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Original Studies |
Department of Endocrinology (F.R), Leiden University Medical Center, Leiden 2333AA, The Netherlands; Guilford, Connecticut (S.M.P.); Department of Medicine, National Science Foundation Center for Biological Timing, University of Virginia Health Sciences Center (J.D.V.), Charlottesville, Virginia 22908
Address correspondence and requests for reprints to: Dr. F. Roelfsema, Department of Endocrinology, Leiden University Medical Center, Albinusdreef 2, 2333AA, Leiden, The Netherlands. E-mail: roelfsema{at}rullf2.MedFac.LeidenUniv.nl
| Abstract |
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| Introduction |
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A recently introduced measure of asynchrony or conditional irregularity, cross-ApEn (8) affords such a statistical capability applied to a pair of (hormone) signals. The usefulness of cross-ApEn for evaluating coupled endocrine systems was recently demonstrated in an analysis of LH-testosterone (T) synchrony in cohorts of younger vs. older males (9). In particular, the older males exhibited markedly more jointly asynchronous LH-T dynamics than did the younger group, leading us to hypothesize that, analogous to one-dimensional signal analysis, regularity and synchronicity generally correspond more to (normal) physiology, whereas greater irregularity (apparent process randomness) and increased (two-variable) asynchronicity correspond to pathophysiology, aging, and other variants of network disruption. Below, we investigate the emerging hypothesis that ACTH-cortisol bihormonal secretory dynamics are more asynchronous in Cushings disease than in controls. Validating this theme would both offer further evidence of this broadly-stated paradigm and provide some initial insights into explicit network manifestations of secretory tumors beyond the vivid one-variable increases in irregularity seen for ACTH and cortisol, individually (4).
| Patients and Methods |
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Fourteen female and six male patients (mean age 37 yr, range 1774 yr) were studied. In all patients the diagnosis of Cushings disease was established by elevated 24-h urinary excretion of free cortisol, subnormal or absent overnight suppression of plasma cortisol by 1 mg oral dexamethasone, absent or subnormal suppression of urinary cortisol excretion during an oral 2-day dexamethasone test (low-dose Liddle test), suppression of plasma cortisol concentration by 190 nmol/L or more during a 7-h iv infusion with dexamethasone at a dose of 1 mg/h (10), positive immunostaining for ACTH of the pituitary adenoma, and clinical cortisol dependency for several months after selective removal of the adenoma. Four patients had undergone previous transsphenoidal surgery. Two other patients had been treated many years earlier by unilateral adrenalectomy and pituitary radiation, which was the standard therapy for Cushings disease in our institute before the application of transsphenoidal surgery in the early 1970s. All these six subjects had clinical and biochemical relapse during follow-up studies.
The patients were hospitalized the evening before the sampling studies. On the following morning, an indwelling iv cannula was inserted in a large vein of the forearm, and blood samples were withdrawn at 10-min intervals starting at 0900 h and for the next 24 h. A slow iv infusion of 0.9% NaCl and heparin (1 U/mL) was used to keep the line open. The subjects were free to move around, but not to sleep during daytime. Meals were served at 0800, 1230, and 1730 h. Lights were turned off between 22002400 h, depending on the sleeping habits of the patient. As controls, 12 healthy male and 17 healthy female volunteers underwent the same plasma sampling study. Their mean age was 42 yr, range 3063 yr (NS vs. patients).
Plasma samples for ACTH were collected on ice in chilled ethylenediamine tetraacetate-containing siliconized glass tubes, and samples for cortisol were collected in heparinized tubes. The samples were centrifuged at 4 C, and within 30 min the plasma was separated, frozen, and stored at -20 C until the assay was performed. All samples from any subject were run in duplicate in the same assay (see below).
Informed consent was obtained from all subjects and patients, and the study was approved by the ethical committee of the Leiden University Hospital.
Assays
Plasma ACTH concentrations were measured in duplicate by
immunoradiometric assay, using reagents obtained from the Nichols
Institute (San Juan Capristrano, CA). In our hands the detection limit
of this assay was 3.0 ng/L. The intra- and interassay precision varied
from 2.87.5%. The cross-reactivity of this assay with
MSH, LH,
FSH, TSH, GH, and PRL was less than 0.1%. Plasma cortisol
concentrations were measured by RIA (Sorin Biomedica, Milan, Italy).
The detection limit of this assay was 25 nmol/L. The intra- and
interassay precision varied from 24%.
Cross-approximate entropy (cross-ApEn)
To quantify asynchrony (conditional irregularity), we use cross-ApEn, as introduced in ref 8, definition 5. As noted there, cross-ApEn can be employed to compare sequences from two distinct yet intertwined variables in a network, herein applied to the joint ACTH-cortisol time-series. Larger cross-ApEn values indicate greater joint signal asynchrony. The precise mathematical definition is thematically similar to that for ApEn:
Let u = (u(1), u(2), ... . u(N)) and v =
(v(1), v(2), ... . v(N)) be two N-length sequences.
Fix input parameters m and r. Form vector
sequences x(I) = (u(I), u(I+1),... . u(I+m-1)) and
y(j) = (v(j), v(j+1),... . v(j+m-1)) from u
and v, respectively. For each I
N-m+1, set
Ci m(r)(v u) = (number of
j
N-m+1 such that d[x(I),
y(j)]
r)/(N-m+1), where d[x(I),
y(j)] = maxk = 1,2... . .
m( u(I+k-1)-v(j+k-1) ), i.e. the maximum
difference in their respective scalar components. The
Ci m(r)s measure within a
tolerance r the regularity, or frequency, of (v-) patterns
similar to a given (u-) pattern of window length m. Then
define
m(r)(v u) as the average
value of ln
m(r)(v u), and
finally define cross-ApEn (m, r, N)(v u) =
m(r)(v u)-
m+1(r)(v u).
For this study, we applied cross-ApEn with m = 1, and r = 0.2
to standardized ACTH ( = u) and cortisol ( = v)
time-series data, i.e. for each subject we applied
cross-ApEn to the
{u*(I),v*(j)}series,
where u*(I) = (u(I)-mean
u)/SD u and
v*(j) = (v(j)-mean
v)/SD v. This standardization, in
conjunction with the choices of m and r, ensures appropriate
replicability properties for cross-ApEn for the data lengths studied
(1, 2, 3, 8).
Deconvolution analysis
Multiple parameter deconvolution was used to estimate various specific measures of hormone secretion and half-life from all plasma hormone concentrations and their dose-dependent intrasample variances considered simultaneously (11). In normal subjects basal secretion constituted only a small part of the 24-h cortisol and ACTH production. In most patients, however, basal release forms a substantial part of total production. The latter is the sum of basal production and pulsatile production, which were estimated as described (12, 13). For the present study only the total production rates are reported. Detailed data on the deconvolution parameters of ACTH and cortisol secretion in Cushings disease were published recently (14). Here, we relate these data to cross-ApEn calculations.
Statistical analysis
Data are given as the mean ± SEM, unless otherwise mentioned. Statistical comparison of data in patients and controls (or male vs. female) was performed with the two-tailed Students t-test for unpaired data. Linear regression analysis and ANOVA were applied where appropriate, and cross-correlation analysis both on raw data and after prewhitening of the data series. Significant parametric differences were corroborated by non-parametric tests (Mann-Whitney U test, Wilcoxon signed rank test). Calculations were made with SPSS Windows version 7.0 and with Systat (SPSS Inc., Chicago, ILL). P < 0.05 was considered significant.
| Results |
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We then explored whether ApEn or cross-ApEn exhibits diurnal variation in patients and controls. To this end the 24-h period was divided into three equal parts of eight hours, starting at 0900 h in the morning. ApEn(1, 20%) for ACTH in patients was 1.085 ± 0.036, 1.124 ± 0.038 and, 1.087 ± 0.027 in the respective 8-h blocks (ANOVA P = 0.264), and the respective means for the controls were 0.937 ± 0.054, 0.948 ± 0.041, and 0.826 ± 0.031 (ANOVA P = 0.076). ApEn(1, 20%) for cortisol in patients was 1.083 ± 0.037, 1.173 ± 0.035, and 1.168 ± 0.032 (ANOVA P = 0.016), and for controls 0.923 ± 0.036, 0.897 ± 0.033 and 0.821 ± 0.035(ANOVA P = 0.135). The ANOVAs for the mean concentrations of cortisol and ACTH during the 8-h blocks were statistically insignificant for the patients (P = 0.171 and 0.948, respectively) and highly significant for controls (P < 0.0005, individual data not given).
There was an overall significant difference of cross-ApEn between
patients and controls (P < 0.005). Gender had no
statistical influence on the results. In controls, the ANOVA was
significant (P = 0.036), manifesting a clear decrease
in cross-ApEn during the third period, i.e. during the night
and early morning, from 1.224 ± 0.059 and 1.262 ± 0.051 in
the first two 8-h blocks to 1.086 ± 0.036. In patients, we also
found a significant diurnal variation (P = 0.002),
showing lower cross-ApEn values during the first part of the period,
i.e. daytime. The values determined were 1.361 ±
0.048, 1.485 ± 0.054, and 1.505 ± 0.034, respectively. This
diversity of cross-ApEn is clearly demonstrated in Fig 3
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| Discussion |
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An independent technique for investigating the coupling between ACTH and cortisol pulses was the application of copulsatility analysis (15). Although we found for both patients and controls a highly significant coincidence of pulses within the biologically relevant time window, the coupling tightness was much higher in controls than in patients, adding independent evidence for the asynchrony of the pituitary-adrenal axis in Cushings disease. At this point we want to stress that copulsatility does not bear on subordinate dynamics, in contrast to both ApEn and cross-ApEn, which algorithmically do so by comparisons over all pieces of time series, and not only peaks or nadirs. Thus, if primary ACTH pulses remained "answered" by an adrenal cortisol pulse, with the latters subordinate features altered, cross-ApEn would detect this, while the copulsatility analysis would not, even apart from considerations as to the quality of the copulsatility algorithm and its statistical implementation.
The utility of cross-ApEn is also evidenced when the analyses are compared with those of the cross-correlation function (CCF) of the ACTH and cortisol time sequences. As noted above, there is a large control-patient CCF value subgroup overlap, upon standard removal of (spurious) autocorrelations prior to the CCF analyses. As discussed in ref. 9, this observation is not surprising because, as indicated there, the autocorrelation function and CCF are typically most effective in linear systems, e.g. ARMA models, oftentimes less so for other classes of models. Nonetheless, the present results reinforce the complementarity and nonredundancy of cross-ApEn, copulsatility, and CCF, as techniques to potentially detect changes in bivariate data behavior.
In our normal subjects, we found an age-related increase of cross-ApEn pointing to a decrease in the synchrony of ACTH and cortisol release with advancing age. A similar finding has been reported for the LH-testosterone system in healthy males and was attributed to a decreased feedback signal strength or to diminished GnRH-LH-testosterone system responsiveness to feedforward and feedback signal control (9). However, there is a primary mechanistic difference between the results of the present analyses and those of the LH-T study. Specifically, in that study, each of LH and T exhibited a significant increase in serial irregularity with increasing age, in addition to the joint signal change in asynchrony. In contrast, within the control group of the present study, there was an insignificant correlation between age and ApEn of cortisol (r = 0.207, P = 0.450) and a borderline correlation between age and ApEn of ACTH (r = 0.409, P = 0.046). This suggests the new inference that aging affects network or ensemble aspects of the ACTH-cortisol system, i.e. conduits, links, and/or global control mechanisms, more so than it does individual glandular secretory activity. Further studies will be necessary to pinpoint the precise physiologic changes that elicit the presently seen statistical contrasts.
Interestingly, we also found a clear, nonsex-dependent diurnal variation of cross-ApEn, with the lowest values (highest synchrony) during the night period, i.e. when the ACTH-cortisol system comes to its maximal activity during sleep. At this portion of the 24-h cycle, the normal system shows tight coupling in contrast with the Cushings disease patients. The physiological pathways by which this coupling is accomplished are not clear at this time, as the nodal components of the regulatory system did not exhibit evident diurnal properties. The observation as to the diurnal variation in cross-ApEn is only valid if the application of 48 data points for the calculation of cross-ApEn is justified and when the circulating hormone concentrations are well above the detection limit in the 3 time segments. Monte Carlo simulation experiments show only slight degradation of the typical theoretical limits of (cross-)ApEn replicability for 48 data points (1, 2, 3, 8). The application of 48 data points to determine diurnal changes is therefore justified, and if anything, the uncertainty in the application of 8-h blocks would tend to diminish differences. Furthermore, in all 3 time segments, both for patients and controls, ACTH and cortisol concentrations were detectable well above the detection limits of the assays, so that assay noise could not have influenced the calculation of ApEn and cross-ApEn.
Finally, although we have shown increased cross-ApEn of ACTH-cortisol secretion in Cushings disease, it is not proven at this point whether the increased cross-ApEn is caused by Cushings disease or by the increased ACTH-cortisol secretion. Additional studies in other states of hypercortisolism, such as untreated congenital adrenal hyperplasia, and the cortisol resistance syndrome will ultimately be required to provide an answer to this question. Nonetheless, the present study further shows that cross-ApEn values can be dissociated from secretion levels per se, as increased cross-ApEn is found with advancing age without increased secretion and with no relation existed between cortisol and ACTH secretion rates and cross-ApEn values in Cushings disease.
Received April 11, 1997.
Revised July 30, 1997.
Revised October 7, 1997.
Accepted October 22, 1997.
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