Calculation of HA concentration in the interstitium

Our calculations assume that the HA we are measuring was located entirely in the intercellular interstitial spaces in vivo. This assumption is based on work carried out by Prehm (1984) when he demonstrated that HA is produced at the plasma membrane and extruded extracellularly. Since we now have estimates of the cell-free interstitial volume in rats of the same age and at the same levels within the inner medulla we can determine a local HA concentration. This will be in µg HA (mg wet wt of whole papillary slice)^-1 divided by the percentage cell-free IS (Table 3). HA concentrations were similarly measured at 1, 2 and 3 weeks of age in a separate experiment (Table 2). Tissue concentrations of HA showed an age-dependent increase over the 3 week period. The tendency for the HA concentration to fall to near undetectable levels about 2 mm from the tip was maintained at 3 weeks of age.

Calculation of the effective oncotic pressure of mixtures of HA and A

During our previous studies on interstitial fluid protein concentration we used Moyses (1986) estimation of the oncotic pressure of albumin (_A):

_A = 1·424 (2·5C_A + 0·13C_A² + 0·012C_A³) (in cmH₂O). (1)

When C_A is 0·91 ± 0·06 g dl^-1 (0·134 mmol l^-1) (MacPhee & Michel, 1995b), the oncotic pressure _A will be 3·69 cmH₂O. Note that C_A = 0·91 g dl^-1 is an estimate of the mean albumin concentration for the whole papilla; any tip to base gradients in albumin concentration will therefore not be evident. Secondly, C_A it is not a measure of total interstitital protein, only of free albumin, as an unknown quantity of albumin will remain associated with HA by electrostatic charges (Niedermeier, Gramling & Pigman, 1966; Peitzsch & Reed, 1992). Centrifugation at the low forces used is unlikely to release water or albumin closely associated within an HA gel matrix. Bound albumin will be constantly in flux with free albumin and so both will be part of the total pool of albumin in the papilla, as measured by other means. It is the free albumin, however, that will contribute to oncotic pressure across the AVR wall. In addition, other plasma proteins will be present in the IS to varying degrees depending on their reflection coefficients () at the AVR wall, which have not yet been measured. Their concentrations in the IS will be proportional to, but likely to be much lower than that in the plasma. Therefore, we can estimate the total protein concentration (C_P) to be equal to C_A/0·6 = 1·52 g dl^-1 (assuming A is 60 % of plasma protein). When C_P is 1·52 g dl^-1, _P will be 4·14 cmH₂O. In addition to plasma proteins, other interstitial proteins may be present, such as those associated with proteoglycans; their contribution is not known but is assumed here to be small.

The osmotic pressure () of HA (_HA) alone is:

_HA = 2·8C + 5·75 C ² = 0·595 mmHg, or 0·81 cmH₂O, (2)

as determined by Wiederhielm, Fox & Lee (1976), where C is the concentration in g per 100 ml (0·16 g (100 ml)^-1) and yields in mmHg.

Wiederhielm et al. (1976) modelled the interaction of HA and albumin and found that the exclusion effects of HA caused the osmotic pressure of a mixture of HA and albumin to be greater than the sum of the two parts. He then compared measured values for HA-A mixtures with his theoretical results and concluded that the data supported the conclusion that the mixture could be regarded as a two compartment system. A reasonable estimate of the partition coefficient () for A (i.e. the proportion of the space in an HA solution available for A) in an HA solution can be made using the approximation of Michel (1984); in brief,

= (e^-V_x)/(1-V_f), (3)

where V_f is the volume fraction of HA in the system and V_x is the volume from which A is excluded, i.e.:

V_x = V_f [(r_HA + r_A)/(r_HA)]², (4)

where r_HA is the radius of HA = 0·5 nm (HA is assumed to be cylindrical), and r_A is the radius of A = 3·8 nm (albumin is assumed to be an oblate ellipsoid). V_f for HA will equal the mean specific volume × concentration of HA = 0·65 × 0·16 g (100 ml)^-1 = 0·00104; and therefore will be 0·9269. The adjusted concentration of A in an HA matrix will be:

C_A/ = 0·91/0·9269 = 0·982 g dl^-1

for our minimal estimate of C_P (C_min), and

C_P/ = 1·52/0·9269 = 1·64

for our maximal estimate of (_max is 6·4 cmH₂O). A mixture of HA and protein will then have a total osmotic pressure somewhere between:

_HA + _min = 0·81 + 3·69 = 4·50 cmH₂O

and _HA + _max = 0·81 + 6·40 = 7·21 cmH₂O.

The total effective oncotic pressure (E) takes into account the reflection coefficients () to HA and A at the AVR wall. As the for HA is unknown but probably high (HA has a molecular weight close to 10⁶), a of 1 was assumed in these calculations (see Discussion). The reflection coefficient to albumin ( = 0·718) has been previously determined during reabsorption experiments in vivo (MacPhee & Michel, 1995b). The E_min will then equal the osmotic pressure (OP) of HA alone (0·81 × _HA = 0·81 cmH₂O) + the OP of A in the HA mixture (3·69 × _A = 2·65), i.e.:

E_min = 0·81 + 2·65 = 3·46 cmH₂O,

and

E_max = 0·81 + (7·21 × _A) = 0·81 + 5·18 = 6·0 cmH₂O.

Due to the high permeability of AVR to water and protein the reflection coefficients to salts and urea are assumed to be correspondingly low. Experiments performed by Pallone (1991) also suggest that osmotic gradients due to salt and urea gradients are negligible in the AVR.

	DISCUSSION

Top Abstract Introduction Methods Results Discussion References

Interstitial volumes

Estimates of interstitial volume have previously been made on adult male Sprague-Dawley rats (Knepper, Danielson, Saidel & Post, 1977) using 5 µm sections stained with Haematoxylin and Eosin and a similar point counting system. Interstitium, however, was defined as any space not occupied by either renal tubules or vasculature, and therefore did not distinguish between interstitial cells (IC) and cell-free interstitial space (IS). Knepper and colleagues found that the total interstitial space decreased from about 22 % (interpolated from his Fig. 1) near the papillary tip to about 10 %; this can be compared with the small decrease from about 40 to 35 % seen in the papilla of young rats in this study. Knepper's results also differ markedly in this respect from those of Pfaller (1982) who found that in adult Wister rats total interstitial volume decreased from 33 to 22 % over approximately the same distance. The similarity between the values seen in young Sprague-Dawley rats in this study and those of adult Wistar rats in Pfaller's suggests that the finding of larger interstitial volumes may be a result of the use of electron microscopy versus light microscopy, rather than the age or strain of the rats.

In the case of the young Sprague-Dawley rats, IS and IC were found to have a reciprocal relationship over the first 1400 µm from the tip, reaching a plateau thereafter. The young rats had double the volume of interstitial cells (IC) seen in adult rats, accounting for the difference in the total interstitial volumes. One explanation might be that during the first few weeks of life while the urinary concentrating mechanism is maturing, IC are especially active in production of HA and other glycosaminoglycans (GAGs), and are therefore either much larger or greater in number than in the adult rat. Since IC and IS can be calculated separately, it was therefore possible to calculate the local interstitial concentration of HA in the free interstitial space and hence estimate its local contribution to the total oncotic pressure of the interstitium.

It must also be asked what effect the sudden decrease in HA concentration near the base of the papilla (Table 4) might have on fluid and protein movement through the interstitium. Such a sharp decrease in the concentration of HA may result in a local decrease in albumin concentration in the IS favouring diffusion upwards (other things being equal), i.e. towards the outer medulla with its lymphatic drainage at the cortico-medullary junction. In addition, at this point albumin will no longer be bound to HA and this may alter the electrostatic charge gradients in the interstitium (Niedermeier et al. 1966; Peitzsch & Reed, 1992), and hence the diffusion rates through the interstitium. It would certainly be helpful to be able to dissect the albumin gradients as well as the HA gradients in the inner medulla.

Calculation of estimated osmotic pressure of HA and albumin mixtures

Since HA has been estimated to constitute 96 % of GAGs produced by the renal medullary interstitial cells (Pitcock et al. 1988), the minor contribution of other GAGs to the oncotic pressure () in the medullary interstitial matrix has been ignored in the calculations. The second main contributor to total interstitial will be the interstitial proteins. These consist of proteins carried into the interstitium by convection with water, and those diffusing into the interstitium through the walls of the vasa recta. The reflection coefficient for albumin (_A) has been estimated to be 0·59-0·78 in the AVR (and 0·718 during reabsorption experiments) of Sprague-Dawley rats (Pallone, 1992; MacPhee & Michel, 1995b), and close to 1 in the DVR (Pallone, 1992). Reflection coefficients for the larger macromolecules (e.g. fibrinogen and globulins) have not yet been measured in the AVR, but they are likely to be fairly close to 1 and therefore make only a minor contribution to interstitial oncotic pressure. Thus our value for _{HA + A} of between 3·46 and 6·0 cmH₂O may slightly underestimate the total oncotic pressure in the interstitium.

The quantification of albumin in the medullary interstitium itself has been difficult. Qualitative studies using radioisotopes (Lassen, Longley & Lilienfield, 1958), fluoresence (Pomerantz, Slotkoff & Lilienfield, 1965) and Evans Blue (Wilde & Vorburger, 1967) have demonstrated a considerable pool of extravascular albumin. In previous experiments the mean albumin concentration in the papillary tissue fluid was found to be approximately 0·91 % albumin (see MacPhee & Michel, 1995b). Levick (1994) has pointed out in the context of a discussion of albumin flux across the synovium that sieving effects may contribute to local accumulation of albumin on the abluminal surface, forming a barrier as fluid is drawn into the vessel through small 'pores' (of whatever type). This will tend to raise the local albumin concentration near the point of entry of fluid and so diminish the oncotic pressure gradient across the wall, with the result that hydrostatic pressure gradients will have a relatively greater effect. Using a different approach Pallone (1994) hypothesized that in hydropenic Munich- Wister rats the luminal contents of segments of AVR isolated by wax blocks would equilibrate rapidly with the interstitium; his estimate of interstitial protein concentration was 3·4 ± 0·5 g dl^-1.

Various estimates have also been made for the contribution of hydrostatic pressure to the balance of Starling forces across the AVR. Using our calculated E for HA + A in the IS (Table 4a) of 3·46 cmH₂O, this suggests that during our in vivo reabsorption experiments interstitial hydrostatic pressure (P_i) must have been about 1·4 cmH₂O. If E was as high as our maximal estimate (Table 4b) P_i becomes negative (-1·1), reducing the net inward driving force to 5·4 cmH₂O. The rhythmic contractions of the ureter may result in intermittent alterations in these values, and possibly large variations in pressure; unfortunately no measurements have been made with the renal pelvis intact due to technical difficulties.

Table 4. Solving for interstitial hydrostatic (P_i) and oncotic (_i) pressures

a) Solving for Pi using our calculated i (min: where Cp = [A] = 0·91 g dl-1)
Under conditions such that fluid flux = 0		Then under free flow conditions
Interstitium	AVR lumen	Interstitium	AVR lumen
Pi = ?	Pc = 12·7 *	Pi = 1·4	Pc = 6·0 *
Emin = 3·46	Ec = 17·6 * (5 % BSA)	Ei = 3·46	Ec = 18·5 * (plasma)
Pi will = 1·4 cmH2O		Net inward pressure = 9·3 cmH2O
b) Solving for Pi using our calculated i (max: where Cp = [A/0·6] = 1·52 g dl-1)
Under conditions such that fluid flux = 0		Then under free flow conditions
Interstitium	AVR lumen	Interstitium	AVR lumen
Pi = ?	Pc = 12·7 *	Pi = -1·1	Pc = 6·0 *
Emax = 6·0	Ec = 17·6 * (5 % BSA)	Emax = 6·0	Ec = 18·5 * (plasma)
Pi will = -1·1 cmH2O		Net inward pressure = 5·4 cmH2O
c) Solving for i using our experimentally determined Pi
Under conditions such that fluid flux = 0		Then under free flow conditions
Interstitium	AVR lumen	Interstitium	AVR lumen
Pi = 0·9 *	Pc = 12·7 *	Pi = 0·9 *	Pc = 6·0 *
Ei = ?	Ec = 17·6 * (5 % BSA)	Ei = 5·8	Ec = 18·5 * (plasma)
>Ei will = 5·8 cmH2O		>Net inward pressure = 7·6 cmH2O

Both of these estimates of P_i (i.e. -1·1 and 1·4) are lower than that of > 3·8 cmH₂O obtained by Pallone (1994) and considerably lower than that of 9·1 cmH₂O found by Garcia-Estañ & Roman (1989) using implanted capsules in adult Sprague-Dawley rats. In the latter case it was noted at the end of the experiment that the implanted capsules were actually located close to the cortico-medullary junction, and it may be that these values are close to cortical interstitial pressures. No experiments have been done using capsules in the inner medulla (i.e. the first 2 mm of the papillary tip). The low interstitial pressures found in this study are, however, consistent with values obtained by the authors using a totally different method, i.e. an estimate of 0·9 cmH₂O based on the difference between in vitro and in vivo closing pressures of the AVR (MacPhee & Michel, 1995a).

The balance of Starling forces across the AVR

During previous in vivo micropuncture experiments a segment of an AVR was perfused with Evans Blue-albumin solution with an oncotic pressure similar to plasma (MacPhee & Michel, 1995b), and the pressure in the micropipette supplying the albumin adjusted so that no blue dye was visible in the interstitium. At this balance point the intraluminal pressure will equal the sum of the interstitial hydrostatic and oncotic pressures (P_i and _i). Using our new estimate of _i from this study, we can then estimate P_i in vivo in the exposed papilla (see Table 4 and below). Knowing _i we can now estimate the net inward pressure for fluid reabsorption that will probably exist under normal (free flow) conditions in the same vessels. We can check these results for internal consistency by using our independent and experimentally determined estimate of P_i (MacPhee & Michel, 1995b), and solving for _i.

Our present data (Table 4) suggest that under free flow conditions in the AVR and using our estimate of E_i based on measured concentrations of HA and A there is a net inward driving force of between 5·4 and 9·3 cmH₂O available for fluid reabsorption. Using our previous experimental estimate of P_i of 0·91 cmH₂O (Table 4c), and solving for E_i, we obtained 5·8 cmH₂O, which would result in a net inward pressure of 7·6 cmH₂O in a free flow situation. The validity of these results is enhanced by noting that both our experimental estimates of what interstitial oncotic pressure must be in vivo, and our calculated oncotic pressure based on measured HA and albumin concentrations, yield internally consistent results (between 5·4 and 9·3, and 7·6 cmH₂O) in terms of net inward driving pressures for fluid flux in the AVR. A further internal consistency is found in that our estimate of E_i = 5·8 cmH₂O (from Table 4c), based on the experimentally determined P_i, could result from a C_P of 1·64 g dl^-1 (i.e. a C_A of 0·98), which is very close to our measured value of 0·91.

HA concentration changes with age and concentrating ability

The finding of an increasing HA concentration over the first 3 weeks postnatally which parallels the increasing mean urine osmolarity supports the idea of a relationship between HA content and concentrating ability. One interesting example of an association between HA and concentrating ability is found in the Brattleboro (BB) strain of rat which has a hereditary defect in concentrating ability. In the homozygous rat (DI/DI), antidiuretic hormone (ADH) is very low, associated with greatly reduced levels of interstitial GAGs (< 20 % control) in the papillary interstitium, as determined by staining of sections with Azur Blue dyes (McAuliffe, 1980). Another change noted in BB rats was a decrease in size and presence of cell processes of type I interstitial cells and an increase in type II cells. McAuliffe has suggested that lack of stimulation of the IC by ADH in BB rats may lead to decreased production of GAGs, and that reduced levels of GAGs (with their high negative charge) may alter the tip to base gradients of small solutes such as Na⁺ and so alter interstitial osmolality and hence the concentrating mechanism. In contrast to the mechanism proposed by Koefoed & Knudsen (1961), i.e. a driving force generated by the continual turnover of HA, it may be that it is the concentration of HA present in the interstitium at any given place and time that determines, in conjunction with albumin etc., the total interstitial colloid oncotic pressure and hence driving force for fluid reabsorption and therefore the efficiency of the concentrating mechanism. Certainly, a role for the turnover rate may be important and needs to be investigated further, not only in normal animals but in those with concentrating defects. Another potential role for HA is in the endothelial cell junctions (Aukland et al. 1994), as well as in the fenestrae or the glycocalyx, where the shrinking or swelling of GAGs may influence the permeability of the capillary wall.

In summary, new estimates of medullary interstitial volume and of inner medullary interstitial HA content have been made in age-matched rats to facilitate calculations of local papillary hyaluronan concentrations. The EM study suggests that interstitial cells and interstitial space have a reciprocal relationship over the first 1800 µm of the rat papillary tip, such that the total interstitial volume is kept relatively constant (35-40 %), along with the hyaluronan concentration (0·16 g dl^-1). HA concentration tends to drop off sharply to near zero between 1600 and 1800 µm from the tip in rats of 1, 2, and 3 weeks of age. Over the first 3 weeks of life HA concentrations in the tip region are increasing slowly in parallel with the increase in mean urine osmolarities. Knowing the HA concentration, we can now estimate its contribution alone, and in combination with serum albumin, to the total oncotic pressure of the inner medullary interstitium. As a result, we estimate, based on our calculated values for HA, that the effective oncotic pressure of the interstitial fluid is between 3·46 and 6·0 cmH₂O, resulting in vivo in a net inward force of 3·46-9·3 cmH₂O available for driving fluid reabsorption into the AVR.

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Acknowledgements

This project was partially supported by The Wellcome Trust (grant reference 18741/1.27). The author would like to thank Professors C. Charles Michel and Roger Green for helpful comments on the manuscript.

Author's email address

P. J. MacPhee: macphee{at}omega.bg

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