Utilizing machine learning to predict MRI signal outputs from iron oxide nanoparticles through the PSLG algorithm

Abstract

In this research, we predict the output signal generated by iron oxide-based nanoparticles in Magnetic Resonance Imaging (MRI) using the physical properties of the nanoparticles and the MRI machine. The parameters considered include the size of the magnetic core of the nanoparticles, their magnetic saturation (Ms), the concentration of the nanoparticles (C), and the magnetic field (MF) strength of the MRI device. These parameters serve as input variables for the model, while the relaxation rate R₂ (s^-1) is taken as the output variable. To develop this model, we employed a machine learning approach based on a neural network known as SA-LOOCV-GRBF (SLG). In this study, we compared two different random selection patterns: SLG disperse random selection (DSLG) and SLG parallel random selection (PSLG). The sensitivity to neuron number in the hidden layers for DSLG was more pronounced compared to the PSLG pattern, and the mean square error (MSE) was calculated for this evaluation. It appears that the PSLG method demonstrated strong performance while maintaining less sensitivity to increasing neuron numbers. Consequently, the new pattern, PSLG, was selected for predicting MRI behavior.

Keywords: Iron oxide nanoparticles; Machine learning; Magnetic resonance imaging (MRI); RBF neural network.

Fig. 1

The schematic of SA-LOOCV-GRBF (SLG) algorithm.

Fig. 2

The schematic of c and σ random generation of PSLG algorithm.

Fig. 3

The schematic of c and σ random generation of DSLG algorithm.

Fig. 4

Schematic illustrating the random selection position method within the input range of (x_min, x_max). This method is utilized in the distributed SLG (DSLG) with distributed random selection and the parallel SLG (PSLG) algorithm with parallel random selection for nonlinear parameters (c and σ) in a Gaussian function, with an input number of 4.

Fig. 5

The MSE calculation in each step of neuron number (M) adding in (A) disperse SA-LOOCV-GRBF (DSLG) and parallel SA-LOOCV-GRBF (PSLG) patterns together, (B) MSE change for PSLG pattern.

Fig. 6

Performance evaluation of the PSLG model compared to the DSLG model, (A) Actual MRI output signals (actual output) versus model predictions by the PSLG model, (points close to the (x = y) line indicate superior modeling performance), (B) Number of iterations required for the PSLG model to achieve the output results, indicating convergence of the cv function at the optimal SA state, (C) Comparison of predicted outputs of the DSLG model against actual MRI data, indicating significant deviation from the x = y line, (D) Number of iterations required for the DSLG model to achieve the output results.

Fig. 7

Analysis of MRI signal (s^− 1) variations with Magnetic Field (Tesla) and nanoparticle size (NPs size, nm), (A) Relationship between Magnetic Field and signal intensity at different saturated magnetic saturation (Ms, emu/g) for PSLG method. (B) Fluctuations in signal strength due to variations in Magnetic Field at different Ms for DSLG method. (C) Signal intensity as a function of Nps size and concentration (mM), for PSLG, (D) Signal intensity as a function of Nps size and concentration (mM), for DSLG.

Fig. 8

Comparative analysis of signal variations with magnetic saturation (Ms) and nanoparticle concentration in different models, (A) In the PSLG model, the signal (1/T₂) along with Ms (emu/g) at three different sizes of Nps (5, 11 and 31 nm). (B) The DSLG method, the signal (1/T2) along with Ms (emu/g) at three different sizes of Nps (5, 11 and 31 nm). (C) A nonlinear relationship between signal (1/T2) and concentration is observed in the PSLG model at three different MF (1.41, 4.2 and 11.7 Tesla). (D) relationship between signal (1/T₂) and concentration is observed in the DSLG model at three different MF (1.41, 4.2 and 11.7 Tesla).

Fig. 9

Performance evaluation of the Random Forest (RF) model compared to the Parallel SA-LOOCV-GRBF (PSLG) model. (A) Actual output versus model predictions by the RF model for Y_real and Y_noisy, (points close to the (x = y) line indicate superior modeling performance). (B) Comparing the prediction of Y_real and Y_noisy by RF method versus Y_real and Y_noisy. (C) Comparison of predicted outputs of the PSLG model against actual data for Y_real and Y_noisy, indicating significant deviation from the x = y line. (D) Comparing the prediction of Y_real and Y_noisy by PSLG method versus Y_real and Y_noisy.