For a system under the influence of chemical exchange, the evolution of the transverse magnetisation is given by the Bloch (1946) equations as modified by McConnell (1958) for chemical exchange - the Bloch-McConnell equations. For a two state exchange jumping between states A and B, the equation is:
The analytic or closed-form frequency-domain solution for this equation however remains intractable. Solutions can nevertheless be found by either making assumptions or restrictions about the exchange process and then analytically solving 11.1 or by finding numeric solutions. The modelling of relaxation dispersion data can hence be categorised into these two distinct methodologies:
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