JOURNALOP APPLIED PHYSIOLOGY Vol. 39, No, , 5, November 1975. Printed
in U.S.A.
Sodium kinetics in aorta of spontaneously
JOSEP G. LLAURADO AND JANE A. MADDEN Biomedical Engineering Group, Marquette University and the Medical at Veterans Administration Hospital, Wood (Milwaukee), Wisconsin
LLAURADO, JOSEP G., AND JANE A. MADDEN. Sodium kinetics in aorta of spontaneously hypertensive rats. J. Appl. Physiol. 39(5) : 868-872. 1975.-Transport rate constants (kij) for Na exchanges in isolated aorta of normotensive and spontaneously hypertensive rats (SHR) were determined with the use of 22Na as a tracer and the aid of digital computer simulation. A three-compartment model consisting of 1) extracellular, 2) intracellular, and 3) “endointracellular” spaces (compartments) was found to describe adequately the kinetics of 22Na. Results show that in SHR: i) kol, which is related to the overall Na outflow from tissue, was increased by 41%; G) k12, describing Na movements from intrato extracellular compartment, was increased by 67y0; iz?) k21, representative of Na movements from extrato intracellular compartment, was decreased by 39%. These results indicate a faster turnover of Na and a relative accumulation or translocation of Na into the extracellular space in aorta of SHR. The findings are interpreted in the light of recent reports on the role of Na in contractile response or reactivity of arteries. A humoral mechanism operative at the arterial wall level for the development of hypertension is suggested. The main significance of the methodology employed in this work is that the values found for the kij are not subject to fluctuations intrinsic to auxiliary indicators of extracellular space. compartmental flow; electrolytes; of hypertension; sodium exchange;
analysis; computer simulation; continuous outextracellular-intracellular; humoral mechanism isotope tracers; SAAM computer program; transport rate constants
CONCEPT that arterial hypertension is usually accompanied by a shift of the ionic pattern in-the arterial wall has been repeatedly put forward nature of change(s) for several years, but no specific appears to have been firmly established. Although an increase in total Na content of the arterial wall in hypertensive animals has been reported (11, 27, 29, 41) in general, but not every time (25), definite information about the characteristics of the alterations at the subtissue level is lacking. Since tissues ordinarily have more than one compartment or space, it would be of interest to explore the existence of altered exchanges or shifts of electrolytes between extracellular (EC) and intracellular (IC) spaces rather than changes in the total amount. Conventional approaches to study compartmental or space distribution of tissue electrolytes are based on determinations of total tissue electrolyte and on estimates of EC volume as derived from chemical indicators (chloride, inulin, sucrose, etc.). By suitably combining these two quantities (36), some inferences can be made about IC electrolytes. Yet, the variability of EC space measurement is so considerable (20-47 y0 for smooth muscle (8), 8-35 for voluntary muscle (32), 6-80 for liver (45) as collected in the indicated references) that the same workers who have used these methods have commented upon their high degree of uncertainty. In previous work (33), with the aid of digital computer simulation, a procedure was established and validated for determining THE
hypertensive
College 53193
rats
of Wisconsin
Na transport rate constants and relative Na EC/IC space in arterial wall with the sole use of radioactive Na as tracer. Further, the method was used to demonstrate some effects of aldosterone on Na distribution in canine arterial wall (34) and to study Na distribution in rat liver (40). The availability of spontaneously hypertensive rats (SHR) has given new impetus to studies of experimental hypertension. As far as we are aware, no attempt has been made to describe Na exchanges among the different compartments (EC, IC, etc.) of the arterial wall in terms of transport rate constants describing true kinetic models and to compare Na transport rate constants in normal and hypertensive arteries. The present experiment was designed to evaluate the effect of well-developed hypertension on Na transport rate constant in the aorta of SHR.
MATERIALS
AND
METHODS
Methods have been described in detail earlier (33-35). Consequently, only necessary departures from previous methodology and salient points will be mentioned. Biological procedure. Male white rats of the spontaneously hypertensive inbred Wistar line were obtained (from Purina Laboratory Animals, Vincentown, N. J.) and maintained on ordinary pellet diet and tap water. Animals were about 180 g in size at the beginning of the experiment and about 270 g at the end (6 wk later). Systolic blood pressure measurements were made under light ether anesthesia on the rat’s tail every week with a small-animal indirect blood pressure apparatus and plethysmograph (obtainable from Buffington Clinical Systems, Cleveland, Ohio) connected to an oscilloscope. There was a marked difference (Table 1) between SHR and control groups. At the time of the actual experiment the animal was quickly guillotined, the thorax opened, and the aortic arch removed. From then onward, the previously described procedure (33) was followed in general lines. Basically, it consists of incubating the tissue at 37.5’C in a Krebs medium containing 22Na except that here as a refinement a 15-h incubation was carried out in Difco (Difco Laboratories, Detroit, Mich.) TC medium 199. After achieving constant specific activity, the tissue was subjected to a continuous outflow of 22Na with isotopically inactive Krebs solution in an apparatus specially built in the laboratory (33) which assures constant temperature (37.5’C) and flow (15 ml/s). Radioactivity counts in the tissue at time 0, i.e., before starting the washout, and every 10 s thereafter were recorded. It was shown previously (39) that with the present computational approach all essential information can be extracted from a lo- to 15-min outflow record. Although the use of genetic strains of hypertensive animals offers certain advantages as experimental models of hypertension, because the hypertension develops without the intervention of either surgery or other manipulatory practices, it may cast some reservations regarding adequate control animals. Owing to the unavailability of nonhypertensive inbred Wistar rats at the time of this study, the Sprague-Dawley strain of Wistar rats (customary in our laboratory) was used as control. Other workers (21, 25, 38) have also taken this decision and, furthermore, it has been shown
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (150.216.068.200) on January 13, 2019.
SODIUM
KINETICS
IN
ARTERIAL
WALL
OF
HYPERTENSIVE
FIG. 1. Proposed model of Na distribution in rat aorta wall consisting of three compartments : 1) extracellular; 2) intracellular; 3) “endointracellular.” Intercompartmental transport rate constants are symbolized by the k;j .
(25) that there is no difference in aorta total Na or K composition between Sprague-Dawley and another Wistar strain of rats. Computational procedure. The printout digital values of counts in the course of time were punched into computer cards that made up the data input for the SAAM (Simulation, Analysis, And Modeling) computer program developed by Berman (1). Although for the understanding of this paper no familiarity with computer programming is necessary, the interested reader is referred to pertinent articles (1, 2, 33-35). Transport rate constant, kij , is defined (4) as the fraction of compartment j which enters i in unit time (Fig. 1). In a previous paper (33) this parameter was symbolized by Xij because the standardized nomenclature (4) was not yet promoted. The simulation procedure for the “inflow” is necessitated to find the initial conditions for each compartment at the beginning of the outflow. The mathematical basis for the validity of this simulation procedure was presented earlier (33, 35). Later Gunn and Patlak (18) have added a physical argument for its justification. The questions of uniqueness (33, 35) of the set of numerical values of the kij , and of sensitivity (34) of the model have been previously covered. The computer output for the outflow is, therefore, a double curve: i) a theoretically calculated curve which is compared point by point with ii) the experimentally obtained curve. Agreement between these two curves based on the least-squares fit is the criterion for acceptance of the set of kij . Development of model. It is generally agreed that any proposed model of a biologic function must be consonant with a) previous knowledge reported by other workers, and b) the observed data from actual experiments. Acceptance of a three-compartment model as shown in Fig. 1 was based on previous experimental evidence from arterial wall reported by several workers (10, 11, 14, 3 1, 43, 44), our previous findings on dog carotid (33-35) and the COUNTS
PER. 10
869
ANIMALS
readily obtained agreement of the present experimental data with the calculated results. The three-compartment model should be interpreted as consisting of an EC, and IC and an “endointracellular” space. Without committing ourselves to the exact location of this additional component within the cell, we point out that its existence has been indicated by other workers (10, 13, 37, 44). Since by outflow methods only dynamic aspects of Na exchange are detected, present results are not intended to add anything to the question of the osmotically inactive Na found by others (8, 23). From numerical values for the transport rate constants it is possible to calculate the ratio of EC to IC sodium compartments (34, 35) as per the equation written at the bottom of Table 1. It should be noted that in this paper the terms EC and IC spaces are used by convention in the same way as results obtained from inulin or sucrose determinations are attributed to EC space. Strictly, but cumbersomely speaking, we should refer, for instance, to compartment 1 as “that compartment characterized by exchanging Na with other compartments at such transport rate constants in and out.” The terms EC and IC are, therefore, used with this reservation. RESULTS
Typical plots of computer output for the kinetic model of 22Na exchange in rat aorta are shown in Fig. 2 for a control specimen and in Fig. 3 for a SHR specimen. Ordinates in these figures represent in logarithmic scale radioactivity counts per 10 s and abscissae represent time. The left side of the illustrations is the plot of the computer simulated inflow. The right side of Figs. 2 and 3 describes the decline of tissue radioactivity counts in the course of time and illustrates the agreement for the outflow of 22Na between experimentally observed data and theoretical results calculated according to the numerical values of the transport rate constants (kij) arrived at by computer iteration. In Table 1 values for the transport rate constants are comparatively shown. For the physical interpretation of these parameters, Fig. 1 should be regarded. The following changes were observed in the SHR group as compared with the control group: 1) Transport rate constant kol, which is related to the overall Na outflow was increased by 41%. 2) Transport rate from the tissue, constant k12 , describing Na movements from IC to EC compartment, was increased by 67y0. 3) Transport rate constant
SEC
f
OBSERVED SIMULATED
INFLOW
AND SIMULATED TIME
IN
FIG. 2. Plot of computer output for kinetic model of 22Na exchange in rat aorta. This is an illustrative record for a control specimen. Left: computer simulated inflow. Right: comparison of experimentally ob-
OUTFLOW . OUTFLOW
1
MINUTES
tained dental
outflow data (*) and computer points are printed as (X).
simulated
outflow
(+)
; coinci-
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (150.216.068.200) on January 13, 2019.
J. l ,+ +
G. LLAURADO
AND
J. A. MADDEN
+
+
++++ +
COUNTS
PER 10 SEC 4
-10”
I) +
OBSERVED
4
OUTFLOW AND
SIMULATED
SIMULATED
INFLOW
OUTFLOW
FIG. 3. Plot of computer output for kinetic model of 22Na exchange in rat aorta. This is an illustrative record for a spontaneously hypertensive rat specimen. Left: computer simulated inflow. Right: com-
parison of experimentally obtained simulated outflow (+) ; coincidental
TABLE I. Comparative values of final blood pressure and transport rate constants for Na in aorta of rats ______.----_ _ -.-__.-.-- _---__________-
normal rats to 6.3 in SHR indicate a relative accumulation or translocation of Na into the EC space. Although it had been suggested (7, 11, 17) that increased total Na in arteries of hypertensive animals represents an increase in EC Na, Jones recently concluded that there was no alteration in either total Na (25) or IC Na concentration (26). The latter conclusion (26) seems, however, unwarranted as it was based on a statistically insufficient sample (one specimen?). Because our results are in terms of kinetically modeled transport rate constants no immediate comparison is possible with published data, but the value of the Na EC/IC ratio for normal animals can be used to show the consistency of our results. The Na EC/IC ratio can be calculated as being 1.3, 1.7, or 2.2 in rat aorta (20), 2 in canine carotid (14, 22) but as large as 20.3 in sheep carotid (28). The ratio of 1.7 found in this work falls within the range of other workers’ values (14, 20, 22). As recently pointed out (3) it is possible that the type of model used to characterize Na outflow curves determines the calculated parameters to some degree. Even if absolute parameter values are difficult to achieve with certainty (3, lo), it seems reasonable that values obtained from normal and hypertensive arteries by applying the same theoretical model after using the same experimental method lend themselves to a fairly reliable comparison, especially if studies are carried out with the exclusive use of Na and the aid of computer simulation which avoid the many inaccuracies (8, 32, 45) inherent in the ancillary use of extracellular space indicators. That Na metabolism or distribution in tissues is somehow associated with the development or maintenance of chronic long-term hypertension has been known for many years, and recently reemphasized through a detailed systems analysis of circulatory regulation (19). Yet, the intimate nature of this association has remained obscure and elusive, though there have been some notable findings, namely, Na ions carry most of the depolarizing current of arterial action potentials (28), and Na plays the dominant role in ionic transfers in response to changes in arterial transmural pressures (12, 17) (the so-called concentration gradient theory). The present results showing marked changes of Na distribution in aorta of SHR provide an experimental unifying substratum at the subtissue level for the recent observations reported by others regarding electrolyte-dependent augmented responses of arterial wall to norepinephrine (22) and angiotensin (15, 22). The question naturally arises as to whether the Na tissue redistribution found in hypertensive arteries is a causative factor of the hypertensive state or is a consequence of the hypertensive
Variable
BP* k 01 h2
k 21 h k32 EC/IC Na ratio-t
Control
(TZ = 8)
102.8&-0.98 44.1ztI .77 8.4zt0.14
3.1AO.35 1.2hO.50 0.76zkO.23
1.7~tO.38
Hypertensive
(rt = 6)
190.0*1.91
Level
-- -
P < 0.0001
62.kt5.71 14.0zt1.22
P < 0.02
P < 0.001 P < 0.02 NS P < 0.05
1.9Zto.24 l.OZtO.41 0.16ztO.04
6.3&l
Signif
.06
P < 0.01
Transport rate constant (kij) is defined as the fraction of Na in one compartment (2nd subscript) which enters another (1st subscript) in unit time. For instance, k2i means the fraction of compartment 1 which enters compartment 2 in one second. Refer to Fig. 1 for identification of transport rate constants. Values of kij are mean AX SE, per second, multiplied by lo3 to facilitate comparison. The Student t-test was applied to ascertain significance levels. * BP = blood pressure; values are mean A SE, in mmHg. t The following expression was used (34; 35) to calculate the ratio of EC/IC Na: EC/IC = QAQ2 -I- Q3) = (QdQd/ = quantity of material (kdh~/~~ + kdhd, w h ere the Q’s symbolize in the respective compartments. of Na movements from EC to IC compartk21 , representative ment, was decreased by 39%. 4) Although k32 was also changed, no further emphasis is made on this change owing to its relatively high associated SE. 5) Application of the equation shown at bottom of Table 1 gives the ratio of EC/IC Na. This ratio was 1.7 for the control group and 6.3 for the SHR group. DISCUSSION
The finding of a significantly increased kol, the transport rate constant from tissue to outside (Fig. l), indicates a faster Na turnover in the aorta of SHR. It is of interest that similar results for Na in hypertensive arteries were independently obtained, namely, increased “exchangeable” Na in rat aorta (46), increased rate of initial efflux in canine carotid (43), and increased turnover in rat aorta (26). On the other hand, the findings (Table 1) of an increased klz, a decreased k21, and an augmentation of the EC/IC ratio from 1.7 in
outflow data (*) and computer points are printed as ( X).
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (150.216.068.200) on January 13, 2019.
SODIUM
KINETICS
IN
ARTERIAL
WALL
OF
HYPERTENSIVE
condition. It was suggested that ionic exchange alterations are directly involved in changes of vascular tension (12, 17), that these alterations are not themselves the result of a change in tension (12, 17), and that they are primary rather than secondary alterations dependent on abnormal outputs from sympathetic and adrenal regulatory systems (25). Most studies of arterial wall Na have been carried out on relatively large arteries, whereas increased peripheral resistance, the determinant of the hypertensive disease, is mainly related to a diminished caliber of small arteries and arterioles and much less to a contraction of the aorta or carotid. In other words, to lend more credence to a probable causative mechanism, one should find at least some kind of gross Na and water abnormalities in the small arteries and arterioles. Of great interest are, therefore, the results of Koletsky et al. (29) who found a significant rise in bulk Na and water in the fine threads of mesenteric artery divisions and their branches in rats made hypertensive and of Tobian et al. who reported increased bulk Na (41) and water (42) in the walls of mesenteric arterioles of hypertensive rats. They pointed out (42) that the excess water would thicken the arteriolar wall and reduce the lumen, thus increasing resistance to flow. Excess water has also been associated with increased vessel stiffness in hypertension (9). This change of stiffness would reduce the degree of wall expansion with each pulse wave. Furthermore, EC-to-IC concentration changes of the electrolytes themselves have been shown to have intrinsic effects on the contractile response or reactivity of arteries (12, 17, 22). Finally, it appears of interest to combine the finding of altered Na distribution in hypertensive arteries with scattered fragmentary evidence involving aldosterone, the chief regulator of bodily Na. It has been reported that arterial hypertension may be associated with hyperaldosteronism in man (5, 6, 16) and in the rat (30);
871
ANIMALS
that arterial wall is one of the tissues which shows high concentration and protracted disappearance of tritiated aldosterone (24) ; and that aldosterone promotes in arterial wall an increase of EC Na at the expense of IC Na (34), a change in the same direction as the rise of Na EC/IC ratio found in SHR. Therefore, it seems reasonable to postulate the following integrative humoral mechanism operative at the arterial wall level for the development of hypertension : elevated circulating aldosterone may lead to translocation of Na into the EC space of the vessel wall, followed by accompanying water retention in it, diminution of lumen with change of wall stiffness, concomitant ion effects on vessel contractile response and/or reactivity, and increased peripheral resistance manifested by hypertension. This mechanism, of course, is not intended to be inclusive of all types of hypertension or exhaustive of contributing factors. Naturally, superimposed on this description we have effects of angiotensin, catecholamines, neural system, etc. The suggested mechanism may first appear a large speculative step, yet all the links of the chain have been shown experimentally, though severally. We thank Dr. George A. Smith of Wood Veterans Administration Center for constructive criticism of the manuscript and Mrs. Jeaninne T. Leming of the Medical College of Wisconsin, Milwaukee, Wis., for editorial assistance. This work was supported in part by research grants of the Wisconsin Heart Association and the Marquette University Committee on Research. It is also VA Research Project 5301-01. Present address of J. A. Madden: Departamento de Fisiologia e Farmacologia, Universidade Federal de Pernambuco, Recife, Pernambuco, Brazil. Received
for publication
7 February
1975.
REFERENCES Compartmental analysis in kinetics. In: Computers in edited by R. W. Stacy and B. D. Waxman. New York : Academic, 1965, vol. II, p. 173-201. BERMAN, M., AND R. SCHOENFELD. Invariants in experimental data on linear kinetics and the formulation of models. J. APPZ. Physics 27: 1361-1370, 1956. BRADING, A. F. Ion distribution and the role of calcium in cellular function. Phil. Trans. Roy. Sot. London, Ser. B 265 : 35-46, 1973. BROWNELL, G. L., M. BERMAN, AND J. S. ROBERTSON. Nomenclature for tracer kinetics. Intern. J. AppZ. Radiation Isotopes 19: 24% 262, 1968. CONN, J. W., E. L. COHEN, D. R. ROBNER, AND R. M. NESBIT. Normokalemic primary aldosteronism-a detectable cause of curable “essential” hypertension. J. Am. Med. Assoc. 193 : 200-206, 1965. CONN, J. W., D. R. ROBNER, E. L. COHEN, AND R. M. NESBIT. Normokalemic primary aldosteronism-its masquerade as “essential” hypertension. J. Am. Med. Assoc. 195 : 21-26, 1966. DE LA RIVA, I. J,, P. BLAQUIER, AND N. BASSO. Water and electrolytes during experimental renal and DCA hypertension. Am. J. Physiol. 2 19 : 1559-l 563, 1970. DE LA RIVA, I. J., P. BLAQUIER, N. BASSO, AND A. C. TAQUINI. Water and electrolyte distribution in the artery wall. Acta Physiol. Latinoam. 14 : 307-3 14, 1964. FEIGL, E. O., L. H. PETERSON, AND A. W. JONES. Mechanical and chemical properties of arteries in experimental hypertension. J. CZin. Invest. 42 : 1640-1647, 1963. FRIEDMAN, S. M. Lithium substitution and the distribution of sodium in the rat tail artery. Circulation Res. 24 : 168-175, 1974. FRIEDMAN, S. M. An ion exchange approach to the problem of intracellular sodium in the hypertensive process. Circulation Res. 24-25, Suppl. I: 123-128, 1974. FRIEDMAN, S. M., AND D. B. ALLARDYCE. Sodium and tension in an artery segment. Circulation Res. 11 : 84-89, 1962. GAMBLE, J. L., -JR. Potassium binding and oxidative phosphorylation in mitochondria and mitochondrial fragments. J. BioZ. Chem. 228: 955-971, 1957.
1. BERMAN, Biomedical 2.
3. 4.
5.
6.
7.
8.
9.
10. 11.
12. 13.
M.
Research,
14. GARRAHAN, exchange 15.
16.
17.
18. 19. 20.
21.
22. 23. 24.
25.
26.
P., M. F. VILLAMIL, AND J. A. ZADUNAISKY. Sodium and distribution in the arterial wall. Am. J. Physiol. 209: 955-960, 1965. GAVRAS, H., H. R. BRUNNER, E. D. VAUGHAN, JR., AND J. H. LARAGH. Angiotensin-sodium interaction in blood pressure maintenance of renal hypertensive and normotensive rats. Science 180 : 1369-1372, 1973. GENEST, J., G. LEMIEUX, A. DAVIGNON, E. KOIW, W. NOWACZYNSKI, AND P. STEYERMARK. Human arterial hypertension: a state of mild chronic hyperaldosteronism? Science 123 : 503-505, 1956. GUIGNARD, J.-P. AND S. M. FRIEDMAN. Intraluminal pressure and ionic distribution in the tail artery of rats. Circulation Res. 27: 505-512, 1970. GUNN, R. B., AND C. S. PATLAK. The uptake curve in tracer kinetics. Math. Biosci. 6 : 19-24, 1970. GUYTON, A. C., T. G. COLEMAN, AND H. J. GRANGER. Circulation: overall regulation. Ann. Rev. Physiol. 34: 13-46, 1972. HAGEMEIJER, F., G. RORIVE, AND E. SCHOFFENIELS. The ionic composition of rat aortic smooth muscle fibres. Arch. Intern. Physiol. Biochim. 73 : 453-475, 1965. HANSEN, T. R., G. D. ABRAMS AND D. F. BOHR. Role of pressure in structural and functional changes in arteries of hypertensive rats. Circulation Res. 24-25, Suppl. I: 101-107, 1974. HARRIS, G. S., AND W. A. PALMER. Effect of increased sodium ion on arterial sodium and reactivity. CZin. Sci. 42 : 301-309, 1972. HEADINGS, V. E., P. A. RONDELL, AND D. F. BOHR. Bound sodium in artery wall. Am. J. Physiol. 199 : 783-787, 1960. HOLLANDER, W., D. M. KRAMSCH, A. V. CHOBANIAN, AND J. C. MELBY. Metabolism and distribution of intravenously administered d-aldosterone-1 , Z-H3 in the arteries, kidneys, and heart of dog. Circulation Res. 18-l 9, Suppl. I : 35-47, 1966. JONES, A. W. Altered ion transport in vascular smooth muscle from spontaneously hypertensive rats. Circulation Res. 33 : 563-572, 1973. JONES, A. W. Altered ion transport in large and small arteries from spontaneously hypertensive rats and the influence of calcium. Circulation Res. 24-25. I SUDD~. I : 117-122. II , 1974.
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (150.216.068.200) on January 13, 2019.
872 27. JONES, A. W., E. 0. FEIGL, AND L. H. PETERSON. Water and electrolyte content of normal and hypertensive arteries in dogs. Circulation Res. 15 : 386-392, 1964. 28. KEATINGE, W. R. Sodium flux and electrical activity of arterial smooth muscle. J. Physiol., London 194 : 183-200, 1968. 29. KOLETSKY, S., H. RESNICK, AND D. BEHRIN. Mesenteric artery electrolytes in experimental hypertension. Proc. Sot. Exptl. Biol. Med. 102: 12-15, 1959. 30. KUMAR, D., A. E. D. HALL, R. NAKASHIMA, AND A. G. GORNALL. Studies on aldosterone. II. Hypertension as a cumulative effect of aldosterone administration. Can. J. Biochem. Physiol. 35 : 113-l 18, 1957. 31. LING, G. N. A Physical Theory of the Living State: The AssociationInduction Hypothesis. New York : Blaisdell, 1962, p. 198, p. 322. 32. LING, G. N., AND M. H. KROMASH. The extracellular space of voluntary muscle tissues. J. Gen. Physiol. 50 : 677-694, 1967. J. G. Digital computer simulation as an aid to the 33. LLAURADO, study of arterial wall Na kinetics. J. A@. Physiol. 27: 544-550, 1969. 34. LLAURADO, J. G. Some effects of aldosterone on sodium transport rate constants in isolated arterial wall: studies with computer simulation and analysis. Endocrinology 87 : 5 17-526, 1970. J. G. Relationship between kinetics of inflow and 35. LLAURADO, outflow as the basis of a computer simulation for solving compartmental models : example of’ electrolyte transfers in cardiovascular Studies with Radioisotopes in Medicine. Vienna: tissues. In: Dynamic Intern. Atomic Energy Agency, 197 1, p. 13-26. 36. LLAURADO, J. G. Compartmental approaches to water and electrolyte distribution. In: Engineering Principles in Physiology, edited by J. H. U. Brown and D. S. Gann. New York : Academic, 1973, vol. II, p. 347-372.
J. G.
LLAURADO
AND
J. A. MADDEN
J. O., AND J. C. HALL. Effect of aldosterone on liver 37. MALBICA, mitochondria isolated from adrenalectomized rats. Am. J. Physiol. 214: 1054-1062, 1968. N. T. STOWE, R. R. SMEBY, AND F. M. 38. SEN, S., G. C. HOFFMAN, BUMPUS. Spontaneous hypertension and erythrocytosis in rats. In : S’on taneous Hypertension : Its Pathogenesis and Complications, edited by K. Okamoto. New York: Springer, 1972, p. 227-230. 39. SMITH, G. A., AND J. G. LLAURADO. Retrieval of transport rates from truncated data of kinetic models. Proc. Ann. Conf. Eng. Med. Biol. 13: 292, 1971. 40. SMITH, G. A., AND J. G. LLAURADO. Computer modeling of nonsteady state sodium kinetics in liver. IEEE Trans. Biomed. Eng. 21 : 433-443, 1974. 41. TOBIAN, L., J. JANECEK, A. TOMBOULIAN, AND D. FERREIRA. Sodium and potassium in the walls of arterioles in experimental renal hypertension. J. Clin. Invest. 40 : 1922-l 925, 1961. 42. TOBIAN, L., R. OLSON, AND G. CHESLEY. Water content of arteriolar wall in renovascular hypertension. Am. J. Physiol. 216 : 22-24, 1969. 43. VILLAMIL, M. F., P. NACHEV, AND C. R. KLEEMAN. Effect of prolonged infusion of angiotensin II on ionic composition of the arterial wall. Am. J. PhyJiol. 2 18 : 1281-1286, 1970. 44. VILLAMIL, M. F., V. RETTORI, L. BARAJAS, AND C. R. KLEEMAN. Extracellular space and the ionic distribution in the isolated arterial wall. Am. J. Physiol. 214: 1104-l 112, 1968. 45. WILLIAMS, J. A., AND D. M. WOODBURY. Determination of extracellular space and intracellular electrolytes in rat liver in uivo. J. Physiol., London 2 12 : 85-99, 197 1. 46. ZECH, P., P. BOULETREAU, AND J. P. BOISSEL. Activite specifique de l’aorte mesuree par le sodium radioactif chez le rat uninephrectomise en hypertension exptrimentale (DOCA + sel). Compt. Rend. Sot. Biol. 162: 1371-1375, 1968.
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (150.216.068.200) on January 13, 2019.
in U.S.A.
Sodium kinetics in aorta of spontaneously
JOSEP G. LLAURADO AND JANE A. MADDEN Biomedical Engineering Group, Marquette University and the Medical at Veterans Administration Hospital, Wood (Milwaukee), Wisconsin
LLAURADO, JOSEP G., AND JANE A. MADDEN. Sodium kinetics in aorta of spontaneously hypertensive rats. J. Appl. Physiol. 39(5) : 868-872. 1975.-Transport rate constants (kij) for Na exchanges in isolated aorta of normotensive and spontaneously hypertensive rats (SHR) were determined with the use of 22Na as a tracer and the aid of digital computer simulation. A three-compartment model consisting of 1) extracellular, 2) intracellular, and 3) “endointracellular” spaces (compartments) was found to describe adequately the kinetics of 22Na. Results show that in SHR: i) kol, which is related to the overall Na outflow from tissue, was increased by 41%; G) k12, describing Na movements from intrato extracellular compartment, was increased by 67y0; iz?) k21, representative of Na movements from extrato intracellular compartment, was decreased by 39%. These results indicate a faster turnover of Na and a relative accumulation or translocation of Na into the extracellular space in aorta of SHR. The findings are interpreted in the light of recent reports on the role of Na in contractile response or reactivity of arteries. A humoral mechanism operative at the arterial wall level for the development of hypertension is suggested. The main significance of the methodology employed in this work is that the values found for the kij are not subject to fluctuations intrinsic to auxiliary indicators of extracellular space. compartmental flow; electrolytes; of hypertension; sodium exchange;
analysis; computer simulation; continuous outextracellular-intracellular; humoral mechanism isotope tracers; SAAM computer program; transport rate constants
CONCEPT that arterial hypertension is usually accompanied by a shift of the ionic pattern in-the arterial wall has been repeatedly put forward nature of change(s) for several years, but no specific appears to have been firmly established. Although an increase in total Na content of the arterial wall in hypertensive animals has been reported (11, 27, 29, 41) in general, but not every time (25), definite information about the characteristics of the alterations at the subtissue level is lacking. Since tissues ordinarily have more than one compartment or space, it would be of interest to explore the existence of altered exchanges or shifts of electrolytes between extracellular (EC) and intracellular (IC) spaces rather than changes in the total amount. Conventional approaches to study compartmental or space distribution of tissue electrolytes are based on determinations of total tissue electrolyte and on estimates of EC volume as derived from chemical indicators (chloride, inulin, sucrose, etc.). By suitably combining these two quantities (36), some inferences can be made about IC electrolytes. Yet, the variability of EC space measurement is so considerable (20-47 y0 for smooth muscle (8), 8-35 for voluntary muscle (32), 6-80 for liver (45) as collected in the indicated references) that the same workers who have used these methods have commented upon their high degree of uncertainty. In previous work (33), with the aid of digital computer simulation, a procedure was established and validated for determining THE
hypertensive
College 53193
rats
of Wisconsin
Na transport rate constants and relative Na EC/IC space in arterial wall with the sole use of radioactive Na as tracer. Further, the method was used to demonstrate some effects of aldosterone on Na distribution in canine arterial wall (34) and to study Na distribution in rat liver (40). The availability of spontaneously hypertensive rats (SHR) has given new impetus to studies of experimental hypertension. As far as we are aware, no attempt has been made to describe Na exchanges among the different compartments (EC, IC, etc.) of the arterial wall in terms of transport rate constants describing true kinetic models and to compare Na transport rate constants in normal and hypertensive arteries. The present experiment was designed to evaluate the effect of well-developed hypertension on Na transport rate constant in the aorta of SHR.
MATERIALS
AND
METHODS
Methods have been described in detail earlier (33-35). Consequently, only necessary departures from previous methodology and salient points will be mentioned. Biological procedure. Male white rats of the spontaneously hypertensive inbred Wistar line were obtained (from Purina Laboratory Animals, Vincentown, N. J.) and maintained on ordinary pellet diet and tap water. Animals were about 180 g in size at the beginning of the experiment and about 270 g at the end (6 wk later). Systolic blood pressure measurements were made under light ether anesthesia on the rat’s tail every week with a small-animal indirect blood pressure apparatus and plethysmograph (obtainable from Buffington Clinical Systems, Cleveland, Ohio) connected to an oscilloscope. There was a marked difference (Table 1) between SHR and control groups. At the time of the actual experiment the animal was quickly guillotined, the thorax opened, and the aortic arch removed. From then onward, the previously described procedure (33) was followed in general lines. Basically, it consists of incubating the tissue at 37.5’C in a Krebs medium containing 22Na except that here as a refinement a 15-h incubation was carried out in Difco (Difco Laboratories, Detroit, Mich.) TC medium 199. After achieving constant specific activity, the tissue was subjected to a continuous outflow of 22Na with isotopically inactive Krebs solution in an apparatus specially built in the laboratory (33) which assures constant temperature (37.5’C) and flow (15 ml/s). Radioactivity counts in the tissue at time 0, i.e., before starting the washout, and every 10 s thereafter were recorded. It was shown previously (39) that with the present computational approach all essential information can be extracted from a lo- to 15-min outflow record. Although the use of genetic strains of hypertensive animals offers certain advantages as experimental models of hypertension, because the hypertension develops without the intervention of either surgery or other manipulatory practices, it may cast some reservations regarding adequate control animals. Owing to the unavailability of nonhypertensive inbred Wistar rats at the time of this study, the Sprague-Dawley strain of Wistar rats (customary in our laboratory) was used as control. Other workers (21, 25, 38) have also taken this decision and, furthermore, it has been shown
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (150.216.068.200) on January 13, 2019.
SODIUM
KINETICS
IN
ARTERIAL
WALL
OF
HYPERTENSIVE
FIG. 1. Proposed model of Na distribution in rat aorta wall consisting of three compartments : 1) extracellular; 2) intracellular; 3) “endointracellular.” Intercompartmental transport rate constants are symbolized by the k;j .
(25) that there is no difference in aorta total Na or K composition between Sprague-Dawley and another Wistar strain of rats. Computational procedure. The printout digital values of counts in the course of time were punched into computer cards that made up the data input for the SAAM (Simulation, Analysis, And Modeling) computer program developed by Berman (1). Although for the understanding of this paper no familiarity with computer programming is necessary, the interested reader is referred to pertinent articles (1, 2, 33-35). Transport rate constant, kij , is defined (4) as the fraction of compartment j which enters i in unit time (Fig. 1). In a previous paper (33) this parameter was symbolized by Xij because the standardized nomenclature (4) was not yet promoted. The simulation procedure for the “inflow” is necessitated to find the initial conditions for each compartment at the beginning of the outflow. The mathematical basis for the validity of this simulation procedure was presented earlier (33, 35). Later Gunn and Patlak (18) have added a physical argument for its justification. The questions of uniqueness (33, 35) of the set of numerical values of the kij , and of sensitivity (34) of the model have been previously covered. The computer output for the outflow is, therefore, a double curve: i) a theoretically calculated curve which is compared point by point with ii) the experimentally obtained curve. Agreement between these two curves based on the least-squares fit is the criterion for acceptance of the set of kij . Development of model. It is generally agreed that any proposed model of a biologic function must be consonant with a) previous knowledge reported by other workers, and b) the observed data from actual experiments. Acceptance of a three-compartment model as shown in Fig. 1 was based on previous experimental evidence from arterial wall reported by several workers (10, 11, 14, 3 1, 43, 44), our previous findings on dog carotid (33-35) and the COUNTS
PER. 10
869
ANIMALS
readily obtained agreement of the present experimental data with the calculated results. The three-compartment model should be interpreted as consisting of an EC, and IC and an “endointracellular” space. Without committing ourselves to the exact location of this additional component within the cell, we point out that its existence has been indicated by other workers (10, 13, 37, 44). Since by outflow methods only dynamic aspects of Na exchange are detected, present results are not intended to add anything to the question of the osmotically inactive Na found by others (8, 23). From numerical values for the transport rate constants it is possible to calculate the ratio of EC to IC sodium compartments (34, 35) as per the equation written at the bottom of Table 1. It should be noted that in this paper the terms EC and IC spaces are used by convention in the same way as results obtained from inulin or sucrose determinations are attributed to EC space. Strictly, but cumbersomely speaking, we should refer, for instance, to compartment 1 as “that compartment characterized by exchanging Na with other compartments at such transport rate constants in and out.” The terms EC and IC are, therefore, used with this reservation. RESULTS
Typical plots of computer output for the kinetic model of 22Na exchange in rat aorta are shown in Fig. 2 for a control specimen and in Fig. 3 for a SHR specimen. Ordinates in these figures represent in logarithmic scale radioactivity counts per 10 s and abscissae represent time. The left side of the illustrations is the plot of the computer simulated inflow. The right side of Figs. 2 and 3 describes the decline of tissue radioactivity counts in the course of time and illustrates the agreement for the outflow of 22Na between experimentally observed data and theoretical results calculated according to the numerical values of the transport rate constants (kij) arrived at by computer iteration. In Table 1 values for the transport rate constants are comparatively shown. For the physical interpretation of these parameters, Fig. 1 should be regarded. The following changes were observed in the SHR group as compared with the control group: 1) Transport rate constant kol, which is related to the overall Na outflow was increased by 41%. 2) Transport rate from the tissue, constant k12 , describing Na movements from IC to EC compartment, was increased by 67y0. 3) Transport rate constant
SEC
f
OBSERVED SIMULATED
INFLOW
AND SIMULATED TIME
IN
FIG. 2. Plot of computer output for kinetic model of 22Na exchange in rat aorta. This is an illustrative record for a control specimen. Left: computer simulated inflow. Right: comparison of experimentally ob-
OUTFLOW . OUTFLOW
1
MINUTES
tained dental
outflow data (*) and computer points are printed as (X).
simulated
outflow
(+)
; coinci-
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (150.216.068.200) on January 13, 2019.
J. l ,+ +
G. LLAURADO
AND
J. A. MADDEN
+
+
++++ +
COUNTS
PER 10 SEC 4
-10”
I) +
OBSERVED
4
OUTFLOW AND
SIMULATED
SIMULATED
INFLOW
OUTFLOW
FIG. 3. Plot of computer output for kinetic model of 22Na exchange in rat aorta. This is an illustrative record for a spontaneously hypertensive rat specimen. Left: computer simulated inflow. Right: com-
parison of experimentally obtained simulated outflow (+) ; coincidental
TABLE I. Comparative values of final blood pressure and transport rate constants for Na in aorta of rats ______.----_ _ -.-__.-.-- _---__________-
normal rats to 6.3 in SHR indicate a relative accumulation or translocation of Na into the EC space. Although it had been suggested (7, 11, 17) that increased total Na in arteries of hypertensive animals represents an increase in EC Na, Jones recently concluded that there was no alteration in either total Na (25) or IC Na concentration (26). The latter conclusion (26) seems, however, unwarranted as it was based on a statistically insufficient sample (one specimen?). Because our results are in terms of kinetically modeled transport rate constants no immediate comparison is possible with published data, but the value of the Na EC/IC ratio for normal animals can be used to show the consistency of our results. The Na EC/IC ratio can be calculated as being 1.3, 1.7, or 2.2 in rat aorta (20), 2 in canine carotid (14, 22) but as large as 20.3 in sheep carotid (28). The ratio of 1.7 found in this work falls within the range of other workers’ values (14, 20, 22). As recently pointed out (3) it is possible that the type of model used to characterize Na outflow curves determines the calculated parameters to some degree. Even if absolute parameter values are difficult to achieve with certainty (3, lo), it seems reasonable that values obtained from normal and hypertensive arteries by applying the same theoretical model after using the same experimental method lend themselves to a fairly reliable comparison, especially if studies are carried out with the exclusive use of Na and the aid of computer simulation which avoid the many inaccuracies (8, 32, 45) inherent in the ancillary use of extracellular space indicators. That Na metabolism or distribution in tissues is somehow associated with the development or maintenance of chronic long-term hypertension has been known for many years, and recently reemphasized through a detailed systems analysis of circulatory regulation (19). Yet, the intimate nature of this association has remained obscure and elusive, though there have been some notable findings, namely, Na ions carry most of the depolarizing current of arterial action potentials (28), and Na plays the dominant role in ionic transfers in response to changes in arterial transmural pressures (12, 17) (the so-called concentration gradient theory). The present results showing marked changes of Na distribution in aorta of SHR provide an experimental unifying substratum at the subtissue level for the recent observations reported by others regarding electrolyte-dependent augmented responses of arterial wall to norepinephrine (22) and angiotensin (15, 22). The question naturally arises as to whether the Na tissue redistribution found in hypertensive arteries is a causative factor of the hypertensive state or is a consequence of the hypertensive
Variable
BP* k 01 h2
k 21 h k32 EC/IC Na ratio-t
Control
(TZ = 8)
102.8&-0.98 44.1ztI .77 8.4zt0.14
3.1AO.35 1.2hO.50 0.76zkO.23
1.7~tO.38
Hypertensive
(rt = 6)
190.0*1.91
Level
-- -
P < 0.0001
62.kt5.71 14.0zt1.22
P < 0.02
P < 0.001 P < 0.02 NS P < 0.05
1.9Zto.24 l.OZtO.41 0.16ztO.04
6.3&l
Signif
.06
P < 0.01
Transport rate constant (kij) is defined as the fraction of Na in one compartment (2nd subscript) which enters another (1st subscript) in unit time. For instance, k2i means the fraction of compartment 1 which enters compartment 2 in one second. Refer to Fig. 1 for identification of transport rate constants. Values of kij are mean AX SE, per second, multiplied by lo3 to facilitate comparison. The Student t-test was applied to ascertain significance levels. * BP = blood pressure; values are mean A SE, in mmHg. t The following expression was used (34; 35) to calculate the ratio of EC/IC Na: EC/IC = QAQ2 -I- Q3) = (QdQd/ = quantity of material (kdh~/~~ + kdhd, w h ere the Q’s symbolize in the respective compartments. of Na movements from EC to IC compartk21 , representative ment, was decreased by 39%. 4) Although k32 was also changed, no further emphasis is made on this change owing to its relatively high associated SE. 5) Application of the equation shown at bottom of Table 1 gives the ratio of EC/IC Na. This ratio was 1.7 for the control group and 6.3 for the SHR group. DISCUSSION
The finding of a significantly increased kol, the transport rate constant from tissue to outside (Fig. l), indicates a faster Na turnover in the aorta of SHR. It is of interest that similar results for Na in hypertensive arteries were independently obtained, namely, increased “exchangeable” Na in rat aorta (46), increased rate of initial efflux in canine carotid (43), and increased turnover in rat aorta (26). On the other hand, the findings (Table 1) of an increased klz, a decreased k21, and an augmentation of the EC/IC ratio from 1.7 in
outflow data (*) and computer points are printed as ( X).
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (150.216.068.200) on January 13, 2019.
SODIUM
KINETICS
IN
ARTERIAL
WALL
OF
HYPERTENSIVE
condition. It was suggested that ionic exchange alterations are directly involved in changes of vascular tension (12, 17), that these alterations are not themselves the result of a change in tension (12, 17), and that they are primary rather than secondary alterations dependent on abnormal outputs from sympathetic and adrenal regulatory systems (25). Most studies of arterial wall Na have been carried out on relatively large arteries, whereas increased peripheral resistance, the determinant of the hypertensive disease, is mainly related to a diminished caliber of small arteries and arterioles and much less to a contraction of the aorta or carotid. In other words, to lend more credence to a probable causative mechanism, one should find at least some kind of gross Na and water abnormalities in the small arteries and arterioles. Of great interest are, therefore, the results of Koletsky et al. (29) who found a significant rise in bulk Na and water in the fine threads of mesenteric artery divisions and their branches in rats made hypertensive and of Tobian et al. who reported increased bulk Na (41) and water (42) in the walls of mesenteric arterioles of hypertensive rats. They pointed out (42) that the excess water would thicken the arteriolar wall and reduce the lumen, thus increasing resistance to flow. Excess water has also been associated with increased vessel stiffness in hypertension (9). This change of stiffness would reduce the degree of wall expansion with each pulse wave. Furthermore, EC-to-IC concentration changes of the electrolytes themselves have been shown to have intrinsic effects on the contractile response or reactivity of arteries (12, 17, 22). Finally, it appears of interest to combine the finding of altered Na distribution in hypertensive arteries with scattered fragmentary evidence involving aldosterone, the chief regulator of bodily Na. It has been reported that arterial hypertension may be associated with hyperaldosteronism in man (5, 6, 16) and in the rat (30);
871
ANIMALS
that arterial wall is one of the tissues which shows high concentration and protracted disappearance of tritiated aldosterone (24) ; and that aldosterone promotes in arterial wall an increase of EC Na at the expense of IC Na (34), a change in the same direction as the rise of Na EC/IC ratio found in SHR. Therefore, it seems reasonable to postulate the following integrative humoral mechanism operative at the arterial wall level for the development of hypertension : elevated circulating aldosterone may lead to translocation of Na into the EC space of the vessel wall, followed by accompanying water retention in it, diminution of lumen with change of wall stiffness, concomitant ion effects on vessel contractile response and/or reactivity, and increased peripheral resistance manifested by hypertension. This mechanism, of course, is not intended to be inclusive of all types of hypertension or exhaustive of contributing factors. Naturally, superimposed on this description we have effects of angiotensin, catecholamines, neural system, etc. The suggested mechanism may first appear a large speculative step, yet all the links of the chain have been shown experimentally, though severally. We thank Dr. George A. Smith of Wood Veterans Administration Center for constructive criticism of the manuscript and Mrs. Jeaninne T. Leming of the Medical College of Wisconsin, Milwaukee, Wis., for editorial assistance. This work was supported in part by research grants of the Wisconsin Heart Association and the Marquette University Committee on Research. It is also VA Research Project 5301-01. Present address of J. A. Madden: Departamento de Fisiologia e Farmacologia, Universidade Federal de Pernambuco, Recife, Pernambuco, Brazil. Received
for publication
7 February
1975.
REFERENCES Compartmental analysis in kinetics. In: Computers in edited by R. W. Stacy and B. D. Waxman. New York : Academic, 1965, vol. II, p. 173-201. BERMAN, M., AND R. SCHOENFELD. Invariants in experimental data on linear kinetics and the formulation of models. J. APPZ. Physics 27: 1361-1370, 1956. BRADING, A. F. Ion distribution and the role of calcium in cellular function. Phil. Trans. Roy. Sot. London, Ser. B 265 : 35-46, 1973. BROWNELL, G. L., M. BERMAN, AND J. S. ROBERTSON. Nomenclature for tracer kinetics. Intern. J. AppZ. Radiation Isotopes 19: 24% 262, 1968. CONN, J. W., E. L. COHEN, D. R. ROBNER, AND R. M. NESBIT. Normokalemic primary aldosteronism-a detectable cause of curable “essential” hypertension. J. Am. Med. Assoc. 193 : 200-206, 1965. CONN, J. W., D. R. ROBNER, E. L. COHEN, AND R. M. NESBIT. Normokalemic primary aldosteronism-its masquerade as “essential” hypertension. J. Am. Med. Assoc. 195 : 21-26, 1966. DE LA RIVA, I. J,, P. BLAQUIER, AND N. BASSO. Water and electrolytes during experimental renal and DCA hypertension. Am. J. Physiol. 2 19 : 1559-l 563, 1970. DE LA RIVA, I. J., P. BLAQUIER, N. BASSO, AND A. C. TAQUINI. Water and electrolyte distribution in the artery wall. Acta Physiol. Latinoam. 14 : 307-3 14, 1964. FEIGL, E. O., L. H. PETERSON, AND A. W. JONES. Mechanical and chemical properties of arteries in experimental hypertension. J. CZin. Invest. 42 : 1640-1647, 1963. FRIEDMAN, S. M. Lithium substitution and the distribution of sodium in the rat tail artery. Circulation Res. 24 : 168-175, 1974. FRIEDMAN, S. M. An ion exchange approach to the problem of intracellular sodium in the hypertensive process. Circulation Res. 24-25, Suppl. I: 123-128, 1974. FRIEDMAN, S. M., AND D. B. ALLARDYCE. Sodium and tension in an artery segment. Circulation Res. 11 : 84-89, 1962. GAMBLE, J. L., -JR. Potassium binding and oxidative phosphorylation in mitochondria and mitochondrial fragments. J. BioZ. Chem. 228: 955-971, 1957.
1. BERMAN, Biomedical 2.
3. 4.
5.
6.
7.
8.
9.
10. 11.
12. 13.
M.
Research,
14. GARRAHAN, exchange 15.
16.
17.
18. 19. 20.
21.
22. 23. 24.
25.
26.
P., M. F. VILLAMIL, AND J. A. ZADUNAISKY. Sodium and distribution in the arterial wall. Am. J. Physiol. 209: 955-960, 1965. GAVRAS, H., H. R. BRUNNER, E. D. VAUGHAN, JR., AND J. H. LARAGH. Angiotensin-sodium interaction in blood pressure maintenance of renal hypertensive and normotensive rats. Science 180 : 1369-1372, 1973. GENEST, J., G. LEMIEUX, A. DAVIGNON, E. KOIW, W. NOWACZYNSKI, AND P. STEYERMARK. Human arterial hypertension: a state of mild chronic hyperaldosteronism? Science 123 : 503-505, 1956. GUIGNARD, J.-P. AND S. M. FRIEDMAN. Intraluminal pressure and ionic distribution in the tail artery of rats. Circulation Res. 27: 505-512, 1970. GUNN, R. B., AND C. S. PATLAK. The uptake curve in tracer kinetics. Math. Biosci. 6 : 19-24, 1970. GUYTON, A. C., T. G. COLEMAN, AND H. J. GRANGER. Circulation: overall regulation. Ann. Rev. Physiol. 34: 13-46, 1972. HAGEMEIJER, F., G. RORIVE, AND E. SCHOFFENIELS. The ionic composition of rat aortic smooth muscle fibres. Arch. Intern. Physiol. Biochim. 73 : 453-475, 1965. HANSEN, T. R., G. D. ABRAMS AND D. F. BOHR. Role of pressure in structural and functional changes in arteries of hypertensive rats. Circulation Res. 24-25, Suppl. I: 101-107, 1974. HARRIS, G. S., AND W. A. PALMER. Effect of increased sodium ion on arterial sodium and reactivity. CZin. Sci. 42 : 301-309, 1972. HEADINGS, V. E., P. A. RONDELL, AND D. F. BOHR. Bound sodium in artery wall. Am. J. Physiol. 199 : 783-787, 1960. HOLLANDER, W., D. M. KRAMSCH, A. V. CHOBANIAN, AND J. C. MELBY. Metabolism and distribution of intravenously administered d-aldosterone-1 , Z-H3 in the arteries, kidneys, and heart of dog. Circulation Res. 18-l 9, Suppl. I : 35-47, 1966. JONES, A. W. Altered ion transport in vascular smooth muscle from spontaneously hypertensive rats. Circulation Res. 33 : 563-572, 1973. JONES, A. W. Altered ion transport in large and small arteries from spontaneously hypertensive rats and the influence of calcium. Circulation Res. 24-25. I SUDD~. I : 117-122. II , 1974.
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (150.216.068.200) on January 13, 2019.
872 27. JONES, A. W., E. 0. FEIGL, AND L. H. PETERSON. Water and electrolyte content of normal and hypertensive arteries in dogs. Circulation Res. 15 : 386-392, 1964. 28. KEATINGE, W. R. Sodium flux and electrical activity of arterial smooth muscle. J. Physiol., London 194 : 183-200, 1968. 29. KOLETSKY, S., H. RESNICK, AND D. BEHRIN. Mesenteric artery electrolytes in experimental hypertension. Proc. Sot. Exptl. Biol. Med. 102: 12-15, 1959. 30. KUMAR, D., A. E. D. HALL, R. NAKASHIMA, AND A. G. GORNALL. Studies on aldosterone. II. Hypertension as a cumulative effect of aldosterone administration. Can. J. Biochem. Physiol. 35 : 113-l 18, 1957. 31. LING, G. N. A Physical Theory of the Living State: The AssociationInduction Hypothesis. New York : Blaisdell, 1962, p. 198, p. 322. 32. LING, G. N., AND M. H. KROMASH. The extracellular space of voluntary muscle tissues. J. Gen. Physiol. 50 : 677-694, 1967. J. G. Digital computer simulation as an aid to the 33. LLAURADO, study of arterial wall Na kinetics. J. A@. Physiol. 27: 544-550, 1969. 34. LLAURADO, J. G. Some effects of aldosterone on sodium transport rate constants in isolated arterial wall: studies with computer simulation and analysis. Endocrinology 87 : 5 17-526, 1970. J. G. Relationship between kinetics of inflow and 35. LLAURADO, outflow as the basis of a computer simulation for solving compartmental models : example of’ electrolyte transfers in cardiovascular Studies with Radioisotopes in Medicine. Vienna: tissues. In: Dynamic Intern. Atomic Energy Agency, 197 1, p. 13-26. 36. LLAURADO, J. G. Compartmental approaches to water and electrolyte distribution. In: Engineering Principles in Physiology, edited by J. H. U. Brown and D. S. Gann. New York : Academic, 1973, vol. II, p. 347-372.
J. G.
LLAURADO
AND
J. A. MADDEN
J. O., AND J. C. HALL. Effect of aldosterone on liver 37. MALBICA, mitochondria isolated from adrenalectomized rats. Am. J. Physiol. 214: 1054-1062, 1968. N. T. STOWE, R. R. SMEBY, AND F. M. 38. SEN, S., G. C. HOFFMAN, BUMPUS. Spontaneous hypertension and erythrocytosis in rats. In : S’on taneous Hypertension : Its Pathogenesis and Complications, edited by K. Okamoto. New York: Springer, 1972, p. 227-230. 39. SMITH, G. A., AND J. G. LLAURADO. Retrieval of transport rates from truncated data of kinetic models. Proc. Ann. Conf. Eng. Med. Biol. 13: 292, 1971. 40. SMITH, G. A., AND J. G. LLAURADO. Computer modeling of nonsteady state sodium kinetics in liver. IEEE Trans. Biomed. Eng. 21 : 433-443, 1974. 41. TOBIAN, L., J. JANECEK, A. TOMBOULIAN, AND D. FERREIRA. Sodium and potassium in the walls of arterioles in experimental renal hypertension. J. Clin. Invest. 40 : 1922-l 925, 1961. 42. TOBIAN, L., R. OLSON, AND G. CHESLEY. Water content of arteriolar wall in renovascular hypertension. Am. J. Physiol. 216 : 22-24, 1969. 43. VILLAMIL, M. F., P. NACHEV, AND C. R. KLEEMAN. Effect of prolonged infusion of angiotensin II on ionic composition of the arterial wall. Am. J. PhyJiol. 2 18 : 1281-1286, 1970. 44. VILLAMIL, M. F., V. RETTORI, L. BARAJAS, AND C. R. KLEEMAN. Extracellular space and the ionic distribution in the isolated arterial wall. Am. J. Physiol. 214: 1104-l 112, 1968. 45. WILLIAMS, J. A., AND D. M. WOODBURY. Determination of extracellular space and intracellular electrolytes in rat liver in uivo. J. Physiol., London 2 12 : 85-99, 197 1. 46. ZECH, P., P. BOULETREAU, AND J. P. BOISSEL. Activite specifique de l’aorte mesuree par le sodium radioactif chez le rat uninephrectomise en hypertension exptrimentale (DOCA + sel). Compt. Rend. Sot. Biol. 162: 1371-1375, 1968.
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (150.216.068.200) on January 13, 2019.
