Effect of tumor shape,size, and tissue transport properties on drug delivery to solid tumors

Background

The computational methods provide condition for investigation related to the process of drug delivery, such as convection and diffusion of drug in extracellular matrices, drug extravasation from microvessels or to lymphatic vessels. The information of this process clarifies the mechanisms of drug delivery from the injection site to absorption by a solid tumor. In this study, an advanced numerical method is used to solve fluid flow and solute transport equations simultaneously to investigate the effect of tumor shape and size on drug delivery to solid tumor.

Methods

The advanced mathematical model used in our previous work is further developed by adding solute transport equation to the governing equations. After applying appropriate boundary and initial conditions on tumor and surrounding tissue geometry, the element-based finite volume method is used for solving governing equations of drug delivery in solid tumor. Also, the effects of size and shape of tumor and some of tissue transport parameters such as effective pressure and hydraulic conductivity on interstitial fluid flow and drug delivery are investigated.

Results

Sensitivity analysis shows that drug delivery in prolate shape is significantly better than other tumor shapes. Considering size effect, increasing tumor size decreases drug concentration in interstitial fluid. This study shows that dependency of drug concentration in interstitial fluid to osmotic and intravascular pressure is negligible.

Conclusions

This study shows that among diffusion and convection mechanisms of drug transport, diffusion is dominant in most different tumor shapes and sizes. In tumors in which the convection has considerable effect, the drug concentration is larger than that of other tumors at the same time post injection.

     

Effect of tumor shape and size on drug delivery to solid tumors

ABSTRACT: Tumor shape and size effect on drug delivery to solid tumors are studied, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for predefined tumor geometries. The governing equations are solved using a numerical method, the element-based finite volume method. Interstitial fluid pressure and velocity are used to show the details of drug delivery in a solid tumor, under an assumption that drug particles flow with the interstitial fluid. Drug delivery problems have been most extensively researched in spherical tumors, which have been the simplest to examine with the analytical methods. With our numerical method, however, more complex shapes of the tumor can be studied. The numerical model of fluid flow in solid tumors previously introduced by our group is further developed to incorporate and investigate non-spherical tumors such as prolate and oblate ones. Also the effects of the surface area per unit volume of the tissue, vascular and interstitial hydraulic conductivity on drug delivery are investigated.     

A Simple,Quantitative Method Using Alginate Gel to Determine Rat Colonic Tumor Volume In Vivo

Many studies of the response of colonic tumors to therapeutics use tumor multiplicity as the endpoint to determine the effectiveness of the agent. These studies can be greatly enhanced by accurate measurements of tumor volume. Here we present a quantitative method to easily and accurately determine colonic tumor volume. This approach uses a biocompatible alginate to create a negative mold of a tumor-bearing colon; this mold is then used to make positive casts of dental stone that replicate the shape of each original tumor. The weight of the dental stone cast correlates highly with the weight of the dissected tumors. After refinement of the technique, overall error in tumor volume was 16.9% ± 7.9% and includes error from both the alginate and dental stone procedures. Because this technique is limited to molding of tumors in the colon, we utilized the Apc^Pirc/+ rat, which has a propensity for developing colonic tumors that reflect the location of the majority of human intestinal tumors. We have successfully used the described method to determine tumor volumes ranging from 4 to 196 mm³. Alginate molding combined with dental stone casting is a facile method for determining tumor volume in vivo without costly equipment or knowledge of analytic software. This broadly accessible method creates the opportunity to objectively study colonic tumors over time in living animals in conjunction with other experiments and without transferring animals from the facility where they are maintained.Colon cancer is the third leading cause of cancer in men and women, with more than 100,000 new cases diagnosed each year in the United States alone. This disease is not limited to humans—cancers of the colon and rectum also affect companion species, such as dogs, albeit less frequently than in humans.²⁰ Colorectal cancers generally develop from precancerous polyps, which can be detected and removed during colonoscopy screening before they become invasive cancers. However, not all precancers will become cancerous,²³ and a better understanding of early tumor growth dynamics in models of the disease can simultaneously increase the rate of detection of polyps destined to become cancerous and decrease the rate of unnecessary removal of benign polyps.Sizing of tumors creates an additional dimension beyond studies examining tumor multiplicity alone. Terminal sizing of tumors uses an eyepiece reticule under a dissection microscope to measure the maximal diameter of each tumor. However, this method likely misrepresents tumor volume for several reasons. First, tumors often are not symmetrical in shape, thereby limiting the interpretation of even multiple linear measurements. When volume calculations rely on the use of a formula, the irregular shape of solid tumors may require the testing of many different formulas to find the optimal one for that particular measurement and model.⁸ Second, if tumor sizing occurs after fixation, the original shape of the tumor can be affected. However, when tumor sizing occurs before fixation, the added time to size the tumors may result in degradation of the intestinal tissue, limiting further analysis. An alternate method of tumor sizing involves using the surrogate of tumor weight, the current ‘gold standard,’ for terminal studies. Tumor weight correlates closely with tumor size, although tumor density may vary depending on the tumor type. In addition, this technique is limited to use at the terminal time point. Methods that determine true tumor volume are powerful; those that can be applied in vivo to study the tumor longitudinally are even more compelling.It recently has been recognized that not all early colonic tumors grow; some remain static for years whereas a few spontaneously regress.²³ Importantly, the early growth profile of a tumor may correlate with its eventual fate.²³ This aspect of tumor biology is a newly emerging area that deserves deeper study. The current gold standard for determining longitudinal tumor volume is CT, given that tumor weight is available only through terminal experiments. In mice, microCT colonography can be used to detect a 16% change in tumor volume with 95% confidence in living animals.⁵ However, the cost of CT equipment limits this technology to shared facilities, and the pathogen status of these facilities may preclude returning animals to the place where they were original housed, limiting the opportunities for longitudinal study. Importantly, many institutions do not have access to microCT technology, and even if available, 3D renderings must be recreated to determine tumor volume, a process requiring specialized software and detailed computing knowledge. Furthermore, CT exposes animal subjects to radiation, which may interfere with the tumor biology. Although MRI can be used to determine tumor volume accurately in the absence of ionizing radiation, specialized scanners and software are required, and enemas or intravenous treatments are needed to visualize tumors clearly.²⁶Another imaging modality uses the surface area of signal due to proteins expressing a fluorescent marker, such as red fluorescent protein, as a surrogate for tumor volume.¹⁷ However, tumor volume measured by fluorescent surface area¹² may not accurately represent tumor volume in irregularly shaped tumors. In addition, this method necessitates a surgical procedure to orthotopically transplant fluorophore-expressing cells, raising questions of immune interactions between the recipient animal and the donor cells or to the surgery itself. If nude or immunocompromised animals are used in the procedure, the ability to study the immune aspect of tumor biology is reduced or eliminated.Alternatively, tumor volume can be estimated from endoscopic images. The study of tumors by colonoscopy has become routine for both mouse^6,10 and rat^1,15 models of the disease. In contrast to terminal assessments, colonoscopy allows tumors to be visualized in vivo over time, capturing the dynamics of tumor growth. Documentation of this aspect of tumor biology can greatly enrich studies evaluating chemopreventive or therapeutic agents.^6,15 Quantitative methods for determining tumor volume take this benefit a step further, allowing the investigation of the effects of background strain, therapeutic agents, environmental factors, or other modifiers of tumor growth pattern. One method to estimate tumor size uses the fraction of luminal cross-section occluded by tumor.² However, the colonic lumen expands as the animal grows, and its size often increases to accommodate the growing tumor, to prevent intestinal blockage. Optical methods to extrapolate tumor sizes from 2D images obtained in vivo during colonoscopy are achieved by inserting a flexible metal rod of known dimensions into the working channel of the endoscope.¹⁰ However, because colonic tumors can differ in shape (some are flat whereas others are pedunculated), area measurements may not translate accurately to tumor volume.To overcome these limitations and to add another tool to the growing cancer-research toolbox, we have developed a method using a biologically inert alginate to create negative molds of colonic tumors. These molds are filled with dental stone to achieve a positive cast of each tumor. A conversion factor then is used to calculate the volume of the original tumor from the dry weight of the dental stone cast. This procedure, which requires no specialized or expensive equipment and no complicated analytical methods, can be performed within the facility where the rats are housed and takes less than 15 min, including the 8 to 12 min during which the alginate sets. Therefore, our new method offers possibilities to study the dynamics of tumor growth in virtually any animal facility, regardless of the health status of subject animals or equipment availability.     

Role of TAP-1 and/or TAP-2 antigen presentation defects in tumorigenicity of mouse melanoma

Mutations in transporters associated with antigen processing (TAP-1 and -2) required for the transport of cytosolic endogenous peptides to the endoplasmic reticulum correlate with increased metastatic potential and reduced host survival in several malignancies. To address the possible function of TAP as a "tumor suppressor" gene, we show that correction of TAP-1 and/or TAP-2 defects in B16 mouse melanoma enhanced the cell surface expression of MHC class I molecules and significantly reduced the rate of subcutaneous tumor growth and pulmonary metastatic burden. Cytotoxic assays confirmed increased sensitivity of TAP-1 and/or TAP-2 transfected clones of B16 melanoma to cytotoxic T lymphocytes. These results indicate that the expression of TAP limits the malignant potential of tumors with implications for CD8(+) T cell-based immunotherapy in controlling growth of certain TAP-deficient malignancies.     

Relative Expression of mRNAS Coding for Glutaminase Isoforms in CNS Tissues and CNS Tumors

Glutaminase (GA) in mammalian tissues occurs in three isoforms: LGA (liver-type), KGA (kidney-type) and GAC (a KGA variant). Our previous study showed that human malignant gliomas (WHO grades III and IV) lack expression of LGA mRNA but are enriched in GAC mRNA relative to KGA mRNA. Here we analyzed the expression of mRNAs coding for the three isoforms in the biopsy material derived from other central nervous system tumors of WHO grades I–III. Non-neoplastic resective epileptic surgery samples served as control, as did cultured rat astrocytes and neurons. The GAC mRNA/KGA mRNA expression ratio was as a rule higher in the neoplastic than in control tissues, irrespective of the cell type dominating in the tumor or tumor malignancy. LGA mRNA expression was relatively very low in cultured astrocytes, and very low to absent in astrocytoma pilocyticum, ependymoma and subependymal giant cell astrocytoma (SEGA), tumors of astrocytic origin. LGA mRNA expression was almost as high as that of KGA and GAC mRNA in cultured neurons and epileptic surgery samples which were enriched in neurons. LGA mRNA was also relatively high in ganglioglioma which contains a discernable proportion of neuronal cells, and in oligodendroglioma. The results show that low expression of LGA mRNA is a feature common to normal astrocytes and astroglia-derived tumor cells or ependymomas and can be considered as a cell-type, rather than a malignancy marker.     

Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach

A hybrid differential-discrete mathematical model has been used to simulate biofilm structures (surface shape, roughness, porosity) as a result of microbial growth in different environmental conditions. In this study, quantitative two- and three-dimensional models were evaluated by introducing statistical measures to characterize the complete biofilm structure, both the surface structure and volume structure. The surface enlargement, coefficient of roughness, fractal dimension of surface, biofilm compactness, and solids hold-up were found to be good measures of biofilm structure complexity. Among many possible factors affecting the biofilm structure, the influence of biomass growth in relation to the diffusive substrate transport was investigated. Porous biofilms, with many channels and voids between the "finger-like" or "mushroom" outgrowth, were obtained in a substrate-transport-limited regime. Conversely, compact and dense biofilms occurred in systems limited by the biomass growth rate and not by the substrate transfer rate. The surface complexity measures (enlargement, roughness, fractal dimension) all increased with increased transport limitation, whereas the volume measures (compactness, solid hold-up) decreased, showing the change from a compact and dense to a highly porous and open biofilm.     

Skin hyperkeratosis and papilloma formation in transgenic mice expressing a ras oncogene from a suprabasal keratin promoter.

The promoter region of the suprabasal keratin 10 gene has been used to direct expression of a mutant human Harvey-ras oncogene to the differentiating cells of the mouse epidermis. Transgenic animals develop hyperkeratosis of the skin and forestomach--the two sites known to express high levels of the keratin 10 polypeptide in vivo. Papillomas subsequently develop on the skin surface, initially at sites subject to biting or scratching such as the base of the tail or behind the ears. The results suggest that the "second event" involved in tumor development in these transgenic animals is the local induction of a mild wounding stimulus. Furthermore, because the H-ras transgene is expressed in suprabasal cells, it appears that cells which have left the stem cell compartment can be induced to form at least benign tumors in vivo.     

Computer simulation of the hydrostatic skeleton. The physical equivalent, mathematics and application to worm-like forms

The functional principles of a hydrostatic skeleton were combined to obtain a physical model which includes geometry, number and length-tension relationships of the elastic elements in the body wall, internal volume and internal pressure. The model skeleton with pre-set internal volume assumes a certain shape and develops a specific internal pressure in order to minimize the potential energy stored in the elastic elements. This shape is calculated as equilibrium state by using finite element methods and optimization techniques. This model is flexible enough to accommodate different geometries and length-tension-relationships of the elastic elements. Presently, the model is implemented with linear length-tension relationships and certain geometrical restrictions, such as uniform width over the entire animal, and rectangular cross sections; the general case is outlined. First simulations with the "unit-worm" yield stable solutions, i.e. stable shapes for all combinations of parameters tested so far. They define the conditions for bringing all muscles to an optimal operating point. We detected a pressure maximum with increasing volume, assessed the contribution of circular muscles to bending, and determined the shapes of animals with different muscle activations in each body half (Chapman-matrix). We summarize our results by the volume rule and stabilization rule, two simple concepts which predict changes in shape as the result of muscle activation.     

Green fluorescent protein (GFP)-expressing tumor model derived from a spontaneous osteosarcoma in a vascular endothelial growth factor (VEGF)-GFP transgenic mouse

Vascular endothelial growth factor (VEGF) mediates tumor angiogenesis, growth, and metastasis. Murine models of metastatic tumors in which green fluorescent protein (GFP) expression is driven by the VEGF promoter can be imaged both intravitally and externally and thus offer many possibilities for real-time studies of tumor angiogenesis, metastasis, and treatment in vivo. In our defined-flora animal facility, an 11-month-old female transgenic mouse with a C3H background (VEGF(P)-GFP/C3H) developed a spontaneous tumor that expressed GFP under the control of VEGF. Necropsy and histopathologic examination revealed an osteosarcoma with lung metastases. Fresh tumor fragments were transplanted successfully into other VEGF(P)-GFP/C3H transgenic mice. During the first five generations, the tumor "take rate" was 100% (25 of 25 animals), with a latent period of 8 days and an average tumor volume of 1500 mm3 at 36 days. Transplanted tumors have maintained their original histopathologic characteristics and metastatic behavior. In addition, the tumor grows in wild-type C3H mice with an 83% take rate (10 of 12 animals) and as monolayer cells in vitro. GFP was expressed strongly in tumor tissue, lung metastatic foci, and cultured tumor cells. Real-time growth of tumors grown in dorsal skin chambers in C3H mice could be visualized using GFP fluorescence. In addition, GFP fluorescence of metastatic lesions in lungs of C3H mice was clearly visible by multiphoton laser scanning microscopy. This in vitro and in vivo transplantable and metastatic osteosarcoma (Os-P0107) is an attractive model for further study of tumor pathophysiology and treatment efficiency affecting VEGF expression.     

RANTES-mediated control of excitatory amino acid release in mouse spinal cord

O⁶‐methylguanine‐DNA methyltransferase (MGMT) is a DNA‐repair protein promoting resistance of tumor cells to alkylating chemotherapeutic agents. Glioma cells are particularly resistant to this class of drugs which include temozolomide (TMZ) and carmustine (BCNU). A previous study using the RNA microarray technique showed that decrease of MGMT mRNA stands out among the alterations in gene expression caused by the cell growth‐depressing transfection of a T98G glioma cell line with liver‐type glutaminase (LGA) [Szeliga et al. (2009) Glia, 57, 1014]. Here, we show that stably LGA‐transfected cells (TLGA) exhibit decreased MGMT protein expression and activity as compared with non‐transfected or mock transfected cells (controls). However, the decrease of expression occurs in the absence of changes in the methylation of the promoter region, indicating that LGA circumvents, by an as yet unknown route, the most common mechanism of MGMT silencing. TLGA turned out to be significantly more sensitive to treatment with 100–1000 μM of TMZ and BCNU in the acute cell growth inhibition assay (MTT). In the clonogenic survival assay, TLGA cells displayed increased sensitivity even to 10 μM TMZ and BCNU. Our results indicate that enrichment with LGA, in addition to inhibiting glioma growth, may facilitate chemotherapeutic intervention.     

Computational Modeling of 3D Tumor Growth and Angiogenesis for Chemotherapy Evaluation

Solid tumors develop abnormally at spatial and temporal scales, giving rise to biophysical barriers that impact anti-tumor chemotherapy. This may increase the expenditure and time for conventional drug pharmacokinetic and pharmacodynamic studies. In order to facilitate drug discovery, we propose a mathematical model that couples three-dimensional tumor growth and angiogenesis to simulate tumor progression for chemotherapy evaluation. This application-oriented model incorporates complex dynamical processes including cell- and vascular-mediated interstitial pressure, mass transport, angiogenesis, cell proliferation, and vessel maturation to model tumor progression through multiple stages including tumor initiation, avascular growth, and transition from avascular to vascular growth. Compared to pure mechanistic models, the proposed empirical methods are not only easy to conduct but can provide realistic predictions and calculations. A series of computational simulations were conducted to demonstrate the advantages of the proposed comprehensive model. The computational simulation results suggest that solid tumor geometry is related to the interstitial pressure, such that tumors with high interstitial pressure are more likely to develop dendritic structures than those with low interstitial pressure.     

Simulating PDGF-Driven Glioma Growth and Invasion in an Anatomically Accurate Brain Domain

Gliomas are the most common of all primary brain tumors. They are characterized by their diffuse infiltration of the brain tissue and are uniformly fatal, with glioblastoma being the most aggressive form of the disease. In recent years, the over-expression of platelet-derived growth factor (PDGF) has been shown to produce tumors in experimental rodent models that closely resemble this human disease, specifically the proneural subtype of glioblastoma. We have previously modeled this system, focusing on the key attribute of these experimental tumors—the “recruitment” of oligodendroglial progenitor cells (OPCs) to participate in tumor formation by PDGF-expressing retrovirally transduced cells—in one dimension, with spherical symmetry. However, it has been observed that these recruitable progenitor cells are not uniformly distributed throughout the brain and that tumor cells migrate at different rates depending on the material properties in different regions of the brain. Here we model the differential diffusion of PDGF-expressing and recruited cell populations via a system of partial differential equations with spatially variable diffusion coefficients and solve the equations in two spatial dimensions on a mouse brain atlas using a flux-differencing numerical approach. Simulations of our in silico model demonstrate qualitative agreement with the observed tumor distribution in the experimental animal system. Additionally, we show that while there are higher concentrations of OPCs in white matter, the level of recruitment of these plays little role in the appearance of “white matter disease,” where the tumor shows a preponderance for white matter. Instead, simulations show that this is largely driven by the ratio of the diffusion rate in white matter as compared to gray. However, this ratio has less effect on the speed of tumor growth than does the degree of OPC recruitment in the tumor. It was observed that tumor simulations with greater degrees of recruitment grow faster and develop more nodular tumors than if there is no recruitment at all, similar to our prior results from implementing our model in one dimension. Combined, these results show that recruitment remains an important consideration in understanding and slowing glioma growth.     

Proteomic screening of anaerobically regulated promoters from Salmonella and its antitumor applications

Solid tumors often contain hypoxic and necrotic areas that can be targeted by attenuated Salmonella typhimurium VNP20009 (VNP). We sought to develop a hypoxia- inducible promoter system based on the tumor-specific delivered strain VNP to confine expression of therapeutic gene specifically or selectively within the tumor microenvironment. A hypoxia-inducible promoter - adhE promoter was screened from the hypoxia-regulated endogenous proteins of Salmonella through two-dimensional gel electrophoresis and matrix-assisted laser desorption ionization-time-of-flight/time-of-flight MS-based proteomics approaches. The efficiency and specificity of the selected adhE promoter were validated first in both bacteria and animal tumor models. The adhE promoter could specifically drive GFP gene expression under hypoxia, but not under normoxia. Furthermore, luciferase reporter expression controlled by the system was also confined to the tumors. Finally, we investigated the anticancer efficacy of VNP delivering human endostatin controlled by our adhE promoter system in both murine melanoma and Lewis lung carcinoma models. Our results demonstrated that by the dual effects of tumoricidal and anti-angiogenic activities, the recombinant Salmonella strain could generate enhanced antitumor effects compared with those of unarmed VNP treatment or untreated control. The recombinant VNP could retard tumor growth significantly and extend survival of tumor-bearing mice by inducing more apoptosis and more severe necrosis as well as inhibiting blood vessel density within tumors. Therefore, VNP carrying the endostatin gene under our tumor-targeted expression system holds promise for the treatment of solid tumors.     

Evaluation of surface colonization kinetics in continuous culture

Two equations, describing surface colonization, were evaluated and compared using suspended glass slides in a continuous culture ofPseudomonas aeruginosa. These equations were used to determine surface growth rates from the number and distribution of cells present on the surface after incubation. One of these was the colonization equation which accounts for simultaneous attachment and growth of bacteria on surfaces: $$N = (A/\mu )e^{\mu t} - A/\mu $$ where N=number of cells on surface (cells field^?1); A=attachment rate (cells field^?1h^?1);μ=specific growth rate (h^?1); t=incubation period (h). The other was the surface growth rate equation which assumes that the number of colonies of a given size (C_i) will reach a constant value (C_max) which is equal to A divided byμ: $$\mu = \frac{{\ln \left( {\frac{N}{{C_i }} + 1} \right)}}{t}$$ Both equations gave similar results and the time required to approximate C_max may not be as long as was previously thought. In all cases both A andμ continuously decreased throughout the incubation period. These decreases may be due to various effects of microbial accumulation on the surface. Both equations accurately determined surface growth rates despite highly variable attachment rates. Growth rates were similar for both the liquid phase of the culture and the solid-liquid interface (0.4 h^?1). Use of the surface growth rate equation is favored over the use of the colonization equation since the former does not require a computer to solve forμ and the counting procedure is simplified.     

Elastic Free Energy Drives the Shape of Prevascular Solid Tumors

It is well established that the mechanical environment influences cell functions in health and disease. Here, we address how the mechanical environment influences tumor growth, in particular, the shape of solid tumors. In an in vitro tumor model, which isolates mechanical interactions between cancer tumor cells and a hydrogel, we find that tumors grow as ellipsoids, resembling the same, oft-reported observation of in vivo tumors. Specifically, an oblate ellipsoidal tumor shape robustly occurs when the tumors grow in hydrogels that are stiffer than the tumors, but when they grow in more compliant hydrogels they remain closer to spherical in shape. Using large scale, nonlinear elasticity computations we show that the oblate ellipsoidal shape minimizes the elastic free energy of the tumor-hydrogel system. Having eliminated a number of other candidate explanations, we hypothesize that minimization of the elastic free energy is the reason for predominance of the experimentally observed ellipsoidal shape. This result may hold significance for explaining the shape progression of early solid tumors in vivo and is an important step in understanding the processes underlying solid tumor growth.     

A growth-controlled model of the shape of a sunflower head

A mathematical model is presented which predicts the shape of a sunflower receptacle (or the compact receptacle of various other taxa) and the pattern of its floral parts (florets) from the time of their initiation to maturity. The model assumes that the expansion and curving of the receptacle surface is just sufficient to accommodate the development of the florets, thus minimizing the quantity of plant tissue involved. The model assumes a fixed angular separation (divergence) between successive florets, an S-shaped (sigmoidal) growth function followed by each florets, and a fixed time delay (period) between the initiation of successive florets. It is further assumes that the shape and relative position occupied by the florets on the receptacle surface are invariant in time. By this theory, the shape of the receptacle surface is fully determined once the mathematical form of the growth function is specified. Using the logistic growth function, the theory is tested against the measured shapes of plant receptacles from different taxa at various points in their development. The least-squares adjusted fits to the theory are, in most cases, very good indeed.     

Numerical modeling of fluid flow in solid tumors

A mathematical model of interstitial fluid flow is developed, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for a predefined tumor geometry. The interstitial fluid pressure and velocity are calculated using a numerical method, element based finite volume. Simulations of interstitial fluid transport in a homogeneous solid tumor demonstrate that, in a uniformly perfused tumor, i.e., one with no necrotic region, because of the interstitial pressure distribution, the distribution of drug particles is non-uniform. Pressure distribution for different values of necrotic radii is examined and two new parameters, the critical tumor radius and critical necrotic radius, are defined. Simulation results show that: 1) tumor radii have a critical size. Below this size, the maximum interstitial fluid pressure is less than what is generally considered to be effective pressure (a parameter determined by vascular pressure, plasma osmotic pressure, and interstitial osmotic pressure). Above this size, the maximum interstitial fluid pressure is equal to effective pressure. As a consequence, drugs transport to the center of smaller tumors is much easier than transport to the center of a tumor whose radius is greater than the critical tumor radius; 2) there is a critical necrotic radius, below which the interstitial fluid pressure at the tumor center is at its maximum value. If the tumor radius is greater than the critical tumor radius, this maximum pressure is equal to effective pressure. Above this critical necrotic radius, the interstitial fluid pressure at the tumor center is below effective pressure. In specific ranges of these critical sizes, drug amount and therefore therapeutic effects are higher because the opposing force, interstitial fluid pressure, is low in these ranges.     

Anti‐tumor effect of SLPI on mammary but not colon tumor growth

Secretory leukocyte protease inhibitor (SLPI) is a serine protease inhibitor that was related to cancer development and metastasis dissemination on several types of tumors. However, it is not known the effect of SLPI on mammary and colon tumors. The aim of this study was to examine the effect of SLPI on mammary and colon tumor growth. The effect of SLPI was tested on in vitro cell apoptosis and in vivo tumor growth experiments. SLPI over‐expressing human and murine mammary and colon tumor cells were generated by gene transfection. The administration of murine mammary tumor cells over‐expressing high levels of SLPI did not develop tumors in mice. On the contrary, the administration of murine colon tumor cells over‐expressing SLPI, developed faster tumors than control cells. Intratumoral, but not intraperitoneal administration of SLPI, delayed the growth of tumors and increased the survival of mammary but not colon tumor bearing mice. In vitro culture of mammary tumor cell lines treated with SLPI, and SLPI producer clones were more prone to apoptosis than control cells, mainly under serum deprivation culture conditions. Herein we demonstrated that SLPI induces the apoptosis of mammary tumor cells in vitro and decreases the mammary but not colon tumor growth in vivo. Therefore, SLPI may be a new potential therapeutic tool for certain tumors, such as mammary tumors. J. Cell. Physiol. 228: 469–475, 2013. © 2012 Wiley Periodicals, Inc.