Scientific letter
Avoiding misinterpretations of Kappa angle for clinical research studies with Pentacam
Evitar las malinterpretaciones del ángulo Kappa para los estudios de investigación clínica con Pentacam
Manuel Rodríguez-Vallejoa,
, David P. Piñeroc,d, Joaquín Fernándeza,b
Corresponding author
manuelrodriguezid@qvision.es
Corresponding author at: Department of Ophthalmology (Qvision), Vithas Virgen del Mar Hospital, 04120 Almería, Spain.
Corresponding author at: Department of Ophthalmology (Qvision), Vithas Virgen del Mar Hospital, 04120 Almería, Spain.
a Department of Ophthalmology (Qvision), Vithas Virgen del Mar Hospital, 04120 Almería, Spain
b Department of Ophthalmology, Torrecárdenas Hospital Complex, 04009 Almería, Spain
c Department of Optics, Pharmacology and Anatomy, University of Alicante, Alicante, Spain
d Department of Ophthalmology (OFTALMAR), Vithas Medimar International Hospital, Alicante, Spain
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Piñero, Joaquín Fernández" "autores" => array:3 [ 0 => array:4 [ "nombre" => "Manuel" "apellidos" => "Rodríguez-Vallejo" "email" => array:1 [ 0 => "manuelrodriguezid@qvision.es" ] "referencia" => array:2 [ 0 => array:2 [ "etiqueta" => "<span class="elsevierStyleSup">a</span>" "identificador" => "aff0005" ] 1 => array:2 [ "etiqueta" => "<span class="elsevierStyleSup">*</span>" "identificador" => "cor0005" ] ] ] 1 => array:3 [ "nombre" => "David P." "apellidos" => "Piñero" "referencia" => array:2 [ 0 => array:2 [ "etiqueta" => "<span class="elsevierStyleSup">c</span>" "identificador" => "aff0015" ] 1 => array:2 [ "etiqueta" => "<span class="elsevierStyleSup">d</span>" "identificador" => "aff0020" ] ] ] 2 => array:3 [ "nombre" => "Joaquín" "apellidos" => "Fernández" "referencia" => array:2 [ 0 => array:2 [ "etiqueta" => "<span class="elsevierStyleSup">a</span>" "identificador" => "aff0005" ] 1 => array:2 [ "etiqueta" => "<span class="elsevierStyleSup">b</span>" "identificador" => "aff0010" ] ] ] ] "afiliaciones" => array:4 [ 0 => array:3 [ "entidad" => "Department of Ophthalmology (Qvision), Vithas Virgen del Mar Hospital, 04120 Almería, Spain" "etiqueta" => "a" "identificador" => "aff0005" ] 1 => array:3 [ "entidad" => "Department of Ophthalmology, Torrecárdenas Hospital Complex, 04009 Almería, Spain" "etiqueta" => "b" "identificador" => "aff0010" ] 2 => array:3 [ "entidad" => "Department of Optics, Pharmacology and Anatomy, University of Alicante, Alicante, Spain" "etiqueta" => "c" "identificador" => "aff0015" ] 3 => array:3 [ "entidad" => "Department of Ophthalmology (OFTALMAR), Vithas Medimar International Hospital, Alicante, Spain" "etiqueta" => "d" "identificador" => "aff0020" ] ] "correspondencia" => array:1 [ 0 => array:3 [ "identificador" => "cor0005" "etiqueta" => "⁎" "correspondencia" => "Corresponding author at: Department of Ophthalmology (Qvision), Vithas Virgen del Mar Hospital, 04120 Almería, Spain." ] ] ] ] "titulosAlternativos" => array:1 [ "es" => array:1 [ "titulo" => "Evitar las malinterpretaciones del ángulo Kappa para los estudios de investigación clínica con Pentacam" ] ] "resumenGrafico" => array:2 [ "original" => 0 "multimedia" => array:7 [ "identificador" => "fig0010" "etiqueta" => "Figure 2" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr2.jpeg" "Alto" => 1256 "Ancho" => 2083 "Tamanyo" => 135255 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0010" class="elsevierStyleSimplePara elsevierViewall">Report of pupil center in Pentacam which is the distance from the vertex normal to the pupil center in Cartesian or Polar coordinates.</p>" ] ] ] "textoCompleto" => "<span class="elsevierStyleSections"><p id="par0005" class="elsevierStylePara elsevierViewall">It has been reported that Kappa angle has an important role in laser refractive surgery procedures and implantation of multifocal intraocular lenses.<a class="elsevierStyleCrossRef" href="#bib0075"><span class="elsevierStyleSup">1</span></a> The definition of Kappa angle in the literature is quite confusing because the same angle has been described by different names or the same term has been used to describe 2 different angles.<a class="elsevierStyleCrossRef" href="#bib0080"><span class="elsevierStyleSup">2</span></a> Kappa angle is defined as the angle difference between the visual axis and pupillary axis. Visual axis is a theoretical axis defined as the line connecting the fixation point with the foveola, passing through the two nodal points of the eye.<a class="elsevierStyleCrossRef" href="#bib0085"><span class="elsevierStyleSup">3</span></a> The pupillary axis can be determined locating a source such that the reflected image of this source (when viewed from the source) is centered on the entrance pupil (first Purkinje image over the pupil center).<a class="elsevierStyleCrossRef" href="#bib0085"><span class="elsevierStyleSup">3</span></a> Although the Kappa angle is used commonly in literature, the Lambda angle is really measured as the angle between the pupillary axis and the line of sight, the latter defined as the line joining the fixation point and the pupil center.<a class="elsevierStyleCrossRefs" href="#bib0075"><span class="elsevierStyleSup">1,2</span></a> The reason why Kappa angle term can be used instead of Lambda angle is because visual axis and line of sight are nearly identical when the point of fixation is not very close to the pupil,<a class="elsevierStyleCrossRef" href="#bib0090"><span class="elsevierStyleSup">4</span></a> thus it is commonly accepted to name Kappa angle as the angular difference between line of sight and pupillary axis.<a class="elsevierStyleCrossRefs" href="#bib0075"><span class="elsevierStyleSup">1,4</span></a></p><p id="par0010" class="elsevierStylePara elsevierViewall">Corneal topographers are not centered over the line of sight but are centered over the first Purkinje image, which is the reflected image of the luminous fixation point from the anterior corneal surface also named vertex normal, topographer axis point, or coaxially sighted corneal light reflex if observer (topographer camera) views the eye along the same path as a light source.<a class="elsevierStyleCrossRefs" href="#bib0080"><span class="elsevierStyleSup">2,5</span></a> The distance from the center of the entrance pupil measured by the topographer and the light reflex is neither the lambda angle but it is the distance from vertex normal (topographer axis) to the corneal sighting center (line of sight).<a class="elsevierStyleCrossRefs" href="#bib0090"><span class="elsevierStyleSup">4,6</span></a> The pupillary axis therefore is not measured by corneal topographers and is more temporal to the light reflex and to the corneal sighting center (pupil center shown by the topographer).<a class="elsevierStyleCrossRef" href="#bib0105"><span class="elsevierStyleSup">7</span></a></p><p id="par0015" class="elsevierStylePara elsevierViewall">Early studies reporting Kappa angle with anterior segment devices were conducted with the Orbscan<a class="elsevierStyleCrossRef" href="#bib0110"><span class="elsevierStyleSup">8</span></a> (Bausch & Lomb, Rochester, New York, USA) which defines the Kappa angle as the angle difference between the axis of fixation and the optical axis perpendicular to the lens.<a class="elsevierStyleCrossRef" href="#bib0115"><span class="elsevierStyleSup">9</span></a> This definition neither correspond to the Kappa angle, but corresponds to the distance from optical axis of the lens and the first Purkinje image. <a class="elsevierStyleCrossRef" href="#fig0005">Fig. 1</a> shows the same eye measured with Orbscan IIz (A) and Pentacam HR (B), while Orbscan describes the distance from the first Purkinje image to optical axis of the lens, Pentacam describes just the distance from the first Purkinje image to the pupil center (corneal sighting center or line of sight).</p><elsevierMultimedia ident="fig0005"></elsevierMultimedia><p id="par0020" class="elsevierStylePara elsevierViewall">Prakash et al.<a class="elsevierStyleCrossRef" href="#bib0120"><span class="elsevierStyleSup">10</span></a> suggested that the occurrence of photic phenomenon was related to the Kappa angle measured with Orbscan after implantation of the multifocal intraocular lens. In our opinion, their conclusions should be interpreted with caution because the measure is not really the Kappa angle and previous studies reporting normal distribution of the angle from the Orbscan<a class="elsevierStyleCrossRef" href="#bib0110"><span class="elsevierStyleSup">8</span></a> might not be transferable to other anterior segment devices. Anterior segment imaging devices do not report kappa angle but report a 2-dimensional Cartesian displacement that roughly correlates with the concept of kappa angle.<a class="elsevierStyleCrossRefs" href="#bib0080"><span class="elsevierStyleSup">2,6</span></a> Chang–Waring<a class="elsevierStyleCrossRef" href="#bib0080"><span class="elsevierStyleSup">2</span></a> correctly addressed this issue and proposed the term chord mu (μ) or Chang–Waring chord<a class="elsevierStyleCrossRef" href="#bib0125"><span class="elsevierStyleSup">11</span></a> in order to avoid the misunderstandings generated by the previous literature. Pentacam and other corneal topographers measure the chord mu defined as the distance from the pupil center (line of sight) to the light reflex (topographer axis). Care should be taken by the clinical researcher interpreting the names given by commercial devices because, as we pointed out, Orbscan Kappa angle does not comply with the definition of chord mu. Furthermore, other devices as the iTrace (Tracey Technologies, Houston, TX) use other angles as the alpha angle defined as the distance from vertex normal to center of white to white which is not really the alpha angle whose correct definition is the angle between the optical axis of the eye and the visual axis.<a class="elsevierStyleCrossRef" href="#bib0085"><span class="elsevierStyleSup">3</span></a></p><p id="par0025" class="elsevierStylePara elsevierViewall">Pentacam (Oculus Optikgeräte GmbH, Wetzlar, Germany) is a Scheimpflug imaging device that reports the pupil center distance from the vertex normal as, as far as we know, commonly perform all the topographers. Therefore, it considers the vertex normal as the center of coordinates with negative values for indicating that the pupil is temporal or inferior to the light reflex in the right eye. Conversely, for the left eyes it uses positive values for indicating that the pupil is temporal and the same negative value for inferior location of the pupil center as it is shown in <a class="elsevierStyleCrossRef" href="#fig0010">Fig. 2</a>. Using the vertex normal as the center of coordinates might be confusing for the clinician because traditionally, the light reflex is evaluated considering the center of the pupil as the reference system in such a way that a positive angle is defined as the light reflex nasal to the pupil and a negative angle as the light reflex temporal to the pupil.<a class="elsevierStyleCrossRefs" href="#bib0110"><span class="elsevierStyleSup">8,12</span></a> If this is not specified in the research, the non-expert reader might be confused about the location of the light reflex, believing that it is normally located to temporal<a class="elsevierStyleCrossRef" href="#bib0135"><span class="elsevierStyleSup">13</span></a> instead of nasal.<a class="elsevierStyleCrossRef" href="#bib0140"><span class="elsevierStyleSup">14</span></a> In conclusion, Kappa angle is a term which should not be used with corneal topographers as Pentacam. The term chord mu should be used when reporting offset values between vertex normal and pupil center. Furthermore, a description shall be given as how interpret the values respect to the reference (vertex is reference or pupil is reference) and qualitative features (temporal/nasal, superior/inferior) because corneal topographers do not follow the historical nomenclature used in clinical practice. Special attention should be taken applying statistical analyses with data obtained from right and left eyes directly exported from corneal topographers because the coordinates system of one of the eyes should be flipped before combining all data. The combination of both eyes without applying this conversion can result in errors of interpretation.</p><elsevierMultimedia ident="fig0010"></elsevierMultimedia><span id="sec0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0005">Conflicts of interest</span><p id="par0030" class="elsevierStylePara elsevierViewall">No conflicting relationship exists for any author.</p></span></span>" "textoCompletoSecciones" => array:1 [ "secciones" => array:2 [ 0 => array:2 [ "identificador" => "sec0005" "titulo" => "Conflicts of interest" ] 1 => array:1 [ "titulo" => "References" ] ] ] "pdfFichero" => "main.pdf" "tienePdf" => true "multimedia" => array:2 [ 0 => array:7 [ "identificador" => "fig0005" "etiqueta" => "Figure 1" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr1.jpeg" "Alto" => 2105 "Ancho" => 1583 "Tamanyo" => 293742 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0005" class="elsevierStyleSimplePara elsevierViewall">Differences between Orbscan (A) and Pentacam (B). Orbscan reports Kappa angle as the distance from vertex normal to optical axis of the lens.</p>" ] ] 1 => array:7 [ "identificador" => "fig0010" "etiqueta" => "Figure 2" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr2.jpeg" "Alto" => 1256 "Ancho" => 2083 "Tamanyo" => 135255 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0010" class="elsevierStyleSimplePara elsevierViewall">Report of pupil center in Pentacam which is the distance from the vertex normal to the pupil center in Cartesian or Polar coordinates.</p>" ] ] ] "bibliografia" => array:2 [ "titulo" => "References" "seccion" => array:1 [ 0 => array:2 [ "identificador" => "bibs0015" "bibliografiaReferencia" => array:14 [ 0 => array:3 [ "identificador" => "bib0075" "etiqueta" => "1" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Measurement of angle kappa and centration in refractive surgery" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:3 [ 0 => "C.Y. 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| Year/Month | Html | Total | |
|---|---|---|---|
| 2024 October | 115 | 44 | 159 |
| 2024 September | 147 | 104 | 251 |
| 2024 August | 149 | 76 | 225 |
| 2024 July | 183 | 68 | 251 |
| 2024 June | 149 | 85 | 234 |
| 2024 May | 142 | 80 | 222 |
| 2024 April | 131 | 65 | 196 |
| 2024 March | 114 | 65 | 179 |
| 2024 February | 114 | 67 | 181 |
| 2024 January | 112 | 76 | 188 |
| 2023 December | 121 | 61 | 182 |
| 2023 November | 113 | 105 | 218 |
| 2023 October | 106 | 72 | 178 |
| 2023 September | 82 | 85 | 167 |
| 2023 August | 73 | 60 | 133 |
| 2023 July | 103 | 56 | 159 |
| 2023 June | 88 | 59 | 147 |
| 2023 May | 95 | 68 | 163 |
| 2023 April | 78 | 60 | 138 |
| 2023 March | 101 | 59 | 160 |
| 2023 February | 97 | 64 | 161 |
| 2023 January | 81 | 70 | 151 |
| 2022 December | 135 | 63 | 198 |
| 2022 November | 105 | 61 | 166 |
| 2022 October | 133 | 36 | 169 |
| 2022 September | 103 | 45 | 148 |
| 2022 August | 92 | 46 | 138 |
| 2022 July | 80 | 34 | 114 |
| 2022 June | 73 | 31 | 104 |
| 2022 May | 92 | 21 | 113 |
| 2022 April | 97 | 31 | 128 |
| 2022 March | 118 | 60 | 178 |
| 2022 February | 201 | 28 | 229 |
| 2022 January | 214 | 47 | 261 |
| 2021 December | 139 | 31 | 170 |
| 2021 November | 163 | 46 | 209 |
| 2021 October | 147 | 67 | 214 |
| 2021 September | 148 | 50 | 198 |
| 2021 August | 151 | 68 | 219 |
| 2021 July | 140 | 60 | 200 |
| 2021 June | 185 | 69 | 254 |
| 2021 May | 153 | 132 | 285 |
| 2021 April | 962 | 243 | 1205 |
| 2021 March | 372 | 99 | 471 |
| 2021 February | 161 | 36 | 197 |
| 2021 January | 230 | 55 | 285 |
| 2020 December | 225 | 58 | 283 |
| 2020 November | 245 | 62 | 307 |
| 2020 October | 178 | 58 | 236 |
| 2020 September | 224 | 71 | 295 |
| 2020 August | 235 | 48 | 283 |
| 2020 July | 263 | 79 | 342 |
| 2020 June | 273 | 46 | 319 |
| 2020 May | 268 | 70 | 338 |
| 2020 April | 274 | 63 | 337 |
| 2020 March | 318 | 59 | 377 |
| 2020 February | 340 | 42 | 382 |
| 2020 January | 403 | 76 | 479 |
| 2019 December | 449 | 40 | 489 |
| 2019 November | 238 | 52 | 290 |
| 2019 October | 328 | 92 | 420 |
| 2019 September | 249 | 169 | 418 |
| 2019 August | 237 | 153 | 390 |
| 2019 July | 170 | 161 | 331 |
| 2019 June | 263 | 173 | 436 |
| 2019 May | 292 | 167 | 459 |
| 2019 April | 304 | 197 | 501 |
| 2019 March | 174 | 127 | 301 |
| 2019 February | 143 | 47 | 190 |
| 2019 January | 150 | 66 | 216 |
| 2018 December | 144 | 71 | 215 |
| 2018 November | 173 | 71 | 244 |
| 2018 October | 174 | 64 | 238 |
| 2018 September | 84 | 16 | 100 |
| 2018 July | 1 | 1 | 2 |
| 2018 May | 0 | 22 | 22 |
| 2018 April | 0 | 30 | 30 |
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