Regulation of amniotic fluid volume: mathematical model based on intramembranous transport mechanisms

Abstract

Experimentation in late-gestation fetal sheep has suggested that regulation of amniotic fluid (AF) volume occurs primarily by modulating the rate of intramembranous transport of water and solutes across the amnion into underlying fetal blood vessels. In order to gain insight into intramembranous transport mechanisms, we developed a computer model that allows simulation of experimentally measured changes in AF volume and composition over time. The model included fetal urine excretion and lung liquid secretion as inflows into the amniotic compartment plus fetal swallowing and intramembranous absorption as outflows. By using experimental flows and solute concentrations for urine, lung liquid, and swallowed fluid in combination with the passive and active transport mechanisms of the intramembranous pathway, we simulated AF responses to basal conditions, intra-amniotic fluid infusions, fetal intravascular infusions, urine replacement, and tracheoesophageal occlusion. The experimental data are consistent with four intramembranous transport mechanisms acting in concert: 1) an active unidirectional bulk transport of AF with all dissolved solutes out of AF into fetal blood presumably by vesicles; 2) passive bidirectional diffusion of solutes, such as sodium and chloride, between fetal blood and AF; 3) passive bidirectional water movement between AF and fetal blood; and 4) unidirectional transport of lactate into the AF. Further, only unidirectional bulk transport is dynamically regulated. The simulations also identified areas for future study: 1) identifying intramembranous stimulators and inhibitors, 2) determining the semipermeability characteristics of the intramembranous pathway, and 3) characterizing the vesicles that are the primary mediators of intramembranous transport.

presently, the mechanisms that regulate amniotic fluid volume (AFV) are not well understood in spite of multiple unique insights over the last 25 years. Most of these insights have been derived from studies in late gestation, chronically catheterized fetal sheep. A key observation is that there are two primary flows into and two primary flows out of the amniotic compartment in late gestation (8, 13, 14, 21, 39, 40, 58). The inflows are fetal urine and lung liquid secretion, whereas fetal swallowing of amniotic fluid (AF) and intramembranous (IM) absorption are the outflows. In primates, including humans, intramembranous absorption (IMA) refers to the transfer of amniotic water and solutes across the amnion and into the underlying vasculature in the fetal surface of the placenta (41, 60). In ungulates, including sheep, AF water and solutes are transferred across the amnion primarily into the vascularized chorion (11, 37).

A second key observation is that IM transport includes both passive bidirectional water and solute fluxes plus an active unidirectional mechanism that transport AF in bulk across the amnion into fetal blood. Further, under a variety of experimental conditions, only the unidirectional bulk IM transport appears to be regulated, while passive fluxes across the IM pathway are unaltered (5, 15, 16, 25, 29, 30, 31, 57, 62). Although active and passive IM transport mechanisms have been proposed (5, 16, 25, 34), the transport characteristics of the IM pathway are not well understood, and it is not known whether such mechanisms are adequate to explain experimentally measured AFVs and solute concentrations over time. Thus, the first objective of this study was to develop a computer model of the regulation of AFV based on proposed characteristics of IM transport that allows simulation of AF dynamics in late-gestation fetal sheep. This model would provide insight into the various components of IMA and allow evaluation of the importance of their contribution to the regulation of AFV. A second objective was to identify model shortfalls in order to define areas of research that would best advance the current understanding of AFV regulation.

Previous Computer Models

Previous studies have presented computer simulations of fluid balance in the fetus. In 1978, on the basis of limited data and a variety of assumptions regarding placental transport mechanisms, Wilbur et al. (64) concluded that fluid acquisition in the human fetus is determined primarily by small transplacental concentration differences of low-molecular-weight solutes. A decade later, Faber and Anderson (28), using similar techniques, concluded that fluid acquisition by the ovine fetus is limited by a low placental transport capacity for electrolytes from mother to fetus. However, these two modeling studies examined partition of fluid between mother and conceptus but did not consider partition of fluid between fetus and AF. Further, the studies did not take into account the experimental observations that large amounts of electrolytes and water are readily transferred from mother to fetus (26, 35, 66, 69) and from fetus to the mother (9, 30, 55) with little change in fetal osmolality or solute concentrations.

Subsequent computer modeling studies focused on AFV regulation using data and transport concepts partly derived from fetal sheep to simulate changes in AFV across gestation in human fetuses. Mann et al. (51) assumed that only water crossed the IM pathway in spite of studies showing rapid diffusion of solutes, such as sodium, potassium, chloride, and urea across the isolated human and sheep amnion (42, 49, 67). Curran et al. (23) expanded that model by allowing sodium to transfer intramembranously and made conclusions regarding the contribution of swallowing vs. IMA to the regulation of AFV. However, neither of these studies included what has subsequently been shown to be the largest component of IM transport, i.e., the unidirectional bulk transfer of AF together with all dissolved solutes out of the amniotic compartment and into fetal blood. That transport is presumably mediated by vesicular transcytosis (5, 16, 25, 34). However, IMA rates have not been determined in any species other than sheep so the validity of the simulations and their relevance to the regulation of AFV in humans and other species cannot be determined.

In the present study, fetal sheep data that quantified AFV and the IM transfer of both water and solutes was used for model development. All data were collected in our laboratories over the past 25 years. These data allow comprehensive testing of AFV regulation based on hypothesized IM transport mechanisms.

Model Basics

In late-gestation fetal sheep after skin keratinization in the second trimester, transcutaneous exchange between fetal blood and AF is absent. Transmembranous exchange between AF and maternal blood within the uterine wall is negligibly low, even for small molecules such as urea and water (4, 37, 61). In addition, fetal oral-nasal secretions appear to be small relative to other amniotic flows (8). Thus, transcutaneous exchange, transmembranous exchange and secretions from the fetal head were not included in model development. These exclusions leave four primary amniotic flows: fetal urine excretion, lung liquid secretion, swallowing of AF, and IMA (8, 13, 14, 16, 21, 34, 39, 40, 58). As the first three of these can be experimentally measured, the purpose of the computer simulations was to approximate the transport characteristics of the IM pathway that are consistent with experimentally determined AFVs and solute concentrations over time. This same computer model also can be used without input of experimental data to simulate AF volume and compositional responses to a variety of conditions.

Intramembranous Absorption Components

Volume flow.

Although it had been suggested that transport occurs across the amnion into and out of AF (1, 47, 61), the first recognition that IM transport contributes importantly to the regulation of AFV was in 1989 with the observation that warm water injected into the AF appeared in the fetal circulation more quickly than could be explained by fetal swallowing. In fact, absorption was more rapid if swallowing of AF was prevented by esophageal ligation (37). Thus, a component of IM volume absorption (IMA) is passive and its rate is dependent on the osmolality (osm) difference between fetal blood (fb) and AF (af):

$$\mathrm{I}\mathrm{M}{\mathrm{A}}_{\mathrm{O}\mathrm{S}\mathrm{M}}=K_{\mathrm{f}\mathrm{c}}\times \left(\mathrm{O}\mathrm{S}{\mathrm{M}}_{\mathrm{f}\mathrm{b}}-\mathrm{O}\mathrm{S}{\mathrm{M}}_{\mathrm{a}\mathrm{f}}\right)$$ (1)

where K_fc is the filtration coefficient (fc) of the IM pathway. K_fc was calculated from measured osmolalities and passive IM volume flow rate (described below). As membrane water channels do not allow passage of most osmotically relevant solutes except urea (50), the reflection coefficient (σ) was assumed equal to unity, with the result that there is little solute drag contribution of passive IM water flow to IM transport of solutes. Although it has been suggested that water may pass through tight junctions between amnion cells in mice (46), there are no data suggesting that tight junctions contribute to the regulation of AFV in fetal sheep. If tight junctions allow water but not solute passage, they would be indistinguishable from water channels in in vivo studies.

In addition to the osmotic component, IM volume absorption has a major unidirectional component that occurs against hydrostatic differences, against concentration differences, and in the absence of osmotic differences (2, 5, 16, 25, 30, 34). This active transport component is presumed to be a vesicular transcytotic pathway that moves AF in bulk together with dissolved solutes from the AF outward across the amnion into fetal blood (2, 5, 16, 30, 34). Thus, total (tot) IM volume absorption rate is the sum of osmotically induced passive plus active vesicular (ves) transports:

$${\text{IMA}}_{\text{tot}}={\text{IMA}}_{\text{OSM}}+{\text{IMA}}_{\text{ves}}$$ (2)

In order to calculate a value for the IM filtration coefficient (1), the osmotic contribution to total IM volume flow is needed. The simulations discussed below suggested that the osmotically mediated component averages 15% of total flow under basal conditions. With this assumption, the IM filtration coefficient K_fc was calculated from experimentally determined osmolalities and IMA_tot using Eqs. 1 and 2.

Solute flow.

Similar to water transport, the IM flux (F) of individual solutes has at least two components: a passive component due to concentration (C) differences between AF and fetal blood plus an active component due to bulk vesicular transport (2, 5, 15, 34):

$$F_{\mathrm{s}}=P_{\mathrm{s}}\times \left(C_{\mathrm{s}\mathrm{,}\mathrm{a}\mathrm{f}}-C_{\mathrm{s}\mathrm{,}\mathrm{f}\mathrm{b}}\right)+\mathrm{I}\mathrm{M}{\mathrm{A}}_{\mathrm{v}\mathrm{e}\mathrm{s}}\times C_{\mathrm{s}\mathrm{,}\mathrm{a}\mathrm{f}}$$ (3)

where P_s is a passive permeability coefficient of solute s. Note that the unidirectional component of solute transport is assumed to nonselectively transport amniotic water with all dissolved solutes at AF concentrations, including large molecules such as albumin (30, 34, 52), irrespective of AF solute concentrations.

Experimental Intramembranous Fluxes

IM volume and solute fluxes cannot be measured directly under experimental conditions but instead have been calculated from experimentally determined values of the initial (i) and final (f) AFVs plus time (t) integrated amniotic inflows and outflows (2, 5, 15, 34). The basic equation for calculating total IM volume absorption rate can be derived by rearrangement of the following volume mass balance equation:

$$\mathrm{A}\mathrm{F}{\mathrm{V}}_{\mathrm{f}}\mathrm{=}\mathrm{A}\mathrm{F}{\mathrm{V}}_{\mathrm{i}}\mathrm{+}{\displaystyle \mathrm{\int }\mathrm{\left(}\mathrm{U}\mathrm{r}\mathrm{F}\mathrm{l}\mathrm{o}\mathrm{+}\mathrm{L}\mathrm{u}\mathrm{F}\mathrm{l}\mathrm{o}\mathrm{-}\mathrm{S}\mathrm{w}\mathrm{F}\mathrm{l}\mathrm{o}\mathrm{-}\mathrm{I}\mathrm{M}{\mathrm{A}}_{\mathrm{t}\mathrm{o}\mathrm{t}}\mathrm{\right)}\mathrm{d}\mathit{t}}$$ (4)

where UrFlo is the urine flow rate, LuFlo is the lung liquid secretion rate, and SwFlo is the volume swallowing rate. These flows are typically measured over a period of days. In our recent studies (5, 19, 34, 57), the fetal trachea was catheterized so that LuFlo could be accurately determined. The catheterization allows all lung secretions to continuously enter and mix with the AF. In the model, all swallowed fluid was assumed to be AF whether or not the trachea was catheterized. Normally, only half of lung secretions enter the AF (12). The remainder is swallowed as it exits the trachea, with 12%–18% of swallowed fluid being lung liquid and 82%–88% is AF in late-gestation ovine fetuses with an intact (noncatheterized) trachea (12).

Similar to using Eq. 4 for calculation of the IM volume absorption rate, the IM flux of solute s (F_s) was calculated following rearrangement of the solute mass balance equation:

$$\mathrm{A}\mathrm{F}{\mathrm{V}}_{\mathrm{f}}\times C_{\mathrm{s}\mathrm{,}\mathrm{f}}=\mathrm{A}\mathrm{F}{\mathrm{V}}_{\mathrm{i}}\times C_{\mathrm{s}\mathrm{,}\mathrm{i}}+{\displaystyle \int \left(\mathrm{U}\mathrm{r}\mathrm{F}\mathrm{l}\mathrm{o}\times C_{\mathrm{s}\mathrm{,}\mathrm{u}\mathrm{r}}+\mathrm{L}\mathrm{u}\mathrm{F}\mathrm{l}\mathrm{o}\times C_{\mathrm{s}\mathrm{,}\mathrm{L}\mathrm{u}}-\mathrm{S}\mathrm{w}\mathrm{F}\mathrm{l}\mathrm{o}\times C_{\mathrm{s}\mathrm{,}\mathrm{a}\mathrm{f}}-{\mathit{F}}_{\mathrm{s}}\right)\mathrm{d}t}$$ (5)

where AF solute mass = volume × concentration. Note that the IM volume absorption rates (IMA_tot, IMA_ves, and IMA_osm) are not used in the calculation of IM solute flux F_s.

Intramembranous Permeability Coefficients

At the beginning of each simulation, the model was initialized under control conditions by calculating permeability coefficients, the IM filtration coefficient, and transport constants. By starting with steady-state conditions and calculating F_s using Eq. 5, all values in Eq. 3 can be determined experimentally except individual solute permeabilities and IMA_ves. By assuming IMA_ves = 0.85 × IMA_tot under basal conditions (discussed below), permeability coefficients for each solute can be calculated with Eq. 3 using initial solute concentrations (Table 1), AFV, and amniotic flow rates (Table 2). Table 3 lists mean permeabilities for the simulations discussed below. These can be compared with permeabilities estimated experimentally from the regression relationship between IM volume flux and IM solute flux (Table 3).

Table 1.

Initial solute concentrations and osmolalities used in the model when experimental values were not available

Solute	Fetal Blood	Amniotic Fluid	Fetal Urine	Lung Liquid
Sodium	137	117	65	137
Potassium	4.4	7	10	4.4
Chloride	103	78	20	147
Calcium	1.4	1	0.4	0.5
Glucose	1.2	0.2	0.2	0.1
Lactate	1.2	2.2	0.3	0.2
Bicarbonate	28	14	8	5
Urea	7.9	10.7	14.3	7.1
Other	31.7	43.6	71.3	14.5
Osmolality	300	260	180	300

Values represent average means from several of studies in late-gestation fetal sheep (5, 17, 34). Urea and “other” concentrations are described in the text. Units are given as millmoles per liter for all solutes. Osmolality units are given as mosmol/kg H₂O.

Table 2.

Initial amniotic inflow and outflow rates used in the model when experimental values were not available

Variable	Flow Rate, ml/min	Flow Rate, ml/day
Urine production	0.8	1152
Lung liquid secretion	0.25	360
Swallowing	0.4	576
Intramembranous absorption	0.65	936
Unidirectional bulk flow	0.55	792
Water channel flow	0.1	144

Data are average values from several studies in late-gestation fetal sheep (5, 17, 34). Simulations used flows in milliliters per minute, whereas flows in milliliters per day provide a broader perspective relative to amniotic fluid volume regulation. Intramembranous absorption rate is the sum of unidirectional bulk and water channel flows (see text).

Table 3.

Solute permeabilities, transport constants, and filtration coefficients of the intramembranous pathway in simulations described in text

Solute	Model Permeability/Filtration Coefficient	Model Transport Constant, μmol/min	Literature Permeability, (Reference)
Sodium	1.37 ± 0.29		0.67 (16)
Potassium	1.08 ± 0.29	9.10 ± 2.16	2.89 (34)
Cchloride	2.23 ± 0.38		1.26 (16)
			4.08 (34)
Calcium	1.07 ± 0.09		0.20 (16)
Glucose	0.24 ± 0.12
Lactate	0.59 ± 0.09	2.40 ± 0.49	3.08 (34)
Bicarbonate	0.40 ± 0.09		0.15 (16)
Urea	0.96 ± 0.26
Other	0.63 ± 0.19
Water	0.00225 ± 0.00028		0.00137 (38)

Values are expressed as means ± SE for simulations 4–10; n = 7, except n = 2 for potassium transport constant. Solute permeability units are milliliters per minute; water filtration coefficient units are given as milliliters per minute per mmHg; transport constant units are given as micromoles per minute.

Calculation of IM lactate permeability presented a unique challenge. IM lactate permeability calculated from Eq. 3 was negative in every case. Therefore, lactate permeability was assumed to equal one fourth of the chloride permeability (discussed below). From this permeability and IM lactate fluxes calculated with Eq. 5, a transport constant for lactate was calculated from initial steady-state conditions and added to Eq. 3, so that the lactate fluxes calculated with Eqs. 3 and 5 were equal. This lactate transport constant was assumed to be constant during the simulations, and values are shown in Table 3. In two simulations, AF potassium behaved similarly and a transport constant was added to Eq. 3 for potassium.

Experimental Values as Input to the Model

At the beginning of each simulation, we used either the measured values of solute concentrations or, when not available, mean values from previous studies (Table 1) for initialization. Solute concentrations are typically measured with automated analyzers. In our laboratories, this includes seven solutes: sodium, potassium, chloride, calcium, glucose, lactate, and bicarbonate. Osmolalities, however, are only occasionally measured. In our laboratories, osmolalities are measured on samples at the time of collection. Important contributors to osmolalities are the solutes urea and fructose (in sheep) because of their relatively high concentrations. Urea concentrations in sheep have rarely been reported, and fructose concentrations have not been reported in dynamic studies of AFV regulation over time in fetal sheep. For the simulations, we used mean fetal blood, urine, and AF urea concentrations (Table 1) from experimental studies (53, 59, 70). Fructose plus other solutes present in AF were included in the model as a lumped (combined) unknown 8th solute concentration (ukn) calculated from measured osmolality (Osm) and measured known (kn) concentrations:

$$C_{\mathrm{u}\mathrm{n}\mathrm{k}}=\mathrm{O}\mathrm{s}\mathrm{m}/0.95-{\displaystyle \sum {\mathit{C}}_{\mathrm{k}\mathrm{n}}}$$ (6)

The constant 0.95 was used to account for activity coefficients less than unity for solutes at physiological concentrations.

Fetal Flow Dependencies

We used fetal urine flow and composition under experimental conditions as input to the model when available. If not available, then urine flow rate and composition were calculated on the basis of the observation that fetal urine flow increases in response to intra-amniotic fluid infusions (15, 19, 36, 57). For this urine flow rate calculation, excess fluid within the fetal body (ExFl in milliliters) was calculated from the volume mass balance equation (Eq. 4) above. Urine flow rate was then calculated from the initial urine flow rate as

$$\mathrm{U}\mathrm{r}\mathrm{F}\mathrm{l}\mathrm{o}=\mathrm{U}\mathrm{r}\mathrm{F}\mathrm{l}{\mathrm{o}}_{\mathrm{i}}\mathrm{\times }\mathrm{\left(}\mathrm{1}\mathrm{+}\mathrm{0.0005}\mathrm{\times }\mathrm{E}\mathrm{x}\mathrm{F}\mathrm{l}\mathrm{\right)}$$ (7)

Further, in the experiments, most of the intra-amniotically infused fluid was gradually transferred from the fetal circulation across the placenta into the maternal circulation (9, 15, 36, 57). To adjust for fluid loss from the fetal to maternal compartment, excess fetal fluid was assumed to be lost to the mother at a rate of 1% per minute and vice versa.

Fetal swallowing during experimental periods was calculated on the basis of the observation that daily swallowed volume depended on experimental conditions. In normoxic fetuses, swallowing increased as AFV was elevated (9, 15, 18, 20, 36, 57, 63). For the computer simulations, we used a function curve from our recent swallowing study (20) that relates daily swallowed volume to AFV over a wide range of experimental AFVs:

$$\mathrm{S}\mathrm{w}\mathrm{F}\mathrm{l}\mathrm{o}\mathrm{=}\mathrm{S}\mathrm{w}\mathrm{F}\mathrm{l}{\mathrm{o}}_{\mathrm{i}}\mathrm{\times }\mathrm{2}\mathrm{\times }\mathrm{\left(}\mathrm{A}\mathrm{F}\mathrm{V}\mathrm{-}\mathrm{292}\mathrm{\right)}\mathrm{/}\mathrm{\left[}\mathrm{A}\mathrm{F}\mathrm{V}\mathrm{-}\mathrm{292}\mathrm{+}\mathrm{\left(}\mathrm{A}\mathrm{F}{\mathrm{V}}_{\mathrm{i}}\mathrm{-}\mathrm{292}\mathrm{\right)}\mathrm{\right]}$$ (8)

The value 292 represents the AFV at or below which swallowing is zero, and SwFlo_i is the initial volume swallowing rate measured under control conditions.

In the model, lung liquid secretion rate was held constant. This was based on our experimental findings that lung liquid production rate did not undergo significant changes over a range of experimental conditions (5, 19, 57).

In order to stimulate various experimental conditions, IM volume absorption rate and IM solute fluxes were calculated from Eqs. 1–3 and the interactions between IM stimulators and inhibitors.

Stimulators and Inhibitors of Intramembranous Absorption

In sheep, fetal urine contains a stimulator of the active, bulk, unidirectional component of IMA (5). Further, ovine AF contains a nonrenal, nonpulmonary inhibitor of IMA, presumably secreted by the fetal membranes (19). For the simulations, we initially assumed that the stimulator (st) and inhibitor (in) are produced at constant rates and that they are cleared from the AF by fetal swallowing and by the vesicular component of IMA. Their initial AF concentrations were set to a value of unity. Their AF concentrations over time were calculated from a mass balance equation using their production rates, clearance rates, and changes in AF volume. A question central to model development, but little explored, is how the stimulator and inhibitor interact to produce their combined effects on unidirectional IMA transport (19). Their combined effects were set as a function of their concentrations and the initial IMA_ves:

$$\text{I}\text{M}{\text{A}}_{ves}=\text{I}\text{M}{\text{A}}_{ves,i}\times \left(1+C_{st}/C_{in}\right)/2$$ (9)

With IMA_osm = 15% of total flow under basal conditions, this equation approximates the observation that IMA_tot rate was reduced by an average of 50% when fetal urine was replaced with lactated Ringer solution (5). We initially used the multiplier (1 + C_st/C_in)/2 in Eq. 9 for the first five simulations described below but found in later simulations that the IMA_ves,i multiplier (1 + 2 × C_in/C_st)/3 better represented the experimental results.

Methodological Issues

In chronically catheterized fetal sheep, AFV most commonly is measured either with indicator dilution techniques or by drainage. In late-gestation, ovine fetuses with indicator dilution, AFV averages ∼800–900 ml when measured in fetuses with (17) and without (63) urachal ligation. When the indicator dilution and drainage techniques are used in the same animal on the same day, the resulting volumes were linearly related and highly correlated (r = 0.99). However, the indicator volume averaged 150 ml higher than the drainage volume (16). Four physical factors contribute to this difference: 1) With drainage, even though the fetus appears vacuum-packed at autopsy, there is fluid in the cracks and crevices between legs, body and under the neck that is measured with indicator techniques but not with drainage. 2) Late-gestation ovine fetuses are wooly and the wool traps AF that is not removed with drainage. 3) The tips of the amniotic catheters, typically 3–4 per fetus, used in the drainage studies are covered with multiperforated 10–20-ml plastic vials to prevent catheter blockage (30, 71); their volume is included in the indicator dilution but not drainage volumes. 4) In the study that compared the two methods, multiple large-diameter, long catheters were used. Following indicator injection plus withdrawal and reinjection through the catheters to promote mixing, the catheter volume would be included in the indicator, but not drainage volume. To account for the difference in AFVs measured with the two methods in the model, we assumed the difference equaled 100 ml when standard-diameter catheters are used. When simulating values measured with indicator dilution, the initial AFV was assumed to be 800 or 900 ml (15, 63) when measured volumes were not available. When simulating AFVs determined by drainage, the actual AFV was assumed to be 100 ml above the drainage volume but only (AFV − 100) ml was displayed by the model.

Computer Simulations

In order to simulate AF dynamics, the model was initialized by calculating permeability, filtration, and transport constants, as described above. Then the above equations were integrated over time using a computer. We used simple Euler integration techniques with a time increment (dt) of 1 min.

Simulation 1: sensitivity analysis.

A sensitivity analysis was conducted to determine the extent to which variation in each input or output from the AF compartment would alter AFV. As an example, Fig. 1A shows the simulated changes in AFV following a 50% increase or decrease in swallowing using the above equations. This was accomplished by multiplying the swallowing that would otherwise occur by either 0.5 or 1.5 without altering the AFV-induced changes in swallowing rate (Eq. 8). Note that, for increased swallowing, AFV reached a new steady state in 2–3 days. The new steady state was achieved largely because swallowing decreased as AFV was reduced. In contrast, with a 50% decrease in swallowing, AFV continued to increase over several days (44). This occurred because the increase in swallowing due to AFV expansion together with the AFV-induced changes in IMA and urine flow was insufficient to stabilize the volume.

Fig. 1.

A: simulated changes in amniotic fluid volume (solid lines) over 9 days following either a 50% increase or 50% decrease in the volume swallowing rate. Dashed line, initial amniotic fluid volume (800 ml). Dotted vertical line, time at which change in swallowing occurred. See text. B: sensitivity analysis of the effects on amniotic fluid volume 9 days after changing individual amniotic inflows or outflows. See text.

The effects on AFV after 9 days of altering each of the amniotic inflows and outflows over the range of −100% to +100% of their initial values are shown by the sensitivity analysis in Fig. 1B. There are several noteworthy observations. First, alterations in either the passive IM permeability of all solutes (labeled Perm in Fig. 1B) or conductance of water channels (W Chan) had the least effect on AFV. Eliminating flow through water channels increased AFV by less than 25%, while eliminating passive solute conductance decreased AFV by less than 25%. The decrease occurred because, with sodium and chloride no longer diffusing into the AF from fetal blood, AF osmolality decreased and passive IMA increased. Second, as shown in Fig. 1B, changes in swallowing, urine flow, lung liquid secretion, or vesicular unidirectional transport each had large effects on AFV. Third, as illustrated in Fig. 1A, during the early stages of model development, AFV typically did not stabilize over 9 days whenever AFV was greater than ∼1,500 ml because there was either insufficient or no compensation by the other flows. Fourth, the sensitivity analysis is not unique because it is dependent on each of the assumptions made in model development. For example, the curved dotted line in Fig. 1B shows that the changes in AFV due to variations in urine flow rate were much larger when the renal IM stimulator was produced at a constant rate (labeled urine w/o in the figure) than when production of the stimulator increased in direct proportion to urine flow rate (labeled urine w/ in the figure).

Simulation 2: fetus-to-fetus variations in AFV.

AFV and IMA rate vary in individual fetuses under control conditions. Figure 2 compares experimental AFVs and IMA rates (solid circles) with simulated values (curved line) 2 days after a step change in the vesicular component of IMA. The curved line was calculated by starting with mean experimental values during the control conditions and varying the rate of vesicular transport by multiplying IMA_ves by a constant (varied from 0 to 2 to represent decreases and increases in IMA_ves rate). Production of the renal IM stimulator and AF inhibitor was constant, while swallowing (Eq. 8) and urine flow (Eq. 7) varied as AFV and fetal fluid balance changed. We refer to this negative relationship between AFV and IMA rate as the AFV function curve. There are two important conclusions from the simulation results shown in Fig. 2: first, variations in IMA rate appear to be a major contributor to fetus-to-fetus differences in AFV; second, the changes in AFV, which occur during fetal urine replacement (open circles in Fig. 2), are consistent with the concept that only the unidirectional component of IMA was altered during fetal urine replacement.

Fig. 2.

Amniotic fluid volume and intramembranous absorption (IMA) rate in individual fetuses during control conditions (●) and during isovolumic fetal urine replacement (○). Experimental data from Anderson et al. (5). Dashed line is bivariate regression line. Curved solid line is the amniotic fluid volume function curve and shows model values produced by varying the vesicular component of intramembranous absorption. IMA represents mean values over 2 days and amniotic fluid volume (AFV) is the volume after 2 days of altered IMA rate.

Simulation 3: IM sodium fluxes.

In addition to volume fluxes, solutes rapidly cross the IM pathway. Figure 3 compares the stimulated IM flux of sodium with experimental fluxes under the two experimental conditions of Fig. 2, i.e., during control conditions and during isovolumic replacement of fetal urine with lactated Ringer solution (5). Stimulations were initialized with mean experimental AF volume, inflows, outflows, and solute concentrations during the control period. Then, the rate of vesicular transport was varied over the range of 0% to 200% of normal for a 2-day period, during which fetal urine either entered the AF or was replaced with lactated Ringer solution. Passive membrane permeability was unchanged in the model. An important conclusion from the comparison of simulated and experimental sodium flux data is that the experimental variations in IM sodium flux under both conditions are due to alterations in bulk IM absorption, while passive IM fluxes were not altered. Note that, although the lines in Fig. 3 are in agreement with the experimental data, the simulated values do not cover the same range as the experimental data. This occurs because individual fetuses are not adequately represented by mean values from all fetuses combined. This is exemplified by the observations that each fetus has unique function curves relating flows and volumes (19, 31).

Fig. 3.

Intramembranous sodium fluxes as a function of intramembranous volume absorption rate. Solid lines are simulated values and solid circles (●) are experimental values in individual fetuses (5). The lines were generated by starting with mean experimental values during control conditions and then altering intramembranous vesicular transport from 0% to 200% of the initial value for 2 days during which time fetal urine either entered the AF (control) or was replaced with lactated Ringer solution. Dashed line is zero net flux.

Simulation 4: intra-amniotic infusion of water.

Figure 4 compares a computer simulation with experimental data (38) of an intra-amniotic infusion of warm distilled water at a rate of 6 ml/min for 6 h. The initial AFV was assumed to be 800 ml. During the simulations, the osmotic component of IMA was varied from 0% to 40% of total IMA. A value of 15% most closely matched the experimental changes over the first 2 h of the water infusion (Fig. 4). Higher or lower initial water channel flow reduced correspondence between simulated and experimental changes in this and other simulations. With the osmotic component of IMA above 40%, solute permeabilities could not be calculated because there was insufficient IM solute flux to balance Eqs. 3 and 5 under initial conditions.

Fig. 4.

Comparison of simulated amniotic fluid osmolality, sodium concentration (top), and chloride concentration (middle) with experimental data during intra-amniotic water infusion at 6 ml/min for 6 h. The dotted lines show initial simulations, assuming the intramembranous filtration coefficient was constant. The solid lines are simulated values, assuming that the filtration coefficient increased as amniotic osmolality (bottom) decreased. Experimental data are solid circles (means ± SE) from Gilbert and Brace (38).

The dotted lines in Fig. 4 show the initial simulation with the IM filtration coefficient (K_fc) constant at the value 0.00363 ml·min⁻¹·kg⁻¹ water. Comparison of the simulated and experimental data beyond 2 h shows that more of the infused water was leaving the amniotic compartment than represented by the dotted line. As low osmolality has been reported to increase aquaporin gene expression in the amnion (56), we adjusted the IM filtration coefficient to account for the increase in gene expression and achieve a closer agreement between the computer simulations and experimental data using the formula: K_fc = K_fc,i × [1 − 0.03 × (Osm_af − Osm_af,i)]. The solid lines in Fig. 4 show the resulting simulations.

In Fig. 4, AF solute concentrations and osmolality approach a steady state after 6 h of water infusion in agreement with the observational data (38). However, AFV (not shown) continued to increase in contrast to what was assumed in the original study.

Simulation 5: tracheoesophageal shunt.

A surgically placed tracheoesophageal shunt diverted fetal lung liquid away from the AF into the stomach and prevented the fetus from swallowing AF. With the shunt in place, fetal urine continued to enter the AF and AFV increased progressively at an average rate of 240 ml/day to average 3,025 ml after 9 days. Further, although significantly increased from its initial value, IMA rate remained low, averaging 0.34 ml/min or 489 ± ml/day, in spite of the large increase in AFV (44).

These experimental observations were difficult to simulate. The fetus was not under steady-state conditions, as required for model initialization at the time of placement of the shunt, but rather was undergoing surgery. As an approximation, we either extrapolated from day 1 values to obtain values for the start of the stimulation or used day 1 values to represent day 0 values. We also assumed that the initial urine urea concentration was 25 mmol/l rather than basal values (Table 1) due to low urine flow rates and the stress of surgery.

The tracheoesophageal shunt was simulated by setting swallowing and lung secretion to zero in the model. The dotted lines in Fig. 5 show initial model projections. The waviness of the simulated lines in this and other figures was due to day-to-day changes in fetal urine production. The simulated AFV after 9 days of tracheoesophageal occlusion (4,385 ml) was much higher than experimental values because the IMA rate increased in the animals but not in the model. The latter occurred because, with C_in = C_st in the model, IMA_ves would be unchanged (Eq. 9). It is possible that the AF inhibitor of IMA is slowly metabolized, or its production is reduced as AFV expands, or it passively diffuses out of the AF compartment. To represent these possibilities, the simulation was run assuming that the production of the IM inhibitor was inversely proportional to AFV, i.e., doubling AFV reduced inhibitor production by 50%. With this change, simulated AFV was 3,672 ml after 9 days, a better approximation but again greater than the experimental value of 3,025 ml. The solid line in Fig. 5 shows simulated AFV, assuming that doubling AFV reduced inhibitor production by 70%. This modification led to an agreement between simulated and experimental AFVs and is consistent with the assumption of changes in inhibitor production/effectiveness during the 9-day study. This represents an evolution of the model.

Fig. 5.

Amniotic fluid volume (top) and intramembranous absorption (IMA) (bottom) responses to placement of a tracheoesophageal shunt in late-gestation ovine fetuses. Experimental data (means ± SE) from Jellyman et al. (44). Dotted line denotes simulated values assuming production of intramembranous inhibitor was constant. Solid line denotes simulated values assuming production of intramembranous inhibitor decreased as amniotic fluid volume increased (see text).

Rather than placing a tracheaesophageal shunt, a separate group of fetuses underwent esophageal ligation, resulting in the fetuses being unable to swallow AF (44). Although not measured, all secreted lung liquid entered the AF. The experimental changes in AFV over 9 days following esophageal ligation were essentially identical to those following placement of a trachea-esophageal shunt (44). However, the simulated AFV following esophageal ligation was greater than experimental values by a volume slightly less that the volume of lung liquid secreted over the 9 days. Thus, the model simulation suggests that little lung liquid was secreted over 9 days following fetal surgery and esophageal ligation. Multiple studies have shown that fetal stress reduces lung liquid secretion or even converts secretion to absorption (65). It is possible though unlikely that lung liquid secretion was suppressed following fetal surgical catheter placement and esophageal ligation.

Simulation 6: replacement of AF.

In many recent studies in which the drainage technique was used to determine AFV, AF was drained at the beginning of each control and experimental period and replaced with 1 liter of lactated Ringer solution. To explore the effects of AF replacement with lactated Ringer solution, we divided our experimental data into two groups, those with either low or high AFVs at the end of the 5-day postsurgery recovery period. This division was made because there were large differences among individual fetuses. Figure 6 compares the simulated responses to experimental values 2 days after AF replacement with 1 liter of lactated Ringer solution in these two groups of fetuses. Both panels in Fig. 6 show that AFV returned toward the prereplacement volume, regardless of whether the initial AFV was less than or greater than the 1,000 ml replacement. With low initial AFV, the return occurred because fetal swallowing and IMA increased after the 1 liter replacement. With high initial AFV, the return toward prereplacement volume occurred primarily because IMA and swallowing were reduced. In both cases, the alterations in vesicular transport in the model occurred because of the effects of altered AFV on inhibitor production described above.

Fig. 6.

Experimental (●; means ± SE) and simulated (solid lines) responses to drainage of amniotic fluid and replacement with one liter of lactated Ringer solution. Top: amniotic fluid volume = 652 ± 207 ml on postsurgery day 5 (day 0) prior to AF replacement. Bottom: amniotic fluid volume = 1,180 ± 137 ml on postsurgery day 5 prior to AF replacement.

Simulation 7: fetal urine replacement.

When fetal urine was continuously drained to the exterior, discarded, and replaced isovolumically with lactated Ringer solution, AFV doubled after 2 days, and IMA rate averaged half of prereplacement values over the 2-day period (5). Figure 7 compares simulated and experimental values. The increase in AFV occurred in spite of a 50% increase in swallowing due to a large reduction in IM transport. Although there was good agreement of simulated with experimental AFV and swallowed volume, the simulation appeared to overestimate the decrease in IMA rate. However, this appearance occurs largely because the changes in IMA rate were not linear over time. The high IMA rates during the first day after starting the replacement are not represented by the nearly flat line during the second day.

Fig. 7.

Comparison of simulated and experimental AFV (top), amniotic flows, and compositional responses to continuously replacing fetal urine with lactated Ringer solution. Solid circles (●; means ± SE) from Anderson et al. (5); solid lines denote simulated values. At time zero, amniotic fluid was drained and replaced with 1 liter of lactated Ringer solution, and urine replacement was initiated. Experimental values of swallowing (middle) and IMA (bottom) rates are plotted at the midpoint of the time over which they were measured.

There was also good agreement of simulated and experimental amniotic osmolalities, sodium concentration, and chloride concentration during fetal urine replacement (Fig. 7). AF chloride concentration was particularly interesting as both simulated (109.4) and experimental (111.1 ± 1.9) concentrations (mmol/l) exceeded fetal blood concentration (107 ± 1.1) at the end of the two-day urine replacement.

Simulation 8: intra-amniotic infusion of Ringer lactate.

During an intra-amniotic infusion of lactated Ringer solution at 1.39 ml/min (2 l/day), AFV increased by 2,300 ml at the end of 2 days and IMA rate increased by an average of 1,020 ml/day during the infusion (19). Figure 8 compares these responses with the values simulated by the model. For this simulation, fetal swallowing was increased by 10% above that calculated from Eq. 8.

Fig. 8.

Experimental (●; means ± SE) and simulated (solid lines) responses to intra-amniotic infusion of lactated Ringer solution. Data from Brace et al. (19). At time zero, amniotic fluid was drained, replaced with 1 liter of lactated Ringer solution, and a continuous infusion of lactated Ringer solution at 1.39 ml/min was initiated and continued for 2 days.

Although Fig. 8 shows reasonable agreement between simulated and experimental values of AFV, swallowing, and IMA rate, there was poor agreement with AF osmolality, sodium concentration, and chloride concentration. The values of these variables increased during the experimental period but decreased during the simulation. At the end of the 2-day infusion, simulated osmolality (254 vs. 270 mosmol/kg H₂O), sodium concentration (115 vs. 127 mmol/l), and chloride concentration (92 vs. 100 mmol/l) were all more than one SE below experimental values. The simulated decreases occurred because urine flow rate increased while urine osmolality remained hypotonic to AF and because lactated Ringer solution is hypotonic to AF. Altering model parameters did little to improve model fit to the experimental data. Increasing the passive component of IMA to 4 times normal only modestly improved agreement. Although the differences between simulated and experimental values are unexplained, they do show that there is a fundamental component of our model that does not adequately represent the relative constancy of AF solute concentrations. Other investigators have noted that AF composition is maintained at the expense of volume (48, 68).

As part of the above study (19), the 2 l/day infusion was repeated while fetal urine was continuously replaced with lactated Ringer solution. The resulting experimental changes in AFV and IMA rate were essentially the same as when fetal urine entered the AF. Our model did not adequately simulate the experimental changes when fetal urine was replaced because simulated AFV increased by 4,250 ml after 2 days in contrast to the observed 1,935 ml. The reason for this is unclear, but it does suggest that the fundamental interactions of the stimulator and inhibitor with IM vesicular transport represented by Eq. 9 are not sufficiently comprehensive.

Simulation 9: intravascular lactate infusion.

In late-gestation fetal sheep, concentrated sodium lactate was infused intravascularly to increase fetal plasma lactate concentration to ∼3 times normal (54). This produced an extensive polyhydramnios with amniotic plus allantoic fluid volumes totaling four liters above normal at autopsy after the 3-day infusion and 1-day recovery (54). Further, there was an extensive polyuria during the infusion. Figure 9 compares simulated and experimental data, assuming a linear relationship between the measured amniotic fluid index (AFI) and AFV (45). The simulated response roughly approximates the measured AFV response during the infusion. However, during the 1-day recovery, the model predicted a sharp drop in AFV as urine flow rate declined, in contrast to the maintained elevation in experimental AFI. Further, as in simulation 8 above, the simulated AF sodium concentration and osmolality were lower than the experimental values, even after passive IM water flow was increased to 4 times its initial value. This occurred because fetal urine remained hypotonic to AF.

Fig. 9.

Comparison of simulated (solid lines) and experimental (mean ± SE) AFV (■), fetal (□), amniotic fluid (●), and fetal urinary (○) compositional responses to intravascular infusion of concentrated sodium lactate. Experimental data from Powell and Brace (54). Infusion was over days 1–4 (shaded bar). Fetal urine flow rate, urine composition, and fetal blood composition were used as inputs to simulate amniotic fluid volume and composition.

In a separate study, rather than infusing sodium lactate, an equivalent amount of 5 M NaCl was infused intravascularly into late-gestation ovine fetuses for 3 days (55). As estimated from the AFI, amniotic plus allantoic fluid volumes increased transiently during the infusion by 44%, returned to normal by the end of the 3rd day, and was reduced below normal at the end of the 1-day recovery period. The simulated AFV during NaCl infusion increased transiently during the infusion but to a much greater extent, reaching a peak of 3,760 ml based on the experimental urine flow rate and composition. At the end of the 1-day recovery, simulated fluid volume was reduced 300 ml below the initial value due to increased IMA absorption and swallowing. Thus, there is rough agreement between the experimental and simulated responses to the fetal polyuria produced by intravascular infusion of 5 M NaCl. Overall, a comparison of the latter two simulations supports the conclusion that fetal plasma lactate acts osmotically at the placenta to attract maternal water and solutes into the fetal circulation (which the fetus transfers to the AF) but sodium chloride does not (54, 55).

Simulation 10: intra-amniotic lactate infusion.

During the intravascular lactate infusion (simulation 9), AF lactate concentration increased from a basal value of 2 mmol/l to average 13 mmol/l during the infusion (54). To explore potential osmotic effects of lactate within the amniotic compartment, concentrated sodium lactate was infused into AF for 3 days (59). Experimental AF lactate concentration averaged 2.2 mmol/l prior to infusion, 18.9 mmol/l during the 3-day infusion, and 5.8 mmol/l during the 1-day recovery period. Simulated values were similar, averaging 2.2 mmol/l prior to infusion, 17.9 mmol/l during the infusion, and 3.3 mmol/l at the end of the 1-day recovery. The experimental and simulated AF volume and compositional response are shown in Fig. 10. Overall, there is good agreement, indicating that, unlike the osmotic effect of plasma lactate at the placenta, AF lactate is not effective osmotically. This is largely because of the relatively small contribution of passive osmotic forces to total IMA in combination with what may be a low reflection coefficient of the IM pathway (38).

Fig. 10.

Simulated (solid lines) and experimental (●; means ± SE) AFV and AF compositional responses to intra-amniotic lactate infusion for 3 days (shaded bar). Data from Scheve and Brace (59). The waviness in simulated responses was due to variations in fetal urine production.

Other model simulations.

When lactated Ringer solution was continuously infused into the AF at a rate of 3 l/day while AF was simultaneously withdrawn at the same rate and discarded, AFV increased by an average of 430 ml over 3.6 days (71). Our model does not predict an increase but rather a 10-ml decrease over the same time period. The small decrease occurred due to a reduction in inhibitor production that resulted from replacing AF with 1 liter of lactated Ringer solution at the start of the washout. Again, this suggests that Eq. 9 does not adequately represent the interactions between the IM stimulator, IM inhibitor, and IMA rate when both concentrations are reduced to low values.

Four days of hypoxic hypoxia in fetal sheep caused an extensive polyuria with AFV increasing by 20% of the volume of excess urine (62). The AFV and composition changes in response to hypoxic were simulated by using the experimental fetal urine flow and composition changes. The simulated AFV increase was greater than the experimental values, while the simulated AF osmolality, sodium concentration, and chloride concentrations were lower than the experimental values. In this case, increasing the IM filtration coefficient during hypoxia improved the correspondence between the simulated and experimental AFV and compositions.

DISCUSSION

The present computer model was developed with the purpose of gaining insight into the regulation of AF volume and composition, and the contribution of IMA to this regulation. The model was based on the experimental observations that a stimulator (5) and an inhibitor (19) of IMA are present in AF that play primary roles in regulating the rate of IM transport and thereby AFV. Overall, the model reasonably predicted the AFV and IMA responses to experimental perturbations for roughly half of the studies in which AFV and IMA were measured or could be estimated. These successes support the concept that IM transport across the amnion includes both passive and active components. The passive component allows bidirectional IM fluxes of solutes and water, according to their concentration and osmolality differences. The active component is a unidirectional bulk transport of AF together with all dissolved solutes and is a major component of IM absorption, as has been proposed previously (5, 16, 21, 25, 30, 34). The next critical step toward a better understanding of the regulation of AFV likely will be the identification of both the stimulator and inhibitor of IMA and the determination of IMA rate as a function of their AF concentrations.

The present computer model provides an integration of the current concepts of AFV regulation. Agreements between simulated and experimental AF responses to experimental perturbations support the view that the current concepts adequately represent the AFV regulatory mechanisms in many cases. An added benefit is that the model can be used not only to simulate responses to perturbations that have not yet been attempted in vivo but also to examine the contribution of individual pathways to the regulation of AFV. For example, the sensitivity analysis of Fig. 1 shows that each of the four major fluid pathways potentially make large contributions to the regulation of AFV. Of these, the volume contribution of fetal lung liquid to AFV has not been explored; it would be informative to explore the effects and time course of lung liquid drainage on AFV.

Perhaps more important than the predictive successes are the model failures, as the latter form the basis for future directions and studies needed to elucidate the cellular mechanisms that regulate AFV. These fall into two general areas: 1) interaction between IMA, the IM stimulator(s), and the IM inhibitor(s), and 2) near-osmotic equilibrium between AF and fetal blood in spite of large differences in measured osmolalities. For the first of these, Eq. 9 assumes that the stimulator and inhibitor alter IMA through changes in the ratio of their concentrations over the full range of concentrations. For the 2 liter/day intra-amniotic infusions discussed in simulation 8 above, the calculated AFV depended strongly on whether fetal urine entered the AF or was replaced with a saline solution, whereas experimentally AFV did not. This difference could be resolved if the IM stimulator was ineffective at AF concentrations less than half normal. The same is true of simulation 5, in which calculated AFV changes were different with placement of a trachea-esophageal shunt vs. esophageal ligation, but changes were the same experimentally. Identifying the stimulator and inhibitor plus determining the relationship between their AF concentrations and IMA rate is crucial. This should also resolve our inability to predict the increase in AFV during AF washout that was described above.

The second area relates to our inability to accurately predict AF osmolality and solute concentrations described in simulations 4, 8, and 9 above. For simulation 4, although the filtration coefficient may have increased during the water infusion, there is a more likely explanation. The large increase in IM water absorption during the infusion may be due to changes in effective osmolality difference between AF and fetal blood rather than total (i.e., measured) osmolality difference across the IM pathway. In sheep, fetal and maternal blood are in osmotic equilibrium across the placenta, even though measured fetal osmolality is lower than maternal osmolality. This has been described as the osmotic paradox and is due to differences in reflection coefficients of individual solutes and solute concentration differences at the placental interface (27). Collectively, the inability to simulate AF osmolalities and solute concentrations described above suggests that the osmotic paradox contributes importantly to IM water fluxes. Even though there are large differences in measured osmolalities, AF and fetal blood likely are in near-osmotic equilibrium across the IM pathway under basal conditions. This would occur because of large differences in reflection coefficients of individual solutes and differences in solute concentration. The possibility is supported by the calculation of a low overall reflection coefficient of the IM pathway during intra-amniotic water infusion (38). The effect of near-osmotic equilibrium across the amnion would be a higher IM filtration coefficient than calculated by the model (Table 3). Further, during experimental perturbations, the contribution of passive water flow through water channels could be much larger than simulated. Additionally, an osmotic paradox across the amnion may explain the relative constancy of AF solute concentrations in spite of changes in AFV under many experimental conditions.

Overall, in most simulations, the best fit between calculated and experimental values was achieved with a water channel flow of 15% of total IM flow under basal conditions. In fetal sheep, when the osmotic difference between AF and fetal blood was eliminated experimentally, IMA rate decreased by ∼25% from the value with a normal osmotic gradient (30), suggesting that passive osmotic forces contribute 25% to total IM volume absorption under normal conditions. In contrast, under physiological conditions, IMA rate was not significantly correlated with the AF to fetal blood osmotic difference (16), suggesting little osmotic water movement occurs across the amnion. To explore this, we pooled unpublished data from recent studies in fetal sheep and found that IMA rate was not correlated with the osmotic differences between fetal blood and AF (r = 0.071; P = 0.74, n = 24) under a variety of experimental conditions combined. These differences in passive water movement between 25% and 0% of total IM volume flow could be due to near-osmotic equilibrium across the IM pathway, i.e., a transamnion membrane osmotic paradox.

This concept is supported by the observation that, in some but not all fetuses, when urine was replaced, IMA became negative, i.e., there was a net volume movement across the amnion into rather than out of the AF (5). This occurred, even though measured AF osmolality remained below fetal blood osmolality. A reversal of IM volume flow against the osmotic gradient also occurred in some but not all fetuses when fetal urine is drained but not replaced (unpublished observations). With low-reflection coefficients of individual solutes of the IM pathway, the reversal of IM volume flow would be due to a combination of two events: 1) reversal of the differences in the effective osmotic gradient, even though the difference in total osmolality was not reversed and 2) a large reduction in vesicular transport due to the loss the of renal stimulator.

The calculation of IM permeabilities using Eq. 3 failed for lactate and occasionally for potassium (calculated permeabilities were negative). This occurred because their AF concentrations were higher than could be explained on the basis of urine inflow, lung inflow, and passive plus vesicular transport between AF and fetal blood. As noted in previous studies (54), ovine AF lactate concentration (Table 1) averaged twice fetal blood concentrations and was several times higher than that in fetal urine or lung liquid. It is well established that the ovine placenta not only transports glucose from the maternal into the fetal circulation but also converts a large fraction of the glucose taken from the maternal circulation into lactate before passing it on to the fetal circulation (6, 22). Thus, although unexplored, a likely explanation for the high AF lactate concentration is that the amniochorion, like the placenta, converts glucose to lactate and transports lactate into the AF.

Similarly, AF potassium concentration was higher in two studies than could be explained by urinary and lung inflows plus passive and vesicular transport between AF and fetal blood. In a study of swallowing in fetal sheep, Harding et al. (43) noted that the potassium concentration in swallowed fluid was sometimes greater than either AF or fetal lung liquid and concluded that the high potassium concentration was likely due to fetal salivary secretions. Salivary secretions are a likely explanation of the high AF potassium concentration. Active transport of potassium across the amnion into the AF may also contribute (24), but the amount would be small.

In studies that utilized the drainage method for determining AFV, rather than returning the drained AF, 1 liter of lactated Ringer solution was infused as a replacement fluid. The advantage was that all experiments started with the same volume and same composition of AF. However, there are also several disadvantages. First, the stimulator(s) and inhibitor(s) of IMA present in AF would be removed (except for the 100 ml residual volume). Second, the time required to reach a new steady state following AF replacement has yet to be explored although simulation 6 above (Fig. 6) suggests that 2 days may be adequate. Third, the concentrations of sodium, chloride, and lactate in the replacement fluid are higher than what would be found in normal AF. This results in IM solute flux rates during the control period that may differ from normal. Fourth, although starting the control period with an AFV of 1 liter, AFV was changing during the control period, with volume at the end of the control period ranging from an average of 556 ± 98 ml to 857 ± 172 ml after 2–4 days (4, 16, 53, 67). Thus, there was fluid loss from the amniotic compartment during the control period, and this occurred through a combination of increased IMA and swallowing.

With a tracheoesophageal shunt (simulation 5, Fig. 5), the IMA rate increased over the 9-day study. This was simulated by reducing inhibitor production as AFV increased. The agreement between simulated and experimental values supports the concept that the IM inhibitor that is present in AF either is metabolized over a period of days, passively diffuses out of the AF, or its production is reduced when AFV is elevated. Reduced inhibitor production might be a response to membrane stretch. However, inflating intra-amniotic balloons in fetal sheep with volumes of 650 ml or 1,300 ml did not alter the volume of AF within the uterus, suggesting that membrane stretch in sheep does not alter AF dynamics (32). Alternatively, AFV was more than 2,000 ml above normal after 9 days of the tracheoesophageal shunt. It is possible that the membranes were responding to stretch with such an excessive volume.

An interesting conclusion drawn from simulation 2 is that a large part of the differences in AFV among individual fetuses is due to differences in IMA rate (Fig. 2). What causes the individual variations in IMA rate is unknown. Fetal weight may be a factor. In both humans and sheep, AFV increases in early gestation as the fetus grows. However, in both species during the last several weeks of gestation, AFV does not change over time, as the fetus continues to grow (10, 17). The changes in IMA rate during this time and its relationship to fetal weight have yet to be explored. However, fetal urine production increases during this period, while AFV remains stable (17), so it is likely that IMA rate will also be increased.

The applicability of the present model to the human fetus has yet to be explored as IMA rates have been measured only in fetal sheep. Similarities between ovine and human fetal weights, AFVs, and urine production rates in late gestation have often been cited as indirect evidence that observations in sheep may be relevant to human fetuses. Even though rapid IMA absorption has been demonstrated in primates, including humans (41, 60), there are differences in placentation and architecture of the IM pathway that likely impact functionality of the IM pathway. In sheep, the connective tissue between amnion and chorion is vascularized while the chorionic membrane is extensively vascularized (11). These two vascular beds are the site of IMA absorption in sheep. In late-gestation primates, the amnion and chorionic membrane are avascular, and IMA occurs across the fetal surface of the chorionic plate (i.e., the placenta). Further, there are differences in AF composition with higher sodium, chloride, and lactate concentrations and lower potassium and urea concentrations in humans than in sheep (3, 7, 33). Whether these AF compositional differences result in species differences in AF dynamics is unknown, but the effects of high AF lactate concentrations in simulation 10 and NaCl infusions discussed in simulation 9 suggest any effects of composition may be small.

Perspectives and Significance

The present computer model integrates current concepts of IM transport with the regulation of AFV. The agreements between simulated and experimental responses show that these concepts are quantitatively consistent with experimental observations of IM volume and solute fluxes under many, but not all, experimental conditions. Overall, the simulations show that changes in the bulk, unidirectional (presumed vesicular) component of IM transport are a major determinant of experimentally induced changes in AFV, whereas passive transport of water and solutes across the IM pathway change little if at all.

The shortcomings of the model also clarify three major areas in which more studies are needed to advance the current understanding of the AFV regulatory mechanisms. First, and perhaps most essential, is determination of the biochemical identity of the IMA regulatory factors that are present in AF, that is, the renally derived stimulator of IMA and the nonrenal, nonpulmonary inhibitor. This will allow IMA rate to be quantified as a function of their AF concentrations. That, in turn, should greatly improve the predictive utility of the present model.

The second major area is determination of the permeability characteristics (individual reflection coefficients) of the IM pathway so that, rather than total osmolalities, the effective osmolalities can be determined. This is needed to understand how IMA can reverse direction against an osmotic gradient when vesicular transport is reduced during withdrawal of the renal IM stimulator. It also would provide an understanding of the near constancy of AF solute concentrations under some experimental conditions, whereas the computer model predicts substantial changes. Knowing effective osmolalities would also enhance our understanding of the role of passive water movement across the amnion in regulating AFV. It is likely to have a larger role than can be currently determined.

Third, the type and characteristics of the vesicles responsible for IM transport need to be studied. This would allow the factors that enhance and inhibit IMA to be better understood and may provide insight into the identity of the IM stimulator and inhibitor that are present in AF.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

Author contributions: R.A.B., D.F.A., and C.Y.C. conception and design of research; R.A.B., D.F.A., and C.Y.C. performed experiments; R.A.B., D.F.A., and C.Y.C. analyzed data; R.A.B., D.F.A., and C.Y.C. interpreted results of experiments; R.A.B. prepared figures; R.A.B., D.F.A., and C.Y.C. drafted manuscript; R.A.B., D.F.A., and C.Y.C. edited and revised manuscript; R.A.B., D.F.A., and C.Y.C. approved final version of manuscript.