On the theoretical limits of detecting cyclic changes in cardiac high-energy phosphates and creatine kinase reaction kinetics using in vivo ³¹P MRS

Adenosine triphosphate (ATP) is absolutely required to fuel normal cyclic contractions of the heart. The creatine kinase (CK) reaction is a major energy reserve reaction that rapidly converts creatine phosphate (PCr) to ATP during the cardiac cycle and at times of stress and ischemia, but is significantly impaired in conditions such as hypertrophy and heart failure. Because the magnitudes of possible in vivo cyclic changes in cardiac high-energy phosphates (HEPs) during the cardiac cycle are not well known from previous work, this study uses mathematical modeling to assess whether, and to what extent, cyclic variations in HEPs and in the rate of ATP synthesis through CK (CK flux) could exist in the human heart, and whether they could be measured with current in vivo ³¹P MRS methods. Multi-site exchange models incorporating enzymatic rate equations were used to study the cyclic dynamics of the CK reaction, and Bloch equations were used to simulate ³¹P MRS saturation transfer measurements of the CK reaction. The simulations show that short-term buffering of ATP by CK requires temporal variations over the cardiac cycle in the CK reaction velocities modeled by enzymatic rate equations. The maximum variation in HEPs in the normal human heart beating at 60min^-1 was approximately 0.4m m and proportional to the velocity of ATP hydrolysis. Such HEP variations are at or below the current limits of detection by in vivo ³¹P MRS methods. Bloch equation simulations show that ³¹P MRS saturation transfer estimates the time-averaged, pseudo-first-order forward rate constant, k_f,ap′, of the CK reaction, and that periodic short-term fluctuations in k_f′ and CK flux are not likely to be detectable in human studies employing current in vivo ³¹P MRS methods.