A parallel adaptive finite element simplified spherical harmonics approximation solver

Fluorescence molecular imaging/tomography may play an important future role in preclinical research and clinical diagnostics. Time-and frequency-domain fluorescence imaging can acquire more measurement information than the continuous wave (CW) counterpart, improving the image quality of fluorescence molecular tomography. Although diffusion approximation (DA) theory has been extensively applied in optical molecular imaging, high-order photon migration models need to be further investigated to match quantitation provided by nuclear imaging. In this paper, a frequency-domain parallel adaptive finite element solver is developed with simplified spherical harmonics (SP N) approximations. To fully evaluate the performance of the SP N approximations, a fast time-resolved tetrahedron-based Monte Carlo fluorescence simulator suitable for complex heterogeneous geometries is developed using a convolution strategy to realize the simulation of the fluorescence excitation and emission. The validation results show that high-order SP N can effectively correct the modeling errors of the diffusion equation, especially when the tissues have high absorption characteristics or when high modulation frequency measurements are used. Furthermore, the parallel adaptive mesh evolution strategy improves the modeling precision and the simulation speed significantly on a realistic digital mouse phantom. This solver is a promising platform for fluorescence molecular tomography using high-order approximations to the radiative transfer equation. Nomenclature , ∂∂ domain and its boundary r position vectorˆs, ˆ s outgoing and incoming directions of photons ω modulation frequency ψ x,m excitation (x) and emission (m) radiances μ x,m a , μ x,m s , g absorption and scattering coefficients, and anisotropy factor of the domain at excitation and emission wavelengths μ xf a absorption coefficient of the fluorophore c b light speed in the domain p(·) scattering phase function Q, τ quantum efficiency and lifetime of the fluorophore cos θ scattering angle φ x,m excitation and emission fluence n b , n m refractive indices of the domain and the medium S illumination source R(·) reflectivity ratio θ b , θ m , θ c incidence, transmission and critical angle J + x,m exiting partial current at excitation and emission wavelengths γ n , ϕ n Legendre moments of ψ and composite moments of γ n coefficients of boundary conditions at excitation and emission wavelengths T , T c volumetric mesh and its subdomain N c , N P , N T c number of CPUs, nodes of the mesh, elements in T c τ e , ∂τ e volumetric and surface elements ϕ l,x,m i,p value at …