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

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

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

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

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

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

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

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

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

Exact numerical simulation of Maxwell’s Equations Initial pulse satisfies :   E = 0 and   B = 0 Time evolution given by : E ⁄t = 1/n2   B and B ⁄t = –  E First tests : Snell’s law and Fresnel coefficients

Snell’s law for beams n1 n2 n1 sin a1 = n2 sin a2 a1 a2 Reflected Incident a2 Refracted n1 sin a1 = n2 sin a2

Light bouncing off air-glass interface Time-resolved treatment

Light bouncing off a random scatterers Time-resolved treatment

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