FPGA-Assisted Strategy toward Efficient Reconstruction (FAStER) in Diffuse Optical Tomography Yuanyuan Jiang, Sovanlal Mukherjee, James E. Stine, Charles F. Bunting, Daqing Piao * School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, OK, 74078, USA Corresponding author: daqing.piao@okstate.edu Abstract: The finite-element computation of photon fluence and adjoint photon fluence necessary to image reconstruction in steady-state DOT has been implemented on field-programmable-gate- array (FPGA). Preliminary results encourage further exploration toward efficient DOT image reconstruction using FPGA. ©2010 Optical Society of America OCIS codes: (170.6960) Tomography; (170.3010) Image reconstruction techniques. 1. INTRODUCTION Diffuse optical tomography (DOT) utilizes near-infrared (NIR) light to interrogate biological tissues at a depth up to several centimeters to recover the distribution of internal optical properties based on boundary measurements. The image reconstruction of DOT is most often rendered by diffusion-model-based forward computation and iterative non-linear optimization [1], which is inevitably computationally expensive. Consequently, using application-specific computer architecture to accelerate the DOT computation becomes attractive. A number of computer architectures useful for accelerating the data acquisition and processing in optical imaging have been demonstrated recently. Examples include using field-programmable gate array (FPGA) technology to accelerate raw data processing in optical imaging [2, 3], using FPGAs or graphic processing units (GPUs) to accelerate Monte Carlo computation of photon migration [4-6], using FPGAs to solve partial differential equations (PDEs) governing heat transfer [7] or wave propagation [8], and using GPU to perform finite-element-method (FEM) computation [9]. In this work the FEM solution to photon diffusion in biological tissue is implemented using an FPGA. The FPGA executes conjugate gradient (CG) solver of 12 linear equations formulated in an FEM framework, which are associated with 6 sources and 6 detectors, for computing the photon fluence rate and the adjoint fluence rate. Preliminary results demonstrate that a lower-end FPGA outperforms a higher-end PC in CG-based solution of the 12 linear equations, thereby encouraging further exploration toward efficient DOT image reconstruction using FPGA. 2. METHOD AND MATERIALS 2.1 Development of an open-code FEM-based forward solver for steady-state diffuse optical tomography Implementing the DOT image reconstruction routine in FPGA requires an algorithm architecture that is transparent to FPGA. An open-code forward FEM solver for steady-state DOT reconstruction is developed. The solver is based on the steady-state photon diffusion equation [1] ) ( ) ( ) ( ) ( ) ( r q r r r r a r r r r r − = Φ ⋅ − Φ ∇ ⋅ ∇ μ κ (where a μ is the absorption coefficient, κ is the diffusion coefficient, Φ is the photon fluence rate at position r r , and q is the source at r r ), and the boundary condition [1] of 0 ) ( ˆ 2 ( ) = Φ ∇ ⋅ + Φ Ω r Ω n A r r r κ (where Ω r r corresponds the point on the boundary, is a unit vector pointing outward (from the tissue to probe) and normal to the tissue-probe interface, and n ˆ A is the boundary mismatch factor determined by the relative refractive indices of the tissue domain and the probe (air) domain). These equations formulate into the FEM framework 0 )] 2 /( ) ( ) ( [ Q A B C K a = Φ + + μ κ , where the K , and are volume integrals of each element with regard to C Q κ , a μ and q , and is the surface integral of the boundary element. The FEM forward solver results in a set of linear equations containing sparse matrices. The inverse problem performs a non-linear optimization of the objective function of B estimation t emen Φ − measu b Φ = ting the pixel or voxel-wise values of r by a upd κ and a μ . he inverse solver requires finding / T κ ∂ Φ∂ and a μ ∂ Φ / ∂ , w integrated into the forward computation process by using the adjoint method of deriving the Green’s function associated with an impulse source at the detector position, as shown in Fig. 1(a) (b). Therefore, the number of sources, hich are s , and the number of detectors, s generate s 2 ts of linear equations for solving by the CG method. se Our open-code FEM-solver is developed in MATLAB (Mathworks, Inc. Natick, MA) platform. A comparison of our solver with the NIRFAST package [10] is given in Fig. 1(c), where the target has an absorption coefficient of 0.02 mm -1 and a reduced scattering coefficient of 1.2 mm -1 , in a background of 0.002 mm -1 absorption and 0.8 mm -1 reduced scattering. The performance of our solver is comparable to that of NIRFAST, at the same 1% noise-level. 2.2 Implementation of the conjugate gradient solution of the linear equations in FPGA OSA / BIOMED/DH 2010 BSuD18.pdf