Mathematical models of bipolar disorder
We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin wit...
| Main Authors: | , , , , , |
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| Format: | Journal article |
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Elsevier
2009
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| _version_ | 1797105338387791872 |
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| author | Daugherty, D Roque-Urrea, T Urrea-Roque, J Troyer, J Wirkus, S Porter, M |
| author_facet | Daugherty, D Roque-Urrea, T Urrea-Roque, J Troyer, J Wirkus, S Porter, M |
| author_sort | Daugherty, D |
| collection | OXFORD |
| description | We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here. |
| first_indexed | 2024-03-07T06:46:05Z |
| format | Journal article |
| id | oxford-uuid:fae4d28e-f7aa-4769-b4a5-8e4f855f2b76 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:46:05Z |
| publishDate | 2009 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:fae4d28e-f7aa-4769-b4a5-8e4f855f2b762022-03-27T13:09:45ZMathematical models of bipolar disorderJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fae4d28e-f7aa-4769-b4a5-8e4f855f2b76Mathematical Institute - ePrintsElsevier2009Daugherty, DRoque-Urrea, TUrrea-Roque, JTroyer, JWirkus, SPorter, MWe use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here. |
| spellingShingle | Daugherty, D Roque-Urrea, T Urrea-Roque, J Troyer, J Wirkus, S Porter, M Mathematical models of bipolar disorder |
| title | Mathematical models of bipolar disorder |
| title_full | Mathematical models of bipolar disorder |
| title_fullStr | Mathematical models of bipolar disorder |
| title_full_unstemmed | Mathematical models of bipolar disorder |
| title_short | Mathematical models of bipolar disorder |
| title_sort | mathematical models of bipolar disorder |
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