Practical height correction for diffuse optical ...

Practical height correction for diffuse optical spectroscopy to account for curved tissue surfaces Johannes D. Johansson, Miguel Mireles, Parisa Farzam and Turgut Durduran ICFO – The Institute of Photonic Sciences Av. Carl Friedrich Gauss, num. 3 08860 Castelldefels (Barcelona), Spain [email protected]

Abstract: Non-contact broadband diffuse optical spectroscopy that is meant for longitudinal study of superficial tumor models suffers from systematic errors due to tissue surface. We propose a practical height correction algorithm to minimize these errors. OCIS codes: (170.1470) Blood or tissue constituent monitoring; (170.7050) Turbid media;

1. Introduction Broadband diffuse optical spectroscopy (DOS) is a useful tool for studying blood oxygenation and total hemoglobin concentration in tissues. Non-contact DOS in small animal models suffers from systematic errors due to tissue curvature. It is possible to account for these errors using various methods that can estimate the 3D tissue surface and utilize in numerical solvers such as the finite-element method (FEM). However, in our case, this is not practical due to the large number of wavelengths, time points and variations in the animal orientation during re-placement of the animal. Therefore, we have sought to develop a practical correction algorithm for fast estimation of the hemodynamic parameters. The aim of this study is to develop such a simple height-correction scheme that allows for the use of semi-infinite models in tumors that protrude from the tissue in varying degrees.

2. Material and methods Monte Carlo (MC) simulations [1] of the light intensity on the surface of a tumor modeled as a half-sphere with a light source on hitting the top were made using locally developed software (MBio, ICFO, Figure 1). The simulated light intensities, IMC, were compared to the fluence from semi-infinite diffusion models in the P 1 and pseudo-P3 [2,3] approximation using either the apparent source-detector separation in the 2D image, ρa, or a height-adjusted cartesian source-detector separation, ρh. The P1 diffusion model [4] is calculated on the tissue surface as

I P1

(1)

k  3 a  s is the effective attenuation coefficient, r1   2  1 /  s  is the distance to a virtual point 2

where source,

zb 

3 s  e  kr1 e  kr2      4  r1 r2 

r2   2  2 zb  1 /  s  is the distance to a mirror point sink with the extrapolated boundary 2

2 1  Reff where the effective reflection coefficient for the index of refraction mismatch Reff ≈ 0.47 for  s 31  Reff 

air over water. The pseudo-P3 model [2,3] is calculated as

3 s  e  r1 e  r2 e  r3 e  r4     4  r1 r2 r3 r4 

I P3





Where the distance to the real source is r3



   

(2)

  , the distance to a mirror point sink for the real source is

2 r4   2  2 zb  . The attenuation coefficient is        2    / 18 with, neglecting the  

anisotropy factor of the scattering,

  55a a   s   35 a   s 2

and 

 3780 a  a   s  . The 3

remaining parameters are the same as for the P 1 approximation. Wang et al [2] placed the first source-sink pair at 2/µs´ and 2zb + 2/µs´ but we find better agreement with the simulated data if the pair is placed at the same positions as in the P1 model instead. For this preliminary study, we focus on estimating the scattering coefficient since that is most sensitive to the errors in the tissue curvature and we are showing results from a single wavelength. The full study is extended to a large number of wavelengths that allows us to minimize absorption-scattering cross-talk by using spectral priors.

I MC 1, a 

I  , ˆ  ,   They were calculated by least squares minimization of min where ρ1 is a source P 1 s a I MC  0, a  I P  0 , ˆ s ,  a  2

detector separation 0.2 cm further away than the reference separation ρ0. ρ is always the apparent separation, ρa, for the Monte Carlo simulation while it can be either the apparent or height-corrected separation for the P1 and pseudoP3 models. The absorption coefficient was assumed to be known a priori.

3. Results Here we present one example from a set of simulations where the modelled tissue had an absorption coefficient, µa, of 0.248 /cm and a reduced scattering coefficient, µs ´, of 10.94 /cm. The index of refraction for water, n = 1.33, was assumed for the tissue. Simulated intensities are presented in figures 1 and 2. Fitted scattering values for different source-detector separations are presented in figure 2.

Figure 1. Left: Modeled geometry with apparent (ρa) and height-adjusted source-detector separations (ρh). Right: Light intensity from Monte Carlo simulation. The light source is placed on top of a tumor modeled as a half-sphere with a radius of 5 mm (edge marked with black ring).

Figure 2. Left: Simulated intensities from Monte Carlo and semi-infinite P1 and P3 models without and with height correction of sourcedetector separation (µa = 0.248 /cm µs´ = 10.94 /cm). Right: Scattering values estimated from I(ρ1 = ρ0 + 0.2 cm)/I(ρ0) assuming a priori knowledge of the true absorption. The shaded are indicates distances shorter than 1/ µs´ and the vertical dotted line indicates when the edge of the tumour is reached for ρa and ρ1,a respectively.

4. Discussion In this study, we have used a simple height correction to improve the fit of analytical semi-infinite models to a curved surface. More complicated methods, such as iterative MC simulations or FEM simulations [5], could be used to give more accurate fits. Since we want to make fits for a large number of measurements with many wavelengths in longitudinal studies of tumor models in small animals, we prefer to be able to use simple analytical expressions in order to calculate the estimates in a reasonable time. As only one wavelength was simulated, the absorption coefficient was assumed to be known a priori instead of being a separately fitted parameter. In real measurements, multiple wavelengths are used together with known chromophore spectra to allow fitting for absorption and scattering at once. A height map of the scanned tissue is straightforward to obtain by illuminating the tissue with an oblique angle and measure the displacement from a reference height. In conclusion, correcting for height in the source-detector separation improves the fitting of the scattering and allows for the use of a semi-infinite model even if the actual geometry is curved.

5. Acknowledgements The authors would like to acknowledge the support by Fundacio Cellex Barcelona, Marie Curie IEF (FP7 MOBODICT), Ministerio de Economía y Competitividad (PHOTOSTROKE), Institucio CERCA (DOCNEURO, PROVAT-002-11), Generalitat de Catalunya, European Regional Development Fund (FEDER/ERDF) and LASERLAB Europe III (BIOPTHICAL).

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