4D Model of Bloch NMR Flow Equation for Differentiation of Intra-axial Tumors using MR Fingerprinting based Relaxometry

Abstract

Intra-axial tumors are lesions within the brain parenchyma in which glioblastoma multiforme is the most occurring and metastatic primary brain tumor. In order to improve patience survival, it is important that early differentiation between primary and metastatic malignant brain tumors is possible so that patients are provided with appropriate diagnostic and management options. In addition to this, accurate prognostic information is required for effective disease management [1]. Advanced imaging techniques such as DTI, MRS, perfusion MRI, PET have had positive influence on brain tumor evaluation over the years. However, few challenges are still evident. For example, there is currently no single neuroimaging technique which can easily, reliably and consistently be employed in a day-to-day setting to differentiate intra-axial brain tumors based on both their origin and histopathologic grading [1]. The problem of tissue discrimination is even more challenging in a post-treatment scenario in which patients need to be monitored for pseudo-response, pseudo-progression and radiation necrosis. In order, to address these problems, this study has developed a computational MR method which uses MRF-based relaxometry for real time tumor imaging. In this study, three common types of intra-axial brain tumors (glioblastomas, lower grade gliomas and metastases) were considered. Vasogenic edema (around metastatic lesions) and edema with neoplastic cellular infiltration (around glioblastomas) have free protons while the lesions themselves have bound protons which easily respond to B0 and B1 magnetic fields. The motion of these proton spins is described time-independent Bloch NMR flow equation [2, 3]. If the RF field is applied such that My is sampled at maximum magnitude, M0 ≈ 0 and Eqn (1) therefore becomes Eqn (3). Assuming that the fluid velocity and the applied field have the forms in Eqn (4), we have final solution in Eqn (5) (subject to Eqn (6)). Results Mean T1 and T2 relaxation times sampled at B0 field of 3.0T have been taken from an experimental MR fingerprinting study [1]. We made use of the upper limits of the ranges of the relaxation times and from the results given in Eqns (5) and (6), we have developed a Wolfram Mathematica computer program which gives the images in Figs. 1-3. We run the program for various spatial resolution and x within micrometer ranges gives the best results are thus presented. From these images, it could be observed that the method presented in this study is able to show differences not only between different tumor regions but also the composition of those regions. It is particularly interesting that these results were obtained with tumors sizes in the micrometer ranges. For example, in Fig. 1, glioblastoma multiforme, metastases and lower grade gliomas have unique transverse magnetization values and in addition to this, they also have unique patterns at low gradient field magnitudes (G) and x = 3μm. In fig. 2 however, glioblastoma multiforme and combined tumor did not show a significant contrast except at high G values and x close to 3μm. In fig. 3, contralateral white matter region is clearly discrimated from other regions. The patters for the components are quite similar but their My values significantly different. Conclusion Since T1 and T2 relaxation times are molecular fingerprints, this study could prove to be crucial in understanding the biological characteristics of various tumor types, their complex aggressive tumor behavior and lack of response to treatment. Secondly, the unique properties of Bessel function has helped in descriminating between glioblastoma multiforme and solitary metastasis as shown in fig 1(a), 1(b), 2(a), 2(b), 3(a) and 3(b). Finally, because small changes in T1,T2 translates into unique My images, this study could help in better grading of brain tumors simulations for treatment planning, monitoring of treatment and assessment of tumor recurrence.