Algebraic reconstruction of 3D spatial EPR images from high numbers of noisy projections: An improved image reconstruction technique for high resolution fast scan EPR imaging

Partial Acquisition of Spectral Projections Accelerates Four-dimensional Spectral-spatial EPR Imaging for Mouse Tumor Models: A Feasibility Study

PURPOSE

Our study aimed to accelerate the acquisition of four-dimensional (4D) spectral-spatial electron paramagnetic resonance (EPR) imaging for mouse tumor models. This advancement in EPR imaging should reduce the acquisition time of spectroscopic mapping while reducing quality degradation for mouse tumor models.

PROCEDURES

EPR spectra under magnetic field gradients, called spectral projections, were partially measured. Additional spectral projections were later computationally synthesized from the measured spectral projections. Four-dimensional spectral-spatial images were reconstructed from the post-processed spectral projections using the algebraic reconstruction technique (ART) and assessed in terms of their image qualities. We applied this approach to a sample solution and a mouse Hs766T xenograft model of human-derived pancreatic ductal adenocarcinoma cells to demonstrate the feasibility of our concept. The nitroxyl radical imaging agent 2H,15N-DCP was exogenously infused into the mouse xenograft model.

RESULTS

The computation code of 4D spectral-spatial imaging was tested with numerically generated spectral projections. In the linewidth mapping of the sample solution, we achieved a relative standard uncertainty (standard deviation/| mean |) of 0.76 μT/45.38 μT = 0.017 on the peak-to-peak first-derivative EPR linewidth. The qualities of the linewidth maps and the effect of computational synthesis of spectral projections were examined. Finally, we obtained the three-dimensional linewidth map of 2H,15N-DCP in a Hs766T tumor-bearing leg in vivo.

CONCLUSION

We achieved a 46.7% reduction in the acquisition time of 4D spectral-spatial EPR imaging without significantly degrading the image quality. A combination of ART and partial acquisition in three-dimensional raster magnetic field gradient settings in orthogonal coordinates is a novel approach. Our approach to 4D spectral-spatial EPR imaging can be applied to any subject, especially for samples with less variation in one direction.

Directional TV algorithm for fast EPR imaging

Precise radiation guided by oxygen images has demonstrated superiority over the traditional radiation methods. Electron paramagnetic resonance (EPR) imaging has proven to be the most advanced oxygen imaging modality. However, the main drawback of EPR imaging is the long scan time. For each projection, we usually need to collect the projection many times and then average them to achieve high signal-to-noise ratio (SNR). One approach to fast scan is to reduce the repeating time for each projection. While the projections would be noisy and thus the traditional commonly-use filtered backprojection (FBP) algorithm would not be capable of accurately reconstructing images. Optimization-based iterative algorithms may accurately reconstruct images from noisy projections for they may incorporate prior information into optimization models. Based on the total variation (TV) algorithms for EPR imaging, in this work, we propose a directional TV (DTV) algorithm to further improve the reconstruction accuracy. We construct the DTV constrained, data divergence minimization (DTVcDM) model, derive its Chambolle-Pock (CP) solving algorithm, validate the correctness of the whole algorithm, and perform evaluations via simulated and real data. The experimental results show that the DTV algorithm outperforms the existing TV and FBP algorithms in fast EPR imaging. Compared to the standard FBP algorithm, the proposed algorithm may achieve 10 times of acceleration.

Redox-Sensitive Mapping of a Mouse Tumor Model Using Sparse Projection Sampling of Electron Paramagnetic Resonance

Aims: This work aimed to establish an accelerated imaging system for redox-sensitive mapping in a mouse tumor model using electron paramagnetic resonance (EPR) and nitroxyl radicals. Results: Sparse sampling of EPR spectral projections was demonstrated for a solution phantom. The reconstructed three-dimensional (3D) images with filtered back-projection (FBP) and compressed sensing image reconstruction were quantitatively assessed for the solution phantom. Mouse xenograft models of a human-derived pancreatic ductal adenocarcinoma cell line, MIA PaCa-2, were also measured for redox-sensitive mapping with the sparse sampling technique. Innovation: A short-lifetime redox-sensitive nitroxyl radical (¹⁵N-labeled perdeuterated Tempone) could be measured to map the decay rates of the EPR signals for the mouse xenograft models. Acceleration of 3D EPR image acquisition broadened the choices of nitroxyl radical probes with various redox sensitivities to biological environments. Conclusion: Sparse sampling of EPR spectral projections accelerated image acquisition in the 3D redox-sensitive mapping of mouse tumor-bearing legs fourfold compared with conventional image acquisition with FBP. Antioxid. Redox Signal. 36, 57-69.

High fidelity triangular sweep of the magnetic field for millisecond scan EPR imaging

Linearity of the magnetic field sweep is important for high resolution continuous wave EPR imaging. Driving the field with triangular wave function is the most efficient way to scan EPR projections. However, the magnetic field sweep profile can be significantly distorted during fast millisecond projection scan. In this work, we introduce a method to generate highly linear and properly symmetrical triangular sweeps of the magnetic field using calibrated harmonics of the triangular wave function. First, the frequency response function of the EPR magnet and its power circuitry was obtained. For this, the field sweeping coil was driven with sinusoidal signals of different frequencies and the actual magnetic field inside the magnet was recorded. To cover wide range of frequencies, the measurements were carried out independently using gaussmeter, Hall-effect linear sensor integrated circuit, and an inductance coil. For each frequency, the system gain and the phase delay were determined. These data were used to adjust the amplitudes and the phases of individual harmonics of the triangular wave function. After the calibration, the maximum deviation of the magnetic field from the linear function was 0.05% of sweep width for 4 ms scan. The maximum discrepancy between the forward and the reverse scan was less than 0.04%. Sweep overhead time for changing the scan direction was 5%. The proposed approach allows generation of high fidelity triangular magnetic field sweeps with accuracy better than 0.1% for the range of the magnetic field sweep widths up to 48 G and scan duration from 10 s down to 1 ms.

A balanced total-variation-Chambolle-Pock algorithm for EPR imaging

Total variation (TV) minimization algorithm is an effective algorithm capable of accurately reconstructing images from sparse projection data in a variety of imaging modalities including computed tomography (CT) and electron paramagnetic resonance imaging (EPRI). The data divergence constrained, TV minimization (DDcTV) model and its Chambolle-Pock (CP) solving algorithm have been proposed for CT. However, when the DDcTV-CP algorithm is applied to 3D EPRI, it suffers from slow convergence rate or divergence. We hypothesize that this is due to the magnitude imbalance between the data fidelity term and the TV regularization term. In this work, we propose a balanced TV (bTV) model incorporating a balance parameter and demonstrate its capability to avoid convergence issues for the 3D EPRI application. Simulation and real experiments show that the DDcTV-CP algorithm cannot guarantee convergence but the bTV-CP algorithm may guarantee convergence and achieve fast convergence by use of an appropriate balance parameter. Experiments also show that underweighting the balance parameter leads to slow convergence, whereas overweighting the balance parameter leads to divergence. The iteration-behavior change-law with the variation of the balance parameter is explained by use of the data tolerance ellipse and gradient descent principle. The findings and insights gained in this work may be applied to other imaging modalities and other constrained optimization problems.