Fractional Beer-Lambert law in laser heating of biological tissue
In this article we propose an alternative formulation to model a thermal-optical coupled problem involving laser heating. We show that by using the Fractional Beer-Lambert Law (FBLL) instead of the Beer-Lambert Law (BLL) as the governing equation of the optical problem, the formulation of the laser...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022796?viewType=HTML |
| _version_ | 1818231000232099840 |
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| author | Carlos Lizama Marina Murillo-Arcila Macarena Trujillo |
| author_facet | Carlos Lizama Marina Murillo-Arcila Macarena Trujillo |
| author_sort | Carlos Lizama |
| collection | DOAJ |
| description | In this article we propose an alternative formulation to model a thermal-optical coupled problem involving laser heating. We show that by using the Fractional Beer-Lambert Law (FBLL) instead of the Beer-Lambert Law (BLL) as the governing equation of the optical problem, the formulation of the laser heat source changes, along with consequently, the distribution of temperatures. Our theoretical findings apply to laser thermal keratoplasty (LTK), used to reduce diopters of hyperopia. We show that the FBLL offers a new approach for heat conduction modeling of laser heating, which is more flexible and could better fit the data in cases where the BLL approach does not fit the data well. Our results can be extended to laser heating of other biological tissues and in other general applications. Our findings imply a new insight to improve the accuracy of thermal models, since they involve a new formulation of the external heat source rather than the heat equation itself. |
| first_indexed | 2024-12-12T10:43:26Z |
| format | Article |
| id | doaj.art-bd121b744127406682c747054a79f06d |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-12T10:43:26Z |
| publishDate | 2022-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-bd121b744127406682c747054a79f06d2022-12-22T00:26:58ZengAIMS PressAIMS Mathematics2473-69882022-06-0178144441445910.3934/math.2022796Fractional Beer-Lambert law in laser heating of biological tissueCarlos Lizama0Marina Murillo-Arcila1Macarena Trujillo 21. Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencias, Universidad de Santiago de Chile, Santiago, Chile2. Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Valencia, Spain3. BioMIT, Department of Applied Mathematics, Universitat Politècnica de València, Valencia, SpainIn this article we propose an alternative formulation to model a thermal-optical coupled problem involving laser heating. We show that by using the Fractional Beer-Lambert Law (FBLL) instead of the Beer-Lambert Law (BLL) as the governing equation of the optical problem, the formulation of the laser heat source changes, along with consequently, the distribution of temperatures. Our theoretical findings apply to laser thermal keratoplasty (LTK), used to reduce diopters of hyperopia. We show that the FBLL offers a new approach for heat conduction modeling of laser heating, which is more flexible and could better fit the data in cases where the BLL approach does not fit the data well. Our results can be extended to laser heating of other biological tissues and in other general applications. Our findings imply a new insight to improve the accuracy of thermal models, since they involve a new formulation of the external heat source rather than the heat equation itself.https://www.aimspress.com/article/doi/10.3934/math.2022796?viewType=HTMLpartial differential equationsfractional beer-lambert lawlaplace transformthermal therapiesheat equationcorneal laser irradiation |
| spellingShingle | Carlos Lizama Marina Murillo-Arcila Macarena Trujillo Fractional Beer-Lambert law in laser heating of biological tissue AIMS Mathematics partial differential equations fractional beer-lambert law laplace transform thermal therapies heat equation corneal laser irradiation |
| title | Fractional Beer-Lambert law in laser heating of biological tissue |
| title_full | Fractional Beer-Lambert law in laser heating of biological tissue |
| title_fullStr | Fractional Beer-Lambert law in laser heating of biological tissue |
| title_full_unstemmed | Fractional Beer-Lambert law in laser heating of biological tissue |
| title_short | Fractional Beer-Lambert law in laser heating of biological tissue |
| title_sort | fractional beer lambert law in laser heating of biological tissue |
| topic | partial differential equations fractional beer-lambert law laplace transform thermal therapies heat equation corneal laser irradiation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022796?viewType=HTML |
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