A mixture theory model of fluid and solute transport in the microvasculature of normal and malignant tissues. II: Factor sensitivity analysis, calibration, and validation

The treatment of cancerous tumors is dependent upon the delivery of therapeutics through the blood by means of the microcirculation. Differences in the vasculature of normal and malignant tissues have been recognized, but it is not fully understood how these differences affect transport and the applicability of existing mathematical models has been questioned at the microscale due to the complex rheology of blood and fluid exchange with the tissue. In addition to determining an appropriate set of governing equations it is necessary to specify appropriate model parameters based on physiological data. To this end, a two stage sensitivity analysis is described which makes it possible to determine the set of parameters most important to the model’s calibration. In the first stage, the fluid flow equations are examined and a sensitivity analysis is used to evaluate the importance of 11 different model parameters. Of these, only four substantially influence the intravascular axial flow providing a tractable set that could be calibrated using red blood cell velocity data from the literature. The second stage also utilizes a sensitivity analysis to evaluate the importance of 14 model parameters on extravascular flux. Of these, six exhibit high sensitivity and are integrated into the model calibration using a response surface methodology and experimental intra- and extravascular accumulation data from the literature (Dreher et al. in J Natl Cancer Inst 98(5):335–344, 2006). The model exhibits good agreement with the experimental results for both the mean extravascular concentration and the penetration depth as a function of time for inert dextran over a wide range of molecular weights.     

A mixture theory for charged-hydrated soft tissues containing multi-electrolytes: passive transport and swelling behaviors.

A new mixture theory was developed to model the mechano-electrochemical behaviors of charged-hydrated soft tissues containing multi-electrolytes. The mixture is composed of n + 2 constituents (1 charged solid phase, 1 noncharged solvent phase, and n ion species). Results from this theory show that three types of force are involved in the transport of ions and solvent through such materials: (1) a mechanochemical force (including hydraulic and osmotic pressures); (2) an electrochemical force; and (3) an electrical force. Our results also show that three types of material coefficients are required to characterize the transport rates of these ions and solvent: (1) a hydraulic permeability; (2) mechano-electrochemical coupling coefficients; and (3) an ionic conductance matrix. Specifically, we derived the fundamental governing relationships between these forces and material coefficients to describe such mechano-electrochemical transduction effects as streaming potential, streaming current, diffusion (membrane) potential, electro-osmosis, and anomalous (negative) osmosis. As an example, we showed that the well-known formula for the resting cell membrane potential (Hodgkin and Huxley, 1952a, b) could be derived using our new n + 2 mixture model (a generalized triphasic theory). In general, the n + 2 mixture theory is consistent with and subsumes all previous theories pertaining to specific aspects of charged-hydrated tissues. In addition, our results provided the stress, strain, and fluid velocity fields within a tissue of finite thickness during a one-dimensional steady diffusion process. Numerical results were provided for the exchange of Na+ and Ca++ through the tissue. These numerical results support our hypothesis that tissue fixed charge density (CF) plays a significant role in modulating kinetics of ions and solvent transport through charged-hydrated soft tissues.     

Expression of PDE11A in normal and malignant human tissues.

Cyclic nucleotide phosphodiesterase 11A (PDE11A) is the newest member in the PDE family. Although the tissue distribution of PDE11A mRNA has been shown, its protein expression pattern has not been well studied. The goal of this report is to investigate the distribution of PDE11A proteins in a wide range of normal and malignant human tissues. We utilized a polyclonal antibody that recognized all four PDE11A isoforms. Its specificity was demonstrated by Western blot analysis on a recombinant human PDE11A protein and native PDE11A proteins in various human tissues. Immunohistochemistry showed that PDE11A is widely expressed. Various degrees of immunoreactivity were observed in the epithelial cells, endothelial cells, and smooth muscle cells of all tissues examined. The highest expression was in the epithelial, endothelial, and smooth muscle cells of the prostate, Leydig, and spermatogenic cells of the testis, the tubule epithelial cells in the kidney, the epithelial and endothelial cells in the adrenal, the epithelial cells and macrophages in the colon, and the epidermis in the skin. Furthermore, PDE11A expression was also detected in several human carcinomas. Our results suggest that PDE11A might be involved in multiple physiological processes in various organs via its ability to modulate intracellular cAMP and cGMP levels.     

Corneal endothelium transports fluid in the absence of net solute transport

The corneal endothelium transports fluid from the corneal stroma to the aqueous humor, thus maintaining stromal transparency by keeping it relatively dehydrated. This fluid transport mechanism is thought to be driven by the transcellular transports of HCO₃⁻ and Cl⁻ in the same direction, from stroma to aqueous. In parallel to these anion movements, for electroneutrality, there are paracellular Na⁺ and transcellular K⁺ transports in the same direction. The resulting net flow of solute might generate local osmotic gradients that drive fluid transport. However, there are reports that some 50% residual fluid transport remains in nominally HCO₃⁻ free solutions. We have examined the driving force for this residual fluid transport. We confirm that in nominally HCO₃⁻ free solutions, 48% of control fluid transport remains. When in addition Cl⁻ channels are inhibited, 30% of control fluid movement still remains. Addition of a carbonic anhydrase inhibitor has no further effect. These manipulations combined inhibit the transcellular transport of all anions, without which there cannot be any net transport of solute and consequently no local osmotic gradients, yet there is residual fluid movement. Only the further addition of benzamil, an inhibitor of epithelial Na⁺ channels, abolishes fluid transport completely. Our data are inconsistent with transcellular local osmosis and instead support the paradigm of paracellular fluid transport driven by electro-osmotic coupling.     

Corneal endothelium transports fluid in the absence of net solute transport

The corneal endothelium transports fluid from the corneal stroma to the aqueous humor, thus maintaining stromal transparency by keeping it relatively dehydrated. This fluid transport mechanism is thought to be driven by the transcellular transports of HCO(3)(-) and Cl(-) in the same direction, from stroma to aqueous. In parallel to these anion movements, for electroneutrality, there are paracellular Na(+) and transcellular K(+) transports in the same direction. The resulting net flow of solute might generate local osmotic gradients that drive fluid transport. However, there are reports that some 50% residual fluid transport remains in nominally HCO(3)(-) free solutions. We have examined the driving force for this residual fluid transport. We confirm that in nominally HCO(3)(-) free solutions, 48% of control fluid transport remains. When in addition Cl(-) channels are inhibited, 30% of control fluid movement still remains. Addition of a carbonic anhydrase inhibitor has no further effect. These manipulations combined inhibit the transcellular transport of all anions, without which there cannot be any net transport of solute and consequently no local osmotic gradients, yet there is residual fluid movement. Only the further addition of benzamil, an inhibitor of epithelial Na(+) channels, abolishes fluid transport completely. Our data are inconsistent with transcellular local osmosis and instead support the paradigm of paracellular fluid transport driven by electro-osmotic coupling.     

Analysis of the microvasculature and tissue type ratios in normal vs. benign and malignant breast tissue

OBJECTIVE: To analyze the microvasculature and tissue type ratios in normal vs. benign and malignant breast tissue to establish a baseline for expected values against which future imaging studies can be benchmarked. STUDY DESIGN: Using computer-assisted techniques on immunostained breast tissue (normal [n = 28], fibrocystic [n = 37], fibroadenomas [n = 19], invasive carcinomas [n = 19]), values were obtained for microvessel density (MVD), mean vessel area (MVA), vessel orientation (shape) and epithelial:stromal ratio (E:S). Measurement reproducibility and the effects of fibroadenoma stromal hyalinization and fibrocystic disease severity were also tested. RESULTS: Value ranges for the 4 diagnostic groups were significantly different (P < .001). For invasive breast carcinomas, E:S and MVD were significantly higher (P < .001) but MVA was smaller as compared to that in fibroadenomas. Peripherally vs. centrally there was no significant difference in MVD, MVA or vessel shape in the neoplasms. Decreases in E:S and MVD correlated with fibroadenoma stromal hyalinization. Increases in E:S and MVA correlated with more severe fibrocystic disease. Correlation coefficients for measurement reproducibility were high across the diagnostic categories. CONCLUSION: This study established a specific, reproducible, computer-assisted technique and baseline of expected values for morphologic criteria in normal, benign and malignant breast tissue that may be used in the future to correlate new breast imaging responses with these underlying biologic properties.     

Haymaker gene expression in malignant and normal gynecologic tissues.

We previously reported that cell lines established from human carcinomas and leukemias/lymphomas expressed high levels of an intracellular membrane-bound protein, Haymaker, whereas cell lines derived from non-malignant connective tissue cells and lymphoid cells expressed low levels of this gene product. To determine whether these findings reflect neoplastic transformation or, alternatively, tissue specificity, we examined by immunohistochemical and molecular methods the expression of Haymaker in gynecologic organs with and without tumor. A highly specific, affinity-purified rabbit polyclonal antibody against a 25-mer Haymaker peptide was used for immunohistochemical staining and morphometric analysis of 85 tissue specimens. Immunohistochemical studies demonstrate, for the first time, that Haymaker protein is highly expressed in epithelial cells of the endometrium of the normal uterus and to a somewhat lesser extent in the mucosa of the normal vagina and cervix, but is poorly expressed or absent in cells of the connective tissue and smooth muscle strata of these organs (p < 0.005). Significant differences in Haymaker expression, as assessed by immunohistochemistry, between malignant and normal gynecologic tissues were not observed (p = 0.27). The expression of Haymaker protein does not appear, therefore, to be a marker of malignant transformation of the epithelium of gynecologic organs but rather distinguishes both normal and malignant epithelial cells from normal connective tissue and smooth muscle cells.     

A mathematical model of solute coupled water transport in toad intestine incorporating recirculation of the actively transported solute

A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2-4) in agreement with experiments. The virtual solute concentration of fluid emerging from lis is then significantly larger than the concentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emerging downstream lis is taken up by cells through the serosal membrane and pumped back into lis, i.e., the solute would have to be recirculated. With input variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Ussing, J. Membr. Biol. 168:241-251), computations predict that 60-80% of the pumped flux stems from serosal bath in agreement with the experimental estimate of the recirculation flux. Robust solutions are obtained with realistic concentrations and pressures of lis, and with the following features. Rate of fluid absorption is governed by the solute permeability of mucosal membrane. Maximum fluid flow is governed by density of pumps on lis-membranes. Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux of water through cells exceeds inward water flux between cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water, i.e., the model generates pseudo-solvent drag. The associated flux-ratio equation is derived.     

Superoxide dismutase in normal and malignant tissues in different species.

1. Superoxide dismutase (superoxide: superoxide oxido-reductase, E.C. 1.15.1.1) in different species was determined quantitatively and qualitatively. Although quantitative differences were minor, there were significant differences in the isoenzyme patterns among the species. 2. No quantitative differences were found in superoxide dismutase (SOD) activities in the brains of mice between 1 and 23 days of age. The mitochondrial isoenzyme increased with age, attaining maximal levels between 9 and 12 days. In the six, regions of adult rat brain studied, highest values of SOD were found in the hypothalamus and lowest in the cortex. 3. SOD levels generally were lower in several transplantable mouse and rat tumors than in normal tissues of these species. Mn-SOD was not detected in the tumors studied by the methods employed.     

Effect of oscillating fluid shear on solute transport in cortical bone

The consequences of an oscillatory fluid shear mechanism on nutrient transport in bone during physical activity and ultrasonic therapy are discussed. During movement, periodic stress on bone creates transient pressure gradients that circulate interstitial fluid through calcified bone. A transport model derived from oscillatory Taylor-Aris dispersion phenomena was used to predict a ratio of effective-to-molecular diffusivity, K/D, for solutes of varying sizes up to 50 nm in diameter, in pores filled with interstitial fluid and pericellular matrix. The magnitude of the estimated transport enhancement depended on the molecular size, pore dimension, applied frequency and the displacement of the fluid during pressurization. For oscillation frequencies and amplitudes corresponding to those experienced during normal human activity, transport enhancements of up to 100 fold are expected for molecules larger than 5 nm in diameter. Enhancements of up to one order of magnitude, due to ultrasound stimulations in the MHz frequency range, are also expected for 7-nm-sized solutes. No effects are anticipated for ions, whose molecular diffusion time is too fast relative to the oscillation frequency. This model is expected to be useful for understanding differences in bone growth as a function of type of movement or to develop new physical therapies.     

Biorheology and fluid flux in swelling tissues. I. Bicomponent theory for small deformations, including concentration effects

A theory for the rheological behavior and fluid flux in swelling tissues under small deformations is presented. Tissues are considered as bicomponent solid-fluid mixtures. Concentration effects are included. The driving forces (body, surface and interactive), are discussed and their constitutive relationships to the tissue's deformation are specified. Mass and momentum balance equations are developed for each component and for the tissue as a whole. The concept of swelling stress emerges from the theory as an anisotropic generalization of the commonly used swelling pressure. It is shown to be a measure of the total chemical potential combining both mechanical and concentration effects. The theory shows that concentration effects modify the tissue's bulk stiffness in a manner consistent with experimental observations.     

A mixture theory analysis for passive transport in osmotic loading of cells

The theory of mixtures is applied to the analysis of the passive response of cells to osmotic loading with neutrally charged solutes. The formulation, which is derived for multiple solute species, incorporates partition coefficients for the solutes in the cytoplasm relative to the external solution, and accounts for cell membrane tension. The mixture formulation provides an explicit dependence of the hydraulic conductivity of the cell membrane on the concentration of permeating solutes. The resulting equations are shown to reduce to the classical equations of Kedem and Katchalsky in the limit when the membrane tension is equal to zero and the solute partition coefficient in the cytoplasm is equal to unity. Numerical simulations demonstrate that the concentration-dependence of the hydraulic conductivity is not negligible; the volume response to osmotic loading is very sensitive to the partition coefficient of the solute in the cytoplasm, which controls the magnitude of cell volume recovery; and the volume response is sensitive to the magnitude of cell membrane tension. Deviations of the Boyle-van't Hoff response from a straight line under hypo-osmotic loading may be indicative of cell membrane tension.     

A model of unsteady-state transvascular fluid and protein transport in the lung

Models of steady-state fluid and solute transport in the microcirculation are used primarily to characterize filtration and permeability properties of the transport barrier. Important transient relationships, such as the rate of fluid accumulation in the tissue, cannot be predicted with steady-state models. In this paper we present three simple models of unsteady-state fluid and protein exchange between blood plasma and interstitial fluid. The first treats the interstitium as a homogeneous well-mixed compliant compartment, the second includes an interstitial gel, and the third allows for both gel and free fluid in the interstitium. Because we are primarily interested in lung transvascular exchange we used the multiple-pore model and pore sizes described by Harris and Roselli (J. Appl. Physiol.: Respirat . Environ. Exercise Physiol. 50: 1-14, 1981) to characterize the microvascular barrier. However, the unsteady-state transport theory presented here should apply to other organ systems and can be used with different conceptual models of the blood-lymph barrier. For a step increase in microvascular pressure we found good agreement between theoretical and experimental lymph flow and lymph concentrations in the sheep lung when the following parameter ranges were used: base-line interstitial volume, 150-190 ml; interstitial compliance, 7-10 ml/Torr; initial interstitial fluid pressure, -1 Torr; pressure in initial lymphatics, -5 to -6 Torr; and conductivity of the interstitium and lymphatic barrier, 4.25 X 10(-4) ml X s-1 X Torr-1. Based on these values the model predicts 50% of the total change in interstitial water volume occurs in the first 45 min after a step change in microvascular pressure.(ABSTRACT TRUNCATED AT 250 WORDS)     

A novel leupeptin-sensitive serine endopeptidase present in normal and malignant rat mammary tissues

Summary N-Methyl-N-nitrosourea (MNU)-induced rat mammary adenocarcinomas contain high levels of a novel leupeptin-sensitive serine endopeptidase. Its properties apparently differ from those of other similar endopeptidases reported to be present in various normal and malignant mammalian tissues. The same leupeptinsensitive serine endopeptidase was also detected in normal rat mammary tissues, but at levels approximately 20 times lower than those in MNU-induced mammary tumors.This enzyme, which is a trypsin-like serine endopeptidase, preferentially hydrolyzes various synthetic endopeptidase substrates at the carboxyl side of an arginyl residue. It has an apparent Mr of approximately 160,000 and a Stokes radius of 49\rA, as determined by gel filtration. Its isoelectric points range from 4.5 to 4.8, and it has a pH optimum of approximately 7.0. The enzyme is stable from pH 4.0 to 7.0, but is extremely unstable above pH 7.0. Besides leupeptin, its activity is inhibited by antipain, aprotinin, N-p-tosyl-L-lysine chloromethyl ketone and phenylmethylsulfonyl fluoride, but is not inhibited by soybean trypsin inhibitor. Many other potential inhibitors or activators such as 2-mercaptoethanol, p-hydroxymercuribenzoic acid and EDTA have no effect on its activity. The enzyme is adsorbed to p-aminobenzamidine agarose affinity beads at pH 6.5 and elutes at pH 4.0.Abbreviations BAPA -N-benzoyl-DL-arginine-4-nitroanilide (all other optically active amino acids in the substrates or inhibitors are of the L-configuration except for the valyl residue in DL-Val-Leu-Arg-4NA) - 4NA 4-nitroanilide - Bz -N-benzoyl - Cbz -N-benzyloxycarbonyl - Suc -N-succinyl - Tos p-toluenesulfonyl - CH₂Cl chloromethyl ketone - DMBA 7,12-dimethylbenz(a)anthracene - MNU N-methyl-Nnitrosourea - Mr apparent relative molecular mass     

Expression of the human copper influx transporter 1 in normal and malignant human tissues.

The major copper influx transporter, copper transporter 1 (hCTR1), controls the cellular accumulation of cisplatin in mammalian cells. The goal of this study was to determine the pattern of hCTR1 expression in normal and malignant human tissues. Tissue arrays were stained with an antibody specific for hCTR1 using standard immunohistochemical techniques. Particularly strong staining was noted in the alpha cells of the pancreatic islets, enteroendocrine cells of the gastric mucosa and bronchioles, C cells of the thyroid, and a subset of cells in the anterior pituitary. Frequency and intensity of hCTR1 staining in malignant tissues reflected the levels found in their normal tissue counterparts. For example, neither normal prostate nor prostate cancers expressed hCTR1, whereas it was commonly expressed in both normal colonic epithelium and in colon carcinomas. Strong staining was observed in a limited number of cases of carcinoid tumors, Ewing's sarcoma, and undifferentiated carcinomas. Although all tissues require copper, expression of hCTR1 was highly variable among normal tissues and among the major human malignancies, with the highest levels found in enteroendocrine cells. No hCTR1 expression was found in several common types of cancer, suggesting that hCTR1 expression is not commonly enhanced by transformation.