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Cited by 52Stress Responses and CortisolAdrenal Hormones and DisordersCircadian rhythm and melatonin

Modeling the hypothalamus-pituitary-adrenal axis: A review and extension

Open access
Hosseinichimeh, Niyousha, Rahmandad, Hazhir, Wittenborn, Andrea K.·2015·Mathematical Biosciences
DOI 10.1016/j.mbs.2015.08.004PMC PMC4568136
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Abstract

Multiple models of the hypothalamus-pituitary-adrenal (HPA) axis have been developed to characterize the oscillations seen in the hormone concentrations and to examine HPA axis dysfunction. We reviewed the existing models, then replicated and compared five of them by finding their correspondence to a dataset consisting of ACTH and cortisol concentrations of 17 healthy individuals. We found that existing models use different feedback mechanisms, vary in the level of details and complexities, and offer inconsistent conclusions. None of the models fit the validation dataset well. Therefore, we re-calibrated the best performing model using partial calibration and extended the model by adding individual fixed effects and an exogenous circadian function. Our estimated parameters reduced the mean absolute percent error significantly and offer a validated reference model that can be used in diverse applications. Our analysis suggests that the circadian and ultradian cycles are not created endogenously by the HPA axis feedbacks, which is consistent with the recent literature on the circadian clock and HPA axis.

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Crossref · 10.1016/j.mbs.2015.08.004

Cites

55 of 55 references verified0 citation errors · 0 not checkable

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Nothing to recompute.

Claims the paper makes

11 of 75 cited sources checked · 7 supported · 1 flagged · accuracy not yet measured

  • Findingown data

    The models by (24), (27), and (25) had MAPE results close to 90% for cortisol.

    “In this case, the models by (24), (27), and (25) underestimated cortisol significantly, thus leading to MAPE results close to 90% which represent an order of magnitude difference between simulations and data.”
    Quote in the paperSubstantial claim1 of 3 sources checked
    • cites [24] Vinther, 2011, The minimal model of the hypothalamic–pituitary–adrenal axis, J. Math. Biol. source
    • cites [27] Andersen, 2013, Mathematical modeling of the hypothalamic–pituitary–adrenal gland (HPA) axis, including hippocampal mechanisms, Math. Biosci. source
    • cites [25] Sriram, 2012, Modeling cortisol dynamics in the neuro-endocrine axis distinguishes normal, depression, and post-traumatic stress disorder (PTSD) in humans, PLoS Comput. Biol. source

      In Results > Parameter estimation (page unavailable), the paper reports good agreement between its predicted and experimental cortisol time series for all three groups, rather than substantial underestimation. It does not report MAPE near 90% or an order-of-magnitude difference between simulations and data. (LLM, conf=0.84)

      Checked by a reasoning model — may be wrong.

      Experimental — accuracy not yet measured
  • Findingcitation

    Previous HPA axis models offer conflicting results on the possibility of getting ultradian and/or circadian oscillations from the structure of the HPA axis itself.

    “Previous models have included different structures, rest on a variety of assumptions, and offer conflicting results on the possibility of getting ultradian and/or circadian oscillations from the structure of the HPA axis itself (24–27).”
    Quote in the paperSubstantial claim1 of 4 sources checked
    • cites [24] Vinther, 2011, The minimal model of the hypothalamic–pituitary–adrenal axis, J. Math. Biol. source
    • cites [25] Sriram, 2012, Modeling cortisol dynamics in the neuro-endocrine axis distinguishes normal, depression, and post-traumatic stress disorder (PTSD) in humans, PLoS Comput. Biol. source
    • cites [26] Jelić, 2005, Mathematical modeling of the hypothalamic–pituitary–adrenal system activity, Math. Biosci. source
    • cites [27] Andersen, 2013, Mathematical modeling of the hypothalamic–pituitary–adrenal gland (HPA) axis, including hippocampal mechanisms, Math. Biosci. source
  • Findingreasoning

    Five models from the literature met the criteria for replication.

    “Five models from the literature fit these criteria (24–27, 30).”
    Quote in the paperSubstantial claim2 of 5 sources checked
    • cites [24] Vinther, 2011, The minimal model of the hypothalamic–pituitary–adrenal axis, J. Math. Biol. source
    • cites [25] Sriram, 2012, Modeling cortisol dynamics in the neuro-endocrine axis distinguishes normal, depression, and post-traumatic stress disorder (PTSD) in humans, PLoS Comput. Biol. source
    • cites [26] Jelić, 2005, Mathematical modeling of the hypothalamic–pituitary–adrenal system activity, Math. Biosci. source
    • cites [27] Andersen, 2013, Mathematical modeling of the hypothalamic–pituitary–adrenal gland (HPA) axis, including hippocampal mechanisms, Math. Biosci. source
    • cites [30] Conrad, 2009, Modeling the hypothalamus–pituitary–adrenal system: homeostasis by interacting positive and negative feedback, J. Biol. Phys. source
  • Findingown data

    The models by (24), (27), and (25) underestimated cortisol significantly.

    “In this case, the models by (24), (27), and (25) underestimated cortisol significantly, thus leading to MAPE results close to 90% which represent an order of magnitude difference between simulations and data.”
    Quote in the paperSubstantial claim1 of 3 sources checked
    • cites [24] Vinther, 2011, The minimal model of the hypothalamic–pituitary–adrenal axis, J. Math. Biol. source
    • cites [27] Andersen, 2013, Mathematical modeling of the hypothalamic–pituitary–adrenal gland (HPA) axis, including hippocampal mechanisms, Math. Biosci. source
    • cites [25] Sriram, 2012, Modeling cortisol dynamics in the neuro-endocrine axis distinguishes normal, depression, and post-traumatic stress disorder (PTSD) in humans, PLoS Comput. Biol. source
  • Findingcitation

    In model (25), dropping the nonlinear elimination terms did not eliminate the circadian oscillation.

    “However, dropping those terms in the model did not eliminate the oscillation.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [25] Sriram, 2012, Modeling cortisol dynamics in the neuro-endocrine axis distinguishes normal, depression, and post-traumatic stress disorder (PTSD) in humans, PLoS Comput. Biol. source

      The Materials and Methods section describes nonlinear Michaelis–Menten elimination in the model, and the Discussion links that kinetics to intrinsic oscillations. Neither section reports what happens when the elimination terms are dropped; searches for their removal and for oscillations without enzymatic degradation found no such test in our copy. Page numbers were not available. (LLM, conf=0.72)

      Experimental — accuracy not yet measured
  • May combine two claims. 36
  • Classified as probably not a substantial claim. 23

  • May combine two claims.

    Premisecitation

    The five replicated models were all deterministic ordinary differential equation models that captured the interactions in the HPA axis and their evolution through time.

    “They were all deterministic ordinary differential equation models that captured the interactions in the HPA axis and their evolution through time.”
    Quote in the paperNot a substantial claim2 of 5 sources checked
    • cites [24] Vinther, 2011, The minimal model of the hypothalamic–pituitary–adrenal axis, J. Math. Biol. source
    • cites [25] Sriram, 2012, Modeling cortisol dynamics in the neuro-endocrine axis distinguishes normal, depression, and post-traumatic stress disorder (PTSD) in humans, PLoS Comput. Biol. source
    • cites [26] Jelić, 2005, Mathematical modeling of the hypothalamic–pituitary–adrenal system activity, Math. Biosci. source
    • cites [27] Andersen, 2013, Mathematical modeling of the hypothalamic–pituitary–adrenal gland (HPA) axis, including hippocampal mechanisms, Math. Biosci. source
    • cites [30] Conrad, 2009, Modeling the hypothalamus–pituitary–adrenal system: homeostasis by interacting positive and negative feedback, J. Biol. Phys. source

      Section 2 (Model) presents a time-dependent system of ordinary differential equations for interacting HPA-axis components, supporting the description of this paper’s model. The paper does not identify five replicated models or establish that all five were deterministic ODE models. (LLM, conf=0.83)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In model (30), the mathematical part showed that the model had a stable equilibrium.

    “The mathematical part of the study showed that the model had a stable equilibrium.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [30] Conrad, 2009, Modeling the hypothalamus–pituitary–adrenal system: homeostasis by interacting positive and negative feedback, J. Biol. Phys. source

  • May combine two claims.

    Premisecitation

    The circadian rhythm exists even at the organ level in culture and at the cellular level.

    “It has been shown that the circadian rhythm exists even at the organ level in the culture and the cellular level (48, 49).”
    Quote in the paperNot a substantial claim1 of 2 sources checked
    • cites [48] Yamazaki, 2000, Resetting central and peripheral circadian oscillators in transgenic rats, Science source
    • cites [49] Yoo, 2004, PERIOD2::LUCIFERASE real-time reporting of circadian dynamics reveals persistent circadian oscillations in mouse peripheral tissues, Proc. Natl. Acad. Sci. USA source

  • Probably not a substantial claim: may not pass S4 (based).

    Findingnone given

    There is no commonly used model of the HPA axis in the field.

    “There is no commonly used model of the HPA axis in the field.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning

    There is limited understanding of the relative validity of HPA axis models, making it difficult to select a model for a new application.

    “Also, there is limited understanding of their relative validity, making it difficult to select a model for a new application.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Findingnone given

    Only one previous study used multiple observations to calibrate the model.

    “Only one of the previous studies used multiple observations to calibrate the model.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: Feeding more observations may improve the existing model.

  • May combine two claims.

    Findingown data

    k2 and w3 values averaged at 0.00521 (stdev 0.002) and 0.0221 (stdev 0.01) respectively across different subjects.

    “Moreover, k2 and w3 values were averaged at 0.00521 (stdev 0.002) and 0.0221 (stdev 0.01) respectively across different subjects.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The model underestimated the cortisol level during the peak time and overestimated it in the afternoon when cortisol was reaching the minimum level.

    “Fitted graphs of the first nine observations in Figure 4 showed that the model underestimated the cortisol level during the peak time and overestimated it in the afternoon when cortisol was reaching the minimum level (see Figure 4.c and 4.g).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The system included no inherent oscillatory modes and these observations were confirmed in multiple simulation experiments.

    “The system included no inherent oscillatory modes and these observations were confirmed in multiple simulation experiments.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    This specification had the lowest AIC, meaning that adding parameters for each individual was worth the additional costs.

    “In addition, this specification had the lowest AIC which meant that adding parameters for each individual was worth the additional costs.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The fifth estimation exercise showed significant deterioration, suggesting that individual variations in exogenous circadian stimulation of cortisol are a critical part of understanding cortisol variations across individuals.

    “The results (Table 5, specification 5) show significant deterioration suggesting that individual variations in exogenous (to HPA) circadian stimulation of cortisol are a critical part of understanding cortisol variations across individuals.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Adding the individual-level circadian rhythm reduced the MAPE to 27.0% and provided a better fit.

    “Adding the individual-level circadian rhythm (Figure 5) reduced the MAPE to 27.0% (Table 5, specification 4) and provided a better fit (Figure 6).”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The measurements are frequent in comparison with the delays involved in the balancing feedback loops.

  • May combine two claims.

    Findingown data

    Our analysis showed that Andersen and colleagues' model is the best available HPA axis model and our extension and procedure for calibration of their model improves the fit.

    “Our analysis showed that Andersen and colleagues’ model is the best available HPA axis model and our extension and procedure for calibration of their model improves the fit.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [27] Andersen, 2013, Mathematical modeling of the hypothalamic–pituitary–adrenal gland (HPA) axis, including hippocampal mechanisms, Math. Biosci. source

  • May combine two claims.

    Findingnone given

    Some of the models that create the ultradian oscillation use physiologically unrealistic parameters or their ACTH level deviates substantially from the data.

    “Some of the models that create the ultradian oscillation use physiologically unrealistic parameters or their ACTH level deviates substantially from the data.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    We calibrated the best-performing model from the literature (27) and improved the MAPE of cortisol by more than 71% using parameter estimation and individual level circadian terms.

    “We calibrated the best-performing model from the literature (27) and improved the MAPE of cortisol by more than 71% using parameter estimation and individual level circadian terms.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [27] Andersen, 2013, Mathematical modeling of the hypothalamic–pituitary–adrenal gland (HPA) axis, including hippocampal mechanisms, Math. Biosci. source

  • May combine two claims.

    Premisereasoning

    When feasible, partial prediction stops the propagation of process noise and provides more accurate parameter estimates.

    “When feasible, this method stops the propagation of the process noise and thus provides more accurate parameter estimates.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [38] Homer, 2012, Partial-model testing as a validation tool for system dynamics (1983), Syst. Dyn. Rev. source

  • May combine two claims.

    Premisecitation

    Partial model calibration, as opposed to calibrating the whole model in one step, shows which part of the model works better and gives more reliable estimates.

    “Moreover, partial model calibration, as opposed to calibrating the whole model in one step, shows which part of the model works better and gives more reliable estimates (38).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [38] Homer, 2012, Partial-model testing as a validation tool for system dynamics (1983), Syst. Dyn. Rev. source

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Interpretationreasoning

    If circadian and ultradian oscillations are externally driven, fitting them to HPA axis models will result in biased parameter estimates, which may reduce the usefulness of the models for other applications.

    “However, if these oscillations are indeed externally driven, trying to fit them to the HPA axis models will result in biased parameter estimates for these models which may reduce the usefulness of the models for other applications.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Theil statistics help reveal the source of errors by breaking the mean squared error into bias, unequal variation, and unequal covariation.

    “Theil statistics help to reveal the source of errors by breaking the mean squared error into three components: bias (Um), unequal variation (Us), and unequal covariation (Uc).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [39] Sterman, 1984, Appropriate summary statistics for evaluating the historical fit of system dynamics models, Dynamica

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisenone given

    MAPE suffers from asymmetry in errors: if simulation predictions are smaller than data, MAPE is capped at 100%, whereas larger simulation values can lead to very large MAPE outcomes.

    “Nevertheless, MAPE suffers from asymmetry in errors: if the simulation predictions are smaller than the data, MAPE is capped at 100%, whereas larger values for simulations can lead to very large MAPE outcomes.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Study design and conductreasoning

    MAPE is the most relevant fit measure for this analysis because data and simulations vary in range and hormone concentration units vary across the selected models.

    “MAPE is most useful when data and simulations vary in their range (e.g., oscillations) and in the absence of the formal likelihood function. In addition, the unit of hormone concentrations varies across the models that we have selected to validate and compare (i.e., mol/dm3 versus ng/ml). Therefore, MAPE is the most relevant fit measure for this analysis.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    Some parameters in Andersen and colleagues' model come from the literature and others are chosen to be mathematically and physiologically relevant.

    “Some of the parameters come from the literature and others are chosen to be mathematically and physiologically relevant.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [27] Andersen, 2013, Mathematical modeling of the hypothalamic–pituitary–adrenal gland (HPA) axis, including hippocampal mechanisms, Math. Biosci. source

  • May combine two claims.

    Premisecitation

    In model (24), with realistic parameter values a unique fixed point exists which is globally stable, so the model is unable to generate ultradian oscillation.

    “The authors showed that with realistic parameter values a unique fixed point exists which is globally stable. Thus, the model is unable to generate ultradian oscillation.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [24] Vinther, 2011, The minimal model of the hypothalamic–pituitary–adrenal axis, J. Math. Biol. source

  • May combine two claims.

    Premisecitation

    Andersen and colleagues' model was developed to investigate the existence of oscillations and they did not resolve the inverse problem to estimate the parameters.

    “Their model was developed to investigate the existence of oscillations and they did not resolve the inverse problem to estimate the parameters.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [27] Andersen, 2013, Mathematical modeling of the hypothalamic–pituitary–adrenal gland (HPA) axis, including hippocampal mechanisms, Math. Biosci. source

  • May combine two claims.

    Premisecitation

    In model (27), the model had a unique fixed point and could not generate any oscillation if physiologically reasonable parameters were used.

    “The model had a unique fixed point and it could not generate any oscillation if physiologically reasonable parameters are used.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [27] Andersen, 2013, Mathematical modeling of the hypothalamic–pituitary–adrenal gland (HPA) axis, including hippocampal mechanisms, Math. Biosci. source

  • May combine two claims.

    Premisecitation

    The degradation rate w3 is 0.009 [1/min], found using the half-life of cortisol concentration reported in the literature.

    “The degradation rate, w3, is 0.009 [1/min] and it is found by using the half-life of the cortisol concentration reported in the literature (8).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [8] Carroll, 2007, Pathophysiology of hypercortisolism in depression, Acta Psychiatr. Scand. source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    In model (26), the model generates ultradian oscillation and circadian oscillation was treated as an external input.

    “The model generates the ultradian oscillation. The circadian oscillation was treated as an external input.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [26] Jelić, 2005, Mathematical modeling of the hypothalamic–pituitary–adrenal system activity, Math. Biosci. source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    There are three stocks (CRH, ACTH, and Cortisol hormones) and three feedbacks from cortisol on CRH and ACTH in (27).

    “There are three stocks (i.e., CRH, ACTH, and Cortisol hormones) and three feedbacks from cortisol on CRH and ACTH in (27) (Figure 2).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [27] Andersen, 2013, Mathematical modeling of the hypothalamic–pituitary–adrenal gland (HPA) axis, including hippocampal mechanisms, Math. Biosci. source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    In model (27), the model can achieve two stable fixed points by perturbing the parameters, with solutions converging to one of the two fixed points depending on initial values.

    “It can achieve two stable fixed points by perturbing the parameters. Solutions converged to one of the two fixed points depending on the initial values.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [27] Andersen, 2013, Mathematical modeling of the hypothalamic–pituitary–adrenal gland (HPA) axis, including hippocampal mechanisms, Math. Biosci. source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisenone given

    AIC helps to select the best model by rewarding goodness of fit while penalizing extra parameters.

    “AIC helps to select the best model by rewarding goodness of fit while penalizing extra parameters.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    The current literature provides additional evidence about alternative sources of these cycles.

    “In fact, the current literature provides additional evidence about those alternative sources (9).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [9] Dickmeis, 2013, The circadian clock and glucocorticoids – interactions across many time scales, Mol. Cell. Endocrinol. source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisenone given

    Circadian rhythms of hormones are synchronized by environmental cues such as light, but they are generated by an endogenous system called the circadian clock.

    “Although circadian rhythms of hormones are synchronized by environmental cues such as light, they are generated by an endogenous system called the circadian clock.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    ρ comes from the literature (27).

    “ρ comes from the literature (27).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [27] Andersen, 2013, Mathematical modeling of the hypothalamic–pituitary–adrenal gland (HPA) axis, including hippocampal mechanisms, Math. Biosci. source

  • May combine two claims.

    Premisecitation

    The circadian clock includes the SCN and cellular clocks in almost all tissues of the body which regulate the system in a hierarchical manner.

    “In sum, the circadian clock includes the SCN and cellular clocks in almost all tissues of the body which regulate the system in a hierarchical manner.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [9] Dickmeis, 2013, The circadian clock and glucocorticoids – interactions across many time scales, Mol. Cell. Endocrinol. source

  • May combine two claims.

    Interpretationown data

    Overall the original model by Anderson and colleagues provides a good match to the causal mechanisms from cortisol to CRH and ACTH and the new calibrations offer limited improvements.

    “Overall the original model by Anderson and colleagues provides a good match to the causal mechanisms from cortisol to CRH and ACTH and the new calibrations offer limited improvements.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [27] Andersen, 2013, Mathematical modeling of the hypothalamic–pituitary–adrenal gland (HPA) axis, including hippocampal mechanisms, Math. Biosci. source

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationreasoning

    Inclusion of individual level circadian terms might improve the fit, but introduce many new free parameters which would risk significant overfit and failure of the optimization algorithm to find a reliable global fit for the more biologically relevant parameters.

    “Inclusion of individual level circadian terms, as we did in the previous part, might improve the fit, but introduce many new free parameters which would risk significant overfit and failure of the optimization algorithm to find a reliable global fit for the more biologically relevant parameters.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premiseown data

    The causal links from cortisol to CRH and ACTH are more complex and include multiple parallel mechanisms.

    “The causal links from cortisol to CRH and ACTH are more complex and include multiple parallel mechanisms.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    In typical circadian oscillations, the hormone is at minimum between 8 p.m. and 4 a.m., increases to maximum between 4 a.m. and 12 p.m., then declines to minimum from 12 p.m. to 8 p.m.

    “In typical circadian oscillations, the hormone is at the minimum level between 8 p.m. and 4 a.m. It increases to a maximum level between 4 a.m. and 12 p.m. then it declines to a minimum level from 12 p.m. to 8 p.m. (8).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [8] Carroll, 2007, Pathophysiology of hypercortisolism in depression, Acta Psychiatr. Scand. source

  • May combine two claims.

    Premisecitation

    The suprachiasmatic nucleus (SCN) of the hypothalamus controls the circadian system, but it is not limited to SCN.

    “The current understanding of the system is that the suprachiasmatic nucleus (SCN) of the hypothalamus controls the circadian system, but it is not limited to SCN (9).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [9] Dickmeis, 2013, The circadian clock and glucocorticoids – interactions across many time scales, Mol. Cell. Endocrinol. source

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given

    The parameters of the circadian function capture individual differences that are not observable, such as daily routines, age, race, and sex.

    “The parameters of the circadian function captures the individual differences that are not observable, such as daily routines, age, race, and sex.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Study design and conductnone given

    To ensure convergence to good solutions for this nonlinear optimization, we conducted 601,326 independent searches from random points on the parameter space.

    “Moreover, to ensure convergence to good solutions for this nonlinear optimization we conducted 601,326 independent searches from random points on the parameter space.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    SCN coordinates the regulation of cellular clocks by sending hormonal and electrical signals.

    “SCN coordinates the regulation of cellular clocks by sending hormonal and electrical signals (50).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [50] Albrecht, 2012, Timing to perfection: the biology of central and peripheral circadian clocks, Neuron source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationnone given

    Improving the quality of the fit between fully endogenous models and healthy human data may not be easy because much of the unexplained variation is due to individual level differences in environmental and genetic variables, which fall outside of the boundary of HPA axis models.

    “Improving the quality of the fit between fully endogenous models and healthy human data may not be easy because much of the unexplained variation is due to individual level differences in environmental and genetic variables, which fall outside of the boundary of HPA axis models.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation

    In the experiment presented in (51), the pituitary was only isolated from the CRH impact and it could interact with the rest of the body.

    “However, in the experiment presented in (51), the pituitary was only isolated from the CRH impact and it could interact with the rest of the body.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [51] Engler, 1990, Studies of the regulation of the hypothalamic–pituitary–adrenal axis in sheep with hypothalamic-pituitary disconnection. II. Evidence for in vivo ultradian hypersecretion of proopiomelanocortin peptides by the isolated anterior and intermediate pituitary, Endocrinology source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    The literature of the circadian clock claims that circadian cycles are regulated by neural signals from the SCN to the PVN of the hypothalamus and by SCN projection to the adrenal gland through the autonomic nervous system.

    “It is also consistent with the literature of the circadian clock (9) which claims that the circadian cycles is regulated by neural signals from the SCN to the PVN of the hypothalamus and by SCN projection to the adrenal gland through the autonomic nervous system.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [9] Dickmeis, 2013, The circadian clock and glucocorticoids – interactions across many time scales, Mol. Cell. Endocrinol. source

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationreasoning

    The parameters related to individualized trends in cortisol would need to be re-calibrated to each subject because the parameters of the circadian function are individual-level.

    “However, the parameters related to individualized trends in cortisol would need to be re-calibrated to each subject because the parameters of the circadian function are individual-level and they would need to be estimated for each particular patient.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning

    We would expect the key parameters highlighted in Table 8 will not change much in such extensions because the underlying mechanisms they represent are unchanged.

    “Nevertheless we would expect the key parameters highlighted in table 8 will not change much in such extensions because the underlying mechanisms they represent are unchanged.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationreasoning

    It is speculated that multiple mechanisms may create the rhythm, and the role of the HPA axis in creating the rhythm endogenously will at best be marginal.

    “So, it is speculated that multiple mechanisms may create the rhythm, and the role of the HPA axis in creating the rhythm endogenously will at best be marginal.”
    Quote in the paperSubstantial claim
48 of 48

  • The authors state this as an assumption.

    Feeding more observations may improve the existing model.

    “Thus, we assumed that feeding more observations may improve the existing model.”

  • The authors state this as an assumption.

    The degradation rate of cortisol reported in the literature is correct.

    “If we assume that the degradation rate of cortisol reported in the literature is correct, only one parameter, k2, is needed to be estimated in part A.”

  • The authors state this as an assumption.

    The measurements are frequent in comparison with the delays involved in the balancing feedback loops.

    “Assuming that the measurements are frequent in comparison with the delays involved in the balancing feedback loops, the equation can be converted to a difference equation:”

  • The paper relies on this without support.

    CRH stimulates ACTH secretion in the pituitary and ACTH causes the adrenal glands to release cortisol.

    “CRH stimulates ACTH secretion in the pituitary and ACTH causes the adrenal glands to release cortisol.”
4 of 4

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Cortisol levels are typically low from 8:00 pm to 4:00 am, peak between 4:00 am and 12:00 pm, and then decline back to minimal levels from 12:00 pm until 8:00 pm.

    “As suggested by Hosseinichimeh et al. (2015) and Carroll et al. (2007), cortisol levels are typically low from 8:00 pm to 4:00 am, peak between 4:00 am and 12:00 pm, and then decline back to minimal levels from 12:00 pm until 8:00 pm.”

    From Model Predictive Controller to Regulate Cortisol Levels in Individuals With Adrenal Insufficiency (2026) · cites this paper as Hosseinichimeh et al. (2015)

  • In Hosseinichimeh et al. meta-analysis, the model proposed by Andersen et al. provides the best overall open loop fits.

    “In recent work by Hosseinichimeh et al. [22], a meta-analysis of five models published before 2015 are performed using the partial prediction method and the authors conclude that the model proposed by Andersen et al. [2] provides the best overall open loop fits.”

    From Patient specific modeling of the HPA axis related to clinical diagnosis of depression (2017) · cites this paper as [22]

Cites

Flagged first, then by citations

Research works printed but not linked: 1

  1. Sterman, 1984, Appropriate summary statistics for evaluating the historical fit of system dynamics models, Dynamica, 10, 51

Cited by

Sorted by citations

Related

Authors
Hosseinichimeh, N., Rahmandad, H., & Wittenborn, A. K.
Affiliations
  • Virginia Tech (US)
  • Massachusetts Institute of Technology (US)
  • Michigan State University (US)
Corresponding author
Hosseinichimeh, Niyousha
ORCID
Venue
Mathematical Biosciences
Publisher
Elsevier BV
Published
2015-10
Volume
268
Pages
52-65
ISSN
0025-5564 (ISSN-L)
DOI
10.1016/j.mbs.2015.08.004
PMC
PMC4568136
OpenAlex
W1474235225
Cited by
51
References
55
Citations by year
2026: 2 · 2025: 1 · 2024: 1 · 2023: 1 · 2022: 6 · 2021: 6 · 2020: 8 · 2019: 5 · 2018: 9 · 2017: 4 · 2016: 7 · 2015: 1
FWCI
0.56
Type
journal article
Language
en
Open access
Licence
www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations
  • Mathematical Biosciences (publishedVersion)
  • PubMed (publishedVersion)
  • Europe PMC (PubMed Central) (acceptedVersion)
  • PubMed Central (acceptedVersion)
  • DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc-nd)
  • PMC
Funders
  • National Institutes of Health
  • National Institute of Mental Health (R21MH100515)
Topics
  • Life Sciences › Neuroscience › Behavioral Neuroscience › Stress Responses and Cortisol
  • Health Sciences › Medicine › Endocrinology, Diabetes and Metabolism › Adrenal Hormones and Disorders
  • Life Sciences › Neuroscience › Endocrine and Autonomic Systems › Circadian rhythm and melatonin
Keywords
hypothalamic-pituitary-adrenal axis, ACTH, cortisol, feedback mechanisms, circadian rhythm, ultradian rhythms, model calibration, individual fixed effects, mathematical model validation, HPA axis dysregulation
MeSH terms
Humans, Hypothalamo-Hypophyseal System, Models, Biological, Pituitary-Adrenal System

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-12.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-12.

Cited sources are checked by gpt-6-sol.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

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