Deconvolution of Serum Cortisol Levels by Using Compressed Sensing

Abstract

The pulsatile release of cortisol from the adrenal glands is controlled by a hierarchical system that involves corticotropin releasing hormone (CRH) from the hypothalamus, adrenocorticotropin hormone (ACTH) from the pituitary, and cortisol from the adrenal glands. Determining the number, timing, and amplitude of the cortisol secretory events and recovering the infusion and clearance rates from serial measurements of serum cortisol levels is a challenging problem. Despite many years of work on this problem, a complete satisfactory solution has been elusive. We formulate this question as a non-convex optimization problem, and solve it using a coordinate descent algorithm that has a principled combination of (i) compressed sensing for recovering the amplitude and timing of the secretory events, and (ii) generalized cross validation for choosing the regularization parameter. Using only the observed serum cortisol levels, we model cortisol secretion from the adrenal glands using a second-order linear differential equation with pulsatile inputs that represent cortisol pulses released in response to pulses of ACTH. Using our algorithm and the assumption that the number of pulses is between 15 to 22 pulses over 24 hours, we successfully deconvolve both simulated datasets and actual 24-hr serum cortisol datasets sampled every 10 minutes from 10 healthy women. Assuming a one-minute resolution for the secretory events, we obtain physiologically plausible timings and amplitudes of each cortisol secretory event with R 2 above 0.92. Identification of the amplitude and timing of pulsatile hormone release allows (i) quantifying of normal and abnormal secretion patterns towards the goal of understanding pathological neuroendocrine states, and (ii) potentially designing optimal approaches for treating hormonal disorders.

Quantifying Pituitary-Adrenal Dynamics and Deconvolution of Concurrent Cortisol and Adrenocorticotropic Hormone Data by Compressed Sensing

“…The participants were recruited via advertisements in local newspapers to serve as healthy controls for a study on women with fibromyalgia; participants with abnormal laboratory test results or current medical problems were excluded [5], [16]. None of the participants had received glucocorticoids or estrogen/progesterone within the year or 4 months before the study, respectively [5], [16]. Clinical characteristics of the participants are given in Table I.…”

“…For 3 consecutive nights, at the General Clinical Research Center of the Brigham and Women's Hospital, participants had 8 hours of scheduled sleep in the dark at their habitual sleep-wake times and three meals and two snacks; on day 4, all participants started a constant routine protocol that was designed to minimize the effects of stress, posture changes, eating, and ambulatory temperature on the participants [5], [16]. Blood drawing for hormones analyzed in this study was performed during the third night of sleep and during the first 16 hours of the constant routine [5], [16]. Therefore, this dataset can be used to quantify ACTH and cortisol variations as a function of the circadian and the ultradian patterns.…”

“…The sparsity is determined by λ (the sparsity of u increases with λ), and λ balances between sparsity and the residual error. We use an extension of the FOCUSS algorithm called GCV-FOCUSS+ [5]. The GCV-FOCUSS+ algorithm is based on FOCUSS+ [20] that solves for nonnegative u such that u has a certain maximum sparsity n (i.e., n = 22 for the HPA axis), and uses the generalized cross-validation (GCV) technique [9] for estimating the regularization parameter.…”

“…It is possible to obtain a good initial estimate for the timing of the pulses that result in cortisol secretion by first deconvolving the cortisol data using the model and the algorithm in [5]. This algorithm detects the significant pulses that result in cortisol release.…”

“…only cortisol) and are mostly based on pulse detection algorithms [25] or assume that the timing of the secretory events belong to a certain class of stochastic processes [14]. We recently showed that hormone secretory events can be recovered using compressed sensing [5]. Compressed sensing allows for reconstruction of sparse signals (i.e., signals in which only a small number of coefficients are large and most coefficients are zero or close to zero) using fewer measurements than required by the Shannon/Nyquist sampling theorem [1].…”