Intensity-curvature highlight of human brain magnetic resonance imaging vasculature

Intensity‐curvature functional‐based filtering in image space and k‐space: Applications in magnetic resonance imaging of the human brain

“…(d) K-space filtering is effective in reconstructing the vessels (see (i), (k), and (l) in Figure 9) however not as much as the image space filtering is. Moreover, the findings reported earlier (Ciulla, Rechkoska, Risteski et al, 2018;Ciulla et al 2018b), as far as regards the highlight of human brain vessels imaged with MRI, are here extended to a wider array of model polynomial functions, to another MRI modality (T2), and most importantly, they are extended because of another type of k-space filtering technique, which yields the reconstruction of the human brain vessels in MRI. Noteworthy, the state of the art in processing MR with the aim to perform vessels imaging includes phase imaging (Rauscher et al, 2008), susceptibility mapping (Haacke et al, 2010), and venoprocessed susceptibility-weighted imaging (SWI) (Haacke et al, 2004).…”

“…In the G42D(x, y) formula, the constants "a" and "b" make parametric the surfaces. The intensity-curvature term (ICT) before interpolation is given in equation 16 in Ciulla et al (2018b), and the intensity-curvature term (ICT) after interpolation is given in equation 17 in Ciulla et al (2018b). Similarly to what seen previously in Figure 3, the ICF in Figure 5 provides the T2 MRI with complementary information about the visibility of the vessel structures (compare (a) versus (d)).…”

“…The formula of the bivariate cubic model function is reported in equation 1 in Ciulla et al (2018b). The intensity-curvature term (ICT) before interpolation is given in equation 10 in Ciulla et al (2018b), and the intensity-curvature term (ICT) after interpolation is given in equation 11 in Ciulla et al (2018b). The formula of the B32D function is parametric in "a," "α 2 " and "α 3 ."…”

“…This section reports on the ICF of another form of bivariate cubic Lagrange model function. The formula of this function is reported in equation 5 in Ciulla et al (2018b). In this implementation of the G42D(x, y) formula, the purpose of the convolutions "α 2 " and "α 3 " is the same as the purpose of the convolutions used in the formula B32D(x, y), which is to create gradients using the pixel intensity values neighboring the pixel f(0, 0) which is the pixel to recalculate.…”

Intensity-curvature functional based digital high pass filter of the bivariate cubic B-spline model polynomial function

“…Since its inception, the ICF has been used to study human brain tumors which are imaged with MRI [38] and human brain vasculature which is also imaged with MRI [39], and to mathematically characterize the input and output functions of the ICF-based filters using three different model polynomial functions [1]. The appearance of the ICF image as HPF signal demands an explanation.…”