Bi-exponential Magnetic Resonance Signal Model for Partial Volume Computation

Abstract

Accurate quantification of small structures in magnetic resonance (MR) images is often limited by partial volume (PV) effects which arise when more than one tissue type is present in a voxel. PV may be critical when dealing with changes in brain anatomy as the considered structures such as gray matter (GM) are of similar size as the MR spatial resolution. To overcome the limitations imposed by PV effects and achieve subvoxel accuracy different methods have been proposed. Here, we describe a method to compute PV by modeling the MR signal with a biexponential linear combination representing the contribution of at most two tissues in each voxel. In a first step, we estimated the parameters (T1, T2 and proton density) per tissue. Then, based on the bi-exponential formulation one can retrieve fractional contents by solving a linear system of two equations with two unknowns, namely tissue magnetizations. Preliminary tests were conducted on images acquired on a specially designed physical phantom for the study of PV effects. Further, the model was tested on BrainWeb simulated brain images to estimate GM and white matter (WM) PV effects. Root mean squared error was computed between the BrainWeb ground truth and the obtained GM and WM PV maps. The proposed method outperformed traditionally used methods by 33% and 34% in GM and WM, respectively.

Finite product representation via multiplicative calculus and its applications to exponential signal processing

“…One method of overcoming the PV effect was introduced in [5]. Let's now consider the mathematical model as an application to newly derived method.…”

“…The MR signal representation is then used for diagnosis of several diseases. Therefore, the paper [5] uses a direct and independent calculation of the unknown parameters rather than using some assumptions. The model relies on Spin Echo (SE) signal function for a single tissue as;…”

“…It is possible to list typical application areas such as resistor capacitor(RC) element filtration, harmonic exponential modelling of transitional speech segment (see [11]), exponential signals in noise (see [16]), magnetic resonance (MR) in image processing (see [5]). Signal representation in magnetic resonance has a great application in medical electronics.…”

“…The paper [5] is aiming to find the best matching parameters of M 0 , T E, T 2, T R and T 1. The model involves exponential functions, therefore, we highly recommend to use multiplicative least square method and minimization algorithms introduced in [15] to reveal the unknown parameters.…”

“…The signal (32) was originally given in [5] which involves a linear combination of mono exponential with unknown parameters M 0 , T E, T 2, T R and T 1. The paper [5] is aiming to find the best matching parameters of M 0 , T E, T 2, T R and T 1.…”