Tumor Interstitial Pressure: The EPR Penetration Barrier

Tumor Physiology

Interstitial fluid pressure P₀ 18 mmHg

Tissue hydraulic conductivity K 1.0×

Nanoparticle

Particle diameter d 60 nm

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Mean penetration

0 μm

Perivascular trapped

Peak convection v

0 μm/s

Diffusivity D

0 μm²/s

How it works

The barrier, not the leak. The EPR effect's first half — nanoparticles crossing leaky tumor vessel walls — is only half the story. What happens next decides whether the drug actually reaches distant cancer cells: transport through the tumor interstitium, which is opposed by abnormally high interstitial fluid pressure (IFP).

For a roughly spherical tumor, Baxter & Jain's steady-state model gives the radial IFP profile:

P(r) = P0 · [ 1 − sinh(αr)/(αr) ÷ sinh(αR)/(αR) ]
α = √( Lp·S/V / K ),   R = tumor radius

Because tumor vessels are leaky along the whole tumor (not just at the rim), P(r) sits nearly flat at P0 through most of the interior and only relaxes toward normal (≈0) within one length-scale 1/α of the surface. Convective velocity is driven by Darcy's law:

v(r) = −K · dP/dr

A flat pressure profile means dP/dr ≈ 0 in the core — almost no outward convective push — so particles released from a central vessel stall near it and must rely on slow Brownian diffusion (Stokes–Einstein, D = k_BT / 6πηr_p) to move any further. Convection only turns back on near the tumor rim, where it mostly washes drug back into normal tissue rather than deeper in.

P0 slider — raises the plateau pressure; higher P0 flattens the interior gradient further and traps more particles perivascularly.
Conductivity K — denser, less permeable stroma (low K) shrinks the convective rim 1/α and adds drag to diffusion.
Particle diameter — larger particles diffuse slower (D ∝ 1/d), so they depend more heavily on the convective rim they may never reach.

This is why some clinical strategies pair nanomedicines with IFP-lowering co-therapies (e.g. anti-angiogenics, hyaluronidase) — flattening P0 restores some convective penetration depth.

Vessel wall Free nanoparticle Perivascular trapped

Radial pressure P(r)

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