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Geometric Resistance to Blood Flow in Solid Tumors Perfused ex Vivo: Effects of Tumor Size and Perfusion Pressure¹

Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890

In a vascular network blood flow rate is proportional to the arteriovenous pressure difference and inversely proportional to the viscous and geometric resistances. The geometric resistance to tumor blood flow was determined by perfusing tissue-isolated mammary adenocarcinoma (R3230AC; N = 40; tumor weight, 1.8 ± 1.2 (SD) g; range, 0.5–6.6 g) ex vivo with an acellular Krebs-Henseleit medium (viscosity, 0.9 g/m/s) at rates of 0.1 to 60 ml/h and arteriovenous pressure differences of 0 to 120 mm Hg.

Below perfusion pressures of 40 mm Hg, pressure-flow behavior was always nonlinear, indicating elevated geometric resistance and a reduction in vascular cross-sectional area with decreasing microvessel pressure. However, above 40 mm Hg, pressure-flow behavior was linear demonstrating a constant geometric resistance, z₀ and a constant vascular cross-sectional area for flow. z₀ increased linearly from 1.6 to 17.3 x 10⁸ g/cm³ as tumor weight increased from 0.5 to 6.6 g. This dependence of z₀ upon tumor size is in agreement with the decrease in tumor perfusion rates with tumor growth observed in vivo. Comparison with previous studies of normal organs and tissues shows that z₀ in tumors can be as much as 1–2 orders of magnitude higher, depending upon tumor weight. This dependence of geometric resistance on perfusion pressure and tumor size offers novel insights into the dynamics of tumor microcirculation and has significant clinical implications.

¹ This work is dedicated to Dr. Pietro M. Gullino on his 70th birthday.

Supported by The National Cancer Institute (CA37239). Preliminary reports of this work were presented at the 36th Annual Radiation Research Society Meeting, Philadelphia, PA, April 18–20, 1988; Microcirculation Society Annual Meeting, Las Vegas, NV, April 30–May 1, 1988; and Annual Meeting of Biomedical Engineering Society, Las Vegas, NV, May 2–5, 1988.

² Recipient of NIH Predoctoral Traineeship, 1986–1988.

³ To whom requests for reprints should be addressed.

Received 10/24/88. Revised 3/28/89. Accepted 4/ 3/89.

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