HomeScienceVascular refilling coefficient is not a good marker of whole-body capillary hydraulic...

Vascular refilling coefficient is not a good marker of whole-body capillary hydraulic conductivity in hemodialysis patients: insights from a simulation study


At first glance, the refilling coefficient Kr, as proposed by Tabei et al.11,12 and given by Eq. (3), may seem as a useful marker of the whole-body capillary hydraulic conductivity (LpS) in dialysis patients with a potential use in the assessment of patient’s fluid status or estimation of the dry weight14,15. However, their definition of Kr assumes that plasma oncotic pressure (πpl) is effectively the only variable Starling force during HD, while other parameters potentially influencing Kr—including the hydrostatic pressure gradient between capillary blood and interstitial fluid (ΔP = Pc—Pis), interstitial oncotic pressure (πis), and lymph flow (L)—are assumed to be constant. In the present study, we challenged these assumptions and hypothesized that in real dialysis conditions (when all of the above-mentioned factors may be subject to changes), Kr may actually not be an accurate marker of LpS. Our model-based simulations confirm this hypothesis.

Changes in the Starling forces during HD

On the one hand, we showed that ΔP can, indeed, be assumed as almost constant during HD (given that the decrease in the capillary blood pressure that promotes vascular refilling is estimated to be almost the same as the decrease in the interstitial hydrostatic pressure that acts in the opposite way, as shown in Fig. 5). Our simulations also showed that, even though the total lymph flow is subject to a marked reduction during HD, when expressed in the units of Starling forces (mm Hg), its intradialytic changes are very small compared to the main (classic) Starling forces and can be hence neglected without affecting the assessment of Kr. On the other hand, as shown in Fig. 5, the dialysis-induced changes in the interstitial oncotic pressure should not be neglected. In fact, they are expected to be of the same order of magnitude as the changes in the plasma oncotic pressure and, when accounted for, the net increase in the transcapillary pressure gradient that drives vascular refilling is much smaller compared to the increase in plasma oncotic pressure alone. As a result, even if LpS remains constant (as in our basal simulations), Kr decreases during HD in an exponential-like manner, which is due to the overestimation of the effective net Starling force driving vascular refilling. Therefore, the decrease of Kr observed by Tabei et al.11 and Iimura et al.12, contrary to their hypothesis, does not imply a dialysis-induced reduction in LpS, since such a decrease is an entirely expected behavior of Kr related to the aforementioned assumptions.

Possible changes in LpS during HD

Iimura et al. hypothesized that the reduction of Kr during HD may be caused by a dialysis-induced decrease of plasma ANP that they observed in their study12, with likely limited impact of plasma noradrenaline38. This was a plausible hypothesis as it is well known that plasma ANP is elevated before dialysis and decreases during HD39,40 (due to its suppressed secretion following the reduction of atrial pressure as well as due to its clearance in the dialyzer41) and that ANP raises microvascular permeability, as has been shown in both animals42,43 and humans44. Moreover, Schneditz et al.2 and Yashiro et al.15,45 showed that the whole-body capillary filtration coefficient (estimated similarly to Kr) is positively correlated with the level of overhydration, which suggested that a decrease in LpS during HD may be related to a progressing reduction in overhydration (likely associated with a drop in ANP). However, our simulations indicate that, even if LpS was actually decreasing during HD (for whatever reason), it should not affect Kr, as shown in Fig. 6.

Previous studies

It was shown previously by Pietribiasi et al. that the decrease in Kr observed during HD could be largely explained by the assumed lack of intradialytic changes in the interstitial Starling forces and the flow of lymph (except for patients with the highest initial Kr)46. They also showed that those assumptions could be valid only if the capillary blood pressure (assumed constant) decreased during dialysis approximately three times more than the interstitial fluid pressure46, which is rather unlikely given the autoregulatory capacity of the capillary beds24. The present study provides a more complete mathematical analysis of the vascular refilling process, given that in our model the capillary blood pressure is a variable that depends on the state of the whole cardiovascular system (particularly the venous system), as opposed to a constant value assumed in the model with one plasma compartment. Moreover, compared to the model by Pietribiasi et al., the model used in the present study accounts for the two most important plasma protein fractions (albumin and globulins) and their different behavior in terms of transcapillary leakage and refilling, thus providing a likely better estimation of plasma and interstitial oncotic pressures. Furthermore, in the description of fluid transport across the capillary walls we included the impact of osmotic pressure of small solutes (the last term in Eq. 4). Even though the concentrations of ions and small molecules on the two sides of the capillary wall are normally equilibrated due to their high permeability and a very low reflection coefficient, transient transcapillary concentration gradients may occur during dialysis (especially for the solutes being removed in the dialyzer, such as urea or creatinine).

A few years before the refilling coefficient was defined by Tabei et al.11, Schneditz et al. used a similar approach to calculate LpS (which they called simply Lp)2. They considered a three-phase experimental procedure during the first hour of HD: (1) 20 min of blood volume equilibration with pure dialysis and no ultrafiltration, (2) 20 min of intense ultrafiltration (equivalent to 1 h of scheduled ultrafiltration), and (3) 20 min of blood volume recovery with no ultrafiltration. They found no significant difference between Lp calculated for the ultrafiltration phase and the recovery phase, although there were some differences in individual patients. More importantly, however, Schneditz and colleagues were able to fit the relative blood volume (RBV) curves from both ultrafiltration and recovery phases using model-based simulations with a constant (fitted) value of Lp and accounting for the changes of the interstitial oncotic pressure. If the latter were not included in their model, they most probably would not be able to fit the RBV curves using a constant Lp value, since in such a case Lp would need to change during HD just like Kr in the study by Tabei et al. or in our simulations.

Schneditz et al.2 proposed that the changes in blood volume observed over a short period of ultrafiltration during the initial phase of HD could be used in a model-based approach to estimate the (assumingly constant) whole-body filtration coefficient (LpS), which could be then used to determine the safe ultrafiltration rate for the remaining of the dialysis session. We agree that this could be theoretically possible; however, this would need to be done during the very early phase of HD, when the refilling rate is most sensitive to LpS (see Fig. 2), which may be problematic given that during this phase body fluids are typically not in a steady state47, and hence the observed blood volume changes may not always enable an accurate fitting of the model (note that Schneditz et al. started all their experiments with a 20-min equilibration phase). Moreover, as shown by our sensitivity analysis, even though LpS clearly affects the refilling process (and the value of Kr) at the early phase of HD, it cannot be accurately estimated from Kr alone, given the interference from several other, often unmeasurable, parameters (see Fig. 7).

Revised starling principle

As mentioned in the Introduction, one of the limitations of the present study is that in our model we used the classic Starling principle of microvascular fluid exchange, thus ignoring the possible differences in terms of oncotic and hydrostatic pressure between the bulk interstitial fluid and the sub-glycocalyx fluid, i.e. the fluid between the abluminal side of glycocalyx and the tight junction strand within the inter-endothelial clefts in continuous (non-fenestrated) capillaries, as advocated by the revised or extended Starling principle10,17,48. The classic approach allowed us to refer directly to the discussed works by Tabei et al. as well as to other studies mentioned above, all of which employed the classic Starling principle. In order to reflect the extended Starling principle, our model would need to be substantially extended by either: (1) adding a sub-glycocalyx compartment (or possibly more sub-compartments of the interstitial fluid, as proposed by Curry and Michel21) with the description of convection and diffusion of macromolecules between that compartment and the interstitial fluid, which would depend on the flow rate (velocity) of the filtration flow through the orifices in the junction strand, or (2) employing a spatially distributed model of pressure and protein concentration fields behind the glycocalyx, as done by Hu and Weinbaum28, or (3) modelling the capillary wall as a two-membrane system (glycocalyx + endothelium), as done by Facchini et al49,50. Any of the above approaches would increase substantially the level of complexity of our already relatively complex model, but, more importantly, as outlined below, we believe that the possible error introduced by using the classic approach should not affect our conclusions with respect to the deficiencies of Kr.

Firstly, as shown in the simulations by Hu and Weinbaum28 and the experiments by Adamson et al.51, a large difference in the oncotic pressure between the sub-glycocalyx fluid and the interstitial fluid is observed only at very high filtration rates, when filtration of the macromolecule-deficient fluid through the inter-endothelial clefts washes out the macromolecules from the space behind the glycocalyx, while the high velocity of flow through the orifices in the junction strand precludes them from diffusing upstream from the interstitial fluid (assuming that there is an alternative trans-endothelial pathway for the macromolecule transport to the interstitial fluid, i.e. the large pores, as used in our model, which may represent either the vesicular transport or larger gaps in endothelium and glycocalyx20,28). In this case, the oncotic pressure of the sub-glycocalyx fluid is very low (even close to zero at very high filtration rates), and hence the trans-glycocalyx oncotic pressure gradient opposing filtration is very high. So, at the beginning of HD, when there is still filtration through the inter-endothelial clefts (small pores), using the interstitial instead of sub-glycocalyx oncotic pressure in the Starling equation may underestimate the oncotic pressure gradient and hence overestimate filtration through the small pores. In our model, this would automatically mean an underestimation of filtration through large and ultrasmall pores, given that we define the initial steady-state conditions in such a way as to obtain the overall filtration rate equal to the assumed rate of lymph absorption (for this we adjust the initial mean capillary blood pressure). Also, just like the oncotic pressure behind the glycocalyx may be different (lower) from the oncotic pressure of the interstitial fluid, the sub-glycocalyx hydrostatic/hydraulic pressure may be different (higher) from the hydrostatic pressure of the interstitial fluid (again, this is a phenomenon observed mainly at high filtration rates28). Overall, the profile of the oncotic and hydrostatic/hydraulic pressure on the abluminal side of glycocalyx is such that the actual filtration takes place only around the orifices in the junction strand, whereas in the other parts of the clefts the flow rate is zero or near zero28. When the filtration rate is low or close to normal, the phenomena described above are either not observed52 or much less conspicuous with the sub-glycocalyx oncotic pressure reaching almost 90% of the oncotic pressure in the bulk interstitial fluid28,51.

When the flow direction in the inter-endothelial clefts changes to the opposite, i.e. when fluid is absorbed from tissues, as for the majority of the modelled dialysis sessions (mainly due to increase in plasma oncotic pressure and partly due to decrease in capillary blood pressure), the oncotic pressure of the sub-glycocalyx fluid is no longer lower than that of the interstitial fluid; in fact, it is even higher due to reflection of macromolecules from the glycocalyx layer and their accumulation in the sub-glycocalyx space21 (the magnitude of this effect would depend on the rate of fluid absorption and the velocity of fluid through the junction strand openings that would affect the diffusion of macromolecules back to the interstitial fluid). In most tissues with continuous (non-fenestrated) endothelia, such as skeletal muscles and skin, such absorption of fluid from the tissue following a reduction in capillary blood pressure or increase in plasma oncotic pressure is possible only transiently until a new steady state is established across the glycocalyx (a state of filtration, as indicated by the Michel-Weinbaum model22,23,53 and as shown experimentally, albeit only in frog and rat microvessels51,53)—this takes usually 15–30 minutes10,48 but may continue for more than an hour17,21. During HD, however, there is no step-like change in the conditions for microvascular exchange, as typically considered in the studies devoted to the extended Starling principle, nor a more gradual but still relatively quick change of microvascular conditions as in hemorrhage or following an infusion in fluid therapy54,55. Instead, during a typical HD session there is a progressing (lasting 3–5 h) increase in the plasma oncotic pressure (mainly due to ultrafiltration in the dialyzer, and partly due to reduced transcapillary protein leakage) as well as a less prominent but also progressing decrease in the capillary blood pressure, both of which preclude the system from reaching a steady state and provide a continuous drive for fluid absorption, as shown in several studies2,3,4,56,57.

In our model, the rate of capillary fluid absorption may be somewhat overestimated by using the interstitial instead of sub-glycocalyx oncotic pressure, but, given the associated overestimation of the initial rate of filtration through the small pores (as described above), it is unlikely that these overestimations are significant on the whole-body level. As already mentioned, our overestimation of initial filtration rate through the small pores translates into underestimation of filtration through the large pores. If the initial filtration through the large pores was in fact higher, it would have been also higher for the whole dialysis session (becoming only slightly reduced due to decreasing capillary blood pressure), and hence the transcapillary absorption of fluid would need to be even larger than in our model to provide sufficient vascular refilling (note that the latter could not be achieved through the lymphatic system alone, given that the assumed flow of lymph was 8 L/day in normal conditions, raised to around 9.6 L/day in the pre-dialysis state of fluid overload, whereas the ultrafiltration in the dialyzer was 3 L over 4 h; it would not be possible even if capillary filtration ceased during HD, which is not the case for the large pore pathway25,26). Moreover, the glycocalyx-related phenomena are much less conspicuous in fenestrated capillaries58,59, and hence they would be somewhat less important on the whole-body level.

Overall, even if the Michel-Weinbaum model was appropriate for the assessment of the whole-body microvascular fluid exchange in humans (which is doubted by some researchers60,61), we believe that the possible inaccuracies resulting from ignoring the differences between the sub-glycocalyx fluid and the interstitial fluid in the equation describing the fluid exchange through the small pores (endothelial clefts and glycocalyx) would not invalidate our general observations with regard to Kr.

Blood priming procedure and steady-state conditions

Tabei et al. calculated Kr at each hour of HD and then extrapolated the results to the beginning of HD using exponential curves11. As shown by our simulations, this would have been a correct approach in the case with the priming fluid discarded at the beginning of the HD procedure (see Fig. 2). However, when the priming fluid is not discarded but infused to the patient (as done in the experiments by Tabei et al.), the overall shape of the Kr curve is markedly different in the early phase of HD, when Kr becomes transiently negative (see Fig. 4). Moreover, regardless of the priming procedure, after filling of the extracorporeal circuit with the patient’s blood, the body fluids are not in a steady state, which further distorts the calculation of Kr, which assumes that at time point 0 there is no vascular refilling. Tabei et al. waited 15 min after filling the extracorporeal circuit with blood in an attempt to obtain a steady state before starting ultrafiltration. However, according to our simulations, one would need around 1 h to reach steady-state conditions after the infusion of the priming saline (or at least 45 min to come close to the steady state).

Estimation of plasma volume changes

Another limitation of Kr is that to calculate it one needs to know the instantaneous rate of plasma volume changes in absolute terms. While this rate can be easily calculated within a mathematical model framework, obtaining real-world clinical data would require an accurate estimation of initial (pre-dialysis) plasma volume and reliable tracking of its subsequent relative changes. To this end, several approaches have been proposed. Schneditz et al. calculated the initial plasma volume from the pre-dialysis hematocrit and blood volume estimated from the lean body mass, and then used blood and plasma density measurements to calculate the relative plasma volume changes during HD2. They analysed a relatively short period of time (20 min) for which they assumed a constant rate of plasma volume changes. Tabei et al.11, on the other hand, calculated the initial blood volume from the total body weight and used hematocrit measurements to estimate relative plasma volume changes during HD to which they fitted an exponential curve, the derivative of which was used as the instantaneous rate of plasma volume changes (as done also by Pietribiasi et al.5). Both approaches are, however, not ideal—the first one neglecting the short-term differences in the rate of plasma volume changes (particularly high in the early phase of HD, when Kr should be estimated), and the second one requiring longer periods of measurements to derive an analytical form of the plasma volume curve (fitted to data). Moreover, the second approach assumes that the total volume of erythrocytes remains constant during HD, which may not necessarily be true, particularly with hyper- or hyponatremic dialysis fluid62,63. As for the estimation of the initial absolute blood volume, instead of using anthropometric formulae (likely inaccurate in fluid overloaded dialysis patients, as shown by Mitra et al. using indocyanine green64), one may use the blood dilution technique proposed more recently by Schneditz and Kron65,66, although this is again not unambiguous when done at the beginning of HD67.

Protein transport

Furthermore, the refilling coefficient defined by Tabei et al.11 assumes that proteins cannot pass through the capillary walls (σ = 1), which leads to overestimation of the effective plasma oncotic pressure in Eqs. (1) and (4). Moreover, HD may cause not only a change in the total concentration of plasma proteins but also may affect the composition of plasma proteins due to protein leakage through large capillary pores and protein refilling through small pores25. As a result, plasma oncotic pressure calculated from the total plasma proteins may lead to a further bias in the estimation of LpS by Kr. Therefore, when calculating the changes in plasma and interstitial oncotic pressures during HD one should track not the total protein content but various protein fractions, at least differentiating between albumin and non-albumin proteins that can have largely different reflection coefficients and permeability through the capillary walls, thus affecting the changes of the oncotic pressure.

Whole-body aggregation

A more general limitation of Kr is that it is meant to represent the whole-body refilling coefficient as a substitute of the aggregated hydraulic conductivity of all capillaries in the body (LpS). Capillaries in various tissues may, however, show different properties in terms of water permeability, which may change during HD to various extent, thus affecting the average value. Moreover, during HD the pattern of blood flow distribution among different microvascular beds may change, thus further affecting the aggregated LpS2, which would then change not because of changes in the circulating hormones or fluid status but simply because of an altered blood flow distribution. Note that such a change in blood flow distribution could affect Kr not only through a direct change in LpS but also through a potential change in the aggregated protein reflection coefficient.


Source link



Please enter your comment!
Please enter your name here

Most Popular

Recent Comments

%d bloggers like this: