Light propagation through biological tissue and other diffusive media: theory, solutions, and software. - "SPIE digital library."
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| Format: | Elektronisch E-Book |
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| Sprache: | English |
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Bellingham, Wash. (1000 20th St. Bellingham WA 98225-6705 USA)
SPIE
2010
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| Schriftenreihe: | SPIE Press monograph
193 |
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| Online-Zugang: | DE-1050 Volltext |
| Beschreibung: | This book provides foundational information on modeling light propagation through diffusive media, with special emphasis on biological tissue. A summary of the theoretical background on light propagation through diffusive media is provided with the aid of easy-to-use software designed to calculate the solutions of the diffusion equation Includes bibliographical references and index Acknowledgements -- Disclaimer -- List of Acronyms -- List of Symbols -- 1. Introduction -- References I. THEORY. 2. Scattering and absorption properties of diffusive media -- 2.1. Approach followed in this book -- 2.2. Optical properties of a turbid medium. 2.2.1. Absorption properties; 2.2.2. Scattering properties -- 2.3. Statistical meaning of the optical properties of a turbid medium -- 2.4. Similarity relation and reduced scattering coefficient -- 2.5. Examples of diffusive media -- References 3. The radiative transfer equation and diffusion equation -- 3.1. Quantities used to describe radiative transfer -- 3.2. The radiative transfer equation -- 3.3. The Green's function method -- 3.4. Properties of the radiative transfer equation. 3.4.1. Scaling properties; 3.4.2. Dependence on absorption -- 3.5. Diffusion equation. 3.5.1. The diffusion approximation -- 3.6. Derivation of the diffusion equation -- 3.7. Diffusion coefficient -- 3.8. Properties of the diffusion equation. 3.8.1. Scaling properties; 3.8.2. Dependence on absorption -- 3.9. Boundary conditions. 3.9.1. Boundary conditions at the interface between diffusive and non-scattering media; 3.9.2. Boundary conditions at the interface between two diffusive media -- References II. SOLUTIONS. 4. Solutions of the diffusion equation for homogeneous media -- 4.1. Solution of the diffusion equation for an infinite medium -- 4.2. Solution of the diffusion equation for the slab geometry -- 4.3. Analytical Green's functions for transmittance and reflectance -- 4.4. Other solutions for the outgoing flux -- 4.5. Analytical Green's function for the parallelepiped -- 4.6. Analytical Green's function for the infinite cylinder -- 4.7. Analytical Green's function for the sphere -- 4.8. Angular dependence of radiance outgoing from a diffusive medium -- References 5. Hybrid solutions of the radiative transfer equation -- 5.1. General hybrid approach to the solutions for the slab geometry -- 5.2. Analytical solutions of the time-dependent radiative transfer equation for an infinite homogeneous medium. 5.2.1. Almost exact time-resolved Green's function of the radiative transfer equation for an infinite medium with isotropic scattering; 5.2.2. Heuristic time-resolved Green's function of the radiative transfer equation for an infinite medium with non-isotropic scattering; 5.2.3. Time-resolved Green's function of the telegrapher equation for an infinite medium -- 5.3. Comparison of the hybrid models based on the radiative transfer equation and telegrapher equation with the solution of the diffusion equation -- References 6. The diffusion equation for layered media -- 6.1. Photon migration through layered media -- 6.2. Initial and boundary value problems for parabolic equations -- 6.3. Solution of the DE for a two-layer cylinder -- 6.4. Examples of reflectance and transmittance of a layered medium -- 6.5. General property of light re-emitted by a diffusive medium. 6.5.1. Mean time of flight in a generic layer of a homogeneous Cylinder; 6.5.2. Mean time of flight in a two-layer cylinder; 6.5.3. Penetration depth in a homogeneous medium; 6.5.4. Conclusion -- References 7. Solutions of the diffusion equation with perturbation theory -- 7.1. Perturbation theory in a diffusive medium and the born approximation -- 7.2. Perturbation theory: solutions for the infinite medium. 7.2.1. Examples of perturbation for the infinite medium -- 7.3. Perturbation theory: solutions for the slab. 7.3.1. Examples of perturbation for the slab -- 7.4. Perturbation approach for hybrid models -- 7.5. Perturbation approach for the layered slab and for other geometries -- 7.6. Absorption perturbation by use of the internal pathlength moments -- References III. SOFTWARE AND ACCURACY OF SOLUTIONS. 8. Software -- 8.1. Introduction -- 8.2. The diffusion&perturbation program -- 8.3. Source code: solutions of the diffusion equation and hybrid models. 8.3.1. Solutions of the diffusion equation for homogeneous media; 8.3.2. Solutions of the diffusion equation for layered media; 8.3.3. Hybrid models for the homogeneous infinite medium; 8.3.4. Hybrid models for the homogeneous slab; 8.3.5. Hybrid models for the homogeneous parallelepiped; 8.3.6. General purpose subroutines and functions -- References 9. Reference Monte Carlo results -- 9.1. Introduction -- 9.2. Rules to simulate the trajectories and general remarks -- 9.3. Monte Carlo program for the infinite homogeneous medium -- 9.4. Monte Carlo programs for the homogeneous and the layered slab -- 9.5. Monte Carlo code for the slab containing an inhomogeneity -- 9.6. Description of the Monte Carlo results reported in the CD-ROM. 9.6.1. Homogeneous infinite medium; 9.6.2. Homogeneous slab; 9.6.3. Layered slab; 9.6.4. Perturbation due to inhomogeneities inside the homogeneous slab -- References 10. Comparisons of analytical solutions with Monte Carlo results -- 10.1. Introduction -- 10.2. Comparisons between Monte Carlo and the diffusion equation: homogeneous medium. 10.2.1. Infinite homogeneous medium; 10.2.2. Homogeneous slab -- 10.3. Comparison between Monte Carlo and the diffusion equation: homogeneous slab with an internal inhomogeneity -- 10.4. Comparisons between Monte Carlo and the diffusion equation: layered slab -- 10.5. Comparisons between Monte Carlo and hybrid models. 10.5.1. Infinite homogeneous medium; 10.5.2. Slab geometry -- 10.6. Outgoing flux: comparison between Fick and extrapolated boundary partial current approaches -- 10.7. Conclusions. 10.7.1. Infinite medium; 10.7.2. Homogeneous slab; 10.7.3. Layered slab; 10.7.4. Slab with inhomogeneities inside; 10.7.5. Diffusive media -- References Appendix A: The first simplifying assumption of the diffusion approximation -- Appendix B: Fick's law -- Appendix C: Boundary conditions at the interface between diffusive and non-scattering media -- Appendix D: Boundary conditions at the interface between two diffusive media -- Appendix E: Green's function of the diffusion equation in an infinite homogeneous medium -- Appendix F: Temporal integration of the time-dependent Green's function -- Appendix G: Eigenfunction expansion -- Appendix H: Green's function of the diffusion equation for the homogeneous cube obtained with the Eigenfunction method -- Appendix I: Expression for the normalizing factor -- References -- Index |
| Beschreibung: | 1 Online-Ressource (1 online resource (xxii, 274 p. ill.) S.) |
| ISBN: | 0819476587 9780819476586 9780819481832 |
| DOI: | 10.1117/3.824746 |
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| 245 | 1 | 0 | |a Light propagation through biological tissue and other diffusive media |b theory, solutions, and software. - "SPIE digital library." |c Fabrizio Martelli ... [et al.] |
| 264 | 1 | |a Bellingham, Wash. (1000 20th St. Bellingham WA 98225-6705 USA) |b SPIE |c 2010 | |
| 300 | |a 1 Online-Ressource (1 online resource (xxii, 274 p. |b ill.) S.) | ||
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| 490 | 1 | |a SPIE Press monograph |v PM193 | |
| 500 | |a This book provides foundational information on modeling light propagation through diffusive media, with special emphasis on biological tissue. A summary of the theoretical background on light propagation through diffusive media is provided with the aid of easy-to-use software designed to calculate the solutions of the diffusion equation | ||
| 500 | |a Includes bibliographical references and index | ||
| 500 | |a Acknowledgements -- Disclaimer -- List of Acronyms -- List of Symbols -- 1. Introduction -- References | ||
| 500 | |a I. THEORY. 2. Scattering and absorption properties of diffusive media -- 2.1. Approach followed in this book -- 2.2. Optical properties of a turbid medium. 2.2.1. Absorption properties; 2.2.2. Scattering properties -- 2.3. Statistical meaning of the optical properties of a turbid medium -- 2.4. Similarity relation and reduced scattering coefficient -- 2.5. Examples of diffusive media -- References | ||
| 500 | |a 3. The radiative transfer equation and diffusion equation -- 3.1. Quantities used to describe radiative transfer -- 3.2. The radiative transfer equation -- 3.3. The Green's function method -- 3.4. Properties of the radiative transfer equation. 3.4.1. Scaling properties; 3.4.2. Dependence on absorption -- 3.5. Diffusion equation. 3.5.1. The diffusion approximation -- 3.6. Derivation of the diffusion equation -- 3.7. Diffusion coefficient -- 3.8. Properties of the diffusion equation. 3.8.1. Scaling properties; 3.8.2. Dependence on absorption -- 3.9. Boundary conditions. 3.9.1. Boundary conditions at the interface between diffusive and non-scattering media; 3.9.2. Boundary conditions at the interface between two diffusive media -- References | ||
| 500 | |a II. SOLUTIONS. 4. Solutions of the diffusion equation for homogeneous media -- 4.1. Solution of the diffusion equation for an infinite medium -- 4.2. Solution of the diffusion equation for the slab geometry -- 4.3. Analytical Green's functions for transmittance and reflectance -- 4.4. Other solutions for the outgoing flux -- 4.5. Analytical Green's function for the parallelepiped -- 4.6. Analytical Green's function for the infinite cylinder -- 4.7. Analytical Green's function for the sphere -- 4.8. Angular dependence of radiance outgoing from a diffusive medium -- References | ||
| 500 | |a 5. Hybrid solutions of the radiative transfer equation -- 5.1. General hybrid approach to the solutions for the slab geometry -- 5.2. Analytical solutions of the time-dependent radiative transfer equation for an infinite homogeneous medium. 5.2.1. Almost exact time-resolved Green's function of the radiative transfer equation for an infinite medium with isotropic scattering; 5.2.2. Heuristic time-resolved Green's function of the radiative transfer equation for an infinite medium with non-isotropic scattering; 5.2.3. Time-resolved Green's function of the telegrapher equation for an infinite medium -- 5.3. Comparison of the hybrid models based on the radiative transfer equation and telegrapher equation with the solution of the diffusion equation -- References | ||
| 500 | |a 6. The diffusion equation for layered media -- 6.1. Photon migration through layered media -- 6.2. Initial and boundary value problems for parabolic equations -- 6.3. Solution of the DE for a two-layer cylinder -- 6.4. Examples of reflectance and transmittance of a layered medium -- 6.5. General property of light re-emitted by a diffusive medium. 6.5.1. Mean time of flight in a generic layer of a homogeneous Cylinder; 6.5.2. Mean time of flight in a two-layer cylinder; 6.5.3. Penetration depth in a homogeneous medium; 6.5.4. Conclusion -- References | ||
| 500 | |a 7. Solutions of the diffusion equation with perturbation theory -- 7.1. Perturbation theory in a diffusive medium and the born approximation -- 7.2. Perturbation theory: solutions for the infinite medium. 7.2.1. Examples of perturbation for the infinite medium -- 7.3. Perturbation theory: solutions for the slab. 7.3.1. Examples of perturbation for the slab -- 7.4. Perturbation approach for hybrid models -- 7.5. Perturbation approach for the layered slab and for other geometries -- 7.6. Absorption perturbation by use of the internal pathlength moments -- References | ||
| 500 | |a III. SOFTWARE AND ACCURACY OF SOLUTIONS. 8. Software -- 8.1. Introduction -- 8.2. The diffusion&perturbation program -- 8.3. Source code: solutions of the diffusion equation and hybrid models. 8.3.1. Solutions of the diffusion equation for homogeneous media; 8.3.2. Solutions of the diffusion equation for layered media; 8.3.3. Hybrid models for the homogeneous infinite medium; 8.3.4. Hybrid models for the homogeneous slab; 8.3.5. Hybrid models for the homogeneous parallelepiped; 8.3.6. General purpose subroutines and functions -- References | ||
| 500 | |a 9. Reference Monte Carlo results -- 9.1. Introduction -- 9.2. Rules to simulate the trajectories and general remarks -- 9.3. Monte Carlo program for the infinite homogeneous medium -- 9.4. Monte Carlo programs for the homogeneous and the layered slab -- 9.5. Monte Carlo code for the slab containing an inhomogeneity -- 9.6. Description of the Monte Carlo results reported in the CD-ROM. 9.6.1. Homogeneous infinite medium; 9.6.2. Homogeneous slab; 9.6.3. Layered slab; 9.6.4. Perturbation due to inhomogeneities inside the homogeneous slab -- References | ||
| 500 | |a 10. Comparisons of analytical solutions with Monte Carlo results -- 10.1. Introduction -- 10.2. Comparisons between Monte Carlo and the diffusion equation: homogeneous medium. 10.2.1. Infinite homogeneous medium; 10.2.2. Homogeneous slab -- 10.3. Comparison between Monte Carlo and the diffusion equation: homogeneous slab with an internal inhomogeneity -- 10.4. Comparisons between Monte Carlo and the diffusion equation: layered slab -- 10.5. Comparisons between Monte Carlo and hybrid models. 10.5.1. Infinite homogeneous medium; 10.5.2. Slab geometry -- 10.6. Outgoing flux: comparison between Fick and extrapolated boundary partial current approaches -- 10.7. Conclusions. 10.7.1. Infinite medium; 10.7.2. Homogeneous slab; 10.7.3. Layered slab; 10.7.4. Slab with inhomogeneities inside; 10.7.5. Diffusive media -- References | ||
| 500 | |a Appendix A: The first simplifying assumption of the diffusion approximation -- Appendix B: Fick's law -- Appendix C: Boundary conditions at the interface between diffusive and non-scattering media -- Appendix D: Boundary conditions at the interface between two diffusive media -- Appendix E: Green's function of the diffusion equation in an infinite homogeneous medium -- Appendix F: Temporal integration of the time-dependent Green's function -- Appendix G: Eigenfunction expansion -- Appendix H: Green's function of the diffusion equation for the homogeneous cube obtained with the Eigenfunction method -- Appendix I: Expression for the normalizing factor -- References -- Index | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Light / Transmission / Mathematical models | |
| 650 | 4 | |a Tissues / Optical properties | |
| 700 | 1 | |a Martelli, Fabrizio |d 1969- |e Sonstige |0 (DE-588)1286927714 |4 oth | |
| 830 | 0 | |a SPIE Press monograph |v 193 |w (DE-604)BV043195265 |9 193 | |
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| 912 | |a ZDB-50-SPI | ||
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-020543067 | |
| 966 | e | |u https://doi.org/10.1117/3.824746 |l DE-1050 |p ZDB-50-SPI |x Verlag |3 Volltext | |
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| indexdate | 2024-10-11T04:00:07Z |
| institution | BVB |
| isbn | 0819476587 9780819476586 9780819481832 |
| language | English |
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| series | SPIE Press monograph |
| series2 | SPIE Press monograph |
| spelling | Light propagation through biological tissue and other diffusive media theory, solutions, and software. - "SPIE digital library." Fabrizio Martelli ... [et al.] Bellingham, Wash. (1000 20th St. Bellingham WA 98225-6705 USA) SPIE 2010 1 Online-Ressource (1 online resource (xxii, 274 p. ill.) S.) txt rdacontent c rdamedia cr rdacarrier SPIE Press monograph PM193 This book provides foundational information on modeling light propagation through diffusive media, with special emphasis on biological tissue. A summary of the theoretical background on light propagation through diffusive media is provided with the aid of easy-to-use software designed to calculate the solutions of the diffusion equation Includes bibliographical references and index Acknowledgements -- Disclaimer -- List of Acronyms -- List of Symbols -- 1. Introduction -- References I. THEORY. 2. Scattering and absorption properties of diffusive media -- 2.1. Approach followed in this book -- 2.2. Optical properties of a turbid medium. 2.2.1. Absorption properties; 2.2.2. Scattering properties -- 2.3. Statistical meaning of the optical properties of a turbid medium -- 2.4. Similarity relation and reduced scattering coefficient -- 2.5. Examples of diffusive media -- References 3. The radiative transfer equation and diffusion equation -- 3.1. Quantities used to describe radiative transfer -- 3.2. The radiative transfer equation -- 3.3. The Green's function method -- 3.4. Properties of the radiative transfer equation. 3.4.1. Scaling properties; 3.4.2. Dependence on absorption -- 3.5. Diffusion equation. 3.5.1. The diffusion approximation -- 3.6. Derivation of the diffusion equation -- 3.7. Diffusion coefficient -- 3.8. Properties of the diffusion equation. 3.8.1. Scaling properties; 3.8.2. Dependence on absorption -- 3.9. Boundary conditions. 3.9.1. Boundary conditions at the interface between diffusive and non-scattering media; 3.9.2. Boundary conditions at the interface between two diffusive media -- References II. SOLUTIONS. 4. Solutions of the diffusion equation for homogeneous media -- 4.1. Solution of the diffusion equation for an infinite medium -- 4.2. Solution of the diffusion equation for the slab geometry -- 4.3. Analytical Green's functions for transmittance and reflectance -- 4.4. Other solutions for the outgoing flux -- 4.5. Analytical Green's function for the parallelepiped -- 4.6. Analytical Green's function for the infinite cylinder -- 4.7. Analytical Green's function for the sphere -- 4.8. Angular dependence of radiance outgoing from a diffusive medium -- References 5. Hybrid solutions of the radiative transfer equation -- 5.1. General hybrid approach to the solutions for the slab geometry -- 5.2. Analytical solutions of the time-dependent radiative transfer equation for an infinite homogeneous medium. 5.2.1. Almost exact time-resolved Green's function of the radiative transfer equation for an infinite medium with isotropic scattering; 5.2.2. Heuristic time-resolved Green's function of the radiative transfer equation for an infinite medium with non-isotropic scattering; 5.2.3. Time-resolved Green's function of the telegrapher equation for an infinite medium -- 5.3. Comparison of the hybrid models based on the radiative transfer equation and telegrapher equation with the solution of the diffusion equation -- References 6. The diffusion equation for layered media -- 6.1. Photon migration through layered media -- 6.2. Initial and boundary value problems for parabolic equations -- 6.3. Solution of the DE for a two-layer cylinder -- 6.4. Examples of reflectance and transmittance of a layered medium -- 6.5. General property of light re-emitted by a diffusive medium. 6.5.1. Mean time of flight in a generic layer of a homogeneous Cylinder; 6.5.2. Mean time of flight in a two-layer cylinder; 6.5.3. Penetration depth in a homogeneous medium; 6.5.4. Conclusion -- References 7. Solutions of the diffusion equation with perturbation theory -- 7.1. Perturbation theory in a diffusive medium and the born approximation -- 7.2. Perturbation theory: solutions for the infinite medium. 7.2.1. Examples of perturbation for the infinite medium -- 7.3. Perturbation theory: solutions for the slab. 7.3.1. Examples of perturbation for the slab -- 7.4. Perturbation approach for hybrid models -- 7.5. Perturbation approach for the layered slab and for other geometries -- 7.6. Absorption perturbation by use of the internal pathlength moments -- References III. SOFTWARE AND ACCURACY OF SOLUTIONS. 8. Software -- 8.1. Introduction -- 8.2. The diffusion&perturbation program -- 8.3. Source code: solutions of the diffusion equation and hybrid models. 8.3.1. Solutions of the diffusion equation for homogeneous media; 8.3.2. Solutions of the diffusion equation for layered media; 8.3.3. Hybrid models for the homogeneous infinite medium; 8.3.4. Hybrid models for the homogeneous slab; 8.3.5. Hybrid models for the homogeneous parallelepiped; 8.3.6. General purpose subroutines and functions -- References 9. Reference Monte Carlo results -- 9.1. Introduction -- 9.2. Rules to simulate the trajectories and general remarks -- 9.3. Monte Carlo program for the infinite homogeneous medium -- 9.4. Monte Carlo programs for the homogeneous and the layered slab -- 9.5. Monte Carlo code for the slab containing an inhomogeneity -- 9.6. Description of the Monte Carlo results reported in the CD-ROM. 9.6.1. Homogeneous infinite medium; 9.6.2. Homogeneous slab; 9.6.3. Layered slab; 9.6.4. Perturbation due to inhomogeneities inside the homogeneous slab -- References 10. Comparisons of analytical solutions with Monte Carlo results -- 10.1. Introduction -- 10.2. Comparisons between Monte Carlo and the diffusion equation: homogeneous medium. 10.2.1. Infinite homogeneous medium; 10.2.2. Homogeneous slab -- 10.3. Comparison between Monte Carlo and the diffusion equation: homogeneous slab with an internal inhomogeneity -- 10.4. Comparisons between Monte Carlo and the diffusion equation: layered slab -- 10.5. Comparisons between Monte Carlo and hybrid models. 10.5.1. Infinite homogeneous medium; 10.5.2. Slab geometry -- 10.6. Outgoing flux: comparison between Fick and extrapolated boundary partial current approaches -- 10.7. Conclusions. 10.7.1. Infinite medium; 10.7.2. Homogeneous slab; 10.7.3. Layered slab; 10.7.4. Slab with inhomogeneities inside; 10.7.5. Diffusive media -- References Appendix A: The first simplifying assumption of the diffusion approximation -- Appendix B: Fick's law -- Appendix C: Boundary conditions at the interface between diffusive and non-scattering media -- Appendix D: Boundary conditions at the interface between two diffusive media -- Appendix E: Green's function of the diffusion equation in an infinite homogeneous medium -- Appendix F: Temporal integration of the time-dependent Green's function -- Appendix G: Eigenfunction expansion -- Appendix H: Green's function of the diffusion equation for the homogeneous cube obtained with the Eigenfunction method -- Appendix I: Expression for the normalizing factor -- References -- Index Mathematisches Modell Light / Transmission / Mathematical models Tissues / Optical properties Martelli, Fabrizio 1969- Sonstige (DE-588)1286927714 oth SPIE Press monograph 193 (DE-604)BV043195265 193 https://doi.org/10.1117/3.824746 Verlag Volltext |
| spellingShingle | Light propagation through biological tissue and other diffusive media theory, solutions, and software. - "SPIE digital library." SPIE Press monograph Mathematisches Modell Light / Transmission / Mathematical models Tissues / Optical properties |
| title | Light propagation through biological tissue and other diffusive media theory, solutions, and software. - "SPIE digital library." |
| title_auth | Light propagation through biological tissue and other diffusive media theory, solutions, and software. - "SPIE digital library." |
| title_exact_search | Light propagation through biological tissue and other diffusive media theory, solutions, and software. - "SPIE digital library." |
| title_full | Light propagation through biological tissue and other diffusive media theory, solutions, and software. - "SPIE digital library." Fabrizio Martelli ... [et al.] |
| title_fullStr | Light propagation through biological tissue and other diffusive media theory, solutions, and software. - "SPIE digital library." Fabrizio Martelli ... [et al.] |
| title_full_unstemmed | Light propagation through biological tissue and other diffusive media theory, solutions, and software. - "SPIE digital library." Fabrizio Martelli ... [et al.] |
| title_short | Light propagation through biological tissue and other diffusive media |
| title_sort | light propagation through biological tissue and other diffusive media theory solutions and software spie digital library |
| title_sub | theory, solutions, and software. - "SPIE digital library." |
| topic | Mathematisches Modell Light / Transmission / Mathematical models Tissues / Optical properties |
| topic_facet | Mathematisches Modell Light / Transmission / Mathematical models Tissues / Optical properties |
| url | https://doi.org/10.1117/3.824746 |
| volume_link | (DE-604)BV043195265 |
| work_keys_str_mv | AT martellifabrizio lightpropagationthroughbiologicaltissueandotherdiffusivemediatheorysolutionsandsoftwarespiedigitallibrary |