Department of Cardiology, Leiden University Hospital, Leiden, The Netherlands

Correspondence: For correspondence or reprints contact: Klaas R. Visser, PhD. Department of Cardiology, University Hospital Groningen, P.O. Box 30.001, NL-9700 RB Groningen, The Netherlands.

ABSTRACT

Heterogeneity of left ventricular myocardial perfusion is an importantclinical characteristic. Different aspects of this heterogeneitywere analyzed. Methods: The coefficient of variation (v), characterizingheterogeneity, was modeled as a function of the number ofsegments (n), characterizing spatial resolution of the measurement,using two independent pairs of mutually dependent parameters: thefirst pair describes v as a power function of n, and the second pairadds a correction for n small, n was varied by joining equal numbersof neighboring segments. Local similarity of the perfusion wascharacterized by the correlation between the perfusions of neighboring segments.Genesis of the perfusion distribution was modeledby repeated asymmetric subdivision of the perfusion into avolume among two equal subvolumes. These analyses were appliedto study the differences between 16 syndrome X patients and 16 age- and sex-matchedhealthy volunteers using 13N-ammonia parametric PET perfusion data with a spatial resolution of 480 segments.Results: The heterogeneity of patients is higher for the whole rangeof spatial resolutions considered (2 n 480; for n = 480, v =0.22 ± 0.03 and 0.18 ± 0.02;p <0.005). This is because the firstpair of parameters differs between patients and volunteers (p <0.005), whereas the second pair does not (p >0.1). For both groupsof subjects there is a significant positive local correlation for distancesup to 30 segments. This correlation is a formal description ofthe patchy nature of the perfusion distribution. Conclusion: Whencomparing values of v, these should be based on the same value ofn. The model makes it possible to calculate v for all values of n 480. Mean perfusion together with the two pairs of parameters arenecessary and sufficient to describe all aspects of the perfusiondistribution. For n small, heterogeneity estimation is less reliable.Patients have a higher heterogeneity because their perfusion distributionis more asymmetrical from the third to the seventh generationof subdivision (8 n 128). Therefore, a spatial resolution of n 128 is recommended for parametric imaging of perfusion with PET.Patients have only a very slightly more patchy distribution thanvolunteers. The differences in perfusion between areas with lowperfusion and areas with high perfusion is larger in patients.Key Words:perfusion distribution;left ventricle;fractal dimension;syndrome X

Key Words: • SPECT • exercise tests • stent implantation

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