Steven M. Pincus

Aging and the complexity of cardiovascular dynamics.

Biomedical signals often vary in a complex and irregular manner. Analysis of variability in such signals generally does not address directly their complexity, and so may miss potentially useful information. We analyze the complexity of heart rate and beat-to-beat blood pressure using two methods motivated by nonlinear dynamics (chaos theory). A comparison of a group of healthy elderly subjects with healthy young adults indicates that the complexity of cardiovascular dynamics is reduced with aging. This suggests that complexity of variability may be a useful physiological marker.

Assessing Serial Irregularity and Its Implications for Health

Abstract: Approximate entropy (ApEn) is a recently formulated family of parameters and statistics quantifying regularity (orderliness) in serial data, with developments within theoretical mathematics as well as numerous applications to multiple biological contexts. We discuss the motivation for ApEn development, from the study of inappropriate application of dynamical systems (complexity) algorithms to general time‐series settings. ApEn is scale invariant and model independent, evaluates both dominant and subordinant patterns in data, and discriminates series for which clear feature recognition is difficult. ApEn is applicable to systems with at least 50 data points and to broad classes of models: it can be applied to discriminate both general classes of correlated stochastic processes, as well as noisy deterministic systems. Moreover, ApEn is complementary to spectral and autocorrelation analyses, providing effective discriminatory capability in instances in which the aforementioned measures exhibit minimal distinctions. Representative ApEn applications to human aging studies, based on both heart rate and endocrinologic (hormonal secretory) time series, are featured. Heart rate (HR) studies include gender‐ and age‐related changes in HR dynamics in older subjects, and analyses of “near‐SIDS” infants. Endocrinologic applications establish clear quantitative changes in joint LH‐testosterone secretory dynamics in older versus younger men (a “partial male menopause”), via cross‐ApEn, a related two‐variable asynchrony formulation; a disruption in LH‐FSH‐NPT (penile tumescence) synchrony in older subjects; and changes in LH‐FSH secretory dynamics across menopause. The capability of ApEn to assess relatively subtle disruptions, typically found earlier in the history of a subject than mean and variance changes, holds the potential for enhanced preventative and earlier interventionist strategies.

Motivations and Methods for Analyzing Pulsatile Hormone Secretion

Endocrine glands communicate with remote target cells via a mixture of continuous and intermittent signal exchange. Continuous signaling allows slowly varying control, whereas intermittency permits large rapid adjustments. The control systems that mediate such homeostatic corrections operate in a species-, gender-, age-, and context-selective fashion. Significant progress has been made in understanding mechanisms of adaptive interglandular signaling in vivo. Principal goals are to understand the physiological origins, significance, and mechanisms of pulsatile hormone secretion. Key analytical issues are: 1) to quantify the number, size, shape, and uniformity of pulses, nonpulsatile (basal) secretion, and elimination kinetics; 2) to evaluate regulation of the axis as a whole; and 3) to reconstruct dose-response interactions without disrupting hormone connections. This review will focus on the motivations driving and the methodologies used for such analyses.

Effects of age on the irregularity of LH and FSH serum concentrations in women and men

We evaluated an apparent distinction between follicle-stimulating hormone (FSH) and luteinizing hormone (LH) dynamics: visually, it appears that the pattern of serum concentrations of FSH is more irregular than that of LH in younger human females. We studied healthy humans, with LH and FSH serum samples obtained every 10 min for 24 h. Three groups were studied: 24 young females [8 early follicular (EFol), 8 late follicular (LFol), and 8 midluteal (MLut)]; 8 postmenopausal females; and 17 males 21-79 yr of age. To quantify serial irregularity, we utilized approximate entropy (ApEn), a scale- and model-independent statistic. For young females, FSH was consistently more irregular than LH per subject: among the younger subjects, ApEn(FSH) - ApEn(LH) = 0.342 +/- 0.270; ApEn(FSH) > ApEn(LH), P < 0.00001; ApEn(FSH) > ApEn(LH) for 23 of 24 subjects. For each cycle stage, pairwise ApEn(FSH) > ApEn(LH): P < 0.005 for both LFol and MLut, P < 0.01 for EFol. Notably, for the postmenopausal women, the irregularity difference vanished:ApEn(FSH) - ApEn(LH) = 0.008 +/- 0.205. Males exhibited qualitatively similar results: ApEn(FSH)- ApEn(LH) was significantly and negatively correlated with age (r = -0.75, P = 0.0006). The capability to quantify (the extent of) differences between FSH and LH release, beyond the general 1:1 correspondence between primary LH and FSH pulses, suggests a means to assess bihormonal changes as a clinical marker of altered reproductive status in a variety of settings, e.g., a perimenopausal milieu. Mechanistically, the erosion of unequal FSH-LH regularity with age is consistent with a loss of synchrony control within the integrated hypothalamo-pituitary-gonadal axis.

Characteristics of luteinizing hormone secretion in younger versus older premenopausal women

OBJECTIVES The objectives of this study were to document specific attributes of pulsatile luteinizing hormone secretion in middle-aged women before discernible alterations in their menstrual cycles and to compare the results to corresponding data obtained in younger women. STUDY DESIGN After documenting normal cycle length, biphasic basal body temperatures, and normal midluteal progesterone in younger and middle-aged women during an initial cycle, daily blood samples and samples withdrawn at 10-minute intervals for 8 hours during the midfollicular phase were obtained during a subsequent cycle. RESULTS Assessment of luteinizing hormone pulses with the pulse detection algorithm Cluster demonstrated a prolonged interpulse interval and increased pulse width in the older women. Assessment of luteinizing hormone secretory bursts and half-life with the deconvolution analysis procedure demonstrated a prolonged interburst interval and half-life in the older women. Appraisal of approximate entropy revealed greater orderliness of luteinizing hormone release in the older women. CONCLUSIONS Middle-aged women exhibit alterations in hypothalamic-pituitary function that may account in part for age-related changes in reproductive potential.

Preliminary evidence for the evolution in complexity of heart rate dynamics during autonomic maturation in neonatal swine

Previous studies suggest that the autonomic nervous system plays an important role in the generation of complex heart rate dynamics. Therefore, we hypothesized that the complexity (irregularity) of cardiac interbeat intervals would evolve with the maturation of autonomic innervation to the heart. Twelve healthy newborn piglets were implanted with ECG transmitters and studied at one or more different ages up to 33 days of age, the period during which pigs develop functional sympathetic innervation of the heart from the stellate ganglia. Three animals underwent right stellate ganglionectomy, two a left stellate ganglionectomy, two a right cardiac vagotomy and five a sham procedure. The statistic, approximate entropy (ApEn), was used to quantify the regularity of interbeat interval fluctuations. Sham-operated animals showed an increase in the standard deviation (SD) and irregularity (ApEn) of cardiac interval fluctuations with increasing age. Right stellate ganglionectomized piglets had lower interbeat interval ApEn values, but similar SDs by 26-27 days of age compared to sham-operated animals. Left stellate ganglionectomy, which affects cardiac inotropy rather than chronotropy, had no effect on cardiac interval irregularity, while vagotomy had an indeterminant effect. The increasing irregularity of interbeat interval dynamics during autonomic maturation and the apparent attenuation of heartbeat irregularity when right stellate ganglion innervation is interrupted, provides empirical support for the notion that complex heartbeat dynamics in the mature animal are the result of a network of autonomic neural pathways that enables an organism to adapt to stress.

Modelling the nonlinear time dynamics of multidimensional hormonal systems

In most hormonal systems (as well as many physiological systems more generally), the chemical signals from the brain, which drive much of the dynamics, can not be observed in humans. By the time the molecules reach peripheral blood, they have been so diluted so as to not be assayable. It is not possible to invasively (surgically) measure these agents in the brain. This creates a difficult situation in terms of assessing whether or not the dynamics may have changed due to disease or aging. Moreover, most biological feedforward and feedback interactions occur after time delays, and the time delays need to be properly estimated. We address the following two questions: (1) Is it possible to devise a combination of clinical experiments by which, via exogenous inputs, the hormonal system can be perturbed to new steady-states in such a way that information about the unobserved components can be ascertained; and, (2) Can one devise methods to estimate (possibly, time-varying) time delays between components of a multidimensional nonlinear time series, which are more robust than traditional methods? We present methods for both questions, using the Stress (ACTH-cortisol) hormonal system as a prototype, but the approach is more broadly applicable.

Pituitary apoplexy in acromegaly, a long-term follow-up study in two patients

Pituitary apoplexy is a serious complication in about 3% of patients with a pituitary adenoma. Very often, the diagnosis of a functioning or non-functioning adenoma is made in retrospect. In this report, we describe two patients in whom the diagnosis of acromegaly was made before the apoplexy. In one patient, surgical intervention was necessary because of remaining clinical and biochemical activity; in the other patient conservative follow-up was pursued. Seven and nine years after apoplexy, respectively, the patients were clinically and biochemically in remission. During the follow-up, three and five years after apoplexy, respectively, the patients underwent a 10-min venous sampling procedure for 24 hours, and the GH secretory profile was investigated with multiparameter deconvolution analysis and by approximate entropy (ApEn), a scale- and model-independent regularity measure. The deconvolution analysis revealed an increased basal (nonpulsatile) GH secretion rate, while the total 24 h secretion rate was normal compared with 13 healthy male control subjects. ApEn was much larger for each patient than for any control subject value, indicating markedly more irregular GH secretion. We hypothesize that these subtle abnormalities are caused by non-specific damage as a result of the vascular insult, leading to abnormal vascular supply, or abnormal autocrine and paracrine GH regulation within the remaining gland.