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

Abstract

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.

On the properties of the intensity-curvature measurement approaches: the classic-curvature and the intensity-curvature functional

“…Indeed, filtering is here performed through the CC and the ICF images which are treated as filter masks. The CC and the ICF images can build the visually perceptible third dimension which can highlight the tumor structures and anatomy of the human brain (see also Figures 5e and 5f in previous work [21] as far as regards the ICF). The meaning and the nature of the visually perceptible third dimension in the CC and the ICF images is the capability to filter the MRI.…”

“…As already seen in Figures 1, 2 and 3, the analogy between the images shown in Figure 6 Figure 6, likewise shown already in Figures 3 and 4, the filtered images in (e), (f) and (g) appear illuminated in a similar fashion seen already in previous research through the signal resilient to interpolation. [21] This aspect will become more apparent in (1) a contrast-brightness effect which makes it possible to highlight the features of the intra-ventricular tumor; and (2) the imaging of the sulci and gyri, which makes it possible to observe the anatomy the details of the brain cortex.…”

Calculation of the Classic-Curvature and the Intensity-Curvature Term Before Interpolation of a Bivariate Polynomial

“…In order to frame into the literature the works of this research, which recalls works reported earlier [7,[12][13][14][15][16][17], it is necessary to consider the rationale of the study presented in this paper. So far, no studies have been reported attempting to achieve the characterization of the intensity-curvature term before interpolation.…”

“…This paper is concerned with the calculation of the classic-curvature image [12] and the calculation of the intensity-curvature functional term before interpolation image [13][14][15][16][17] using MRI data consisting of a twodimensional image of a human brain affected by a tumor.…”

“…This paper departs from a bivariate model function fitted to MRI data of the human brain in pathological state (tumor) and the mathematical procedure developed herein consists of two steps [7,[12][13][14][15][16][17]]:…”