Bulletin of Mathematical Biology

, Volume 66, Issue 4, pp 791–808 | Cite as

A simplified physical model of pressure wave dynamics and acoustic wave generation induced by laser absorption in the retina



Shock waves have been proposed in the literature as a mechanism for retinal damage induced by ultra-short laser pulses. For a spherical absorber, we derive a set of linear equations describing the propagation of pressure waves. We show that the formation of shock fronts is due to the form of the absorber rather than the inclusion of nonlinear terms in the equations. The analytical technique used avoids the need for a Laplace transform approach and is easily applied to other absorber profiles. Our analysis suggests that the ’soft’ nature of the membrane surrounding retinal melanosomes precludes shock waves as a mechanism for the retinal damage induced by ultra-short pulse lasers. The quantitative estimates of the pressure gradients induced by laser absorption which are made possible by this work, together with detailed meso-scale or molecular modelling, will allow alternative damage mechanisms to be identified.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Brinkman, R., G. Huttmann, J. Rogener, J. Roider, R. Birngruber and C. P. Lin (2000). Origin of retinal pigment epithelium cell damage by pulsed laser irradiance in the nanosecond to microsecond time regimen. Lasers Surg. Med. 27, 451–464.CrossRefGoogle Scholar
  2. Jacques, S. L. and D. J. McAuliffe (1991). The melanosome—threshold temperature for explosive vaporization and internal absorption-coefficient during pulsed laser irradiation. Photochem. Photobiol. 53, 769–775.Google Scholar
  3. Press, W. H., S. A. Teukolsky, W. T. Vetterling and B. P. Flannery (1992). Numerical Recipes, 2nd edn, Cambridge University Press.Google Scholar
  4. Schraermeyer, U. (1996). The intracellular origin of the melanosome in pigment cells. Areview of ultrastructural data. Histol. Histopathol. 11, 445–462.Google Scholar
  5. Sun, J. M. and B. S. Gerstman (1999). Photoacoustic generation for a spherical absorber with impedance mismatch with the surrounding media. Phys. Rev. E 59, 5772–5789.CrossRefGoogle Scholar
  6. Sun, J. M., B. S. Gerstman and B. Li (2000). Bubble dynamics and shockwaves generated by laser absorption of a photoacoustic sphere. J. Appl. Phys. 88, 2352–2362.CrossRefGoogle Scholar
  7. Thompson, C. R., B. S. Gerstman, S. L. Jacques and M. E. Rogers (1996). Melanin granule model for laser-induced thermal damage in the retina. Bull. Math. Biol. 58, 513–533.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2004

Authors and Affiliations

  1. 1.Defence Science and Technology LaboratoryMalvern, WorcestershireUK
  2. 2.Department of PhysicsUniversity of WarwickCoventryUK

Personalised recommendations