Rho GTPase-mediated cytoskeletal organization in Schlemm's canal cells play a critical role in the regulation of aqueous humor outflow facility

The increased intraocular pressure (IOP) has been considered to be an increased resistance of the aqueous humor outflow through the inner wall of Schlemm's canal (SC) and/or the juxtacanalicular tissue (JCT). The Rho GTPase-regulated actomyosin organization appears to be an important mechanistic determinant of aqueous humor outflow facility. Therefore, in this study, we have evaluated the effects of modulating Rho GTPase activity on actomyosin cytoskeletal organization, monolayer permeability/barrier function of human SC cells, and aqueous humor outflow facility in enucleated porcine eyes ex vivo. Human SC cells, isolated from cadaver eyes, were treated with either Rho GTPase activators such as thrombin and lysophosphatidic acid (LPA), or a specific inhibitor (C3-exoenzyme) of Rho GTPases. Treatment of SC cells with thrombin and LPA led to increased formation of stress fibers, focal adhesion, and increased myosin light chain phosphorylation, whereas treatment with C3-exoenzyme showed the opposite effects like H-7 and ECA, known for increasing the outflow facility in porcine eyes. The findings presented here suggest that LPA and thrombin, presumably through activation of Rho GTPase-mediated actomyosin cytoskeletal reorganization in SC cells, cause a decrease in monolayer permeability of SC cells as well as a decrease in outflow facility of porcine eyes in ex vivo. Our results suggest that decrease in aqueous humor outflow may be correlated better with the changes in cytoskeletal organizations of SC, which could be the prime locus of the outflow resistance.     

Guanylate cyclase activators, cell volume changes and IOP reduction

Glaucoma afflicts millions of people worldwide and is a major cause of blindness. The risk to develop glaucoma is enhanced by increases in IOP, which result from deranged flow of aqueous humor. Aqueous humor is a fluid located in the front of the eye that gives the eye its buoyancy and supplies nutrients to other eye tissues. Aqueous humor is secreted by a tissue called ciliary processes and exits the eye via two tissues; the trabecular meshwork (TM) and Schlemm's canal. Because the spaces through which the fluid flows get smaller as the TM joins the area of the Schlemm's canal, there is resistance to aqueous humor outflow and this resistance creates IOP. There is a correlation between changes in TM and Schlemm's canal cell volume and rates of aqueous humor outflow; agents that decrease TM and Schlemm's canal cell volume, increase the rate of aqueous humor outflow, thus decreasing IOP. IOP is regulated by guanylate cyclase activators as shown in humans, rabbits and monkeys. There are two distinct groups of guanylate cyclases, membrane guanylate cyclase and soluble guanylate cyclase (sGC); activation of both have been shown to decrease IOP. Members of the membrane guanylate cyclase family of receptors bind to peptide ligands, while the sGC responds to gases (such as NO and CO(2)) and compounds (such as YC1, [3-(5'-hydroxymethyl-2'furyl)-1-benzyl indazole), a benzyl indazole derivative, and BAY-58-2667); activation of either results in formation of cyclic GMP (cGMP) and activation of protein kinase G (PKG) and subsequent phosphorylation of target proteins, including the high conductance calcium activated potassium channel (BKca channel). While activators of both membrane guanylate cyclase and sGC have the ability to lower IOP, the IOP lowering effects of sGC are noteworthy because sGC activators can be topically applied to the eye to achieve an effect. We have demonstrated that activators of sGC increase the rate at which aqueous humor exits the eye in a time course that correlates with the time course for sGC-induced decreases in TM and Schlemm's canal cell volume. Additionally, sGC-induced decrease in cell volume is accompanied by both K(+) and Cl(-) efflux induced by activation of K(+) and Cl(-) channels, including the BKca channel and/or K(+)Cl(-) symport. This suggests that parallel K(+)Cl(-) efflux, and resultant H(2)O efflux result in decreases in cell volume. These observations suggest a functional role for sGC activators, and suggest that the sGC/cGMP/PKG systems are potential therapeutic targets in the treatment of glaucoma.     

Mapping Molecular Differences and Extracellular Matrix Gene Expression in Segmental Outflow Pathways of the Human Ocular Trabecular Meshwork

Elevated intraocular pressure (IOP) is the primary risk factor for glaucoma, and lowering IOP remains the only effective treatment for glaucoma. The trabecular meshwork (TM) in the anterior chamber of the eye regulates IOP by generating resistance to aqueous humor outflow. Aqueous humor outflow is segmental, but molecular differences between high and low outflow regions of the TM are poorly understood. In this study, flow regions of the TM were characterized using fluorescent tracers and PCR arrays. Anterior segments from human donor eyes were perfused at physiological pressure in an ex vivo organ culture system. Fluorescently-labeled microspheres of various sizes were perfused into anterior segments to label flow regions. Actively perfused microspheres were segmentally distributed, whereas microspheres soaked passively into anterior segments uniformly labeled the TM and surrounding tissues with no apparent segmentation. Cell-tracker quantum dots (20 nm) were localized to the outer uveal and corneoscleral TM, whereas larger, modified microspheres (200 nm) localized throughout the TM layers and Schlemm’s canal. Distribution of fluorescent tracers demonstrated a variable labeling pattern on both a macro- and micro-scale. Quantitative PCR arrays allowed identification of a variety of extracellular matrix genes differentially expressed in high and low flow regions of the TM. Several collagen genes (COL16A1, COL4A2, COL6A1 and 2) and MMPs (1, 2, 3) were enriched in high, whereas COL15A1, and MMP16 were enriched in low flow regions. Matrix metalloproteinase activity was similar in high and low regions using a quantitative FRET peptide assay, whereas protein levels in tissues showed modest regional differences. These gene and protein differences across regions of the TM provide further evidence for a molecular basis of segmental flow routes within the aqueous outflow pathway. New insight into the molecular mechanisms of segmental aqueous outflow may aid in the design and delivery of improved treatments for glaucoma patients.     

Dexamethasone alters F-actin architecture and promotes cross-linked actin network formation in human trabecular meshwork tissue

Elevated intraocular pressure is an important risk factor for the development of glaucoma, a leading cause of irreversible blindness. This ocular hypertension is due to increased hydrodynamic resistance to the drainage of aqueous humor through specialized outflow tissues, including the trabecular meshwork (TM) and the endothelial lining of Schlemm's canal. We know that glucocorticoid therapy can cause increased outflow resistance and glaucoma in susceptible individuals, that the cytoskeleton helps regulate aqueous outflow resistance, and that glucocorticoid treatment alters the actin cytoskeleton of cultured TM cells. Our purpose was to characterize the actin cytoskeleton of cells in outflow pathway tissues in situ, to characterize changes in the cytoskeleton due to dexamethasone treatment in situ, and to compare these with changes observed in cell culture. Human ocular anterior segments were perfused with or without 10(-7) M dexamethasone, and F-actin architecture was investigated by confocal laser scanning microscopy. We found that outflow pathway cells contained stress fibers, peripheral actin staining, and occasional actin "tangles." Dexamethasone treatment caused elevated IOP in several eyes and increased overall actin staining, with more actin tangles and the formation of cross-linked actin networks (CLANs). The actin architecture in TM tissues was remarkably similar to that seen in cultured TM cells. Although CLANs have been reported previously in cultured cells, this is the first report of CLANs in tissue. These cytoskeletal changes may be associated with increased aqueous humor outflow resistance after ocular glucocorticoid treatment.     

Differential P1-purinergic modulation of human Schlemm's canal inner-wall cells

Intraocular pressure is directly dependent on aqueous humor flow into, and resistance to flow out of, the eye. Adenosine has complex effects on intraocular pressure. Stimulation of A₁ and A_2A adenosine receptors changes intraocular pressure oppositely, likely through opposing actions on the outflow of aqueous humor. While the cellular sites regulating outflow resistance are unknown, the cells lining the inner wall of Schlemm's canal (SC) are a likely regulatory site. We applied selective adenosine receptor agonists to SC cells in vitro to compare the responses to A₁ and A_2A stimulation. Parallel studies were conducted with human inner-wall SC cells isolated by a novel enzyme-assisted technique and with cannula-derived mixed inner- and outer-wall SC cells. A₁ agonists increased whole cell currents of both inner-wall and cannula-derived SC cells. An A_2A agonist reduced currents most consistently in specifically inner-wall SC cells. Those currents were also increased by A_2B, but not consistently affected by A₃, stimulation. A₁, A_2A, and A₃ agonists all increased SC-cell intracellular Ca²⁺. The electrophysiological results are consistent with the possibility that inner-wall SC cells may mediate the previously reported modulatory effects of adenosine on outflow resistance. The results are also consistent with the presence of functional A_2B, as well as A₁, A_2A, and A₃ adenosine receptors in SC cells. intraocular pressure; aqueous humor outflow; ion transport; adenosine agonists     

Mechanisms of ATP release, the enabling step in purinergic dynamics

The only effective intervention to slow onset and progression of glaucomatous blindness is to lower intraocular pressure (IOP). Among other modulators, adenosine receptors (ARs) exert complex regulation of IOP. Agonists of A(3)ARs in the ciliary epithelium activate Cl(-) channels, favoring increased formation of aqueous humor and elevated IOP. In contrast, stimulating A(1)ARs in the trabecular outflow pathway enhances release of matrix metalloproteinases (MMPs) from trabecular meshwork (TM) cells, reducing resistance to outflow of aqueous humor to lower IOP. These opposing actions are thought to be initiated by cellular release of ATP and its ectoenzymatic conversion to adenosine. This view is now supported by our identification of six ectoATPases in trabecular meshwork (TM) cells and by our observation that external ATP enhances TM-cell secretion of MMPs through ectoenzymatic formation of adenosine. ATP release is enhanced by cell swelling and stretch. Also, enhanced ATP release and downstream MMP secretion is one mediator of the action of actin depolymerization to reduce outflow resistance. Inflow and outflow cells share pannexin-1 and connexin hemichannel pathways for ATP release. However, vesicular release and P2X(7) release pathways were functionally limited to inflow and outflow cells, respectively, suggesting that blocking exocytosis might selectively inhibit inflow, lowering IOP.     

S1P₂ receptor regulation of sphingosine-1-phosphate effects on conventional outflow physiology

Elevated intraocular pressure is the main risk factor in primary open-angle glaucoma, involving an increased resistance to aqueous humor outflow in the juxtacanalicular region of the conventional outflow pathway which includes the trabecular meshwork (TM) and the inner wall of Schlemm's canal (SC). Previously, sphingosine-1-phosphate (S1P) was shown to decrease outflow facility in porcine and human eyes, thus increasing outflow resistance and intraocular pressure. Owing to S1P's known effect of increasing barrier function in endothelial cells and the robust expression of the S1P? receptor on the inner wall of SC, we hypothesized that S1P? receptor activation promotes junction formation and decreases outflow facility. The effects of subtype-specific S1P receptor compounds were tested in human and porcine whole-eye perfusions and human primary cultures of SC and TM cells to determine the receptor responsible for S1P effects on outflow resistance. The S1P?-specific agonist SEW2871 failed to both mimic S1P effects in paired human eye perfusions, as well as increase myosin light chain (MLC) phosphorylation in cell culture, a prominent outcome in S1P-treated SC and TM cells. In contrast, the S1P? antagonist JTE-013, but not the S1P? or S1P?,? antagonists, blocked the S1P-promoted increase in MLC phosphorylation. Moreover, JTE-013 prevented S1P-induced decrease in outflow facility in perfused human eyes (P < 0.05, n = 6 pairs). Similarly, porcine eyes perfused with JTE-013 + S1P did not differ from eyes with JTE-013 alone (P = 0.53, n = 3). These results demonstrate that S1P? , and not S1P? or S1P?, receptor activation increases conventional outflow resistance and is a potential target to regulate intraocular pressure.     

Electron probe X-ray microanalysis of intact pathway for human aqueous humor outflow

Intraocular pressure (IOP) is regulated by the resistance to outflow of the eye's aqueous humor. Elevated resistance raises IOP and can cause glaucoma. Despite the importance of outflow resistance, its site and regulation are unclear. The small size, complex geometry, and relative inaccessibility of the outflow pathway have limited study to whole animal, whole eye, or anterior-segment preparations, or isolated cells. We now report measuring elemental contents of the heterogeneous cell types within the intact human trabecular outflow pathway using electron-probe X-ray microanalysis. Baseline contents of Na(+), K(+), Cl(-), and P and volume (monitored as Na+K contents) were comparable to those of epithelial cells previously studied. Elemental contents and volume were altered by ouabain to block Na(+)-K(+)-activated ATPase and by hypotonicity to trigger a regulatory volume decrease (RVD). Previous results with isolated trabecular meshwork (TM) cells had disagreed whether TM cells express an RVD. In the intact tissue, we found that all cells, including TM cells, displayed a regulatory solute release consistent with an RVD. Selective agonists of A(1) and A(2) adenosine receptors (ARs), which exert opposite effects on IOP, produced similar effects on juxtacanalicular (JCT) cells, previously inaccessible to functional study, but not on Schlemm's canal cells that adjoin the JCT. The results obtained with hypotonicity and AR agonists indicate the potential of this approach to dissect physiological mechanisms in an area that is extremely difficult to study functionally and demonstrate the utility of electron microprobe analysis in studying the cellular physiology of the human trabecular outflow pathway in situ.     

Potential role of lysosomal dysfunction in the pathogenesis of primary open angle glaucoma

Primary open angle glaucoma (POAG) is a late onset disease usually accompanied by elevated intraocular pressure (IOP) that results from the failure of the trabecular meshwork (TM) to maintain normal levels of aqueous humor outflow resistance. Cells in the TM are subjected to chronic oxidative stress through reactive oxygen species (ROS) present in the aqueous humor (AH) and generated by normal metabolism. Exposure to ROS is thought to contribute to the morphological and physiological alterations of the outflow pathway in aging and POAG. Our results indicate that chronic exposure of TM cells to oxidative stress causes the accumulation of nondegradable material within the lysosomal compartment leading to diminished lysosomal activity and increased SA-β-Gal expression. Because the lysosomal compartment is responsible for maintaining general cellular turnover, such impaired activity may lead to a progressive cellular decline in the TM cell function and thus contribute to the progression of POAG.     

Measurement of Outflow Facility Using iPerfusion

Elevated intraocular pressure (IOP) is the predominant risk factor for glaucoma, and reducing IOP is the only successful strategy to prevent further glaucomatous vision loss. IOP is determined by the balance between the rates of aqueous humour secretion and outflow, and a pathological reduction in the hydraulic conductance of outflow, known as outflow facility, is responsible for IOP elevation in glaucoma. Mouse models are often used to investigate the mechanisms controlling outflow facility, but the diminutive size of the mouse eye makes measurement of outflow technically challenging. In this study, we present a new approach to measure and analyse outflow facility using iPerfusion^™, which incorporates an actuated pressure reservoir, thermal flow sensor, differential pressure measurement and an automated computerised interface. In enucleated eyes from C57BL/6J mice, the flow-pressure relationship is highly non-linear and is well represented by an empirical power law model that describes the pressure dependence of outflow facility. At zero pressure, the measured flow is indistinguishable from zero, confirming the absence of any significant pressure independent flow in enucleated eyes. Comparison with the commonly used 2-parameter linear outflow model reveals that inappropriate application of a linear fit to a non-linear flow-pressure relationship introduces considerable errors in the estimation of outflow facility and leads to the false impression of pressure-independent outflow. Data from a population of enucleated eyes from C57BL/6J mice show that outflow facility is best described by a lognormal distribution, with 6-fold variability between individuals, but with relatively tight correlation of facility between fellow eyes. iPerfusion represents a platform technology to accurately and robustly characterise the flow-pressure relationship in enucleated mouse eyes for the purpose of glaucoma research and with minor modifications, may be applied in vivo to mice, as well as to eyes from other species or different biofluidic systems.     

Adenovirus conducted connective tissue growth factor on extracellular matrix in trabecular meshwork and its role on aqueous humor outflow facility

Deposition of extracellular matrix (ECM) in trabecular meshwork, such as fibronectin, collagen IV, elastin. leads to increased resistance of trabecular meshwork in primary open angle glaucoma (POAG). Connective tissue growth factor (CTGF) is known to regulate the ECM deposits. In this study, we detect the effect of adenovirus conducted CTGF (Adv-CTGF) transfection on either the expression of ECM components or aqueous humor outflow facility. Adv-CTGF was used to transfect rat trabecular meshwork cells in vivo and in vitro. Aqueous humor outflow facility was test by microbeads perfusion. Protein expression of CTGF, fibronectin, and collagen IV was determined using Western blot. In the Adv-CTGF group, the outflow facility displayed a significant decrease from baseline. It appears as though the transfection with Adv-CTGF significantly affects the aqueous humor outflow pattern. A negative correlation between IOP and PEFL indicated that a decrease in the area of bead deposition corresponded to an overall decrease of outflow, leading to an elevated IOP. Adv-CTGF can enhance the expression of CTGF, fibronectin and collagen IV. CTGF is the novel target for treatment of POAG. It is necessary to further study to test inhibition of CTGF expression for treatment of POAG.     

Velocity field of pulsatile flow in a porous tube

This paper describes velocity fields for fully developed periodic laminar flow in a rigid tube with a porous wall. We obtained an analytical solution of the flow by the linear approximation of the Navier-Stokes equation. Unlike the previous works with a constant seepage rate along the axis, we used a wall velocity which contained hydraulic permeation constant Lp. The axial velocity profile shows a local maximum velocity near the wall at a large Womersley number alpha. This suggests that concentration polarization in porous tubular membrane may be reduced at high frequencies if a membrane device is operated under pulsatile flow conditions. The magnitude of wall permeation velocity decreases linearly along the tube axis because the damping of the pressure difference between the inside and the outside of the tube is very small.     

Nature and distribution of vascular resistance in hypoxic pig lungs

We used the vascular occlusion technique in pig lungs isolated in situ to describe the effects of hypoxia on the distribution of vascular resistance and to determine whether the resistive elements defined by this technique behaved as ohmic or Starling resistors during changes in flow at constant outflow pressure, changes in outflow pressure at constant flow, and reversal of flow. During normoxia, the largest pressure gradient occurred across the middle compliant region of the vasculature (delta Pm). The major effect of hypoxia was to increase delta Pm and the gradient across the relatively noncompliant arterial region (delta Pa). The gradient across the noncompliant venous region (delta Pv) changed only slightly, if at all. Both delta Pa and delta Pv increased with flow but delta Pm decreased. The pressure at the arterial end of the middle region was independent of flow and, when outflow pressure was increased, did not increase until the outflow pressure of the middle region exceeded 8.9 Torr during normoxia and 18.8 Torr during hypoxia. Backward perfusion increased the total pressure gradient across the lung, mainly because of an increase in delta Pm. These results can be explained by a model in which the arterial and venous regions are represented by ohmic resistors and the middle region is represented by a Starling resistor in series and proximal to an ohmic resistor. In terms of this model, hypoxia exerted its major effects by increasing the critical pressure provided by the Starling resistor of the middle region and the ohmic resistance of the arterial region.     

Resistance of intrathoracic airways of healthy subjects during periodic flow.

The resistance and reactance of lower airways were measured as functions of the frequency and amplitude of periodic flow in three healthy subjects by relating flow, produced with a piston pump, to the difference between lateral tracheal and alveolar pressure, estimated plethysmorgraphically. Resistance consistently increased with frequency; reactance was small never exceeding resistance. This result cannot be explained by distortion of velocity profiles by inertia because, in long pipes, resistance increases only when inertial forces are large and reactance exceeds resistance. Theoretical analyses of airway resistance suggested that the results reflected inhomogeneity. In lung models which considered airway wall distensibility and inertial reactance of airways, resistance increased with frequency and inertial reactance was small. These results imply that in health, as in lung disease, resistance is determined by the distribution of resistance and reactance within the lung and is not simply the total resistance of the individual airways. As flow amplitude increased at constant frequency, flow-pressure relationships became distorted and resistance increased, due probably to motion of airway walls and further distortion of velocity profiles     

A mathematical model of twin-twin transfusion syndrome with pulsatile arterial circulations

The twin-twin transfusion syndrome (TTTS) is a severe complication of monochorionic twin pregnancies caused by a net transfusion of blood from one twin (the donor) to the other (the recipient) through placental anastomoses. To examine the pathophysiology of TTTS evolving through clinical stages I to IV, we extended our mathematical model to include pulsating circulations propagating along the arterial tree as well as placental and cerebral vascular resistances, and arterial wall thickness and stiffness. The model demonstrates that abnormal umbilical arterial flow (TTTS stage III) in the donor twin results from increased placental resistance as well as reduced resistance in the cerebral arteries. In contrast, recipient twin abnormal umbilical arterial flow requires a significantly greater increase in placental resistance, resulting from the compressive effects of high amniotic fluid pressure. Thus simulated abnormalities of donor umbilical arterial pulsations occur in the donor more commonly and earlier than in the recipient. The "normal" staging sequence (I, II, III, IV) correlates with the presence of compensating placental anastomoses, constituting the majority of monochorionic twin placentas. However, TTTS stage III may occur before manifestations of stage II (lack of donor bladder filling), in our model correlating with severe TTTS from a single arteriovenous anastomosis, an infrequent occurring placental angioarchitecture. In conclusion, this mathematical model describes the onset and development of the four stages of TTTS, reproduces a variety of clinical manifestations, and may contribute to identifying the underlying pathophysiology of the staging sequence in TTTS.     

On an equation modeling the flow in the canal of Schlemm

In a recent paper Tandon and Autar showed how the model equations for flow of aqueous humor in the canal of Schlemm with a flexible inner wall can be reduced to a second-order boundary value problem for the fluid pressure. They then proceeded to solve this using an approximate iterative scheme. In this paper we show how the problem can be reduced to a first-order one for the canal thickness that can be analyzed in the phase plane. This crucial reduction and subsequent analysis reveals important properties of the solution not apparent from the approximate treatment of Tandon and Autar. Furthermore, by solving the first-order problem exactly in terms of definite integrals, the important questions of existence and uniqueness for given parameter values can be addressed.     

Regulation of anterior chamber drainage by bicarbonate-sensitive soluble adenylyl cyclase in the ciliary body

Glaucoma is a leading cause of blindness affecting as many as 2.2 million Americans. All current glaucoma treatment strategies aim to reduce intraocular pressure (IOP). IOP results from the resistance to drainage of aqueous humor (AH) produced by the ciliary body in a process requiring bicarbonate. Once secreted into the anterior chamber, AH drains from the eye via two pathways: uveoscleral and pressure-dependent or conventional outflow (C(t)). Modulation of "inflow" and "outflow" pathways is thought to occur via distinct, local mechanisms. Mice deficient in the bicarbonate channel bestrophin-2 (Best2), however, exhibit a lower IOP despite an increase in AH production. Best2 is expressed uniquely in nonpigmented ciliary epithelial (NPE) cells providing evidence for a bicarbonate-dependent communicative pathway linking inflow and outflow. Here, we show that bicarbonate-sensitive soluble adenylyl cyclase (sAC) is highly expressed in the ciliary body in NPE cells, but appears to be absent from drainage tissues. Pharmacologic inhibition of sAC in mice causes a significant increase in IOP due to a decrease in C(t) with no effect on inflow. In mice deficient in sAC IOP is elevated, and C(t) is decreased relative to wild-type mice. Pharmacologic inhibition of sAC did not alter IOP or C(t) in sAC-deficient mice. Based on these data we propose that the ciliary body can regulate C(t) and that sAC serves as a critical sensor of bicarbonate in the ciliary body regulating the secretion of substances into the AH that govern outflow facility independent of pressure.     

Finite element analysis of the pressure-induced deformation of Schlemm’s canal endothelial cells

The endothelial cells lining the inner wall of Schlemm’s canal (SC) in the eye are relatively unique in that they support a basal-to-apical pressure gradient that causes these cells to deform, creating giant vacuoles and transendothelial pores through which the aqueous humor flows. Glaucoma is associated with an increased resistance to this flow. We used finite element modeling and estimates of cell modulus made using atomic force microscopy to characterize the pressure-induced deformation of SC cells and to estimate the maximum pressure drop that SC cells can support. We examined the effects of cell geometry, cell stiffness, and the contribution of the cell cortex to support the pressure-generated load. We found that the maximum strain generated by this loading occurs at the points of cell–substrate attachment and that the cortex of the cells bears nearly all of this load. The ability of these cells to support a significant transcellular pressure drop is extremely limited (on the order of 5 mmHg or less) unless these cells either stiffen very considerably with increasing deformation or have substantial attachments to their substratum away from their periphery. This puts limits on the flow resistance that this layer can generate, which has implications regarding the site where the bulk of the flow resistance is generated in healthy and glaucomatous eyes.     

Simulation of a cross-flow shrinking-bed reactor for the hydrolysis of lignocellulosics.

An idealized model is developed for the case in which biomass slurry is conveyed through an annulus, with water or steam entering through an inner porous wall and liquid product leaving through an outer porous wall. It is assumed that the ratio of occluded liquid to solid in the slurry is a constant, Rws, and that non-occluded water is immediately removed from the reactor. The goal of > 90% sugar yield with > 10% sugar in the product is almost reached (88% glucose yield, 91% xylose yield, 47 g/l glucose and 45 g/l xylose) at 240 degrees C, 1% acid. Rws = 1 and a radial wash water flow of three times the initial mass flow of solids to the reactor per meter of reactor length per g/l of sugar concentration in the occluded water. If Rws is limited to 3, the yield falls to 85% and the total sugar concentration to 61 g/l. Even without cross-flow wash, the yields can be increased by about 16 percentage points, compared to plug flow, by extracting excess liquid through the outer wall as it is formed. At 200 degrees C, where one might prefer to operate for ease of control and concern about the possibility of making fermentation inhibitors at higher temperatures, the maximum glucose yield in a plug-flow reactor is low (12-13%) whereas in a cross-flow reactor, at a high cross-flow wash rate, it can still be quite high (60-83%) but at a very low concentration (0.57-1.47%). In these simulations it is assumed that one-half of the inerts is solubilized. The formation of oligomers is neglected.