Non‐parametric deconvolution provides an objective assessment of GH responsiveness to GH‐releasing stimuli in normal subjects
Authors: Sartorio Alessandro , De Nicolao Giuseppe , Pizzini Giacomo , Liberati Diego 
Published: November 2003

OBJECTIVE Deconvolution analysis has been proposed as an effective method for analysing the physiology of GH secretion. In the literature, it has been applied to spontaneous secretion data characterized by long and uniform sampling paradigms. In the present study we investigated the applicability of non‐parametric deconvolution to the analysis of response‐to‐stimuli (RTS) data characterized by infrequent and non‐uniform sampling.PATIENTS Thirty‐six healthy adult male volunteers (age range 24–37 years) were randomly subdivided into two groups (group I, n=30; group II, n=6).DESIGN Subjects of group I were tested with a single 1 μg/kg body weight GH‐releasing hormone (GHRH) bolus, administered at 0 minutes. Subjects of group II were tested, in random order, with a 4‐ or 5‐day interval, with (1) two consecutive 1 μg/kg body weight GHRH boluses at 0 and 120 minutes and (2) two consecutive 1 μg/kg body weight hexarelin boluses, administered at 0 and 120 minutes.MEASUREMENTS GH levels were determined at 0, 15, 30, 45, 60, 90 and 120 minutes (group I) and −30, 0, 15, 30, 45, 60, 120, 135, 150, 165, 180 and 240 minutes (group II). A numerically efficient regularization‐based non‐parametric deconvolution algorithm incorporating non‐negativity constraints was used to estimate the time profile of the instantaneous secretion rate (ISR). Confidence limits allowing for both measurement error and kinetic model uncertainty were computed using a Monte‐Carlo procedure. In order to validate the deconvolution method, a simulated benchmark problem was set up.RESULTS The analysis of the benchmark problem showed that the proposed method is capable of providing an accurate reconstruction of the ISR (as measured by the root mean square (RMS) error). Moreover, it appeared that reliable confidence limits cannot be obtained unless the kinetic model uncertainty is taken into account. The analysis of the data showed a clear rise in the ISR subsequent to the first bolus (either GHRH or hexarelin), with most of the response occurring within 60 minutes of the stimulus. In group I, it was also seen that discarding the samples collected at times 90 and 120 minutes only marginally affected the estimate of the cumulated ISR over 0–60 minutes (the variation was always less than 3%). The analysis of GH responsiveness to repeated stimuli (group II) showed that the amount of hormone secreted after the second bolus was clearly reduced in comparison with that elicited by the first stimulus, most of the response occurring within 60 minutes of the injection. The amount of GH secreted after the second stimulus ranged from 13 to 36% (GHRH 17–36%; hexarelin 13–36%) of the overall amount of hormone secreted after time 0 minutes.CONCLUSIONS Even with relatively few samples, non‐ parametric deconvolution of response‐to‐stimulus data is capable of providing a reliable, smooth and non‐negative estimate of the GH instantaneous secretion rate that offers a realistic representation of the GH secretory dynamics. The non‐parametric approach compares favourably with respect to discrete deconvolution methods, that yield discontinuous instantaneous secretion rates profiles, and parametric methods that would require more stringent assumptions on the shape of the instantaneous secretion rate. When assessing confidence limits it is essential to take into account both measurement error and kinetic model uncertainty. Using deconvolution in normal subjects, the estimated instantaneous secretion rate between 0 and 60 minutes is scarcely affected by samples taken after time 60 minutes. Since most of the secretory response takes place during this time interval, there is motivation for investigating the use of shorter sampling protocols in conjunction with deconvolution analysis. Although pulse detection and the assessment of the shape of spontaneous pulses have not been investigated, it could be interesting to apply non‐parametric deconvolution to spontaneous secretion data as well.