Extended finite element method with simplified spherical harmonics approximation for the forward model of optical molecular imaging.

*(English)*Zbl 1261.92030Summary: An extended finite element method (XFEM) for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SP\(_N\)). In the XFEM scheme of SP\(_N\) equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC) method, the validation results show the merits and potential of the XFEM for optical imaging.

##### MSC:

92C55 | Biomedical imaging and signal processing |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

35Q92 | PDEs in connection with biology, chemistry and other natural sciences |

##### Software:

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\textit{W. Li} et al., Comput. Math. Methods Med. 2012, Article ID 394374, 10 p. (2012; Zbl 1261.92030)

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##### References:

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