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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Circ Res. Author manuscript; available in PMC 2010 December 22.
Published in final edited form as:
PMCID: PMC3008666

Regional Distribution of Diffusible Tracers and Carbonized Microspheres in the Left Ventricle of Isolated Dog Hearts


Microspheres of different sizes, 125I-labeled antipyrine (I-Ap), and 42KCl or 86RbCl were injected into the aortic inflow of isolated, Langendorff, perfused, nonworking dogs hearts at blood flows of 1.3–4.8 ml/min g−1. After 15 seconds to 5 minutes, the left ventricle was sectioned into about 300 ordered pieces, and the amount of each tracer was determined. For all tracers, the relative density of deposition was generally higher in the endocardial region, except in one heart in which the aortic pressure and the total coronary flow were low. The deposition of 42K and that of I-Ap were essentially similar in three hearts over a large range of regional variation. This finding suggests either that both tracers were distributed in proportion to flow or that a small diminution in relative density of deposition of 42K in high-flow regions due to lower transcapillary extraction was quantitatively similar to a decrease in the residual fraction of I-Ap in these same regions due to faster washout in the first 15–30 seconds after injection. Large microspheres were deposited preferentially in regions of high flow, exaggerating the apparent heterogeneity of regional flows. The distribution of the smaller microspheres was closer to that for I-Ap or 42K.

Keywords: myocardial blood flow, tracer exchanges, capillary permeability, iodoantipyrine, radioactive microspheres, 42-potassium, 86-rubidium, indicator-dilution curves, tissue residue functions, flow-limited washout

As a method of determining the distribution of blood flow, the use of microscopic particles such as macroaggregated albumin (1), rigid carbonized microspheres (27), or aggregated albumin microspheres (8) appears to be well validated for large tissue regions (2, 3). However, when the tissue regions are small, the proportionality between deposition and regional flow may fail (4, 7) or be moderated by the physical properties of the spheres (9) and perhaps by the pattern of arteriolar branchings.

For different reasons, the intratissue deposition of diffusible indicators after an intra-arterial bolus injection may not delineate flow patterns in small regions. Highly diffusible indicators such as tracer water or antipyrine equilibrate rapidly between blood and tissue, but they are washed out more rapidly from high-flow regions than they are from low-flow regions. Substances such as sodium and potassium for which the capillary membrane is a permeability barrier are equilibrated very slowly, and the fraction escaping from blood into tissue is less in regions with high flow than it is in those with low flow.

The purpose of the present experiments was to define a method for determining the true distribution of regional myocardial blood flow. We hoped to find at least two tracer particles of different sizes or diffusibilities that had identical regional distributions, so that we could argue that flow was the factor common to both and therefore that the distribution of either provided an estimate of the distribution of flow.

The present report is the first to provide data on the distribution of three different classes of tracers injected simultaneously in a single bolus: different sizes of microspheres (rigid particles), potassium or rubidium (partially barrier limited), and iodoantipyrine (flow limited) were used. Their deposition in small regions of the isolated, blood-perfused dog heart was determined by dividing the left ventricular myocardium into about 300 samples from apex to base, around the circumference, and through the wall. Detailed comparisons then permitted consideration of the mechanisms controlling the distribution and the deposition of these tracers.

We did not succeed in defining the ideal indicator of local regional perfusion, but an upper limit for regional perfusion heterogeneity was provided by the use of the smallest size of microspheres and a lower limit was provided by the use of iodoantipyrine. The method tested in this paper on isolated heart preparations should be applicable to hearts in situ, but our observation that the subendocardial perfusion rate was higher than the subepicardial rate should not be extrapolated to the normal working heart.

General Principles Underlying the Methodology

The early users of large, tracer-labeled microspheres equated their observations of complete trapping in a capillary bed with the idea that microsphere distribution was proportional to flow; however, this interpretation is untenable when the spheres are larger than the branches of the arterial system. Clearly, the problem is a practical one when the objective is to estimate, with high spatial resolution, the distribution of flow within an organ, because particles large enough to be trapped are necessarily larger than the smallest branches, the capillaries. Thus, we thought that it was essential to compare the distributions of different sizes of spheres, the rationale being that the deposition of the smallest ones must be most nearly proportional to flow. If two different sizes of small spheres are distributed similarly and larger spheres are distributed differently, then it could be argued that the effects of vascular geometry or local stream velocities on the larger spheres are substantial and that the effects on the two different-sized smaller spheres are negligible. The logical deduction, by elimination, would therefore be that the local flow distribution is the determinant of the distribution of deposition of the two groups of small spheres.

The use of diffusible indicators has the problem that the tracer is not firmly trapped: it leaves the bloodstream and inevitably returns to it at a later time. Furthermore, not all of it leaves. The fraction of the injected dose of tracer that is transiently deposited in each region equals the regional flow (F), expressed as a fraction of the total flow, times the extraction (E). E is defined as the fraction of tracer that is removed from the blood during its first passage from the artery to the vein draining the region. When return of tracer from tissue to blood is slow, as is true for potassium, this definition is valid. The deposition of 86RbCI, a potassium analogue, has also been used to examine regional myocardial blood flow (1012). However, the relative contents of these tracers in different regions cannot be directly translated into relative flows, because both potassium and rubidium extractions are diffusion limited or permeability limited in dog hearts (1315) and extraction decreases with increasing perfusion rate. For the quantities of potassium taken up by different regions to be proportional to the flows, the extractions must be similar in all regions in spite of differences in flow. When extraction diminishes with higher flow, the increase in F • E is proportionately less than the increase in flow.

The blood-tissue exchange of 125I-labeled iodoantipyrine (I-Ap), a highly diffusible indicator, is flow limited in dog hearts for wide ranges of plasma flows (16). Therefore, the instantaneous extraction of I-Ap at any point along a capillary is the ratio of its local extravascular volume of distribution to its total local intravascular and extravascular volume of distribution; this ratio should be close to unity since the capillary blood volume is small. With E being the same everywhere, the deposition is proportional to F alone, if the tracer does not return from tissue to blood. However, the tracer returns rapidly, and the corollary to rapid blood-tissue equilibration (the basis for flow-limited exchange) is that washout is proportional to local flow, which means that there is more rapid loss of tracer from high-flow regions than there is from low-flow regions. Thus, ideally, the I-Ap distribution should be obtained as soon as all the injected dose has entered the organ and before any of it has left. This “ideal time” is dependent on the brevity of the injection and on the flow, which is different in different regions; therefore, it is not possible to measure the content at the ideal time for all regions. Since the time for entry of indicator into the organ is only a few seconds and the washout takes a few minutes even for I-Ap (16), the least error will be incurred if the regional contents are measured a few seconds after the average of the regional ideal times.

Clearly, long delays must be avoided because, at times late in the washout phase, more tracer is retained in low-flow regions than in high-flow regions. This problem is not avoided by using a continuous infusion, as Paradise et al. (17) did for skeletal muscle by the technique of Thompson et al. (18). The continuous-infusion method has two disadvantages. (1) The longer the infusion, the less are the differences in regional content, all regions eventually equilibrating with the inflow. (2) Content is not proportional to flow except initially, for a few seconds at most, and therefore the use of a mathematical model such as a first-order mixing chamber is required to interpret the regional concentrations in terms of regional flows.

If blood flow is stopped several seconds after a bolus injection, the tissue contents of 42K and I-Ap tend to be slightly less than in proportion to flow in high-flow regions and slightly more than in proportion to flow in low-flow regions. The distribution of both tracers can only be somewhat less heterogeneous than the distribution of regional flows. In the Discussion, we argue that this deviation is small in both cases. Nevertheless, exact similarity of the distributions of 42K and I-Ap can only be coincidence unless their distributions are governed dominantly by the flow. Furthermore, equivalence of the distribution of I-Ap and microspheres constitutes strong evidence in favor of their distributions being proportional to regional flow.


Isolated Heart Preparation

These studies were carried out on isolated, blood-perfused dog hearts prepared as previously described (16, 19). The hearts were beating spontaneously. External work was not performed, because the left ventricle was kept empty by a vent through the apex. The total retrograde aortic flow was controlled by a previously calibrated constant-flow pump. Mean perfusion pressures, measured in the cannula at the time of tracer injection, were 90–158 mm Hg (mean 137 mm Hg) (Table 1); mean perfusion pressures were not allowed to exceed 160 mm Hg at any time during the experiment. In this heart preparation there was a tendency for the vascular resistance to increase slowly over several hours. Flows from the coronary sinus and the veins to the right heart were drained off through a cannula in the pulmonary artery. The pressure at the outlet of this cannula was held slightly negative to keep the right ventricle empty. The flow was measured by timed volume collection. Drainage from the left ventricular cavity, which is the sum of the aortic leak and the left thebesian flow, was also measured. The temperature of the perfusing blood was kept constant at 38°C.

Experimental Data

An external gamma-detector system was placed over the surface of the left ventricle to record radioactivity after injection of the gamma-emitting isotopes, In the later experiments, the flow was stopped as soon as the level of detected gamma activity reached a plateau or first began to diminish.

Isotopic Labels

Carbonized microspheres (Nuclear Products Division, 3M Co.) with diameters of 15, 35, and 50 µm were variously tagged with 169Yb (peak energy 0.110 Mex), 141Ce (peak energy 0.145 Mev), 51Cr (peak energy 0.320 Mev), and 85Sr (peak energy 0.514 Mev). The supplier stated that the densities of these microspheres were 1.3–1.6 g/ml. Light microscopic examination supported the manufacturer’s specification that the standard deviation for the distribution of the diameters was less than 5 µm. Spheres less than 10 µm in diameter were used in two experiments (nos. 5 and 6); their size distribution was not examined. We thought that even if a very large fraction of the microspheres (up to 25%) were not trapped during first passage, recirculation after return to the supporting dog would be negligible and the sizes of the retained spheres would be 7–10 µm. The escaping fraction of these spheres was measured by collecting and counting the total venous outflow in one experiment (no. 6) and was only 1.7%. In three recent experiments with small spheres with a narrower size distribution (9 ± 1 µm), the escaping fractions were 0.7, 1.2, and 2.0%.

The diffusible indicators used were 42KC1 and 86RbCl (Cambridge Nuclear) and 125I-labeled iodoantipyrine (I-Ap) (Radiochemical Centre). I-Ap was diluted on the day of the experiment so that free iodide should have constituted less than 2% of the total activity (20).

Experimental Procedures

Nine isolated heart preparations were used. In three, two sets of 15-µm microspheres, tagged differently, were mixed together for injection. In another experiment, 42KC1 was injected in a large bolus with 50-µm microspheres; however, because too few microspheres were injected, only the potassium data are presented. In the five other preparations, microspheres of two different diameters, tagged differently, were injected in combination with 42KC1 or 86BbC1 or with 42KC1 and I-Ap. In every experiment, all of the indicators used were premixed in one syringe and injected into the aortic cannula in a cross-stream direction to aid mixing in the cannula and the aortic root. Although poor mixing conceivably could influence the relative fractions entering the right and left coronary arteries, there seems to be little likelihood of it influencing delivery to epicardial or endocardial regions.

The different microspheres were always premixed with 0.1 ml of polyoxyethylene-80-sorbitan monovaleate (Tween-80) and placed in an ultrasonic bath for 10–15 minutes at 50 w of ultrasonic power. In the first seven experiments, the microspheres were then suspended in 30 ml of freshly heparinized blood; in the last two, they were suspended in 2 ml of isotonic saline. The resulting mixture was kept agitated by a Teflon-coated magnetic stirrer. From 6–15 ml of the blood mixture or 1 ml of the saline mixture of indicators was injected. The duration of injection varied, depending on the volume of the injectate, and ranged from 2 to 30 seconds. The calculated number of microspheres injected was 200–3,000/0.1 g muscle for microspheres larger than 15 µm and 24,000–150,000/0.1 g muscle for 15-µm microspheres.

Since the goal of this study was a comparison of the deposition of four intimately mixed tracers injected into the inflow, a redistribution of regional flows did not invalidate the comparison. However, if no change in vascular resistance occurs one can assume that redistribution does not occur; under this condition the data can more readily be interpreted in terms of regional flows, which was a secondary objective of the study.

The injections of these large numbers of spheres caused negligible changes in vascular resistance; in this constant-flow system, resistance changes were directly proportional to changes in perfusion pressure. In no experiment did the rise in pressure following injection exceed 3 mm Hg, and it averaged less than 2 mm Hg. In six more recent experiments using microspheres with a narrow size distribution around 10 µm, 5–8 × 106 spheres suspended in 2 ml of dextran were injected into the inflow of Langendorff-perfused hearts weighing about 60 g; in all six, the maximum resultant pressure rise was less than 2 mm Hg, and the rise lasted less than 15 seconds. In a similar experiment, 5 × 106 10-µm spheres and 1 × 106 35-µm spheres injected in 2 ml of dextran also caused a pressure rise of less than 2 mm Hg. Therefore, we feel confident that local resistance changes did not influence the regional distribution. Some rather casual tests lead us to suspect that a high concentration of Tween-80 is a frequent cause of resistance changes seen by other investigators.

When only microspheres were injected, the time the perfusion was stopped was not critical and was 4–5 minutes after the injection. After injection of the diffusible tracers, early stoppage of flow was needed to prevent the washout of the tracers. The content of tracers in the heart was monitored by external detection of the higher energy gamma-emitters, 86Rb or 42K, in the last four experiments (nos. 6–9), The perfusion was stopped within 5 seconds of reaching the peak count rate, at which time in the most crucial last two experiments (nos. 8 and 9) the count rate had diminished by less than 10% from its peak. Making this observation on 86Rb or 42K is more critical than it is on I-Ap or spheres, since a fraction of the Rb+ or K+ is not extracted during transcapillary passage and has a short transit time like albumin. More precise estimation of the amount of escaped tracer was obtained by collection and counting of the venous effluent in these last four experiments. In experiment no. 6, the total effluent up to the time the perfusion was stopped contained 2.2% of the injected dose of 86Rb and 1.7% of the 141Ce-labeled spheres. In experiment no. 7, in which a prolonged injection was used, only 6% of the I-Ap and an innaccurately measured but smaller fraction of 42K had escaped. In the best experiments, nos. 8 and 9, the fractions of 42K and I-Ap in the venous outflows were less than 0.1% of the injected dose, which implies that the earliest effluent was still mainly in the coronary veins at the time the heart was stopped and probably drained out when the heart was sliced.

Immediately after flow was stopped, the heart was removed and sliced along planes parallel to the atrioventricular junction at intervals of 1 cm, producing four to six rings of tissue per heart (Fig. 1). The right ventricular free wall was removed, leaving only the tissues surrounding the left ventricular cavity. The slices of left ventricle were then placed on a sheet of Dry Ice to reduce diffusional movement of the soluble indicators (which might be 1–3 mm during the hours of sectioning) and to harden the muscle to prevent distortion and to facilitate subsequent sectioning. Each ring, except the apical one, was then cut radially into eight segments (Fig. 1) so that the septum was always denoted by segments 6 and 7. By using a specially constructed implement consisting of parallel stainless steel blades separated by 1-mm spaces, each segment was sliced manually parallel to the epicardial surface into 7 to 12 pieces. These sections, with dimensions of about 15 × 8 × 1 mm, where then weighed. Their weights ranged from 0.02 to 0.48 g. The mean ± sd for 2,585 pieces from the nine left ventricles was 0.12 ± 0.07 g. There were 250–350 samples per preparation.

Top: Plane of dog heart as seen by observer prior to slicing. Bottom Left: Coronal rings of left ventricle; top ring is base of heart. Arrows point to position of major coronary vessels on these rings. Bottom Right: Diagram of division of one left ventricular ...

The radioactivity in these samples was counted in a gamma counter (Autowell II, Picker Corp.), without adding solvent, so that all the slices were in the same geometric position at the bottom of the tube. Selective energy-window settings were carefully chosen in accordance with the relative doses of the different tracers and their emission spectrums so that spillover ratios were accurately reproducible and minimized.

Data Analysis

The wet weights of the sections and their gross isotopic activities were punched on IBM cards. Net counts for each isotopic species were obtained by conventional means (16) with a CDC 3500 computer (Control Data Corporation). We expressed the deposition density (di) in a tissue sample as counts/min g−1 or di = ci/gi, where ci is the isotopic activity per unit time and gi is the weight of the ith piece of tissue.

Various procedures were utilized to portray these results. In one, the spatial distribution of each piece for each isotope (expressed as a fraction of total density in all the sections analyzed, di/Σdi was represented graphically by using a computer-driven plotter (Cal-Comp) (Fig. 2). The distribution in each ring of tissue was represented by 12 concentric circles on which were superimposed sinusoidal excursions whose amplitudes were directly proportional to the fractional deposition density. When the number of sections in each segment of a ring varied, their density values were interpolated to fit the number of concentric circles drawn. Patterns such as these gave us a general view of the distribution of deposition for the parts of the heart studied for each isotope and allowed comparisons between isotopes and between small tissue pieces within the same heart.

Diagrams of spatial distribution of relative densities of deposition of different indicators. Top concentric circles represent the basal ring of the left ventricle, and bottom circles represent the apical ring. Septal and free wall regions are left and ...

The next method of analysis showed the profile of deposition densities for the different isotopes in each radial segment of the left ventricle. For each isotope and in each piece of tissue, the deposition density, di, was normalized by multiplying it by the ratio of the total weight of the left ventricle, W, to the total isotopic activity of that isotope in the ventricle, Σci. This procedure gave the mean relative density for the whole ventricle a value of unity. These relative densities for each isotope were then plotted sequentially from epicardium to endocardium (Fig. 3) so that a small rectangle represented a left ventricular radial segment. For septal segments 6 and 7 the sequence was from right ventricular endocardium to left ventricular endocardium. The relative density of an isotope exceeded 4.0 in a very few segments; because high values appeared to be due only to scatter, an arbitrary upper limit of 4.0 was used for display purposes.

Isotopic density pattern in sir left ventricles (hearts 3 and 5–9). Only data for middle rings (each consisting of eight segments) are shown; basal and apical rings were excluded. Each rectangle represents one ventricular radial segment, identified ...

In another method, the relative density of deposition of a label was expressed in terms of its relative mass. With the subsequent assumption that the total amount of isotope retained in the left ventricular tissue could be equated with the flow to that region, the density was translated to fractional flow.

Lastly, by taking at least two adjacent pieces from the endocardium and two from the corresponding outer wall of a segment so that the total weight for each region exceeded 0.1 g, we calculated the inner wall–outer wall ratio of these deposition densities (counts/min g−1) for each segment and for each ring. Apical rings were too thin-walled to merit this analysis. However, one cannot analyze the distribution of these ratios in terms of their numerical values, because the linear range for the ratios less than unity has a different arithmetic step size than that for the ratios greater than unity. We preferred to express the relative difference between inner and outer wall deposition densities in terms of a gradient so that for ratios greater than unity the gradient was the ratio minus 1.0 and for ratios of unity the gradient was zero. For ratios less than unity, the gradient was a negative value calculated as 1.0–1.0/ratio. This way of expressing the relative isotopic density allowed comparison of inner and outer wall depositions between indicators and in different locations in the left ventricle.


Table 1 gives the details of experiments on nine isolated hearts. All hearts were perfused with blood at flows ranging from 1.3 to 4.8 ml/min g−1 of left ventricular tissue. These flows were obtained by assuming that 70% of the total coronary flow (4) went to the left ventricle and the septum. These flows were all higher than the normal flows in the working heart, which is to be expected at the perfusion pressures used for the first eight experiments. In the ninth experiment, the perfusion pressure was lower than average, and the flow was lowest. Although fairly high doses of the 15-µm microspheres were used, neither vascular blockage by spheres nor vasoactivity induced by the Tween-80 was apparent, since no sudden increases or decreases in perfusion pressure (reflecting changes in vascular resistance, flow constant) were seen after injection. This finding is not surprising, because one can calculate that a dose of 60 × 104 particles/g, if distributed evenly, would fill only one capillary in ten. Assuming a capillary length of 0.5 mm and a capillary density of 3,000/mm2 cross section, then there are approximately 6 × 106 capillaries/g. Since microscopic examination showed that capillaries often contained short chains of microspheres and, as will be shown, the microspheres tended to go preferentially to regions of higher-than-average flow, the actual fraction of blocked capillaries was much less than one would estimate from a uniform distribution.

Distribution of Left Ventricular Deposits

When 86RbCl and < 10- and 50-µm microspheres were injected (Fig. 2, top), the 86RbCl was distributed rather uniformly throughout the heart, but there was a slightly greater relative deposition in the endocardial layers. The < 10-µm microspheres had a more uneven distribution; there was a definite preferential endocardial deposition. This preference was marked for the 50-µm microspheres and, although there was a tendency for the greatest deposition of 50-µm microspheres to occur at locations where the deposition of < 10-µm microspheres was maximum, there was substantial variation. The occurrence of a heavy ring of epicardial deposition of the 50-µm microspheres in the apical region may be an artifact due to the presence of the cannula through the apical myocardium venting the left ventricular cavity, thereby damaging the myocardium locally and introducing abnormalities in flow and particle deposition.

With infection of 42KC1, I-Ap, and 15- and 35-µm microspheres, a higher endocardial density of the microspheres was again clearly seen (Fig. 2, bottom). Differences between I-Ap and 42KC1 were small. In contrast to Figure 2 (top) where the smaller microspheres (<10 µm) were distributed similarly to 86RbCl and very differently from 50-µm microspheres, the distribution of 15-µm microspheres was similar to that of 35-µm microspheres, and both were more densely deposited in the endocardial region than were 42KCI and I-Ap. From data of the type shown in Figure 2, there emerged no evidence, among the nine hearts, of a reproducible geometric pattern of deposition emphasizing any particular radial segment or coronal ring.

Quantitative descriptions of regional densities of the various tracers relative to the average density for the whole ventricle are shown in Figure 3. The data for heart 3 compare two different batches of 15-µm microspheres: simultaneously injected microspheres labeled with 85Sr and with l69Yb had virtually identical distributions. In every segment of these two rings, including septal segments 6 and 7, left ventricular endocardial preponderance clearly occurred; the values of relative deposition in the endocardium were 1.5–4 times the left ventricular average denoted by the horizontal bar on the left ordinate of each small rectangle.

Data from hearts 5 and 6 also showed relatively greater endocardial deposition. Moreover, substantial differences between microspheres of different sizes and 42KC1 or 86RbCl emerged. Although there was much scatter, there was a reproducible pattern. The third rectangle from the left on the bottom row for heart 6 illustrates this effect most clearly. The deposition of 86RbCl showed only a slight predominance in the endocardial region. The deposition of small microspheres (< 10 µm) was relatively greater in the endocardium and less in the epicardium, and the 50-µm microspheres showed an endocardial deposition of two to four times the left ventricular average, the epicardial regions being relatively deprived. Similar patterns occurred in 14 of 16 rectangles for experiment 6. Similarly, in experiment 5, the 15-µm spheres showed greater endocardial deposition in 24 of 24 transmural segments.

In the most extensive experiments of this series, (hearts 7–9, Fig. 3) the distributions of the two diffusible tracers, I-Ap and 42KC1, were similar. In these three experiments, the blood flow was stopped 12–18 seconds after the injection of the four tracers had ended. In our previous experiments (21), much of the unextracted 42K and 131I-albumin had washed out by 20 seconds, so it is reasonable to assume that the residual tracer was principally that which had entered the extravascular region. Experimentally, heart 7 differed from heart 8 in having a 26-second injection in comparison with a 3-second injection. The longer injection time appeared to lead to a slight increase in the difference between microspheres and I-Ap and 42KC1, which may be explained simply on the basis that relatively more of the diffusible tracers was washed out from the high-flow regions than from the low-flow regions during both the period of the injection and the additional time before the heart was stopped.

With heart 9, the perfusion pressure was much less than average, and in a good many segments the distribution of deposited tracers differed from that seen in the other experiments. The distribution pattern did not show endocardial predominance with any consistency, but in many segments there was an epicardial predominance. Whether deposition was greater in the epicardium or the endocardium, there was a tendency for the largest microspheres (in this case, 35 µm) to be more densely deposited than were the other indicators in the part of each segment with above-average deposition.

Frequency Distribution of Densities of Indicator Deposition

The differences between 35- and 15-µm microspheres are not so apparent in the data for hearts 7–9 in Figure 3 as are the differences between the < 10-µm microspheres and the larger ones (hearts 5 and 6). In an attempt to examine the question in more detail, the data for the whole of each of the former three hearts were used in Figure 4 to show the distributions of the observed densities of deposition in the three hearts for the four simultaneously injected indicators, 42KC1, I-Ap, and 15- and 35-µm microspheres. These distribution functions all have the same mean relative density, unity. The ordinate is the fractional mass of heart per unit deposition density. So that the four distributions for each heart might be distinguished, the points at a midclass value of (ci/gi)/(Σci/Σgi) for each indicator were joined by the coded lines denoting the indicator. In the three experiments at measured flows of 1.8–4.8 ml/min g−1, the 15- and 35-µm microspheres differed from 42KC1 and I-Ap in showing greater frequency of estimates of both low and high deposition densities.

Frequency distribution of densities of deposition in left ventricles of three isolated hearts for simultaneously injected indicators (left = heart 8, middle = heart 7, right = heart 9). The measured average flow, F, in ml/min g−1 is given above ...

The difference between 15- and 35-µm spheres is not brought out by these plots but does show up in the transmural gradients in deposition. A natural consequence of preferential deposition of microspheres in higher-than-average flow regions is a relative deprivation of regions of low flows. The final result is the spreading of the distribution of microspheres, which is most apparent in the middle section of Figure 4.

It should be noted that erroneous values for the average density would be obtained by simply averaging the values of (c/g)i (that is, not appropriately normalizing the abscissa) unless all the samples were of equal size.

If the fractional deposition were precisely proportional to flow, these curves would give the shape of the frequency distribution of regional blood flows. The dimensionless ordinate would give the fractional mass of tissue having a given relative perfusion rate, and the dimensionless abscissa would be the regional perfusion rate divided by the average perfusion rate for the left ventricle. The close similarity between I-Ap and 42KC1 distributions suggests that these two tracers most nearly have a flow-proportional distribution, but they both may have errors in the same direction.

Transmural Gradients in Tracer Deposition

Gradients are shown in Table 2 for certain of the experiments chosen to span the gamut of results. A gradient of 0 means uniform transmural deposition. A gradient of +1.0 means that there is twice as much deposition in the endocardial layer as there is in the epicardial layer of the segment. A gradient of −1.0 means that the density of deposition is twice as great in the epicardial layers. In all experiments except no. 9, the gradients for all tracers were positive, indicating predominant endocardial deposition. In each case, this endocardial predominance was larger for microspheres than it was for 42KC1 or I-Ap, and, when more than one size of microsphere was injected, the gradient was more positive for the larger microspheres. In experiment 9, in which the perfusion pressure was low, negative gradients were seen (although these were not uniformly negative), indicating predominant epicardial deposition. However, whether the gradients were positive or negative, with fair consistency they were greater for microspheres than they were for 42KC1 or I-Ap and greater with large microspheres than they were with small microspheres.

Gradients of Deposition of Tracer in Various Regions of Left Ventricle

Figure 5 shows gradients averaged over the whole of each heart for each of the four different tracers injected simultaneously. When the diffusible tracers clearly showed positive gradients (greater deposition in the left ventricular endocardium than in the epicardium or the right ventricular endocardium), as in experiments 7 and 8, the microspheres showed much greater preferential deposition in the endocardial region and exaggerated the apparent heterogeneity of flow. When there was no gradient for diffusible tracers, the microsphere deposition apparently was also uniform, as in experiment 9. In the three hearts in which the only tracers were two differently labeled 15-µm microspheres injected simultaneously, the endocardial predominance was great, the gradients varying from 2.2 to 6.3. We could not ascertain why these experiments seemed to differ from those in which several tracers were injected simultaneously.

Plot of mean gradient for whole heart against diameter of indicator (42KCl and I-Ap have diameters of L10 nm). Gradient for whole heart is obtained from sum of isotopic activities for inner and outer left ventricular layers, each normalized to sum of ...

Detailed comparisons of the deposition of 15- and 35-µm microspheres in the experiments with hearts 7–9 are shown in Figure 6. Most of the data points are in the positive region (right upper quadrant), indicating a generally higher endocardial deposition. The slope of the regression line for all of the data is 1.40. As expected, this value is larger than the ratio of the gradients calculated for the whole heart for 15- and 35-µm microspheres (Fig. 5: the ratios are 1.13–1.17 for hearts 7 and 8). The regression line for heart 9 alone also passed close to the origin, and the mean of the ratios of gradients G35/ G15 in each transmural segment was greater than unity, showing preferential deposition of larger spheres in higher flow regions in the presence of either epicardial or endocardial preponderance.

Gradients for 35-µm microspheres (G35) plotted against those for 15-µm microspheres (G15) for similar segments of the left ventricle in hearts 7 (triangles), 8 (solid circles), and 9 (crosses). Broken line represents line of identity; ...

If flow selectively influenced the distribution of one of the indicators, then the regression line would rotate about the origin, changing its slope from unity but maintaining a zero intercept. If the geometric arrangement tended to produce preferential deposition in the endocardial region for larger microspheres, the regression lines would show positive intercepts on the ordinate and would parallel the line of identity if there were no selective influence of flow on larger microspheres. Both geometric influences and the influence of flow velocity would be shown by a combination of changes in intercept and shifts in slope away from unity. The data of Figure 6 show a slope of 1.4 and an intercept near zero. This finding suggests that flow predominantly influences the maldistribution of the large microspheres, but the data do not preclude the possibility of some geometric influence.

Influence of Time of Cessation of Perfusion

Comparison of the data from heart 5 with those from heart 8 suggests that prolongation of the time between injection and circulatory stoppage permits washout of 42KC1 and I-Ap. Since washout is greatest from regions of highest flow, this effect decreases the residue rapidly in high-flow regions and slowly in low-flow regions; it also decreases the heterogeneity of regional density of tracer deposition. Smaller gradients for 42KC1 and I-Ap were seen in heart 5 (stopped 66 seconds after injection) than in heart 8 (15 seconds) (Table 2, Fig. 3). Because of the delayed flow stoppage, the heterogeneity of distribution of microspheres in heart 5 was greater in comparison with the distribution of 42KC1 or I-Ap than it was in comparison with the true distribution of flow. For this reason, in comparisons between diffusible tracers and microspheres we relied on the data from hearts 7–9. This timing problem had no influence on comparisons between microspheres of different sizes.


Resolution Provided by Multiple-Sample Technique

Because our tissue samples were small, we think that our method offered better spatial resolution than do methods which utilize larger pieces of tissue. A simultaneous requirement is that the measurement error for the quantity of tracer in each sample does not increase as sample size decreases; this effect was avoided by using sufficiently high doses and long counting times for the diffusible tracers and by injecting large numbers of microspheres. Buckberg et al. (22) recognized this source of error. Domenech et al. (4) injected relatively few microspheres, about 25,000/heart or 250/g for a 100-g heart. Although our samples averaged only 0.12 g, our larger doses were about 500,000/g or 50,000/sample, giving us, according to the calculations of Buckberg et al. (22) about 2% precision at the 99% confidence level. Even with the smallest samples (0.02 g), the lowest dose of microspheres (240,000/g), and the lowest relative flow (20% of average organ flow), the precision would be better than 10%, since there would be about 1,000 microspheres/sample. This number is high enough to obviate the influence of other sources of error, such as variation in the specific activities and sizes of the microspheres. We have no information on the uniformity of the labeling; the manufacturer has suggested that the spheres are labeled more in proportion to volume than to surface area. With our high densities of tracer deposition, the counting error was relatively small even when more than two tracers were present and made a small contribution to the variation in the apparent tracer density distributions.

The use of larger tissue samples decreases the resolution. Lower apparent gradients in transmural deposition are an inevitable consequence of dividing the wall into two to four layers as others have done (4, 6, 12, 23, 24). This effect of sample size may explain why McNay and Abe (25), who divided the renal cortex into four layers, obtained different microsphere profiles than did Katz et al. (7), who used kidney slices 0.35–0.6 mm thick.

Distribution of Diffusible Tracers

Whether one thinks that the diffusible tracers or the microspheres delineate the true flow, the apparent spread of relative flows over a six- to ten-fold range suggests very marked heterogeneity. Since all portions of the beating heart have to contract regularly in synchrony, one would expect small and large regions to have flows and metabolic activities that do not differ markedly from the mean values. The explanation could be moment-to-moment variation in flow or “twinkling”–transient slowing of the flow to one small region as it increases transiently to another region. This observation is also compatible with the very large scatter which has been seen in xenon-washout curves on local intramyocardial tissue injection (Fig. 1 top left, ref. 19). Furthermore, this broad heterogeneity of regional flow is comparable to that suggested by the analysis of transcoronary transport functions for indocyanine green in intact dogs for which the regional variations in flow have been suggested to be approximately sixfold (26). Similar distributions have also been obtained by the analysis of washout curves of I-Ap after coronary artery injection; in those experiments, the analysis of Van Liew (27) was used by Bassingthwaighte et al. (28) to provide estimates of heterogeneity suggesting that regional flows ranged from one-third to five times the average flow.

In the Methods section, we pointed out that heterogeneity would probably be underestimated by I-Ap distribution because of earlier washout from high-flow regions and by 42KCI or 86RbCl because of decreased initial extraction in high-flow regions. Gradients are therefore also underestimated. The magnitudes of the errors cannot be calculated readily. In the last three experiments (Fig. 5), the hearts were stopped 12–18 seconds after injection, during which time only a small fraction of tracer was washed out. If as much as a third (an exaggerated estimate) were washed out of the high-flow regions, the estimated gradients for I-Ap would not be more than 1.5 times the values shown in Figure 5 (particle size nearly zero), which would not account for the difference between I-Ap and 15-µm microspheres. The range of initial extractions of 42KC1 observed by Tancredi et al. (21) was 0.38 to 0.68 with flows from 0.5 to 1.6 ml/min g−1, which is less variation than is predicted from a Krogh capillary-tissue cylinder model (14, 15), implying that the deposition technique is somewhat more accurate than this model would predict. Thus, we believe that the most accurate estimates of regional distribution of flows in the normal heart are probably obtained by using I-Ap and by sampling the tissue contents within 5−10 seconds after injection. Despite its low extraction, 42KC1 with its large extravascular volume of distribution provides similar estimates.

Effects of Microsphere Size

Microspheres were deposited preferentially in regions showing higher-than-average deposition of permeating tracers. The distribution of larger microspheres was more biased than that of small microspheres. Since the various tracers were injected simultaneously and the exaggeration occurred no matter whether the diffusible tracers were more densely deposited in the epicardium (experiment 9) or in the endocardium (the other experiments) and since the heterogeneity of densities of I-Ap and 42KC1 tended only to be slightly less and not more than the heterogeneity of the distribution of flows, we concluded that microspheres 15 µm or more in diameter tend to go preferentially to regions of higher flow. The probable mechanism is that, at each branch point, microspheres tend to enter the branch with the higher velocity so that the fraction entering this branch is larger than the fraction of flow which enters, as Fung (29) described for erythrocytes.

This interpretation is also suited to the observations of Katz et al. (7): the deposition of 35- and 80-µm microspheres in the outer renal cortex was greater than that of 15-µm microspheres, and deposition in the juxtamedullary region was relatively less for the larger microspheres than it was for the smaller microspheres. McNay and Abe (25) did not see such a difference between 27- and 36-µm microspheres in the renal cortex, probably because of the small difference in the diameters and the larger size of the tissue samples in the presence of significant statistical variability. Results similar to ours were obtained by Domenech et al. (4), who found that the ratios of microsphere deposition in subendocardial regions to that in subepicardial regions of canine left ventricles increased with larger microspheres.

The near-zero intercept of the regression line of Figure 6 suggests that the geometry or the form of branching of the coronary vascular bed has a negligible influence on the microsphere distribution. Before coming firmly to this conclusion, we would prefer to see comparisons between 10-µm microspheres having a very narrow range of diameters and larger microspheres in situations in which the flow is first predominantly to either inner or outer wall and then (with different tracer labeling on the microspheres) with physiological conditions changed so that flow is predominantly to the opposite side of the wall. This study is in essence an extension of experiment 9, and a plot similar to that of Figure 6 should show the influences of invariant geometric factors and of flow separately.

Transmural Gradients in Ventricular Myocardial Flow

Our experiments were on non-working, blood-perfused hearts, obviously not the ideal physiological situation. A growing number of reports on intact hearts suggest that the blood flow to the endocardium is at least as great as that to the outer layers of the ventricular wall in this preparation as well. Domenech et al. (4) observed this tendency in beating ventricles whether or not external work was being done. Small positive gradients, suggesting but not proving endocardial predominance, were found by Buckberg et al. (30) (0.01 to 0.11) and by Becker et al. (6) (0.04 to 0.17) even though their slices were thicker. Presumably, our higher gradients for microspheres are due to our method of calculation permitted by the good spatial resolution obtained by using smaller sample sizes and larger doses of spheres; however, it is not clear whether ventricular contraction might have some effect.

Residual concentrations of diffusible tracers at the end of prolonged infusions of tritiated water (23), I-Ap (24), or 86RbCl (12) also showed small positive gradients. It is not surprising that the gradients obtained by such techniques were small, since a 5- to 10-minute infusion of I-Ap or tritiated water should lead to virtually complete equilibrium between blood and tissue in all parts of the heart and therefore zero gradients. A shorter infusion followed by circulation arrest within 5–10 seconds will yield deposition gradients closer to the true flow gradients. Accordingly, the gradients we report for I-Ap, 42KC1, and 86RbCl, determined after brief injections, are much greater than those obtained after longer infusions.

The positive gradients (endocardial deposition greater) are too large to be explained by the observation of Myers and Honig (31) and of Kirk and Honig (32) that the inner layers of the wall of working hearts contain more blood. Our results and those mentioned above at first seem incompatible with their observations of slower NaI clearance and lower O2 tension in the endocardium, but in their experiments the endocardial intratissue pressures were high during systole and negative gradients in flow could have existed. In our experiment 9, a low perfusion pressure seemed to be the cause of the observed negative gradients. By constricting the coronary arteries, others have produced relatively high epicardial tracer deposition (6, 24, 30) and tissue substrate levels (33).


Technical assistance was provided by Craig Benson, Patricia L. Spivak, Allen R. Wanek, and William Dunnette. Jane Irving assisted in the preparation of the manuscript.

This investigation was supported in part by U. S. Public Health Service Grants HL-9719 and RR-7 from the National Institutes of Health, Grant 69-1014 from the American Heart Association, and Grant CDC-2 from Control Data Corporation.


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