2. Numerical Simulations of Laser-Tissue Interactions Shannon M. Mandel Sophomore Intense Laser Physics Theory Unit Illinois State University Supervisor : Dr. H. Wanare

3. Examples of diffusive random media  Biological Tissue Diagnostics of cancerous tissue Radiation therapy  Water and Air Atmospheric studies and oceanography Communications Remote sensing Pollution studies  Earth Geological studies Propagation of pressure waves Electromagnetic & acoustic probing

4. Our Interest How does light interact with a diffusive random medium like a tissue?  Tumors are hidden inside the tissue tumor

5. Properties of Random media Index of refraction n(r) characterizes any medium Homogeneous media Inhomogeneous media Continuous n(r) Discontinuous n(r)

6. High Scattering versus High Absorption Both phenomena lead to attenuation in tissues

7. Why not simple X-Ray? It can damage the cells It only creates a shadowgram CAT scan, PET are again invasive X-ray source X-ray screen

8. Existing non-invasive techniques Magnetic resonance imaging Bulky and Expensive Photodynamic therapy Requires tumor seeking photosensitive dyes Ultrasound methods Cannot detect tumors of size < 1 cm Problem: Resolution Solution: Infrared light

9. Infrared radiation Advantages Q Noninvasive laser-tissue interaction Q High resolution Q Propagates very far in tissue Q Rugged and cheap sources available Q Reliable detectors But problems in theoretical modeling...

10. Disadvantages of the Diffusion Approximation No coherent effects like interference No polarization Inaccurate at low penetration depth Near-field effects are neglected need a more complete theory

11. Exact numerical simulation of Maxwell’s Equations Initial pulse satisfies :   E = 0 and   B = 0 Time evolution given by :  E ⁄  t = 1/n 2   B and  B ⁄  t = –   E First tests : Snell’s law and Fresnel coefficients

12. n1n1 Snell’s law for beams n2n2   n 1 sin    n 2 sin   Incident Reflected Refracted

13. Light bouncing off air-glass interface Time-resolved treatment

14. Light bouncing off a random scatterers

15. Summary and Outlook Exact solution of the Maxwell’s equations Model a tissue as a collection of spheroids of random refractive indices Systematically test the conventional diffusion approximation Understand near-field effects