Matrix-algebra-based calculations of the time evolution of the binary spin-bath model for magnetization transfer

[Display omitted] ► Modeling of magnetization transfer is achieved employing matrix algebra. ► A polynomial interpolation technique allows for efficient computation. ► The time evolution of the binary spin-bath model is calculated without unwarranted simplifications. ► Digitized RF pulse envelopes as generated on an MR scanner are considered during simulations. ► Application to magnetization transfer experiments in agar gel and human brain yields agreement with published data. Quantification of magnetization-transfer (MT) experiments are typically based on the assumption of the binary spin-bath model. This model allows for the extraction of up to six parameters (relative pool sizes, relaxation times, and exchange rate constants) for the characterization of macromolecules, which are coupled via exchange processes to the water in tissues. Here, an approach is presented for estimating MT parameters acquired with arbitrary saturation schemes and imaging pulse sequences. It uses matrix algebra to solve the Bloch–McConnell equations without unwarranted simplifications, such as assuming steady-state conditions for pulsed saturation schemes or neglecting imaging pulses. The algorithm achieves sufficient efficiency for voxel-by-voxel MT parameter estimations by using a polynomial interpolation technique. Simulations, as well as experiments in agar gels with continuous-wave and pulsed MT preparation, were performed for validation and for assessing approximations in previous modeling approaches. In vivo experiments in the normal human brain yielded results that were consistent with published data.