Calculation of T1, T2, and proton spin density images in nuclear magnetic resonance imaging

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For nuclear magnetic resonance imaging, the spin-lattice relaxation time T 1, the spin-spin relaxation time T 2, and the spin density images are computed from a series of T 1- and T 2-weighted images on a pixel-by-pixel basis. In the most general case, T 1 and T 2 values are related to the image intensity nonlinearly. This fact together with the large number of pixels involved renders the computation a time-consuming process. The effect of pulse profile on the intensity should also be considered. A rapid and stable algorithm is presented to optimize the computation process based on a detailed analysis of the intensity expressions. The pulse sequence used is a spin-echo type, and the proposed method is applicable to any type of pulse profile. A series of images taken at different repetition times but the same echo time are used to calculate the T 1 image. Similarly, images taken at the same repetition time but different echo times are used to compute the T 2 image. Finally these T 1 and T 2 images are incorporated in the calculation of the spin density image. The slice profile function and its derivatives are tabulated by numerical integration and interpolations are applied when the evaluations are required. Numerical analyses are given based on the simulations, and experimental results are also presented.