Med. & Biol. Eng. & Comput., 1977, 15, 579-588

Control of water.excretion by antidiuretic hormone: Some aspects of modelling the system F. M. T o a t e s

K. O a t l e y

Psychology Division, Preston Polytechnic, Preston, Lancs., England

Laboratory of Experimental Psychology, University of Sussex, Falmer, Brighton, Sussex, England

A b s t r a c t - - T h e antidiuretic-hormone (a,d.h,) controlled water-excretion subsystem o f an earlier computer simulation is critically examined in the light of other studies in the area o f fluid balance, circulatory control and a.d.h, secretion rate etc. The model forms a convenient framework for the interpretation of a number of studies in terms of a theory of a.d.h, control, and modifications to the earl/er model are proposed. It is argued that the concept o f an a.d.h. threshold needs clarification, and reasons are suggested as to why nature has placed water excretion under the control of an antidiuretic rather than a diuretic hormone.

1 Introduction IN 1970 we published a paper on the computer simulation of thirst and body-fluid regulation in the rat (TOATESand OATLEV, 1970). The model consisted of subsystems representing the stomach, intestine, extracellular and cellular fluid compartments, renal mechanisms and drinking. Each parameter was based upon published physiological results, and although simplifying assumptions were made, the performance indicated that the model incorporated the essential physiology of the system. It provided some useful theoretical guidelines for theories of thirst (see, for example, FITZSIMONS, 1972; McFARLAND, 1971; UTTLEY, 1976; OATLEY, 1973, 1974; TOATES, 1974, 1975, 1977). In this follow up study, we direct attention to just one aspect of the model, the antidiuretic-hormonecontrolled excretion of water, and present a more detailed examination. We also consider where, on closer analysis, some changes and refinements in the original model are indicated, and we discuss the model in the context of other simulation studies. We believe that such comparisons and amendments may be useful to future researchers working on models of renal control. 2 Equation for defining urine flow F1NCHAM (1963) appears to be the first to have produced a computer model of the renal system. He examined the hormonal mechanism of water and sodium reabsorption and their mode of interaction with glomerular filtration rate. Although he considered that the factors controlling glomerular filtration rate (g.f.r.) were insufficiently clear to be inFirst received 25th November 1976 and in final form 5th January 1977

Medical & Biological Engineering & Computing

cluded in his simulation, Fincham drew a distinction between changes in excretion due to changes in g.f.r. and those attributed to altered hormone levels. Other models have placed emphasis either upon circulatory or hormonal control of urine output. In the model of GUYTON and COLEMAN (1967), urine flow is shown as a function only of arterial pressure. When the arterial pressure falls to 60-70 mmHg, urine flow becomes zero, while a rise in arterial pressure from 100 to 200 mmHg causes a six to seven fold increase in the rate of urine production. No hormonal mechanisms were included, from which one should presumably not conclude that hormones are unimportant in determining the functional relationship between arterial pressure and urine flow. If one considers only extracellular volume regulation (a cellular compartment was not included in the model) it may be possible to establish a direct relationship between arterial pressure and urine flow, with antidiuretic hormone taking the form of a hidden intermediate variable. By contrast, REEVE and KULHANEK (1967) based their analogue-computer model of body-fluid regulation on the assumption that urine flow is dependent solely upon a.d.h, concentration, apart from a minimal flow caused by solute excretion. Since changes in urine flow are mediated by changes both in g.f.r, and hormone concentration, at least for dogs ( B A R A T Z and INGRAHAM, 1960); both aspects were included in the simulation of TOATES and OATLEY (1970). FINCHAM (1963) proposed two possible equations for defining urine flow: (i) urine flow is equal to a constant fraction of glomerular filtration rate minus a part which is a function of a.d.h, concentration, i.e. urine flow rate = (g.f.r. x Ka) - f (a.d.h. conc) (la)

November 1977

579

(ii) urine flow is equal to a constant fraction of glomerular filtration rate multiplied by a function of a.d.h, concentration, i.e. urine flow rate = (g.fr. • K2) x f (a.d.h. conc) (lb) Fincham went on to rule out eqn. l a on the following grounds. Taking typical values for man, suppose urine flow is normally 1 ml/min. The constant K~, the proportion of g.f.r, available for excretion, is 0.2. Glomerular filtration rate is 120 ml/min, which means that f(a.d.h.) is 23 ml/min. If g.f.r, should rise to 240 ml/min and f(a.d.h.) remains constant, urine flow rises to the very high value of 25 ml/min, which, according to Fincham, cannot be the case. By contrast, applying eqn. lb to the same situation means that urine flow rises to only 2 ml/min. Fincham therefore assumed that eqn. lb provides the most realistic representation of the physiological system. In the model of KOSHIKAWA and SUZUKI (1968), urine flow also depend upon g.f.r, in the way defined by eqn. lb. Fincham argued that, since after removal of the posterior pituitary the urine flow rate rises to a value equal to about 20% of the g.f.r., proximal tubular reabsorption of 80% of g.f.r, occurs. This figure is commonly quoted in the literature (for example, GUYTON, 1971). Therefore, a maximum of 2 0 ~ of g.f.r, is free to be excreted. KOSHIKAWAand SuzuKI (cited by NA~ASAKAet aL, 1966) in their model of renal control also calculated that there is a fixed proximal tubular reabsorption of water of 80~/o while distal reabsorption is under the control of a.d.h. The precise equation that Fincham used to define urine flow was

the statement that g.f.r, is almost constant in the face of changes in a.p. can not be applied to the dog and rat (PITTS, 1970; SMITH, 1951). WESSON et al. (1950) found that after extracellular volume expansion in dogs, g.f.r, increased by 5 7 ~ above its normal value of 43 ml/min. If reabsorption were at its maximum, this expansion would cause a rise of 24.5 ml/rain in urine flow rate. In fact, urine flow increased by 10 ml/min. If we suppose that a maximum of 20yo of g.f.r, can be excreted, the maximum urine flow would be 13.5 ml/min. That it is 10 m l / min is entirely compatible with eqn. lb. LEAF et aL (1954) attempted to show the relationship between glomerular filtration rate and urine flow rate under conditions in which a.d.h, m a y be assumed to be constant. During water diuresis (when a.d.h, activity was taken to be zero or minimal) changes in g.f.r, induced by compression of the renal artery were accompanied by a linear change in urine flow, Following water deprivation the same procedure produced an almost linear relationship between g.f.r, and urine flow. 3 Control of glomerular filtration rate

A study by LANDWEHR et aL (1967) was concerned with the measurement of glomerular filtration rate in rats under normal conditions. It was found to be 0.45 ml/min/100 gm body weight. The work of MEREDITH (1957), also on rats, was based on a figure of 0.5 ml/min/100 gm body weight. In our simulation a figure of 0.5 ml/min/100 gm body weight was used, but since only 2 0 ~ of this may be excreted, the value of 0.1 ml/min/100 gm body weight appeared in the model. The remaining 8 0 ~ is an urine flow = 0-2 x g . f r . • (1 c) internal circulation and not of relevance here. FINCHAM(1963), after examination of the evidence, i.e. of the form represented in eqn. lb, where considered that g.f.r, is related to blood volume, the f(a.d.h.) can vary between 0 and 1. Thus urine flow exact nature of the linkage being somewhat unclear. can vary between the limits of 0 and 0-2 g.fr., TOATES and OATLEY (1970) made glomerular filtraaccording to the value off(a.d.h.), and this was the tion rate a linear function of extracellular volume, equation employed in our simulation. but it is now realised that this is not a good represenSuch an equation accords with physiological tation of the physiology of the system, since it measurements (see BRENNER et al., 1968; P~TTS, implies that g.f.r, can only become zero by extra1970), but there is also evidence to show that it cellular volume reaching zero, which is not the case may apply only within limits. GUVTON (1971) argues in practice. that as g.f.r, rises above a certain level then the BARATZ and INGRAHAM (1960), working with reabsorptive capacity of the tubules is exceeded, and dogs, showed that when arterial pressure falls to what is known as the overflow phenomenon appears, about one half of normal, g.f.r, is zero (GuYTON, with very large amounts of water being excreted. 1971). TO be precise, g.f.r, is dependent upon blood Thus for a 1 5 ~ increase in g.f.r, urine flow can volume rather than total extracellular fluid volume, increase by 4 5 0 ~ . This is the situation represented by and the relationship obtained by extrapolation to Fincham's eqn. la. This phenomenon must form the rats appears to be such that a loss of blood volume basis of GtJYTON and COLEMAN (1967) function of 2 ml/min/100 gm body weight (which causes a relating arterial pressure (a.p.) to urine flow in drop in one half of arterial pressure) causes g.f.r, to humans, since, according to GUYTON (1971), g.f.r. fall to zero. can increase only very slightly above its normal value A suitable equation for defining the 20% of g.f.r. when arterial pressure increases. which is available for excretion is given by Guyton's work is based on man and there is reason to believe that species differences exist. F o r example g . f r . (20~) = 0.1+ (blood volume- 7.7) • O.05 (3) 580

Medical & Biological Engineering & Computing

November 1977

for a t00 gm rat. F o r an animal of weight W, the constants 0.1 and 7.7 (blood volume for a 100 gm rat) must be multiplied by the ratio W/100. The equation suggests that increases above normal in blood volume will lead to increases in g.f.r., and this is indeed the case. It is known that in dogs (BARATZ and INaRAHAM, 1960) an increase in arterial pressure of 7~/~ causes g.f.r, to rise by 259/0 (it is assumed in the model that blood volume and arterial pressure are closely connected). Species differences appear to be important because, according to PITTS (1970), infusion of iso- and hypertonic saline into dogs increases the filtration rate whereas in humans such infusions have little or no effect. PITTS (1970) showed that salt loading can increase g.f.r, by 100~/o in the dog. According to eqn. 3, developed to represent decrease in volume, for a 1 ml]100 gm body weight increase in blood volume, g.f.r, increases by 50%. This is indeed the kind of increase which as been found experimentally in dogs. Eqn. 3 appears then to hold true as a first approximation for increases as well as decreases from normal. The results of COLE (1955) for intravenous infusions of saline suggest a lag between changes in in blood volume and changes in g.f.r., and in our simulation this was represented by an exponential delay of time constant 15 min. This provides a reasonable fit to the data of WESSON et al. (1950). A lag has also been mentioned by WESSONet al. (1948). Can any physiological significance be attached to such a time constant between changes in blood volume and change in g.f.r.? According to the account given by VANDER et al. (1970), g.f.r is primarily controlled by alterations in glomerular capillary pressure. Such a change is produced by: (a) a drop in arterial blood pressure (b) a decrease in the diameter of arterioles that connect the renal artery to the glomeruli. When there is a decrease in blood volume, sympathetic stimulation of the renal arterioles by means of the renal nerves and by adrenalin from the adrenal medulla causes constriction of the renal arterioles, and hence g.f.r, is lowered. Increases in blood volume have the opposite effect. The time constant may possibly be associated with this process. The modification to the model proposed here accords with the simulation of BLAINE et aL (1972) based upon more detailed modelling of the physiology associated with glomerular filtration. According to their model: g . f r . = K x filtration pressure

equal and opposite to the sum of the tubular pressure and the oncotic pressure, filtration pressure and hence g.f.r, will be zero. The model presented here is a simplification in that g.f.r, is a function only of blood volume and not of colloid pressure. Ingestion of large quantities of saline solution sufficient to bring the plasma colloid osmotic pressure clown to 5 m m H g can increase g.f.r. by 15-20% (GuvxoN, 1971). However, under normal circumstances, changes in glomerular capillary pressure will be the main factor in determining g.f.r. 4 Secretion of antidiuretic hormone Since the stimuli for thirst (e.g. haemorrhage, water deprivation) are also stimuli for increased secretion of a.d.h., parallels between the two systems are frequently drawn. For example, it is possible that the same or at least similar receptors are employed in each case. F o r this reason in the review of renal function that follows, reference will frequently be made to thirst. FINCHAg (1963), in his analogue computer model of body fluids in man, proposed the following equation to describe the secretion rate of antidiuretic hormone sl = S l + a l ( p ( s ) - P ( s ) ) + b l ( V b - v b )

where $1 is the rate of secretion of hormone under conditions of fluid balance in the body, st is the actual level of secretion and will differ from $1 as a function of departures from normal in the body fluid and sodium content, and p(s) is the actual plasma sodium concentration which has a value P(s) under normal conditions. Thus increases in plasma sodium concentration above normal lead to an increased secretion of a.d.h., according to the constant al. Fincham determined this constant from the result of VERNEY (1947) that a 3" 3~/o increase in plasma sodium concentration was sufficient to double the rate of secretion of a.d.h. V b is the normal value of blood volume and v b its actual value at any given time. Decreases in blood volume give rise to an increased secretion of a.d.h. The gain b~ was determined on the basis that a decrease in blood volume of 40~/0 will double a.d.h. secretion rate. This may be true of humans, but as will be shown later it would be a gross underestimate if applied to rats. REEVE and KULHANEI~ (1967) presented two equations f=

g~(Ap)+g2(Av)

where K is a constant filtration pressure = glomerular capillary press u r e - tubular p r e s s u r e - oneotie pressure glomerular eapillary pressure = f (afferent arteriolaf pressure) afferent arteriolar pressure = f (blood volume)

Thus it may be seen that if blood volume is reduced to the point where glomerular capillary pressure is Medical & Biological Engineering & Computing

(4)

v~ = g 3 ( f )

. . . . . .

. . . . . . . .

(5a) (5b)

to describe the secretion of antidiuretic hormone Osmoreceptors were assumed to be responsive to changes in water chemical potential Ap, and volume receptors measured any change occurring in blood volume Av. Eqn. 5a relates strength of stimnli to rate of frequency of firing of osmoreceptors a.nd November 1977

581

volume receptors, such as to give their summed frequency of firing. Eqn. 5b relates firing frequency to rate of a.d.h, secretion vs. To simplify their analogue simulation, Reeve and Kulhanek pooled the osrnoreceptor and volume-receptor stimuli into a single stimulus which was percentage deviation of body water volume from normal. A nonlinear function relating rate of a.d.h, secretion to percentage change in body water was calculated. F o r a 2 ~ loss of body water, a.d.h, secretion increases roughly 7-fold, whereas a 29/ooincrease in body water reduced a.d.h, secretion to zero. TOATES and OATLEY (1970), in their digital computer model based on the rat, used an equation similar to Fincham's to model the secretion rate of a.d.h. However, whereas Fincham assumed that changes in sodium concentration p e r s e influenced a.d.h, secretion, Toates and Oatley considered the effect to be mediated by a cell which is used to signal the state of the cellular fluid compartment. A crucial factor in deciding whether a rise in osmotic pressure p e r s e or a loss of water from the cells is the stimulus for a.d.h, release is the effect of injecting a substance such as urea which causes a rise i n osmotic pressure but passes freely through the cell boundary. VERNEY (1947) found that urea injections produced no antidiuretic effect, despite the fact that the osmotic increase was the same as that caused by sodium chloride which did show an antidiuretic effect. The same question arises in the context of thirst, and here also cell-water loss rather than a rise in osmotic pressure is the necessary stimulus (GILMAN, 1937). It is assumed, then, that blood-volume receptors and cellular-volume receptors influence a.d.h, secre-

tion. Such an assumption is sensible physiologically since these two quantities are the most affected by water deprivation. In rats 48 h of water deprivation produced a 2 8 ~ plasma-volume reduction (KuTSOrtER, 1968), although in terms of absolute quantity the cellular compartment contributes most of the water loss after a long period of water deprivation (FITzSIMONS, 1971). In contrast to the volume effects, earlier researchers failed to detect any change in the composition of the blood after three days of water deprivation (MEYER; WETTENDORFF;cited by CANNON, 1947). FrrSlMONS and OATLEY (1968) found only a 2" 8 8 ~ increase in serum sodium concentration after 48 h of water deprivation, and only a 1~oo following 24h of deprivation. Osmotic pressure therefore appears to be relatively unaffected by water deprivation. Fig. 1 shows a modified form of the model of renal control. In the earlier model (TOATES and OATLEY, 1970), as a simplification, departures from normal of cellular and extracellular volume affected the secretion rate of a.d.h, and aldosterone. In Fig. 1, extracellular error is replaced by error in blood volume, since blood-volume receptors in the low-pressure side of the circulation appear to be the specific stimulus for a.d.h, secretion (GAUER and HENRY, 1963). Also, in the previous model, as a first approximation, the assumption was made that errors in a fluid compartment in either direction may be multiplied by the same constant to give their effect on secretion rate. This now appears to be an oversimplification of the truth, and so the nonlinear nature of the operation is included. Reduction of extracellular fluid volume without any observed change in mean arterial pressure, produced by peritoneal dialysis leads to a dramatic

blood volume

;o, 3o, ADH quonWcy in the blood

arterial pressure

'[

cellular volume

[

/

ADH

rlormo[ value

Fig. 1 A.D.H. release system

582

Medical & Biological Engineering & Computing

November 1977

increase in blood vasopression concentration (SHARE, 1969). However, extracellular factors apart from the blood-volume receptors in the low-pressure side of the circulation appear to control a.d.h, secretion. Receptors in the arterial side of the circulation also influence plasma vasopressin concentration (SHARE, 1969). SHARE and LEvY (1962) concluded that a pressure reduction in the carotid sinuses causes decreased activity of the baroreceptors. This then leads to a reduction in the inhibition exerted on the mechanism that controls vasopressin secretion. Evidence to support this view was presented by SHARE (1969). Carotid sinus receptors were postulated by HENRY and PEARCE (1956), and for the cat (CLARK and ROCHA E SILVA, 1967; BELESLIN et al., 1967) and rat (GINSBERG and BROWN, 1957) it has been argued that a.d.h, secretion is more closely associated with blood-pressme reduction than with blood-volume reduction. Owing to lack of more detailed experimental data, it is probably more reasonable to assume that, following a reduction in blood volume, the increased secretion of a.d.h, is mediated in equal parts by blood-volume receptors and arterial-pressure receptors. Thus the equation proposed for defining the secretion rate of a.d.h, is given by

f = n+al(BVN-- BV)+bl(CVN- CV) + el ( A P ~ - AP)

(6)

where f = secretion rate n = normal secretion rate BVN = normal blood volume

BV = CVN = CV = APN = AP =

actual blood volume normal cell volume cell volume normal arterial pressure arterial pressure

al, bl and cl are dependent upon the sign of the error to which they refer; otherwise they are linear. This is a first approximation to the true state of affairs.

5 Nature of the a.d.h, controller Eqn. 6 says some formal things about our understanding of the physiology of a.d.h, release. Firstly, it implies that secretion rate may be varied up and down from its normal value by excitatory and inhibitory pathways. These would converge on a synapse, where addition and subtraction can occur, and there is probably a final common efferent pathway (ARNDT, 1965). Such an algebraic summation of stimuli is very much in keeping with the physiologist's view of renal function (SMITH, 1957). Working with sheep, JOHNSON et aL (1970) showed Medical & Biological Engineering & Computing

that the effect of a hypotonic stimulus together with haemorrhage cancelled. The hypotonic stimulus when presented on its own decreased a.d.h, secretion, and the haemorrhage increased secretion rate. Eqn. 6 also has something to say about the nature of the controller that regulates the water content of the body. The system is believed to contain only one integrator and that is the body fluids themselves. If one were to infuse the body fluids with isotonic and hypotonic saline, urine flow rate would increase until it was equal and opposite to the rate of infusion. For urine flow to increase a.d.h, concentration might be expected to decrease. According to eqn. 6, for a.d.h, production rate to be held constant at a rate other than its normal value there must exist a departure from normal in either cellular volume, extracellular volume, or arterial pressure. For an infusion of fluid at a constant rate one would expect to see urine flow rise slowly until in the steady-state urine flow is equal and opposite to infusion rate. Up until the steady state has been reached, body-fluid volume would be increased, since there is a net flow into the body fluids. In the steady state, the surplus volume will remain at a constant value. This is indeed what occurs in practice (COLE, 1955). Eqn. 6 says that a.d.h, secretion rate is a function of body fluid and a.p. only. The system is insensitive to the rate of change of volume. Again this accords with a physiological understanding of the system. Dehydrated animals may make up for a water deficit by swallowing water at a very fast rate, but they do not develop a diuresis (STRAUSS, 1957) despite the rapid change in the body fluid compartments as a function of time. Rate sensitivity in such a situation would obviously defeat the object of the control system. According to the model, a.d.h, secretion is graded and not an 'all-or-none' response. This question was raised by MILLERSCHOEN and RIGGS (1969). They point out that if a.d.h, secretion were of the all or none kind, a.d.h, concentration could be adjusted by varying the time the system is in the on state, like an all-or-none thermostatically controlled heating system. They rejected, on the following grounds amongst others, the idea that the system functions in this way: (i) When water is infused an increase in urine flow is observed. If this were to correspond with the time that plasma osmolality took to reach the threshold for the a.d.h, mechanism to be switched on the time of the observed urine flow change would depend upon the rate of infusion. Their experiments showed no such dependence. (ii) For a constant rate of infusion a constant urine flow rate was found. A threshold mechanism might be expected to produce cyclic oscillations in urine flow. In Fig. 1, errors in celIular and extracellular compartments and in arterial pressure form inputs to the November 1977

583

renal system. The net rate of production of a.d.h, is given by its secretion rate minus its destruction rate. In the model, secretion rate is the input to an integrator. Therefore changes in secretion rate may be calculated on the basis of experimental results which measured changes in hormone concentration. Indeed, most researchers in this area work on the assumption that changes in concentration of vasopressin in the plasma reflect changes in secretion rate (SHARE,1969). According to SHARE (1968) a 50~/o blood loss causes a 16-fold increase in a.d.h, concentration in dogs. TATAand BUZALKOV(1966) found that in rats a 25~o blood loss produced a 16- to 40-fold increase in a.d.h, concentration. GINSBERGand HEELER(1953) found that a.d.h, concentration increased bY a factor of 20 in rats following a 30~o reduction in blood volume. In rats a haemorrhage of 3 0 ~ is associated with a 50Yoo drop in arterial pressure (SMTo et aL, 1969). It would therefore seem reasonable to assume that a 3 0 ~ loss of blood is associated with a fall of 50~o in arterial pressure and that the blood lossper se produces an approximately 10-fold increase in secretion rate and the arterial pressure reduction another 10-fold increase. Increases in blood volume above normal are accompanied by an increase in arterial pressure, and for the inhibition of a.d.h. secretion it is probably safe to assume equal contributions from volume and pressure receptors. 6 Conflict of interests between compartments Following a hypertonic saline injection into the vascular compartment, water will move from the cells into the extracellular space. The gain of water by the vascular compartment will be the stimulus for a reduction of a.d.h, secretion, whereas the loss of water from the cells will attempt to promote a.d.h. secretion. In this conflict situation, for rats if not for other species (GINSBERG and BROWN, 1957; GAUER and HENRY, 1963), the extracellular stimulus appears to dominate. This is in contrast to what occurs in thirst where the cellular stimulus is not cancelled by the extracellular surplus. Indeed extracellular expansion has no effect on cellular thirst (CORmT, 1967). The situation is complicated by the fact that irrespective of a.d.h, concentration water will be excreted by means of osmotic diuresis as a result of salt excretion (THOMPSON and BARNETT, 1954). If antidiuretic hormone is given with a load of hypertonic saline it has almost n o ' antidiuretic effect, since salt requires water for its excretion (PETERS, 1948). In this respect the model presented earlier (TOATES and OATLEY, 1970) is somewhat inadequate. To accord with the physiology of the system, a minimum urine flow of some 2 ml/mEq of excreted sodium needs to be included, water being the passenger of the sodium flow. This value accords with the maximum sodium concentration of the urine which is about 3-4 times isotonic for tats 584

(RADFORD, 1959). In accordance with Ginsberg and Brown's result, the gain relating change in a.d.h. secretion to cellular loss of fluid is such that a slight transient decrease in a.d.h, secretion is obtained following a simulated intravascular saline infusion. This aspect of the model must remain tentative until Ginsberg and Brown's result is confirmed. No interstitial fluid volume receptors appear to be present either for renal control or for drinking. The evidence suggests that interstitial fluid volume plays no role (FITzS~MONS, 1971 ; SNARE, 1969), although an influence on renal control cannot be entirely ruled out (SoNNENBERGand PEARCE,1962). It appears that the gain constants associated with a decrease in blood volume and arterial pressure and their effect on a.d.h, secretion are larger than the gains which apply to increases above normal. REEVE and KULnANEK (1967) calculated the function relating a.d.h, secretion rate to change in bodywater content on the basis of experiments on humans, and a nonlinearity of this kind is indicated. The calculation of O'CoNNER (1962) shows a similar effect. Therefore models which assumed linearity in this respect (TOATESand OATLEY, 1970; KOSHIKAWA and SUZUKI, 1968) appear somewhat inadequate. In contrast to extracellular volume, preliminary investigations using our model indicated that in the case of cellular errors a deficit carried much tess weight than a surplus. It is important to emphasise species differences in the urine response to departures from normal in the size of the body fluid compartments. Isotonic saline loading promotes very little urine flow in humans, but a prompt rise in rats and dogs (KELLOGet al., 1954; SMITH, 1957). An interesting conflict arises when the extracellular fluid is depleted of electrolytes. This procedure causes a movement of water from the extracellular compartment into the cellular. The gain of fluid by the cellular space will be the stimulus to inhibit a.d.h, secretion, but the loss of fluid by the extracellular compartment will be the stimulus to increase secretion rate. If the gain associated with blood volume loss is very high, we would predict a reduction in urine flow due to (amongst other possible reasons) the domination of the extracellular stimulus for a.d.h, release. This indeed appears to be the case in practice. The immediate renal response of a rat to removal of extracellular electrolyte is a cessation of urine production (SEMPLE, 1952). Unfortunately, circulatory changes can not be separated from hormonal changes, and so it can not be said for certain that increased a.d.h, secretion occurs, although this does appear to be the case (LEAF and FRAZ1ER, 1961). VANCE (1968) showed that the sodium-deficient rat only very slowly excretes a water load by comparison with a loaded control. The antidiuretic state caused by salt depletion is accompanied by thirst. CIZEK et aL (1951) in a study on electrolyte depletion in

Medical & Biological Engineering & Computing

November 1977

dogs reported that tbe 'water intake in the present experiments bore a rough relation to the degree of plasma volume reduction'. FITZSIMONS (1961) doubted that volume could be the factor responsible for sodium-deficient thirst because MCCANCE (1936) had earlier shown that relief of thirst could be obtained simply by administering sodium chloride before any water was made available for drinking. This is not, however, necessarily inconsistent with the thirst stimulus being one of volume. Sodium chloride would produce an osmotic shift of water from the cells to the extracellular space and this would relieve thirst. MCCANCEhad in fact reported that the volume of the body fluids was relatively well maintained; there is just a faulty distribution. Thus, during extracellular electrolyte depletion, constancy of osmolality appears to be sacrificed in the interests of constancy of volume. Similarly, but more tentatively for the renal system of the rat it seems that, following salt loading, extracellular volume dominates over extracellular osmolality. For the rat at least the conclusions of the present study are in disagreement with those of FINCHAM (1963) and REEVE and KULHANEK(1967) based on humans, that blood volume is an influence secondary to the osmotic pressure of the plasma. The present study is in agreement with ARNDT (1965) that ' . . . during a competition of the control systems of osmotic pressure and fluid volume the former is acutely overruled if the homeostasis of fluid volume is jeopardised'. There is, almost certainly, a profound species difference. SMITH (1951) notes that the renal system of humans shows little resistance to volume expansion since 1000 ml loads of isotonic saline are retained in the body for hours or days. By contrast, water promotes a prompt and dramatic diuresis. In rats both isotonic saline and water cause a sharp rise in urine flow (KELLOG et al., 1954). 7 Sodium excretion A question raised by the computer models of renal function is the effect of water loading on sodium excretion, and the mechanisms contributing to the response. KOSHIKAWA and SUZUKI (1968) argued that the increase in both sodium excretion and mine N a / K ratio following water ingestion in humans might be due to the inhibition of aldosterone secretion. LEAF et al. (1953) observed in humans an increased sodium excretion in response to excess water in the body, and was interpreted 'as a homeostatic response to overexpansion of fluid volume'. Loss of sodium would cause a greater part of the load to be held in the cellular compartment (i.e. blood-volume homeostasis). Although KELLOG et aL (1954), working with rats, also noted a slight increase in urine sodium following a water load, the increase in potassium excretion exactly paralleled the sodium response. Also the increase immediately followed loading rather than being delayed as in Koshikawa's results. Thus it seems possible that for Medical & Biological Engineering & Computing

rats, at least, the change can be attributed to an increase in g.f.r, rather than a decrease in reabsorption. However, it is interesting that a phenomenon observed by Koshikawa and Suzuki can possibly be attributed to just such a decrease in reabsorption, although the authors did not comment upon it. Koshikawa and Suzuki compared the response of their model to data collected on human subjects for repeated loading of water. In practice, urine flow rises sharply in the first 90 min but then drops considerably. The model of Koshikawa and Suzuki did not respond with a decrease at all, and this they attributed to the fact that no volume control of a.d.h, was included. What they did not not comment upon is the reason for the volume deficit in the course of water loading. We adjusted our original simulation so as to exclude any mechanism for increasing aldosterone secretion as a result of a cellular surplus (the gain being made zero) and 'loaded' the system with water. For small rates of loading, sodium is lost to the extent that the amount of water moving into the cells from the extracellular space creates a mild hypo-volemia in the plasma with, as Koshikawa and Suzuki suggest, promotion of a.d.h, secretion. Urine flow is slightly retarded. Thus it is possible, although highly tentative, that overloading the cells with water has no effect on sodium excretion and all that Koshikawa and Suzuki need is a volume influence on a.d.h, for their model to represent accurately the real system. 8 A D H threshold Another problem to which the model can be directed is the subject of the existence of an a.d.h. threshold. The literature very often implies the existence of such a threshold. Thus LEAFand FRAZIER (1961) claim that Verney demonstrated ' . . . an increase of only 1-2~o in the effective osmotic pressure of plasma going to the head of an animal results in release of antidiuretic hormone'. Similarly, AUBRY et al. (1965) states: ' . . . Verney calculated that as small a rise as 1% in the osmotic pressure of the plasma would stimulate discharge of vasopressin from the neurohypohysis'. KUTSCHER(1966) compared his own results for thirst with those of Verney for a.d.h, release: 'Drinking may be produced by cell shrinkage of less than 1~oo. This value is also close to the threshold of osmotic pressure increase in serum needed to release a.d.h, in dogs'. In fact it is not at all clear that VERNEY(1947) did find that an increase of 1~oo is necessary to initiate a.d.h, secretion. His graph relating increase in osmotic pressure to a.d.h, secretion is not easily interpreted, and elsewhere in the same article Verney states that ' . . . an increase of some 1~o only (54 mmHg) in the osmotic pressure of the aortic blood would suffice to produce the same degree of inhibition, i.e. a reduction of some 10~oo of the

November 1977

585

maximum rate of which the kidney is capable during water diuresis'. Clearly a 1~ increase can not both begin secretion of a.d.h, and at the same time cause a drastic change in water excretion. Others have shown that under normal conditions of body water content a.d.h, is constantly being secreted and this is implied by eqn. 4. O'CONNER (1962) calculated that at a normal value of plasma osmotic pressure the rate of release of a.d.h, is about 0'07 m U / m i n and is brought to zero only when plasma osmotic pressure falls by about 2 ~ . In conscious undisturbed dogs with free access to water, the vasopressin concentration is about 1 to 2 p U / m i (SNARE, 1969). A similar figure applies to humans. If it were the case that a.d.h, is only released after osmolality rises to a threshold value above normal, the diuretic response to a load of water could not be attributed to an inhibiton of a.d.h. secretion. However, the accepted account of the mechanism of water diuresis is that it is brought about by inhibition of a.d.h, secretion. Conditions of normal fluid balance must therefore be accompanied by a certain level of a.d.h, secretion since it is known that the hormone is constantly being destroyed. It may be necessary for osmolality to rise to a certain threshold value before any change in urine flow can be detected. This in fact forms the criterion used to measure the threhold in the study of AUBRY et al. (1965). If it were necessary, as KUTSCHER(1966) suggests, for osmotic pressure to reach a threshold comparable to the thirst threshold before a.d.h, is released, then clearly if water is available for the animal to drink osmotic pressure will not rise sufficiently to cause secretion of a.d.h., since drinking will always return it to normal (except during sleep perhaps, or when competing motivations are strong). If, under normal conditions, a.d.h, is never released, or is released in only very small quantities, there would be little to distinguish the normal animal from one suffering from diabetes insipidus. This is clearly not the case. 9 Antidiuretic or a diuretic hormone ? Simulation work sometimes raises fundamental questions about the construction and evolution of physiological systems. One such question is: why has nature provided an antidiuretic rather than a diuretic hormone? Possibly the effect of a failure of antidiuretic hormone secretion, i.e. the excess urination and thirst of diabetes insipidus, is less dangerous than the failure of a hypothetical diuretic hormone, i.e. cessation or sharp reduction in urine flow and retention of the waste products of metabolism in the body. However, another more compelling reason suggests itself. When fluid is suddenly lost from the body, as, for example, in haemorrhage, it is essential for urine flow rate to fall immediately. This is of course achieved by an increase in production of a.d.h., but if the erganism were to have been 586

equipped with a diuretic hormone this would need to be quickly eliminated from the body following fluid loss. However, such hormone elimination would necessitate urine loss which by definition cannot occur. Conversely, when the body is loaded with excess fluid, urination is high and this is entirely compatible with elimination of the hormone from the blood (i.e. an antidiuretic hormone) rather than production of hormone (i.e. a diuretic hormone). References

ARNDT, J. O. (1965) Diuresis induced by water infusion into the carotid loop and its inhibition by small haemorrhage. Pflugers Arch. f. gesam. Physiol. 282, 313-322. AUBRY, R. H., NANKIN, H. R., MoSEs, A. M. and STREETEN,D. H. P. (1965) Measurement of the osmotic threshold for vasopressin release in human subjects and its modification by cortiso/. J. Clin. Endocrin. Metab. 25, 1481-1492. BARATZ, R. A. and INGRAHAM, R. C. (1960) Renal hemodynamics and anti-diuretic hormone release associated with volume regulation. Amer. J. Physiol. 198, 565-570. BELESLIN, D., BISSET, G. W., HALDAR, J. and POLAK, R. L. (1967) The release of vasopressin without oxytocin in response to haemorrhage. Proc. Roy. Soc. B. 166, 443-458. BLAINE, E. H., DAVIS, J. O. and HARRIS, P. D. (1972) A steady-state control analysis of the renin-angiotensinaldosterone system. Circul. Res. 30, 713-730. BRENNER, B. M., BENNETT,C. M. and BERLINER,R. W. (1968) The relationship between glomerular filtration rate and sodium reabsorption by the proximal tubule of the rat nephron, or. Clin. Invest. 47, 1358-1374. CANNON, W. B. (1947) The wisdom of the body. Kegan Paul, Trench, Trubner & Co. CIZEK, L. J., SEMVLE,R. E., HUANG,K. C. and GREGERSEN, M. I. (1951) Effect of extravascular electrolyte depletion on water intake in dogs. Am. J. Physiol. 164, 415-422. CLARK,B. J. and ROCHAE SILVA, M. (1967) An afferent pathway for the selective release of vasopressin in response to carotid occlusion and haemorrhage in the cat. J. PhysioL (Lond.) 191, 529-542. COLE, D. F. (1955) The excretion of intravenously administered saline by the rat. Acta Endocrinol. 19, 397-405. CoRmx, J. D. (1967) Effect of hypervolemia on drinking in the rat. J. comp. physioL Psychol. 64, 250-255. FINCHAM, W. F. (1963) A study of the mechanism regulating the composition of the human blood by means of a n electrical analogue computer. Ph.D. thesis, University of London. FITZSJMONS,J. T. (1961) Drinking in rats depleted of body fluid without increase in osmotic pressure. J. Physiol. (Lurid.) 159, 297-309. FITZSIMONS, J. T. (1971) The physiology of thirst: A review of the extraneural aspects of the mechanism of drinking. In Progress in physiological psychology (Eds. Stellar, E., and Sprague, J. M.), Academic Press. FITZSIMONS,J. T. (1972) Thirst. Physiol. Rev. 52, 468-561. FITZSlMONS, J. T. and OATLEV,K. (1968) Additivity of stimuli for drinking in rats. J. Cutup. Physiol. Psychol. 55, 145-154.

Medical & Biological Engineering & Computing

November 1977

GAUER, O. I:l. and HENRY, J. P. (1963) Circulatory basis of fluid volume control. Physiol. Rev. 43, 423481. GILMAN, A. (1937) q-he relation between blood osmotic pressure, fluid distribution and voluntary water intake. Amer. J. Physiol. 120, 323-328. GINSBERG, M. and BROWN, L. M. (1957) The effects of haemorrhage and plasma hypertonicity on the neurohypophysis. In The neurohypophysis (Ed. H. Heller) Butterworths. GINSBERG, M. and HEELER, H. (1953) Anti-diuretic activity in blood obtained from various parts of the cardiovascular system. J. Endocrin. 9, 274-282. GUYTON, A. C. (1971) Textbook of medical physiology. Saunders. GUYTON, A. C. and COLEMAN,T. G. (1967) Long term regulation of the circulation: ifiterrelationships with body fluid volumes. In Physical bases of circulatory transport: regulation and exchange. (Eds. Reeve, E. B. and Guyton, A. C.). Saunders. HENRY, J. P. and PEARCE,J. W. (1956) The possible role of cardiac atrial stretch receptors in the induction of changes in urine flow J. Physiol. (Lond.) 131, 572-585. JOHNSON, J, A., ZEHR, J. E. and MOORE, W. W. (1970) Effects of separate and concurrent osmotic and volume stimuli on plasma A D H in sheep. Amer. J. Physiol. 218, 1273-1280. KELLOGG, R. H., BURACK,W. R. and ISSELBACHER,K. J. (1954) Comparison of diuresis produced by isotonic saline solutions and by water in rats studied by steady state method. Ibid. 177, 27-37. KOSHIKAWA, S. and SUZtJKL K. (1968) Study of osmoregulation as a feedback system. Med. & Biol. Eng. 6, 149-158. KUTSCI-IER,C. L. (1966) An osmetric analysis of drinking in salt injected rats. PhysioL Behav. 1, 79-83. KUTSCHER, C. L. (1968) Plasma volume change during water-deprivation in gerbils, hamsters, guinea pigs and rats. Comp. Biochem. Physiol. 25, 929-936. LANDWEHR,D. L., KLOSE, R. M. and GLEBISCH,G. (1967) Renal tubular sodium and water reabsorption in the isotonic sodium chloride loaded rat. Am. J. Physiol. 212, 1327-1333. LEAF, A., BARTTER,F. C., SANTOS,R. F. and WRONG, O. (1953) Evidence in man that urinary electrolyte loss induced by pitressin is a function of water retention. J. Clin. Invest. 32, 868-878. LEAF, A. and FRAZIER, H. S. (1961) Some recent studies on the actions of neurohypophyseal hormones. Recent Prog. in Cardiovas. Dis. 4, 47-64. LEAF, A., KERR, W. S., WRONG, O. and CHAT/LEON,J. Y. (1954) Effect of graded compression of the renal artery on water and solute excretion. Amer. J. Physiol. 179, 191-200. MCCANCE, R. A. (1936) Experimental sodium chloride deficiency in man. Proc. Roy. Soc. (Lond.) BlI9, 245-268. MEREDITH, J. E. (1957) An investigation of the mechanisms maintaining sodium and water balance in animals. Ph.D. thesis, University of Durham. MCFARLAND, D. J. (1971) Feedback mechanisms in animal behaviour. Academic. MILLERSCHOEN,N. R. and R]GGS, D. S. (1969) Homeostatic control of plasma osmolality in the dog and the effect of ethanol. Amer. J. Physiol. 217, 431437. NAGASAKA,M., SH]MIZU,K., MAEDA,T., YOSHITOSHI,Y., KOSHIKAWA, S. and SUZUKI, K. (1966) Control of Medical & Biological Engineering & Computing

body fluid volume regarded as a feedback system. Med. & Biol. Eng. 4, 567-574. OATLEY, K. (1973) Simulation and theory of thirst. In: The neuropsychology of thirst: New findings and advances in concepts (Eds. Epstein, A. N. Kissileff H. R. and Stellar, E.). V. H. Winston. OATLEY,K. (1974) Circadian rhythms and representations of the environment in motivational systems. In: Motivational control systems analysis (Ed. D. J. McFarland). Academic. O'CONNER, W. J. (1962) Renal function. Edward Arnold PETERS, J. P. (1948) The role of sodium in the production of edema. New Eng. J. Med. 239, 353-362. PI1-TS, R. F. (1970) Physiology of the kidney and body fluids. Year Book Medical Publishers. RAOEORO, E. P. (1959) Factors modifying water metabolism in rats fed dry diets. Amer. J. Physiol. 196, 1098-1108. REEVE, E. B. and KVLHANEK, L. (1967) Regulation of body water content: A preliminary analysis. In: Physical bases of circulatory transport: Regulation and exchange. (Eds. Reeve, E. B. and Guyton, A. C.) Saunders. SAXTO,T., YOSmDA, S. and NAI(AO, K. (1969) Release of antidiuretic hormone from neurohypophysis in response to haemorrhage and infusion of hypertonic saline in dogs. Endocrinol. 85, 72-78. SEMPLE, R. E. (1952) Compensatory changes in the rat following removal of electrolytes by intra-peritoneal dialysis. Amer. J. Physiol. 168, 55-65. SHARE, L. (1968) Control of plasma A D H titer in haemorrhage: role of atrial and arterial receptors. Ibid., 215, 1384-1389. SHARE, L. (1969) Extracellular fluid volume and vasopression secretion. In: Frontiers in neuroendocrinology (eds. Ganong, W. F. and Martini, L.) Oxford University Press. SNARE, L. and LEVY, M. N. (1962) Cardiovascular receptors and blood titer of anti-diuretic hormone. Amer. J. Physiol. 203, 425428. SM]'rH, H. W. (1951) The kidney: structure and function in health and disease. Oxford University Press. SMITH, H. W. (1957) Salt and water volume receptors. Amer. J. Med. 23, 623-652. SONNENBERG, H. and PEARCE, J. W. (1962) Renal response to measured blood volume expansion in differently hydrated dogs. Amer. J. Physiol. 203, 344-352. STRAUSS, M. B. (1957) Body water in man. Little Brown. TarA, P. S. and BUZALKOV, R. (1966) Vasopressin studies in the rat. III Inability of ethanol anesthesia to prevent ADH secretion due to pain and hemorrhage. Pflugers Archiv. 290, 294-297. THOMPSON, D. D. and BARRETT, M. J. (1954) Urine flow and solute excretion during osmotic diuresis. Amer. J. Physiol. 176, 33-38. TOATES, F. M. (1974) Computer simulation and the homeostatic control of behaviour. In: Motivational control systems analysis. (Ed. D. J. McFarland) Academic. TOATES, F. M. (1975) Control theory in biology and experimental psychology. Hutchinson Educational Ltd. TOATES, F. M. (1977) A physiological control theory of the hunger-thirst ineraction. In: Hunger models: computable theory of feeding control (Ed. D. A. Booth). Academic (in Press). November 1977

587

TOATES,F. M. and OATLEY,K. (1970) Computer simulation of thirst and water balance. Meal. & BioL Eng. 8, 71-87. UTTLEY,A. M. (1976) Simulation studies of learning in an informan network. Brain Research 102, 37-53. VANCE, W. B. t1968) Decreased urine formation in sodium depleted rats. Psychon. Sci. 12, 102. WANDER, A. J., SHERMAN, J. H. and LUCIANO D. S. (1970) Human physiology. McGraw-Hill. VERNEV E. B. (1947) The anti-diuretic hormone and the

factors which determine its release. Proc. Roy. Soc. (Lond.) B135, 25-106. WESSON, L. G., ANSLOW, W. P., RA~SZ, L..G., BOLOMEY, A. A. and LADD, M. (1950) Effect of sustained expansion of extracellular fluid volume upon filtration rate, renal plasma flow and electrolyte and water excretion in the dog. Amer. J. PhysioL 162, 677-686. WESSON, L. G., ANSLOW,W. B. and SMITU, H. W. 0948) The excretion of strong electrolytes. Bull. N Y Acad. Med. 24, 586-606.

L6 controle de 1'6xcretion d'eau par le syst6me des hormones anti-diuretiques: certains aspects se rapportant au mod61e du syst6me Sommaire---Le sous-syst~me de controle de l'excr~tion de l'eau par les hormones anti-diur6tiques (Systemea.d.h.) d6coulant d'une simulation d'ordinateur ant6rieure, est examin6 d'une faqon critique sur le plan d'autres 6tudes effectu6es dans les domaines de l'6quilibre fluide, du contr61e de la circulation et du r6gime de la s6cr6tion-h.a.d., etc. Le mod61e constitute un canevas utile /~ l'interpr6tation certain nombre d'etudes en termes d'une th6orie du contr61e-h.a.d, et g cet 6gard, certaines modifications du premier mod61e sont recommandees. On peut discuter que la notion d'un scull A D H fasse appel ~. certaines clarifications et des raisons sont formul6es /t savoir pourquoi la nature a plac6 l'excr6tion de l'eau sous le contr61e d'une hormone anti-diur6tique en pr6f6rence h une hormone diurdtique.

Kontrolle der wasserabscheidung durch antidiuretisches hormon : gewisse aspekte zur darstellung des systems im modell Zusammenfassung--Ein durch antidiuretisches Hormon kontrolliertes Wasserabscheide-Untersystem einer friiheren Computersimulierung wird kritisch im Lichte anderer Untersuchungen fiber die Ausgeglichenheit der Sekretion, Zirkulationskontrolle und Ausscheidungsrate unter Verwendung yon antidiuretischem Hormon usw. verglichen. Das Modell bildet einen passenden Rahmen fiir die Interpretation mehrerer Untersuchungen hinsichtlich einer Theorie der ADH-Kontrolle, und es werden )tmderungen am friiheren Modell vorgeschlagen. Es wird angeftihrt, dag das Konzept einer ADH-Schwelle Kl/irung braucht, und es werden Griande angeregt, warum die Natur die Wasserabscheidung unter die Kontrolle eines antidiuretischen und nicht unter die eines diuretischen Hormons gestellt hat.

588

Medical & Biological Engineering & Computing

November 1977