1 Two methods for modelling the propagation of terahertz radiation in a layered structure. GILLIAN C. WALKER 1*, ELIZABETH BERRY 1, STEPHEN W. SMYE 2, NICK N. ZINOV’EV 3, ANTHONY J. FITZGERALD 1, ROBERT. E. MILES 3, MARTYN CHAMBERLAIN 3 AND MICHAEL A. SMITH 1 1 Academic Unit of Medical Physics, University of Leeds, UK 2 Department of Medical Physics and Engineering, Leeds Teaching Hospitals NHS Trust, UK 3 Institute of Microwaves and Photonics, University of Leeds, UK ( * Author for correspondence,

2 Objectives n Create a modelling tool to simulate the passage of THz radiation through biological tissue. –Biological tissue is highly inhomogeneous. –The interactions that occur with THz and biological tissue are complex.

3 Outline n Modelling Biological Tissue n In Vitro Phantom n Thin Film Matrix Model n Monte Carlo Model n Results n Discussion n Future Work

4 Modelling the interaction of THz radiation with biological tissue. n THz radiation is being investigated as an imaging tool for skin. n It has been shown that TPI can resolve the stratum corneum, epidermis and dermis. (Cole et al. Laser Plasma Generation and Diagnostics, SPIE Proc 2001; 4286.) n A three-layer system of parallel sided slabs, each with frequency dependent physical properties could be used to simulate human skin.

5 The modelling problem Incident THz Spectrum Transmitted THz Spectrum

6 In vitro phantom Water/Propanol-1 solution Spacer  m TPX - 2 mm

7 Physical Properties of Water/Propanol -1 n The absorption coefficient and index of refraction of water and propanol-1 were calculated using the Cole-Cole model. (Kindt et al. Journal of Physical Chemistry 1996;100 : ) n These were averaged using volume weighting to give the physical properties of the specific water/propanol-1 solution.

8 Physical Properties of Water/Propanol-1

9 Thin Film Matrix Model n A method for calculating the change in electric field as it passes through the layered medium. n Implementation of the boundary conditions for the electric and magnetic components of the incident radiation at each boundary result in a matrix formulation of the problem.

10 Thin Film Matrix Model

11 Thin Film Matrix Model

12 Thin Film Matrix Model

13 Monte Carlo Model n Creating a Photon Distribution. –A THz pulse is recorded in units proportional to electric field. –A photon distribution is created by randomly sampling the spectrum and a Poisson distribution to account for the coherent nature of the radiation. –One million photons were included in an incident ensemble.

14 The Monte Carlo Model n The position of each photon is tracked in the sample. n The probability of a photon crossing a boundary within the sample is determined by the Fresnel coefficients. n In the water/propanol-1 solution the Beer- Lambert law is sampled as the probability distribution for an absorption event. n The number of photons transmitted and reflected is counted to give the output spectra.

15 Presentation of Results n The results of the Monte Carlo simulation were in expressed as a photon distribution while the experimental results were in arbitrary units proportional to electric field. n The experimental results were converted into photon distributions. The number of photons included in each respective ensemble were calculated as a fraction of one million, the fraction given by the experimental area to the incident spectrum area.

16 Graphical comparison Transmitted spectraIncident spectra photons a1a2 a2/a1* photons

17 Results - Full Spectrum

18 Results - Up to 1 THz

19 Results - Full Spectrum

20 Discussion n The model results show good agreement with the experimental results reproducing all major features. n Up to 1 THz, where the physical parameters have been verified there is close agreement with model and simulated amplitude. n Generally the Thin Film Matrix Model more closely reproduces the experimental results.

21 Future Work n Investigations into how the absorption coefficient and index of refraction affect the simulated results are being carried out. n Implementation of a fitting routine to extract physical parameters from the tissue.

22 Future Work 50%-250% of the absorption coefficient Experimental result

23 Future Work n The Monte Carlo model is to be used to investigate scattering of THz radiation. n The models are to be used to simulate results from human skin for both transmission and reflection data, in vitro and in vivo.

24 Acknowledgements n This work was supported by the Engineering and Physical Sciences Research Council (GR/N39678) n We are grateful for the contributions of the members of the EU Teravision project (IST ), especially W. Th. Wenckebach, T.U. Delft.