Multisite EPR oximetry from multiple quadrature harmonics

Abstract

Multisite continuous wave (CW) electron paramagnetic resonance (EPR) oximetry using multiple quadrature field modulation harmonics is presented. First, a recently developed digital receiver is used to extract multiple harmonics of field modulated projection data. Second, a forward model is presented that relates the projection data to unknown parameters, including linewidth at each site. Third, a maximum likelihood estimator of unknown parameters is reported using an iterative algorithm capable of jointly processing multiple quadrature harmonics. The data modeling and processing are applicable for parametric lineshapes under nonsaturating conditions. Joint processing of multiple harmonics leads to 2-3-fold acceleration of EPR data acquisition. For demonstration in two spatial dimensions, both simulations and phantom studies on an L-band system are reported.

Figure 1

Illustration of the forward modeling concept. The top-left square panel displays the spatial dimensions of a 2D spatial, 1D spectral object with three EPR active sites (U = 3). The other three square panels show the decomposition of the object into three subobjects. The vertical arrows indicate the lines of integration for the Radon transform for a particular gradient orientation. The shaded areas residing on the horizontal lines are the spatial profiles resulting from the Radon transform of the 2D spatial subobjects. These spatial profiles are then convolved with the respective lineshapes (not shown) of the subobjects to generate projections, indicated by black sold line on the horizontal axis. The final projection, shown above the top-left square panel, of the object is the sum of the projections from all the subobjects.

Figure 2

Fitting results for stage 1 and stage 2 for the 2D simulated phantom shown in Fig. 3. For incoherent reconstruction of stage 1 (a), curve fitting is performed on the root-sum-square (RSS) of the simulated quadrature harmonics. For stage 2, the six quadrature harmonics (b and c) are jointly fitted. Only the maximum field gradient projection is shown, and only the first three harmonics are depicted. The two vertical dotted lines separate the three harmonics.

Figure 3

Multisite reconstruction for 40 × 40 simulated phantom with five sites. Input phantom (a), stage 1 spin density reconstruction (b), image segmentation based on stage 1 (c), and the final spin density reconstruction from stage 2 (d). The reconstructions represent a spatial dimension of 11.3 × 11.3 mm² and image resolution of 40 × 40 pixels.

Figure 4

Estimated linewidths for the five-site simulated phantom. Error bars represents ±2 std. UM-1 represents linewidth estimation from undermodulated y_I,1 harmonic component; OM-1 represents linewidth estimation from overmodulation y_I,1; and OM-6 represents linewidth estimation based on the joint processing of y_I,1, y_Q,1, y_I,2, y_Q,2, y_I,3, and y_Q,3. The horizontal dashed lines indicate the true linewidth values.

Figure 5

Fitting results for stage 1 and stage 2 for the 2D L-band oximetry experiment. For incoherent reconstruction of stage 1 (a), curve fitting is performed on the root-sum-square (RSS) of the measured quadrature harmonics. For stage 2, the six quadrature harmonics (b and c) are jointly fitted. Only the maximum field gradient projection is shown, and only the first three harmonics are depicted. The two vertical dotted lines separate the three harmonics.

Figure 6

Reconstruction for the four-site L-band multisite oximetry phantom. Stage 1 spin density reconstruction (a), image segmentation based on stage 1 (b), and the final spin density reconstruction from stage 2 (c). Spatial dimensions for the reconstruction are 11.3 × 11.3 mm² and image resolution is 40 × 40 pixels.

Figure 7

Estimated linewidths for the four-site L-band multisite phantom. Error bars represents ±2 std. UM-1 represents linewidth estimation from undermodulated y_I,1 harmonic component; OM-1 represents linewidth estimation from overmodulation y_I,1; and OM-6 represents linewidth estimation based on the joint processing of y_I,1, y_Q,1, y_I,2, y_Q,2, y_I,3, and y_Q,3. The horizontal dashed lines indicate the true linewidth values.