Fluence mapping inside the highly scattering medium using ...

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The photons addressing the internal point 2 can be “labeled/modulated” using strongly focused ultrasound and detected at the surface of the medium (AO). Assuming incoming fluence rate ϕ1,2 in internal point 2 (labeling volume) and that all the photons entering the labeling volume get labeled (labeling efficiency is unity) and leave without absorption. The power of detected tagged photons at point 1, can be written as, ( ) By applying photon path reversibility principle Pr(1,2)= Pr(2,1), and rearranging aforementioned equations for fluence at point 2 and power of tagged photons measured at 1, we get the expression for local fluence rate at point 2, √ (1) If we take into account all the parameters regarding labeling volume and detection system, the expression for the absolute local fluence rate can be written as. √ √ ( ) This expression for local fluence contains excitation parameter P1, instrumental parameters (Ω1, A1 and A2) and externally measureable quantity Pl,1. Hence, Eqn. 2 suggests that local light fluence can be measured in optically inhomogeneous medium experimentally. Reflection mode AO is a technique which allows local labeling of light using ultrasonic modulation and detection of ultrasonically modulated light in reflection mode [11]. 3. Numerical experiment To proof our methodology we used Monte Carlo simulation program for light transport in turbid media [12]. We modified the program to be able to “label” photons addressing a certain region of interest in medium. This region of interest, we call labeling volume, was considered of spherical shape in our simulations. We simulated a scattering medium of dimensions 40x40x4 cm 3 , containing a spherical absorber/labeling volume of diameter 1 mm. The optical properties of background medium µs ’ =7.5/cm and µa=0.01/cm were different from the optical properties of labeling volume µs ’ =7.5/cm and µa=1/cm. In simulations we injected 10^7 photons into the medium through a circular aperture A1 of diameter 3 mm. Photons addressing the labeling volume during their random walk through the scattering medium were “labeled”. Labeled photons leaving the medium through aperture A1 within the opening angle of 25 degrees were detected to simulate reflection mode AO. We used Eqn. 2 to estimate the fluence at the position of labeling volume in scattering medium. The quantities P1 and Pl,1 power of incident photons and detected labeled photons respectively in Eqn. 2, were replaced by the weight of injected photons and detected labeled photons. Results from Monte Carlo simulations presented in Fig. 1b, show that estimation of the local fluence inside the scattering medium using our proposed methodology. 4. Experimental validation Acousto optics is a technique that allows such local labeling of light [13], and detection of ultrasonically labeled in reflection configuration [11]. However, unlike presented theoretical model (Eqn. 1) the labeling volume of AO is of complicated shape and its labeling efficiency is unknown. As a result measuring fluence in absolute terms using reflection mode AO is not possible at this stage. Therefore, we used Eqn. 1 instead and show that we can measure fluence variation in scattering medium. We used speckle contrast detection method to measure ultrasonically modulated backscattered light []. The speckle contrast decreases in the presence of ultrasound. Change in speck contrast (ΔC) between US ON and OFF is can be measured and it is approximately proportional to the intensity of locally ultrasonically modulated light [14]. This means Eqn. 1 can be written as, √ The experiment was performed on a soft tissue mimicking cubical phantom of dimensions 3x3x3 mm 3 . The phantom was made of 3% Agar gel and a dilution of 4% Intralipid (20%), resulting in approximate reduced scattering coefficient 7.5 cm -1 . US transducer was attached to the xy translation stage. Speckle contrast change (ΔC) in the backscattered light was measured by scanning the ultrasound focus along the optical axis (x-axis). To validate our results we measured the fluence invasively using an optical fiber. Fig. 4 shows the normalized fluence, measured acousto-optically (red) using Eqn. 1 and with the fiber (black). Horizontal axis represents the depth from the surface along optical axis (x-axis). We measured the fluence acousto optically twice, before (Fig. 2a) and after (Fig. 2b) measuring the fluence with the fiber, to see if introducing the fiber into the medium effects the local fluence, results show no significant change.
Fig. 4. Comparison of acousto optically measured (circles) light fluence with invasively measured (squares) light fluence using optical fiber, in both cases the measured signal has been normalized to maximum value of one. a) measurement before inserting the fiber into medium, b) measurement after inserting the fiber into medium. Results presented in Fig. 4, show that acousto optically measured local light fluence, using our proposed methodology, is in good agreement with invasively measured fluence using optical fiber. Presented results are average of fifteen AO measurements and error bars are obtained by calculating the error propagation based on standard deviation in acoustic measurements. The error in estimated fluence increases with depth as it is expected since SNR in reflection mode AO becomes lower at higher depth. We presented a theory that proposes a method to measure the local light fluence in scattering medium experimentally, without the need of any prior knowledge about the optical properties of the medium. Our theoretical and numerical simulation model assumes a simplistic labeling volume and unit tagging efficiency. However, it is not the case at experimental level, when using AO as labeling technique. Therefore, we simplified our model (Eqn. 2) to use reflection mode AO as technique to measure local fluence in scattering medium, which gives the fluence map in relative terms with an unknown pre-factor. Here in this proceeding, we have shown in real experimental settings that using reflection mode AO local light fluence can be measured. Our present experiments are done on homogeneous scattering medium and our goal in future is to investigate the applicability of this method in heterogeneous (scattering and absorption) medium. 5. Reference [1] R. I. Siphanto, K. K. Thumma, R. G. M. Kolkman, T. G. van Leeuwen, F. F. M. de Mul, J. W. van Neck, L. N. A. van Adrichem, and W. Steenbergen, Optics Express 13 (2005) 89. [2] S. Manohar, S. E. Vaartjes, J. C. G. van Hespen, J. M. Klaase, F. M. van den Engh, W. Steenbergen, and T. G. van Leeuwen, Optics Express 15 (2007) 12277. [3] X. D. Wang, Y. J. Pang, G. Ku, G. Stoica, and L. H. V. Wang, Optics Letters 28 (2003) 1739. [4] A. Lev, E. Rubanov, and B. Sfez, Photons Plus Ultrasound: Imaging and Sensing 2005 5697 (2005) 190. [5] H. F. Zhang, K. Maslov, and L. V. Wang, Photons Plus Ultrasound: Imaging and Sensing 2008: The Ninth Conference on Biomedical Thermoacoustics, Optoacoustics, and Acoustic-Optics 6856 (2008) T8561. [6] B. T. Cox, S. R. Arridge, K. P. Kostli, and P. C. Beard, Photons Plus Ultrasound: Imaging and Sensing 2005 5697 (2005) 49. [7] B. T. Cox, J. G. Laufer, and P. C. Beard, Biomed Opt Express 1 (2010) 201. [8] A. Bratchenia, R. Molenaar, and R. P. H. Kooyman, Laser Physics 21 (2011) 601. [9] K. Daoudi, A. Hussain, E. Hondebrink, and W. Steenbergen, Optics Express 20 (2012) 14117. [10] X. A. Xu, H. L. Liu, and L. V. Wang, Nature Photonics 5 (2011) 154. [11] A. Lev and B. G. Sfez, Optics Letters 27 (2002) 473. [12] S. L. Jacques, Photochemistry and Photobiology 67 (1998) 23. [13] F. A. Marks, H. W. Tomlinson, and G. W. Brooksby, Proceedings of Photon Migration and Imaging in Random Media and Tissues 1888 (1993) 500. [14] J. Li, G. Ku, and L. H. V. Wang, Applied Optics 41 (2002) 6030.
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