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

Abstract

Objective: This paper expands on the basis of previous research confirming through empirical evidence both meaning and nature of the classic-curvature and the intensity-curvature functional images. Methods: Eleven subjects affected by human brain tumors were scanned using Magnetic Resonance Imaging (MRI). Twodimensional MRI images were selected to study the subjects using the intensity-curvature measurement approaches called: classic-curvature and intensity-curvature functional. The bivariate cubic polynomial and the bivariate linear function were fitted to the MRI images in order to compute the classic-curvature and the intensity-curvature functional respectively. Results: This work shows one novelty related to the use of the two intensity-curvature measurement approaches when furthering the study of tumors detected with MRI. The novelty is the highlight of the accumulation of the contrast agent through the visually perceptible third dimension perpendicular to the imaging plane. Conclusions: The meaning and the nature of the aforementioned intensity-curvature measurement approaches is suggested to be the high pass filtered MRI signal.

The Properties of The Intensity-Curvature Measurement Approaches: Applications In Magnetic Resonance Imaging of The Human Brain

“…While studying human brain tumors the ICF showed the visually perceptible third dimension in proximity of the accumulation of fluids, next to the tumor mass (Ciulla et al, 2014). Moreover, the CC appears to be similar to the ICF, because (when calculated using the bivariate cubic model polynomial function) it also displays the visually perceptible third dimension (Ciulla et al, 2016a). This work presents evidence that the CC and the ICF are not quite the same as high pass filtered signals.…”

“…To date, the CC and the ICF images can be calculated fitting to the image data a wide array of model polynomial functions, and the most clear and well defined ICF can be obtained fitting the bivariate linear function (Ciulla et al, 2018). The suggestion that CC and ICF images were similar to MRI high pass filtered signal was made through the work reported in Ciulla et al (2016a). This work further clarifies that both CC and ICF are different from high pass filtered signal.…”

“…When calculated from the bivariate cubic model polynomial function, the intensity-curvature terms are similar to the CC. The similarity consists of the visually perceptible third dimension, which is prominent because of the presumed accumulation of fluids (Ciulla et al, 2016a). It can be therefore inferred that the visually perceptible third dimension of the E o (x, y) and the E IN (x, y) images might also be the indicator of fluids accumulation.…”

“…2) The two intensity-curvature terms (ICTs) appear to be very much alike because the intensity-curvature functional calculated from the bivariate cubic model polynomial function is almost equal to '1' across the full spatial extent of the MRI image and thus is unusable. The novelty of the works herein reported can be summarized in three main points: (i) the ICTs display the visually perceptible third dimension (Ciulla et al, 2016a) likewise the classic-curvature when calculated fitting to the MRI data the bivariate cubic model polynomial function (as shown in this paper), (ii) the visually perceptible third dimension might be related to the accumulation of fluids in proximity of the vessels, and (iii) the k-space magnitude of the ICTs is different from the k-space of the high pass filtered signal (as it shall be seen in figure 7), hence the nature of the ICTs is not high pass filtered signal. As far as regards, the second point of discussion, clearly, the use of the intensitycurvature terms replaces the use of the unusable intensity-curvature functional (ICF).…”

The Intensity-Curvature of Human Brain Vessels Detected with Magnetic Resonance Imaging

“…Note that the aforementioned behaviour of the ICF is not common to other mathematical functions, such as for instance the bivariate linear model function. It is due to acknowledge that the ICF is similar to MRI high pass filtered signal and as such it is useful as an alternative high pass filter of the MRI signal (Ciulla et al, 2016). It is also due to report, as Fig.…”