Evaluation and mitigation of deformable image registration uncertainties for MRI-guided adaptive radiotherapy.

PURPOSE: We evaluate the performance of a deformable image registration (DIR) software package in registering abdominal magnetic resonance images (MRIs) and then develop a mechanical modeling method to mitigate detected DIR uncertainties. MATERIALS AND METHODS: Three evaluation metrics, namely mean displacement to agreement (MDA), DICE similarity coefficient (DSC), and standard deviation of Jacobian determinants (STD-JD), are used to assess the multi-modality (MM), contour-consistency (CC), and image-intensity (II)-based DIR algorithms in the MIM software package, as well as an in-house developed, contour matching-based finite element method (CM-FEM). Furthermore, we develop a hybrid FEM registration technique to modify the displacement vector field of each MIM registration. The MIM and FEM registrations were evaluated on MRIs obtained from 10 abdominal cancer patients. One-tailed Wilcoxon-Mann-Whitney (WMW) tests were conducted to compare the MIM registrations with their FEM modifications. RESULTS: For the registrations performed with the MIM-CC, MIM-MM, MIM-II, and CM-FEM algorithms, their average MDAs are 0.62 ± 0.27, 2.39 ± 1.30, 3.07 ± 2.42, 1.04 ± 0.72 mm, and average DSCs are 0.94 ± 0.03, 0.80 ± 0.12, 0.77 ± 0.15, 0.90 ± 0.11, respectively. The p-values of the WMW tests between the MIM registrations and their FEM modifications are less than 0.0084 for STD-JDs and greater than 0.87 for MDA and DSC. CONCLUSIONS: Among the three MIM DIR algorithms, MIM-CC shows the smallest errors in terms of MDA and DSC but exhibits significant Jacobian uncertainties in the interior regions of abdominal organs. The hybrid FEM technique effectively mitigates the Jacobian uncertainties in these regions.

Kinetic modeling of tumor regression incorporating the concept of cancer stem-like cells for patients with locally advanced lung cancer.

BACKGROUND: Personalized medicine for patients receiving radiation therapy remains an elusive goal due, in part, to the limits in our understanding of the underlying mechanisms governing tumor response to radiation. The purpose of this study was to develop a kinetic model, in the context of locally advanced lung cancer, connecting cancer cell subpopulations with tumor volumes measured during the course of radiation treatment for understanding treatment outcome for individual patients. METHODS: The kinetic model consists of three cell compartments: cancer stem-like cells (CSCs), non-stem tumor cells (TCs) and dead cells (DCs). A set of ordinary differential equations were developed to describe the time evolution of each compartment, and the analytic solution of these equations was iterated to be aligned with the day-to-day tumor volume changes during the course of radiation treatment. A least squares fitting method was used to estimate the parameters of the model that include the proportion of CSCs and their radio-sensitivities. This model was applied to five patients with stage III lung cancer, and tumor volumes were measured from 33 cone-beam computed tomography (CBCT) images for each of these patients. The analytical solution of these differential equations was compared with numerically simulated results. RESULTS: For the five patients with late stage lung cancer, the derived proportions of CSCs are 0.3 on average, the average probability of the symmetry division is 0.057 and the average surviving fractions of CSCs is 0.967, respectively. The derived parameters are comparable to the results from literature and our experiments. The preliminary results suggest that the CSC self-renewal rate is relatively small, compared to the proportion of CSCs for locally advanced lung cancers. CONCLUSIONS: A novel mathematical model has been developed to connect the population of cancer stem-like cells with tumor volumes measured from a sequence of CBCT images. This model may help improve our understanding of tumor response to radiation therapy, and is valuable for development of new treatment regimens for patients with locally advanced lung cancer.

On the improvement of CBCT image quality for soft tissue-based SRS localization.

PURPOSE: We explore the optimal cone-beam CT (CBCT) acquisition parameters to improve CBCT image quality to enhance intracranial stereotactic radiosurgery (SRS) localization and also assess the imaging dose levels associated with each imaging protocol. METHODS: Twenty-six CBCT acquisition protocols were generated on an Edge® linear accelerator (Varian Medical Systems, Palo Alto, CA) with different x-ray tube current and potential settings, gantry rotation trajectories, and gantry rotation speeds. To assess image quality, images of the Catphan 504 phantom were analyzed to evaluate the following image quality metrics: uniformity, HU constancy, spatial resolution, low contrast detection, noise level, and contrast-to-noise ratio (CNR). To evaluate the imaging dose for each protocol, the cone-beam dose index (CBDI) was measured. To validate the phantom results, further analysis was performed with an anthropomorphic head phantom as well as image data acquired for a clinical SRS patient. RESULTS: The Catphan data indicates that adjusting acquisition parameters had direct effects on the image noise level, low contrast detection, and CNR, but had minimal effects on uniformity, HU constancy, and spatial resolution. The noise level was reduced from 34.5 ± 0.3 to 18.5 ± 0.2 HU with a four-fold reduction in gantry speed, and to 18.7 ± 0.2 HU with a four-fold increase in tube current. Overall, the noise level was found to be proportional to inverse square root of imaging dose, and imaging dose was proportional to the product of total tube current-time product and the cube of the x-ray potential. Analysis of the anthropomorphic head phantom data and clinical SRS imaging data also indicates that noise is reduced with imaging dose increase. CONCLUSIONS: Our results indicate that optimization of the imaging protocol, and thereby an increase in the imaging dose, is warranted for improved soft-tissue visualization for intracranial SRS.

Deriving detector-specific correction factors for rectangular small fields using a scintillator detector.

The goal of this study was to investigate small field output factors (OFs) for flat-tening filter-free (FFF) beams on a dedicated stereotactic linear accelerator-based system. From this data, the collimator exchange effect was quantified, and detector-specific correction factors were generated. Output factors for 16 jaw-collimated small fields (from 0.5 to 2 cm) were measured using five different detectors including an ion chamber (CC01), a stereotactic field diode (SFD), a diode detector (Edge), Gafchromic film (EBT3), and a plastic scintillator detector (PSD, W1). Chamber, diodes, and PSD measurements were performed in a Wellhofer water tank, while films were irradiated in solid water at 100 cm source-to-surface distance and 10 cm depth. The collimator exchange effect was quantified for rectangular fields. Monte Carlo (MC) simulations of the measured configurations were also performed using the EGSnrc/DOSXYZnrc code. Output factors measured by the PSD and verified against film and MC calculations were chosen as the benchmark measurements. Compared with plastic scintillator detector (PSD), the small volume ion chamber (CC01) underestimated output factors by an average of -1.0% ± 4.9% (max. = -11.7% for 0.5 × 0.5 cm2 square field). The stereotactic diode (SFD) overestimated output factors by 2.5% ± 0.4% (max. = 3.3% for 0.5 × 1 cm2 rectangular field). The other diode detector (Edge) also overestimated the OFs by an average of 4.2% ± 0.9% (max. = 6.0% for 1 × 1 cm2 square field). Gafchromic film (EBT3) measure-ments and MC calculations agreed with the scintillator detector measurements within 0.6% ± 1.8% and 1.2% ± 1.5%, respectively. Across all the X and Y jaw combinations, the average collimator exchange effect was computed: 1.4% ± 1.1% (CC01), 5.8% ± 5.4% (SFD), 5.1% ± 4.8% (Edge diode), 3.5% ± 5.0% (Monte Carlo), 3.8% ± 4.7% (film), and 5.5% ± 5.1% (PSD). Small field detectors should be used with caution with a clear understanding of their behaviors, especially for FFF beams and small, elongated fields. The scintillator detector exhibited good agreement against Gafchromic film measurements and MC simulations over the range of field sizes studied. The collimator exchange effect was found to be impor-tant at these small field sizes. Detector-specific correction factors were computed using the scintillator measurements as the benchmark.

A multi-institutional comparison of retrospective deformable dose accumulation for online adaptive magnetic resonance-guided radiotherapy.

Background and Purpose: Application of different deformable dose accumulation (DDA) solutions makes institutional comparisons after online-adaptive magnetic resonance-guided radiotherapy (OA-MRgRT) challenging. The aim of this multi-institutional study was to analyze accuracy and agreement of DDA-implementations in OA-MRgRT. Material and Methods: One gold standard (GS) case deformed with a biomechanical-model and five clinical cases consisting of prostate (2x), cervix, liver, and lymph node cancer, treated with OA-MRgRT, were analyzed. Six centers conducted DDA using institutional implementations. Deformable image registration (DIR) and DDA results were compared using the contour metrics Dice Similarity Coefficient (DSC), surface-DSC, Hausdorff-distance (HD95%), and accumulated dose-volume histograms (DVHs) analyzed via intraclass correlation coefficient (ICC) and clinical dosimetric criteria (CDC). Results: For the GS, median DDA errors ranged from 0.0 to 2.8 Gy across contours and implementations. DIR of clinical cases resulted in DSC > 0.8 for up to 81.3% of contours and a variability of surface-DSC values depending on the implementation. Maximum HD95%=73.3 mm was found for duodenum in the liver case. Although DVH ICC > 0.90 was found after DDA for all but two contours, relevant absolute CDC differences were observed in clinical cases: Prostate I/II showed maximum differences in bladder V28Gy (10.2/7.6%), while for cervix, liver, and lymph node the highest differences were found for rectum D2cm3 (2.8 Gy), duodenum Dmax (7.1 Gy), and rectum D0.5cm3 (4.6 Gy). Conclusion: Overall, high agreement was found between the different DIR and DDA implementations. Case- and algorithm-dependent differences were observed, leading to potentially clinically relevant results. Larger studies are needed to define future DDA-guidelines.

Using patient-specific phantoms to evaluate deformable image registration algorithms for adaptive radiation therapy.

The quality of adaptive treatment planning depends on the accuracy of its underlying deformable image registration (DIR). The purpose of this study is to evaluate the performance of two DIR algorithms, B-spline-based deformable multipass (DMP) and deformable demons (Demons), implemented in a commercial software package. Evaluations were conducted using both computational and physical deformable phantoms. Based on a finite element method (FEM), a total of 11 computational models were developed from a set of CT images acquired from four lung and one prostate cancer patients. FEM generated displacement vector fields (DVF) were used to construct the lung and prostate image phantoms. Based on a fast-Fourier transform technique, image noise power spectrum was incorporated into the prostate image phantoms to create simulated CBCT images. The FEM-DVF served as a gold standard for verification of the two registration algorithms performed on these phantoms. The registration algorithms were also evaluated at the homologous points quantified in the CT images of a physical lung phantom. The results indicated that the mean errors of the DMP algorithm were in the range of 1.0 ~ 3.1 mm for the computational phantoms and 1.9 mm for the physical lung phantom. For the computational prostate phantoms, the corresponding mean error was 1.0-1.9 mm in the prostate, 1.9-2.4mm in the rectum, and 1.8-2.1 mm over the entire patient body. Sinusoidal errors induced by B-spline interpolations were observed in all the displacement profiles of the DMP registrations. Regions of large displacements were observed to have more registration errors. Patient-specific FEM models have been developed to evaluate the DIR algorithms implemented in the commercial software package. It has been found that the accuracy of these algorithms is patient dependent and related to various factors including tissue deformation magnitudes and image intensity gradients across the regions of interest. This may suggest that DIR algorithms need to be verified for each registration instance when implementing adaptive radiation therapy.

On the correction of respiratory motion-induced image reconstruction errors in positron-emission tomography-guided radiation therapy.

Background and purpose: Free breathing (FB) positron emission tomography (PET) images are routinely used in radiotherapy for lung cancer patients. Respiration-induced artifacts in these images compromise treatment response assessment and obstruct clinical implementation of dose painting and PET-guided radiotherapy. The purpose of this study is to develop a blurry image decomposition (BID) method to correct motion-induced image-reconstruction errors in FB-PETs. Materials and methods: Assuming a blurry PET is represented as an average of multi-phase PETs. A four-dimensional computed-tomography image is deformably registered from the end-inhalation (EI) phase to other phases. With the registration-derived deformation maps, PETs at other phases can be deformed from a PET at the EI phase. To reconstruct the EI-PET, the difference between the blurry PET and the average of the deformed EI-PETs is minimized using a maximum-likelihood expectation-maximization algorithm. The developed method was evaluated with computational and physical phantoms as well as PET/CT images acquired from three patients. Results: The BID method increased the signal-to-noise ratio from 1.88 ± 1.05 to 10.5 ± 3.3 and universal-quality index from 0.72 ± 0.11 to 1.0 for the computational phantoms, and reduced the motion-induced error from 69.9% to 10.9% in the maximum of activity concentration and from 317.5% to 8.7% in the full width at half maximum of the physical PET-phantom. The BID-based corrections increased the maximum standardized-uptake values by 17.7 ± 15.4% and reduced tumor volumes by 12.5 ± 10.4% on average for the three patients. Conclusions: The proposed image-decomposition method reduces respiration-induced errors in PET images and holds potential to improve the quality of radiotherapy for thoracic and abdominal cancer patients.

Incorporating uncertainty bounds in daily deformable dose accumulation for adaptive radiation therapy of head-and-neck cancer.

BACKGROUND: The widespread use of deformable dose accumulation (DDA) in adaptive radiotherapy (ART) has been limited due to the lack of clinically compatible methods to consider its related uncertainties. PURPOSE: We estimate dose reconstruction uncertainties in daily DDA during CT-guided radiotherapy of head-and-neck cancer (HNC). We project confidence intervals of cumulative dose-volume parameters to the parotids and determine threshold values to guide clinical decision-making in ART. METHODS: Doses from daily images (megavoltage CTs [MVCTs]) of 20 HNC patients treated with tomotherapy were reconstructed and accumulated in the planning CT (PCT) utilizing a commercial DDA algorithm (PreciseART, Accuray, Inc.). For each mapped fraction, we warped the planning contours to the MVCT. Dose-volume histograms (DVHs) calculated in the MVCT (with warped contour and native dose) and the PCT (with native contour and mapped dose) were compared; the observed inconsistencies were associated with dose reconstruction errors. We derived uncertainty bounds for the transferred dose to voxels within the structure of interest in the PCT. The confidence intervals of cumulative dose-volume parameters were mid-treatment projected and evaluated as predictors of the end of treatment cumulative metrics. The need for plan adaptation was tested by comparing the projected uncertainty bounds with the treatment constraint points. RESULTS: Among all cases, the uncertainty in mean values of daily dose distributions mapped to the reference parotid's contours averaged between 2.8% and 3.8% of typical single fraction planning values and less than 1% for the planning target volume (PTV) D95%. These daily inconsistencies were higher in the ipsilateral compared to the contralateral parotid and increased toward the end of treatment. The magnitude of the uncertainty bounds for the cumulative treatment mean dose, D50%, and V20 Gy to the parotids, and PTV D95% were on average 3.5%, 6.6%, 4.6%, and 0.4% of the planned or prescribed values, with confidence intervals of 97.1%-107.0%, 98.2%-110.4%, 95.6%-111.1%, and 98.2%-100.2% respectively. The uncertainty intervals projected at mid-treatment intersected with the end of treatment bounds in 82% of the parotid's metrics; half of them presented an overlapping percentage greater than 60%. In five patients, the cumulative mean doses were projected at mid-treatment to exceed the total treatment constraint point by at least 3%; this threshold was exceeded at the end of treatment in the five cases. Underdosing was projected in only one case; the cumulative PTV D95% at the end of treatment was below the clinical threshold. CONCLUSION: Uncertainty bounds were incorporated into the results of a commercial DDA tool. The cohort's statistics showed that the parotids' cumulative DVH metrics frequently exceeded the planning values if confidence intervals were included. Most of the uncertainty bounds of the PTV metrics were kept within the clinical thresholds. We verified that mid-treatment violation projections led to exceeding the constraint point at the end of the treatment. Based on a 3% threshold, approximately one fourth of the patients are expected to be replanned at mid-treatment for parotids sparing during HNC radiotherapy.

Development of a multi-layer quality assurance program to evaluate the uncertainty of deformable dose accumulation in adaptive radiotherapy.

PURPOSE: Deformable dose accumulation (DDA) has uncertainties which impede the implementation of DDA-based adaptive radiotherapy (ART) in clinic. The purpose of this study is to develop a multi-layer quality assurance (MLQA) program to evaluate uncertainties in DDA. METHODS: A computer program is developed to generate a pseudo-inverse displacement vector field (DVF) for each deformable image registration (DIR) performed in Accuray's PreciseART. The pseudo-inverse DVF is first used to calculate a pseudo-inverse consistency error (PICE) and then implemented in an energy and mass congruent mapping (EMCM) method to reconstruct a deformed dose. The PICE is taken as a metric to estimate DIR uncertainties. A pseudo-inverse dose agreement rate (PIDAR) is used to evaluate the consequence of the DIR uncertainties in DDA and the principle of energy conservation is used to validate the integrity of dose mappings. The developed MLQA program was tested using the data collected from five representative cancer patients treated with tomotherapy. RESULTS: DIRs were performed in PreciseART to generate primary DVFs for the five patients. The fidelity index and PICE of these DVFs on average are equal to 0.028 mm and 0.169 mm, respectively. With the criteria of 3 mm/3% and 5 mm/5%, the PIDARs of the PreciseART-reconstructed doses are 73.9 ± 4.4% and 87.2 ± 3.3%, respectively. The PreciseART and EMCM-based dose reconstructions have their deposited energy changed by 5.6 ± 3.9% and 2.6 ± 1.5% in five GTVs, and by 9.2 ± 7.8% and 4.7 ± 3.6% in 30 OARs, respectively. CONCLUSIONS: A pseudo-inverse map-based EMCM program has been developed to evaluate DIR and dose mapping uncertainties. This program could also be used as a sanity check tool for DDA-based ART.

Generation of a novel phase-space-based cylindrical dose kernel for IMRT optimization.

PURPOSE: Improving dose calculation accuracy is crucial in intensity-modulated radiation therapy (IMRT). We have developed a method for generating a phase-space-based dose kernel for IMRT planning of lung cancer patients. METHODS: Particle transport in the linear accelerator treatment head of a 21EX, 6 MV photon beam (Varian Medical Systems, Palo Alto, CA) was simulated using the EGSnrc/BEAMnrc code system. The phase space information was recorded under the secondary jaws. Each particle in the phase space file was associated with a beamlet whose index was calculated and saved in the particle's LATCH variable. The DOSXYZnrc code was modified to accumulate the energy deposited by each particle based on its beamlet index. Furthermore, the central axis of each beamlet was calculated from the orientation of all the particles in this beamlet. A cylinder was then defined around the central axis so that only the energy deposited within the cylinder was counted. A look-up table was established for each cylinder during the tallying process. The efficiency and accuracy of the cylindrical beamlet energy deposition approach was evaluated using a treatment plan developed on a simulated lung phantom. RESULTS: Profile and percentage depth doses computed in a water phantom for an open, square field size were within 1.5% of measurements. Dose optimized with the cylindrical dose kernel was found to be within 0.6% of that computed with the nontruncated 3D kernel. The cylindrical truncation reduced optimization time by approximately 80%. CONCLUSIONS: A method for generating a phase-space-based dose kernel, using a truncated cylinder for scoring dose, in beamlet-based optimization of lung treatment planning was developed and found to be in good agreement with the standard, nontruncated scoring approach. Compared to previous techniques, our method significantly reduces computational time and memory requirements, which may be useful for Monte-Carlo-based 4D IMRT or IMAT treatment planning.

Patient-specific synthetic magnetic resonance imaging generation from cone beam computed tomography for image guidance in liver stereotactic body radiation therapy.

Objective: Despite its prevalence, cone beam computed tomography (CBCT) has poor soft-tissue contrast, making it challenging to localize liver tumors. We propose a patient-specific deep learning model to generate synthetic magnetic resonance imaging (MRI) from CBCT to improve tumor localization. Methods: A key innovation is using patient-specific CBCT-MRI image pairs to train a deep learning model to generate synthetic MRI from CBCT. Specifically, patient planning CT was deformably registered to prior MRI, and then used to simulate CBCT with simulated projections and Feldkamp, Davis, and Kress reconstruction. These CBCT-MRI images were augmented using translations and rotations to generate enough patient-specific training data. A U-Net-based deep learning model was developed and trained to generate synthetic MRI from CBCT in the liver, and then tested on a different CBCT dataset. Synthetic MRIs were quantitatively evaluated against ground-truth MRI. Results: The synthetic MRI demonstrated superb soft-tissue contrast with clear tumor visualization. On average, the synthetic MRI achieved 28.01, 0.025, and 0.929 for peak signal-to-noise ratio, mean square error, and structural similarity index, respectively, outperforming CBCT images. The model performance was consistent across all three patients tested. Conclusion: Our study demonstrated the feasibility of a patient-specific model to generate synthetic MRI from CBCT for liver tumor localization, opening up a potential to democratize MRI guidance in clinics with conventional LINACs.

Use of a DVH overlay technique for quality assurance of deformable image registration-based dose accumulation.

PURPOSE: We present a DVH overlay technique as a quality assurance (QA) metric for deformable image registration-based dose accumulation (DIR-DA). We use the technique to estimate the uncertainty in a DIR-DA for a revised treatment plan, and to compare two different DIR algorithms. MATERIALS AND METHODS: The required inputs to the DVH overlay workflow are deformably registered primary and secondary images, primary regions-of-interest (ROIs), and secondary dose distribution. The primary ROIs were forward warped to the secondary image, the secondary dose was inversely warped to the primary image, and the DVHs for each image were compiled. Congruent DVHs imply minimal inverse consistency error (ICE) within an ROI. For a pancreas case re-planned after 21 fractions of a 29-fraction course, the workflow was used to quantify dose accumulation error attributable to ICE, based on a hybrid contour-and-intensity-based DIR. The usefulness of the workflow was further demonstrated by assessing the performance of two DIR algorithms (one free-form intensity-based, FFIB, the other using normalized correlation coefficients, NCC, over small neighborhood patches) as applied toward kilovoltage computed tomography (kVCT)-to-megavoltage computed tomography (MVCT) registration and five-fraction dose accumulation of ten male pelvis cases. RESULTS: For the re-planned pancreas case, when applying the DVH-overlay-based uncertainties the resulting accumulated dose remained compliant with all but two of the original plan objectives. Among the male pelvis cases, FFIB and NCC DIR showed good invertibility within the planning target volume (PTV), according to the DVH overlay QA results. NCC DIR exhibited better invertibility for the bladder and rectum compared with FFIB. However, compared with FFIB, NCC DIR exhibited less regional deformation for the bladder and a tendency for increased local contraction of the rectum ROI. For the five-fraction summations, ICE for the PTV V100%Rx is comparable for both algorithms (FFIB 0.8 ± 0.7%, NCC 0.7 ± 0.3%). For the bladder and rectum V70%Rx , ICE is greater for FFIB (1.8 ± 0.7% for bladder, 1.7 ± 0.6% for rectum) than for NCC (1.0 ± 0.3% for bladder, 1.0 ± 0.4% for rectum). CONCLUSIONS: The DVH overlay technique identified instances in which a DIR exhibits favorable invertibility, implying low ICE in a DIR-based dose accumulation. Differences in the overlaid DVHs can also estimate dose accumulation errors attributable to ICE for given ROIs.

Measurement of regional compliance using 4DCT images for assessment of radiation treatment.

PURPOSE: Radiation-induced damage, such as inflammation and fibrosis, can compromise ventilation capability of local functional units (alveoli) of the lung. Ventilation function as measured with ventilation images, however, is often complicated by the underlying mechanical variations. The purpose of this study is to present a 4DCT-based method to measure the regional ventilation capability, namely, regional compliance, for the evaluation of radiation-induced lung damage. METHODS: Six 4DCT images were investigated in this study: One previously used in the generation of a POPI model and the other five acquired at Henry Ford Health System. A tetrahedral geometrical model was created and scaled to encompass each of the 4DCT image domains. Image registrations were performed on each of the 4DCT images using a multiresolution Demons algorithm. The images at the end of exhalation were selected as a reference. Images at other exhalation phases were registered to the reference phase. For the POPI-modeled patient, each of these registration instances was validated using 40 landmarks. The displacement vector fields (DVFs) were used first to calculate the volumetric variation of each tetrahedron, which represents the change in the air volume. The calculated results were interpolated to generate 3D ventilation images. With the computed DVF, a finite element method (FEM) framework was developed to compute the stress images of the lung tissue. The regional compliance was then defined as the ratio of the ventilation and stress values and was calculated for each phase. Based on iterative FEM simulations, the potential range of the mechanical parameters for the lung was determined by comparing the model-computed average stress to the clinical reference value of airway pressure. The effect of the parameter variations on the computed stress distributions was estimated using Pearson correlation coefficients. RESULTS: For the POPI-modeled patient, five exhalation phases from the start to the end of exhalation were denoted by P(i), i = 1, ..., 5, respectively. The average lung volume variation relative to the reference phase (P5) was reduced from 18% at P1 to 4.8% at P4. The average stress at phase P(i) was 1.42, 1.34, 0.74, and 0.28 kPa, and the average regional compliance was 0.19, 0.20, 0.20, and 0.24 for i = 1, ..., 4, respectively. For the other five patients, their average R(v) value at the end-inhalation phase was 21.1%, 19.6%, 22.4%, 22.5%, and 18.8%, respectively, and the regional compliance averaged over all six patients is 0.2. For elasticity parameters chosen from the potential parameter range, the resultant stress distributions were found to be similar to each other with Pearson correlation coefficients greater than 0.81. CONCLUSIONS: A 4DCT-based mechanical model has been developed to calculate the ventilation and stress images of the lung. The resultant regional compliance represents the lung's elasticity property and is potentially useful in correlating regions of lung damage with radiation dose following a course of radiation therapy.

A TCP model incorporating setup uncertainty and tumor cell density variation in microscopic extension to guide treatment planning.

PURPOSE: Tumor control probability (TCP) models have been proposed to evaluate and guide treatment planning. However, they are usually based on the dose volume histograms (DVHs) of the planning target volume (PTV) and may not properly reflect the substantial variation in tumor burden from the gross tumor volume (GTV) to the microscopic extension (ME) and to the margin of PTV. In this study, the authors propose a TCP model that can account for the effects of setup uncertainties and tumor cell density decay in the ME region. METHODS: The proposed TCP model is based on the total surviving clonogenic tumor cells (CTCs) after irradiation of a known dose distribution to a region with a CTC distribution. The CTC density was considered to be homogeneous within the GTV, while decreasing exponentially in the ME region. The effect of random setup uncertainty was modeled by convolving the dose distribution with a Gaussian probability density function, represented by a standard deviation, sigma. The effect of systematic setup uncertainty was modeled by summing each calculated TCP for all potential offsets in a Gaussian probability, represented by sigma. The model was then applied to simplified cases to demonstrate the concept. TCP dose responses were calculated for various GTV volumes, DVH shapes, CTC density decay coefficients, probabilities of lymph node metastasis, and random and systematic errors. The slopes of the dose falloff to cover the CTC density decay in the ME region and the margins to compensate setup errors were also analyzed in generalized cases. RESULTS: The sigmoid TCP dose response curve shifted to the right substantially for a larger GTV, while modestly for cold spots in DVH. A dose distribution with a uniform dose within the GTV, and a linear dose falloff in the ME region, tended to cause a minimal TCP deterioration if a proper dose falloff slope was used. When the dose falloff slope was less steep than a critical slope represented by kT, the D50, which is the prescription dose at TCP=50%, and gamma50, which is the TCP slope at TCP=50%, varied little with different dose falloff slopes. However, both D50 and gamma50 deteriorated fast when the slopes were steeper than kT. The random setup error tended to shift the TCP curve to the right, while the systematic error tended to compress the curve downward. For combined random and systematic errors, we demonstrated that based on the model, a margin of mean square root of (0.75 sigma)2 + (1.15 sigma)2 added to the GTV was found to cause a TCP change corresponding to 2% drop at TCP=90%, or 0.5 Gy shift in D50. CONCLUSIONS: This study conceptually demonstrated that a TCP model incorporating the effects of tumor cell density variation and setup uncertainty may be used to guide radiation treatment planning.

Analysis of deformable image registration accuracy using computational modeling.

Computer aided modeling of anatomic deformation, allowing various techniques and protocols in radiation therapy to be systematically verified and studied, has become increasingly attractive. In this study the potential issues in deformable image registration (DIR) were analyzed based on two numerical phantoms: One, a synthesized, low intensity gradient prostate image, and the other a lung patient's CT image data set. Each phantom was modeled with region-specific material parameters with its deformation solved using a finite element method. The resultant displacements were used to construct a benchmark to quantify the displacement errors of the Demons and B-Spline-based registrations. The results show that the accuracy of these registration algorithms depends on the chosen parameters, the selection of which is closely associated with the intensity gradients of the underlying images. For the Demons algorithm, both single resolution (SR) and multiresolution (MR) registrations required approximately 300 iterations to reach an accuracy of 1.4 mm mean error in the lung patient's CT image (and 0.7 mm mean error averaged in the lung only). For the low gradient prostate phantom, these algorithms (both SR and MR) required at least 1600 iterations to reduce their mean errors to 2 mm. For the B-Spline algorithms, best performance (mean errors of 1.9 mm for SR and 1.6 mm for MR, respectively) on the low gradient prostate was achieved using five grid nodes in each direction. Adding more grid nodes resulted in larger errors. For the lung patient's CT data set, the B-Spline registrations required ten grid nodes in each direction for highest accuracy (1.4 mm for SR and 1.5 mm for MR). The numbers of iterations or grid nodes required for optimal registrations depended on the intensity gradients of the underlying images. In summary, the performance of the Demons and B-Spline registrations have been quantitatively evaluated using numerical phantoms. The results show that parameter selection for optimal accuracy is closely related to the intensity gradients of the underlying images. Also, the result that the DIR algorithms produce much lower errors in heterogeneous lung regions relative to homogeneous (low intensity gradient) regions, suggests that feature-based evaluation of deformable image registration accuracy must be viewed cautiously.

4-Dimensional computed tomography-based ventilation and compliance images for quantification of radiation-induced changes in pulmonary function.

INTRODUCTION: 4-Dimensional computed tomography (4DCT)-based ventilation imaging is a promising technique for evaluating pulmonary function, but lung elasticity and mechanics are usually not part of the ventilation image analysis. In this study we demonstrate a 4DCT-based imaging technique that can be used to calculate regional lung compliance changes after radiotherapy (RT). METHODS: Six lung cancer patients were included in this study. Four of the patients had 4DCT images acquired pre-RT, 3 and 9 months post-RT. Ventilation and compliance were calculated from the deformable image registration (DIR) of 4DCTs, performed from the end-inhale to the end-exhale breathing phase. Regional compliance was defined as the ratio of volumetric variation and associated stress in each voxel, representing lung elasticity and computed using a FEM-based framework. Ventilation, compliance and CT density were calculated for all pre-RT and post-RT 4DCTs and evaluation metrics were computed. RESULTS: Average CT density changes were 13.6 ± 11.4HU after 3 months and 26.9 ± 15.8HU after 9 months. Ventilation was reduced at 3 months, but improved at 9 months in regions with dose ≥ 35 Gy, encompassing about 10% of the lung volume; compliance was reduced at both time-points. Radiation dose ≥ 35 Gy caused major change in lung density and ventilation, which was higher than that previously reported in the literature (i.e. 24 Gy). CONCLUSION: Lung tissue response is diverse with respect to CT density, ventilation and compliance. Combination of ventilation and compliance with CT density could be beneficial for understanding radiation-induced lung damage and consequently could help develop improved treatment protocols for lung cancer patients.

Four-dimensional computed tomography-based biomechanical measurements of pulmonary function and their correlation with clinical outcome for lung stereotactic body radiation therapy patients.

BACKGROUND: Functional image guided radiotherapy allows for the delivery of an equivalent dose to tumor targets while sparing high ventilation lung tissues. In this study, we investigate whether radiation dose to functional lung is associated with clinical outcome for stereotactic body radiation therapy (SBRT) patients. METHODS: Four-dimensional computed tomography (4DCT) images were used to assess lung function. Deformable image registration (DIR) was performed from the end-inhale phase to the end-exhale phase with resultant displacement vectors used to calculate ventilation maps. In addition to the Jacobian-based ventilation we introduce a volumetric variation method (Rv) based on a biomechanical finite element method (FEM), to assess lung ventilation. Thirty NSCLC patients, treated with SBRT, were evaluated in this study. 4DCT images were used to calculate both Jacobian and Rv-based ventilation images. Areas under the receiver operating characteristic curve (AUC) were used to assess the predictive power of functional metrics. Metrics were calculated over the whole lung as well as high and low ventilated regions. RESULTS: Ventilation in dose regions between 1 and 5 Gy had higher AUC values compared to other dose regions. Rv based ventilation imaging method also showed to be less spatially variant and less heterogeneous, and the resultant Rv metrics had higher AUC values for predicting grade 2+ dyspnea. CONCLUSIONS: Low dose delivered to high ventilation areas may also increase the risk of compromised pulmonary function. Rv based ventilation images could be useful for the prediction of clinical toxicity for lung SBRT patients.

A deliverable four-dimensional intensity-modulated radiation therapy-planning method for dynamic multileaf collimator tumor tracking delivery.

PURPOSE: To develop a deliverable four-dimensional (4D) intensity-modulated radiation therapy (IMRT) planning method for dynamic multileaf collimator (MLC) tumor tracking delivery. METHODS AND MATERIALS: The deliverable 4D IMRT planning method involves aligning MLC leaf motion parallel to the major axis of target motion and translating MLC leaf positions by the difference in the target centroid position between respiratory phases of the 4D CT scan. This method ignores nonlinear respiratory motion and deformation. A three-dimensional (3D) optimal method whereby an IMRT plan on each respiratory phase of the 4D CT scan was independently optimized was used for comparison. For 12 lung cancer patient 4D CT scans, individual phase plans and deformable dose-summed 4D plans using the two methods were created and compared. RESULTS: For each of the individual phase plans, the deliverable method yielded similar isodose distributions and dose-volume histograms. The deliverable and 3D optimal methods yielded statistically equivalent dose-volume metrics for both individual phase plans and 4D plans (p > 0.05 for all metrics compared). The deliverable method was affected by 4D CT artifacts in one case. Both methods were affected by high vector field variations from deformable registration. CONCLUSIONS: The deliverable method yielded similar dose distributions for each of the individual phase plans and statistically equivalent dosimetric values compared with the 3D optimal method, indicating that the deliverable method is dosimetrically robust to the variations of fractional time spent in respiratory phases on a given 4D CT scan. Nonlinear target motion and deformation did not cause significant dose discrepancies.

An energy transfer method for 4D Monte Carlo dose calculation.

This article presents a new method for four-dimensional Monte Carlo dose calculations which properly addresses dose mapping for deforming anatomy. The method, called the energy transfer method (ETM), separates the particle transport and particle scoring geometries: Particle transport takes place in the typical rectilinear coordinate system of the source image, while energy deposition scoring takes place in a desired reference image via use of deformable image registration. Dose is the energy deposited per unit mass in the reference image. ETM has been implemented into DOSXYZnrc and compared with a conventional dose interpolation method (DIM) on deformable phantoms. For voxels whose contents merge in the deforming phantom, the doses calculated by ETM are exactly the same as an analytical solution, contrasting to the DIM which has an average 1.1% dose discrepancy in the beam direction with a maximum error of 24.9% found in the penumbra of a 6 MV beam. The DIM error observed persists even if voxel subdivision is used. The ETM is computationally efficient and will be useful for 4D dose addition and benchmarking alternative 4D dose addition algorithms.

Assessment of dose reconstruction errors in image-guided radiation therapy.

Dose reconstruction can be used to improve the accuracy of dose evaluation throughout a treatment course. Its working mechanism is based on deformable image registration (DIR). The purpose of this paper is to develop a method to estimate the dose reconstruction error associated with the inaccuracy of DIR algorithms. To reach this goal, we quantified dominant errors in DIR in terms of unbalanced energy (UE), which were compared with the standard displacement error (SDE). Their high similarity, characterized by Pearson correlation coefficient, was verified through nine 'demons' registration instances performed within simulated reference frames. Based on the similarity, the dose-warping discrepancy at each voxel was defined as a line integral of the dose gradient within the voxel's neighborhood whose boundary was determined by the voxel's UE value. From this definition, the dose reconstruction error was then calculated at each voxel on nine prostate computed tomography images, obtained from a patient treatment course. The average of the Pearson correlation coefficients between UE and SDE over the simulated registration instances was above 70%. The mean value of the dose reconstruction errors in a target volume was calculated for each of nine treatment fractions. The averaged percentage of these mean values with respect to the prescribed dose on the target volume was 1.68%. These results are consistent with contour-based mean dose error evaluations. This paper has established a relation between a registration error and its induced dose reconstruction discrepancy. It allows an automatic validation method to be developed to estimate the dose accumulation error at each voxel in clinical settings.