Applied Computational Engineering in Magnetic Resonance Imaging: A Tumor Case Study

— This paper solves the biomedical engineering problem of the extraction of complementary and/or additional information related to the depths of the anatomical structures of the human brain tumor imaged with Magnetic Resonance Imaging (MRI). The combined calculation of the signal resilient to interpolation and the Intensity-Curvature Functional provides with the complementary and/or additional information. The steps to undertake for the calculation of the signal resilient to interpolation are: (i) fitting a polynomial function to the signal, (ii) the calculation of the classic-curvature of the signal, (iii) the calculation of the Intensity-Curvature term before interpolation of the signal, (iv) the calculation of the Intensity-Curvature term after interpolation of the signal, (v) the solution of the equation of the two aforementioned Intensity-Curvature terms of the signal provides with the signal resilient to interpolation. The Intensity-Curvature Functional is the result of the ratio between the two Intensity-Curvature terms before and after interpolation. Because of the fact that the signal resilient to interpolation and the Intensity-Curvature Functional are derived through the process of re-sampling the original signal, it is possible to obtain an immense number of images from the original MRI signal. This paper shows the combined use of the signal resilient to interpolation and the Intensity-Curvature Functional in diagnostic settings when evaluating a tumor imaged with MRI. Additionally, the Intensity-Curvature Functional can identify the tumor contour line.