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A Mathematical Consideration on the Dix-Hallpike maneuver
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Sung Wan Byun
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J Korean Bal Soc. 2008;7(2):188-192.
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 Abstract
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- Background and Objectives: At the beginning of the Dix-Hallpike maneuver, one of the two functional pair planes of the vertical canals is presumed to lie in the sagittal plane. However, this presumption is not correct. This paper aims to describe this problem more clearly and speculate on clinical implications. Mathematical and theoretical reasoning will be discussed.
Materials and Methods: Two sets, each composed of three perpendicular planes, were modeled for simplified semicircular canals in the anatomical position with a 3D modeler. After a yaw rotation of 45°, the surface normal of the vertical canal plane is compared with that of the true sagittal plane.
Results: The angle between the two normals was approximately 21.1 degrees. The theoretical vertical canal plane did not lie in the sagittal plane at the beginning position of Dix-Hallpike maneuver.
Conclusions: More exact Dix-Hallpike maneuvers may require a roll tilting about 20° toward the affected side.
Key words: Benign paroxysmal positional vertigo, Dix-Hallpike maneuver, Semicircular canals
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Jongkees’ Formula Reevaluated: Mathematical Significance of CP and Negative SCV Value
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Sung Wan Byun
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J Korean Bal Soc. 2005;4(2):238-242.
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Abstract
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- Background
and Objectives: In caloric test, the CP (canal paresis) value was derived from Jongkees formula. The input parameters of the formula were initially nystagmus duration (seconds), which were replaced later with more stable parameters : slow component velocity (SCV, deg/sec). The nystagmus duration cannot be negative value, but SCV can be, especially in acute vestibular loss with excessive spontaneous nystagmus (SN) which is not overcome by caloric nystagmus. This study aims to investigate the occurrence of negative SCV, to check proper processing of negative SCV values in nystagmography software, and to consider the athematical significance of CP and negative SCV values.
Materials and Method: Tests with negative SCV values were examined in 690 alternate binaural bithermal caloric tests (open loop system).
Results
Nine percents (62 of 690 tests) showed negative SCV values. The reported CP was erroneously calculated from debased zero SCV values instead of negative SCV values. The underestimated CP (mean 52.1%, SD 21.8%) can be corrected (mean 80.9%, SD 21.8%) by recalculations with negative SCV values.
Conclusion
To produce correct CP values in caloric tests, negative values should be properly processed about the SCV value of caloric nystagmus with opposite direction of physiologic response. The mathematical significance of CP was horizontal coordinate of intersection point of the warm line (LW-RW) and cold line (LC-RC) in butterfly patterncalorigram. Detailed description is presented in figures.
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