(D-123) A computational model of the relationship between intratumoral hyperthermia and fluid pressure

Introduction:: Disorders of the tumor microenvironment include hyperpermeability of blood vessels and the compression of lymphatic and blood vessels due to the solid stress transmitted by the solid components of the extracellular matrix (e.g. cells, collagen fibers). The increased permeability of the vasculature combined with a compromised drainage system results in an increase of the fluid pressure in the interstitial space, with intratumoral pressures typically in the range from 5 mmHg up to 40-45 mmHg.

In the context of drug delivery either by systemic or local injection, high intratumoral pressure represents a barrier for achieving adequate drug distribution throughout the tumor. A number of studies have demonstrated the potential of increasing the blood flow in tumor microvasculature as a means to decompress blood vessels and thereby decrease the intratumoral pressure. Hyperthermia, localized heating of tissue to temperatures in the range ~39-45 °C, can be a strategy to modulate the tumor blood flow.

We present a computational modeling study, informed by in vivo experiments in a rat tumor model, for characterizing hyperthermia-mediated modulation of intratumoral pressure profiles.


Materials and Methods:: We conducted an in silico and in vivo analysis of the relationship between hyperthermia and interstitial pressure in the following manner. We first modeled hyperthermia as delivered by a monopolar needle electrode, applying 500 kHz radiofrequency (RF) current, similar to RF tumor ablation devices in current clinical use, but with applied power adapted to limit peak temperatures. Figure 1 illustrates the geometry of the computational model with current delivered with a 21-gauge needle placed in the center of a 13 mm diameter tumor, surrounded by tissue modeled with properties of muscle. The dispersive return electrode was modelled at the bottom surface of the muscle-mimicking cylinder. The model was employed to simulate sub-ablative (0.5 W) and ablative (1 W) hyperthermia for 15 minutes. Quasi-electrostatic, bioheat transfer, and fluid dynamics equations, were implemented with COMSOL Multiphysics (see supplemental material, Figure S1). Temperature-dependent blood perfusion models for the tumor and muscle regions were assigned according to measurements previously reported by Song et al (IEEE Trans. Biomed. Eng., 1984). The temperature-dependent blood perfusion values couple the thermal model to the mass conservation equation, which is solved to determine the intra-tumoral pressure. The tumor is modeled as a poro-elastic material, as described by Netti et al. (Cancer Res., 1995). The initial conditions assigned to the tumor pressure were 9 mmHg in the whole tumor and 0 mmHg at the boundary between the tumor and the muscle and between the needle and the tumor, as measured experimentally in an in vivo rat tumor model (McArdle RH7777).


Results, Conclusions, and Discussions:: Figure 2A illustrates the pressure and thermal distributions within the tumor and adjacent tissue regions after 15 minutes heating with 0.5 W. More than 50% of the tumor region is within sub-ablative temperatures (40 – 43°C). Figure 2B and 2C show in detail the temperature (T) and intra-tumoral pressure (Pi) across the time at different radial distances from the needle. Temperatures exceeding 42 °C, where the blood flow starts to decrease according to the model we adopted, cover the tumor up to 5 mm from the tip. Thermal and pressure profiles following 1 W heating for 15 minutes are provided in the supplement (Figure S2).


The simulations show a perturbation of the initial homogenous distribution of the intratumoral pressure as a response to the temperature. Toward the periphery of the tumor, the temperature increases at a slower rate compared to the core. The increase of the blood perfusion when the temperature is below 43°C (Figure 1) drives the decrease of the intratumoral pressure. In the core of the tumor, where the heating is rapid given the proximity to the source, the pressure has a little or null change at the end of the procedure compared to the initial conditions.

The term of the transient fluid redistribution in the mass conservation equation we implemented for a poroelastic material, describes the deformation of the solid component to accommodate the fluid component in response to the time-varying pressure. If the temperature rapidly increases as occurs in the core of the tumor, the time constant linked to the trans-capillary exchange is dominant compared to the time constant related to the interstitial diffusion. The trend of the pressure suggests that in proximity to the heating source the pressure could require more time to decrease after the initial increasing due to the fast trans-capillary extravasation.

The results indicate that the final values of pressure do not depend only on the temperature reached at the end of the procedure but also on the transient temperature profile.



This study provides an initial understanding on the coupling between local heating and the spatiotemporal fluid dynamics in the tumor microenvironment.




Acknowledgements (Optional): : Funding from NIH grant R37CA269622

References (Optional): : C.W. Song et al. "Implications of blood flow in hyperthermic treatment of tumors", IEEE Trans. Biomed. Eng., vol. 31, no. 1, pp. 9 - 16.

P. A. Netti, et al. "Time-dependent behavior of interstitial fluid pressure in solid tumors: implications for drug delivery ", Cancer Res., vol. 55, no. 22, pp. 5451 - 5458