Relaxation-based viscosity mapping for magnetic particle imaging

Abstract

Magnetic particle imaging (MPI) has been shown to provide remarkable contrast for imaging applications such as angiography, stem cell tracking, and cancer imaging. Recently, there is growing interest in the functional imaging capabilities of MPI, where 'color MPI' techniques have explored separating different nanoparticles, which could potentially be used to distinguish nanoparticles in different states or environments. Viscosity mapping is a promising functional imaging application for MPI, as increased viscosity levels in vivo have been associated with numerous diseases such as hypertension, atherosclerosis, and cancer. In this work, we propose a viscosity mapping technique for MPI through the estimation of the relaxation time constant of the nanoparticles. Importantly, the proposed time constant estimation scheme does not require any prior information regarding the nanoparticles. We validate this method with extensive experiments in an in-house magnetic particle spectroscopy (MPS) setup at four different frequencies (between 250 Hz and 10.8 kHz) and at three different field strengths (between 5 mT and 15 mT) for viscosities ranging between 0.89 mPa · s-15.33 mPa · s. Our results demonstrate the viscosity mapping ability of MPI in the biologically relevant viscosity range.

Viscosity quantification using multi-contrast magnetic particle imaging

“…Using an adaption of the temperature mapping method proposed in [20] we provided the first viscosity quantification of a series of samples within a viscosity range of 1.0-51.8 mPa s with a methodological error of 6%. Thereby, extending the qualitative proof-of-concept given in [19] for a viscosity range of 0.89 mPa s to 15.33 mPa s by our quantitative results. This allows a first comparison of MPI viscosity mapping capabilities with spectroscopic methods which reported methodological errors as low as 0.1% [7] within a viscosity range of 0.96-260 mPa s. The total error of the viscosity estimation is composed of a methodological estimation error and a calibration error.…”

“…A different approach was proposed in [16,17] where 1D x-space MPI signals were evaluated at two drive-field strength allowing to colorize an image based on the Brown and Néel relaxation mechanisms yielding qualitative mobility information of the MPI tracer particles. Furthermore, in [18,19] a proof-ofconcept was provided that viscosity mapping can be achieved through the estimation of relaxation time constants from the two half cycles of the MPI time signal. Another technique developed in [3] generalizes the calibration based algebraic image reconstruction method to exploit the differences in the corresponding particle responses for the imaging of different particle types and aggregation states.…”

Calibration-Free Relaxation-Based Multi-Color Magnetic Particle Imaging

“…Correct (t edge , τ ) pair should restore the mirror symmetry, minimizing the mean squared error (MSE) between positive and mirrored negative signals after the deconvolution, i.e., (12) whereŝ(t) denotes the signal after deconvolution with the estimated relaxation kernel. Here, instead of computing MSE over the entire half period, more weights can be assigned to central time points that typically have higher SNR [31].…”

“…• Upper limit on estimations: Extensive work in nanoparticle relaxometry showed that relaxation time constants are much smaller than the period of the drive field [34], typically less than 10% of the period [31]. Here, we ignore estimations that are larger than one-fourth of the period.…”

“…The nanoparticle diameter was selected as 21 nm, a conservative value given the recent developments in tailored SPIO production [39]. The relaxation times ranged between 1-5 µs, as recently reported in experimental studies performed around 10 kHz [31], [34]. To match experimental conditions, the simulated MPI signal was sampled at 2 MSPS sampling frequency, and additive white Gaussian noise corresponding to a peak signal SNR of 100 was added to the MPI signal.…”