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Department of Integrative Physiology, University of North Texas Health Science Center at Fort Worth, Fort Worth, Texas 76107-2699
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ABSTRACT |
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This is the first investigation of right ventricular (RV)
myocardial oxygen supply/demand balance in a conscious animal. A novel
technique developed in our laboratory was used to collect right
coronary (RC) venous blood samples from seven instrumented, conscious
dogs at rest and during graded treadmill exercise. Contributions of the
RV oxygen extraction reserve and the RC flow reserve to exercise-induced increases in RV oxygen demand were measured. Strenuous
exercise caused a 269% increase in RV oxygen consumption. Expanded
arteriovenous oxygen content difference (A-V
O2) provided 58% of this increase in oxygen demand, and increased RC blood flow
(RCBF) provided 42%. At less strenuous exercise, expanded A-V
O2 provided 60-80% of the required oxygen, and
increases in RCBF were small and driven by increased aortic pressure.
RC resistance fell only at strenuous exercise after the extraction
reserve had been mobilized. Thus RC resistance was unaffected by large
decreases in RC venous PO2 until an apparent
threshold at 20 mmHg was reached. Comparisons of RV findings with
published left ventricular data from exercising dogs demonstrated that
increased O2 demand of the left ventricle is met primarily
by increasing coronary flow, whereas increased O2
extraction makes a greater contribution to RV O2 supply.
oxygen extraction; myocardial oxygen consumption
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INTRODUCTION |
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THE RIGHT VENTRICLE (RV) generates a much lower systolic pressure than the left ventricle (LV) and consequently has a lower oxygen demand. Few investigations have focused on the right coronary (RC) vascular control and RV oxygen supply/demand balance, and, to date, no investigations have reported on these issues in a conscious animal. Recently, our laboratory (6) developed a procedure to obtain RC venous samples from conscious dogs. This procedure was used to investigate RV oxygen balance in exercising dogs.
Myocardial oxygen consumption (M
O2),
coronary blood flow, and oxygen extraction are key variables used to
evaluate oxygen supply/demand relationships.
M
O2 reflects the oxygen demand of the
myocardium when oxygen supply is not limited; coronary blood flow and
oxygen extraction reflect the coronary vascular responses required to
meet the myocardial oxygen demand. This study was designed to define
contributions of RC blood flow (RCBF) and oxygen extraction reserves,
which might be mobilized to increase myocardial oxygen supply when RV
oxygen demand is increased by graded treadmill exercise.
Numerous investigations have focused on cardiac hemodynamic and
metabolic responses to dynamic exercise. LV oxygen extraction is high
(~75%) at rest, therefore, the LV oxygen extraction reserve available for increasing LV oxygen supply during exercise is small (14, 40, 41, 43). Thus increases in LV
M
O2 during exercise always produce
concomitant increases in coronary blood flow (1, 2, 12, 14, 16,
18, 39, 40, 41, 43). On the other hand, the RV has a large
extraction reserve at rest (5, 17, 22, 26, 28), and this
reserve might be mobilized to contribute significantly to RV oxygen
supply during increases in RV oxygen demand. The RV also has a large RC
flow reserve (8, 21, 27, 33, 41), and several studies have
reported that RC flow increases during exercise (2, 23, 25, 30,
31). Interplay between the RV flow and oxygen extraction
reserves has not been described in the conscious animal.
In this investigation, we observed that the RV oxygen extraction reserve was mobilized as exercise progressed, and this reserve contributed importantly to RV oxygen supply during exercise. RC flow initially increased along with an increase in aortic blood pressure, but only during strenuous exercise did RC vascular resistance fall. In addition to defining contributions of RC flow and RV oxygen extraction reserves to RV oxygen supply during exercise, these findings demonstrate that RC resistance is insensitive to large changes in venous oxygen tension, at least above a critical threshold. Results are compared with published LV data, and important differences in mechanisms of ventricular oxygen balance are apparent.
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MATERIALS AND METHODS |
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Animal instrumentation. This investigation was approved by the Institutional Animal Care and Use Committee and was conducted in accordance with the Guide for the Care and Use of Laboratory Animals (NIH Publication 85-23, Revised 1996). Seven adult mongrel dogs of either sex, weighing 24-32 kg, were studied.
Thirty minutes after preanesthesia treatment with PromAce (0.03 mg/kg im), anesthesia was induced by thiopental sodium (5 mg/kg iv). After endotracheal intubation, a surgical plane of anesthesia was maintained by mechanical ventilation with isoflurane gas (1-3%) with equal offset of oxygen (1 liter). Under sterile conditions, a thoracotomy was performed in the fourth right intercostal space, and the dog was instrumented as illustrated in Fig. 1. A Tygon catheter (0.04 in. inner diameter, 0.07 in. outer diameter) was inserted into the aorta through the right internal mammary artery to measure aortic blood pressure. A Konigsberg model P6.5 pressure transducer was inserted through a stab wound in the RV infundibulum and secured with a purse-string suture. A nonbranching section of the right coronary artery (RCA) was dissected free for 1-2 cm to affix a 2-mm diameter Transonics flow transducer. A coronary venous catheter prepared from Micro-Renathane tubing (type MRE-025, 0.012 in. inner diameter, 0.025 in. outer diameter) was inserted into a superficial vein draining the RV myocardium, as described previously (6). The venous catheterization site was in the central region of the RV free wall, well within the perfusion territory of the RCA (20).
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Data collection. After the animals recovered from the surgical procedures, resting measurements were obtained with the animal standing quietly on a treadmill. RC flow was measured with a Transonic T106 series flowmeter. A disposable Isotec pressure transducer (Quest Medical) was positioned at midheart level and connected to the mammary artery catheter to measure aortic blood pressure (AoP). AoP, RCBF, and RV pressure (RVP) were recorded on a multichannel Coulburn chart recorder.
Blood sample collection and analyses.
Arterial and RC venous blood samples were collected to determine oxygen
content, PO2, and glucose and lactate
concentrations. All samples were collected anaerobically and chilled on
ice until analyses. Oxygen content was measured with an Instrumentation Laboratory model 682 Co-Oximeter, and PO2 was
measured with an Instrumentation Laboratory Synthesis 30 blood gas
analyzer. M
O2 was determined by
multiplying the RC arteriovenous difference of oxygen content
(A-V
O2) by RCBF, normalized per gram tissue mass. Oxygen
extraction was computed as A-V
O2 divided by the arterial
oxygen content multiplied by 100. Blood glucose and lactate concentrations were determined by a Radiometer model EML105 Metabolite Analyzer. Glucose and lactate uptakes were calculated by multiplying the RC arteriovenous substrate difference by RCBF
(39).
Exercise protocol. A standardized submaximal exercise protocol was used (38). After baseline measurements were taken with the animal resting quietly on the treadmill, exercise was begun with a 3-mile/h warm-up period for 3 min. The speed of the treadmill was then increased to 4 miles/h for the first level of exercise (exercise 1). This treadmill speed was continued for the remainder of the experiment. For the second level of exercise (exercise 2), the incline of the treadmill was elevated to 4%. Further elevations of the treadmill incline to 8 and 16% were defined as exercise 3 and exercise 4, respectively. The animal was exercised for 3 min at each level. Blood samples were taken and measurements recorded during the last minute at each level of exercise.
Measurement of RCA perfusion territory. After termination of the experiments, the animal was euthanized with pentobarbital sodium (30 mg/kg iv) followed by potassium chloride sufficient to cause ventricular fibrillation. After the chest was opened, the proximal RC artery was clamped and ~15 ml of 2.5% Evans Blue dye was injected into the RC arterial catheter to delineate the perfused territory. In all cases, the RC venous catheter was found to be positioned within the dyed RV wall. This dyed territory was then carefully excised and weighed to normalize RCBF per gram of tissue mass.
Statistical analyses. All values are expressed as means ± SE. Results were analyzed with one-way repeated measures (within subject design) analyses of variance (ANOVA). When significance was found (P < 0.05), a Student-Newman-Keuls multiple comparison test was performed. Statistical procedures were performed with Sigma Stat statistical software, version 2.0, and interpreted according to Keppel (21).
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RESULTS |
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Table 1 presents hemodynamic and
metabolic data collected at rest and during the exercise protocol. AoP
increased 19% to 118 ± 4 mmHg during exercise 1. AoP
remained elevated during the exercise protocol, but did not increase
further (P > 0.05). Heart rate increased 66% to
174 ± 9 beats/min during exercise 1 and increased
further during exercise 3 and exercise 4, reaching 230 ± 6 beats/min at exercise 4. Peak systolic RVP increased
38% to 29 ± 2 mmHg during exercise 1 and then
increased further to 34 ± 3 mmHg at exercise 4.
Arterial oxygen content was 16.8 ± 0.9 ml O2/100 ml
blood at rest and was 17.5 ± 0.9, 18.2 ± 0.8, 18.8 ± 0.8, and 19.3 ± 0.7 ml O2/100 ml blood at
exercise 1, exercise 2, exercise 3,
and exercise 4, respectively. Compared with rest, exercise
stimulated glucose uptake during exercise 1, exercise 2, exercise
3, and this uptake was further enhanced during exercise 4. Lactate uptake was unaffected by exercise until the highest level, when lactate uptake significantly diminished.
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RCBF was 0.59 ± 0.02 ml · min
1 · g
1 at rest and
tended to rise with each exercise step (Fig.
2); exercise 2 and
exercise 3 produced significant but modest increases in RCBF
compared with rest. RCBF at exercise 1, exercise
2, and exercise 3 did not differ significantly. When
compared with exercise 3, exercise 4 produced a
49% increase in RCBF. RC venous PO2
(PvO2) decreased from 29.9 ± 0.6 mmHg at rest to
24.1 ± 1.3 during exercise 1 and decreased further at each successive exercise level (Table 1). Oxygen extraction increased from 46 ± 3% at rest to 68 ± 2% during exercise
1 (Table 1). Exercise 2 produced a further significant
increase in oxygen extraction. At exercise 4 oxygen
extraction reached 82 ± 1%, which was significantly greater than
oxygen extraction at rest, exercise 1, and exercise 2.
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Figure 2 provides information describing the oxygen supply/demand
balance of the RV during exercise-induced increases in oxygen demand.
With the A-V
O2 on the x-axis and RCBF on the
y-axis, the area within the rectangle represents RV
M
O2. Exercise 1 produced a
76% increase RV M
O2. Mean RV
M
O2 increased with exercise 2 and exercise 3, although stepwise comparisons did not detect
significance at P < 0.05; however, exercise
3 RV M
O2 was significantly greater
than exercise 1 RV M
O2.
Exercise 4 produced a large (61% compared with
exercise 3) increase in RV M
O2.
Analysis of the data presented in Fig. 2 allowed us to define relative
contributions of mechanisms responsible for increasing RV oxygen supply
to meet RV oxygen demand. During the initial increase in
M
O2 at the first exercise level, both
RCBF and A-V
O2 significantly increased; the increase in
A-V
O2 provided 82% of the incremental increase in
oxygen supply, and the increase in RCBF provided 18%. Significant
increases in A-V
O2 at exercise 2 and
exercise 3 contributed 81 and 63%, respectively, of the incremental increases in RV M
O2.
Increased A-V
O2 contributed 16% and increased RCBF
contributed 84% of the additional oxygen supply required for the large
incremental increase in RV M
O2 at
exercise 4. Overall, from rest to the most strenuous
exercise, RV M
O2 increased 269%. The
increase in A-V
O2 provided 58% of the overall
incremental increase in oxygen supply, and the increase in RCBF
provided 42%.
Results of the present study were further analyzed by plotting oxygen
supply variables as functions of oxygen demand, i.e., M
O2, averaged for each exercise stage
(Figs. 3-6). This approach normalizes for differences between
experiments that impact oxygen demand, such as afterload, heart rate,
and contractile state of the myocardium. Also plotted on Figs. 3-6
are published data from comparable LV studies (14, 40, 41,
43). Figure 3 confirms that
resting M
O2 is less in RV than in LV,
although blood flows were similar. This is consistent with low resting
RV oxygen extraction. From rest to exercise 3, RCBF
increased only moderately, although RV
M
O2 more than doubled. In contrast, left
coronary (LC) flow appeared to increase linearly from rest to the
highest level of exercise. From moderate to strenuous exercise, blood
flow increased similarly in both ventricles. Therefore, as the RV
oxygen extraction reserve is exhausted, the RV mobilizes its RC flow
reserve, as does the LV, to supply further increases in myocardial
oxygen demand.
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Coronary PvO2 is plotted against
M
O2 in Fig.
4. Changes in coronary
PvO2 reflect changes in myocardial
PO2 and are a sensitive index of changes in
myocardial oxygen supply/demand balance. RV venous
PvO2 decreased steeply from 29.9 to 19.3 mmHg as RV
M
O2 increased from rest to
exercise 3, but then fell more gradually from exercise
3 to exercise 4. Clearly, PvO2 is
higher in RV than in LV at rest and during mild exercise. In contrast
to the steep fall in RV PvO2, exercise-induced
increases in LV M
O2 caused only small
decreases in LC PvO2. At the highest level of
exercise, RV PvO2 was similar to that of the LV at
comparable M
O2.
Coronary resistance was estimated by dividing the driving pressure
(AoP) by coronary flow (36), and this variable is plotted against M
O2 in Fig.
5. RC resistance did not vary
significantly from rest through exercise 3, although RV
M
O2 more than doubled. At exercise
4, RC resistance fell significantly. In contrast, LC resistance
fell abruptly and continuously with exercise-induced increases in LV
M
O2.
RC and LC resistances are plotted against their respective coronary venous PO2 values in Fig. 6. Above 20 mmHg, RV vascular resistance was not significantly affected by large decreases in PvO2 caused by exercise-induced increases in oxygen extraction. Below 20 mmHg, RC resistance fell significantly. With resting PvO2 values near 20 mmHg, any decline in LC PvO2 was associated with concomitant decreases in LC resistance.
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DISCUSSION |
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This report describes the first investigation of RV oxygen supply/demand balance during exercise. Although LV oxygen supply mechanisms have been investigated extensively in exercising animal models (1, 13-16, 18, 24, 40, 41), RV mechanisms have not been investigated, apparently due to the difficulty of collecting RC venous blood samples from conscious animals. This difficulty is due primarily to the small size and fragility of the superficial veins draining the RV and to the absence of a common drainage path, such as the coronary sinus. We recently developed a procedure for collecting RC venous blood samples from conscious dogs (6). Utilizing this procedure in the current investigation, we found the following results. First, the RV has a large oxygen extraction reserve under resting conditions, and this reserve contributes preferentially to supply oxygen when RV oxygen demand increases during light and moderate exercise. Only at more intensive exercise is the substantial RC flow reserve mobilized. Second, RC vascular resistance is not affected by large decreases in RC PvO2 until the RV oxygen extraction reserve has been mobilized. When compared with the LV, the RV relies more on mobilization of a large oxygen extraction reserve to meet increased myocardial oxygen demands of exercise.
RV oxygen extraction reserve.
Myocardial oxygen supply is a function of coronary blood flow and
oxygen extraction. The LV extracts much of the coronary arterial oxygen
(16, 22, 34, 37, 39-41, 43), with resting values
reported as high as 82% (39). LV oxygen extraction does increase with exercise (Fig. 7), and at
very strenuous exercise, LV oxygen extraction values as high as 97%
have been reported (43). Although increased oxygen
extraction contributes to LV oxygen supply during exercise, the oxygen
extraction reserve is relatively small, therefore changes in LV oxygen
demand must be met primarily by altering LC flow (Fig. 3). LV
experiments consistently demonstrate decreased left coronary resistance
during increased LV oxygen demand, even at mild exercise (Fig. 5). In
contrast, RV resting oxygen extraction is only 40-50% (7, 22, 28, and present findings), therefore the RV has a large oxygen extraction
reserve as well as a substantial flow reserve (8, 22, 23,
28). Both of these reserves are potentially available to supply
significant amounts of oxygen when RV oxygen demand increases, as
during exercise.
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1 · 100 g
1 with no increase in flow, or about 53% of the overall
increase in RV M
O2 we observed. However,
as shown, in Fig. 2, the effects of increases in RV
A-V
O2 are amplified by increases in RCBF, especially
during strenuous exercise. Taking into account the higher RCBF that
experienced greater oxygen extraction, 58% of the increased RV oxygen
demand during strenuous exercise was provided by the increase in oxygen
extraction. Furthermore, exercise-induced release of red blood cells
increases the arterial oxygen content and enhances the RV oxygen
extraction reserve. At the less intensive exercise levels of this
study, the oxygen extraction reserve could have supplied the entire
increase in RV M
O2, and, in fact, did supply more than 80% of the required oxygen. Clearly, the RV oxygen extraction reserve is an important factor in RV oxygen supply/demand balance.
Although basal LV oxygen extraction reserve is small (16, 22, 34,
37, 39-41, 43), Dole and Nuno (11) observed a marked expansion of this reserve when heart rate was decreased from 120 to 40 beats/min in atrioventricular-blocked dogs. When LC
perfusion pressure was then reduced from 120 to 80 mmHg,
autoregulation, i.e., vasodilation to maintain constant flow, was
ineffective. As LC perfusion pressure and flow fell, the LV
utilized its oxygen extraction reserve rather than mobilizing its flow
reserve. Although these circumstances clearly differ from
exercise-induced changes in oxygen demand, it should be appreciated
that the LV and RV preferentially use oxygen extraction reserves, if
available, before decreasing coronary vascular resistance. Similar
observations have been made in skeletal muscle, which, like RV, has a
relatively high oxygen extraction reserve at rest (3,
15).
Right coronary flow reserve.
RCBF, the other determinant of RV oxygen supply, has been measured in
exercising dogs (2, 30), horses (25), and
ponies (23, 31). These studies all reported increases in
RC flow, therefore, no differences in RC and LC flow responses to
exercise were noted. In contrast, we detected very modest increases in RCBF during the first three stages of exercise (Fig. 2), and these increases in flow were due to elevated AoP because RC resistance was
not significantly reduced (Fig. 5). Only when a significant portion of
the oxygen extraction reserve had been mobilized during exercise
4 (Table 1) was there a pronounced increase in RCBF (Fig. 2).
Because RCBF can increase to about 4 ml · min
1 · g
1
(28), a large RCBF reserve was still available at the most strenuous exercise employed in this study.
O2 was not measured and, thus the
degree of oxygen demand during exercise cannot be readily equated.
However, in one earlier canine study, Ball et al. (2)
measured RC flow with radioactive microspheres during graded treadmill
exercise. Their resting flows were similar to our results, but with
each increment in heart rate, their flows greatly exceeded those we
observed at comparable heart rates. For example, the RCBF reported by
Ball et al. for moderate exercise (heart rate = 185 ± 2 beats/min) was 2.8 times our measured flow at exercise 3 (heart rate = 191 ± 5 beats/min). Ball et al. also measured
LC flows and concluded that RC and LC flows increase at similar rates
during exercise. Our findings of little change in RC flow during
mobilization of the oxygen extraction reserve (Fig. 2) clearly differ
from the conclusions of Ball et al. The discrepancy is unlikely to be
due to different measurement techniques because resting RC flows are
similar in both studies. One difference is the time of measurement. In
our protocol, data were collected at 3 min of exercise at each level,
whereas Ball et al. injected microspheres at 45 s after initiating
exercise, a time when heart rate had stabilized, but perhaps not RC
flow. In fact, we have observed transient increases in RC flow during
protocol steps that required 60-84 s to subside. It is also
possible that the dogs of Ball et al. had a lesser oxygen extraction
reserve, and, therefore, had to mobilize their flow reserve to a
greater degree. Once the oxygen extraction reserve is exhausted, our
data (Fig. 2) do agree with Ball et al.'s suggestion that RC flow
increases in parallel with LC flow.
Initiation of exercise caused a 19-mmHg increase in mean aortic blood
pressure (Table 1). Because RV M
O2 is
affected by changes in RC perfusion pressure (5), a small
portion of the observed increase in RV
M
O2 was due directly to
increased AoP. However, the focus of this investigation was to
delineate mechanisms of RV oxygen supply during exercise irrespective
of specific factors responsible for increased RV oxygen demand. It
should also be recognized that changes in coronary perfusion pressure
produce changes in coronary blood flow independent of pressure-induced changes in oxygen demand, as demonstrated in the perfused LV by Vergroesen et al. (42). In the current investigation, the
initial rise in RC flow paralleled the rise in AoP; RC resistance was not decreased (Fig. 5), although RV M
O2
was significantly elevated. In contrast, the large increase in RC flow
at the most intensive exercise was associated with a marked decrease in
RC vascular resistance.
We did not determine the mechanism responsible for the decrease in RC
resistance during the most strenuous exercise. Indeed, the mechanism
responsible for left coronary vasodilation during exercise remains
elusive (41). Our data do impact on understanding the role
myocardial oxygen tension might play in regulating coronary arteriolar
tone. Assuming RC PvO2 is a valid index of RV
PO2, it is apparent that values greater than
~20 mmHg are not associated with changes in RC resistance.
Interestingly, resting left coronary venous PO2
is about 20 mmHg (40, 43), and increases in LV oxygen
extraction are associated with left coronary dilation. Whether these
decreases in tissue PO2 directly or indirectly
cause coronary vasodilation remains to be determined.
Substrate selection. In this investigation, RV glucose uptake was enhanced during exercise, in agreement with findings of LV investigations (4, 27). As arterial lactate concentrations rise during dynamic exercise, it is generally accepted that lactate uptake increases, as long as oxygen is available (29). In our investigation, however, arterial concentrations were not significantly elevated during the 12-min exercise protocol, and RV lactate uptake did not increase (Table 1). During the highest exercise level, glucose uptake was further enhanced and lactate uptake decreased, suggesting an increased preference for glucose as a metabolic fuel.
Validation that RC venous samples reflect RCA drainage. For our conclusions to be valid, RC venous blood samples must contain only blood draining RV myocardium supplied by the RCA. Two possible sources of contamination are blood drawn retrogradely from the right atrium and blood originating from vessels other than the RCA. To investigate whether there was contamination from right atrial blood, radioactive microspheres were infused simultaneously for 5 min into the superior and inferior vena cavae of four dogs. Three dogs were instrumented and studied in the conscious state, and one was studied in an acute experiment. During infusion of radioactive microspheres, blood samples were collected from the right atrium and the RC vein and later analyzed for radioactivity. Because circulating microspheres were trapped in the pulmonary circulation, any radioactivity within the RC venous samples would have come from right atrial contamination. Mean radioactivity counts emitted by the blood samples were 2,636 ± 702 for right atrial blood and 2 ± 1 for RC venous blood samples. These data demonstrate that there was no right atrial blood withdrawn into the venous samples using our technique.
It is also possible, given the vascular anatomy of the right heart, that blood from the LV circulation may have contributed significantly to RV venous samples. This possibility of venous contamination was explored in an earlier canine study in our laboratory by Murakami et al. (28). They infused Evans blue dye systemically while perfusing the RCA from an uncontaminated blood supply. With RC perfusion pressure reduced to 80 mmHg and with normal systemic arterial pressure, the LC contribution to RC venous drainage was 1.2 ± 1.0%. In the present study, there was no disparity between RC and LC perfusion pressures, therefore RC venous contamination from other coronary sources should have been negligible. In summary, this report presents the first data describing RV oxygen supply/demand balance during graded exercise. The results documented a substantial RV oxygen extraction reserve at rest that is utilized preferentially during exercise-induced increases in RV M
O2. Small increases in RC flow during
mild exercise were the result of elevated AoP; RC resistance did not
fall until the RV oxygen extraction reserve had been mobilized. In this
process, RC PvO2 decreased to ~20 mmHg without
concomitant RC vasodilation. Strenuous exercise caused a 269% increase
in RV oxygen consumption. Expanded A-V
O2 supplied 58%
of this increase in oxygen demand, and increased RCBF supplied 42%.
Considerable differences exist between the ventricles as to the
relative contributions of the coronary flow and oxygen extraction
reserves mobilized to increase myocardial oxygen supply as oxygen
demand is elevated.
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ACKNOWLEDGEMENTS |
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We thank Arthur G. Williams, Jr., Sue Yi, and Min Fu for expert technical assistance. This work was completed in partial fulfillment of the requirements for the Doctor of Philosophy degree awarded by the University of North Texas Health Science Center at Fort Worth to B. J. Hart.
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FOOTNOTES |
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This work was supported by National Heart, Lung, and Blood Institute Grants HL-35,027 and HL-64785 and American Heart Association Grant-in-Aid 0050316N.
Address for reprint requests and other correspondence: H. F. Downey, Dept. of Integrative Physiology, Univ. of North Texas Health Science Center at Fort Worth, 3500 Camp Bowie Blvd., Fort Worth, TX 76107-2699 (E-mail: fdowney{at}hsc.unt.edu).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 25 July 2000; accepted in final form 18 April 2001.
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