Advertisement

A Comparison of Mathematical Models of Mood in Bipolar Disorder

  • Amy L. CochranEmail author
  • André Schultz
  • Melvin G. McInnis
  • Daniel B. Forger
Chapter
Part of the Springer Series in Bio-/Neuroinformatics book series (SSBN, volume 6)

Abstract

We are far from a comprehensive understanding of the dynamics of mood in bipolar disorder. However, a number of models of mood have emerged to describe the pathological fluctuation in mood that is characteristic of this disorder. These models are surprisingly diverse in their dynamical principles, e.g. whether mood is periodic or whether mania and depression are stable points when ignoring external influences. This chapters presents a selective summary of existing models of mood in bipolar disorder and introduces two new models. We focus on a key question: how to differentiate between models when only time courses of mood are available. For each model we consider, time courses are evaluated through data transformations and statistical techniques, including estimating survival functions and spectral density. We then provide guidelines on how to decide whether a certain modeling assumption, e.g. periodicity, is appropriate.

Keywords

Mixed State Survival Function Autoregressive Model Mood State Stable Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Merikangas, K.R., Jin, R., He, J.P., Kessler, R.C., Lee, S., Sampson, N.A., Viana, M.C., Andrade, L.H., Hu, C., Karam, E.G., et al.: Prevalence and correlates of bipolar spectrum disorder in the world mental health survey initiative. Archives of general psychiatry 68(3), 241–251 (2011)CrossRefGoogle Scholar
  2. 2.
    Goodwin, F.K., Jamison, K.R.: Manic-depressive illness: bipolar disorders and recurrent depression. Oxford University Press (2007)Google Scholar
  3. 3.
    McGuffin, P., Rijsdijk, F., Andrew, M., Sham, P., Katz, R., Cardno, A.: The heritability of bipolar affective disorder and the genetic relationship to unipolar depression. Archives of General Psychiatry 60(5), 497–502 (2003). doi: 10.1001/archpsyc.60.5.497
  4. 4.
    Berrettini, W.: Evidence for shared susceptibility in bipolar disorder and schizophrenia 123(1), 59–64 (2003)Google Scholar
  5. 5.
    Craddock, N., Sklar, P.: Genetics of bipolar disorder. The Lancet 381(9878), 1654–1662 (2013)CrossRefGoogle Scholar
  6. 6.
    Phiel, C.J., Klein, P.S.: Molecular targets of lithium action. Annual review of pharmacology and toxicology 41(1), 789–813 (2001)CrossRefGoogle Scholar
  7. 7.
    Bonsall, M.B., Geddes, J.R., Goodwin, G.M., Holmes, E.A.: Bipolar disorder dynamics: affective instabilities, relaxation oscillations and noise. Journal of The Royal Society Interface 12(112), 20150,670 (2015)Google Scholar
  8. 8.
    Daugherty, D., Roque-Urrea, T., Urrea-Roque, J., Troyer, J., Wirkus, S., Porter, M.A.: Mathematical models of bipolar disorder. Communications in Nonlinear Science and Numerical Simulation 14(7), 2897–2908 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Frank, T.: A limit cycle oscillator model for cycling mood variations of bipolar disorder patients derived from cellular biochemical reaction equations. Communications in Nonlinear Science and Numerical Simulation 18(8), 2107–2119 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Goldbeter, A.: A model for the dynamics of bipolar disorders. Progress in biophysics and molecular biology 105(1), 119–127 (2011)CrossRefGoogle Scholar
  11. 11.
    Nana, L.: Bifurcation analysis of parametrically excited bipolar disorder model. Communications in Nonlinear Science and Numerical Simulation 14(2), 351–360 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Bystritsky, A., Nierenberg, A., Feusner, J., Rabinovich, M.: Computational non-linear dynamical psychiatry: a new methodological paradigm for diagnosis and course of illness. Journal of psychiatric research 46(4), 428–435 (2012)CrossRefGoogle Scholar
  13. 13.
    Steinacher, A., Wright, K.A.: Relating the bipolar spectrum to dysregulation of behavioural activation: A perspective from dynamical modelling. PLoS ONE 8(5), e63345 (2013). doi: 10.1371/journal.pone.0063345
  14. 14.
    Bonnin, C., Sanchez-Moreno, J., Martinez-Aran, A., Solé, B., Reinares, M., Rosa, A., Goikolea, J., Benabarre, A., Ayuso-Mateos, J., Ferrer, M., et al.: Subthreshold symptoms in bipolar disorder: impact on neurocognition, quality of life and disability. Journal of affective disorders 136(3), 650–659 (2012)CrossRefGoogle Scholar
  15. 15.
    Hadaeghi, F., Golpayegani, M.R.H., Murray, G.: Towards a complex system understanding of bipolar disorder: A map based model of a complex winnerless competition. Journal of theoretical biology 376, 74–81 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Kato, T.: The role of mitochondrial dysfunction in bipolar disorder. Drug News Perspect 19(10), 597–602 (2006)CrossRefGoogle Scholar
  17. 17.
    Murray, G., Harvey, A.: Circadian rhythms and sleep in bipolar disorder. Bipolar disorders 12(5), 459–472 (2010)CrossRefGoogle Scholar
  18. 18.
    Kaladchibachi, S.A., Doble, B., Anthopoulos, N., Woodgett, J.R., Manoukian, A.S.: Glycogen synthase kinase 3, circadian rhythms, and bipolar disorder: a molecular link in the therapeutic action of lithium. Journal of Circadian Rhythms 5(1), 3 (2007)CrossRefGoogle Scholar
  19. 19.
    Alloy, L.B., Abramson, L.Y.: The role of the behavioral approach system (bas) in bipolar spectrum disorders. Current Directions in Psychological Science 19(3), 189–194 (2010)CrossRefGoogle Scholar
  20. 20.
    Carver, C.S., White, T.L.: Behavioral inhibition, behavioral activation, and affective responses to impending reward and punishment: the bis/bas scales. Journal of personality and social psychology 67(2), 319 (1994)CrossRefGoogle Scholar
  21. 21.
    Fan, J.: On markov and hidden markov models with applications to trajectories. Ph.D. thesis, University of Pittsburgh (2015)Google Scholar
  22. 22.
    Lopez, A.: Markov models for longitudinal course of youth bipolar disorder. ProQuest (2008)Google Scholar
  23. 23.
    Bonsall, M.B., Wallace-Hadrill, S.M., Geddes, J.R., Goodwin, G.M., Holmes, E.A.: Nonlinear time-series approaches in characterizing mood stability and mood instability in bipolar disorder. Proceedings of the Royal Society of London B: Biological Sciences 279(1730), 916–924 (2012)CrossRefGoogle Scholar
  24. 24.
    Moore, P.J., Little, M.A., McSharry, P.E., Goodwin, G.M., Geddes, J.R.: Mood dynamics in bipolar disorder. International Journal of Bipolar Disorders 2(1), 11 (2014)CrossRefGoogle Scholar
  25. 25.
    van der Werf, S.Y., Kaptein, K.I., de Jonge, P., Spijker, J., de Graaf, R., Korf, J.: Major depressive episodes and random mood. Archives of general psychiatry 63(5), 509–518 (2006)CrossRefGoogle Scholar
  26. 26.
    LL, J., HS, A., PJ, S., et al: The long-term natural history of the weekly symptomatic status of bipolar i disorder. Archives of General Psychiatry 59(6), 530–537 (2002). doi: 10.1001/archpsyc.59.6.530
  27. 27.
    Trivedi, Madhukar H., et al. “The Inventory of Depressive Symptomatology, Clinician Rating (IDS-C) and Self-Report (IDS-SR), and the Quick Inventory of Depressive Symptomatology, Clinician Rating (QIDS-C) and Self-Report (QIDS-SR) in public sector patients with mood disorders: a psychometric evaluation.” Psychological medicine 34.01 (2004): 73-82.Google Scholar
  28. 28.
    Hartigan, J.A., Hartigan, P.: The dip test of unimodality. The Annals of Statistics pp. 70–84 (1985)Google Scholar
  29. 29.
    Fan, J., et al.: A selective overview of nonparametric methods in financial econometrics. Statistical Science 20(4), 317–337 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Solomon, D.A., Leon, A.C., Coryell, W.H., Endicott, J., Li, C., Fiedorowicz, J.G., Boyken, L., Keller, M.B.: Longitudinal course of bipolar i disorder: duration of mood episodes. Archives of general psychiatry 67(4), 339–347 (2010)CrossRefGoogle Scholar
  31. 31.
    Thomson, D.J.: Spectrum estimation and harmonic analysis. Proceedings of the IEEE 70(9), 1055–1096 (1982)CrossRefGoogle Scholar
  32. 32.
    Loughin, T.M.: A systematic comparison of methods for combining p-values from independent tests. Computational statistics & data analysis 47(3), 467–485 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Thomson, D.J.: Multitaper analysis of nonstationary and nonlinear time series data. Nonlinear and nonstationary signal processing pp. 317–394 (2000)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Amy L. Cochran
    • 1
    Email author
  • André Schultz
    • 2
  • Melvin G. McInnis
    • 1
  • Daniel B. Forger
    • 1
  1. 1.University of MichiganAnn ArborUSA
  2. 2.Rice UniversityHoustonUSA

Personalised recommendations