Magnetic moment quantifications of small spherical objects in MRI

Abstract

Purpose The purpose of this work is to develop a method for accurately quantifying effective magnetic moments of spherical-like small objects from magnetic resonance imaging (MRI). A standard 3D gradient echo sequence with only one echo time is intended for our approach to measure the effective magnetic moment of a given object of interest. Methods Our method sums over complex MR signals around the object and equates those sums to equations derived from the magnetostatic theory. With those equations, our method is able to determine the center of the object with subpixel precision. By rewriting those equations, the effective magnetic moment of the object becomes the only unknown to be solved. Each quantified effective magnetic moment has an uncertainty that is derived from the error propagation method. If the volume of the object can be measured from spin echo images, the susceptibility difference between the object and its surrounding can be further quantified from the effective magnetic moment. Numerical simulations, a variety of glass beads in phantom studies with different MR imaging parameters from a 1.5 T machine, and measurements from a SQUID (superconducting quantum interference device) based magnetometer have been conducted to test the robustness of our method. Results Quantified effective magnetic moments and susceptibility differences from different imaging parameters and methods all agree with each other within two standard deviations of estimated uncertainties. Conclusion An MRI method is developed to accurately quantify the effective magnetic moment of a given small object of interest. Most results are accurate within 10% of true values and roughly half of the total results are accurate within 5% of true values using very reasonable imaging parameters. Our method is minimally affected by the partial volume, dephasing, and phase aliasing effects. Our next goal is to apply this method to in vivo studies.

Quantifications of in vivo labeled stem cells based on measurements of magnetic moments

“…Given various magnetic moments and radii of simulated spheres, each simulation was forward modeled on a 1024 3 matrix and cropped down to 32 3 in the spatial frequency domain. Detailed procedures were given in [30]. For display purposes and analyses of HP filters, each of the 32 slices was zero-filled (zero phase value and a predefined constant magnitude intensity outside the 32 × 32 matrix) in image space to 256 2 .…”

“…The procedure of magnetic moment quantifications using CISSCO has been given in [30]. Briefly, each voxel is first interpolated into 1000 subvoxels for subsequent steps.…”

“…Second, the center of an object of interest is identified by minimizing the real part of the overall signal summed within an arbitrary sphere chosen by the user. Third, the magnetic moment p of the object is solved from the following equation $$\text{italicRe}false(S_1-S_{2}false)\text{italicRe}false(f_{23}false(pfalse)false)=\text{italicRe}false(S_2-S_{3}false)\text{italicRe}false(f_{12}false(pfalse)false)$$ where S 1 , S 2 , and S 3 are the complex sums within three concentric pseudo spheres with radii R 1 , R 2 , and R 3 defined by the user, and f 12 ( p ) and f 23 ( p ) are analytical functions given by equations 6, 9, and 10 of [30] and shown below. They represent the normalized theoretical sums of complex signals within pseudo shells defined by the three radii.…”

“…In this work, we propose to use the Complex Image Summation around a Spherical or Cylindrical Object (CISSCO) method [30] to quantify the magnetic moment of SPIO nanoparticle tagged stem cells in a local cluster from MR images. In turn, we estimate the number of cells from each cluster.…”

“…In turn, we estimate the number of cells from each cluster. For the magnetic moment quantification of small objects, the CISSCO method has been tested and shown to provide good accuracy [30]. …”