Stability and Reliability of Enhanced External-Internal Motion Correlation via Dynamic Phase-Shift Corrections Over 30-min Timeframe for Respiratory-Gated Radiotherapy

To assess the stability of patient-specific phase shifts between external- and internal-respiratory motion waveforms, the reliability of enhanced external–internal correlation with phase-shift correction, and the feasibility of guiding respiratory-gated radiotherapy (RGRT) over 30 min. In this clinical feasibility investigation, external bellows and internal-navigator waveforms were simultaneously and prospectively acquired along with two four-dimensional magnetic resonance imaging (4DMRI) scans (6–15 m each) with 15–20 m intervals in 10 volunteers. A bellows was placed 5 cm inferior to the xiphoid to monitor abdominal motion, and an MR navigator was used to track the diaphragmatic motion. The mean phase-domain (MPD) method was applied, which combines three individual phase-calculating methods: phase-space oval fitting, principal component analysis, and analytic signal analysis, weighted by the reciprocal of their residual errors (RE) excluding outliers (RE >2σ). The time-domain cross-correlation (TCC) analysis was applied for comparison. Dynamic phase-shift correction was performed based on the phase shift detected on the fly within two 10 s moving datasets. Simulating bellows-triggered gating, the median and 95% confidence interval for the navigator's position at beam-on/beam-off and %harm (percentage of beam-on time outside the safety margin) were calculated. Averaged across all subjects, the mean phase shifts are found indistinguishable (p > .05) between scan 1 (55˚ ± 9˚) and scan 2 (59˚ ± 11˚). Using the MPD method the averaged correlation increases from 0.56 ± 0.22 to 0.85 ± 0.11 for scan 1 and from 0.47 ± 0.30 to 0.84 ± 0.08 for scan 2. The TCC correction results in similar results. After phase-shift correction, the number of cases that were suitable for amplitude gating (with <10%harm) increased from 2 to 17 out of 20 cases. A patient-specific, stable phase-shift between the external and internal motions was observed and corrected using the MPD and TCC methods, producing long-lasting enhanced motion correlation over 30m. Phase-shift correction offers a feasible strategy for improving the accuracy of tumor-motion prediction during RGRT.

Enhancement of Long-Term External-Internal Correlation by Phase-Shift Detection and Correction Based on Concurrent External Bellows and Internal Navigator Signals

Purpose

The purpose of this study was to enhance the correlation between external and internal respiratory motions by dynamically determining and correcting the patient-specific phase shift between external and internal respiratory waveforms acquired concurrently during respiratory-correlated 4-dimensional magnetic resonance imaging scans.

Methods and Materials

Internal-navigator and external-bellows waveforms were acquired simultaneously during 6- to 15-minute respiratory-correlated 4-dimensional magnetic resonance imaging scans in 10 healthy participants under an institutional review board–approved protocol. The navigator was placed at the right lung–diaphragm interface, and the bellows were placed ∼5 cm inferior to the sternum. Three segments of each respiratory waveform, at the beginning, middle, and end of a scan, were analyzed. Three phase-domain methods were employed to estimate the phase shift, including analytical signal analysis, phase-space oval fitting, and principal component analysis. A robust strategy for estimating the phase shift was realized by combining these methods in a weighted average and by eliminating outliers (>2 σ) caused by breathing irregularities. Whether phase-shift correction affects the external-internal correlation was evaluated. The cross-correlation between the 2 waveforms in the time domain provided an independent check of the correlation enhancement.

Results

Phase-shift correction significantly enhanced the external-internal correlation in all participants across the entire 6- to 15-minute scans. On average, the correlation increased from 0.45 ± 0.28 to 0.85 ± 0.15 for the combined method. The combined method exhibited a 99.5% success rate and revealed that the phase of the external waveform leads that of the internal waveform in all 10 participants by 57 ^o ± 17^o (1.6 ± 0.5 bins) on average. Seven participants exhibited highly reproducible phase shifts over time, evidenced by standard deviations (σ) < 4^o, whereas 8^o < σ < 12^o in the remaining 3 participants. Regardless, phase-shift correction significantly improved the correlation in all participants.

Conclusions

Correcting the phase shift estimated by the phase-domain methods provides a new approach for enhancing the correlation between external and internal respiratory motions. This strategy holds promise for improving the accuracy of respiratory-gated radiation therapy.

Suitability of markerless EPID tracking for tumor position verification in gated radiotherapy

PURPOSE

To maximize the benefits of respiratory gated radiotherapy (RGRT) of lung tumors real-time verification of the tumor position is required. This work investigates the feasibility of markerless tracking of lung tumors during beam-on time in electronic portal imaging device (EPID) images of the MV therapeutic beam.

METHODS

EPID movies were acquired at ∼2 fps for seven lung cancer patients with tumor peak-to-peak motion ranges between 7.8 and 17.9 mm (mean: 13.7 mm) undergoing stereotactic body radiotherapy. The external breathing motion of the abdomen was synchronously measured. Both datasets were retrospectively analyzed in PortalTrack, an in-house developed tracking software. The authors define a three-step procedure to run the simulations: (1) gating window definition, (2) gated-beam delivery simulation, and (3) tumor tracking. First, an amplitude threshold level was set on the external signal, defining the onset of beam-on/-off signals. This information was then mapped onto a sequence of EPID images to generate stamps of beam-on/-hold periods throughout the EPID movies in PortalTrack, by obscuring the frames corresponding to beam-off times. Last, tumor motion in the superior-inferior direction was determined on portal images by the tracking algorithm during beam-on time. The residual motion inside the gating window as well as target coverage (TC) and the marginal target displacement (MTD) were used as measures to quantify tumor position variability.

RESULTS

Tumor position monitoring and estimation from beam's-eye-view images during RGRT was possible in 67% of the analyzed beams. For a reference gating window of 5 mm, deviations ranging from 2% to 86% (35% on average) were recorded between the reference and measured residual motion. TC (range: 62%-93%; mean: 77%) losses were correlated with false positives incidence rates resulting mostly from intra-/inter-beam baseline drifts, as well as sudden cycle-to-cycle fluctuations in exhale positions. Both phenomena can lead to considerable deviations (with MTD values up to a maximum of 7.8 mm) from the intended tumor position, and in turn may result in a marginal miss. The difference between tumor traces determined within the gating window against ground truth trajectory maps was 1.1 ± 0.7 mm on average (range: 0.4-2.3 mm).

CONCLUSIONS

In this retrospective analysis of motion data, it is demonstrated that the system is capable of determining tumor positions in the plane perpendicular to the beam direction without the aid of fiducial markers, and may hence be suitable as an online verification tool in RGRT. It may be possible to use the tracking information to enable on-the-fly corrections to intra-/inter-beam variations by adapting the gating window by means of a robotic couch.

Structural identifiability of viscoelastic mechanical systems

We solve the local and global structural identifiability problems for viscoelastic mechanical models represented by networks of springs and dashpots. We propose a very simple characterization of both local and global structural identifiability based on identifiability tables, with the purpose of providing a guideline for constructing arbitrarily complex, identifiable spring-dashpot networks. We illustrate how to use our results in a number of examples and point to some applications in cardiovascular modeling.