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Exp Clin Cardiol. 2001 Winter; 6(4): 188–194.
PMCID: PMC2858998
Experimental Cardiology

Tracer kinetics analysis of the extracellular spaces in saline perfused hearts



Precise estimation of the cellular water content presupposes a correct definition of the water fraction in tissue extracellular space. Low molecular weight markers (LMM), such as sulphate ion and sucrose, are widely used to define extracellular space size despite indications that they penetrate the cell. In contrast, inulin, with molecular weight of about 5000, is commonly regarded as a cell impermeable extracellular marker.


To compare LMM with inulin as markers in determining extracellular space size.


The size of extracellular space in guinea pig hearts perfused with crystalloid solution (hydrated hearts) was determined morphometrically and by mathematical model analysis of washout kinetics of LMM (35SO4, 14C-sucrose) or 3H-inulin.


Morphometrically, the sizes of vascular and interstitial spaces in the hydrated hearts were estimated to be 102±8 mL/kg wet mass (wm) and 452±17 mL/kg wm, respectively. Comparable data were obtained from model simulation of tracer washout: 67 mL/kg wm for vascular space and 439 to 462 mL/kg wm for interstitial space. Tracer penetration into cellular water, as shown by model analysis, was 28% for LMM and, reported here for the first time, 18% for inulin. The observed edema was probably due entirely to fluid accumulation in the interstitial space.


Intracellular penetration of LMM must be taken into account, especially in modern nuclear magnetic resonance spectroscopic methods of cellular water monitoring in isolated perfused hearts.

Keywords: Extracellular space, Interstitial space, Inulin, Mathematical model, Myocardial edema, Perfused heart

Rates of cellular metabolic reactions depend on the molar concentrations of enzymes and their substrates being dissolved or dispersed in the cellular water. Cardiomyocytes undergo significant cellular edema in various pathological situations, such as early stages of cardiac hypertrophy (1) and ischemia (2). The resulting alterations in cell volume may play an important part in the regulation of cardiac cell function and metabolism (36). Therefore, a precise definition of cellular water volume is essential for accurate and reliable calculations of in vivo fluxes and concentrations, and for investigation of the role of cell volume changes in pathological conditions (7).

The cellular water volume is commonly estimated by subtraction of extracellular water volume from total tissue water content. The accuracy of the total tissue water estimations is rather high (8). However, quantification of myocardial extracellular space size from the partition of specific extracellular markers may often lead to serious artefacts due to penetration of low molecular weight markers (LMM), such as sulphate (9,10), sucrose (9,11) and sorbitol (12), into cardiomyocytes. Intracellular penetration of sucrose was also shown in skeletal muscles, both in vivo (13) and in vitro (14). The accumulation of sucrose inside the cells of in vitro crystalloid perfused isolated rat hearts (9) is higher than that in vivo (15). Taking into account these data, the conclusions of Taylor et al (16) and Polimeni and Buraczewski (10) that low molecular weight substances are unreliable for defining extracellular spaces in saline perfused hearts appear quite justified.

There are at least two possible ways to solve this problem. First, the distribution of high molecular weight tracer can be used; for example, inulin, with a molecular weight of about 5000, is commonly regarded as cell impermeable (11,12,16). Second, the washout kinetics of LMM may be analyzed: the slow entry of the tracer into cells (10,17) may be reflected by the distinct slowest kinetic phase of its washout.

In the present study, we compared both approaches by analyzing the washout kinetics of [3H]inulin and the LMM 35SO42− and [14C]sucrose from isolated perfused guinea pig hearts. The original mathematical model of extracellular calcium exchange in perfused myocardium was used for the analysis (18). A slight modification of this model allows the estimation of kinetic pools of vascular, interstitial and cellular origin. The sizes of the main tissue compartments were also estimated by morphometric analysis of the myocardium. A good correspondence between kinetic and morphological estimations indicates the reliability of the mathematical simulation method for determination of extracellular space size with either inulin or LMM tracers. The intracellular water distribution volumes for extracellular tracers in isolated perfused hearts were found to be 28% for LMM and, reported here for the first time, 18% for inulin.



Hearts excised from male guinea pigs under urethane anesthesia (1.6 g/kg intraperitoneally) were perfused in the Langendorff mode through the aorta at a flow rate of 12 to 15 mL/min and an aortic pressure of 55 to 60 mmHg. The perfusing solution was a modified Tyrode’s solution containing (in mM) NaCl 149, KCl 8, CaCl2 1.8, MgCl2 1.08, glucose 11 and HEPES (pH 7.3, 37°C), gassed with 100% O2. The isovolumic pressure was measured by means of a water filled latex balloon inserted into the left ventricular cavity and connected to a Gould Statham P23Db pressure transducer (Statham Instruments, USA) and a Gould 2400 recorder (Gould Instruments, USA). The end-diastolic pressure was adjusted to 12 to 14 mmHg. Constant drainage of the perfusate from the right ventricle was ensured with a needle (inner diameter 0.8 mm) inserted through the apex. The atria were discarded. Hearts were paced at 3 Hz. This study was performed in accordance with the Guide for the Care and Use of Laboratory Animals published by the US National Institutes of Health (NIH publication No. 85-23, revised 1996).

Tracer washout:

Following 45 min of equilibration, the perfusate was switched to solutions containing LMM, 35SO4 or 14C-sucrose (0.45 μCi/mL), for 5 min or 3H-inulin (1.16 μCi/mL) for 45 min. When radioactive sucrose was used, the perfusate was additionally supplied with 5 mM sucrose. When 35SO4 was used, MgCl2 was replaced by an equimolar amount of MgSO4. Thereafter, the hearts were perfused again with nonradioactive solutions. The effluents were collected for 5 min (LMM) every 5 s or for 20 min (3H-inulin) every 5 to 120 s for radioactivity counting in Bray scintillation solution. The tracer content in the myocardium at the end of washout was determined by direct measurement of radioactivity in the tissue (19) and by exponential analysis of the final linear phase of effluograms. Both approaches yielded comparable results; therefore, the data were analyzed with the latter approach.

Preliminary treatment of tracer washout curves:

Two approaches were used to reduce scattering of experimental points in the effluograms of tracer concentration. First, the time course of total label content in the myocardium was used instead of the commonly used (20) label concentrations in perfusate. These curves were obtained by consecutive integration of effluent radioactivities in probes, beginning with the last sample (19). Last sample radioactivity was summed with residual small radioactivity in the heart. This approach generates smooth curves that are convenient for curve peeling.

Second, taking into account the multiexponential pattern of tracer washout (20,21), the kinetic curves for total label content in the myocardium were further treated according to the method of Solomon (20) by splitting them into mono-exponentials. This method of approximation of experimental curves to ideal ones further diminishes the scatter of experimental points and allows most probable reconstructing of the tracer contents at any time of washout, including the first 5 s, for initial kinetics.

Heart weight estimation:

At the end of the experiment the latex balloon was rapidly removed and the heart was weighed after rapid removal of the aortic segment and drainage needle. This procedure prevents postperfusion heart compression at the expense of leaving some amount of fluid in the heart chambers (16). To diminish this disadvantage, the perfused hearts were subjected to an additional 20 min perfusion with glutaraldehyde (see next subsection) to prevent the postperfusion changes in myocardial volume. The mass of fluid freely flowing out in 10 min from excised myocardium was 101±11 g/kg wet mass (wm) (n=7).

The dry weights of perfused hearts (72 h at 90°C in circulating air) were 98.4±2.4 g/kg wm (n=14). After correction for the aforementioned excess of liquid in the hearts, this value was higher: 109.4±2.7 g dry mass/kg corrected wm.

Morphological studies:

After 45 min of equilibrium, hearts were perfused with 2.5% glutaraldehyde in 0.1 M sodium cacodylate buffer (pH 7.4) for 20 min at room temperature (22) and at a constant flow rate (12 to 15 mL/min). During fixation, the initial complete relaxation of the myocardium was followed by a slowly developing slight contracture (Figure 1). This contracture was associated with a nonsignificant decrease in heart weight: 2.75±0.13 g after fixation (n=7) versus 2.89±0.07 g without fixation (n=8 for a body weight of 506±16 g). Thus, the original hydrated state was essentially preserved after fixation.

Figure 1
Kinetics of isovolumic pressure in the left ventricle on perfusion with fixative. The arrow indicates replacement of perfusate with glutaraldehyde fixative

Tissue specimens of the left ventricle were excised from the fixed heart, cut into 1 mm3 blocks and immersed into fresh glutaraldehyde, washed in buffer, postfixed in 1% osmium tetroxide, dehydrated in a series of graded ethanols and propylene oxide, and embedded in Araldite (Merck, Germany). Semithin (1 μm thick) and ultrathin (70 to 80 nm thick) sections were cut in a Reichert (Austria) or LKB (Sweden) ultramicrotome. Semithin sections were stained with toluidine blue or hematoxylineosin. Ultrathin sections were stained with uranyl acetate and lead citrate and were examined in a JEM-100Cx electron microscope (Nihon Densi, Japan). Morphometric measurements were done in 40 low power fields of semithin sections for each of seven hearts using an IBAS-1 computer system for image analysis (Opton, Germany).


All reagents were of analytical grade. Radioactive tracers were purchased from Amersham (United Kingdom).

Model analysis of tracer washout:

Figure 2 shows the kinetic scheme realized in the mathematical model. The basic model of Aliev (18) describes tracer distribution in capillaries (compartment 1) along their length, in the interstitium (compartment 2) and the intracellular space (compartment 3). Each compartment is characterized by its tracer distribution volume, Vx, and tracer concentration, Cx (18), where x indicates the respective compartment.

Figure 2
Kinetic scheme for the exchange of extracellular tracers in the myocardium. The model considers four compartments. Three of these (1 to 3) are located in tissue; only one (0, External) is outside of the heart walls. C0, C1 and Cv indicate tracer concentrations. ...

In tracer pre-equilibrated hearts, the tracer concentrations are equal in all compartments. At the onset of washout, the tracer-free perfusate passes through capillaries at a volume rate ‘Flow’, clearing them of tracer-containing medium. During subsequent passages, the tracer concentration in the perfusate changes from its constant zero value of C0 at the beginning of the capillary length to C1 at its end. The change in perfusate tracer concentration is due primarily to bilateral diffusional exchange between capillaries and the interstitium, determined by an integral permeability constant, ‘PS’. The interstitial tracer concentration is also affected by the exchange between cardiomyocytes and the interstitium at an integral permeability constant, ‘k3=k4’. The integral permeability here refers to the permeability of the total surface of cells or capillary in a given unit of heart mass (kg wm).

A minor modification of the basic model (18) was introduced to account for features of perfusate flow out from the heart. Despite all attempts to limit the volume of fluid in chambers of perfused heart (by a latex balloon in the left ventricle and drainage of the right ventricle), a small amount of perfusate remained in the chambers and slowed down the rapid kinetics of tracer washout from the vascular compartment. To account for this dilution effect, an additional external compartment, “0”, was introduced, reflecting the volume of perfusate remnants in the heart chambers and some fluid on the heart’s surface. In this compartment, a small part of the perfusate mixes with its content at an assumed volume rate of ‘Flow × a’ and enters the venous effluent with some time delay (Figure 2). This part of the flow also reflects the partial shunting of perfusate outflow through the Thebesian vessels into the left ventricle. The main part of the flow, ‘Flow × (1–α)’, enters the effluent directly. This part of the flow reflects the direct outflow of perfusate through the open coronary sinus. The combination of these partial flows gives effluent with a tracer concentration of ‘Cv’.

The simplest model does not account for the well known phenomenon of flow heterogeneity in capillary and vascular perfusion beds (23). Flow heterogeneity is observed in conditions of high resistance of the vascular bed to perfusion, at around 170 to 320 mmHg × min × g/mL (24). In our experimental conditions, this parameter was very low, 12 to 13 mmHg × min × g/mL, as evaluated by the ratio of the perfusion pressure, 55 to 60 mmHg, to flow rate, 4.61 to 4.68 mL/(min × g wm). According to Rose and Goresky (24), perfusion heterogeneity can be neglected at a resistance below 50 to 60 mmHg × min × g/mL.

The dynamics of tracer contents in hearts during tracer washout, taken as a sum of monoexponentials (Table 1), were subjected to model analysis. Optimal modelling parameters, listed in Table 1 (perfusion rates and total tracer contents) and Table 2 (distribution volumes of compartments 0 to 3, integral permeability constants), were chosen by successive approximation of curves predicted by the model to experimental curves. Each cycle of approximation was started by fitting the final slow phase of tracer washout. The first cycle of simulation used published parameters (18) of the model. Values of coefficient α, 0.35 for both species of tracers, were obtained from the best fit of experimental curves on mathematical modeling. (Details of this modelling online, with Pascal programming, are available from MK Aliev at request and no charge.)

Exponential analysis of the kinetics of radioactive tracer content in hydrated myocardium of guinea pig
Myocardial tracer spaces from mathematical simulation and morphometry of tissue compartments

Statistical analysis:

Where appropriate, data are given as mean ± SEM of n determinations. The quality of the fit was estimated from the coefficient of variation for logarithmic values (24).


Figure 3 shows the kinetics of the tissue contents of LMM, 35SO4 and 14C-sucrose, and of 3H inulin, a heavier marker with a molecular weight of about 5000. The final exponents of tracer contents were clearly seen and were resolved by Solomon’s procedure (20) as slowly exchanging tracer pools with small distribution volumes (Table 1). The small size of this compartment and the very slow kinetics of exchange may be indicative of their cellular origin (9). Accordingly, the half-time of LMM washout (82.8 s) for the final slowly exchanging pool is in perfect agreement with data obtained by Bunger (25) for the same pool of intracellular 14C-lactate washout (90 s) in perfused working guinea pig hearts. In addition, taking into account that membrane permeabilities for glucose and inulin differ from each other by a factor of 3.3 (26), the observed 3.8-fold difference in half-times of exchange of inulin and LMM (311 s versus 82.8 s) certainly indicates that the slow phases have a common origin. It is important to note that the T-system cannot be considered to be a main source of slow tracer washout because of its extremely small volume, even in the intact rat heart (9.5±0.2 mL/kg wm [27]).

Figure 3
Kinetics of contents of 3H-inulin (n=7) and low molecular weight markers (LMM: 35SO4, n=4; 14C-sucrose, n=3) in guinea pig hearts during tracer washout. The kinetic curves for the LMM 35SO4 and 14C-sucrose were superimposable; therefore, they are shown ...

These washout kinetics were finally analyzed by the mathematical model of tracer exchange in the extracellular spaces of perfused myocardium (18). This kinetic model takes into account tracer distribution in capillaries along their length, and in the interstitium and intracellular space, possible binding of tracers on the outside of the sarcolemma, and capillary and cell membrane permeabilities to tracers. With small modifications, the model can also account for mixing of a part of the capillary outflow with some residual perfusate in the heart chambers (Figure 2). The mass of perfusate remnants was directly measured as 101±11 g/kg wm (n=7) after transcapillary perfusion of the hearts with glutaraldehyde to fix their hydrated morphological configuration (see Animals and methods).

Model analysis data, obtained from the best available fitting of experimental curves (Figure 3), are presented in Table 2 as two sets of values. The initial data include the spaces outside of the heart walls, determined by simulation. The corrected data were obtained from the initial data after normalization to the actual mass of perfused myocardium, 0.899 kg; that is, 1 kg of perfused organ minus 0.101±11 kg of measured associated perfusate mass. For example, the interstitial water space derived from inulin measurements, 461.6 mL/kg wm, was calculated as the initial inulin space, 415 mL/ kg wm, divided by the actual mass, 0.899 kg.

In Table 2 the data obtained from mathematical simulation are compared with morphometric estimation of vascular and interstitial spaces. Taking into account that in intact rat hearts the water content in the interstitium is 107±7 mL/kg wm (7), then both methods indicate huge enlargement of interstitial space due to accumulation of water. This phenomenon is specific to saline perfused hearts (16,19,22,28,29). While the interstitial volume estimates are independent of the method used, the perfusion space volume obtained by simulation is lower than that obtained from morphometry (66.7 mL/kg wm versus 102±8 mL/kg wm). This 35 mL difference can be ascribed completely to the volume of capillary endothelial cells, reported to be 36 mL/kg wm (22). The quality of simulation can also be assessed by comparing the model estimates of integral capillary permeability for LMM (23.4 mL/s/kg wm) with capillary permeability for 42KCl (17.7 mL/s/kg wm) obtained by the tracer dilution method (30). These values appear to be reasonably close to each other.

Taken together, these data may indicate the general reliability of model analysis data, including those for cellular contents of LMM (94.6 mL/kg wm) and inulin (61.2 mL/kg wm) (Table 2). The percentage of tracer penetration into cell water may be estimated as follows. In hydrated hearts, the dry matter, 109.4±2.7 g/kg wm (n=14), is located mostly in the cells. Therefore, the cell water volume of 337 mL/kg wm can be estimated as the difference between total cell volume (446±16 mL/kg wm, Table 2) and tissue dry mass content. With this value, the percentage of tracer penetration into cell water may be estimated as 28.1% for LMM (94.6 mL/337 mL × 100%) and 18.2% for inulin (61.2 mL/337 mL × 100%). Compared with inulin, LMM penetration into cardiomyocytes is 1.54-fold higher.

With these data, the ratio of cellular water to dry mass in perfused hearts is about 3.08 (337 mL/109.4 g). Recently this ratio was calculated for intact in vivo hearts to be 3.03 mL cellular water/g dry mass (7). The similarity of these ratios may indicate that in our perfused hydrated hearts the cardiomyocytes essentially preserve their in vivo water contents. In line with this conclusion, cardiomyocytes of hydrated hearts retain their normal morphological appearance (Figure 4). Therefore, recorded edema is probably entirely due to the accumulation of liquid in the interstitial space. Contrasting data obtained by Polimeni and Buraczewski (10) are discussed by Aliev et al (7).

Figure 4
Electron microscopy of longitudinal sections of saline perfused hydrated guinea pig heart showing widening of the interstitium (Int), the thin wall of a capillary with endothelial cells (Ec), and normal ultrastructure of cardiomyocytes (CM), mitochondria ...


The results of the present study confirm numerous previously published data about the penetration of extracellular LMM into cells of saline perfused isolated hearts. At the same time, we observed for the first time indications of intracellular penetration of inulin (18.2% of cell water volume). This rather unexpected result cannot be due to possible errors during mathematical modelling because the intracellular distribution volumes of inulin estimated from modelling (55 mL/kg wm, Table 2) and simpler exponential analysis (60 mL/kg wm, Table 1) are essentially similar.

An even simpler approach can be used to observe the penetration of inulin into cells. The curve in Figure 3 indicates the presence of a significant amount of tissue inulin between the fifth and 20th min of cold perfusion. As judged from the LMM washout curve (Figure 3), tracer washout from the perfusion accessible tissue spaces is essentially complete after 5 min of cold perfusion. Therefore, the remaining inulin would be associated with washed out cells, being either accumulated in them or tightly bound to their surface. Because extracellular markers have commonly been chosen for their negligible ability for nonspecific binding, the intracellular accumulation of inulin remains the only plausible explanation of our data. Because these data may have important methodological consequences (reviewed in 7), we will discuss the details of tracer determinations and related data more particularly.

In vivo, low penetration of LMM into cells has been shown in intact skeletal muscles (13,15). Aliev et al (7), in a recent review, analyzed the reasons for the difference in measured interstitial volumes in intact, in vivo rat hearts (153±11 g/kg wm from the distribution of 14C-inulin [31] and 116±6 g/kg wm from morphometry [20]). Because morphometry is a more direct and reliable method of cell volume quantification, the higher 14C-inulin derived value was attributed to overestimation of this space due to partial penetration of the tracer into the cell (7). Basing on the analyzed data, the values of inulin and LMM (14C-mannitol) penetration into cardiomyocytes of the intact heart were estimated to be 5.5% and 8.5%, respectively, of cell water volume (7). Thus, the penetration of LMM into cardiomyocytes is higher by a factor of 1.54 (8.5% versus 5.5%), like in vitro, and the latter data cannot be considered to be an artefact during saline perfusion of isolated heart. The finding of low penetration of 14C-inulin into the matrix of isolated rat liver mitochondria (32) is in agreement with this statement.

Although the basic mechanisms of inulin and LMM penetration through cellular membranes may be similar in vivo and in vitro, a several-fold increase in this penetration during in vitro saline perfusion deserves special consideration. In saline perfused hearts, washout of plasma proteins leads to saline accumulation in the extracellular spaces due to more filtration at a given hydrostatic pressure. As a result, the fibrillar collagen network (33) ruptures, followed by substantial exfoliation of capillaries from cardiomyocytes (Figure 4) and concomitant increased permeability to markers in affected cells. Page and Page (9) suggested that only a part of the cells is permeable to LMM as a result of cellular heterogeneity in the perfused hearts. Experimental verification of this interesting hypothesis with electron microscope autoradiography may be highly advantageous.

The main result of the present study is the methodological conclusion that intracellular penetration of markers commonly used for evaluation of extracellular water space should be taken into account. We have proposed corrections to intracellular distribution volumes of markers both from the final slow exponent of effluograms and from mathematical simulation of washout kinetics. The mathematical approach is more precise, especially for LMM, whose fast washout kinetics (Table 1, Figure 3) do not allow distinct time separation of the final slow cellular exponent. With LMM, this exponent is partly superimposed by faster exponents of interstitial origin. Consequently, the cellular distribution volume of LMM from the final exponent of tracer washout (117 mL/kg wm, Table 1) turns out to be higher than that from mathematical modelling (85 mL/kg wm, Table 2). Such a difference for inulin is negligible, as stated before, because inulin diffuses more slowly and the partial exponents are more separated in time (Table 1). In addition, mathematical modelling permits separate estimation of the interstitial sizes, and of integral capillary and cell membrane permeabilities.

Extracellular LMM are widely used in nuclear magnetic resonance (NMR) spectroscopic monitoring of total cellular water in isolated organs (2,34). In our opinion, the first direct evidence for LMM penetration into cardiomyocytes of the perfused rat heart was obtained by Clarke et al (34). They used phenylphosphonate (PPA) as a pH sensitive marker for 31P-NMR spectroscopy of the extracellular space. Careful examination of the NMR spectrum in Figure 1 of their paper finds some shoulder-like left-side directed enlargement of PPA resonance. Taking into account the usual pH difference of about 0.4 unit between intra- and extracellular spaces in myocardium and pH sensitivity of PPA, this shoulder-like enlargement may be caused by penetration of PPA into the more acidic environment of cardiomyocytes. Indeed, this shoulder appears quite clearly in the 31P-NMR spectra after 28 min of heart ischemia, when intracellular pH decreases to 6.1 (Figure 2 in Clarke et al [34]).

Our analysis of the data of Clarke et al (34) suggests a novel principle for extracellular space monitoring in perfused hearts. The new PPA-like extracellular LMM with increased pH sensitivity could be examined for continuous monitoring of their intracellular penetration. This may allow the true value of the extracellular water space to be obtained and its variations to be followed.


The authors gratefully acknowledge Dr P Dos Santos, Pessac, France, for helpful discussions and valuable help during preparation of this manuscript, and are grateful to Dr VI Veksler and Dr JA Hoerter, Chatenay-Malabry, France and Dr R Bunger, Bethesda, USA for critical reading of the manuscript. Part of this work was supported by the Russian Foundation for Basic Research, grants 00-04-48330, 01-04-49455 and 00-04-48480 for MKA, ANK and VIK, respectively.


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