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. 2007 Mar 15;67(6):2729-35.
doi: 10.1158/0008-5472.CAN-06-4102.

Effect of vascular normalization by antiangiogenic therapy on interstitial hypertension, peritumor edema, and lymphatic metastasis: insights from a mathematical model

Rakesh K Jain  1 , Ricky T Tong, Lance L Munn
Affiliations

Effect of vascular normalization by antiangiogenic therapy on interstitial hypertension, peritumor edema, and lymphatic metastasis: insights from a mathematical model

Rakesh K Jain et al. Cancer Res. .

Abstract

Preclinical and clinical evidence shows that antiangiogenic agents can decrease tumor vessel permeability and interstitial fluid pressure (IFP) in a process of vessel "normalization." The resulting normalized vasculature has more efficient perfusion, but little is known about how tumor IFP and interstitial fluid velocity (IFV) are affected by changes in transport properties of the vessels and interstitium that are associated with antiangiogenic therapy. By using a mathematical model to simulate IFP and IFV profiles in tumors, we show here that antiangiogenic therapy can decrease IFP by decreasing the tumor size, vascular hydraulic permeability, and/or the surface area per unit tissue volume of tumor vessels. Within a certain window of antiangiogenic effects, interstitial convection within the tumor can increase dramatically, whereas fluid convection out of the tumor margin decreases. This would result in increased drug convection within the tumor and decreased convection of drugs, growth factors, or metastatic cancer cells from the tumor margin into the peritumor fluid or tissue. Decreased convection of growth factors, such as vascular endothelial growth factor-C (VEGF-C), would limit peritumor hyperplasia, and decreased VEGF-A would limit angiogenesis in sentinel lymph nodes. Both of these effects would reduce the probability of lymphatic metastasis. Finally, decreased fluid convection into the peritumor tissue would decrease peritumor edema associated with brain tumors and ascites accumulation in the peritoneal or pleural cavity, a major complication with a number of malignancies.

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Figures

Figure 1
Figure 1
The tumor is modeled as a sphere of radius R embedded in a body fluid (e.g., peritoneal cavity, pleural cavity) or host tissue. The interstitial fluid oozing from the tumor periphery carries therapeutics (e.g., monoclonal antibodies), growth factors (e.g., VEGF-A, VEGF-B, VEGF-C, and VEGF-D), and cells (e.g., metastatic cells) into the surrounding fluid/tissue. The result may be higher fluxes of cancer cells and growth factors from the tumor into the surrounding tissue or body fluid. The growth factors (including VEGF-A, VEGF-B, VEGF-C, and VEGF-D) can induce angiogenesis and lymphangiogenesis, and the cancer cells can contribute to metastatic dissemination via the lymphatic or blood vessels. Fluid seeping from the tumor surface can also cause edema (e.g., around brain tumors) and ascites formation (e.g., ovarian cancer). Antiangiogenic therapy can normalize the tumor vasculature, leading to lower IFP at the center, less steep IFP gradients, and lower fluid flow rates at the tumor margin, thus potentially reducing peritumor edema, ascites formation, and lymphatic metastasis. Furthermore, the normalized vessels may be more resistant to cancer cell intravasation, a prerequisite for hematogenous metastasis.
Figure 2
Figure 2
Pressure and velocity distributions in an isolated tumor (A and B) and a tumor embedded in normal tissue (C and D) as a function of α. A and C, IFP. B and D, velocity profiles. α represents the ratio of rate of fluid filtration across the vessel wall and that across the interstitial matrix. Relative distance <1 represents region within the tumor, whereas >1 represents region outside of the tumor. Note that as α decreases, tumor pressure begins to decrease, and fluid velocity begins to increase in the center of tumors. On the other hand, as α decreases, the velocity at the tumor boundary decreases. For the calculations in C and D, α for normal tissue was assumed to be 2.0. Relative IFP is the actual local IFP divided by the “effective” pressure [Pe = Pv − σ (πv − πi)], which is approximately Pv because πv is close to πi, and σ is nearly zero in tumor tissue. Relative IFVis defined as the local velocity relative to an effective, or average, bulk velocity at the margin, calculated as though IFP were uniform throughout the tumor: K (Pe)/R (see Online Supplement for details).
Figure 3
Figure 3
Relationships between IFP near the tumor center and the fluid convection from the margin. Influence of α on the relative IFP at the center of the tumor and the fluid velocity at the tumor margin for isolated (A) and embedded tumor (C). This information is displayed again in (B) and (D), but with IFVat the boundary shown as a function of the pressure in the tumor center. Note that when a is greater than ∼5, IFP is uniformly high throughout the tumor. Further increases in α cannot produce additional increases in IFP but do increase fluid flux from the margin. This implies that in this regime, where many tumors fall, fluid convection (and probably rates of metastasis) is insensitive to IFP at the center of the tumor.
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