{"title":"A trilogy of the oculomotor system: Part I: Ocular movements, finalities, and measurements.","authors":"Harley E A Bicas","doi":"10.5935/0004-2749.2024-0194","DOIUrl":null,"url":null,"abstract":"<p><p>The paper starts discussing the teleological concept that eye motions - rotations and translations - serve to vision (which supports the notion that torsions are not voluntarily driven, since they do not contribute to expand the visual exploration of space). It proposes that the primary position of the eye (not \"of gaze\") , the standard condition to measure them, must be defined as the coincidence of the orbital (fixed) and the ocular (movable) system of coordinates. However this becomes only a theoretic concept, since practical operations to obtain it are almost unfeasible. Besides, even a \"simple\" horizontal or vertical ocular rotation, though always occurring around a (presumably) fixed point (the center of ocular rotation) may be defined by different trajectories and magnitudes, depending on the two systems of measurement of eye positions and motions. Hence, in a graphical (plane) representation of such spherical coordinates, the so-called \"tangent screen\", an ocular \"tertiary\" position - a combination of a horizontal and a vertical rotations - may be described by four different points. Or, conversely, a specific eye position may be defined by four sets of angular coordinates. The mathematical representation of variation of three special coordinates in a specific rotation is best made by a matrix disposition, so that, multiplication (not commutative) of three matrices (one for each specific plane) generates six different systems (permutations) of measurements. So, though , actually, there are multiple trajectories possible between two points in space, the order in which rotations are considered influences the final result. With different systems of coordinates for each rotation and different possible orders by which they may be considered, one reaches 48 alternative systems for their measurements. Unfortunately, up to now, there I is no an established convention to express ocular rotations. So, usually, people consider that a vertical prism superimposed to a frontally placed horizontal prism, or vice-versa, correspond to equivalent processes. The paper finishes discussing inconveniences of the clinically used unity to measure eye rotations (the prism-diopter) and proposes other unities as alternative solutions.</p>","PeriodicalId":8397,"journal":{"name":"Arquivos brasileiros de oftalmologia","volume":"88 1","pages":"e20240194"},"PeriodicalIF":1.1000,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arquivos brasileiros de oftalmologia","FirstCategoryId":"3","ListUrlMain":"https://doi.org/10.5935/0004-2749.2024-0194","RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/1/1 0:00:00","PubModel":"eCollection","JCR":"Q3","JCRName":"OPHTHALMOLOGY","Score":null,"Total":0}
引用次数: 0
Abstract
The paper starts discussing the teleological concept that eye motions - rotations and translations - serve to vision (which supports the notion that torsions are not voluntarily driven, since they do not contribute to expand the visual exploration of space). It proposes that the primary position of the eye (not "of gaze") , the standard condition to measure them, must be defined as the coincidence of the orbital (fixed) and the ocular (movable) system of coordinates. However this becomes only a theoretic concept, since practical operations to obtain it are almost unfeasible. Besides, even a "simple" horizontal or vertical ocular rotation, though always occurring around a (presumably) fixed point (the center of ocular rotation) may be defined by different trajectories and magnitudes, depending on the two systems of measurement of eye positions and motions. Hence, in a graphical (plane) representation of such spherical coordinates, the so-called "tangent screen", an ocular "tertiary" position - a combination of a horizontal and a vertical rotations - may be described by four different points. Or, conversely, a specific eye position may be defined by four sets of angular coordinates. The mathematical representation of variation of three special coordinates in a specific rotation is best made by a matrix disposition, so that, multiplication (not commutative) of three matrices (one for each specific plane) generates six different systems (permutations) of measurements. So, though , actually, there are multiple trajectories possible between two points in space, the order in which rotations are considered influences the final result. With different systems of coordinates for each rotation and different possible orders by which they may be considered, one reaches 48 alternative systems for their measurements. Unfortunately, up to now, there I is no an established convention to express ocular rotations. So, usually, people consider that a vertical prism superimposed to a frontally placed horizontal prism, or vice-versa, correspond to equivalent processes. The paper finishes discussing inconveniences of the clinically used unity to measure eye rotations (the prism-diopter) and proposes other unities as alternative solutions.
期刊介绍:
The ABO-ARQUIVOS BRASILEIROS DE OFTALMOLOGIA (ABO, ISSN 0004-2749 - print and ISSN 1678-2925 - (ABO, ISSN 0004-2749 - print and ISSN 1678-2925 - electronic version), the official bimonthly publication of the Brazilian Council of Ophthalmology (CBO), aims to disseminate scientific studies in Ophthalmology, Visual Science and Health public, by promoting research, improvement and updating of professionals related to the field.