Diffuse light propagation in biological media by a time-domain parabolic simplified spherical harmonics approximation with ray-divergence effects

Abstract

We present a simplified spherical harmonics approximation for the time-domain radiative transfer equation including the source-divergence effect. This leads to a set of coupled partial differential equations (PDEs) of the parabolic type that model diffuse light propagation in biological-tissue-like media. We introduce a finite element approach for solving these PDEs, thereby obtaining the time-dependent spatial profile of the fluence. We compare the results with the diffusion equation and Monte Carlo simulations. The fluence obtained via our model is shown to reproduce well the Monte Carlo results in all cases and improves on the solution of the diffusion equation in homogeneous diffusive-defying media. Our solution also shows more sensitivity than the diffusion equation to changes in the absorption coefficient of small inclusions.

Computed Tomography-guided Time-domain Diffuse Fluorescence Tomography in Small Animals for Localization of Cancer Biomarkers

“…However, CCD cameras have a limited dynamic range and read-out noise limits their ultimate sensitivity. The second design avoids the potential limitations of CCD camera detection by employing highly sensitive single-photon counting technology based on the use of such detectors as photomultiplier tubes or avalanche photodiodes [10][11][12][13] . The drawback of these more sensitive detection methods is that each detector can only collect light at a single point; therefore, to achieve dense tissue sampling, either many detectors have to be used (which is very expensive), or many projections have to be imaged with the same detector (which can be time consuming).…”

“…Carefully transfer the imaging bed and mouse back to the fluorescence tomography system. Choose the number of source positions to collect data about the mouse for each imaging slice (32), the integration time for each TPSF measurement (1 s), the number of iterations for each source position (10), and the position and number of desired imaging slices from the CT image stack from Step 3.6. The numbers in parentheses are typical values for each imaging parameter yielding ~ 5 minutes of data acquisition per imaging slice.…”

“…The majority of research groups have invested in charge-coupled device (CCD)-based systems that provide abundant tissue-sampling but suboptimal sensitivity [4][5][6][7][8][9] , while our group and a few others [10][11][12][13] have pursued systems based on very high sensitivity detectors, that at this time allow dense tissue sampling to be achieved only at the cost of low imaging throughput. Here we demonstrate the methodology for applying single-photon detection technology in a fluorescence tomography system to localize a cancerous brain lesion in a mouse model.…”

Analytical solution of the simplified spherical harmonics equations in spherical turbid media

“…It has been shown that low order SP N equations provide sufficiently accurate results for biomedical optics [16,6]. For simplicity, we hereby consider the lowest possible order N¼3 (N¼1 is shown to be the DE) to both obtain applicable results and lower the complexity of the calculations presented; calculations for higher orders are similar.…”

Three-dimensional diffuse optical tomography with full multi-view time-domain data

“…Parallel to this, a DOT algorithm that exploits TPSF data and incorporates constrained optimization methods has been is implemented [5]. As the forward model, the time-dependent parabolic simplified spherical harmonics equations (TD-pSP N ) are used [7]. In this work we extend the studies presented in [6] to three-dimensional media and full multi-view TPSF data collection, simulating our mentioned experimental system [5].…”