# Simulation of Light-Tissue Interaction in Biological Tissue

Leaders: | M. Wollweber, B. Roth |

Team: | O. Melchert |

Year: | 2016 |

Our research activities in subproject 1 of HYMNOS are focused on various numerical aspects of optoacoustics in the context of computational biophotonics. Our aim is to perform numerical experiments and to devise measurement protocols that facilitate a better understanding of the features of OA signals that resulting from melanin enriched absorbing structures within tissue. In summary, optoacoustics is a two-part phenomenon consisting of

**Part I:** Optical absorption of laser beams inducing photothermal heating of tissue

**Part II:** Acoustic emission of ultrasound waves due to thermoelastic expansion and stress field relaxation

Note that upon irradiation, tissue layers with higher concentration of melanin absorb a greater amount of photothermal energy and expand more intensely than surrounding layers with lower concentration. Whereas the optical absorption is assumed to occur instantaneously, the acoustic propagation of sound waves is a comparatively slow process that occurs on a microsecond timescale. In this regard, note that typical propagation distances are on the order of cm and that the propagation of acoustic waves in soft tissue (i.e. elastic solids) occurs with a speed of v=1400-1600 m/s. Hence, in subproject 1 the challenge is to combine the absorption of laser light by tissue and the acoustic propagation as a multitimescale problem. Our research activity is centered arround three main topics:

**Topic 1:** The direct OA problem

Here, our aim is to understand the principal features of OA signals resulting from measurements on melanin enriched absorbing structures within tissue and to numerically verify OA signals generated in mulit-layered PVA hydrogel phantoms with focus on (nondestructive) OA.

**Topic 2:** The inverse OA problem

Here, our aim is to solve the OA source reconstruction problem in order to invert OA signals to inintial stress profiles and to infer the optical properties of the underlying material. Therefore we consider the OA problem in the paraxial approximation where the source reconstruction is achieved by the inverse solution of a Volterra integral equation of the second kind, e.g. in terms of a Picard-Lindeloeff iteration scheme.

**Topic 3:** Algorithms in computational biophotonics

Here, we study efficient algorithms for the accurate forward and reverse evaluation of the discrete Fourier-Bessel transform. The transform is used as a numerical tool facilitating a polar convolution of two radially symmetric functions. This is relevant for applications in tissue optics and optoacoustics where a recurrent task is to perform a beam-shape convolution in order to yield the material response to an extended laser beam from its Greens-function response. The latter results from a more complex measurement process modeled in terms of a Monte Carlo approach and is, in the worst case, known on a finite sequence of coordinate values, only. The considered applications require the repeated (hundreds of times) calculation of a forward and reverse Fourier-Bessel transform. Thus, time-efficiency is key and fast numerical procedures are valuable.