Patient specific modeling of the HPA axis related to clinical diagnosis of depression

Depression diagnostics using a nonlinear mathematical oscillatory model

BACKGROUND AND OBJECTIVES

It is known that long-term stress leads to trauma and very often to depression. Usually, the diagnosis of depression is dealt with by psychiatrists who, based on conversations and questions, diagnose the patient's illness and condition. Unfortunately, this diagnosis is not always reliable. To prevent the development of disease, it is necessary to detect illness in a timely manner. One of the indications of the possibility of the onset of disease is a disturbance in the level of hormones in the body, especially cortisol. The purpose of this study was to develop a mathematical model for cortisol variation resulting from stress which would be useful in making conclusions about depressive states.

METHODS

Rapid changes in cortisol concentration, according to ultradian rhythms, which are much faster than the daily circadian rhythm, is modelled as a truly nonlinear oscillator. The mathematical model contains two coupled first order differential equations. The stress is modeled as a pulsating action, described with a periodic trigonometric function, and cortisol production as a cubic nonlinear one. Three models for cortisol variation are considered: 1) the pure nonlinear model, 2) the periodically excited system, 3) and the chaotic system. The results from the study are supported with experimental measurements.

RESULTS

Without stress, cortisol variation is of an oscillatory type with a constant steady-state amplitude. Intensive stress causes a resonant phenomenon in cortisol oscillatory variation. The occasion is short and is usually without consequences. For long stress periods deterministic chaos occurs which permanently changes the levels of cortisol. This phenomenon is an indicator of depression. Results from the suggested models are compared with experimentally obtained ones and good quantitative agreement is obtained.

CONCLUSIONS

The nonlinear oscillator is a good model for indication of depression. The model provides not only general conclusions, but also individual ones, if personal characteristics are taken into consideration. Response of the model depends not only on the input data related to stress, but also on the system parameters that specify each individual. Findings obtained from this study have implications for the medical diagnosis and treatment of depression.

Longitudinal hair cortisol in bipolar disorder and a mechanism based on HPA dynamics

Bipolar disorder (BD) is marked by fluctuating mood states over months to years, often with elevated cortisol levels. Elevated cortisol can also trigger mood episodes. Here, we combine longitudinal hair cortisol and mood measurements with mathematical modeling to provide a potential mechanistic link between cortisol and mood timescales in BD. Using 12 cm hair samples, representing a year of growth, we found enhanced year-scale cortisol fluctuations whose amplitude averaged 4-fold higher in BD (n = 26) participants than controls (n = 59). The proximal 2 cm of hair correlated with recent mood scores. Depression (n = 266) and mania (n = 273) scores from a longitudinal study of BD showed similar frequency spectra. These results suggest a mechanism for BD in which high emotional reactivity excites the slow timescales in the hypothalamic-pituitary-adrenal (HPA) axis to generate elevated months-scale cortisol fluctuations, triggering cortisol-induced mood episodes.

Major depressive disorder and bistability in an HPA-CNS toggle switch

Major depressive disorder (MDD) is the most common psychiatric disorder. It has a complex and heterogeneous etiology. Most treatments take weeks to show effects and work well only for a fraction of the patients. Thus, new concepts are needed to understand MDD and its dynamics. One of the strong correlates of MDD is increased activity and dysregulation of the hypothalamic-pituitary-adrenal (HPA) axis which produces the stress hormone cortisol. Existing mathematical models of the HPA axis describe its operation on the scale of hours, and thus are unable to explore the dynamic on the scale of weeks that characterizes many aspects of MDD. Here, we propose a mathematical model of MDD on the scale of weeks, a timescale provided by the growth of the HPA hormone glands under control of HPA hormones. We add to this the mutual inhibition of the HPA axis and the hippocampus and other regions of the central nervous system (CNS) that forms a toggle switch. The model shows bistability between euthymic and depressed states, with a slow timescale of weeks in its dynamics. It explains why prolonged but not acute stress can trigger a self-sustaining depressive episode that persists even after the stress is removed. The model explains the weeks timescale for drugs to take effect, as well as the dysregulation of the HPA axis in MDD, based on gland mass changes. This understanding of MDD dynamics may help to guide strategies for treatment.

VeVaPy, a Python Platform for Efficient Verification and Validation of Systems Biology Models with Demonstrations Using Hypothalamic-Pituitary-Adrenal Axis Models

In order for mathematical models to make credible contributions, it is essential for them to be verified and validated. Currently, verification and validation (V&V) of these models does not meet the expectations of the system biology and systems pharmacology communities. Partially as a result of this shortfall, systemic V&V of existing models currently requires a lot of time and effort. In order to facilitate systemic V&V of chosen hypothalamic-pituitary-adrenal (HPA) axis models, we have developed a computational framework named VeVaPy-taking care to follow the recommended best practices regarding the development of mathematical models. VeVaPy includes four functional modules coded in Python, and the source code is publicly available. We demonstrate that VeVaPy can help us efficiently verify and validate the five HPA axis models we have chosen. Supplied with new and independent data, VeVaPy outputs objective V&V benchmarks for each model. We believe that VeVaPy will help future researchers with basic modeling and programming experience to efficiently verify and validate mathematical models from the fields of systems biology and systems pharmacology.

The effectiveness of mindfulness-based cognitive therapy combined with medication therapy in preventing recurrence of major depressive disorder in convalescent patients

Objective

This study aims to investigate the effectiveness of mindfulness-based cognitive therapy (MBCT) combined with medication therapy in preventing the recurrence of major depressive disorder (MDD) in convalescent patients.

Methods

A total of 130 patients with convalescent MDD were enrolled in this prospective study. Sixty-five patients were assigned to the experimental group and received medication therapy combined with MBCT, and 65 patients were assigned to the control group and treated with medication alone. The recurrence rate and related hormonal changes were compared between the two groups.

Results

After 1 year of MBCT intervention, eight patients experienced recurrence in the experimental group, a recurrence rate of 12.31%, and 19 patients experienced recurrence in the control group, a recurrence rate of 29.23%. The Hamilton Depression Rating Scale (HAM-D) and the World Health Organization Quality of Life Scale (WHOQOL-BREF) scores in both the experimental and the control groups were significantly improved after treatment (P < 0.05). The difference in the HAM-D scores before and after treatment in the experimental group was 16.74 ± 4.54; this was significantly higher than that of the control group (8 ± 3.89, P < 0.0001). The WHOQOL-BREF scores in the experimental group were significantly improved compared with those of the control group (P < 0.0001). The differences in the levels of corticotrophin-releasing hormone (CRH), adrenocorticotropic hormone, and cortisol before and after treatment in the experimental group and the control group were statistically significant (P < 0.05). The difference in CRH before and after treatment in the experimental group was 16.8 ± 7.2, which was higher than that of the control group (2.75 ± 9.27, P < 0.0001). The intervention with MBCT had a significant impact on the recurrence of MDD [β = 1.206, P = 0.039, 95% (confidence interval) CI = 0.0790–1.229]. The difference in the HAM-D scores also had a significant impact on the recurrence of MDD (β = 1.121, P = 0.0014, 95% CI = 0.805–0.976).

Conclusion

Compared with medication therapy alone, the use of MBCT combined with medication therapy can effectively prevent the recurrence of MDD in convalescent patients.

Monoamine neurotransmitters and mood swings: a dynamical systems approach

Serotonin, dopamine and norepinephrine are monoamine neurotransmitters that modulate our mood state. Hence, imbalances in the levels of these neurotransmitters have been linked to the incidence of several psychiatric disorders. Here, a mathematical model written in terms of ordinary differential equations is proposed to represent the interaction of these three neurotransmitters. It is analytically and numerically shown that this model can experience a Hopf bifurcation. Thus, by varying a parameter value, the neurotransmitter levels can change from a steady state to an oscillatory behavior, which may be at least a partial explanation of the mood swings observed in depressed people.

Understanding virtual patients efficiently and rigorously by combining machine learning with dynamical modelling

Individual biological organisms are characterized by daunting heterogeneity, which precludes describing or understanding populations of ‘patients’ with a single mathematical model. Recently, the field of quantitative systems pharmacology (QSP) has adopted the notion of virtual patients (VPs) to cope with this challenge. A typical population of VPs represents the behavior of a heterogeneous patient population with a distribution of parameter values over a mathematical model of fixed structure. Though this notion of VPs is a powerful tool to describe patients’ heterogeneity, the analysis and understanding of these VPs present new challenges to systems pharmacologists. Here, using a model of the hypothalamic–pituitary–adrenal axis, we show that an integrated pipeline that combines machine learning (ML) and bifurcation analysis can be used to effectively and efficiently analyse the behaviors observed in populations of VPs. Compared with local sensitivity analyses, ML allows us to capture and analyse the contributions of simultaneous changes of multiple model parameters. Following up with bifurcation analysis, we are able to provide rigorous mechanistic insight regarding the influences of ML-identified parameters on the dynamical system’s behaviors. In this work, we illustrate the utility of this pipeline and suggest that its wider adoption will facilitate the use of VPs in the practice of systems pharmacology.

A Modeling and Machine Learning Pipeline to Rationally Design Treatments to Restore Neuroendocrine Disorders in Heterogeneous Individuals

Heterogeneity among individual patients presents a fundamental challenge to effective treatment, since a treatment protocol working for a portion of the population often fails in others. We hypothesize that a computational pipeline integrating mathematical modeling and machine learning could be used to address this fundamental challenge and facilitate the optimization of individualized treatment protocols. We tested our hypothesis with the neuroendocrine systems controlled by the hypothalamic–pituitary–adrenal (HPA) axis. With a synergistic combination of mathematical modeling and machine learning (ML), this integrated computational pipeline could indeed efficiently reveal optimal treatment targets that significantly contribute to the effective treatment of heterogeneous individuals. What is more, the integrated pipeline also suggested quantitative information on how these key targets should be perturbed. Based on such ML revealed hints, mathematical modeling could be used to rationally design novel protocols and test their performances. We believe that this integrated computational pipeline, properly applied in combination with other computational, experimental and clinical research tools, can be used to design novel and improved treatment against a broad range of complex diseases.

Antidepressant-like effects of water extract of Cordyceps militaris (Linn.) Link by modulation of ROCK2/PTEN/Akt signaling in an unpredictable chronic mild stress-induced animal model

ETHNOPHARMACOLOGY RELEVANCE

Cordyceps militaris (Linn.) Link (CM) is a medicinal mushroom traditionally used in tonics for treating several neurological disorders, including epilepsy and anxiety, in Asia. Reports have shown that CM has anti-inflammatory and anti-oxidative effects and may be beneficial for depression management.

AIM OF THE STUDY

This study aimed to investigate the potential of CM as an antidepressant for a long-term unpredictable chronic mild stress (UCMS) rodent models and explore its underlying mechanisms.

MATERIALS AND METHODS

Rats were orally administered with 125 (low, L), 250 (medium, M), and 500 (high, H) mg/kg bodyweight (bw) of the water extract of CM (WCM) for 35 consecutive days in the UCMS protocol. The levels of cerebral serotonin (5-HT), dopamine (DA), and metabolites in the frontal cortex of the rats were measured. Blood was collected to investigate the levels of proinflammatory cytokines, and the brain was dissected to assay the stress-associated ROCK2/PTEN/Akt signaling.

RESULTS

All doses of the WCM prevented abnormal behaviors induced by UCMS, including anhedonia and hypoactivity. The LWCM treatment reduced the turnover rate of 5-HT, and all doses of the WCM reduced the turnover rate of DA in the frontal cortex. The LWCM also attenuated the elevation of serum IL-1β induced by chronic stress. All doses of the WCM attenuated the ROCK2 protein hyperactivation, and the LWCM further increased the down-regulation of p-Akt/Akt signaling.

CONCLUSION

The WCM has antidepressant-like effects, which may result from the regulation of the stress-related ROCK2/PTEN/Akt pathway. Therefore, the WCM may be developed and used for the complementary treatment of depression.

Cortisol in relation to problematic eating behaviours, adiposity and symptom profiles in Major Depressive Disorder

Aims

Major Depressive Disorder (MDD) is associated with an increased risk of chronic disease related to weight gain, problematic eating behaviours and neuroendocrine changes. MDD is frequently associated with altered hypothalamic-pituitary-adrenal axis activity and cortisol secretion, where cortisol has been implicated in regulating energy balance, food intake and depressogenic weight changes. However, little research has examined the relationships between cortisol, adiposity and depressogenic problematic eating behaviours.

Method

Plasma cortisol concentrations were compared between 37 participants with MDD reporting appetite/weight loss, 43 participants with MDD reporting appetite/weight gain, and 60 healthy controls, by sex. Associations between cortisol, indices of adiposity and problematic eating behaviours were then assessed after accounting for demographic variables and depressive symptoms. Depressive symptoms were assessed using the Depression subscale of the Depression, Anxiety and Stress Scale, and eating behaviours with the Dutch Eating Behaviours Questionnaire and Yale Food Addiction Scale.

Results

Participants with MDD reporting appetite/weight loss had higher cortisol compared to controls, and marginally higher cortisol than those with MDD reporting appetite/weight gain. Cortisol negatively and significantly accounted for unique variance in body mass index and waist circumference after accounting for variance associated with age, sex and depressive symptoms, however it was not a significant predictor of problematic eating behaviours, such as emotional eating or food addiction. Cortisol concentrations did not differ between sexes.

Conclusion

The results indicate that cortisol is related to lower indices of adiposity and depressogenic symptoms of appetite/weight loss but is not related to problematic eating behaviours and appetite increases in MDD. These findings provide further evidence that the melancholic and atypical subtypes of MDD are associated with differential neuroendocrine and anthropometric indices, as well as behavioural and symptom profiles. Further research investigating the temporal nature of the identified relationships may assist in facilitating the development of improved interventions for individuals affected by weight changes in MDD.

Applications of cosinor rhythmometry in pharmacology

Study design and data analysis are two important aspects relevant to chronopharmacometrics. Blunders can be avoided by recognizing that most physiological variables are circadian periodic. Both ill health and treatment can affect the amplitude, phase, and/or period of circadian (and other) rhythms, in addition to their mean. The involvement of clock genes in molecular pathways related to important physiological systems underlies the bidirectional relationship often seen between circadian rhythm disruption and disease risk. Circadian rhythm characteristics of marker rhythms interpreted in the light of chronobiologic reference values represent important diagnostic tools. A set of cosinor-related programs is presented. They include the least squares fit of multiple-frequency cosine functions to model the time structure of individual records; a cosinor-based spectral analysis to detect periodic signals; the population-mean cosinor to generalize inferences; the chronobiologic serial section to follow the time course of changing rhythm parameters over time; and parameter tests to assess differences among populations. Relative merits of other available cosinor and non-parametric algorithms are reviewed. Parameter tests to compare individual records and a self-starting cumulative sum (CUSUM) make personalized chronotherapy possible, where the treatment of each patient relies on an N-of-1 design. Methods are illustrated in a few examples relevant to endocrinology, cancer and cardiology. New sensing technology yielding large personal data sets is likely to change the healthcare system. Chronobiologic concepts and methods should become an integral part of these evolving systems.

Water extract of Armillaria mellea (Vahl) P. Kumm. Alleviates the depression-like behaviors in acute- and chronic mild stress-induced rodent models via anti-inflammatory action

ETHNOPHARMACOLOGY RELEVANCE

Armillaria mellea (Vahl) P. Kumm. (AM) is an edible mushroom that has been reported as treatment for several neurological disorders, such as dizziness and epilepsy in Asia. Importantly, AM shares a symbiotic relationship with Gastrodia elata Blume (GE), a medicinal herb with antidepressant-like properties. Researchers believe that AM may possess pharmacological properties similar to GE due to their symbiosis, however, few studies have investigated the pharmacological effect of AM.

AIM OF THE STUDY

The aim of this study was to explore the potential of AM as an antidepressant in forced-swimming test (FST) and unpredictable chronic mild stress (UCMS) rodent models and investigate its possible underlying mechanism.

MATERIALS AND METHODS

Rats were orally administrated with 250, 500, and 1000 mg/kg body weight (bw) water extract of AM (WAM) for 28 and 35 consecutive days prior to the FST and UCMS protocols, respectively. The cerebral serotonin (5-HT) and the metabolites in the frontal cortex of rats were measured. The brain was dissected and the blood was collected to investigate the levels of inflammatory-related signaling pathway.

RESULTS

All doses of WAM reduced the immobility time in the FST without disturbing autonomic locomotion. All doses of WAM prevented stress-induced abnormal behaviors in the UCMS model, including decreased sucrose preference and hypoactivity. 500 and 1000 mg/kg bw WAM attenuated the stress-induced increases in IL-1β and TNF-α in the serum and cerebrum. 1000 mg/kg bw WAM alleviated brain inflammation by reducing the protein expression of ionized calcium binding adaptor molecule 1.

CONCLUSION

WAM exhibited acute and chronic antidepressant-like effects, and may result from the anti-inflammatory actions. Therefore, the development of AM as a dietary therapy or adjuvant for depression treatment should be considered.

A new model for the HPA axis explains dysregulation of stress hormones on the timescale of weeks

Stress activates a complex network of hormones known as the hypothalamic-pituitary-adrenal (HPA) axis. The HPA axis is dysregulated in chronic stress and psychiatric disorders, but the origin of this dysregulation is unclear and cannot be explained by current HPA models. To address this, we developed a mathematical model for the HPA axis that incorporates changes in the total functional mass of the HPA hormone-secreting glands. The mass changes are caused by HPA hormones which act as growth factors for the glands in the axis. We find that the HPA axis shows the property of dynamical compensation, where gland masses adjust over weeks to buffer variation in physiological parameters. These mass changes explain the experimental findings on dysregulation of cortisol and ACTH dynamics in alcoholism, anorexia, and postpartum. Dysregulation occurs for a wide range of parameters and is exacerbated by impaired glucocorticoid receptor (GR) feedback, providing an explanation for the implication of GR in mood disorders. These findings suggest that gland-mass dynamics may play an important role in the pathophysiology of stress-related disorders.

Mathematical Modelling of Endocrine Systems

Hormone rhythms are ubiquitous and essential to sustain normal physiological functions. Combined mathematical modelling and experimental approaches have shown that these rhythms result from regulatory processes occurring at multiple levels of organisation and require continuous dynamic equilibration, particularly in response to stimuli. We review how such an interdisciplinary approach has been successfully applied to unravel complex regulatory mechanisms in the metabolic, stress, and reproductive axes. We discuss how this strategy is likely to be instrumental for making progress in emerging areas such as chronobiology and network physiology. Ultimately, we envisage that the insight provided by mathematical models could lead to novel experimental tools able to continuously adapt parameters to gradual physiological changes and the design of clinical interventions to restore normal endocrine function.

Bridging blood cancers and inflammation: The reduced Cancitis model

A novel mechanism-based model - the Cancitis model - describing the interaction of blood cancer and the inflammatory system is proposed, analyzed and validated. The immune response is divided into two components, one where the elimination rate of malignant stem cells is independent of the level of the blood cancer and one where the elimination rate depends on the level of the blood cancer. A dimensional analysis shows that the full 6-dimensional system of nonlinear ordinary differential equations may be reduced to a 2-dimensional system - the reduced Cancitis model - using Fenichel theory. The original 18 parameters appear in the reduced model in 8 groups of parameters. The reduced model is analyzed. Especially the steady states and their dependence on the exogenous inflammatory stimuli are analyzed. A semi-analytic investigation reveals the stability properties of the steady states. Finally, positivity of the system and the existence of an attracting trapping region in the positive octahedron guaranteeing global existence and uniqueness of solutions are proved. The possible topologies of the dynamical system are completely determined as having a Janus structure, where two qualitatively different topologies appear for different sets of parameters. To classify this Janus structure we propose a novel concept in blood cancer - a reproduction ratio R. It determines the topological structure depending on whether it is larger or smaller than a threshold value. Furthermore, it follows that inflammation, affected by the exogenous inflammatory stimulation, may determine the onset and development of blood cancers. The body may manage initial blood cancer as long as the self-renewal rate is not too high, but fails to manage it if an inflammation appears. Thus, inflammation may trigger and drive blood cancers. Finally, the mathematical analysis suggests novel treatment strategies and it is used to discuss the in silico effect of existing treatment, e.g. interferon-α or T-cell therapy, and the impact of malignant cells becoming resistant.

Nesfatin-1 and cortisol: potential novel diagnostic biomarkers in moderate and severe depressive disorder

Background

This study aimed to determine whether plasma nesfatin-1, cortisol, and inflammatory cytokines could be used as novel noninvasive biomarkers for the diagnosis of moderate and severe depressive disorder (MSDD).

Materials and methods

A total of 70 patients with MSDD and 70 healthy subjects were assessed. Patients with MSDD were selected from Hefei Fourth People’s Hospital, Anhui Mental Health Center, and subjects in the control group were selected from healthy volunteers. Hamilton Depression Rating Scale-17 (HAMD-17) was used to evaluate the two groups. ELISA was used for the measurement of plasma nesfatin-1, cortisol, IL-6, C-reactive protein (CRP), and tumor necrosis factor-α (TNF-α) levels. The diagnostic value of plasma nesfatin-1, cortisol, IL-6, CRP, and TNF-α for MSDD was assessed.

Results

Compared to healthy controls, the HAMD-17 scores and average nesfatin-1, cortisol, IL-6, and CRP levels in patients with MSDD were significantly increased. Moreover, multivariate linear regression analysis showed that HAMD-17 score was positively associated with plasma nesfatin-1 and cortisol. Furthermore, the results of the receiver operating characteristic (ROC) curve analysis revealed an area under curve (AUC) of 0.985 with 94.3% sensitivity and 97.1% specificity of nesfatin-1, and an AUC of 0.957 with 91.4% sensitivity and 85.7% specificity of cortisol in discriminating patients with MSDD from healthy volunteers. A combined ROC analysis using nesfatin-1 and cortisol revealed an AUC of 0.993 with a sensitivity of 97.1% and a specificity of 98.6% in separating patients with MSDD from healthy volunteers.

Conclusion

These results suggest that plasma nesfatin-1 and cortisol might be potential novel biomarkers for the diagnosis of MSDD.

Honokiol Exerts Antidepressant Effects in Rats Exposed to Chronic Unpredictable Mild Stress by Regulating Brain Derived Neurotrophic Factor Level and Hypothalamus-Pituitary-Adrenal Axis Activity

Honokiol (HNK), the main active component of Magnolia officinalis, has shown a variety of pharmacological activities. In the present study, we measured the antidepressant-like effects of HNK in a rat model of chronic unpredictable mild stress (CUMS) and explored its possible mechanisms. The antidepressant-like effects of HNK were assessed in rats by an open field test (OFT), sucrose preference test (SPT) and forced swimming test (FST). Then, serum levels of corticotrophin-releasing hormone (CRH), adrenocorticotropic hormone (ACTH) and corticosterone (CORT) and hippocampal brain-derived neurotrophic factor (BDNF) and glucocorticoid receptor α (GRα) levels were assessed to explore the possible mechanisms. We identified that HNK treatment (2, 4, and 8 mg/kg) alleviated the CUMS-induced behavioural deficits. Treatment with HNK also normalized the CUMS-induced hyperactivity of the limbic hypothalamic-pituitary-adrenal (HPA) axis, as indicated by reduced CRH, ACTH and CORT serum levels. In addition, HNK increased the expression of GRα (mRNA and protein) and BDNF (mRNA and protein) in the hippocampus. These data confirmed the antidepressant-like effects of HNK, which may be related to its normalizing the function of the HPA axis and increasing the BDNF level in the hippocampus.

Perturbing the Hypothalamic-Pituitary-Adrenal Axis: A Mathematical Model for Interpreting PTSD Assessment Tests

We use a dynamical systems model of the hypothalamic-pituitary-adrenal (HPA) axis to understand the mechanisms underlying clinical protocols used to probe patient stress response. Specifically, we address dexamethasone (DEX) and ACTH challenge tests, which probe pituitary and adrenal gland responses, respectively. We show that some previously observed features and experimental responses can arise from a bistable mathematical model containing two steady-states, rather than relying on specific and permanent parameter changes due to physiological disruption. Moreover, we show that the timing of a perturbation relative to the intrinsic oscillation of the HPA axis can affect challenge test responses. Conventional mechanistic hypotheses supported and refuted by the challenge tests are reexamined by varying parameters in our mathematical model associated with these hypotheses. We show that (a) adrenal hyposensitivity can give rise to the responses seen in ACTH challenge tests and (b) enhanced cortisol-mediated suppression of the pituitary in subjects with PTSD is not necessary to explain the responses observed in DEX stress tests. We propose a new two-stage DEX/external stressor protocol to more clearly distinguish between the conventional hypothesis of enhanced suppression of the pituitary and bistable dynamics hypothesized in our model.