Mathematical Modeling: Methods, Applications and Research reviews recent progress in three different propulsion systems which may offer significant advantages for more efficient, compact and adaptive astronautic vehicles in the mid-21st century: swirling nuclear magneto-hydrodynamic propulsion, biomimetic magneto-rheological propulsion and electro-hydrodynamic propulsion systems. The authors introduce an empirical mathematical model. This model has been developed to describe contrast uptake and washout behavior without use of vascular input functions. Though this approach does not require making assumptions about underlying physiology or anatomy, the primary disadvantage of this approach, is that the parameters obtained by this approach do not correspond directly to identifiable physiological or anatomic features. In closing, the authors aim to express how the mathematical modeling is a valid tool for teaching and learning in a competent way and should be incorporated in academic curricula.