Chemical exchange between the bulk water pool and labile protons in solute pools in tissues increases the spin-lattice relaxation rate in the rotating frame R_1ρ (=1/T_1ρ), which can be evaluated using spin-locking pulse sequences. Moreover, exogenous contrast agents may be designed that have specific exchange rates that differ from endogenous tissue compounds. Exchange has been widely studied recently using CEST techniques¹, but such methods distinguish protons according to their chemical shifts whereas appropriate spin-locking techniques may be selectively sensitized to specific rates of exchange, especially at high fields. When three proton pools are present, the variation of R_1ρ with locking field amplitude will display a “double dispersion” with two inflections indicative of the exchange rates between the pools. The Exchange Rate Contrast (ERC), which we have described previously², can theoretically be used to distinguish each pool and create parametric images in which the contrast reflects pool sizes which could potentially be used to quantify metabolite concentrations non-invasively.A theoretical expression for the ERC amplitude for a three-pool mixture was derived by combining three values of R_1ρ at locking fields of ~0, ω₁, and ~∞ using the approximate equation derived from the Chopra model³, $$$R_{1\rho}(\omega_1)\approx R_2^a+p_b\left[R_2^b+ \frac{k_{ba}\Delta \omega_b^2}{k_{ba}^2+\Delta\omega_b^2+\omega_1^2}\right]+p_c\left[R_2^c+ \frac{k_{ca}\Delta \omega_c^2}{k_{ca}^2+\Delta\omega_c^2+\omega_1^2}\right]$$$. This is valid under the reasonable assumptions that $$$k_{ba}\gg R_2^b>R_1^b$$$ and $$$k_{ca}\gg R_2^c>R_1^c$$$. Here $$$R_2^{a,b,c}$$$ are the transverse relaxation rates of each pool, $$$p_{b,c}$$$ are the pool fractions, $$$k_{ba}$$$ is the exchange rate from pool b to pool a, $$$\Delta \omega_{b,c}$$$ are the chemical shifts of the respective pools, and $$$\omega_1$$$ is the spin-lock amplitude. The ERC equation may then be derived by combining the three R_1ρ values as $$$ERC=4\frac{\left[R_{1\rho}\left(0\right)- R_{1\rho}\left(\omega_1\right)\right]\left[R_{1\rho}\left(\omega_1\right)- R_{1\rho}\left(\infty\right)\right]}{\left[R_{1\rho}\left(0\right)- R_{1\rho}\left(\infty\right)\right]^2}$$$. The ERC expression can be written as Eq. 1: $$ERC=4\omega_1^2\alpha\frac{\beta\delta}{\epsilon^2}$$ Here, $$$\alpha=\frac{\left(k_{ba}^2+\Delta\omega_b^2\right)\left(k_{ca}^2+\Delta\omega_c^2\right)}{\left(k_{ba}^2+\Delta\omega_b^2+\omega_1^2\right)^2\left(k_{ca}^2+\Delta\omega_c^2+\omega_1^2\right)^2}$$$, $$$\beta=\left[p_bk_{ba}\Delta\omega_b^2\left(k_{ca}^2+\Delta\omega_c^2+\omega_1^2\right)+p_ck_{ca}\Delta\omega_c^2\left(k_{ba}^2+\Delta\omega_b^2+\omega_1^2\right)\right]$$$, $$$\delta=\left[p_bk_{ba}\Delta\omega_b^2\left(k_{ca}^2+\Delta\omega_c^2\right)\left(k_{ca}^2+\Delta\omega_c^2+\omega_1^2\right)+p_ck_{ca}\Delta\omega_c^2\left(k_{ba}^2+\Delta\omega_b^2\right)\left(k_{ba}^2+\Delta\omega_b^2+\omega_1^2\right)\right]$$$, and $$$\epsilon=\left[p_bk_{ba}\Delta\omega_b^2\left(k_{ca}^2+\Delta\omega_c^2\right)+p_ck_{ca}\Delta\omega_c^2\left(k_{ba}^2+\Delta\omega_b^2\right)\right]$$$. The magnitude of the ERC expression will be governed heavily by the frequency spread between the peaks of each separate pool, with the maximum theoretical contrast being $$$\Delta ERC_{max}=1-4\frac{\left(k_{ba}^2+\Delta\omega_b^2\right)\left(k_{ca}^2+\Delta\omega_c^2\right)}{\left(k_{ba}^2+\Delta\omega_b^2+k_{ca}^2+\Delta\omega_c^2\right)}$$$. Subsequently, three pool Bloch-McConnell simulations were run using the following parameters: B0 = 7T, Δω_b = 1 ppm, Δω_c = 0.5 ppm, k_ba = 20 kHz, k_ca = 0.5 kHz, $$$R_1^a=R_1^b=R_1^c=0.1$$$ Hz, $$$R_2^a=R_2^b=R_2^c=0.4$$$ Hz, ω₁ = 2π*(40 – 5,000) rad/sec, p_b = 1%, and p_c = 0-1%. The simulated ERC points were plotted against the theoretical ERC curves calculated from Eq. 1 and the values corresponding to the ω₁ at the peak of the pool c ERC curve were plotted for all pool fractions to produce a concentration dependent curve. R_1ρ experiments will be performed in ex-vivo solutions to verify the feasibility of the technique under various conditions.Simulated R_1ρ dispersion curves are shown in Figure 1a in which the low frequency dispersion curve increases as the slower exchanging pool fraction increases. The corresponding ERC points are plotted in Figure 1b and the theoretical curves calculated from Eq. 1 are plotted as solid lines. The thick vertical black line indicates the ω₁ value at which the ERC peak of pool c (dotted black line) displays the peak value of 1 ($$$\omega_1=\sqrt{k_{ca}^2+\Delta\omega_c^2}=160$$$ Hz). The value of each ERC peak along the thick vertical black line is plotted in figure 1c to provide insight into how the concentration affects ERC.Exchange Rate Contrast derived from combinations of spin-lock images provides parametric images in which the image intensity depends on the concentration of the exchanging pools, the exchange rate of those pools, and the applied spin-lock amplitude. Fixing the locking field to the frequency of the peak of one exchanging pool effectively compares the magnitudes of the two separate dispersions. Smaller pool fractions produce the largest change in ERC values, demonstrating the region of highest sensitivity for the technique as shown in Figure 1c. This sensitivity may prove advantageous in experimental settings, but certain limitations are anticipated. When the ERC peaks of the individual pools are very close, the overall ERC cannot significantly shift and the available contrast becomes limited. Also, if the dispersion magnitudes are not significantly greater than the uncertainty in R_1ρ measurements, the corresponding ERC image could become very noisy and make quantifying exchange or concentration parameters difficult in practice. Injecting a very fast exchanging exogenous agent would produce a higher frequency dispersion than those caused by native metabolites and make the technique more effective in practice.A novel theoretical expression for Exchange Rate Contrast was derived for three exchanging pools that has been shown through simulations to produce concentration dependent contrast that may prove useful for identifying some exchange agents in the presence of a background of other exchanging protons.