Figure 3.

Calculations of the relative ¹H magnetization enhancements of protons H_ex, due to exchange with hyperpolarized water protons. Unless stated otherwise the relaxation of water was kept constant at $T_1^{H_{2}O}$ = 10 sec, and the initial relative enhancement of water was ${\langle H_{2}O\rangle }_z(0)/{\langle H_{2}O\rangle }_z(\text{Th})$ = 1000. (a) Enhancement as a function of time since the hyperpolarized (HP) water injection, for the different exchange rate(k_ex) values indicated in the bottom panel. Calculations are given for three different values of T₁(H_ex) (top, middle and bottom panels); the dashed orange line in all panels represents the decay of the water polarization with time. (b) Enhancement achievable by H_ex as a function of k_ex, calculated assuming that: a single scan was measured by a 90° pulse at an optimal time after injection of hyperpolarized water (blue lines), that thermal signal averaging was performed over the course of 10 hours with optimal conditions (ie., with 90° pulses and recycle delays given by k_ex and not solely by T₁(H_ex); red lines), or that multiple hyperpolarized scans were done on H_ex at optimum times assuming minimal TR of 100 ms (cyan lines; in this latter case we display the sum of signals collected with 90° pulses divided by square root of the number of scans). Other parameters are the same as in (a). (c) The effect of T₁(H₂O) on the H_ex enhancement, shown for an optimized single scan acquisition (top), or for multiple scans seeking maximum SNR as a function of k_ex. T₁(H_ex) = 2 sec and the T₁(H₂O) is varied – 5, 10 and 15 sec (red, cyan and green lines, respectively).