Direct Exponential Curve Resolution Algorithm Research Articles

Applications and new developments of the direct exponential curve resolution algorithm (DECRA). Examples of spectra and magnetic resonance images

Applications and new developments of the direct exponential curve resolution algorithm (DECRA). Examples of spectra and magnetic resonance images

Multivariate Image Analysis of Magnetic Resonance Images with the Direct Exponential Curve Resolution Algorithm (DECRA): Part 1: Algorithm and Model Study

Antalek and Windig recently presented a fast method to resolve a series of NMR mixture spectra, where the contribution of the components varies with a decaying exponential [B. Antalek and W. Windig,J. Am. Chem. Soc.118, 10,331–10,332 (1996); W. Windig and B. Antalek,Chemom. Intell. Lab. Syst.37, 241–254 (1997)]. The method was called DECRA (direct exponential curve resolution algorithm). In this paper DECRA will be applied to two series of magnetic resonance images. The signal of one series is based uponT2relaxation, and the other is based uponT1relaxation. In order to evaluate the technique, the magnetic resonance images of a phantom where used. A transformation is introduced to enable the application of DECRA to aT1series of magnetic resonance images. A separate paper in this issue will describe the application of the techniques to magnetic resonance images of the human brain.

Multivariate Image Analysis of Magnetic Resonance Images with the Direct Exponential Curve Resolution Algorithm (DECRA): Part 2: Application to Human Brain Images

Owing to the heterogeneity of living tissues, it is challenging to quantify tissue properties using magnetic resonance imaging. Within a single voxel, contributions to the signal may result from several types of1H nuclei with varied chemical (e.g., −CH2−, −OH) and physical environments (e.g., tissue density, compartmentalization). Therefore, mixtures of1H environments are prevalent. Furthermore, each unique type of1H environment may possess a unique and characteristic spin–lattice relaxation time (T1) and spin–spin relaxation time (T2). A method for resolving these unique exponentials is introduced in a separate paper (Part 1. Algorithm and Model System) and uses the direct exponential curve resolution algorithm (DECRA). We present results from an analysis of images of the human head comprising brain tissues.

Direct exponential curve resolution algorithm (DECRA): A novel application of the generalized rank annihilation method for a single spectral mixture data set with exponentially decaying contribution profiles

The generalized rank annihilation method (GRAM) is a powerful method for calibration and self-modeling curve resolution. The mathematical treatment requires two data sets, which implies two experiments. The required relation between the two data sets is strict and minor differences, such as in retention times for hyphenated techniques, violate the mathematical requirements leading to erroneous results. It will be shown in this paper that only one experiment is needed in the case where the contribution of the components in the mixture spectra is of a decaying exponential character. Examples are given of pulsed gradiet spin echo (PGSE) nuclear magnetic resonance (NMR) data. The MATLAB function to reproduce the results is given and is available through Chemolab's archives, together with the data files. The method is called DECRA (direct exponential curve resolution algorithm).