Person:

Brown, Emery

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 R2 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.

Time series are an important data class that includes recordings ranging from radio emissions, seismic activity, global positioning data, and stock prices to EEG measurements, vital signs, and voice recordings. Rapid growth in sensor and recording technologies is increasing the production of time series data and the importance of rapid, accurate analyses. Time series data are commonly analyzed using time-varying spectral methods to characterize their nonstationary and often oscillatory structure. Current methods provide local estimates of data features. However, they do not offer a statistical inference framework that applies to the entire time series. The important advances that we report are state-space multitaper (SS-MT) methods, which provide a statistical inference framework for time-varying spectral analysis of nonstationary time series. We model nonstationary time series as a sequence of second-order stationary Gaussian processes defined on nonoverlapping intervals. We use a frequency-domain random-walk model to relate the spectral representations of the Gaussian processes across intervals. The SS-MT algorithm efficiently computes spectral updates using parallel 1D complex Kalman filters. An expectation–maximization algorithm computes static and dynamic model parameter estimates. We test the framework in time-varying spectral analyses of simulated time series and EEG recordings from patients receiving general anesthesia. Relative to standard multitaper (MT), SS-MT gave enhanced spectral resolution and noise reduction (>10 dB) and allowed statistical comparisons of spectral properties among arbitrary time series segments. SS-MT also extracts time-domain estimates of signal components. The SS-MT paradigm is a broadly applicable, empirical Bayes’ framework for statistical inference that can help ensure accurate, reproducible findings from nonstationary time series analyses.