Inverting CEST or R 1 ρ $$ {R}_{1\uprho} $$ data to generate solute spectra without a priori assumptions

The goal of CEST imaging is to reveal the underlying tissue composition and exchange. However, quantitative CEST analyses typically require strong assumptions about this same composition and exchange. The goal of this paper is to introduce a new CEST analysis (also applicable to rotating frame relaxation rate $R_{1\rho }$ studies) that reveals the underlying spectrum of exchanging solutes without assuming their number, offsets, or exchange rates.

Each exchanging solute adds an additional term to $R_{1\rho }$ , and this linearity is leveraged by applying established methods for solving linear problems when the solution is non-negative and sparse. This signal inversion is demonstrated in simulations and experiments on phantoms.

The simulation and experimental results demonstrate the ability to qualitatively characterize the number of exchanging solutes, their offsets, and their exchange rates, and to do so under difficult fitting conditions such as when multiple solutes are at the same frequency offset. This signal inversion is only grossly accurate and has significant biases, limited range of applicability, and spurious results.

An inversion of the CEST signal is demonstrated that requires minimal assumptions and can qualitatively characterize the distribution of contributing solutes. These results demonstrate proof of concept, but further work is needed to address in vivo conditions, optimize acquisition and analysis methods, and determine trade-offs between sensitivity, accuracy, range of applicability, and prevalence of fitting artifacts. The ultimate ability of the method to characterize the full range of exchanging solutes in vivo is not yet clear.