TABLE 1.

 Summary of general system types for spatiotemporal tracer kinetics.

Model	Figure	Dimension	Studies	Transport equations
1C interstitial diffusion	2A	3D	Koh et al. 46	$\frac{\partial C^e}{\partial t}=D^e{\nabla }^2{C}^e$
1C interstitial convection/ diffusion	2B	3D	Elkin et al. 47	$\frac{\partial C^e}{\partial t}=D^e{\nabla }^2{C}^e-\nabla ·u^e{C}^e$
1C interstitial diffusion with vascular input	2C	2D	Pellerin et al. 27 and Fluckiger et al. 45	$\frac{\partial C^e}{\partial t}=K^{\text{trans}}\left(c_{in}-\frac{C^e}{v_e}\right)+\nabla ·D^e\nabla C^e$
1C interstitial convection/ diffusion with vascular input	2D	2D	Sinno et al. 48 , 49	$\frac{\partial C^e}{\partial t}=K^{\text{trans}}\left(c_{in}-\frac{C^e}{v_e}\right)+\nabla ·D^e\nabla C^e-\nabla ·u^e{C}^e$
1C vascular convection	2E	3D	Zhou et al. 50 and Zhang et al. 51 , 52	$\frac{\partial C^p}{\partial t}=-\nabla ·u^p{C}^p$
1C vascular convection/ diffusion	2F	2D 3D	Zhang et al., 51 Sourbron 53 and Liu et al. 54 , 55 , 56	$\frac{\partial C^p}{\partial t}=-\nabla ·u^p{C}^p+\nabla ·D^p\nabla C^p$
2C interstitial convection/ diffusion with vascular convection and exchange	2G	N/A	Sourbron 19	$\frac{\partial C^p}{\partial t}=-\nabla ·u^p{C}^p-K^{ep}{C}^p+K^{pe}{C}^e$ $\frac{\partial C^e}{\partial t}=-\nabla ·u^e{C}^e+\nabla ·D^e\nabla C^e+K^{ep}{C}^p-K^{pe}{C}^e$
2C vascular convection and exchange	2H	2D	Nævdal et al. 57	$\frac{\partial C^a}{\partial t}=-\nabla ·u^a{C}^a-K^{va}{C}^a$ $\frac{\partial C^v}{\partial t}=-\nabla ·u^v{C}^v+K^{va}{C}^a$
3C interstitial convection/ diffusion with vascular convection and exchange	2I	N/A	Sourbron 19	$\frac{\partial C^a}{\partial t}=-\nabla ·u^a{C}^a-K^{va}{C}^a-K^{ea}{C}^a$ $\frac{\partial C^v}{\partial t}=-\nabla ·u^v{C}^v+K^{va}{C}^a+K^{ve}{C}^e$ $\frac{\partial C^e}{\partial t}=-\nabla ·u^e{C}^e+\nabla ·D^e\nabla C^e+K^{ea}{C}^a-K^{ve}{C}^e$

Notes: Models are named from the transport mechanisms and input type. All models are defined diagrammatically in Figure 2, with each specific sub‐figure indicated here. The transport equations are shown for each model. Studies from the literature concerning the theory or implementation of specific model types are detailed. Cases that utilize different but equivalent equations from the presented models are tagged with superscript letter “a.” Where implementations are available the dimension of the method is shown, any models tagged N/A are purely theoretical.