Fluence mapping inside the highly scattering medium using ...

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.