A stochastic differential equation model of diurnal cortisol patterns

Tracking inflammation status for improving patient prognosis: A review of current methods, unmet clinical needs and opportunities

Inflammation is the body's response to infection, trauma or injury and is activated in a coordinated fashion to ensure the restoration of tissue homeostasis and healthy physiology. This process requires communication between stromal cells resident to the tissue compartment and infiltrating immune cells which is dysregulated in disease. Clinical innovations in patient diagnosis and stratification include measures of inflammatory activation that support the assessment of patient prognosis and response to therapy. We propose that (i) the recent advances in fast, dynamic monitoring of inflammatory markers (e.g., cytokines) and (ii) data-dependent theoretical and computational modeling of inflammatory marker dynamics will enable the quantification of the inflammatory response, identification of optimal, disease-specific biomarkers and the design of personalized interventions to improve patient outcomes - multidisciplinary efforts in which biomedical engineers may potentially contribute. To illustrate these ideas, we describe the actions of cytokines, acute phase proteins and hormones in the inflammatory response and discuss their role in local wounds, COVID-19, cancer, autoimmune diseases, neurodegenerative diseases and aging, with a central focus on cardiac surgery. We also discuss the challenges and opportunities involved in tracking and modulating inflammation in clinical settings.

Sparse System Identification of Leptin Dynamics in Women With Obesity

The prevalence of obesity is increasing around the world at an alarming rate. The interplay of the hormone leptin with the hypothalamus-pituitary-adrenal axis plays an important role in regulating energy balance, thereby contributing to obesity. This study presents a mathematical model, which describes hormonal behavior leading to an energy abnormal equilibrium that contributes to obesity. To this end, we analyze the behavior of two neuroendocrine hormones, leptin and cortisol, in a cohort of women with obesity, with simplified minimal state-space modeling. Using a system theoretic approach, coordinate descent method, and sparse recovery, we deconvolved the serum leptin-cortisol levels. Accordingly, we estimate the secretion patterns, timings, amplitudes, number of underlying pulses, infusion, and clearance rates of hormones in eighteen premenopausal women with obesity. Our results show that minimal state-space model was able to successfully capture the leptin and cortisol sparse dynamics with the multiple correlation coefficients greater than 0.83 and 0.87, respectively. Furthermore, the Granger causality test demonstrated a negative prospective predictive relationship between leptin and cortisol, 14 of 18 women. These results indicate that increases in cortisol are prospectively associated with reductions in leptin and vice versa, suggesting a bidirectional negative inhibitory relationship. As dysregulation of leptin may result in an abnormality in satiety and thereby associated to obesity, the investigation of leptin-cortisol sparse dynamics may offer a better diagnostic methodology to improve better treatments plans for individuals with obesity.

Closed-Loop Fuzzy Energy Regulation in Patients With Hypercortisolism via Inhibitory and Excitatory Intermittent Actuation

Hypercortisolism or Cushing's disease, which corresponds to the excessive levels of cortisol hormone, is associated with tiredness and fatigue during the day and disturbed sleep at night. Our goal is to employ a wearable brain machine interface architecture to regulate one's energy levels in hypercortisolism. In the present simulation study, we generate multi-day cortisol profile data for ten subjects both in healthy and disease conditions. To relate an internal hidden cognitive energy state to one's cortisol secretion patterns, we employ a state-space model. Particularly, we consider circadian upper and lower bound envelopes on cortisol levels, and timings of hypothalamic pulsatile activity underlying cortisol secretions as continuous and binary observations, respectively. To estimate the hidden cognitive energy-related state, we use Bayesian filtering. In our proposed architecture, we infer one's cognitive energy-related state using wearable devices rather than monitoring the brain activity directly and close the loop utilizing fuzzy control. To model actuation in the real-time closed-loop architecture, we simulate two types of medications that result in increasing and decreasing the energy levels in the body. Finally, we close the loop using a knowledge-based control approach. The results on ten simulated profiles verify how the proposed architecture is able to track the energy state and regulate it using hypothetical medications. In a simulation study based on experimental data, we illustrate the feasibility of designing a wearable brain machine interface architecture for energy regulation in hypercortisolism. This simulation study is a first step toward the ultimate goal of managing hypercortisolism in real-world situations.

Characterization of Cortisol Dysregulation in Fibromyalgia and Chronic Fatigue Syndromes: A State-Space Approach

OBJECTIVE

Fibromyalgia syndrome (FMS) and chronic fatigue syndrome (CFS) are complicated medical disorders, with little known etiologies. The purpose of this research is to characterize FMS and CFS by studying the variations in cortisol secretion patterns, timings, amplitudes, the number of underlying pulses, as well as infusion and clearance rates of cortisol.

METHODS

Using a physiological state-space model with plausible constraints, we estimate the hormonal secretory events and the physiological system parameters (i.e., infusion and clearance rates).

RESULTS

Our results show that the clearance rate of cortisol is lower in FMS patients as compared to their matched healthy individuals based on a simplified cortisol secretion model. Moreover, the number, magnitude, and energy of hormonal secretory events are lower in FMS patients. During early morning hours, the magnitude and energy of the hormonal secretory events are higher in CFS patients.

CONCLUSION

Due to lower cortisol clearance rate, there is a higher accumulation of cortisol in FMS patients as compared to their matched healthy subjects. As the FMS patient accumulates higher cortisol residues, internal inhibitory feedback regulates the hormonal secretory events. Therefore, the FMS patients show a lower number, magnitude, and energy of hormonal secretory events. Though CFS patients have the same number of secretory events, they secrete lower quantities during early morning hours. When we compare the results for CFS patients against FMS patients, we observe different cortisol alteration patterns.

SIGNIFICANCE

Characterizing CFS and FMS based on the cortisol alteration will help us to develop novel methods for treating these disorders.

A System Theoretic Investigation of Cortisol Dysregulation in Fibromyalgia Patients with Chronic Fatigue

Fibromyalgia Syndrome (FMS) and Chronic Fatigue Syndrome (CFS) are complex medical conditions with similar symptoms such as anxiety, fatigue, depression, headaches, muscle aches and joint pain. The etiology of both these syndromes is unknown. The objective of this study is to characterize FMS, both in the presence and in the absence of CFS, by analyzing variations in cortisol secretion patterns, timings, amplitudes, and the number of the underlying pulses as well as infusion and clearance rates. The comparison is performed against matched healthy control subjects. We estimate the hormonal secretory events by deconvolving cortisol data using a two-step coordinate descent approach. The first step implements a sparse recovery approach to infer the amplitudes and the timings of the cortisol secretion events from limited cortisol hormone data. The main advantage of this method is estimating the cortisol secretory events using a system theoretic approach. The second step is to estimate the physiological system parameters (i.e. infusion and clearance rates). This approach has been verified on healthy individuals previously. Our results show that the clearance rate of cortisol by the liver is relatively lower in patients as compared to the matched healthy individuals. This suggests that there is a relatively higher accumulation of serum cortisol in patients when compared to matched healthy subjects.

A Cortisol-Based Energy Decoder for Investigation of Fatigue in Hypercortisolism

Hormones play a fundamental role in homeostasis. We develop a state-space model relating the body's internal energy to cortisol hormone secretions. Cortisol is secreted in pulses and follows a 24 h circadian rhythm. Secretory event timings carry important information regarding internal feedback signaling taking place, as do the upper and lower serum cortisol levels. We relate an internal energy state variable to cortisol pulse timings and to the upper and lower serum cortisol envelopes. We derive Bayesian filter equations for state estimation and use the Expectation-Maximization algorithm for model parameter recovery. Results on multi-day simulated data show circadian energy variations in healthy subjects and non-circadian fluctuations throughout 24 h periods in patient models suffering from hypercortisolism. The results shed new light on why patients diagnosed with excess cortisol disorders frequently experience symptoms of daytime fatigue and sleep disturbances at night. The state-space model is also an important first step towards the design of closed-loop controllers for treating hormone-related disorders in a manner that closely emulates the body's own pulsatile feedback mechanisms.

Comparing Methods for Measurement Error Detection in Serial 24-h Hormonal Data

Measurement errors commonly occur in 24-h hormonal data and may affect the outcomes of such studies. Measurement errors often appear as outliers in such data sets; however, no well-established method is available for their automatic detection. In this study, we aimed to compare performances of different methods for outlier detection in hormonal serial data. Hormones (glucose, insulin, thyroid-stimulating hormone, cortisol, and growth hormone) were measured in blood sampled every 10 min for 24 h in 38 participants of the Leiden Longevity Study. Four methods for detecting outliers were compared: (1) eyeballing, (2) Tukey’s fences, (3) stepwise approach, and (4) the expectation-maximization (EM) algorithm. Eyeballing detects outliers based on experts’ knowledge, and the stepwise approach incorporates physiological knowledge with a statistical algorithm. Tukey’s fences and the EM algorithm are data-driven methods, using interquartile range and a mathematical algorithm to identify the underlying distribution, respectively. The performance of the methods was evaluated based on the number of outliers detected and the change in statistical outcomes after removing detected outliers. Eyeballing resulted in the lowest number of outliers detected (1.0% of all data points), followed by Tukey’s fences (2.3%), the stepwise approach (2.7%), and the EM algorithm (11.0%). In all methods, the mean hormone levels did not change materially after removing outliers. However, their minima were affected by outlier removal. Although removing outliers affected the correlation between glucose and insulin on the individual level, when averaged over all participants, none of the 4 methods influenced the correlation. Based on our results, the EM algorithm is not recommended given the high number of outliers detected, even where data points are physiologically plausible. Since Tukey’s fences is not suitable for all types of data and eyeballing is time-consuming, we recommend the stepwise approach for outlier detection, which combines physiological knowledge and an automated process.

Altered ultradian cortisol rhythmicity as a potential neurobiologic substrate for chronic insomnia

Chronic insomnia is highly prevalent and associated with significant morbidity (i.e., confers risk for multiple psychiatric and medical disorders, such as depression and hypertension). Therefore, it is essential to identify factors that perpetuate this disorder. One candidate factor in the neurobiology of chronic insomnia is hypothalamic-pituitary-adrenal-axis dysregulation, and in particular, alterations in circadian cortisol rhythmicity. Cortisol secretory patterns, however, fluctuate with both a circadian and an ultradian rhythm (i.e., pulses every 60-120 min). Ultradian cortisol pulses are thought to be involved in the maintenance of wakefulness during the day and their relative absence at night may allow for the consolidation of sleep and/or shorter nocturnal awakenings. It is possible that the wakefulness that occurs in chronic insomnia may be associated with the aberrant occurrence of cortisol pulses at night. While cortisol pulses naturally occur with transient awakenings, it may also be the case that cortisol pulsatility becomes a conditioned phenomenon that predisposes one to awaken and/or experience prolonged nocturnal awakenings. The current review summarizes the literature on cortisol rhythmicity in subjects with chronic insomnia, and proffers the suggestion that it may be abnormalities in the ultradian rather than circadian cortisol that is associated with the pathophysiology of insomnia.

How to disentangle psychobiological stress reactivity and recovery: A comparison of model-based and non-compartmental analyses of cortisol concentrations

This article seeks to address the prevailing issue of how to measure specific process components of psychobiological stress responses. Particularly the change of cortisol secretion due to stress exposure has been discussed as an endophenotype of many psychosomatic health outcomes. To assess its process components, a large variety of non-compartmental parameters (i.e., composite measures of substance concentrations at different points in time) like the area under the concentration-time curve (AUC) are commonly utilized. However, a systematic evaluation and validation of these parameters based on a physiologically plausible model of cortisol secretion has not been performed so far. Thus, a population pharmacokinetic (mixed-effects stochastic differential equation) model was developed and fitted to densely sampled salivary cortisol data of 10 males from Montreal, Canada, and sparsely sampled data of 200 mixed-sex participants from Dresden, Germany, who completed the Trier Social Stress Test (TSST). Besides the two major process components representing (1) stress-related cortisol secretion (reactivity) and (2) cortisol elimination (recovery), the model incorporates two additional, often disregarded components: (3) the secretory delay after stress onset, and (4) deviations from the projected steady-state concentration due to stress-unrelated fluctuations of cortisol secretion. The fitted model (R² = 99%) was thereafter used to investigate the correlation structure of the four individually varying, and readily interpretable model parameters and eleven popular non-compartmental parameters. Based on these analyses, we recommend to use the minimum-maximum cortisol difference and the minimum concentration as proxy measures of reactivity and recovery, respectively. Finally, statistical power analyses of the reactivity-related sex effect illustrate the consequences of using impure non-compartmental measures of the different process components that underlie the cortisol stress response.

Rhythms dysregulation: A new perspective for understanding PTSD?

Post-traumatic stress disorder (PTSD) is a complex syndrome that may occur after exposure to one or more traumatic events. It associates physiological, emotional, and cognitive changes Brain and hormonal modifications contribute to some impairments in learning, memory, and emotion regulation. Some of these biological dysfunctions may be analyzed in terms of rhythms dysregulation that would be expressed through endocrine rhythmicity, sleep organization, and temporal synchrony in brain activity. In the first part of this article, we report studies on endocrine rhythmicity revealing that some rhythms abnormalities are frequently observed, although not constantly, for both cortisol and sympathetic nervous system (SNS) activity. The most typical changes are a flattening of the diurnal secretion of cortisol and the hyperactivation of the SNS. These results may explain why cognitive functioning, in particular consolidation of emotional memories, attention, learning, vigilance and arousal, is altered in patients with PTSD. The second part of this article focuses on sleep disturbances, one of the core features of PTSD. Abnormal REM sleep reported in various studies may have a pathophysiological role in PTSD and may exacerbate some symptoms such as emotional regulation and memory. In addition, sleep disorders, such as paradoxical insomnia, increase the risk of developing PTSD. We also discuss the potential impact of sleep disturbances on cognition. Finally, temporal synchrony of brain activity and functional connectivity, explored using electroencephalography and functional magnetic resonance imaging, are addressed. Several studies reported abnormalities in alpha, beta and gamma frequency bands that may affect both attentional and memory processes. Other studies confirmed abnormalities in connectivity and recent fMRI data suggest that this could limit top-down control and may be associated with flashback intrusive memories. These data illustrate that a better knowledge of the different patterns of biological rhythms contributes to explain the heterogeneity of PTSD and shed new light on the association with some frequent medical disorders.

A Pharmacokinetic Model of a Tissue Implantable Cortisol Sensor

Cortisol is an important glucocorticoid hormone whose biochemistry influences numerous physiological and pathological processes. Moreover, it is a biomarker of interest for a number of conditions, including posttraumatic stress disorder, Cushing's syndrome, Addison's disease, and others. An implantable biosensor capable of real time monitoring of cortisol concentrations in adipose tissue may revolutionize the diagnosis and treatment of these disorders, as well as provide an invaluable research tool. Toward this end, a mathematical model, informed by the physiological literature, is developed to predict dynamic cortisol concentrations in adipose, muscle, and brain tissues, where a significant number of important processes with cortisol occur. The pharmacokinetic model is applied to both a prototypical, healthy male patient and a previously studied Cushing's disease patient. The model can also be used to inform the design of an implantable sensor by optimizing the sensor dissociation constant, apparent delay time, and magnitude of the sensor output versus system dynamics. Measurements from such a sensor would help to determine systemic cortisol levels, providing much needed insight for proper medical treatment for various cortisol-related conditions.

An optimization formulation for characterization of pulsatile cortisol secretion

Cortisol is released to relay information to cells to regulate metabolism and reaction to stress and inflammation. In particular, cortisol is released in the form of pulsatile signals. This low-energy method of signaling seems to be more efficient than continuous signaling. We hypothesize that there is a controller in the anterior pituitary that leads to pulsatile release of cortisol, and propose a mathematical formulation for such controller, which leads to impulse control as opposed to continuous control. We postulate that this controller is minimizing the number of secretory events that result in cortisol secretion, which is a way of minimizing the energy required for cortisol secretion; this controller maintains the blood cortisol levels within a specific circadian range while complying with the first order dynamics underlying cortisol secretion. We use an ℓ0-norm cost function for this controller, and solve a reweighed ℓ1-norm minimization algorithm for obtaining the solution to this optimization problem. We use four examples to illustrate the performance of this approach: (i) a toy problem that achieves impulse control, (ii) two examples that achieve physiologically plausible pulsatile cortisol release, (iii) an example where the number of pulses is not within the physiologically plausible range for healthy subjects while the cortisol levels are within the desired range. This novel approach results in impulse control where the impulses and the obtained blood cortisol levels have a circadian rhythm and an ultradian rhythm that are in agreement with the known physiology of cortisol secretion. The proposed formulation is a first step in developing intermittent controllers for curing cortisol deficiency. This type of bio-inspired pulse controllers can be employed for designing non-continuous controllers in brain-machine interface design for neuroscience applications.

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

Pulsatile release of cortisol from the adrenal glands is governed by pulsatile release of adrenocorticotropic hormone (ACTH) from the anterior pituitary. In return, cortisol has a negative feedback effect on ACTH release. Simultaneous recording of ACTH and cortisol is not typical, and determining the number, timing, and amplitudes of pulsatile events from simultaneously recorded data is challenging because of several factors: 1) stimulator ACTH pulse activity, 2) kinematics of ACTH and cortisol, 3) the sampling interval, and 4) the measurement error. We model ACTH and cortisol secretion simultaneously using a linear differential equations model with Gaussian errors and sparse pulsatile events as inputs to the model. We propose a novel framework for recovering pulses and parameters underlying the interactions between ACTH and cortisol. We recover the timing and amplitudes of pulses using compressed sensing and employ generalized cross validation for determining the number of pulses. We analyze serum ACTH and cortisol levels sampled at 10-min intervals over 24 h from ten healthy women. We recover physiologically plausible timing and amplitudes for these pulses and model the feedback effect of cortisol. We recover 15 to 18 pulses over 24 h, which is highly consistent with the results of another cortisol data analysis approach. Modeling the interactions between ACTH and cortisol allows for accurate quantification of pulsatile events, and normal and pathological states. This could lay the basis for a more physiologically-based approach for administering cortisol therapeutically. The proposed approach can be adapted to deconvolve other pairs of hormones with similar interactions.

Biological time series analysis using a context free language: applicability to pulsatile hormone data

We present a novel approach for analyzing biological time-series data using a context-free language (CFL) representation that allows the extraction and quantification of important features from the time-series. This representation results in Hierarchically AdaPtive (HAP) analysis, a suite of multiple complementary techniques that enable rapid analysis of data and does not require the user to set parameters. HAP analysis generates hierarchically organized parameter distributions that allow multi-scale components of the time-series to be quantified and includes a data analysis pipeline that applies recursive analyses to generate hierarchically organized results that extend traditional outcome measures such as pharmacokinetics and inter-pulse interval. Pulsicons, a novel text-based time-series representation also derived from the CFL approach, are introduced as an objective qualitative comparison nomenclature. We apply HAP to the analysis of 24 hours of frequently sampled pulsatile cortisol hormone data, which has known analysis challenges, from 14 healthy women. HAP analysis generated results in seconds and produced dozens of figures for each participant. The results quantify the observed qualitative features of cortisol data as a series of pulse clusters, each consisting of one or more embedded pulses, and identify two ultradian phenotypes in this dataset. HAP analysis is designed to be robust to individual differences and to missing data and may be applied to other pulsatile hormones. Future work can extend HAP analysis to other time-series data types, including oscillatory and other periodic physiological signals.

Do venepuncture procedures induce cortisol responses? A review, study, and synthesis for stress research

Venepuncture procedures are frequently employed to continuously monitor humoral stress markers. As such procedures are conceived as "potent psychological and physiological stressors", there is a need to determine whether venepuncture procedures themselves elicit cortisol responses and if so, how to deal with them appropriately. In order to assess the rate of cortisol responses to venepuncture, we conducted a literature review, which suggested that venepuncture procedures induce cortisol responses with a probability of approximately 30%. By utilizing Bayesian analysis, this result was integrated with the cortisol data of 18 healthy men who were exposed to a venepuncture procedure twice (time lag: 1 week). The currently observed response rate of 47% differed substantially from the earlier findings, which we attribute to a self-selective sampling of participants. In addition, participants showing a response to the first venepuncture were highly likely to also show a response to the second one. In this regard, we discuss the presumed conditioning of cortisol responses to venepuncture procedures. To prevent the superposition of venepuncture-induced cortisol responses and responses induced by target stressors, we propose a time- and selection-based strategy: cortisol samples taken about 110min after venepuncture should be virtually adjusted for its superimposing effects. Furthermore, previous experiences of venepuncture were highly predictive for cortisol responsiveness. This association could be utilized in further studies to identify participants who will probably show a cortisol response to venepuncture.

Deconvolution of serum cortisol levels by using compressed sensing

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.

Classification criteria for distinguishing cortisol responders from nonresponders to psychosocial stress: evaluation of salivary cortisol pulse detection in panel designs

OBJECTIVE

Hypothalamic-pituitary-adrenal axis reactivity to acute stimulation is frequently assessed by repeated sampling of salivary cortisol. Researchers often strive to distinguish between individuals who show (responders) and those do not show (nonresponders) cortisol responses. For this, fixed threshold classification criteria, such as a 2.5-nmol/l baseline-to-peak increase, are frequently used. However, the performance of such criteria has not been systematically evaluated.

METHODS

Repeated salivary cortisol data from 504 participants exposed to either the Trier Social Stress Test (TSST; n = 309) or a placebo protocol (n = 195) were used for analyses. To obtain appropriate classifications of cortisol responders versus nonresponders, a physiologically plausible, autoregressive latent trajectory (ALT) mixture model was fitted to these data. Response classifications according to the ALT model and information on the experimental protocol (TSST versus placebo TSST) were then used to evaluate the performance of different proposed classifier proxies by receiver operating characteristics.

RESULTS

Moment structure of cortisol time series was adequately accounted for by the proposed ALT model. The commonly used 2.5-nmol/l criterion was found to be overly conservative, resulting in a high rate of 16.5% false-negative classifications. Lowering this criterion to 1.5 nmol/l or using a percentage baseline-to-peak increase of 15.5% as a threshold yielded improved performance (39.3% and 26.7% less misclassifications, respectively).

CONCLUSIONS

Alternative classification proxies (1.5 nmol/l or 15.5% increase) are able to effectively distinguish between cortisol responders and nonresponders and should be used in future research, whenever statistical response class allocation is not feasible.

Transformation techniques for cross-sectional and longitudinal endocrine data: application to salivary cortisol concentrations

Endocrine time series often lack normality and homoscedasticity most likely due to the non-linear dynamics of their natural determinants and the immanent characteristics of the biochemical analysis tools, respectively. As a consequence, data transformation (e.g., log-transformation) is frequently applied to enable general linear model-based analyses. However, to date, data transformation techniques substantially vary across studies and the question of which is the optimum power transformation remains to be addressed. The present report aims to provide a common solution for the analysis of endocrine time series by systematically comparing different power transformations with regard to their impact on data normality and homoscedasticity. For this, a variety of power transformations of the Box-Cox family were applied to salivary cortisol data of 309 healthy participants sampled in temporal proximity to a psychosocial stressor (the Trier Social Stress Test). Whereas our analyses show that un- as well as log-transformed data are inferior in terms of meeting normality and homoscedasticity, they also provide optimum transformations for both, cross-sectional cortisol samples reflecting the distributional concentration equilibrium and longitudinal cortisol time series comprising systematically altered hormone distributions that result from simultaneously elicited pulsatile change and continuous elimination processes. Considering these dynamics of endocrine oscillations, data transformation prior to testing GLMs seems mandatory to minimize biased results.

Translational applications of evaluating physiologic variability in human endotoxemia

Dysregulation of the inflammatory response is a critical component of many clinically challenging disorders such as sepsis. Inflammation is a biological process designed to lead to healing and recovery, ultimately restoring homeostasis; however, the failure to fully achieve those beneficial results can leave a patient in a dangerous persistent inflammatory state. One of the primary challenges in developing novel therapies in this area is that inflammation is comprised of a complex network of interacting pathways. Here, we discuss our approaches towards addressing this problem through computational systems biology, with a particular focus on how the presence of biological rhythms and the disruption of these rhythms in inflammation may be applied in a translational context. By leveraging the information content embedded in physiologic variability, ranging in scale from oscillations in autonomic activity driving short-term heart rate variability to circadian rhythms in immunomodulatory hormones, there is significant potential to gain insight into the underlying physiology.

A phenomenological model for circadian and sleep allostatic modulation of plasma cortisol concentration

Both circadian rhythmicity and sleep play significant roles in the regulation of plasma cortisol concentration by the hypothalamo-pituitary-adrenal (HPA) axis. Numerous studies have found links between sleep and changes in cortisol concentration, but the implications of these results have remained largely qualitative. In this article, we present a quantitative phenomenological model to describe the effects of different sleep durations on cortisol concentration. We constructed the proposed model by incorporating the circadian and sleep allostatic effects on cortisol concentration, the pulsatile nature of cortisol secretion, and cortisol's negative autoregulation of its own production and validated its performance on three study groups that experienced four distinct sleep durations. The model captured many disparate effects of sleep on cortisol dynamics, such as the inhibition of cortisol secretion after the wake-to-sleep transition and the rapid rise of cortisol concentration before morning awakening. Notably, the model reconciled the seemingly contradictory findings between studies that report an increase in cortisol concentration following total sleep deprivation and studies that report no change in concentration. This work provides a biomathematical approach to combine the results on the effects of sleep on cortisol concentration into a unified framework and predict the impact of varying sleep durations on the cortisol profile.

nSTAT: open-source neural spike train analysis toolbox for Matlab

Over the last decade there has been a tremendous advance in the analytical tools available to neuroscientists to understand and model neural function. In particular, the point process - generalized linear model (PP-GLM) framework has been applied successfully to problems ranging from neuro-endocrine physiology to neural decoding. However, the lack of freely distributed software implementations of published PP-GLM algorithms together with problem-specific modifications required for their use, limit wide application of these techniques. In an effort to make existing PP-GLM methods more accessible to the neuroscience community, we have developed nSTAT--an open source neural spike train analysis toolbox for Matlab®. By adopting an object-oriented programming (OOP) approach, nSTAT allows users to easily manipulate data by performing operations on objects that have an intuitive connection to the experiment (spike trains, covariates, etc.), rather than by dealing with data in vector/matrix form. The algorithms implemented within nSTAT address a number of common problems including computation of peri-stimulus time histograms, quantification of the temporal response properties of neurons, and characterization of neural plasticity within and across trials. nSTAT provides a starting point for exploratory data analysis, allows for simple and systematic building and testing of point process models, and for decoding of stimulus variables based on point process models of neural function. By providing an open-source toolbox, we hope to establish a platform that can be easily used, modified, and extended by the scientific community to address limitations of current techniques and to extend available techniques to more complex problems.

Entrainment of peripheral clock genes by cortisol

Circadian rhythmicity in mammals is primarily driven by the suprachiasmatic nucleus (SCN), often called the central pacemaker, which converts the photic information of light and dark cycles into neuronal and hormonal signals in the periphery of the body. Cells of peripheral tissues respond to these centrally mediated cues by adjusting their molecular function to optimize organism performance. Numerous systemic cues orchestrate peripheral rhythmicity, such as feeding, body temperature, the autonomic nervous system, and hormones. We propose a semimechanistic model for the entrainment of peripheral clock genes by cortisol as a representative entrainer of peripheral cells. This model demonstrates the importance of entrainer's characteristics in terms of the synchronization and entrainment of peripheral clock genes, and predicts the loss of intercellular synchrony when cortisol moves out of its homeostatic amplitude and frequency range, as has been observed clinically in chronic stress and cancer. The model also predicts a dynamic regime of entrainment, when cortisol has a slightly decreased amplitude rhythm, where individual clock genes remain relatively synchronized among themselves but are phase shifted in relation to the entrainer. The model illustrates how the loss of communication between the SCN and peripheral tissues could result in desynchronization of peripheral clocks.

Transcriptional implications of ultradian glucocorticoid secretion in homeostasis and in the acute stress response

Endogenous glucocorticoids are secreted by the hypothalamic-pituitary-adrenal (HPA) axis in response to a wide range of stressors. Glucocorticoids exert significant downstream effects, including the regulation of many inflammatory genes. The HPA axis functions such that glucocorticoids are released in a pulsatile manner, producing ultradian rhythms in plasma glucocorticoid levels. It is becoming increasingly evident that this ultradian pulsatility is important in maintaining proper homeostatic regulation and responsiveness to stress. This is particularly interesting from a clinical perspective given that pathological dysfunctions of the HPA axis produce altered ultradian patterns. Modeling this system facilitates the understanding of how glucocorticoid pulsatility arises, how it can be lost, and the transcriptional implications of ultradian rhythms. To approach these questions, we developed a mathematical model that integrates the cyclic production of glucocorticoids by the HPA axis and their downstream effects by integrating existing models of the HPA axis and glucocorticoid pharmacodynamics. This combined model allowed us to evaluate the implications of pulsatility in homeostasis as well as in response to acute stress. The presence of ultradian rhythms allows the system to maintain a lower response to homeostatic levels of glucocorticoids, but diminished feedback within the HPA axis leads to a loss of glucocorticoid rhythmicity. Furthermore, the loss of HPA pulsatility in homeostasis correlates with a decrease in the peak output in response to an acute stressor. These results are important in understanding how cyclic glucocorticoid secretion helps maintain the responsiveness of the HPA axis.

The Fitzhugh-Nagumo model: Firing modes with time-varying parameters & parameter estimation

In this paper, we revisit the issue of the utility of the FitzHugh-Nagumo (FHN) model for capturing neuron firing behaviors. It has been noted (e.g., see [6]) that the FHN model cannot exhibit certain interesting firing behaviors such as bursting. We illustrate that, by allowing time-varying parameters for the FHN model, one could overcome such limitations while still retaining the low order complexity of the FHN model. We also highlight the utility of the FHN model from an estimation perspective by presenting a novel parameter estimation method that exploits the multiple time scale feature of the FHN model, and compare the performance of this method with the Extended Kalman Filter through illustrative examples.

A feedback control model for cortisol secretion

Existing mathematical models for cortisol secretion do not describe the entire cortisol secretion process, from the neural firing of corticotropin releasing hormone (CRH) in the hypothalamus to cortisol concentration in the plasma. In this paper, we lay the groundwork to construct a more comprehensive model, relating CRH, Adrenocorticotropic hormone (ACTH), and cortisol. We start with an existing mathematical model for cortisol secretion, and combine it with a simplified neural firing model that describes CRH and ACTH release. This simplified neural firing model is obtained using the extended FitzHugh-Nagumo (FHN) model, which includes a time-varying spiking threshold [3]. A key feature of our model is the presence of a feedback loop from cortisol secretion to ACTH secretion.

A mathematical model of aging-related and cortisol induced hippocampal dysfunction

BACKGROUND

The hippocampus is essential for declarative memory synthesis and is a core pathological substrate for Alzheimer's disease (AD), the most common aging-related dementing disease. Acute increases in plasma cortisol are associated with transient hippocampal inhibition and retrograde amnesia, while chronic cortisol elevation is associated with hippocampal atrophy. Thus, cortisol levels could be monitored and managed in older people, to decrease their risk of AD type hippocampal dysfunction. We generated an in silicomodel of the chronic effects of elevated plasma cortisol on hippocampal activity and atrophy, using the systems biology mark-up language (SBML). We further challenged the model with biologically based interventions to ascertain if cortisol associated hippocampal dysfunction could be abrogated.

RESULTS

The in silicoSBML model reflected the in vivoaging of the hippocampus and increased plasma cortisol and negative feedback to the hypothalamic pituitary axis. Aging induced a 12% decrease in hippocampus activity (HA), increased to 30% by acute and 40% by chronic elevations in cortisol. The biological intervention attenuated the cortisol associated decrease in HA by 2% in the acute cortisol simulation and by 8% in the chronic simulation.

CONCLUSION

Both acute and chronic elevations in cortisol secretion increased aging-associated hippocampal atrophy and a loss of HA in the model. We suggest that this first SMBL model, in tandem with in vitroand in vivostudies, may provide a backbone to further frame computational cortisol and brain aging models, which may help predict aging-related brain changes in vulnerable older people.

Modified-release hydrocortisone for circadian therapy: a proof-of-principle study in dexamethasone-suppressed normal volunteers

BACKGROUND

All existing long-term glucocorticoid replacement therapy is suboptimal as the normal nocturnal rise and waking morning peak of serum cortisol is not reproduced.

AIM

To test whether it is possible to reproduce the normal overnight rise and morning peak in serum cortisol using an oral delayed and sustained release preparation of hydrocortisone (Cortisol(ds)).

SUBJECTS AND METHODS

Six healthy normal male volunteers attended on two occasions, in a single-dose, open-label, nonrandomized study. Endogenous cortisol secretion was suppressed by administration of dexamethasone. Cortisol(ds) (formulation A or B) was administered at 2200 h on day 1. Blood samples for measurement of cortisol were taken from 2200 h every 30 min until 0700 h, then hourly until 2200 h on day 2. Fifteen body mass index (BMI)-matched control subjects had serum cortisol levels measured at 20-min intervals for 24 h. Serum cortisol profiles and pharmacokinetics after Cortisol(ds) were compared with those in controls.

RESULTS

Formulations A and B were associated with delayed drug release (by 2 h and 4 h, respectively), with median peak cortisol concentrations at 4.5 h (0245 h) and 10 h (0800 h), respectively, thereby reproducing the normal early morning rise in serum cortisol. Total cortisol exposure was not different from controls.

CONCLUSIONS

For the first time we have shown that it is possible to mimic the normal circadian rhythm of circulating cortisol with an oral modified-release formulation of hydrocortisone, providing the basis for development of physiological circadian replacement therapy in patients with adrenal insufficiency.

The next generation of artificial pancreas control algorithms

Creating a wearable artificial pancreas (AP) by closing the loop between a glucose sensor and an insulin infusion pump has the potential to significantly impact the complications associated with and improve the quality of life of diabetic individuals. Despite recent progress on glucose sensor and insulin infusion technologies, control algorithms built on the simple glucose value efferent and insulin dose afferent model are not efficient and reliable. Based on glucose regulatory mechanisms known to date, their impairment in the diabetic state, and fundamental principles of control theory, some corrections to the present course of research are proposed to facilitate the removal of this barrier. A greater emphasis on model predictive controllers or controllers that exploit a mathematical representation, or model, of the patient's own physiology is proposed. Whole-body physiologically based pharmacokinetics-pharmacodynamics-type models hold the best odds for enabling a successful closed-loop AP. However, two major improvements to the diabetes modeling state of the art are required to make them practical for daily care: integrating hypothalamus-pituitary-adrenal axis and gastrointestinal tract submodels. Although there are simple representations of these in current existence, large concerted efforts between experimentalists and modelers will be required to enhance their accuracy. Finally, changes in hardware that complements controller performance are suggested. For instance, the development of dual control inputs of insulin and glucagon could relax tolerances on controller accuracy.

Stochastic models for prodrug targeting. 1. Diffusion of the efflux drug

In modeling prodrug targeting using the stochastic approach, we first modeled diffusion of the efflux drug. Drug efflux is one of the major reasons for the failure of prodrug strategy: the active agent is pumped out the membrane ("efflux"), causing an insufficient amount to be delivered to the targeted sites and thus diminishing the efficacy of chemotherapy. Because the biological body is a nonlinear nonequilibrium complex system, the molecular transport taking place in vivo often showed stochasticity. The model described here for diffusion of the efflux drug is basically a diffusion process with reflecting/absorbing boundary conditions, divided into two distinctive regions with one allowing the particles to jump to the origin as a result of efflux pumping. We study discrete time birth-death Markov chain and compute the time-dependent spatial probability density function (PDF) of particles. The results showed that the jumping probability, although small, has a significant impact on the evolution of PDF of the efflux drug. The implications of this model were discussed.

A statistical model of diurnal variation in human growth hormone

The diurnal pattern of growth hormone (GH) serum levels depends on the frequency and amplitude of GH secretory events, the kinetics of GH infusion into and clearance from the circulation, and the feedback of GH on its secretion. We present a two-dimensional linear differential equation model based on these physiological principles to describe GH diurnal patterns. The model characterizes the onset times of the secretory events, the secretory event amplitudes, as well as the infusion, clearance, and feedback half-lives of GH. We illustrate the model by using maximum likelihood methods to fit it to GH measurements collected in 12 normal, healthy women during 8 h of scheduled sleep and a 16-h circadian constant-routine protocol. We assess the importance of the model components by using parameter standard error estimates and Akaike's Information Criterion. During sleep, both the median infusion and clearance half-life estimates were 13.8 min, and the median number of secretory events was 2. During the constant routine, the median infusion half-life estimate was 12.6 min, the median clearance half-life estimate was 11.7 min, and the median number of secretory events was 5. The infusion and clearance half-life estimates and the number of secretory events are consistent with current published reports. Our model gave an excellent fit to each GH data series. Our analysis paradigm suggests an approach to decomposing GH diurnal patterns that can be used to characterize the physiological properties of this hormone under normal and pathological conditions.