Abstract
Counterexamples are used to motivate the revision of the established theory of tracer transport. Then dynamic contrast enhanced magnetic resonance imaging in particular is conceptualized in terms of a fully distributed convection–diffusion model from which a widely used convolution model is derived using, alternatively, compartmental discretizations or semigroup theory. On this basis, applications and limitations of the convolution model are identified. For instance, it is proved that perfusion and tissue exchange states cannot be identified on the basis of a single convolution equation alone. Yet under certain assumptions, particularly that flux is purely convective at the boundary of a tissue region, physiological parameters such as mean transit time, effective volume fraction, and volumetric flow rate per unit tissue volume can be deduced from the kernel.
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Keeling, S.L., Bammer, R. & Stollberger, R. Revision of the theory of tracer transport and the convolution model of dynamic contrast enhanced magnetic resonance imaging. J. Math. Biol. 55, 389–411 (2007). https://doi.org/10.1007/s00285-007-0089-3
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DOI: https://doi.org/10.1007/s00285-007-0089-3