Laurence T. Baxter

Transport of fluid and macromolecules in tumors. I. Role of interstitial pressure and convection.

A general theoretical framework for transvascular exchange and extravascular transport of fluid and macromolecules in tumors is developed. The resulting equations are applied to the most simple case of a homogeneous, alymphatic tumor, with no extravascular binding. Numerical simulations show that in a uniformly perfused tumor the elevated interstitial pressure is a major cause for heterogeneous distribution of nonbinding macromolecules, because it (i) reduces the driving force for extravasation of fluid and macromolecules in tumors, (ii) results in nonuniform filtration of fluid and macromolecules from blood vessels, and (iii) leads to experimentally verifiable, radially outward convection which opposes the inward diffusion. The models are used to predict the interstitial pressure, interstitial fluid velocity, and concentration profiles as a function of radial position and tumor size. The model predictions agree with the following experimental data: (i) the interstitial pressure in a tumor is lowest at the periphery of the tumor and increases towards the center; (ii) the radially outward fluid velocity predicted by the fluid transport model is of the same order of magnitude as that measured in tissue-isolated tumors; and (iii) the concentration of macromolecules is higher in the periphery than in the center of tumors at short times postinjection; however, at later times the peripheral concentration is less than the concentration in the center. This work shows that in addition to the heterogeneous distribution of blood supply, hindered interstitial transport, and rapid extravascular binding of macromolecules (e.g., monoclonal antibodies), the elevated interstitial pressure plays an important role in determining the penetration of macromolecules into tumors. If the genetically engineered macromolecules are to fulfill their clinical promise, methods must be developed to overcome these physiological barriers in tumors.

Transport of fluid and macromolecules in tumors: III. Role of binding and metabolism

We have previously developed a general theoretical framework for transvascular exchange and extravascular transport of fluid and macromolecules in tumors. The model was first applied to a homogeneous, alymphatic tumor, with no extravascular binding (Baxter and Jain, 1989). For nonbinding molecules the interstitial pressure was found to be a major contributing factor to the heterogeneous distribution of macromolecules within solid tumors. A steep pressure gradient was predicted at the periphery of the tumor, and verified in recent experiments. The second paper in this series looked at the role of heterogeneous perfusion and lymphatics on the interstitial pressure distribution and concentration profiles of non-binding macromolecules (Baxter and Jain, 1990). The present work presents the role of specific binding and metabolism in macromolecular uptake and distribution. In this investigation the interstitial concentration profiles for IgG and its fragment, Fab, were modeled with a convective-diffusion equation which includes extravascular binding and metabolism as well as transvascular exchange. The effects of molecular weight, binding affinity, antigen density, initial dose, plasma clearance, vascular permeability, metabolism, and necrosis were considered. An expression for optimal affinity was derived. The main conclusion is that an antibody with the highest possible binding affinity should be used except when: (i) there are significant necrotic regions; (ii) the diffusive vascular permeability is very small; and (iii) a uniform concentration is required on a microscopic scale. The highest concentrations are achieved by continuous infusion, but the specificity ratio is highest for bolus injections. Antibody metabolism reduces both the total concentration and the specificity ratio, especially at later times. In addition, specific binding reduces the amount of material sequestered in a necrotic core. Our model is compared with three previous models for antibody binding found in the literature. Unlike previous models, this model combines nonuniform filtration, binding, and interstitial transport to determine macroscopic concentration profiles. In addition to supporting previous conclusions, our model offers some new strategies for therapy.

Fractal Characteristics of Tumor Vascular Architecture During Tumor Growth and Regression

Objective: Tumor vascular networks are different from normal vascular networks, but the mechanisms underlying these differences are not known. Understanding these mechanisms may be the key to improving the efficacy of treatment of solid tumors.

Intratumoral infusion of fluid: estimation of hydraulic conductivity and implications for the delivery of therapeutic agents *

We have developed a new technique to measure in vivo tumour tissue fluid transport parameters (hydraulic conductivity and compliance) that influence the systemic and intratumoral delivery of therapeutic agents. An infusion needle approximating a point source was constructed to produce a radially symmetrical fluid source in the centre of human tumours in immunodeficient mice. At constant flow, the pressure gradient generated in the tumour by the infusion of fluid (Evans blue-albumin in saline) was measured as a function of the radial position with micropipettes connected to a servo-null system. To evaluate whether the fluid infused was reabsorbed by blood vessels, infusions were also performed after circulatory arrest. In the colon adenocarcinoma LS174T with a spherically symmetrical distribution of Evans blue-albumin, the median hydraulic conductivity in vivo and after circulatory arrest at a flow rate of 0.1 microl min(-1) was, respectively, 1.7x10(-7) and 2.3x10(-7) cm2 mmHg(-1) s. Compliance estimates were 35 microl mmHg(-1) in vivo, and 100 microl mmHg(-1) after circulatory arrest. In the sarcoma HSTS 26T, hydraulic conductivity and compliance were not calculated because of the asymmetric distribution of the fluid infused. The technique will be helpful in identifying strategies to improve the intratumoral and systemic delivery of gene targeting vectors and other therapeutic agents.

Extravasation and Interstitial Transport in Tumors

The use of high-molecular-weight agents such as proteins has been of increasing interest for cancer detection and treatment since the development of genetic engineering and hybridoma technology. These agents include monoclonal antibodies (conjugated with radionuclides, toxins, cytokines, or enzymes), growth factors, biological response modifiers, and enzymes. The use of cells, such as lymphokine-activated killer cells or tumor-infiltrating lymphocytes, is also being investigated. The potent toxicity of some of these agents toward cancer cells in vitro has ignited hopes for a “magic bullet.” Although these agents show great potential, results in clinical studies have not been so positive.