Within-layer regional myocardial flows in the left and right ventricles (LV, RV) and in LV with increased myocardial workload (β1-adrenoceptor stimulation) were studied transmurally in anesthetized rabbits. Myocardial flow distribution was visualized with resolutions between 0.1 × 0.1- and 1 × 1-mm2 pixels, using digital radiography combined with the3H-labeled desmethylimipramine deposition technique. The spatial pattern of flow distribution was quantitated by the coefficient of variation of regional flows (CV, related to global flow heterogeneity) and the correlation between adjacent regional flows (CA, inversely related to local flow randomness). CV was lower in LV than in RV [P < 0.05, nonparametric 2-way analysis of variance (NANOVA)]. When resolution was lowered from 0.1 × 0.1- to 1 × 1-mm2 pixels, CV decreased by 70% in both LV and RV. CA was higher in LV than in RV (P < 0.05, NANOVA); the interventricular difference in CA was large over the resolutions between 0.4 × 0.4- and 1 × 1-mm2 pixels. In LV, both CV and CA increased with depth of myocardium (P < 0.05, NANOVA); in subendocardium CV was high comparable with CV in RV (P = 0.47, NANOVA). The enhancement of myocardial workload decreased CV and tended to decrease CA in LV subendocardium (P < 0.05,P = 0.06, respectively; NANOVA). We conclude that 1) microregional flow distribution is less heterogeneous and less random in LV than in RV;2) transmurally, in LV subendocardium global flow heterogeneity was the highest whereas local flow randomness was the lowest, so that clusters of low- or high-flow regions exist in this LV layer; and3) global flow heterogeneity decreased and local flow randomness tended to increase (flow homogenizing occurred) in LV subendocardium with increasing myocardial workload. Thus the distributed pattern of myocardial microregional flows may be adaptable to local myocardial metabolic change.
- radioactive molecular flow tracer
- flow heterogeneity
- local flow randomness
- coronary vasoregulation
coronary vascular tone plays an essential role in determining the distribution of myocardial blood flow (1). The vascular tone, distributed down to small arterioles, is closely coupled with myocardial O2 supply and demand (15, 27, 33), and therefore the spatial distribution of myocardial flow is most likely to be formed at a precapillary arteriolar level under the influence of the O2 supply and demand. Indeed, we recently showed (28) that myocardial flow distribution was largely altered at arteriolar-to-capillary levels by a change in arterial O2 tension. Thus much lower workload and myocardial O2consumption in the right ventricle (RV) than in the left ventricle (LV) (10, 18, 23) will induce differences in a spatial pattern of flow distribution between LV and RV, especially at a microvascular level where the O2 extraction from circulating blood occurs. To date, a large number of comparisons of myocardial perfusion between LV and RV have been made, and discrepancies, especially in the regulation of perfusion to LV and RV, have been described (26). However, there has been no study on a difference in within-layer regional flow distribution between LV and RV at arteriolar-to-capillary levels.
The present study was thus undertaken to determine whether the spatial pattern of within-layer flow distribution in RV differs from that in LV at a microvascular level and whether the flow distribution differs transmurally in the two ventricles. In addition, to assess the physiological significance of pattern characteristics of myocardial flow distribution, we investigated how the increased myocardial workload, evoked by β1-adrenoceptor stimulation, affects flow distribution transmurally in LV myocardium. The within-layer myocardial flows in the free walls of rabbit LV and RV were imaged by our recently developed quantitative digital radiography combined with a molecular deposition technique (28). This technique makes it possible to evaluate myocardial flow distribution with a high level of resolution (0.1 × 0.1-mm2 pixels). The spatial pattern of flow distribution was quantitated by the coefficient of variation of regional flows (CV) and the correlation between adjacent regional flows (CA) with resolutions between 0.1 × 0.1- and 1 × 1-mm2 pixels; CV is a measure related to global flow heterogeneity, and CA is a measure related inversely to local flow randomness.
MATERIALS AND METHODS
Male Japanese White rabbits weighing 2.5–3.5 kg were studied in accordance with the guiding principles of the American Physiological Society and with prior approval of the Committee on Animal Research of Kawasaki Medical School.
After anesthesia was induced with intravenous administration of pentobarbital sodium (30 mg/kg), ventilation was maintained via a tracheotomy and a mixture of O2and room air, adjusted to keep arterial pH and arterial blood gases within physiological limits (pH 7.35–7.45; 35–45 mmHg; 90–140 mmHg). Sodium bicarbonate was infused intravenously as needed. Body temperature was maintained at 37–38°C on a heating blanket. A polyvinyl catheter was introduced into an ear vein for drip infusion of heparinized saline (10 U/ml) and for supplemental infusion of pentobarbital sodium. The chest was opened by a median thoracotomy, and a pericardial cradle was made to suspend the heart. For blood sampling and monitoring LV pressure (LVP), a flexible Teflon catheter was inserted into the LV through the apex. The catheter was connected with a pressure transducer (model 420–4, Camino Labs) via a manometer catheter (model 110–4Fr, Camino Labs). Electrocardiograms were recorded from standard leads. All variables were continuously monitored and recorded with a polygraph system (model RM6200, Nihon Kohden). Rabbits were studied when all hemodynamic parameters had been stabilized.
In group A(n = 6), 50 μCi of tritium-labeled desmethylimipramine ([3H]DMI, Dupont) was injected into the left atrium with a glass syringe over a period of 4–5 s. Although this injection procedure disturbed the hemodynamics through the mechanical stimulus of the left atrial appendage, the disturbance disappeared within several heartbeats and the hemodynamics remained almost steady for at least 1 min. One minute after the injection of [3H]DMI, the heart was arrested with a saturated KCl solution given directly into the LV cavity. The [3H]DMI deposition in a certain small piece of tissue is proportional to the flow perfused into that piece over 1 min (24, 25).
In group B(n = 4), the selective β1-adrenoceptor agonist denopamine (41), provided by Tanabe Pharmaceutical, was infused intravenously at a dose of 10 μg ⋅ kg−1 ⋅ min−1for 10–15 min. The first derivative of LVP (LV dP/dt) obtained by electric differentiation was also monitored and recorded with other hemodynamic variables. Five to ten minutes later, when hemodynamic variables were stabilized, [3H]DMI was infused as in group A.
The whole heart was removed from the chest, and the aorta was cannulated to allow perfusion of the coronaries through Valsalva’s sinus. The coronaries were perfused with 50 ml of an isosmotic cardioplegic rinsing solution (1.0 mM EGTA and 0.2 mg/l nifedipine) and subsequently perfused with 50 ml of 2,3-butanedione monoxime (1.5 g/l) to prevent myocardial contracture (20). The perfusion was carried out carefully to keep air bubbles out of the coronary vessels and at a low flow rate (3.0 ml ⋅ g−1 ⋅ min−1) to minimize the [3H]DMI escape rate. Radioactivity detected from the effluent solutions amounted to a few percent of [3H]DMI radioactivity contained in LV free wall.
Full-wall thickness samples were excised from the equatorial portions of LV and RV in group A. Ingroup B, only LV free wall was sampled. After the removal of papillary muscles, each sample was sandwiched in aluminum sheets without compression and immediately put into a 80°C freezer. With a Tissue-Tek tissue mount, we then mounted a frozen sample in a platelike shape on the stage of a cryostat (HM505E, Zeiss) and divided it into slices of 40-μm thickness from subendocardium to subepicardium. Through this process, quite a lot of subepicardial slices, within which some large coronary vessels lay, were omitted. Furthermore, some slices near the endocardium were also omitted. Those slices were under the influence of uneven endocardial surface, which warped the near-surface layer of subendocardium during freezing of the tissue being sandwiched in aluminum sheets. The remaining ∼30 and ∼15 slices in LV and RV, respectively, were all intended for autoradiographic studies. These slices were carefully put onto a slide glass in the 20°C chamber of the cryostat and checked to ensure that no wrinkles had been made.
Imaging of myocardial blood flow distribution.
The autoradiographic technique for within-layer flow visualization was similar to that described in detail in a previous publication (28). In brief, each slice was exposed to a radioactive energy sensor (Imaging Plate, IP-TR2040, Fujix), which stored the irradiated β-radioactive energy from the myocardial slice with high sensitivity. This radioactive energy was converted into electrical signals in arbitrary units as high-resolution digital data of 100 pixels/mm2 by the Bio-Imaging Analyzer (model HGE, Fujix). A digital radiogram was then acquired by visualizing this digital data in 256 levels of black and white gradations (Fig. 1). Several images with vessel traces or artifactual tears visible to the naked eye were excluded, and the rest were divided almost equally among three transmural layers in LV [subepicardium (Epi), midwall (Mid), and subendocardium (Endo)] and two in RV (Epi, Endo). Five images were arbitrarily selected from each layer for the data analysis.
The short path length of a β-particle emitted from3H [on average 1.1 μm in a material of density 1.3 (31)] ensures that the digital radiographic image almost precisely reflects the distribution of [3H]DMI deposition or flow within a very thin layer. The mean intensity of background was <10% of that of a region overlying the tissue. When corrected for background activity, a square portion (7 ×7 to 12 × 12 mm2) of each image was ready for data analysis.
Two normalized indexes were used for the analysis of regional flow distributions, CV (defined as SD/mean) and CA. CV and CA are related to global flow heterogeneity and inversely related to local flow randomness, respectively. The computation of CA was carried out as follows. Suppose mi is the radioactive intensity of the ith pixel of a digital flow image. First, the spatial correlation function of regional flows r mm apart [C(r)] was calculated according to the equation Equation 1where < > denotes an ensemble average over all the pairs ofith andjth pixels, the centroids of which arer mm apart. CA is then given by Equation 2wherer 0 is the distance between the centroids of pixels that hold one side in common with each other, i.e.,r 0 is equal to a pixel side length.
A value of CA quantitates the degree of coherence of local flow distribution; the closer to 1 it is, the farther from random the local flow distribution is or the more continuous adjacent regional flows are; when it is close to 0, flows are rather random locally. Thus CA is inversely related to local flow randomness.
For further description of myocardial flow distribution, each image was renormalized by performing coarse graining [lowering spatial resolution by increasing pixel area from 0.01 mm2 (original resolution) to 1 mm2]. In every rabbit, CV and CA were computed for every image at each step of coarse graining, and average CV and CA were calculated for LV and RV myocardium and for each transmural layer of the two ventricles. A computer (Macintosh Quadra 650) was used for the data analysis with our developed image-processing system.
Hemodynamic changes in group B and the transmural differences in fractal dimension (FD) within each ventricle were assessed with the paired t-test. Nonparametric two-way analysis of variance for repeated measures (NANOVA, modified Friedman’s rank-sum test) was used to analyze the interventricular, transmural, and between-group differences in CV and CA related to a level of resolution because not every data set had a normal distribution (χ2statistics). The possible effects of ventricle on CV and CA were also tested at each level of resolution with Wilcoxon test. Between-group differences in other variables were assessed with the unpairedt-test. A value ofP < 0.05 was considered statistically significant in all testing. Data are represented as means ± SD.
In group A, systolic LVP averaged 115 ± 6 mmHg, heart rate (HR) 313 ± 23 beats/min, and double product (DP = systolic LVP × HR) 35,890 ± 1,300 mmHg ⋅ beat ⋅ min−1. The hemodynamic variables of individual rabbits are in Table1. Ingroup B, denopamine increased systolic LVP from 104 ± 11 to 115 ± 12 mmHg, LV dP/dt from 6,500 ± 250 to 7,770 ± 410 mmHg/s, and DP from 32,560 ± 5,970 to 35,340 ± 7,030 mmHg ⋅ beat ⋅ min−1(P < 0.05, pairedt-test). There was no significant difference in HR before and after denopamine infusion (314 ± 50 vs. 307 ± 50 beats/min; P = 0.10, paired t-test). The hemodynamics of individual rabbits are in Table 2.
Figure 2 shows a typical example of myocardial flow images of LV Endo and RV Endo in one rabbit fromgroup A at different pixel areas (PA). Successive columns refer successively to PA. The shading is proportional to radiation intensity ([3H]DMI deposition density). The flow images in RV Endo had many light gray pixels compared with LV Endo (mean shade of gray was ∼70% of that of LV Endo), reflecting the lower flow per unit mass in RV Endo than in LV Endo. Each succeeding image represents a twofold blowup of the central portion of the previous image. Myocardial blood flow looked more heterogeneous in RV Endo than in LV Endo. Although flow heterogeneity decreased with increasing PA in both layers, its decrease seemed to be greater in RV Endo than in LV Endo.
In Fig. 3, CV through the myocardial wall of LV and RV obtained from group A are plotted against PA on a double logarithmic scale. There was an overall difference in CV between the two ventricles (P < 0.05, NANOVA); CV was higher in RV than in LV at PA = 0.01, 0.04, and 0.16 mm2(P < 0.05, Wilcoxon test). With increase in PA from 0.01 to 1.0 mm2, CV decreased from 0.20 ± 0.03 to 0.06 ± 0.02 in LV and from 0.25 ± 0.05 to 0.07 ± 0.02 in RV. The logarithm of CV was highly correlated with that of PA in both ventricles (r 2 = 0.996 and 0.999 in LV and RV, respectively).
Figure 4 shows the transmural distributions of mean CV in LV and RV from group A at different PA. There were overall differences in CV between LV Epi, LV Mid, and LV Endo (P < 0.05, NANOVA); CV increased with depth of myocardium (from Epi to Endo). CV of RV Epi and RV Endo was not different from CV of LV Endo (P = 0.47, NANOVA). Overall difference between RV Epi and RV Endo was not significant (P = 0.47, NANOVA). In every layer, the CV-PA relationship fitted well a noninteger power law function. The noninteger power law relationship is regarded as a sign of fractality of flow heterogeneity. Fractal dimensions (FD), satisfying the relation CV ∝ PA1 − FD (3), and r 2 between log10CV and log10PA in each myocardial layer of every rabbit are shown in Table 3. The values of r 2(>0.98) show the high correlation between log10CV and log10PA in every myocardial layer of every rabbit. FD was the lowest in LV Endo (P < 0.05, pairedt-test).
Although myocardial flows showed a marked microheterogeneity, their distributions were far from a random pattern because the values of flow correlations between adjacent regions (CA) were significantly higher than 0. In Fig. 5, CA through the myocardial wall of LV and RV obtained fromgroup A are plotted against pixel size (pixel side length; PS). There was an overall difference in CA between the two ventricles (P < 0.05, NANOVA), indicating a more random flow distribution in RV than in LV. CA was higher in LV than in RV at PS = 0.4, 0.6, and 1.0 mm (P < 0.05;P = 0.08 at PS = 0.8 mm, Wilcoxon test). This difference was extinguished when PS was <0.4 mm. In LV, CA considerably increased with increasing PS from 0.1 to 0.4 mm compared with CA in RV and then became nearly constant, irrespective of PS. CA seemed to be less dependent on PS in RV than in LV.
Figure 6 shows the transmural distributions of mean CA in LV and RV from group A at different PS. A transmural difference in CA was significant in LV (P < 0.05, NANOVA) but not in RV (P = 0.79, NANOVA). CA increased with depth of LV myocardium, i.e., the spatial pattern of myocardial flow distribution was farther from random in LV Endo than in LV Epi.
Figure 7 compares mean CV of LV Epi and LV Endo between groups A andB at different PA (data of LV Mid not shown). After β1-adrenoceptor stimulation, CV decreased in both Epi and Endo, but the difference was significant only in Endo (P < 0.05;P = 0.06 in Epi, NANOVA). Transmurally, CV of Endo in group B was greater than CV of Epi, as ingroup A (P< 0.05, NANOVA). The noninteger power law relationship between CV and PA was also observed. FD andr 2 between log10CV and log10PA in each myocardial layer of every rabbit in group B are shown in Table 3. There was no difference in FD between the two groups (P > 0.23, unpairedt-test). Transmural values of FD ingroup B were also lowest in Endo (P < 0.05, pairedt-test), and FD values of LV Mid were similar to those of LV Epi, as ingroup A.
In Fig. 8, CA of LV Epi and LV Endo ingroups A andB are plotted against PS. There was no overall CA difference between groups A andB in both layers. However, the CA difference between the two groups was substantial in Endo (P = 0.06, NANOVA), whereas CA of Epi in group B was similar to that ingroup A (P= 0.60, NANOVA). The tendency toward CA decrease in Endo indicates that the flow distribution became more random in Endo by β1-adrenoceptor stimulation. Transmurally, CA of Endo in group B was greater than CA of Epi, as ingroup A (P< 0.05, NANOVA).
In the present study, we measured transmurally the within-layer myocardial flow distribution and its transmural difference in both ventricles and in LV during the enhancement of myocardial workload with resolutions between 0.1 × 0.1- and 1 × 1-mm2 pixels. Computing CV (related to global heterogeneity) and CA (inversely related to local randomness) of flow distribution, we derived the following new findings. 1) Regional flows were distributed less heterogeneously and less randomly in LV than in RV; in LV Endo, however, global flow heterogeneity was high, comparable with that in RV. 2) Local flow randomness is the lowest in LV Endo. 3) With increasing myocardial workload, global flow heterogeneity decreased especially in LV Endo, and local flow randomness tended to increase in LV Endo. 4) Myocardial flow heterogeneity has a fractallike nature; its FD, which was not altered by the workload increase, was smallest in LV Endo.
Digital radiography combined with a molecular deposition technique for myocardial microregional flow measurements has many advantages over the conventional microsphere technique. Stochastic and methodological errors are considered to be insignificant because a large number of [3H]DMI molecules can be perfused (>105 molecules/μg tissue on average) without vascular embolization; this is the major error source inherent in the use of microspheres. DMI has high extraction and long retention in rabbit hearts, and it is confirmed that DMI molecules are deposited in the endothelial cells and endothelial lining (24). Although extraction is nearly 100%, a small amount of the injected DMI molecules pass into the effluent, indicating the possibility of DMI deposition in venules as well as in arterioles. However, capillary deposition dominating seems very likely because the capillary surface area is considerably larger (500 cm2/g) compared with arterioles (0.3 cm2/g) and venules (double the arteriolar value). Therefore, the deposition of DMI reflects regional flow distribution quantitatively to a great extent.
The presently observed CV values in LV were small compared with those in the previous study, and only in the present study were transmural CV differences in LV significant, although in both studies CV decreased with depth of LV myocardium. In the previous sample preparation using a rotating freezing microtome (28), myocardial slices were expanded on glass slides in physiological saline. When we measured radioactivity in the saline after handling a single LV slice with the previous method, the total saline radioactivity detected by liquid scintillation counting was ∼2.7 × 104cpm, i.e., 5–10% of 3H activity within a single slice. This3H escape resulted in a decrease in mean autoradiographic density by ∼25% and consequently a 50% increase in CV at PA = 0.01 mm2compared with CV obtained using the present method. The enhanced stochastic noise caused by inhomogeneous deformation during the slice expansion would also contribute to such high CV. Therefore, the CV differences between the two studies are caused by artifacts during sample preparation. Of note, CV consistently decreased with depth of LV myocardium despite this artifactual3H escape.
The heterogeneity of flow distribution results from the spatial and temporal variabilities in flow. However, temporal flow variability is probably less essential in the present study because the spatial pattern of regional flow distribution is reported to be rather temporally stable (6, 22). Furthermore, short-term flow fluctuations were averaged out because the regional flows in this study correspond to the regional flow volumes perfused over 1 min. The tracer is deposited in higher concentrations at the upstream ends of capillary units than at the downstream ends (25), so flows may have more weight in the arteriolar-capillary regions than in venular-capillary regions with the presently observed flow distribution. However, the capillary system exhibits a non-treelike structure, in which cocurrent and countercurrent flows coexist along the cardiac fibers with intracapillary connecting flows. Such a flow structure in the capillary bed may reduce the effects of the above biased deposition of the tracer along the capillaries.
The overall flow distribution showed significantly larger heterogeneity in RV than in LV (Fig. 3). This result is consistent with earlier studies (4, 22), although in these studies the size of region resolved was much larger than ours, and thus the flow heterogeneity was evaluated by composing within-layer and transmural flows. The larger flow heterogeneity in RV may relate to the larger heterogeneity in regional vascular volumes in RV (11), because there is a close relationship between local blood volumes and vascular resistances.
The differences in microheterogeneity of myocardial flow between LV and RV observed in the present study may arise from differences in1) coronary arterial-to-capillary architecture, 2) mechanical effects of cardiac contraction on the vessels, and3) coronary vascular tone between the two ventricles. From the recent studies by Kassab et al. (19, 20), there seem to be no substantial differences in dimensions of the vessels both among the right coronary artery, the left anterior descending artery, and the left circumflex artery and between capillaries in LV and RV free walls. Thus the overall flow distributions of LV and RV determined by coronary anatomy alone are expected to resemble each other in heterogeneity. Such an anatomically determined flow distribution is under the influences of cardiac contraction. Austin et al. (1) evaluated the effect of cardiac contraction on LV myocardial flow heterogeneity by comparing the flow distribution between beating and arrested dog hearts in the absence of coronary tone. Although flow heterogeneity decreased through the myocardial wall, probably because of retrograde perfusion of Epi from Endo (7, 9) on addition of cardiac contraction, there was no substantial change in within-layer flow heterogeneity. That group also compared flow distributions with and without coronary tone while the heart was beating. There were intrinsic differences in flow distributions between the two states; there was no correlation between regional flows with and without coronary tone. Furthermore, compared with the flow distribution without coronary tone (regardless of whether the heart was beating), the flow heterogeneity was greatly decreased with coronary tone. These results indicate that coronary tone is most likely to play an essential role in shaping the flow distribution. O2 consumption is higher in LV than in RV (18, 23), and therefore coronary tone will function globally to a larger extent in LV for matching flows to local O2 demand, leading to lower flow heterogeneity in LV. This idea is supported by the decrease in flow heterogeneity in LV layers, especially in LV Endo when myocardial workload increased with β1-adrenoceptor stimulation (Fig. 7), because we may be sure that the O2 consumption increased with the denopamine-induced increase in myocardial workload (21, 30).
The higher flow heterogeneity in RV can be also explained, at least partly, by the passive rheological properties of blood in the capillary networks. Coronary flow is reported to be lower in RV than in LV (15,18, 23). Thus it is expected that the frequency of flow interruption caused by the flow-dependent rheological behavior of red blood cells or plugging by white blood cells is higher in RV than in LV (32, 38). The flow interruption is inversely related to functional capillary density, the reduction of which increases flow heterogeneity (8).
As for transmural flow distribution in LV, global flow heterogeneity was largest in LV Endo (Fig. 4), although coronary tone in LV Endo, in which O2 extraction is the highest (13, 39), is expected to contribute considerably to the decrease in flow heterogeneity. The most heterogeneous coronary anatomy, conjectured from the fact that flow heterogeneity is highest in LV Endo when the heart is arrested without coronary tone (1), may explain the largest flow heterogeneity in LV Endo. The higher heterogeneity of coronary anatomy in LV Endo probably exceeds the contribution of coronary tone, which decreases flow heterogeneity to a higher degree in LV Endo. The systolic extravascular compressible force appears to vary spatially to a larger extent within LV Endo than within LV Epi and LV Mid because of the existence of the papillary muscle (16), and thereby a heterogeneous distribution of regional myocardial work in LV Endo may also contribute to the transmural difference of within-layer flow heterogeneity to some extent.
A microvascular unit is regarded as a region under unitary control (14). Bassingthwaighte et al. (3) suggested that the flow heterogeneity quantitated by CV would begin to plateau, i.e., flows in smaller regions were more homogeneous as the region size decreased close to the microvascular unit level. By studying 2.5- to 20-mg pieces of dog myocardium with the microsphere method, Mori et al. (29) showed that the resolution dependence of CV was attenuated and CV approached a constant value as the size of tissue pieces decreased to 2.5 mg (1.43mm3). In the present study, however, the resolution dependence of CV was not attenuated despite PA being decreased to 0.01 mm2 (Fig.3). This discrepancy in resolution dependence of CV may be related to methodological differences and species. The vascular embolization caused by microspheres triggers local formation of vasoactive substances and local changes of hemodynamic factors (luminal pressure and shear stress), disturbing flow to a higher degree in smaller regions and inducing the coupling behavior of near-neighbor microvascular units. Stapleton et al. (34) demonstrated a CV value of 0.31 in hamster myocardium by quantitative autoradiography with a resolution of 16 ×16-μm2pixels using 2-iododesmethylimipramine. This value was smaller than extrapolated from our log10CV-log10PA plots. Thus the resolution dependence of CV may be attenuated as PA decreases to <0.01 mm2, where the flow distribution reflects flows within capillary units more than in the present study.
Regional flows were distributed less randomly in LV than in RV and the least randomly in LV Endo under resting conditions (Figs. 5 and 6). These differences are attributed to the degree of local coupling between microvascular units. The anatomic studies showed that each terminal arteriole supplied a myocardial region of 0.2–1 mm3 (5, 36, 40). However, such regions do not necessarily agree with observed vascular units. Steenbergen et al. (35) reported that the width of the smallest hypoxic region was several hundred micrometers during hypoxia. On the other hand, Ince et al. (17) found that the smallest hypoxic region corresponded to a region supplied by a single capillary. These differences are probably caused by different circumstances, e.g., the degree of hypoxia, as mentioned by Hoffman (14). In fact, regional flows are likely to couple with one another both locally and globally through a hierarchical structure of vascular control. The more coordinated behaviors of several neighboring small regulatory units seemingly will provide a larger vascular unit, producing lower local flow randomness. Accordingly, the lowest local flow randomness in LV Endo will show the strong inclination of this layer toward similar flow clustering, probably through the highly coordinated behaviors of neighboring regulatory units.
During the enhancement of myocardial workload evoked by β1-adrenoceptor stimulation, local flow randomness tended to increase in LV Endo (Fig. 8). The local flow homogenization, i.e., the suppression of clustering low- or high-flow regions, may occur in LV Endo during the increased workload. At the same time, the increased workload caused by β1-adrenoceptor stimulation may bring about flow perturbative effects on the local coordination of vascular regulatory units. Thus we speculate that local flow homogenization with some flow perturbation decreases CA, that is, increases local flow randomness. Because near-neighbor regulatory units acted more in union during hypoxia than during normoxia (28), the decreased O2 tension may augment similar flow clustering rather than local flow homogenization.
High linearity between log10CV and log10PA, i.e., a noninteger power law relationship between CV and PA, in each myocardial layer was shown (Fig. 4, Table 3). This relationship was also observed in LV layers with increased workload (Fig. 7). A noninteger power law relationship is closely associated with fractality. The fractal value FD can be uniquely defined from the slope of log10CV-log10PA plots (3). The range of FD extends from 1 to 1.5; FD = 1 corresponds to uniform flow distribution and FD = 1.5 to completely random flow distribution. If CV is a fractal of FD, then CA must be constant, irrespective of PA, because CA = 23 − 2FD − 1 (2, 37). In the present study, however, CA was not always constant, and therefore CV may not be a fractal or an apparent fractal (12). Even though CA can be regarded as constant in the range of PA = 0.01–1 mm2, it is questionable whether there is a definite mechanism for inducing the fractality of CV, because coronary vasculature of two quite different types (treelike topology of arteries and non-treelike topology of capillaries) is greatly influential in producing the fractality of CV in the present range of PA. Asymptotically, however, the slope of log10CV-log10PA plots showed the lowest FD in LV Endo compared with the other layers of LV and RV (Table 3). Furthermore, FD remained unchanged in LV layers subjected to workload increase. Thus FD may be an index of flow distribution inherent in each myocardial layer.
In conclusion, we evaluated the spatial pattern of within-layer myocardial flow distribution and its transmural difference both in LV and in RV with resolutions between 0.01- and 1.0-mm2 pixels by digital radiography combined with a molecular deposition technique. As for LV layers, we also examined the effect of increased workload on flow distribution. Overall myocardial flow distribution showed low global heterogeneity (related to CV) and low local randomness (inversely related to CA and related to FD) in LV compared with RV. Transmurally, in LV Endo global flow heterogeneity was the highest and local flow randomness the lowest, indicating the existence of clusters of high- or low-flow regions there. With increasing myocardial workload, global flow heterogeneity decreased and local flow randomness tended to increase in LV Endo. This flow homogenization with the reduction of global flow heterogeneity may be a manifestation of flow-pattern adaptation through coronary vascular tone, responding to altered local myocardial metabolism.
The authors thank Dr. J. B. Bassingthwaighte (Center for Bioengineering, University of Washington) for expert advice on myocardial flow heterogeneity. We also thank Drs. G. S. Kassab (Department of Bioengineering, University of California-San Diego), P. Sipkema (Department for Physiology, Free University Amsterdam), and A. L. Hazel (Department of Applied Mathematics and Theoretical Physics, University of Cambridge) for their helpful comments during the preparation of the manuscript. M. Kagiyama is gratefully acknowledged for statistical data analysis.
Address for reprint requests and other correspondence: T. Matsumoto, Dept. of Medical Engineering and Systems Cardiology, Kawasaki Medical School, 577 Matsushima, Kurashiki, Okayama 701-0192 Japan (E-mail:).
This study was supported by a Japan Heart Foundation Research Grant, a Research Project Grant (8–206) from Kawasaki Medical School, and by Grants-in-Aid for Scientific Research (09555133) and for Encouragement of Young Scientists (08770541, 09770925) from the Ministry of Education, Science, Sports and Culture, Japan.
- Copyright © 1999 the American Physiological Society