**A. Appendices**

### **A.1 Microvascular fluid exchange and pharmacokinetic modeling**

Unidirectional three-parameter transcapillary permeability model issue extraction by indicator dilution

$$E\_{\rm F} = 1 - \frac{1}{e^{\frac{PS}{CRF}}} \tag{1}$$

*where* EF, brain tissue indicator extraction fraction, a.u.

P, permeability, x10+1 mm/sec

S, surface area, x10+2 mm<sup>2</sup>

Q, blood flow (i.e. CBF), microvascular capillary flow per unit mass of tissue per min, ml/60 sec � g tissue, mm<sup>3</sup> /sec

*if* P�S product - > ∞, *then E*<sup>f</sup> ≈ 1 and all of the indicator is extracted from blood plasma into the EES and is a small molecule permeable across the blood-CSF barrier and the blood-brain barrier and is a barrier permeability indicator

*if* P�S product - > 0, *then E*<sup>f</sup> ≈ 0 and none of the indicator is extracted and the indicator is a macromolecular contrast agent and blood volume indicator

Bidirectional flux two-parameter transcapillary permeability model for hydraulic conductivity with Peclet variable for capillary connective flow

$$\frac{J\_V}{A} = Lp \left[ \Delta P - \sigma^2 \,\,\pi\_c \,\, \frac{\left(1 - \frac{1}{\epsilon^{\mathcal{V}\epsilon}}\right)}{\left(1 - \sigma \frac{1}{\epsilon^{\mathcal{V}\epsilon}}\right)} \right] \tag{2}$$

*where J*v, effective hydraulic flux into tissue in 10�<sup>6</sup> cm per sec

A, surface area for transcapillary exchange in cm-squared

*L*p, hydraulic conductivity coefficient of water permeability in cm per sec � cm H2O σ, reflection coefficient to transcapillary macromolecule transfer across capillary wall, a.u.

*πc*, capillary osmotic pressure in mm Hg or cm H2O

*P*e, Peclet variable ratio for macromolecule convective flow through capillary, a.u.

Bidirectional three-parameter generalized kinetic model (GKM) pharmacodynamic model with vascular plasma volume adjustment term (as per section Refs.)

$$K \text{trans} = \frac{\mathbf{C}\_t(t) - \mathbf{V}\_p \* \mathbf{C}\_t(t)}{\int\_{t}^{t} \frac{\mathbf{C}\_p(t)}{e^{k\_P \cdot (t - \overline{\chi})}} dt} \tag{3}$$

*where C*<sup>t</sup> (*t*), concentration in tissue at time *t* in minutes

*C*<sup>p</sup> (*t*), concentration in plasma at time *t*

Ʈ, imaging time at initial sequence contrast enhancement

*V*p, plasma vascular volume

*V*e, extracellular extravascular volume, tissue interstitium volume

*K*trans, *K*i, positive slope forward (outward) transfer rate constant per minute (or apparent tissue VD (VD') per minute)

*K*ep, *K*b, negative slope reverse (inward) transfer rate per minute *K*trans range: indication.

Upper tier: high-hyperpermeability lesion, i.e. inflammation

Mid tier: mid-hyperpermeability lesion, i.e. high grade tumor

Lower tier: low-hyperpermeability lesion, i.e. low grade tumor

