Ching Yi Hsieh

Quantifying Effective Magnetic Moments of Narrow Cylindrical Objects in MRI

A new procedure for accurately measuring effective magnetic moments of long cylinders is presented. Partial volume, dephasing and phase aliasing effects are naturally included and overcome in our approach. Images from a typical gradient echo sequence at one single echo time are usually sufficient to quantify the effective magnetic moment of a cylindrical-like object. Only pixels in the neighborhood of the object are needed. Our approach can accurately quantify the magnetic moments and distinguish subpixel changes of cross sections between cylindrical objects. Uncertainties of our procedure are studied through the error propagation method. Images acquired with different parameters are used to test the robustness of our method. Alternate approaches and their limitations to extract magnet moments of objects with different orientations are also discussed. Our method has the potential to be applied to any long object whose cross section is close to a disk.

An improved method for susceptibility and radius quantification of cylindrical objects from MRI

A new method is developed to measure the magnetic susceptibilities and radii of small cylinder-like objects at arbitrary orientations accurately. This method for most biological substances only requires a standard gradient echo sequence with one or two echo times, depending on the orientation of an object relative to the main magnetic field. For objects oriented at the magic angle, however, this method is not applicable. As a byproduct of this method, the cross-sectional area as well as signals inside and outside the object can be determined. The uncertainty of each measurement is estimated from the error propagation method. Partial volume, dephasing, and phase aliasing effects are naturally included in the equations of this method. A number of simulations, phantom, and pilot in-vivo human studies are carried out to validate the theory. When the maximal phase value at the boundary of a given cylindrical object is larger than 3 radians, and the phase inside the object is more than 1 radian, the susceptibility can be accurately quantified within 15%. The radius of the object can be determined to subpixel accuracy. This is the case when the signal-to-noise ratio inside the object is about 6:1 or higher and the radius of the object is about one pixel or larger. These conditions are realistic when considering medullary and pial veins for example.

A quantitative study of susceptibility and additional frequency shift of three common materials in MRI

This work quantifies magnetic susceptibilities and additional frequency shifts derived from different samples.

Magnetic moment quantifications of small spherical objects in MRI

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 1.5T 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.

Susceptibility and size quantification of small human veins from an MRI method.

Recently a method called CISSCO (Complex Image Summation around a Spherical or a Cylindrical Object) was introduced for accurately quantifying the susceptibility and the radius of any narrow cylindrical object at any orientation using a typical two-echo gradient echo sequence. This work further optimizes the method for quantifying oxygen saturation in small cerebral veins in the human brain. The revised method is first validated through numerical simulations and then applied to data from phantom and human brain. The effect of phase high pass filtering on the quantified parameters is studied and procedures for mitigating its adverse effects are suggested. Uncertainty of each measurement is estimated from the error propagation method. It is shown that the revised method allows for accurate quantification of both the vessel size and its oxygen saturation even in the case of a low SNR (signal to noise ratio) in the vein. The results are self consistent across different veins within a given subject with a variation of less than 6%. Finally, imaging parameters and some procedures are suggested for accurate susceptibility and radius quantifications of small human veins.

SU‐FF‐I‐28: A Novel Simulated Method of Quantifying Susceptibilities in Objects: The First Step Toward Quantitative Diagnosis in MRI

Quantifying tissue susceptibilities in-vivo is important because certain tissue susceptibilities may reflect health conditions of an individual. Many researchers have accurately measured susceptibilities of different materials using the least-square-fit method when the object sizes occupy at least 50 pixels on MRI. In this abstract we have developed a new approach to measure susceptibilities of small objects from MRI. We first simulated a disk with a radius of 16 pixels on 4096×4096 magnitude and phase images. The disk was a cross section of an infinite tube, perpendicular to the main magnetic field in MRI. The magnitude inside the disk was zero but unity outside the disk. The echo time and the field strength were chosen as 5ms and 1.5T. The phase was then simulated according to the well-known physics laws in magnetostatics, with a −9ppm susceptibility difference inside and outside the tube. Through a low-pass k-space filter, the sizes of images were then converted to 256×256 such that the radius of the disk became roughly 1 pixel. The 256×256 magnitude and phase images would be almost identical to images acquired from a 1.5T MR system, with an air tube of radius 1mm perpendicular to the magnetic field and surrounded by water. Our images were simulated with different tube radii as well as with and without Gaussian noises. Two circles around the disk were drawn on images. The centers of these two circles were coincided with the center of the disk. With each circle, the complex signal was summed. We were able to solve the susceptibility from an inverse approach, based on the known disk sizes, the comparisons of the obtained complex sums, and a theoretical model. Without the presence of noise, the solved susceptibilities were within 1% accuracy compared to −9ppm. With the presence of noise, the results are more complicated.

TH‐D‐304A‐02: Quantifying Magnetic Moments and Susceptibilities of Small Spherical Objects in MRI

Purpose: To quantify magnetic moment and susceptibility of any small object to monitor the progression of neurodegenerate diseases and measure the amount of nanoparticlesin vivo in MRI.Methods and Materials: We have been developing the CISSCO(Complex Image Summation around a Spherical or Cylindrical Object) method in the past [1,2]. This method involves summing up complex signals from voxels within a defined circle or sphere, whose center coincides with the center of the object. The effective magnetic moment of a spherical object can be numerically solved from complex signals within three concentric spheres [2]. The phantom study is presented here. Two different diameter sizes of glass beads, 3mm and 5mm, were imbedded in the gel. The gel phantom was scanned by a 1.5T MRI system with a 3D multi‐echo gradient echo sequence and a spin echosequence. The gradient echo sequence was used to determine the effective magnetic moment. The volume measurements of glass beads were analyzed from the spin echosequence. To confirm the accuracy of the measurements from the CISSCO method, the magnetic moments of glass beads were also measured by SQUID(Superconducting Quantum Interference Device). The magnetic susceptibilities of glass beads were properly calculated and compared between SQUID and MRI.Results: The measuredmagnetic moments and their uncertainties at different echo times agree with each other. The uncertainties of volume measurements from the spin echosequence are less than 5% of the actual volumes of glass beads. In addition, the calculated magnetic susceptibilities from MRI agree well with those from SQUID. Conclusions: Our phantom study demonstrates the feasibility of the CISSCO method that can be used to accurately quantify the magnetic moment and susceptibility of a small object such as microbleeds or implanted nanoparticles. Ref:[1]Cheng et. al, MRI, 2007, pp.1171–1180.[2]Hsieh et.al, Med. Phys., 2008, p. 2906.

SU‐D‐303‐06: Evaluations of Quantified Magnetic Moments From Different MRI Hardware

Purpose: Our quick study here is to validate whether the quantified magnetic moments of the same object are the same from different MRI machines and rf head coils. Methods: We constructed a gel phantom consisting of an empty straw with a diameter of 2.6-mm, a 3-mm diameter glass bead, and a 5-mm diameter glass bead. We imaged the phantom with a 4 echo gradient echo sequence on a 1.5-T Siemens Sonata and a 3-T Verio. On the 1.5-T, we used a quadrature single-channel birdcage coil and an 8-channel coil. On the 3-T, we used a single channel circular-polarized (CP) receiving coil and a 12-channel coil, which outputs only 4 channels. After removing the background phase with the SHARP method [1], we quantified magnetic moments of the three objects at each echo time for each coil, using the CISSCO method described in [2, 3]. Results: The quantified magnetic moments for each object are consistent among 4 echo times and different hardware. In addition, the quantified values agree with the expected values within uncertainties. Conclusion: For each of the three objects, we have demonstrated self consistencies of quantified magnetic moments between four different setups at four different echo times, using the CISSCO method. These results support that, with the appropriate post processing procedures and methods applied on images acquired from any MRI hardware or imaging parameters, we should obtain the same magnetic moment of the same object of interest. However, phase images improperly post processed may or may not lead to the correct quantified magnetic moment of the object. Post processing methods such as quantitative susceptibility mapping or combination of phase images from individual rf channels require further studies. Ref:[1] Schweser et. al, NeuroImage, 2011, pp. 2789–2807. [2] Cheng et. al, MRI, 2015, in press. [3] Cheng et. al, PMB, 2009, pp. 7025–7044. DOD/USAMRAA W81XWH-12-1-0522

MO‐F‐211‐07: Quantifying Magnetic Susceptibility of Veneous Blood by the Complex Sum Method in MRI

Purpose: Changes of venous blood oxygenation level leads to direct changes in the magnetic susceptibility of veins. The oxygenation level reflects the physiological state of a given vein. Therefore, susceptibility quantification of veins has been a strong interest in MRI. Here we will demonstrate a general approach to extracting magnetic susceptibilities of veins at arbitrary orientations from only two or three echoes of a standard 3D gradient echo sequence. Methods: The complex sum method is used. The complex MR signal of each voxel is added around a long cylindrical object of interest. Previous work has accurately quantified effective magnetic moments of given cylindrical objects. If an object has no MR signal, its volume and susceptibility can be further determined by the spin echo approach. On the other hand, when an object of interest (e.g., vein) has an MR signal, the susceptibility of the object and its volume may be uniquely solved using this method. Images acquired with two different echo times in a typical gradient echo sequence are sufficient to quantify the magnetic susceptibility and volume of veins. Several small isolated human cerebral veins were measured at TE=11.6 ms and 19.2 ms in 4.0T. Due to low signal to noise ratio, images at TE=19.2 ms were Bilateral filtered, to preserve the edge but reduce noise. The uncertainties of magnetic susceptibilities were quantified by the error propagation method. Results: The measuredsusceptibility of veins at two different echo times agrees with the value in the textbook (0.40 ppm) within the uncertainty. The volumes of venous vessels, the spin density inside and outside these vessels are also obtained. Conclusions: The in‐vivo measurements demonstrate our method can be used to quantify the magnetic susceptibility of a given narrow and long cylindrical object in human imaging.

TH-D-201C-07: A Quantitative Approach to Extracting Magnetic Susceptibilities of Small Cylindrical Objects from Clinical MRI Sequences

Purpose: Changes of venous blood oxygenation level lead to direct changes in the magnetic susceptibility of veins. The oxygenation level reflects the physiological state of a given vein. Therefore susceptibility quantification of veins has been a strong interest in MRI [1]. Here we will demonstrate a general approach to extracting magnetic susceptibilities of narrow cylindrical objects and veins at arbitrary orientations from only two or three echoes of a standard 3D gradient echo sequence. Method and Materials: Our previous work [2] has accurately quantified effective magnetic moments of given cylindrical objects. If an object has no MR signal its volume and susceptibility can be further determined [2]. When an object of interest (e.g. vein) has an MR signal the susceptibility of the object and its volume may be uniquely quantified from our CISSCO method applied on images acquired with three different echo times. Simulations and phantoms of Gd‐DTPA dopedgel cylinders with diameters less than 5 pixels at arbitrary orientations were imaged at 1.5T. Several small isolated human cerebral veins were also measured from MRimages. The uncertainties of magnetic susceptibilities were quantified by the error propagation method.Results: Differences of measuredsusceptibilities in simulations at echo time (TE) 14ms are within 15% of the input susceptibility (1 ppm). These differences agree very well with the uncertainties estimated from the error propagation method. The measuredsusceptibilities of diluted Gadolinium cylinders from echo time 14 ms images have uncertainties less than 15% estimated from the error propagation method. The measuredsusceptibilities of veins agree with the textbook value [3] within 16%. Conclusion: Simulations phantom studies and in‐vivomeasurements demonstrate our approach can be used to accurately quantify the magnetic susceptibility of a given narrow and long cylindrical object.