Aims: The time constant of left ventricular (LV) relaxation derived from a monoexponential model is widely 12 used as an index of LV relaxation rate, although this model does not reflect the non-uniformity of ventricular 13 relaxation. This study investigates whether the relaxation curve can be better fitted with a “quadratic” model 14 than with the “conventional” monoexponential model and if changes in the LV relaxation waveform due to 15 acute myocardial ischemia could be better detected with the quadratic model. 16 Methods and results: Isovolumic relaxation was assessed with quadratic and conventional models during acute 17 myocardial ischemia performed in 6 anesthetized pigs. Mathematical development indicates that one parameter 18 (Tq) of the quadratic model reflects the rate of LV relaxation, while the second parameter (K) modifies the 19 shape of the relaxation curve. Analysis of experimental data obtained in anesthetized pigs showed that the shape 20 of LV relaxation consistently deviates from the conventional monoexponential decay. During the early phase of 21 acute myocardial ischemia, the rate and non-uniformity of LV relaxation, assessed with the quadratic function, 22 were significantly enhanced. Tq increased by 16% (p < 0.001) and K increased by 12% (p < 0.001) within 30 23 and 60 minutes, respectively, after left anterior descending (LAD) coronary artery occlusion. However, no 24 significant changes were observed with the conventional monoexponential decay within 60 minutes of ischemia. 25 Conclusions: The quadratic model better fits LV isovolumic relaxation than the monoexponential model and can 26 detect early changes in relaxation due to acute myocardial ischemia that are not detectable with conventional 27 methods.