1-030-S-IntraocularGasBubbles

By Brian Winkel

SIMIODE, Cornwall NY USA

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Modeling Scenarios

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Abstract

We offer a mathematical modeling experience using differential equations to model the volume of an intraocular gas bubble used by ophthalmologists to aid the healing of a surgically repaired region of the retina. We ask students to compare the traditional ``empirical'' model used by the ophthalmological profession with  more ``analytic'' models built on first principles and modeled with differential equations by examining the model predictions, after model parameters are estimated, using real patient data.  Finally, we introduce a new way of comparing models,  the Akaike Information Criterion, and apply it to our models.

SPANISH LANGUAGE VERSION  We have placed in Supporting Docs both Student and Teacher Version (LaTeX and PDF Versions) with a Spanish LaTeX Class file, SIMIODE-SPANISH.cls. Names will be x-y-S-Title-StudentVersion-Spanish and x-y--T-Title-TeacherVersion-Spanish.

Cite this work

Researchers should cite this work as follows:

  • Brian Winkel (2015), "1-030-S-IntraocularGasBubbles," https://www.simiode.org/resources/346.

    BibTex | EndNote

Tags

  1. Akaike
  2. develop
  3. directed
  4. error
  5. Excel
  6. eye
  7. intraocular
  8. Mathematica
  9. nonlinear
  10. opthalmology
  11. order
  12. ordinary
  13. parameter
  14. separable
  15. Spanish
  16. surgery

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  • onResources — Method — plgResourcesShare::onResources → /core/plugins/resources/share/share.php:50
  • onResources — Method — plgResourcesCitations::onResources → /core/plugins/resources/citations/citations.php:51
  • onResources — Method — plgResourcesQuestions::onResources → /core/plugins/resources/questions/questions.php:60
  • onResources — Method — plgResourcesWishlist::onResources → /core/plugins/resources/wishlist/wishlist.php:50
  • onResources — Method — plgResourcesFindThisText::onResources → /core/plugins/resources/findthistext/findthistext.php:51
  • onResources — Method — plgResourcesWindowstools::onResources → /core/plugins/resources/windowstools/windowstools.php:235
  • onResources — Method — plgResourcesGooglescholar::onResources → /core/plugins/resources/googlescholar/googlescholar.php:25
  • onResources — Method — plgResourcesOpengraph::onResources → /core/plugins/resources/opengraph/opengraph.php:25
  • onResources — Method — plgResourcesDublincore::onResources → /core/plugins/resources/dublincore/dublincore.php:25
  • onResources — Method — plgResourcesComments::onResources → /app/plugins/resources/comments/comments.php:82
  • onResources — Method — plgResourcesCoins::onResources → /core/plugins/resources/coins/coins.php:25
  • onResourcesSub — Method — plgResourcesGroups::onResourcesSub → /core/plugins/resources/groups/groups.php:45
  • onResourcesSub — Method — plgResourcesRelated::onResourcesSub → /core/plugins/resources/related/related.php:45
  • onResourcesSub — Method — plgResourcesSponsors::onResourcesSub → /core/plugins/resources/sponsors/sponsors.php:45
  • onResourcesSub — Method — plgResourcesWatch::onResourcesSub → /core/plugins/resources/watch/watch.php:46
  • onResourcesSub — Method — plgResourcesCollections::onResourcesSub → /core/plugins/resources/collections/collections.php:31
  • onAfterDispatch — Method — plgSystemMobile::onAfterDispatch → /core/plugins/system/mobile/mobile.php:22
  • onAfterDispatch — Method — plgSystemDebug::onAfterDispatch → /core/plugins/system/debug/debug.php:60
  • onAfterDispatch — Method — PlgSystemHighlight::onAfterDispatch → /core/plugins/system/highlight/highlight.php:25
  • onAfterRender — Method — plgSystemSef::onAfterRender → /core/plugins/system/sef/sef.php:21