APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022;
Chicago
Session B43: Inverse Problems: From Biomedicine to Materials
11:30 AM–2:30 PM,
Monday, March 14, 2022
Room: McCormick Place W-375B
Sponsoring
Units:
GMED DCOMP
Chair: Wojciech Zbijewski, Johns Hopkins University
Abstract: B43.00001 : Introduction to Inverse Problems with Applications to Magnetic Resonance Relaxometry and Myelin Mapping in the Brain*
11:30 AM–12:06 PM
Abstract
Presenter:
Richard G Spencer
(National Institutes of Health - NIH)
Author:
Richard G Spencer
(National Institutes of Health - NIH)
The success of conventional magnetic resonance imaging (MRI) is partly attributable to the fact that it is a Fourier technique. Data is collected in the space reciprocal to spatial coordinates, known as k-space, and then (inverse) Fourier transformed to produce an image. This reconstruction has the very attractive property of being mathematically well-conditioned, with condition number of unity, so that noise in the acquired data is necessarily transmitted to the image domain but is not magnified. Because of this, early studies performed at low magnetic field and with relatively unsophisticated radio frequency technology were able to yield useful images. Correspondingly, the quality of conventional MRI has increased roughly in proportion to improvements in acquisition SNR. However, the situation with the newer technique of MR relaxometry is not so rosy; the reconstruction of acquired data to obtain the distribution function of the parameter of interest is via a version of the inverse Laplace transform. This arises from the classically ill-posed problem of solving the Fredholm equation of the first kind. One implication is that noise is amplified in the reconstruction process. A corollary of this is that brute force efforts to improve SNR rapidly reach the point of diminishing returns, and other means must be undertaken to produce useful results. For this, the inverse problems perspective has proven to be enormously fruitful. We will discuss the basics of inverse problem theory and some developments applicable to MR relaxometry and related experiments. Our main application is to myelin mapping in the brain, and we will show how more accurate myelin quantification permits physiological correlations to be established. Our studies have the twofold goal of improving the capacity of MR to diagnose pathology and monitor disease progression, and of developing methods of general use for inverse problems.
*National Institute on Aging/NIH