Purpose To develop a technique to generate on-board volumetric-cine MRI (VC-MRI) using patient prior images, motion modeling and on-board 2D-cine MRI. Methods One phase of a 4D-MRI acquired during patient simulation is used as patient prior images. 3 major respiratory deformation patterns of the patient are extracted from 4D-MRI based on principal-component-analysis. The on-board VC-MRI at any instant is considered as a deformation of the prior MRI. The deformation field is represented as a linear combination of the 3 major deformation patterns. The coefficients of the deformation patterns are solved by the data fidelity constraint using the acquired on-board single 2D-cine MRI. The method was evaluated using both XCAT simulation of lung cancer patients and MRI data from four real liver cancer patients. The accuracy of the estimated VC-MRI was quantitatively evaluated using Volume-Percent-Difference(VPD), Center-of-Mass-Shift(COMS), and target tracking errors. Effects of acquisition orientation, region-of-interest(ROI) selection, patient breathing pattern change and noise on the estimation accuracy were also evaluated. Results Image subtraction of ground-truth with estimated on-board VC-MRI shows fewer differences than image subtraction of ground-truth with prior image. Agreement between profiles in the estimated and ground-truth VC-MRI was achieved with less than 6% error for both XCAT and patient data. Among all XCAT scenarios, the VPD between ground-truth and estimated lesion volumes was on average 8.43±1.52% and the COMS was on average 0.93±0.58mm across all time-steps for estimation based on the ROI region in the sagittal cine images. Matching to ROI in the sagittal view achieved better accuracy when there was substantial breathing pattern change. The technique was robust against noise levels up to SNR=20. For patient data, average tracking errors were less than 2 mm in all directions for all patients. Conclusions Preliminary studies demonstrated the feasibility to generate real-time VC-MRI for on-board localization of moving targets in radiotherapy.

Purpose To accelerate volumetric cine MRI (VC-MRI) using undersampled 2D-cine MRI to provide real-time 3D guidance for gating/target tracking in radiotherapy. Methods 4D-MRI is acquired during patient simulation. One phase of the prior 4D-MRI is selected as the prior images, designated as MRIprior. The on-board VC-MRI at each time-step is considered a deformation of the MRIprior. The deformation field map (DFM) is represented as a linear combination of the motion components extracted by Principal Component Analysis (PCA) from the prior 4D-MRI. The weighting coefficients of the motion components are solved by matching the corresponding 2D-slice of the VC-MRI with the on-board undersampled 2D-cine MRI acquired. Undersampled Cartesian and radial k-space acquisition strategies were investigated. The effects of k-space sampling percentage (SP) and distribution, tumor sizes and noise on the VC-MRI estimation were studied. The VC-MRI estimation was evaluated using XCAT simulation of lung cancer patients and data from liver cancer patients. Volume Percent Difference (VPD), Center of Mass Shift (COMS) of the tumor volumes and tumor tracking errors were calculated. Results For XCAT, VPD/COMS were 11.93±2.37%/0.90±0.27mm and 11.53±1.47%/0.85±0.20mm among all scenarios with Cartesian sampling (SP=10%) and radial sampling (21spokes, SP=5.2%), respectively. When tumor size decreased, higher sampling rate achieved more accurate VC-MRI than lower sampling rate. VC-MRI was robust against noise levels up to SNR=20. For patient data, the tumor tracking errors in Superior-Inferior (SI), Anterior-Posterior (AP) and Lateral (LAT) directions were 0.46±0.20mm, 0.56±0.17mm and 0.23±0.16mm, respectively, for Cartesian-based sampling with SP=20% and 0.60±0.19mm, 0.56±0.22mm and 0.42±0.15mm, respectively, for radial-based sampling with SP=8% (32 spokes). Conclusions It is feasible to estimate VC-MRI from a single undersampled on-board 2D cine MRI. Phantom and patient studies showed that the temporal resolution of VC-MRI can potentially be improved by 5–10 times using a 2D cine image acquired with 10–20% k-space sampling.

Purpose To investigate the feasibility of using structural-based principal component analysis (PCA) motion-modeling and weighted free-form deformation to estimate on-board 4D-CBCT using prior information and extremely limited angle projections for potential 4D target verification of lung radiotherapy. Methods A technique for lung 4D-CBCT reconstruction has been previously developed using a deformation field map (DFM)-based strategy. In the previous method, each phase of the 4D-CBCT was generated by deforming a prior CT volume. The DFM was solved by a motion-model extracted by global PCA and free-form deformation (GMM-FD) technique, using a data fidelity constraint and deformation energy minimization. In this study, a new structural-PCA method was developed to build a structural motion-model (SMM) by accounting for potential relative motion pattern changes between different anatomical structures from simulation to treatment. The motion model extracted from planning 4DCT was divided into two structures: tumor and body excluding tumor, and the parameters of both structures were optimized together. Weighted free-form deformation (WFD) was employed afterwards to introduce flexibility in adjusting the weightings of different structures in the data fidelity constraint based on clinical interests. XCAT (computerized patient model) simulation with a 30 mm diameter lesion was simulated with various anatomical and respirational changes from planning 4D-CT to onboard volume to evaluate the method. The estimation accuracy was evaluated by the Volume-Percent-Difference (VPD)/Center-of-Mass-Shift (COMS) between lesions in the estimated and “ground-truth” on board 4D-CBCT. Different onboard projection acquisition scenarios and projection noise levels were simulated to investigate their effects on the estimation accuracy. The method was also evaluated against 3 lung patients. Results The SMM-WFD method achieved substantially better accuracy than the GMM-FD method for CBCT estimation using extremely small scan angles or projections. Using orthogonal 15° scanning angles, the VPD/COMS were 3.47±2.94% and 0.23±0.22mm for SMM-WFD and 25.23±19.01% and 2.58±2.54mm for GMM-FD among all 8 XCAT scenarios. Compared to GMM-FD, SMM-WFD was more robust against reduction of the scanning angles down to orthogonal 10° with VPD/COMS of 6.21±5.61% and 0.39±0.49mm, and more robust against reduction of projection numbers down to only 8 projections in total for both orthogonal-view 30° and orthogonal-view 15° scan angles. SMM-WFD method was also more robust than the GMM-FD method against increasing levels of noise in the projection images. Additionally, the SMM-WFD technique provided better tumor estimation for all three lung patients compared to the GMM-FD technique. Conclusion Compared to the GMM-FD technique, the SMM-WFD technique can substantially improve the 4D-CBCT estimation accuracy using extremely small scan angles and low number of projections to provide fast low dose 4D target verification.

Background: The purpose of this study is to improve on-board volumetric cine magnetic resonance imaging (VC-MRI) using multi-slice undersampled cine images reconstructed using spatio-temporal k-space data, patient prior 4D-MRI, motion modeling (MM) and free-form deformation (FD) for real-time 3D target verification of liver and lung radiotherapy.Methods: A previous method was developed to generate on-board VC-MRI by deforming prior MRI images based on a MM and a single-slice on-board 2D-cine image. The two major improvements over the previous method are: (I) FD was introduced to estimate VC-MRI to correct for inaccuracies in the MM; (II) multi-slice undersampled 2D-cine images reconstructed by a k-t SLR reconstruction method were used for FD-based estimation to maintain the temporal resolution while improving the accuracy of VC-MRI. The method was evaluated using XCAT lung simulation and four liver patients' data.Results: For XCAT, VC-MRI estimated using ten undersampled sagittal 2D-cine MRIs resulted in volume percent difference/volume dice coefficient/center-of-mass shift of 9.77%±3.71%/0.95±0.02/0.75±0.26 mm among all scenarios based on estimation with MM and FD. Adding FD optimization improved VC-MRI accuracy substantially for scenarios with anatomical changes. For patient data, the mean tumor tracking errors were 0.64±0.51, 0.62±0.47 and 0.24±0.24 mm along the superior-inferior (SI), anterior-posterior (AP) and lateral directions, respectively, across all liver patients.Conclusions: It is feasible to improve VC-MRI accuracy while maintaining high temporal resolution using FD and multi-slice undersampled 2D cine images for real-time 3D target verification.

Purpose: On-board MRI can provide superb soft tissue contrast for improving liver SBRT localization. However, the availability of on-board MRI in clinics is extremely limited. On the contrary, on-board kV imaging systems are widely available on radiotherapy machines, but its capability to localize tumors in soft tissue is limited due to its poor soft tissue contrast. This study aims to explore the feasibility of using an on-board kV imaging system and patient prior knowledge to generate on-board four-dimensional (4D)-MRI for target localization in liver SBRT. Methods: Prior 4D MRI volumes were separated into end of expiration (EOE) phase (MRI prior ) and all other phases. MRI prior was used to generate a synthetic CT at EOE phase (sCT prior ). On-board 4D MRI at each respiratory phase was considered a deformation of MRI prior . The deformation field map (DFM) was estimated by matching DRRs of the deformed sCT prior to on-board kV projections using a motion modeling and free-form deformation optimization algorithm. The on-board 4D MRI method was evaluated using both XCAT simulation and real patient data. The accuracy of the estimated on-board 4D MRI was quantitatively evaluated using Volume Percent Difference (VPD), Volume Dice Coefficient (VDC), and Center of Mass Shift (COMS). Effects of scan angle and number of projections were also evaluated. Results: In the XCAT study, VPD/VDC/COMS among all XCAT scenarios were 10.16 AE 1.31%/ 0.95 AE 0.01/0.88 AE 0.15 mm using orthogonal-view 30°scan angles with 102 projections. The onboard 4D MRI method was robust against the various scan angles and projection numbers evaluated. In the patient study, estimated on-board 4D MRI was generated successfully when compared to the "reference on-board 4D MRI" for the liver patient case. Conclusions: A method was developed to generate on-board 4D MRI using prior 4D MRI and onboard limited kV projections. Preliminary results demonstrated the potential for MRI-based image guidance for liver SBRT using only a kV imaging system on a conventional LINAC.

To predict real-time 3D deformation field maps (DFMs) using Volumetric Cine MRI (VC-MRI) and adaptive boosting and multi-layer perceptron neural network (ADMLP-NN) for 4D target tracking. One phase of a prior 4D-MRI is set as the prior phase, MRIprior. Principal component analysis (PCA) is used to extract three major respiratory deformation modes from the DFMs generated between the prior and remaining phases. VC-MRI at each time-step is considered a deformation of MRIprior, where the DFM is represented as a weighted linear combination of the PCA components. The PCA weightings are solved by minimizing the differences between on-board 2D cine MRI and its corresponding VC-MRI slice. The PCA weightings solved during the initial training period are used to train an ADMLP-NN to predict PCA weightings ahead of time during the prediction period. The predicted PCA weightings are used to build predicted 3D DFM and ultimately, predicted VC-MRIs for 4D target tracking. The method was evaluated using a 4D computerized phantom (XCAT) with patient breathing curves and MRI data from a real liver cancer patient. Effects of breathing amplitude change and ADMLP-NN parameter variations were assessed. The accuracy of the PCA curve prediction was evaluated. The predicted real-time 3D tumor was evaluated against the ground-truth using volume dice coefficient (VDC), center-of-mass-shift (COMS), and target tracking errors. For the XCAT study, the average VDC and COMS for the predicted tumor were 0.92  ±  0.02 and 1.06  ±  0.40 mm, respectively, across all predicted time-steps. The correlation coefficients between predicted and actual PCA curves generated through VC-MRI estimation for the 1st/2nd principal components were 0.98/0.89 and 0.99/0.57 in the SI and AP directions, respectively. The optimal number of input neurons, hidden neurons, and MLP-NN for ADMLP-NN PCA weighting coefficient prediction were determined to be 7, 4, and 10, respectively. The optimal cost function threshold was determined to be 0.05. PCA weighting coefficient and VC-MRI accuracy was reduced for increased prediction-step size. Accurate PCA weighting coefficient prediction correlated with accurate VC-MRI prediction. For the patient study, the predicted 4D tumor tracking errors in superior–inferior, anterior–posterior and lateral directions were 0.50  ±  0.47 mm, 0.40  ±  0.55 mm, and 0.28  ±  0.12 mm, respectively. Preliminary studies demonstrated the feasibility to use VC-MRI and artificial neural networks to predict real-time 3D DFMs of the tumor for 4D target tracking.

To develop a novel multi-contrast four-dimensional magnetic resonance imaging (MC-4D-MRI) technique that expands single image contrast 4D-MRI to a spectrum of native and synthetic image contrasts and to evaluate its feasibility in liver tumor patients. Methods and materials:The MC-4D-MRI technique integrates multiparametric MRI fusion, 4D-MRI, and deformable image registration (DIR) techniques. The fusion technique consists of native MRI as input, image preprocessing, fusion algorithm, adaptation, and fused multi-contrast MRI as output. Four-dimensional deformation vector fields (4D-DVF) were generated from an original T2/T1-w 4D-MRI by deforming end-of -inhalation (EOI) to nine other phase volumes via DIR. The 4D-DVF were applied to multi-contrast MRI to generate a spectrum of 4D-MRI in different image contrasts. The MC-4D-MRI technique was evaluated in five liver tumor patients on tumor contrast-to-noise ratio (CNR), internal target volume (ITV) contouring consistency, diaphragm motion range, and tumor motion trajectory; and in digital anthropomorphic phantoms on 4D-DIR introduced errors in tumor motion range, centroid location, extent, and volume. Results: MC-4D-MRI consisting of 4D-MRIs in native image contrasts (T1-w, T2-w, and T2/T1-w) and synthetic image contrasts, such as tumor-enhanced contrast (TEC) were generated in five liver tumor patients. Patient tumor CNR increased from 2.6 ± 1.8 in the T2/T1-w MRI, to -4.4 ± 2.4, 6.6 ± 3.0, and 9.6 ± 3.9 in the T1-w, T2-w, and TEC MRI, respectively. Patient ITV interobserver mean Dice similarity coefficient (mDSC) increased from 0.65 ± 0.10 in the original T2/T1-w 4D-MRI, to 0.76 ± 0.14, 0.77 ± 0.12, and 0.86 ± 0.05 in the T1-w, T2-w, and TEC 4D-MRI, respectively. Patient diaphragm motion range absolute differences between the three new 4D-MRIs and original T2/T1-w 4D-MRI were 1.2 ± 1.3, 0.3 ± 0.7, and 0.5 ± 0.5 mm, respectively. Patient tumor displacement phase-averaged absolute differences between the three 4D-MRIs and the original 4D-MRI were 0.72 ± 0.33, 0.62 ± 0.54, and 0.74 ± 0.43 mm in the superior-inferior (SI) direction, and 0.59 ± 0.36, 0.51 ± 0.30, and 0.50 ± 0.24 mm in the anterior-posterior (AP) direction, respectively. In the digital phantoms, phase-averaged absolute tumor centroid shift caused by the 4D-DIR were at or below 0.5 mm in SI, AP, and left-right (LR) directions. Conclusion:We developed an MC-4D-MRI technique capable of expanding single image contrast 4D-MRI along a new dimension of image contrast. Initial 7984

We develop a new approach for studying flux anomalies in quadruply-imaged fold lens systems. We show that in the absence of substructure, microlensing, or differential absorption, the expected flux ratios of a fold pair can be tightly constrained using only geometric arguments. We apply this technique to 11 known quadruple lens systems in the radio and infrared, and compare our estimates to the Monte Carlo based results of Keeton, Gaudi, and Petters (2005). We show that a robust estimate for a flux ratio from a smoothly varying potential can be found, and at long wavelengths those lenses deviating from from this ratio almost certainly contain significant substructure.