Figure 3

The lumped two-compartment system. a) Schematic diagram of lumped two-compartment model, where it is assumed that contrast is well-mixed within each compartment at any instant. Blood with tracer or contrast can flow at a rate F into a compartment with volume fraction v1 and exit on the venous side. The second compartment with volume v2, could represent the interstitial space, and the exchange of contrast between the two compartments is controlled by a parameter PS, representing the permeability surface area product for trans-capillary transport of contrast. b) The lumped two compartment system can be represented by a system of coupled linear differential equations (see appendix A). A solution for a unit impulse of contrast at t = 0, and assuming that there is no contrast in the two two compartments before this arterial input, was calculated for F = 0.88 ml/min/g and PS = 0.3 ml/min/g, assuming v1 = 0.06 ml/g and v2 = 0.18 ml/g. The red line represents the contrast concentration that would be detected per unit voxel volume, and which is calculated as volume-fraction-weighted sum of contributions from the vascular space (solid gray line) and the interstitial space (dashed gray line).