A comparison between equations describing in vivo MT: the effects of noise and sequence parameters

Quantitative models of magnetization transfer (MT) allow the estimation of physical properties of tissue which are thought to reflect myelination, and are therefore likely to be useful for clinical application. Although a model describing a two-pool system under continuous wave-saturation has been available for two decades, generalizing such a model to pulsed MT, and therefore to in vivo applications, is not straightforward, and only recently have a range of equations predicting the outcome of pulsed MT experiments been proposed. These solutions of the 2-pool model are based on differing assumptions and involve differing degrees of complexity, so their individual advantages and limitations are not always obvious. This paper is concerned with the comparison of three differing signal equations. After reviewing the theory behind each of them, their accuracy and precision is investigated using numerical simulations under variable experimental conditions such as degree of T1-weighting of the acquisition sequence and SNR, and the consistency of numerical results is tested using in vivo data. We show that while in conditions of minimal T1-weighting, high SNR, and large duty cycle the solutions of the three equations are consistent, they have a different tolerance to deviations from the basic assumptions behind their development, which should be taken into account when designing a quantitative MT protocol.