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.

Tumor pretargeting for radioimmunodetection and radioimmunotherapy.

UNLABELLED: The limited success of the sole use of monoclonal antibodies for cancer detection and treatment has led to the development of multistep methods using antibodies in conjunction with low molecular weight agents. For tumor pretargeting, it is important to optimize dose and schedule of relevant agents and to understand barriers to targeted delivery. Here, we address these issues for the anti-carcinoembryonic antigen bifunctional antibody-hapten and the streptavidinylated antibody-biotin systems using a recently developed physiologically based pharmacokinetic model. METHODS: For baseline conditions of a standard 70-kg man with a 20-g tumor embedded in the liver, the model was used in conjunction with the Medical Internal Radiation Dosimetry schema to: estimate absorbed doses in tumor and normal tissues; determine the dose dependence of effector agent accumulation in tumor; simulate tumor-to-background effector agent uptake ratio; and calculate the therapeutic ratio for different antibody forms and radionuclides. Alternative drug administration schemes and variable tumor physiological conditions were considered. RESULTS: Model simulations showed that 131I-labeled biotin with the streptavidinylated F(ab')2 provided the highest therapeutic ratio under the optimized conditions. The simulations also showed that biotin with the bifunctional streptavidinylated immunoglobulin G provided the highest tumor-to-liver uptake ratio during the early period. Sensitivity analysis showed that antibody extravasation was the major factor limiting the accretion of the effector agent in tumor, whereas antigen expression in normal tissues and tumor antigen shedding had little effect on the absorbed doses. CONCLUSION: Tumor pretargeting should provide a definite advantage over direct antibody targeting with up to a 200% increase in tumor-to-background ratio in radioimmunodetection and up to a 76% increase in tumor-to-bone marrow therapeutic ratio in radioimmunotherapy. Rapid antibody clearance from the bloodstream before effector agent injection is expected to improve the therapeutic ratio marginally (3%-10%). However, continuous plasmapheresis dramatically increased the tumor-to-background ratio by a factor of 10 in RAID and the tumor-to-bone marrow therapeutic ratio by more than 110% for short-lived radionuclides in RAIT. Apart from drastic measures such as extended plasmapheresis, pretargeting selectivity was neither sensitive enough for radioimmunodetection nor effective enough for radioimmunotherapy in patients with typical solid tumors even using the optimized protocols.

Potential and limitations of radioimmunodetection and radioimmunotherapy with monoclonal antibodies.

UNLABELLED: Recently, we developed a physiologically based pharmacokinetic model capable of predicting antibody biodistribution in humans by scaling up from mice. By applying this model to anticarcinoembryonic antigen murine antibody ZCE025, we address several critical issues in radioimmunodetection and radioimmunotherapy, including the optimal antibody doses, the desirable antibody form for cancer detection, the optimal combinations of antibody forms and radionuclides for cancer treatment and the effectiveness of the modality. METHODS: Under the baseline conditions of a standard 70-kg man with a 20-g tumor embedded in the liver, the model was used to: (a) estimate absorbed doses in tumor and normal tissues, (b) determine dose-dependent antibody uptake in the tumor, (c) simulate tumor-to-background antibody concentration ratio and (d) calculate therapeutic ratios for different antibody forms and radionuclides. Sensitivity analysis further enabled us to determine antibody delivery barriers and to assess the modality under average and favorable tumor physiological conditions. RESULTS: By using ZCE025 under the baseline conditions, the model found that Fab was the most suitable form for cancer diagnosis, while 131l combined with F(ab')2 provided the highest tumor-to-bone marrow therapeutic ratio for cancer treatment. Sensitivity analysis showed that antibody permeability was the major barrier for antibody accretion in tumors. It also demonstrated that normal tissue antigen expression at a level lower than in the tumor had little effect on the therapeutic ratio. CONCLUSION: The model demonstrates that: (a) for radioimmunodetection, the most effective antibody form (Fab for ZCE025) was the lower mol weight form, yet not sensitive enough for hepatic metastasis detection; and (b) for radioimmunotherapy, a relatively fast-clearing antibody form (F(ab')2 for ZCE025) in combination with long half-life beta(-)-emitters was optimal, yet inadequate as the sole therapeutic modality for solid tumors.

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. METHODS: We studied the fractal characteristics of two-dimensional normal and tumor vascular networks grown in a murine dorsal chamber preparation and imaged with an intravital microscopy station. RESULTS: During tumor growth and regression, the vasculature in the tumor has scaling characteristics that reflect the changing state of the tissue. Growing tumors show vascular networks that progressively deviate from their normal pattern, in which they seem to follow diffusion-limited aggregation to a pathological condition in which they display scaling similar to percolation clusters near the percolation threshold. The percolation-like scaling indicates that the key determinants of tumor vascular architecture are local substrate properties rather than gradients of a diffusing substance such as an angiogenic growth factor. During tumor regression the fractal characteristics of the vasculature return to an intermediate between those of growing tumors and those of healthy tissues. Previous studies have shown that percolation-like scaling generally inhibits transport. CONCLUSIONS: In the present context, the percolation-like nature of tumor vasculature implies that tumor vascular networks possess inherent architectural obstacles to the delivery of diffusible substances such as oxygen and drugs.

Physiologically based kinetic model of effector cell biodistribution in mammals: implications for adoptive immunotherapy.

The goal of the present investigation was to develop a physiologically based kinetic model to describe the biodistribution of immunologically active effector cells in normal and neoplastic tissues of mammals based on the current understanding of lymphocyte trafficking pathways and signals. The model was used to extrapolate biodistribution among different animal species and to identify differences among different effector populations and between intra-arterial and systemic injections. Most importantly, the model was used to discern critical parameters for improving the delivery of effector cells. In the model, the mammalian body was divided into 12 organ compartments, interconnected in anatomic fashion. Each compartment was characterized by blood flow rate, organ volume and lymphatic flow rate, and other physiological and immunological parameters. The resulting set of 45 differential equations was solved numerically. The model was used to simulate the following biodistribution data: (a) nonactivated T lymphocytes in rats; (b) interleukin 2-activated tumor-infiltrating lymphocytes in humans; (c) nonactivated natural killer (NK) cells in rats; and (d) interleukin 2-activated adherent NK cells in mice. Comparisons between simulations and data demonstrated the feasibility of the model and the scaling scheme. The similarities as well as differences in biodistribution of different lymphocyte populations were revealed as results of their trafficking properties. The importance of lymphocyte infiltration from surrounding normal tissues into tumor tissue was found to depend on lymphocyte migration rate, tumor size, and host organ. The study confirmed that treatment with effector cells has not been as impressive as originally promised, due, in part, to the biodistribution problems. The model simulations demonstrated that low effector concentrations in the systemic circulation greatly limited their delivery to tumor. This was due to high retention in normal tissues, especially in the lung. Reducing normal tissue retention through decreasing attachment rate or adhesion site density in the lung by 50% could increase the tumor uptake by approximately 40% for tumor-infiltrating lymphocytes and by approximately 60% for adherent NK cells. Our analysis suggested the following strategies to improve effector cell delivery to tumor: (a) bypassing the initial lung entrapment with administration to the arterial supply of tumor; (b) reducing normal tissue retention using effector cells with high deformability or blocking lymphocyte adhesion to normal vessels; and (c) enhancing tumor-specific capture and arrest by modifying the tumor microenvironment.

Effect of transvascular fluid exchange on pressure-flow relationship in tumors: a proposed mechanism for tumor blood flow heterogeneity.

Tumor blood flow (TBF) is characterized by spatial and temporal heterogeneities. Despite the crucial role of TBF in tumor growth, metastasis, and therapy, the mechanisms underlying these heterogeneities are not fully understood. Tumor vessels are, in general, more leaky than normal vessels and this may enhance the efficiency of fluid exchange between the vascular and the interstitial space. The coupling between transvascular fluid exchange and hemodynamics in tumors has not been explored previously. To investigate the role of transvascular fluid exchange on afferent and efferent blood flow, we modeled the tumor vasculature as an equivalent single vessel which is permeable and deformable and embedded in a fluid medium with uniform pressure. Simulations were carried out to examine the effects of vessel leakiness, vessel compliance, and interstitial fluid pressure on (a) pressure-flow relationship, (b) arterial-venous pressure relationship, and (c) pressure profile along the vessel. Experiments suggested by model simulations required an independent control of arterial and venous pressure and tumor blood flow. To this end, we perfused tissue-isolated tumors ex vivo and obtained data on perfusate flow rate vs arterial and venous pressures. The simulations predicted the following trends as a result of an enhanced fluid filtration across the vessel wall: (a) for a fixed arterial-venous pressure difference, efferent flow decreases with increasing venous pressure, (b) changes in venous pressure are not completely transmitted to the arterial side, and (c) the pressure profile along the vessel becomes less steep. The experimental results confirmed these trends and indicated that vascular and interstitial flow are coupled in isolated tumors. The implications of this coupling for the spatial and temporal heterogeneity in TBF are discussed.

Role of tumor vascular architecture in nutrient and drug delivery: an invasion percolation-based network model.

Delivery of diffusible nutrients and drugs in tissues is limited in part by the distance over which substances must diffuse between the vascular space and the surrounding tissues and by upstream losses prior to local delivery by the blood. By examining the fractal behavior of two-dimensional vascular networks in the murine dorsal skinfold chamber preparation, we have identified distinct architectural features of normal and tumor vascular networks that lead to fundamentally different transport behavior. Normal capillaries which are relatively straight and regularly spaced are well modeled by the widely used Krogh cylinder model. In contrast, the fractal dimensions of tumor vascular networks suggest that the tortuous vessels and wide range of avascular spaces found in tumors are better represented by invasion percolation, a well-known statistical growth process governed by local substrate properties. Based on these observations, we have constructed a percolation-based model of tumor vascular growth that enables us to predict the effects of network architecture on transport. We find that the number of avascular spaces in tumors scales with the size of the spaces so that there will exist a few large avascular spaces and many smaller avascular spaces between vessels. We also find that the tortuosity of the vessels, as reflected by the elevated minimum path dimension, produces regions of locally flow-limited transport and reduces flow through the tumor as a whole. Our model helps to explain the long-standing paradox that tumor vasculature has a higher geometrical resistance than normal vasculature despite increases in vessel diameter. A comparison to oxygenation measurements in normal and tumor tissues shows that our model predicts the architectural obstacles to transport in tumors more accurately than the Krogh cylinder model. Our results suggest that clinical interventions that yield more regular vascular geometry may be useful as a supplement to those that improve arterial availability or decrease rates of consumption by the tissue.

Pharmacokinetic analysis of the microscopic distribution of enzyme-conjugated antibodies and prodrugs: comparison with experimental data.

A mathematical model was developed to improve understanding of the biodistribution and microscopic profiles of drugs and prodrugs in a system using enzyme-conjugated antibodies as part of a two-step method for cancer treatment. The use of monoclonal antibodies alone may lead to heterogeneous uptake within the tumour tissue; the use of a second, low molecular weight agent may provide greater penetration into tumour tissue. This mathematical model was used to describe concentration profiles surrounding individual blood vessels within a tumour. From these profiles the area under the curve and specificity ratios were determined. By integrating these results spatially, average tissue concentrations were determined and compared with experimental results from three different systems in the literature; two using murine antibodies and one using humanised fusion proteins. The maximum enzyme conversion rate (Vmax) and the residual antibody concentration in the plasma and normal tissue were seen to be key determinants of drug concentration and drug-prodrug ratios in the tumour and other organs. Thus, longer time delays between the two injections, clearing the antibody from the blood stream and the use of 'weaker' enzymes (lower Vmax) will be important factors in improving this prodrug approach. Of these, the model found the effective clearance of the antibody outside of the tumour to be the most effective. The use of enzyme-conjugated antibodies may offer the following advantages over the bifunctional antibody-hapten system: (i) more uniform distribution of the active agent; (ii) higher concentrations possible for the active agent; and (iii) greater specificity (therapeutic index).

Time-dependent behavior of interstitial fluid pressure in solid tumors: implications for drug delivery.

Elevated interstitial fluid pressure (IFP) may constitute a significant physiological barrier to drug delivery in solid tumors. Strategies for overcoming this barrier have not been developed to date. To identify and characterize various mechanisms regulating IFP and to develop strategies for overcoming the IFP barrier, we modeled the tumor as a poroelastic solid. We used this model to simulate the effect of changes in microvascular pressure and tumor blood flow (TBF) on IFP. To test model predictions, the effects of changes in arterial pressure and TBF on IFP were measured using a tissue-isolated tumor preparation. IFP in the center of an isolated tumor was predicted to follow variation of the arterial pressure with a time delay of the order of magnitude of 10 s, and this delay was found to be 11 +/- 6 s experimentally. Following a cessation of TBF, the time constant of the drop in IFP was predicted to be of the order of 1000 s and was found to be 1500 +/- 900 s experimentally. The former time scale is characteristic of transcapillary fluid exchange, and the latter of percolation of fluid through the interstitial matrix. Relying on the good agreement between theoretical predictions and experimental data, we estimated the effect of blood pressure modulation on macromolecular uptake in solid tumors. Our results show that no appreciable increase of macromolecular uptake should occur either by an acute or by a chronic increase of blood pressure. On the other hand, higher uptake would result from periodic modulation of blood pressure. Therefore, the effectiveness of a vasoconstrictor such as angiotensin II to increase macromolecular delivery should be significantly enhanced by periodic rather than bolus or continuous administration of the vasoactive agent.

Pharmacologic modification of tumor blood flow and interstitial fluid pressure in a human tumor xenograft: network analysis and mechanistic interpretation.

Various vasoactive agents have been used to modify tumor blood flow with the ultimate goal of improving cancer detection and treatment, with widely disparate results. Furthermore, the lack of mechanistic interpretations has hindered understanding of how these agents affect the different physiological parameters involved in perfusion. Thus, there is a need to develop a unified framework for understanding the interrelated physiological effects of pharmacological and physical agents. The goals of this study were (1) to develop a mathematical model which helps determine the location and magnitude of changes in the vascular resistance of tumor and normal tissues and (2) to test the model with our experimental studies and by comparison with results from the literature. The systemic and interstitial pressures and relative tumor blood flow were measured before and after administration of angiotensin II, epinephrine, norepinephrine, nitroglycerin, and hydralazine in SCID mice bearing LS174T human colon adenocarcinoma xenografts. A mathematical model was developed in analogy to electrical circuits which examined the pressure, flow, and resistance relationships for arterial and venous segments of the vasculature of a tumor and surrounding normal tissue. Vasoconstrictor-induced increases in the mean arterial blood pressure led to increases in tumor blood flow and interstitial pressure with the magnitude of change dependent on the agent (percentage change in blood flow: angiotensin > epinephrine > norepinephrine). The vasodilating agents induced decreases in tumor blood flow in parallel to the induced decreases in the systemic pressure, but only the long-acting arterial vasodilator hydralazine was capable of effecting a decrease in tumor interstitial pressure. The model was also found to be consistent with other data available in the literature on norepinephrine, pentoxifylline, nicotinamide, and hemodilution, and was useful in providing input as to the location and degree of the physiological effects of these agents. The results of the data and model show that the steal phenomenon is the dominant mechanism for redistribution of host blood flow to the tumor. However, some degree of arterial control was found to be present in the tumors. Moreover, the parallel increases in tumor interstitial pressure and blood flow contradict any hypothesis suggesting that elevated interstitial fluid pressure precipitates chronic vascular collapse, thus decreasing blood flow.

Biodistribution of monoclonal antibodies: scale-up from mouse to human using a physiologically based pharmacokinetic model.

The efficacy of a novel diagnostic or therapeutic agent depends on its selective localization in a target tissue. Biodistribution studies are expensive and difficult to carry out in humans, but such data can be obtained easily in rodents. We have developed a physiologically based pharmacokinetic model for scaling up data from mice to humans, the first such model for genetically engineered macromolecules that bind to their targets in vivo, such as mAbs. The mathematical model uses physiological parameters including organ volumes, blood flow rates, and vascular permeabilities; the compartments (organs) are connected anatomically. This allows the use of scale-up techniques to predict antibody distribution in humans. The model was tested with data obtained in human patients for the biodistribution of a mAb against carcinoembryonic antigen. The model was further tested for a two-step protocol: bifunctional antibodies and radiolabeled hapten, which compared favorably with data in both mice and humans. The model was useful for optimization of treatment parameters, such as dose and time interval of injections, binding affinities, and choice of molecular carrier. This framework may be applicable to other genetically engineered molecules (e.g., growth factors, antisense oligonucleotides, and gene-carrying vectors).

Physiologically based pharmacokinetic model for specific and nonspecific monoclonal antibodies and fragments in normal tissues and human tumor xenografts in nude mice.

A physiologically based pharmacokinetic model to describe the biodistribution of a specific monoclonal antibody IgG1 (ZCE025) and its fragments (F(ab')2 and Fab) and of a nonspecific IgG1 (MOPC21) in normal tissues and a human colon carcinoma xenograft (T380) in nude mice is developed. The model simulates the experimental data on the concentration of these four macromolecules in plasma, urine, heart, lung, liver, kidney, spleen, bone, muscle, skin, GI tract, and tumor. This is the first such model for macromolecules with specific binding. A two-pore formalism for transcapillary solute exchange is used which avoids the oversimplifications of unidirectional transport or a single effective permeability coefficient. Comparison of the model with our biodistribution data shows that: (a) a physiologically based pharmacokinetic model for specific and nonspecific antibodies is able to explain experimental data using as few adjustable parameters as possible; (b) for antibodies and fragments, the tumor itself has no significant influence on the pharmacokinetics in normal tissues; and (c) the two-pore formalism for transcapillary exchange describes the data better than a single-pore model without introducing extra adjustable parameters. Sensitivity analysis shows that the lymph flow rate and transvascular fluid recirculation rate are important parameters for the uptake of antibodies, while for the retention of specific antibodies, extravascular binding is the key parameter. A single-pore model could also obtain a good fit between model and data by adjusting two parameters; however, the estimated permeability was 1000 times higher than with the two-pore model, and the binding affinity was such that approximately five times more material was bound than free in the extravascular space for nonspecific antibody. Setting the binding affinity to zero or reducing the value of the permeability-surface area product did not allow a good fit, even when the lymph flow rate was varied. The present model may be useful in scaling up antibody pharmacokinetics from mouse to man.

Effect of angiotensin II induced hypertension on tumor blood flow and interstitial fluid pressure.

The effect of angiotensin II-induced hypertension on tumor interstitial fluid pressure (TIFP) and tumor blood flow (TBF) was investigated to examine blood flow and pressure regulation in solid tumors. TIFP measurements were made before and after administration of angiotensin II using the wick-in-needle method in s.c. tumor implants. Relative TBF was continuously monitored by laser doppler velocimetry. The effect of host strain on TIFP was evaluated in MCA-IV mammary carcinoma, transplanted in C3H and SCID mice, and showed no significant difference. The effects of tumor types were evaluated by comparing two murine tumors, MCA-IV mammary carcinoma and FSaII fibrosarcoma, and a human tumor xenograft, LS174T adenocarcinoma, transplanted in SCID mice. Baseline TIFP was elevated in all three tumor lines to significantly different pressures. AII-induced hypertension (approximately 150 mm Hg) had a variable but tumor line-specific effect on TIFP and TBF. The increase in TIFP was correlated with the baseline TIFP (r2 = 0.853) (increasing from 6.9 to 8.7 mm Hg, 10.5 to 15.8 mm Hg, and 21.7 to 29.4 mm Hg in FSaII, MCA-IV, and LS174T, respectively). These data suggest that in addition to blood flow redistribution due to the steal phenomenon, arterial control of TBF and TIFP exists within these solid tumors; however, the extent of control is tumor line dependent and less than that in normal tissues. Moreover, parallel increases in TIFP and TBF do not support the hypothesis that elevated TIFP causes vascular collapse and thus decreases TBF.

Pharmacokinetic analysis of the perivascular distribution of bifunctional antibodies and haptens: comparison with experimental data.

A mathematical model is developed to describe the concentration profiles around individual tumor blood vessels for two-step approaches to cancer treatment. The model incorporates plasma pharmacokinetics, interstitial diffusion, reversible binding between antibody and hapten and between antibody and tumor-associated antigens, and physiological parameters to evaluate present experimental approaches and to suggest new guidelines for the effective use of two-step approaches. Results show considerable interaction between the binding kinetics, initial drug doses, and antigen density, with optimal parameter ranges depending on the desired goal: treatment or detection. The hapten concentration in tumors was found to be nonuniform because of specific binding to antibodies. While binding of the hapten to the bifunctional antibody is necessary for improved retention, too large a binding affinity may lead to very poor penetration of the hapten into regions far away from blood vessels. The time delay between antibody and hapten injection was found to be an important parameter. Longer time delays were found to be advantageous, subject to constraints such as internalization of the antibody and tumor growth during treatment. A proper combination of initial doses for the two species was also seen to be crucial for maximum effectiveness. Comparison of the model with the experimental data of Le Doussal et al. (Cancer Res., 51: 6650-6655, 1991) and Stickney et al. (Cancer Res., 50: 3445-3452, 1990) suggests two novel, yet testable, hypotheses: (a) the early pharmacokinetics of low molecular weight agents can have an important effect on later concentrations using two-step approaches; and (b) metabolism may play an important role in reducing concentrations in the tumor and tumor:plasma concentration ratios. These results should help in the effective design of two-step strategies.

Pharmacokinetic analysis of two-step approaches using bifunctional and enzyme-conjugated antibodies.

Bifunctional antibodies (BFA) and enzyme-conjugated antibodies (ECA) can be used to preferentially deliver a hapten or drug to tumor sites for diagnosis and therapy. We present here a simple pharmacokinetic model for the above two systems by considering only two compartments, the plasma and tumor. The models predict that the longer the time delay between the BFA and hapten or between the ECA and prodrug injections, the higher the tumor:plasma concentration ratio of the hapten or drug. In addition, multiple injections of the hapten or prodrug is predicted to give a more uniform concentration of the hapten or drug in both the tumor and plasma than bolus injection. We suggest that, initially, the most effective dose of BFA should be selected and then the hapten concentration chosen accordingly. The decrease of the ECA injection dose would increase the tumor:plasma concentration ratio of the drug and yet decrease the tumor concentration of the drug. In clinical application of the ECA system, consideration of ECA dose should be balanced between the tumor concentration and the tumor:plasma concentration ratio of the drug. The dose of the prodrug injection is suggested to be equal to the required toxic concentration of the drug in the tumor. There are several ways to improve the tumor:plasma concentration ratio of the hapten or drug, such as changing the binding kinetics of the antibody to tumor or the hapten to BFA and removing the antibody from the plasma before the injection of the hapten or prodrug. One notable difference between the BFA and ECA approaches is that there is an upper limit for maximum hapten concentration in the former, and hence, from the point of drug delivery alone the latter approach is presumably superior. The limitations of the models and therapeutic implications are also discussed.

Transport of fluid and macromolecules in tumors. IV. A microscopic model of the perivascular distribution.

The therapeutic efficacy of various genetically engineered macromolecules is determined by their delivery and distribution in tumors. We have recently developed mathematical models which describe the interstitial velocity, pressure, and concentration profiles of macromolecules over the length scale of a solid tumor (Baxter and Jain, Microvas. Res. 1989, 1990, 1991). Nonspecific and specific antibodies and antibody fragments were chosen as typical macromolecules. The focus of the present investigation was microscopic transport, i.e., the distribution of pressure and solutes around individual blood vessels. Analytical solutions were obtained for interstitial velocities and pressures, while the concentration profiles were calculated numerically using the finite element method. The microscopic model describes flow patterns around an individual blood vessel in an infinite medium and concentration profiles around a single blood vessel in a network of capillaries. Our analysis is novel in that it incorporates interstitial convection, asymmetric filtration, and transcapillary convection to describe interstitial transport in tumors. The purpose of this model was to determine the effect of extravascular binding and interstitial convection on the distribution of macromolecules on a microscopic scale and to test the continuum hypothesis assumed in our previously published macroscopic models. An approximate one-dimensional model was compared with a more accurate two-dimensional model. The results of our microscopic model confirm that the continuum hypothesis used in our previous macroscopic model is reasonable. On a microscopic length scale diffusion is dominant, and short range distortions in the flow field do not significantly affect the penetration of macromolecules into the tissue. In addition, our model confirms the results of Fujimori et al. (Cancer Res., 1989) concerning a "binding site barrier." The implications of our results for cancer therapy are also discussed.

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.

Transport of fluid and macromolecules in tumors. II. Role of heterogeneous perfusion and lymphatics.

We have recently developed a general theoretical framework for transvascular exchange and extravascular transport of fluid and macromolecules in tumors. The model was applied to a homogeneous, alymphatic tumor with no extravascular binding. For this simplified system, 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. Our recent experiments have verified these predicted profiles. The purpose of this investigation was to apply this theoretical framework to the more realistic case of a nonuniformly perfused tumor. The role of lymphatics for macromolecular transport was also studied using the model. The uptake and distribution of IgG and its fragment, Fab, were simulated. The novel result from this work is that necrosis does not reduce the central interstitial pressure in a tumor. Other results showed that (i) macromolecules do not penetrate a necrotic core at early times after injection; (ii) at longer time periods after a bolus injection (days for Fab, months for IgG in a tumor of radius approximately 1cm) a "reservoir" of material may be formed in the necrotic core; (iii) continuous infusion or repeated injections should maintain a higher interstitial concentration of macromolecules; and (iv) lymphatics, if present in a tumor, would rapidly remove material and result in much lower concentration levels. The model is also used to explain some previous experimental data in the literature on antibody distribution.

Interstitial pressure gradients in tissue-isolated and subcutaneous tumors: implications for therapy.

High interstitial fluid pressure (IFP) in solid tumors is associated with reduced blood flow as well as inadequate delivery of therapeutic agents such as monoclonal antibodies. In the present study, IFP was measured as a function of radial position within two rat tissue-isolated tumors (mammary adenocarcinoma R3230AC, 0.4-1.9 g, n = 9, and Walker 256 carcinoma, 0.5-5.0 g, n = 6) and a s.c. tumor (mammary adenocarcinoma R3230AC, 0.6-20.0 g, n = 7). Micropipettes (tip diameters 2 to 4 microns) connected to a servo-null pressure-monitoring system were introduced to depths of 2.5 to 3.5 mm from the tumor surface and IFP was measured while the micropipettes were retrieved to the surface. The majority (86%) of the pressure profiles demonstrated a large gradient in the periphery leading to a plateau of almost uniform pressure in the deeper layers of the tumors. Within isolated tumors, pressures reached plateau values at a distance of 0.2 to 1.1 mm from the surface. In s.c. tumors the sharp increase began in skin and levelled off at the skin-tumor interface. These results demonstrate for the first time that the IFP is elevated throughout the tumor and drops precipitously to normal values in the tumor's periphery or in the immediately surrounding tissue. These results confirm the predictions of our recently published mathematical model of interstitial fluid transport in tumors (Jain and Baxter, Cancer Res., 48: 7022-7032, 1988), offer novel insight into the etiology of interstitial hypertension, and suggest possible strategies for improved delivery of therapeutic agents.

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.