| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
1KIHU–Research Institute for Olympic Sports, Jyväskylä, Finland; and 2Department of Biology of Physical Activity, University of Jyväskylä, Jyväskylä, Finland
Submitted 18 January 2005 ; accepted in final form 26 August 2005
 |
ABSTRACT |
|---|
 TOP ABSTRACT MATERIALS AND METHODSRESULTSDISCUSSIONGRANTSDISCLOSURESREFERENCES |
|---|
autonomic nervous system; parasympathetic; power spectral analysis
HRV has been used widely as a quantitative measure of vagal effects on the heart. Studies (15) on animals have shown a linear within-animal correspondence between the magnitude of HRV and the level of vagal outflow. Studies on humans have demonstrated a within-subject correspondence between the magnitude of HRV and graduated administration of atropine (28), as well as between changes in HRV and 
-blocked R-R interval during behavioral tasks (12). Quite recently, Bloomfield et al. (6) found a monotonous increase in HRV across increasing vagal stimulation due to progressive doses of phenylephrine. In contrast, according to a similar study by Goldberger et al. (10), this relationship is better described by a quadratic than a linear fit. Although the quantitative relationship between the magnitude of HRV and the vagal effects on the heart is unclear, autonomic indexes derived from HRV are widely employed as measures of within-subject changes in vagal activity in physiological, psychological, and clinical examinations.
This study was designed to evaluate the validity of autonomic indexes derived from spectral analysis of HRV in monitoring quantitatively the within-subject changes in vagal effects on the heart. The present blocking approach differed from the standard approach used in the majority of blocking studies. We monitored not only the effects of complete vagal blockade by atropine administration on HRV but also the effects of atropine disappearance on HRV during a recovery period. The purpose was to define the within-subject quantitative relationship between the magnitude of HRV and the vagal effects on the heart in different postures in persons with different endurance-training backgrounds.
|
MATERIALS AND METHODS |
|---|
|
TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSDISCLOSURESREFERENCES |
|---|
The general health status of the subjects was assessed with a brief health questionnaire and a ECG with subjects at rest. The health questionnaire screened autonomic nervous system abnormalities, contraindications to vagal blocking, and inherited propensities to cardiovascular diseases. All subjects were medication free. They were asked to maintain their regular lifestyle and refrain from extra physical exertion starting 3 days before the test sessions. During these days, the consumption of alcohol and caffeinated beverages was prohibited. All subjects were nonsmokers. The subjects gave written, informed consent to participate. They had the right to withdraw from the study at any time. The study was approved by the Ethics Committee of the Central Hospital of Central Finland.
Protocol. Each subject arrived at the laboratory 2 h after breakfast at 8:15 AM. The test day started with measurements of body weight, height, and body fat, followed by the attachment of recording equipment. After catheter insertion into the antecubital vein, instrumentation, and instructions, the subjects rested quietly for 10 min.
The experiments were carried out in a quiet laboratory (23–24°C). First, the subjects underwent the PRE condition in which no blocking agent was administered. Recordings were obtained with the subjects in supine (5 min), sitting (5 min), and standing (3 min) postures. The next step was the blocking procedure as described by Katona et al. (16). Vagal blocking was performed by administering four equal intravenous doses of atropine sulfate (4 x 0.01 mg/kg; Atropin; Leiras Oy, Helsinki, Finland). The doses were given at 3-min intervals. After each dose, 5 ml of saline (0.9% Natrosteril; Medipolar, Oulu, Finland) were flushed. The recordings in supine, sitting, and standing postures were repeated under the complete vagal blockade (POST1). In addition to this standard blocking approach, the recordings in the above-mentioned postures were repeated four times at regular 15-min intervals over a 150-min recovery period, during which the effects of vagal blockade gradually diminished (POST2–POST5).
Data collecting. During the experiments, ECG and RF were recorded continuously with the use of a computer-based data acquisition system (model MP100, Biopac Systems). Three standard disposable electrodes were placed on the chest and connected to an ECG amplifier. For measuring RF, a strain-gauge transducer (TSD101C, Biopac Systems) was attached around the chest at the level of the proximal end of the sternum. The ECG and RF signals were sampled at a rate of 1,000 Hz and digitized with a 16-bit analog-to-digital converter. An automatic peak trigger was used to detect the R-waves and convert the EGC signal to R-R intervals. A similar automatic technique was used to detect the beginning of each respiratory cycle and convert the respiratory signal to respiratory intervals.
To determine the plasma concentration of epinephrine and norepinephrine, a blood sample of 10 ml was taken at the end of PRE, POST1, and POST5. Within 15 min after sampling was completed, the blood sample was centrifuged (3,600 rpm) at 4°C for 7 min, and plasma samples were aliquoted for different hormone measurements and stored at –80°C until the samples were assayed. Plasma catecholamine concentrations were determined by using high-pressure liquid chromatography with an electrochemical detector (model 5100 A, ESA Coulochem Multi-Electrode, ESA, Chelmsford, MA) at Kuopio University Hospital. During the same blocking conditions, a blood sample of 5 ml was taken for determining the plasma concentration of cortisol. The blood sample was centrifuged as previously described, and plasma was stored at –20°C until assayed. Plasma cortisol concentration was determined by time-resolved fluoroimmunoassay (Wallac Oy, Turku, Finland) at the Central Hospital of Central Finland.
HRV analysis. The R-R interval series were checked and edited for artifacts using a detecting algorithm and subsequently verified by visual inspection. All analyses were performed from stationary periods free from ectopic beats and technical artifacts according to the recommendations of the Task Force (31). The original R-R interval series were resampled at a rate of 5 Hz by using linear interpolation to obtain equidistantly sampled time series. A series of 512 samples during each posture (starting at 150 s and 150 s and 80 s after assuming the supine, sitting, and standing postures, respectively) were then extracted to HRV calculations. The Fast Fourier transform method with Hanning window was used to obtain power spectrum estimates of HRV (program on MATLAB 7, The MathWorks, 2004). Low-frequency (LFP, 0.04–0.15 Hz), high-frequency (HFP, 0.15–0.40 Hz), and total power (TP, 0.04–0.40 Hz) were calculated as integrals under the respective power spectral density curve. Spectral powers were expressed in absolute values (LFP, HFP, and TP in ms2), natural log-transformed values [constant 1 was added to the absolute power value (x), and a natural log transformation of their sum was then calculated as y = ln(1 + x); lnLFP, lnHFP, and lnTP in ln(ms2)], and normalized units (i.e., relative to TP; nuLFP, and nuHFP in nu). In addition to these HRV indexes, the mean of R-R intervals (MRRI in ms) and standard deviation of R-R intervals (SDRRI in ms) were calculated for the corresponding period in each posture. The calculations of normalized powers and LFP-to-HFP ratio (LFP/HFP) were included with the knowledge of the criticism against their use as autonomic indexes (see Ref. 9).
Statistical analyses. To evaluate the relationship between the magnitude of HRV and vagal effects on the heart, a within-subject linear regression analysis of recovery time on each HRV index, expressed in minutes, was calculated. Values from POST1 to POST5 were fit to a linear model, separately for supine, sitting, and standing postures. The slopes and intercepts of the linear regression model, as defined for each individual, were interpreted as describing within-subject dynamics between each HRV index and vagal effects on the heart. The coefficient of determination (R2) was interpreted as an estimate of the signal-to-noise ratio when using a particular HRV index as a measure of vagal effects on the heart.
An appropriate parametric or nonparametric test was chosen, depending on the distributional characteristics of the variable. Parametric tests were used for MRRI, SDRRI, lnLFP, lnHFP, lnTP, and RF. Nonparametric tests were used for LFP, HFP, TP, nuLFP, nuHFP, LFP/HFP, regression terms, and hormonal measures.
The paired samples t-test or Wilcoxon signed rank test was used to evaluate whether the variables were affected by vagal blockade (PRE vs. POST1) and whether they had returned to baseline at the end of recovery (PRE vs. POST5). The differences in variables from POST1 to POST5 and the effects of body posture on the variables were evaluated with the one-way repeated measures ANOVA or Friedman's test. Differences between the ES and NES were evaluated with the independent samples t-test or Mann-Whitney test. In all statistical tests, differences were considered significant when P < 0.05, and alpha-level adjustments were made to account for numerous pairwise comparisons as needed.
|
RESULTS |
|---|
|
TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSDISCLOSURESREFERENCES |
|---|
|
|
|
During the recovery from the blockade, MRRI and HRV in sitting and standing postures returned progressively toward the PRE values (see Fig. 1). However, in the sitting and standing postures, MRRI and all HRV indexes obtained at POST5 differed significantly from the corresponding PRE values (P < 0.05–0.001). At the POST5 level, lnLFP, lnHFP, and lnTP in the sitting posture were 19 (SD 14)%, 30 (SD 16)%, and 20 (SD 12)%, respectively, below the PRE values (P < 0.001). The corresponding decrements below the PRE values for lnLFP, lnHFP, and lnTP in the standing posture were 11 (SD 18)%, 39 (SD 15)%, and 13 (SD 15)%, respectively (P < 0.001).
The within-subject linear fits explained 97 (SD 1)% and 97 (SD 2)% of the variance between recovery time and MRRI in sitting and standing postures, respectively. Similar to the supine posture, linear fits also explained a high percentage of the variance between recovery time and lnLFP, lnHFP, and lnTP and a low percentage of the variance between recovery time and nuLFP, nuHFP, and LFP/HFP in sitting and standing postures (see Table 2).
Significant differences in the slopes, intercepts, and R2 values of the within-subject linear fits across all postures are shown in Table 2. A significant difference in the slopes across postures was found for MRRI (P < 0.001), lnLFP (P < 0.01), lnHFP (P < 0.01), and lnTP (P < 0.05). MRRI and lnHFP showed the highest slopes in the supine posture and the lowest slopes in the standing posture. A significant difference in the intercepts across postures was found for MRRI (P < 0.001) and all HRV indexes, except for SDRRI (P < 0.05–0.001). MRRI and lnHFP showed the greatest intercepts in the supine posture and the lowest intercepts in the standing posture. Despite its effects on the slopes and intercepts, body posture did not significantly affect the R2 values of the linear fits.
Effect of endurance-training background. Before the blockade, significant differences between the ES and NES groups were not found for MRRI in any posture, but SDRRI, lnHFP, and lnTP in the supine posture were higher for the ES group than for the NES group (P < 0.05). In the other postures, none of the HRV indexes differed significantly between the groups.
At POST1, significant differences between the ES and NES groups were not found for MRRI in any posture. Only lnLFP in the supine posture and lnHFP in the standing posture were higher for the ES group than for the NES group (P < 0.05) at POST1. Vagal blockade caused greater decreases in SDRRI and lnHFP in the supine posture for the ES group than for the NES group (P < 0.05). However, when the decreases were calculated as percentages of the PRE value, significant group effects were not found.
There were no significant differences between the ES and NES groups in the slopes, intercepts, or R2 values of the linear fits in any posture.
Respiratory frequency. At PRE, RF differed significantly across postures [0.23 (SD 0.06) Hz in supine vs. 0.18 (SD 0.05) Hz in sitting vs. 0.20 (SD 0.07) Hz in standing posture, P < 0.01]. At POST1, RF did not differ across postures. Figure 2 shows RF during the recovery period. When RF values within each posture were compared, RF changed significantly during the recovery period in supine (P < 0.05), sitting (P < 0.05), and standing postures (P < 0.05).
|
|
|
DISCUSSION |
|---|
|
TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSDISCLOSURESREFERENCES |
|---|
Relationship between MRRI and vagal effects on hearts. Our findings concerning the relationship between MRRI and vagal effects on the heart are consistent with the previous findings (4, 17, 19, 25) showing that R-R-interval length is related to the vagal nerve-firing rate in an essentially linear manner. The present results showed that within subjects, MRRI in the supine posture increased linearly with increasing recovery time [R2 = 98 (SD 2)%] and reached its PRE value at the end of the recovery period, even though vagal effects on the heart had not presumably recovered completely (3). Despite the essentially linear quantitative relationship between MRRI and vagal effects on the heart, as shown by previous studies (20) and present findings, MRRI cannot be used as a selective index of vagal effects on the heart, because both vagal and sympathetic nervous systems directly influence the R-R interval length.
Relationship between HRV and vagal effects on hearts. The present results support the previous findings (1, 2, 7, 27, 32) that the vagal nervous system strongly influences HRV, particularly lnHFP. Vagal blockade eliminated 74%, 83%, and 73% of lnLFP, lnHFP, and lnTP, respectively. The most valuable finding of the present study was the pronounced linear within-subject increase in SDRRI, lnLFP, lnHFP, and lnTP as a function of increasing vagal effects on the heart during the recovery from vagal blockade. Correspondingly, LFP, HFP, and TP (i.e., spectral powers expressed in ms2) increased in an exponential manner as a function of increasing vagal effects on the heart.
The linear fit explained 77–87% of the within-subject variance between recovery time and lnHFP, depending on the body posture. The large between-subject variability in the slopes and intercepts of the linear fits revealed that an equivalent increase in recovery time produced an unequivocal increase in lnHFP among individuals. This may reflect real between-subject differences in the quantitative relationship of lnHFP and vagal effects on the heart. Alternatively, it may simply reflect great between-subject differences in atropine metabolism (3). However, the goodness of fit of the linear model between recovery time and lnHFP was high for almost all individuals. These findings indicate that from the quantitative point of view, lnHFP can be used to monitor within-subject changes in vagal effects on the heart.
According to present knowledge, no other studies have examined the within-subject quantitative relationship between HRV indexes and vagal effects on the heart with a decreasing blocking approach, as used in the present study. Thus our results have to be compared with studies that have used different methodologies. The present findings, illustrating a highly linear relationship between recovery time and lnHFP, are in line with the results from laboratory experiments reported by Bloomfield et al. (6). They manipulated blood pressure by phenylephrine and found a monotonous increase in HRV with increasing doses of phenylephrine. In contrast, Goldberger et al. (10), who used phenylephrine and nitroprusside, reported that the relationship between HRV and vagal effects on the sinus node (defined as -blocked R-R interval) is better described by a quadratic than a linear fit. According to their findings, HRV increased as the vagal effect increased until a plateau was reached. Beyond the plateau, HRV decreased even with further increases in vagal effect. The present study differs from the study of Goldberger and colleagues (10) regarding the physiological range of manipulation. We operated within the range of vagal control that is characteristic for most real life situations, whereas Goldberger et al. (10) operated also within the upper part of the physiological range of vagal control, including extremely high levels of vagal activity. Analysis of lnHFP and R-R-interval length from ambulatory 24-h recordings has suggested that the relationship between lnHFP and vagal activity could be linear in some subjects and quadratic in others (18). However, an interpretation of vagal activity from ambulatory data without experimental blockade or control of various psychological and physiological factors is challenging because the length of R-R interval is influenced by both sympathetic and vagal effects on the sinus node.
According to the present results, not only lnHFP but also lnLFP and lnTP demonstrated pronounced linear within-subject increases as a function of increasing vagal effects on the heart during the recovery from vagal blockade. The half-life of atropine elimination is 3.7 (SD 2.3) h (3), and thus the effects of atropine on the heart were most probably present at the end of the 150-min recovery period. At the end of the recovery, lnHFP in the supine posture was still 25% below its PRE value, indicating the presence of the effects of atropine on the heart. The corresponding decrement for lnLFP was only 5%. Because lnLFP had almost returned to its PRE value during the recovery period, it is likely that some other mechanisms in addition to the vagal nervous system are involved in its regulation. These mechanisms affecting lnLFP are not fully understood. Many studies (2, 7, 26, 32) have reported the low-frequency component of HRV to be significantly reduced after vagal blockade, while being relatively unaffected by the administration of a sympathetic blocking agent. Other studies (27), in contrast, have found a reduced low-frequency component of HRV when sympathetic blocking was carried out alone or after vagal blocking to complete a state of dual blocking. These findings suggest a combined sympathovagal mediation of lnLFP. Consequently, despite the presently found highly linear quantitative within-subject relationship between lnLFP and vagal effects on the heart, lnLFP does not provide a selective index of vagal activity.
The present results do not support the use of nuLFP and nuHFP as quantitative indexes of within-subject changes in sympathetic and vagal outflow, respectively, or the use of LFP/HFP as an index of sympathovagal balance, as suggested by Pagani et al. (24). According to the present study, nuLFP, nuHFP, and LFP/HFP showed minor changes during the recovery period, and the linear fit explained only 54% to 68% of the variance between the recovery time and nuLFP, nuHFP, and LFP/HFP. This contrasts with the conclusions of Montano and colleagues (23), who reported that nuLFP, nuHFP, and LFP/HFP detect changes in sympathovagal balance with a high degree of linearity. They based their validation on measurements made at different angles of head-up tilt. However, the use of progressive head-up tilt in validating HRV indexes to measure autonomic function has been strongly criticized (9).
Effects of body posture. Various combinations of vagal and sympathetic activation are characteristic for different body postures. Cacioppo et al. (7) have suggested that vagal activity is highest and sympathetic activity is lowest in the supine posture. The reverse occurs in the standing posture, and a combination is characteristic for the sitting posture. Moreover, their findings illustrated that the vagal nervous system exerts greater neural control over the heart than the sympathetic branch in all postures. The present results regarding the impact of body posture on HRV before the blockade, as well as under full vagal blockade, were consistent with those reported by Cacioppo et al. (7).
The present study also demonstrated that although body posture altered the quantitative relationship between HRV indexes and vagal effects on the heart, the goodness of fit of the linear model between recovery time and HRV indexes did not differ across the postures. The impact of body posture was most pronounced for MRRI and lnHFP. A similar increase in recovery time induced a more pronounced increase in MRRI and lnHFP in the supine posture than in the sitting or standing posture. Moreover, the intercepts of the linear model were greatest in the supine posture and lowest in the standing posture. Thus the postural differences in MRRI and lnHFP before the blockade were substantially reduced by the vagal blockade and gradually re-established during the recovery period.
A likely explanation of these findings arises from various combinations of vagal and sympathetic activation characteristic for different postural states. Although direct influences of the sympathetic nervous system are minimal, increased sympathetic activation may have indirect influences on lnHFP. The response of the sinus node to vagus nerve stimulation has been shown to be proportional to ongoing sympathetic nerve activity in animals (20). Thus it is possible that the smaller the sympathetic influence on the heart is, the more sensitive lnHFP is to increased vagal activity. Another potential explanation for the steeper increase in lnHFP in the supine posture than in the other postures arises from variations in the respiratory gating of vagal motoneurone responsiveness to stimulatory inputs among postural states (8). During the recovery from the blockade, the vagal activity level that is sufficient for normal respiratory gating is achieved faster in the supine posture than in the sitting or standing posture. Moreover, in the standing posture, vagal activity is always below the level that is necessary for maximal respiratory gating (8).
Effect of endurance-training background. In the present study, we compared participants in the ES and NES groups to examine the effects of training background on the quantitative relationship between HRV and vagal effects on the heart. Regular endurance training designed to increase aerobic fitness is associated with a number of alterations in the function of the autonomic nervous system, including increased R-R interval (29) and HRV levels at rest (13, 30).
The present results demonstrated no significant group differences in MRRI at supine rest. Moreover, the golden standard for estimating resting vagal activity, a decrease in MRRI due to vagal blockade, did not differ between the groups. The large variability in MRRI at rest (range from 798 to 1,390 ms) in the NES group probably explains the insignificant difference in MRRI at rest. Despite the similar supine MRRI at PRE in the ES and NES groups, the corresponding values for SDRRI, lnHFP, lnLFP, and lnTP were significantly higher in the ES group than in the NES group. In light of the present findings, an equal MRRI at rest does not necessarily seem to be related to an equal level of HRV at rest.
The most valuable finding in regard to group comparisons was that both groups showed similar within-subject linear increases in MRRI, SDRRI, lnLFP, lnHFP, and lnTP as a function of recovery time. Thus training background did not alter the linear relationship between these HRV indexes and vagal effects on the heart.
Limitations.
Although the assessment of vagal influences on HRV by vagal blockade has been the golden standard among humans, the physiological and psychological side effects of the drug may influence autonomic modulation. Systematic biases may arise, for example, from interactions among sympathetic and vagal nervous systems, nonselective actions of the blocking agent, and incomplete blockade (5). Therefore, the drug and dosage applied in the present study were carefully chosen based on the literature. We used atropine, a specific muscarinic antagonist with a distribution half-life of 
1 min (3), to depress vagal outflow to the sinus node. The applied dose is generally considered to produce complete blockade (14). Thus it is unlikely that vagal blockade was incomplete.
Atropine has an elimination half-life of 3.7 (SD 2.3) h (3), which allowed us to assume that in the within-subject design, the cardiac effects of atropine decrease in a nearly linear manner over the present recovery period of 2.5 h. There is substantial variance in the pharmacokinetics of atropine among individuals, as shown by the great standard deviation of atropine half-life. Consequently, the between-subject differences in atropine metabolism could explain the great between-subject variance in the slopes and intercepts of the within-subject linear fits between recovery time and HRV indexes.
It is known that lnHFP does not accurately mirror vagal effects on the heart when changes occur in RF and/or tidal volume (5, 11). In the present study, the subjects were allowed to breath according to their spontaneous respiratory rhythm. Significant changes were observed in RF during the recovery from vagal blockade. Although the magnitude of changes in RF was small at the group level, substantial within-subject changes were observed. Thus, in some individuals, changes in RF may have decreased the signal-to-noise ratio in the regression analysis of recovery time on lnHFP. Nevertheless, almost all RF values in the present study were within 0.15–0.40 Hz, and the accuracy of lnHFP in measuring vagal effects on the heart was high, even under the setting of spontaneous respiration.
In addition to respiration, baroreflex function is also associated with the magnitude of HRV. In the present study, baroreflex function was not assessed, and, therefore, we cannot exclude the possibility that within-subject changes in baroreflex function might occur during the recovery period.
In the present study, sympathetic effects were not continuously monitored. However, plasma epinephrine and norepinephrine concentrations were measured before the blockade, after full vagal blockade, and at the end of the recovery period. Although plasma epinephrine concentrations showed significant differences across the three conditions, the paired contrast between POST1 and POST5 was not significant. In contrast, corresponding comparisons for plasma norepinephrine concentration showed a small but significant increase from POST1 to POST5. The change in sympathetic effect on the heart during the recovery period may have altered the relationship between MRRI and recovery time. However, it is unlikely that such a small change in sympathetic activity had any effects on the relationship between HRV and recovery time.
In summary and in conclusion, HRV of subjects in the supine, sitting, and standing postures was measured before blockade, under complete vagal blockade, and during recovery from the blockade. The results showed that all HRV, particularly HFP, is predominantly under vagal control. The present results further showed that the within-subject SDRRI, lnLFP, lnHFP, and lnTP increased in an essentially linear manner with decreasing vagal blockade in every body posture and in persons with different endurance-training backgrounds. These findings indicate that from a quantitative point of view, lnHFP can be used to monitor within-subject changes in vagal effects on the heart. On the contrary, nuHFP is not a valid quantitative measure of vagal effects on the heart. In future studies, changes in sympathetic activity and respiratory pattern should be taken into account to improve the accuracy of HRV indexes as measures of vagal activity.
|
GRANTS |
|---|
|
TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSDISCLOSURESREFERENCES |
|---|
|
DISCLOSURES |
|---|
|
TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSDISCLOSURESREFERENCES |
|---|
|
ACKNOWLEDGMENTS |
|---|
|
FOOTNOTES |
|---|
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.
|
REFERENCES |
|---|
|
TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSDISCLOSURESREFERENCES |
|---|
This article has been cited by other articles:
|
|
 |
|
  M. Buchheit, H. Al Haddad, P. B. Laursen, and S. Ahmaidi Effect of body posture on postexercise parasympathetic reactivation in men Exp Physiol, July 1, 2009; 94(7): 795 - 804. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |
