CLINICAL STUDY: CORONARY BLOOD FLOW
Do beta-adrenergic blocking agents increase coronary flow reserve?
Michael Billinger, MDa,
Christian Seiler, MD, FACCa,
Martin Fleisch, MDa,
Franz R. Eberli, MDa,
Bernhard Meier, MD, FACCa and
Otto M. Hess, MD*,a
a Department of Cardiology, Swiss Cardiovascular Center, Bern, Switzerland
Manuscript received May 29, 2001;
revised manuscript received August 3, 2001,
accepted September 4, 2001.
* Reprint requests and correspondence: Prof. Dr. Otto M. Hess, Swiss Cardiovascular Center, Bern University Hospital, CH-3010 Bern, Switzerland
otto.martin.hess{at}insel.ch
 |
Abstract
|
|---|
BACKGROUND
Beta-adrenergic blocking agents are the cornerstone in the treatment of coronary artery disease (CAD). The exact pathophysiologic mechanism is not clear but depends largely on the oxygen-sparing effect of the drug. Thus, the effect of metoprolol on coronary flow reserve and coronary flow velocity reserve (CFVR) was determined in patients with CAD.
METHODS
Coronary blood flow velocity was measured with the Doppler flow wire in 23 patients (age: 56 ± 10) undergoing percutaneous transluminal coronary angioplasty for therapeutic reasons. Measurements were carried out at rest, after 1-min vessel occlusion (postischemic CFVR) as well as after intracoronary adenosine (pharmacologic CFVR) before and after 5 mg intravenous metoprolol. In a subgroup (n = 15), absolute flow was measured from coronary flow velocity multiplied by coronary cross-sectional area.
RESULTS
Rate-pressure product decreased after metoprolol from 9.1 to 8.0 x 103 mm Hg/min (p < 0.001). Pharmacologic CFVR was 2.1 at rest and increased after metoprolol to 2.7 (p = 0.002). Likewise, postischemic CFVR increased from 2.6 to 3.3 (p < 0.001). Postischemic CFVR was significantly higher than pharmacologic CFVR before as well as after metoprolol. Coronary vascular resistance decreased after metoprolol from 3.4 ± 2.0 to 2.3 ± 0.7 mm Hg x s/cm (p < 0.02).
CONCLUSIONS
The following conclusions were drawn from this study. Metoprolol is associated with a significant increase in postischemic and pharmacologic CFVR. However, postischemic CFVR is significantly higher than pharmacologic CFVR. The increase in CFVR by metoprolol can be explained by a reduction in vascular resistance. The increase in CFVR (= increased supply) and the reduction in oxygen consumption (= decreased demand) after metoprolol explain the beneficial effect of this beta-blocker in patients with CAD.
|
Abbreviations and Acronyms
| | CAD | = coronary artery disease | | CFR | = coronary flow reserve | | CFVR | = coronary flow velocity reserve | | i.c. | = intracoronary | | PTCA | = percutaneous transluminal coronary angioplasty | | QCA | = quantitative coronary angiography |
|
The capacity of the coronary arteries to increase flow during hyperemia by a factor of three to four was described as early as in 1939 by Katz and Lindner (1). However, it was not until 1960 that the concept of coronary flow reserve (CFR) was introduced by Coffman and Gregg (2) to assess the capacity of coronary circulation to conduct maximal hyperemic blood flow. Pharmacologic agents commonly used to induce maximal vasodilation include papaverine (3–5), adenosine (4,6) and dipyridamole (4). Hyperemia can also be induced by transient vessel occlusion (7) or dynamic exercise (8).
Coronary flow reserve is the ratio of coronary blood flow during maximal vasodilation divided by resting flow. Because the pressure-flow relationship is linear and steep during maximal vasodilation, peak flow is a function of coronary resistance in the absence of epicardial coronary artery lesions (9). Therapeutic interventions may affect CFR by changing resting or maximal flow. A small increase in resting flow leads, however, to a large decrease in CFR, and vice versa.
Metoprolol has been shown to reduce oxygen consumption of the myocardium and, thus, diminishes myocardial ischemia (= reduced demand). However, a preliminary report using positron emission tomography in healthy volunteers for coronary flow measurements also indicated an improvement in CFR after beta-adrenergic blockade (= increased supply), which was mainly due to an increase in hyperemic flow rather then a decrease in resting flow (10). Thus, the purpose of this study was to assess the effect of intravenous metoprolol on CFR, respectively, coronary flow velocity reserve (CFVR) in patients with coronary artery disease (CAD) using adenosine and postischemic hyperemia as stimulus for maximal flow increase.
|
Methods
|
|---|
Patients.
Twenty-three patients (age: 58 ± 10 years, all men) with one- (n = 17) or two-vessel (n = 6) disease are included in this analysis. Three of the 23 patients had previous myocardial infarction, but none of these patients had a Q-wave infarct (Table 1). All patients underwent percutaneous transluminal coronary angioplasty (PTCA) for clinical purposes (angina pectoris or positive exercise test with ST-segment depression). Patients with diffused or three-vessel disease were excluded from this analysis.
Coronary angiography.
Patients underwent left heart catheterization for diagnostic purposes. Aortic and left ventricular pressure were measured with a pigtail catheter. Biplane left ventricular angiography was performed at the end of diagnostic coronary angiography. Coronary artery lesions were assessed quantitatively as percent diameter stenosis. Vessel diameter at the tip of the flow wire was measured by quantitative coronary angiography (QCA) using the ACA package on Philips DC/Integris system. Collateralization was assessed according to the Rentrop classification (11).
Doppler flow velocity measurements.
Doppler flow velocity was measured with a 0.014 in. Doppler guide wire with a 12-MHz piezoelectric crystal at its tip (FloWire, EndoSonics, Rancho Cordova, California). The validation of this Doppler guide wire has been described previously (12).
Coronary flow velocity reserve was calculated from hyperemic peak flow velocity averaged over two cardiac cycles (averaged peak velocity = APV, cm/s) divided by resting flow velocity (Fig. 1). Pharmacologic CFVR was induced by an intracoronary bolus of 18 µg adenosine for the left and 12 µg for the right coronary artery (13). Postischemic hyperemia was induced by a 1-min balloon occlusion. Coronary vascular resistance was calculated from mean aortic pressure divided by mean coronary flow velocity (mm Hg x s/cm).
View larger version (110K):
[in this window]
[in a new window]
|
Figure 1 Representative recordings of coronary flow velocity signal in a patient with single-vessel disease undergoing percutaneous transluminal coronary angioplasty. The tracings are shown in the panels from top to bottom: electrocardiogram, aortic pressure, instantaneous flow velocity and flow velocity trend. Pharmacologic coronary flow velocity reserve (CFVR) (left): flow velocity at rest = 9.1 cm/s, maximal flow velocity after administration of 18 µg adenosine = 28 cm/s; CFVR: 28/9.1 = 3.1. Determination of postischemic CFVR (right): flow velocity after 1-min balloon occlusion = 28 cm/s; CFVR: 28/9.1 = 3.1. Pharmacologic CFVR after metoprolol (lower panels): flow velocity at rest = 9.7 cm/s, maximal flow velocity after adenosine = 36 cm/s; CFVR: 36/9.7 = 3.7. Postischemic CFVR: postischemic flow velocity = 41 cm/s; CFVR: 41/9.7 = 4.2.
|
|
In a subgroup of 15 patients, coronary flow was calculated from coronary flow velocity multiplied by coronary artery dimension at the tip of the flow wire measured by QCA x 0.3. From these measurements CFR was determined.
Recent data (14,15) indicate that the standard (13) adenosine dose (18 µg for the left and 12 µg for the right coronary artery) may be submaximal in some patients. Therefore, in a group of six patients, the effect of two different adenosine doses (18 and 24 µg) on coronary flow reserve was tested.
Study protocol.
The following study protocol were adhered to: - Diagnostic angiography
- Intracoronary bolus of nitroglycerin (0.2 mg, repeated every 5 to 10 min)
- PTCA
- Control studies a. Rest measurements 1 b. Measurements during hyperemia (adenosine, intracoronary [i.c.]) c. Rest measurements 2 d. Measurements during hyperemia (1-min coronary occlusion)
- Administration of 5 mg metoprolol, intravenous a. Rest measurements 1 b. Measurements during hyperemia (adenosine, i.c.) c. Rest measurements 2 d. Measurements during hyperemia (1-min coronary occlusion).
The present study protocol was approved by the local ethics committee, and all patients gave informed consent.
Statistical analysis.
Comparison of angiographic, hemodymamic and Doppler flow velocity data was performed by an unpaired two-sided Student t test. A two-way analysis of variance for repeated measurements was performed for comparison of hemodynamic and Doppler flow data. Correlation between CFVR and CFR (n = 15) was performed using the square method. The correlation coefficient (r) and the regression equation were calculated from these data. Statistical significance was defined at a p value of <0.05.
|
Results
|
|---|
Average number of diseased vessel was 1.3 per patient. No collateral flow was observed in the majority of patients (n = 18). However, in five patients there was mild collateral flow (grade 1) according to Rentrop classification (16).
Hemodynamics.
There was a significant decrease in heart rate after metoprolol administration (Table 2, Fig. 2). Mean aortic pressure also dropped significantly after metoprolol, but this difference was lost during adenosine infusion. Consecutively, the rate-pressure product decreased significantly.
View larger version (25K):
[in this window]
[in a new window]
|
Figure 2 Rate-pressure product: before (left) and after (right) 5 mg metoprolol, intravenous, at rest as well as during hyperemia. There is a significant reduction in the rate-pressure product after beta-blockade. ADO = adenosine.
|
|
Coronary flow velocity and flow reserve.
Basal coronary flow velocity remained unchanged after 5 mg metoprolol but increased significantly (+147%) during adenosine infusion after beta-blockade than after adenosine infusion alone (+94%; p < 0.001) (Table 2, Fig. 3). Conversely, the postischemic flow increase was significantly larger (+219%) after metoprolol than it was after ischemia alone (+153%; p < 0.005). Maximal flow velocity was significantly higher after metoprolol for both pharmacologic and postischemic vasodilation.
View larger version (29K):
[in this window]
[in a new window]
|
Figure 3 Pharmacologic and postischemic coronary flow velocity reserve (CFVR) increased significantly from 2.1 ± 0.6 to 2.6 ± 0.9, respectively, from 2.7 ± 0.8 to 3.3 ± 1.0 after intravenous administration of 5 mg metoprolol. In two patients, there was no change in pharmacologic CFVR, but in another two patients there was even a decrease in CFVR after beta-blockade. Postischemic CFVR was generally higher than pharmacologic CFVR.
|
|
Similarly, both pharmacologic and postischemic CFVR increased significantly from 2.1 ± 0.6 to 2.6 ± 0.9, respectively, to 2.7 ± 0.8 to 3.3 ± 1.0 after intravenous administration of 5 mg metoprolol (Fig. 3). In two patients there was no change in pharmacologic CFVR, and in two patients CFVR even decreased after beta-blockade. Postischemic CFVR was significantly higher than pharmacologic CFVR.
In a subgroup of 15 patients, coronary cross-sectional area did not change significantly after 5 mg metoprolol (baseline: 6.5 ± 0.7 mm2; after beta-blockade: 6.4 ± 0.5 mm2; p = NS). Therefore, basal flow velocity and volumetric flow remained unchanged after metoprolol. In these patients CFR data were comparable to CFVR data.
The effect of 18 µg and 24 µg adenosine was studied in a group of six patients with normal coronary arteries. There was no further flow increase with the higher adenosine dose (24 µg) than with the reported standard dose (18 µg). Coronary flow reserve in these patients was 2.99 ± 0.64 with 18 µg and 3.03 ± 0.73 with 24 µg (n = 23, n = NS).
Coronary vascular resistance.
Coronary vascular resistance was slightly lower (n = NS) after metoprolol but significantly lower during pharmacologic, respectively, postischemic hyperemia (Fig. 4). Metoprolol further enhanced the drop in vascular resistance with pharmacologic, respectively, postischemic vasodilation (Fig. 4).
View larger version (37K):
[in this window]
[in a new window]
|
Figure 4 Coronary vascular resistance was slightly lower (NS) after metoprolol but significantly lower during pharmacologic, respectively, postischemic vasodilation. ADO = adenosine.
|
|
|
Discussion
|
|---|
Changes in coronary hemodynamics associated with the administration of beta-blockers have been extensively studied in the past. Animal experiments have shown a reduction in coronary blood flow at rest, which has been explained by coronary vasoconstriction (17–19). Previous clinical data using coronary flow measurements suggest that beta-blockers lead to enhanced coronary vascular resistance during hyperemia due to unopposed alpha-adrenergic vasomotor tone (20). However, this study was performed using a nonselective beta-blocker, and only five of nine patients showed an increase of hyperemic coronary vascular resistance after propranolol, whereas, in four patients, coronary flow behaved similarly to our study. In part, this variability may have been related to the less precise method of flow determination by coronary sinus thermodilution. In 10 healthy volunteers, Boettcher and coworkers (10) have reported an increase in CFR after 50 mg oral metoprolol. Absolute coronary flow was measured noninvasively by positron emission tomography. The increase in CFR was achieved by a significant increase in maximal coronary flow, which was enhanced by a significant decrease in resting flow. In this study in patients with CAD, pharmacologically induced and postischemic flow velocity reserve increased after intravenous administration of 5 mg metoprolol due to an increase in maximal flow (Table 3, Fig. 3). At the same time, coronary vascular resistance decreased after beta-blockade but only during maximal vasodilation and not at rest (Fig. 4). The reduction in coronary vascular resistance can be explained by a diminution of the extravascular compressive forces either due to a reduced filling pressure or a decrease in myocardial contractility with a reduction in vascular tone. Comparison of the two vasodilatory stimuli, that is, pharmacologic vasodilation with adenosine versus postischemic vasodilation by 1-min balloon occlusion, clearly showed a stronger effect (Fig. 3) with ischemia. This can be either due to the duration and severity of the ischemic event or the dose of adenosine. Since no additional effect on CFR was observed with a higher (24 µg) than standard (18 µg) dose of adenosine, pharmacologic vasodilation was maximal with the standard dose used in this study.
Study limitations.
Several limitations have to be considered for this article: - Changes in heart rate and mean aortic pressure may affect coronary flow velocity. Metoprolol decreases heart rate and aortic pressure, which might reduce coronary flow velocity. However, despite the decrease in heart rate and mean aortic pressure (Table 2), resting coronary flow velocity did not change in this study. Therefore, these effects seem to be of minor importance for the observed changes in flow velocity. On the other hand, adenosine as a strong vasodilator may lead to a drop in pressure and, thus, may decrease CFR. This was not the case in this analysis. Furthermore, all patients received the same dose at the same time of the study protocol.
- The standard adenosine dose used for maximal hyperemia was 12 µg for the right and 18 µg for the left coronary artery. Recent data (14,15) suggest that these doses may be submaximal in some patients and, thus, may lead to an underestimation of CFR. This could explain why postischemic hyperemia might give higher CFR values than adenosine. Therefore, we measured CFR in a group of six patients after 18 and 24 µg adenosine, i.c. There was no significant difference in CFR (2.99 vs. 3.03, p = NS). Thus, the standard adenosine dose seems to be sufficient to induce maximal vasodilation in most patients.
- Coronary flow velocity measurements may be limited by a change in sampling volume due to the motion of the flow wire within the coronary tree. We, therefore, assured that only patients with a stable and good flow signal were included in this analysis.
- Changes in coronary artery diameter could, theoretically, affect flow velocity measurements. Thus, in 15 patients coronary artery diameter at the tip of the flow wire was measured, and absolute coronary blood flow was calculated from flow velocity and coronary cross-sectional area. Cross-sectional area remained unchanged after beta-blockade and, thus, did not account for changes in coronary flow velocity.
- Cross-sectional area during maximal hyperemia with adenosine was not measured. However, in a previous study we have shown that, after intracoronary nitroglycerin, coronary dimensions did not change further, even with an extremely high dose (2.4 mg/min) of intracoronary adenosine (cross-sectional area before: 7.1 ± 2.6 mm2; during adenosine infusion: 7.2 ± 2.8 mm2). Thus, cross-sectional area is unchanged during adenosine infusion after maximal vasodilation with nitroglycerin and has no effect on coronary flow velocity.
Conclusions.
Metoprolol is associated with a significant increase in CFR despite a reduction in heart rate and coronary perfusion pressure. This improvement in flow reserve is not only seen after pharmacologic vasodilation but also after postischemic hyperemia. The vasodilator response was, however, enhanced after myocardial ischemia when compared with adenosine. Apparently, ischemia seems to be a stronger vasodilator stimulus than adenosine.
In the daily routine, beta-blockers have a large therapeutic indication in the treatment of CAD due to their anti-ischemic and antiarrhythmic effect. The anti-ischemic effect of beta-blockers is based on the oxygen sparing mechanism with a reduction in the rate-pressure product (Fig. 2). However, the improvement in CFR indicates an improved oxygen supply due to the enhancement of maximal vasodilation after metoprolol with a potential reduction in ischemic events. This dual effect is probably responsible for an increase in blood supply and a reduction in oxygen demand rendering beta-blockers an ideal drug for treatment of CAD.
|
Footnotes
|
|---|
Supported by an educational grand of the Swiss Heart Foundation, Bern, Switzerland.
|
References
|
|---|
1. Katz LN, Lindner E. Quantitative relation between reactive hyperemia and the myocardial ischemia which it follows. Am J Physiol. 1939;126:283–288[Free Full Text]
2. Coffman JD, Gregg DE. Reactive hyperemia characteristics of the myocardium. Am J Physiol. 1960;199:1143–1149[Abstract/Free Full Text]
3. Bookstein JJ, Higgins CB. Comparative efficacy of coronary vasodilatory methods. Invest Radiol. 1977;12:121–127[CrossRef][Medline]
4. Christensen CW, Rosen LB, Gal RA, Haseeb M, Lassar TA, Port SC. Coronary vasodilator reserve: comparison of the effects of papaverine and adenosine on coronary flow, ventricular function, and myocardial metabolism. Circulation. 1991;83:294–303[Abstract/Free Full Text]
5. Wilson RF, White CW. Intracoronary papaverine: an ideal coronary vasodilator for studies of the coronary circulation in conscious humans. Circulation. 1986;73:444–451[Abstract/Free Full Text]
6. Rossen JD, Quillen JE, Lopez AG, Stenberg RG, Talman CL, Winniford MD. Comparison of coronary vasodilation with intravenous dipyridamole and adenosine. J Am Coll Cardiol. 1991;18:485–491[Abstract]
7. Marcus M, Wright C, Doty D, et al. Measurements of coronary velocity and reactive hyperemia in the coronary circulation of humans. Circ Res. 1981;49:877–891[Free Full Text]
8. Felder L, Vassalli G, Vassalli F, et al. Clinical significance of coronary flow reserve: effect of papaverine and exercise. Coron Artery Dis. 1994;5:347–358[Medline]
9. Marcus ML, Chilian WM, Kanatsuka H, Dellsperger KC, Eastham CL, Lamping KG. Understanding the coronary circulation through studies at the microvascular level. Circulation. 1990;82:1–7[Abstract/Free Full Text]
10. Bottcher M, Czernin J, Sun K, Phelps ME, Schelbert HR. Effect of beta 1 adrenergic receptor blockade on myocardial blood flow and vasodilatory capacity. J Nucl Med. 1997;38:442–446[Abstract/Free Full Text]
11. Rentrop KP, Thornton JC, Feit F, Van Buskirk M. Determinants and protective potential of coronary arterial collaterals as assessed by an angioplasty model. Am J Cardiol. 1988;61:677–684[CrossRef][Medline]
12. Doucette JW, Corl PD, Payne H, et al. Validation of a Doppler guide wire for intravascular measurement of coronary artery flow velocity. Circulation. 1992;85:1899–1911[Abstract/Free Full Text]
13. Wilson RF, Wyche K, Christensen BV, Zimmer S, Laxson DD. Effects of adenosine on human coronary arterial circulation. Circulation. 1990;82:1595–1606[Abstract/Free Full Text]
14. Jeremias A, Whitbourn RJ, Filardo SD, et al. Adequacy of intracoronary versus intravenous adenosine-induced maximal coronary hyperemia for fractional flow reserve measurements. Am Heart J. 2000;140:651–657[CrossRef][Medline]
15. Jeremias A, Filardo SD, Whitbourn RJ, et al. Effects of intravenous and intracoronary adenosine 5'-triphosphate as compared with adenosine on coronary flow and pressure dynamics. Circulation. 2000;101:318–323[Abstract/Free Full Text]
16. Rentrop KP, Cohen M, Blanke H, Phillips RA. Changes in collateral channel filling immediately after controlled coronary artery occlusion by an angioplasty balloon in human subjects. J Am Coll Cardiol. 1985;5:587–592[Abstract]
17. Young MA, Vatner DE, Vatner SF. Alpha- and beta-adrenergic control of large coronary arteries in conscious calves. Basic Res Cardiol. 1990;85(Suppl 1):97–109[Medline]
18. Vatner SF, Higgins CB, Braunwald E. Effects of norepinephrine on coronary circulation and left ventricular dynamics in the conscious dog. Circ Res. 1974;34:812–823[Abstract/Free Full Text]
19. Marshall RJ, Parratt JR. Comparative effects of propranolol and practolol in the early stages of experimental canine myocardial infarction. Br J Pharmacol. 1976;57:295–303[Medline]
20. Kern MJ, Ganz P, Horowitz JD, et al. Potentiation of coronary vasoconstriction by beta-adrenergic blockade in patients with coronary artery disease. Circulation. 1983;67:1178–1185[Abstract/Free Full Text]
This article has been cited by other articles:
|
|
|
|
 
G. J. Zoghbi, T. A. Dorfman, and A. E. Iskandrian
The Effects of Medications on Myocardial Perfusion
J. Am. Coll. Cardiol.,
August 5, 2008;
52(6):
401 - 416.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
A. S. Go, C. Iribarren, M. Chandra, P. V. Lathon, S. P. Fortmann, T. Quertermous, M. A. Hlatky, and for the Atherosclerotic Disease, Vascular Function
Statin and beta-blocker therapy and the initial presentation of coronary heart disease.
Ann Intern Med,
February 21, 2006;
144(4):
229 - 238.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
K. Sugioka, T. Hozumi, Y. Takemoto, K. Ujino, Y. Matsumura, H. Watanabe, K. Fujimoto, M. Yoshiyama, and J. Yoshikawa
Early recovery of impaired coronary flow reserve by carvedilol therapy in patients with idiopathic dilated cardiomyopathy: A serial transthoracic Doppler echocardiographic study
J. Am. Coll. Cardiol.,
January 18, 2005;
45(2):
318 - 319.
[Full Text]
[PDF]
|
|
|
|
|
|
|
E. I. Skalidis, F. I. Parthenakis, A. P. Patrianakos, M. I. Hamilos, and P. E. Vardas
Regional coronary flow and contractile reserve in patients with idiopathic dilated cardiomyopathy
J. Am. Coll. Cardiol.,
November 16, 2004;
44(10):
2027 - 2032.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
P. Koepfli, C. A. Wyss, M. Namdar, M. Klainguti, G. K. von Schulthess, T. F. Luscher, and P. A. Kaufmann
{beta}-Adrenergic Blockade and Myocardial Perfusion in Coronary Artery Disease: Differential Effects in Stenotic Versus Remote Myocardial Segments
J. Nucl. Med.,
October 1, 2004;
45(10):
1626 - 1631.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
M. Zaugg, C. Schulz, J. Wacker, and M. C. Schaub
Sympatho-modulatory therapies in perioperative medicine
Br. J. Anaesth.,
July 1, 2004;
93(1):
53 - 62.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
M. C. Gerson
Reduction in dipyridamole-induced single-photon emission computed tomography myocardial defect size by beta-blockers: Time to re-examine the patient preparation protocol for pharmacologic stress testing
J. Am. Coll. Cardiol.,
October 15, 2003;
42(8):
1484 - 1486.
[Full Text]
[PDF]
|
|
|
|
|
|
|
L. M. Riou, M. Ruiz, J. M. Rieger, T. L. Macdonald, D. D. Watson, J. Linden, G. A. Beller, and D. K. Glover
Influence of propranolol, enalaprilat, verapamil, and caffeine on adenosine A2A-receptor-mediated coronary vasodilation
J. Am. Coll. Cardiol.,
November 6, 2002;
40(9):
1687 - 1694.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
Top
Abstract
Methods