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NDT Advance Access originally published online on April 5, 2008
Nephrology Dialysis Transplantation 2008 23(7):2142-2146; doi:10.1093/ndt/gfn055
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© The Author [2008]. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org


Distributed model of peritoneal transport: implications of the endothelial glycocalyx

Michael F. Flessner

University of Mississippi Medical Center, Jackson, MS, USA

Correspondence and offprint requests to: Michael Flessner, Department of Medicine/Nephrology, University of Mississippi Medical Center, 2500 North State Street, Jackson, MS 39216-4505, USA. Tel: +1-601-984-5670; Fax: +1-601-984-5765; E-mail: mflessner{at}medicine.umsmed.edu

Keywords: mathematical model; microcirculation; osmosis; pathophysiology; peritoneal dialysis



   Mathematical prediction of clinical events versus physiological research
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Inadequacies of the membrane...
 Glycocalyx within the...
 Possible impact of adding...
 References
 
This commentary discusses the conceptual and mathematical modelling of solute and water transport across the peritoneum and attempts to put a ‘new’ physiologic entity, the endothelial glycocalyx, into perspective. In the clinic, concepts analogous to the membrane barrier in haemodialysis are used to form simplified mathematical schemes to provide rapid estimation of the transport. In contrast, fundamental research on the pathophysiology of the peritoneal barrier demands models that include important elements of the anatomy that have been demonstrated to influence solute and water transport. If potentially critical elements in the barrier, such as the cell-interstitial matrix, are neglected, their importance will never be realized. In this brief article, the potential importance of the endothelial glycocalyx to our understanding of the pathophysiologic changes in the peritoneum is explored.

Peritoneal barrier
The peritoneal barrier is a complex structure made up of blood vessels surrounded by cells and interstitial matrix, which links the cells within the tissue [1]. Overlying this complicated network is a single layer of mesothelial cells and several layers of connective tissue; together these structures are called the peritoneum, which lines the entire pelvic and abdominal cavities. During peritoneal dialysis (PD), transport occurs between the plasma within the tissue microvasculature and the dialysis solution in contact with peritoneum of the tissue. The typical solute pathway is across the capillary endothelium through the interstitium and then across the peritoneum, as illustrated in Figure 1. Although theorized in the past to be a significant barrier to solutes and water [2], the normal anatomic peritoneum has no measurable resistance to small or large solutes, nor does it play a role in osmosis from the tissue to the cavity [3–5]. Indeed, water and proteins readily cross the peritoneum from the cavity into the underlying tissue due to the hydrostatic pressure-driven flow resulting from a large intraperitoneal fluid volume [5–7]. Small solutes, such as urea, creatinine or dextrose, transport chiefly by diffusion across the endothelium and through the tissue space. Osmosis or ultrafiltration from plasma space into the peritoneal cavity is associated with the use of hypertonic solutions [1,8], but the mechanisms are only partially defined.


Figure 1
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  		Fig. 1 Peritoneal barrier represented as a microcirculation distributed within an interstitial-cell matrix. Fluid and solutes transport from the microcirculation to the dialysis solution (arrows). The endothelial glycocalyx lines the blood capillaries (see the inset) and plays a role in the passage of macromolecules across endothelia. Glucose in the peritoneal dialysis (PD) fluid diffuses into the surrounding tissue and sets up an exponentially decreasing concentration profile (thick dotted line) that is equivalent to the interstitial osmolar profile within the tissue surrounding the blood vessels. See the text for more details.

 
Osmosis across the endothelial barrier
Fluid movement from the blood capillaries into the interstitum occurs due to osmosis across Aquaporin 1 and intercellular gaps in the endothelium. The glucose concentration in the peritoneal cavity sets up an exponentially decreasing concentration profile in the surrounding tissue as illustrated in Figure 1, and the osmotic pressure profile within the tissue will have a similar shape [9,10]. Trans-endothelial osmosis therefore is variable depending on the distance of the blood capillary from the peritoneal cavity and its position in the imposed osmotic pressure profile. There is likely little contribution to ultrafiltration from blood vessels further than 500–1000 µm from the serosal surface [9,10].

Water flow from the interstitium
Water transport from the interstitium into the cavity occurs by an unknown mechanism. Since there is no barrier at the peritoneum to either small or large molecular weight solutes, there is no defined osmotic barrier between the peritoneal cavity and the tissue interstitium. There is some shrinkage of muscle cells in the vicinity of the peritoneum where the osmotic concentration is greatest [11]. Water flow from the intracellular space of muscle cells adjacent to the cavity could be a source of a small amount of water. By assuming the peritoneal contact area [12] as 5500 cm2 and the distance-averaged cell volume shrinkage within 50 µm as ~15% with a 480 mOsm/kg pressure in the cavity [11], we estimate the volume flux due to this mechanism as ~24 ml. Another source of water flow from the tissue, the diffusion of water, is too slow to account for the observed flow rates [13], so there has to be some other mechanism.

Mathematical models of the transport system
Mathematical models permit the quantitative estimation of transport rates of solutes and water. All three of the models discussed below are appropriate to model the normal clinical situation, in which they will arrive at the correct estimation of the transport phenomena. A major criterion for the use of such models is the purpose of the model: will it be used to explore pathophysiologic changes in the peritoneal barrier as portrayed in Figure 1, or will it be used to calculate and compare overall solute and water transfer rates in the clinical setting?

Membrane models, such as the Pyle–Popovich model [14] or the three-pore model [15], are one-dimensional and ignore the complex barrier in Figure 1, reducing it to a single membrane with permeability characteristics constrained to fit the clinical data. The Pyle–Popovich concept is similar to a haemodialyzer membrane that utilizes a mass transfer area coefficient (MTAC) to lump all of the resistances of the various structures. The three-pore model is more complex with three different types of ‘pores’ in a single blood capillary membrane that is in direct contact with the dialysis solution: (1) aquaporin water channels, (2) an intercellular gap ‘small pore’ (primarily for solutes of size less than serum albumin) and (3) larger gaps or pores (capable of passing proteins). The Pyle–Popovich and the three-pore model have advantages in which the mathematics are relatively simple and can be solved algebraically on a hand-held calculator. Indeed, it was shown that a later version [16] of the Pyle–Popovich model, used in the Baxter Program PD Adequest, is equivalent to the three-pore model in its mathematical simulations. Because there is no attempt to model the actual tissue barrier, the disadvantage to these models is that neither can separate specific pathophysiologic changes in the peritoneal barrier, such as the inflammatory thickening of the sub-mesothelium from angiogenesis.

The distributed model [17] is a conceptual and mathematical representation of Figure 1 in which a two-dimensional structure forms the basis for simulating the barrier. The distributed model is more complicated because it integrates a distributed microvasculature with the surrounding cells and interstitium within a whole tissue structure. It requires the solution of partial differential equations with several variable parameters for a time-dependent solution. Therefore this model is not as useful in the clinic but is designed for research into fundamental properties of the peritoneal barrier. In the first editions of this model, blood vessels were typically assumed to be distributed uniformly in an interstitium with isotropic properties, but the model is amenable to variation of the local density of blood vessels and of permeability characteristics of the interstitium and blood capillaries [18]. The model has the advantage that pathophysiologic change in the space underlying the mesothelium can be inserted to present a more realistic representation of the transport phenomena.



   Inadequacies of the membrane models in basic research of the peritoneum
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Membrane models are not useful for basic peritoneal research because they are typically empiric in nature and do not attempt to describe physiologic phenomenon. One example of a deficit in the model is the reabsorption of fluid and protein in the peritoneal cavity into the local tissues due to the positive hydrostatic pressure within the cavity [19,20], which drives water and all solutes from the cavity across the peritoneum to local tissue [5,6,21,22]. While this is often attributed to lymphatic uptake [23], only about 10–20% of the actual fluid return from the cavity during dialysis to the blood actually occurs through lymphatics [24–27]. The remainder occurs via flow into localized tissue (in particular the abdominal wall) and is subsequently reabsorbed into the microcirculation [4,5,28–31]. By their design, membrane models do not include lymphatics or an interstitial space. They typically must be ‘fixed’ or manipulated by empirically derived parameters and equations in order to properly simulate the fluid and solute return to the plasma space.

Because the blood capillary model has no tissue surrounding it (similar to the blood vessel in the inset in Figure 1 directly placed in the dialysis fluid), it is very efficient in transfer of solute and water. The capillary barrier of the three-pore model would be contained in <50 g of tissue rather than the ~500 g of tissue that represents a more realistic estimate of the volume of tissue (volume = area x thickness = 5500 cm2 x 0.1 cm [9,12,32]) that is actually exposed to the high glucose concentrations. The presence of the interstitial-cell matrix alters the transport significantly.

A third example of a problem for the membrane models is the assumption of the dialysate-side osmotic pressure as equal to the osmotic pressure in the cavity (the hydrostatic pressure is typically ignored). Basic research [9,10,28] has demonstrated that the osmotic profile (see Fig. 1) is decreasing through the tissue, and blood capillaries are only exposed to a fraction of the actual osmotic pressure in the peritoneal dialysate. When a membrane model is fitted to clinical data, the parameters by design will not match what is occurring in the tissue. A recent paper that utilized the distributed model with the osmotic agent glucose demonstrated a markedly higher reflection coefficient for the capillaries than is typically used in the three-pore theory [33]. Without a tissue space to modify the concentration of the osmotic agent, the three-pore model adjusts its reflection coefficient to low values so as not to overpredict the observed fluid flux. The mathematics of simpler membrane models allows the rapid estimation of the transport, but they give us no insight into the underlying changes in physiology that occur in pathologic inflammation. While the distributed model uses some idealized concepts to simulate the actual barrier contained in the subperitoneal tissue, it does permit the separation of phenomena within the tissue interstitial-cell matrix from the blood capillaries.

The pathophysiology of the peritoneal barrier is now undergoing intense research. Glucose degradation products within the sterile solutions result in an epithelial to mesenchymal transition in the peritoneum with expansion of the sub-mesothelial space [34,35]. Angiogenesis and interstitial expansion occurs with the alteration of fibroblastic cells to very active myofibroblasts [36,37]. Dendritic cells as well as macrophages likely play important roles in the inflammatory change within the peritoneum [38]. Exposure to glucose causes functional changes as well with the increase rates of solute transfer and the decrease rates of fluid removal [39]. A rigid pore system or planer membrane system can be empirically fitted to the observed functional data, but such a model will not provide any insight into the changes in the actual structure and may actually mislead researchers to the wrong conclusions.



   Glycocalyx within the endothelium and the distributed model
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Structure of the glycocalyx
The endothelial glycocalyx is a thin (0.5–1.5 µm) [40,41] layer of anionic polysaccharides on the luminal surface of endothelial cells and was termed glycocalyx by Bennet [42]. Traditional electron microscopic processing destroyed the extracellular coating and therefore early scientists did not observe it. The coating consists of proteoglycans such as heparan and heparan sulphate and glycosaminoglycans (hyaluronan and chondroitin sulphate) with sialic acid residues that confer a high negative charge. The glycocalyx can be visualized by staining with either ruthenium red or lanthanum nitrate. In 1979, Klitzman and Duling [40] defined a layer that excluded red blood cells from the interior of blood capillaries of ~1.2 µm. Duling and many others [41,43,44] have clearly shown that the glycocalyx excludes large molecular weight dextrans, but when it is removed, the dextrans move across the endothelium into the interstitium.

Endothelial permeability and the glycocalyx
The glycocalyx is damaged by ischaemia, inflammation and hyperglycaemia, which all increase capillary permeability. Microvessels formed during angiogenesis typically have decreased glycocalyx and are significantly more permeable [45]. This allows large molecular weight growth factors and other proteins to pass from the circulation out into the tissue in which the new vessels are forming. Marked decreases in the concentration of plasma albumin alter the glycocalyx charge and result in significant increases in capillary permeability [46]. Replacement of plasma with a fluorocarbon emulsion has resulted in marked increases in permeability in rat lung capillaries [47]. Injury to the glycocalyx due to TNF{alpha} [48,49], ischaemia reperfusion [50] and atrial natriuretic peptide [51] results in degradation of endothelial glycocalyx and significant changes in permeability. Alterations of flow and increased fluid shear stress [52,53] result in an increased hyaluronan content of the glycocalyx and is thought to be vasoprotective against coagulation and leukocyte adhesion. Recent research has shown that acute or chronic hyperglycaemia damages the glycocalyx and increases permeability, resulting in increased loss of large molecular dextrans in animals and protein in humans [54,55]. Indeed, it has been shown in Type-I diabetics that proteinuria is the result of a reduced overall glycocalyx within the endothelium [56,57]. Since the solutions bathing peritoneal tissue have very high concentrations of glucose (15–42.5 g/L) and zero concentration of protein, it is interesting to speculate on the possible changes that might occur in the microcirculation exposed to PD solutions.

Glycocalyx and revision of starling's law
Recent experiments have demonstrated that opposing oncotic forces that control filtration are larger than those that have been estimated for simple differences between luminal plasma concentration and the concentration in the interstitium [58]. The actual osmotic pressure difference ({Delta}{pi}) across the endothelium in continuous endothelia is not {Delta}{pi}traditional Starling Eqn = {pi}plasma – {pi}interstitium but is equal to a smaller number {Delta}{pi}revised Starling Eqn = {pi}plasma – {pi}gap, where the gap is just below the glycocalyx in the inter-endothelial gap [59] and has a significantly higher oncotic pressure than in the interstitial space. The magnitude of {pi}gap cannot be directly measured at present but is inferred from experiment [58] and mathematical theory [60]. This complicates not only the principles of Starling's Law, but also the mathematics that govern the transport across the blood capillaries. Since the glycocalyx appears to chiefly affect macromolecular transport across endothelia, its alteration may or may not directly affect trans-endothelial transport of small molecules, such as glucose or creatinine. However, the layer might be altered with the depletion of interstitial protein in tissue adjacent to the peritoneal cavity [61], and this will likely impact the transcapillary balance of forces.



   Possible impact of adding the glycocalyx to the capillary lumen within the distributed model
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The changes demanded by the addition of glycocalyx to a conceptual model and to the corresponding mathematical model are significant [60,62]. Experimental information on the glycocalyx has been chiefly derived from the microcirculation of the muscle, which makes up the majority of the peritoneal barrier in the hollow viscera and the parietal tissue (abdominal wall, retroperitoneum and diaphragm). Therefore, for a conceptual model to take into account peritoneal pathophysiology, it will be necessary to consider this entity within a realistic representation of the barrier. The glycocalyx itself may not affect the transport of urea, creatinine or glucose. However, it has a major role in transport of larger molecular weights solutes. If it is damaged, there is a release into the local tissue of growth factors, cytokines and fibronectin, as well as all other plasma proteins. This will result further angiogenesis and alterations with the interstitial-cell matrix. It is quite likely that the expansion of the sub-mesothelium during chronic inflammation from the process of sterile dialysis occurs in part because of the release of these products through a damaged or altered glycocalyx.

There is a great need for further research on fundamental aspects of the peritoneal barrier. The endothelial glycocalyx lines the inter-endothelial gaps, limits large solute and affects water transport between the plasma in the interstitium. The delicate layer is very sensitive to inflammatory mediators and hyperglycaemia, which alter the trans-endothelial permeability, probably leading to changes in the underlying cell-interstitial matrix, which in turn affects peritoneal transport. However, there have been no direct studies of the endothelial glycocalyx within tissue adjacent to the peritoneum during PD. Since this entity appears to influence trans-endothelial solute and water transport in many tissues throughout the body, it will be important to include the glycocalyx in studies of the peritoneal barrier and its pathophysiology.



   Acknowledgments
 
Dr Flessner was supported with grant RO1-DK48479 from the National Institutes of Health.

Conflict of interest statement. None declared.

(See related article by O. Devuyst and E. Goffin. Water and solute transport in peritoneal dialysis: models and clinical applications. Nephrol Dial Transplant 2008; 23: 2120–2123.)

(See related article by A. Parikova et al. Free water transport, small pore transport and the osmotic pressure gradient. Nephrol Dial Transplant 2008; 23: 2353–2358.)



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Received for publication: 17.12.07
Accepted in revised form: 23. 1.08


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Free water transport, small pore transport and the osmotic pressure gradient three-pore model of peritoneal transport
Nephrol. Dial. Transplant., July 1, 2008; 23(7): 2147 - 2153.
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O. Devuyst and E. Goffin
Water and solute transport in peritoneal dialysis: models and clinical applications
Nephrol. Dial. Transplant., July 1, 2008; 23(7): 2120 - 2123.
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