T Patton

Sensitivity analysis of Jacobian determinant used in treatment planning for lung cancer

Four-dimensional computed tomography (4DCT) is regularly used to visualize tumor motion in radiation therapy for lung cancer. These 4DCT images can be analyzed to estimate local ventilation by finding a dense correspondence map between the end inhalation and the end exhalation CT image volumes using deformable image registration. Lung regions with ventilation values above a threshold are labeled as regions of high pulmonary function and are avoided when possible in the radiation plan. This paper investigates a sensitivity analysis of the relative Jacobian error to small registration errors. We present a linear approximation of the relative Jacobian error. Next, we give a formula for the sensitivity of the relative Jacobian error with respect to the Jacobian of perturbation displacement field. Preliminary sensitivity analysis results are presented using 4DCT scans from 10 individuals. For each subject, we generated 6400 random smooth biologically plausible perturbation vector fields using a cubic B-spline model. We showed that the correlation between the Jacobian determinant and the Frobenius norm of the sensitivity matrix is close to -1, which implies that the relative Jacobian error in high-functional regions is less sensitive to noise. We also showed that small displacement errors on the average of 0.53 mm may lead to a 10% relative change in Jacobian determinant. We finally showed that the average relative Jacobian error and the sensitivity of the system for all subjects are positively correlated (close to +1), i.e. regions with high sensitivity has more error in Jacobian determinant on average.

Tissue-Volume Preserving Deformable Image Registration for 4DCT Pulmonary Images

We propose a 4D (three spatial dimensions plus time) tissue-volume preserving non-rigid image registration algorithm for pulmonary 4D computed tomography (4DCT) data sets to provide relevant information for radiation therapy and estimate pulmonary ventilation. The sum of squared tissue volume difference (SSTVD) similarity cost takes into account the CT intensity changes of spatially corresponding voxels, which is caused by the variations of fraction of tissue within voxels throughout the respiratory cycle. The proposed 4D SSTVD registration scheme considers the entire dynamic 4D data set simultaneously, using both spatial and temporal information. We employed a uniform 4D cubic B-spline parametrization of the transform and a temporally extended linear elasticity regularization of deformation field to ensure temporal smoothness and thus biological plausibility of estimated deformation. We used a multiresolution multi-grid registration framework with limitedmemory Broyden Fletcher Goldfarb Shanno (L-BFGS) optimization procedure for rapid convergence and limited memory consumption. We conducted experiments using synthetic 2D+t images and clinical 4DCT pulmonary data sets and evaluated accuracy and temporal smoothness of the proposed method via manually annotated landmarks.

SU-F-J-09: Radioactive Seed Localization for Breast Lumpectomy - Towards Optimization

PURPOSE The aim of this work is to propose a method to optimize radioactive source localization (RSL) for non-palpable breast cancer surgery. RSL is commonly used as a guiding technique during surgery for excision of non-palpable tumors. A collimated hand-held detector is used to localize radioactive sources implanted in tumors. Incisions made by the surgeon are based on maximum observed detector counts, and tumors are subsequently resected based on an arbitrary estimate of the counts expected at the surgical margin boundary. This work focuses on building a framework to predict detector counts expected throughout the procedure to improve surgical margins. METHODS A gamma detection system called the Neoprobe GDS was used for this work. The probe consists of a cesium zinc telluride crystal and a collimator. For this work, an I-125 Best Medical model 2301 source was used. The source was placed in three different phantoms, a PMMA, a Breast (25%- glandular tissue/75%- adipose tissue) and a Breast (75-25) phantom with a backscatter thickness of 6 cm. Counts detected by the probe were recorded with varying amounts of phantom thicknesses placed on top of the source. A calibration curve was generated using MATLAB based on the counts recorded for the calibration dataset acquired with the PMMA phantom. RESULTS The observed detector counts data used as the validation set was accurately predicted to within ±3.2%, ±6.9%, ±8.4% for the PMMA, Breast (75-25), Breast (25-75) phantom respectively. The average difference between predicted and observed counts was -0.4%, 2.4%, 1.4% with a standard deviation of 1.2 %, 1.8%, 3.4% for the PMMA, Breast (75-25), Breast (25-75) phantom respectively. CONCLUSION The results of this work provide a basis for characterization of a detector used for RSL. Counts were predicted to within ±9% for three different phantoms without the application of a density correction factor.

Detecting Out-of-Phase Ventilation Using 4DCT to Improve Radiation Therapy for Lung Cancer

Functional avoidance radiation therapy (RT) uses lung function images to identify and minimize irradiation of high-function lung tissue. Lung function can be estimated by local expansion ratio (LER) of the lung, which we define in this paper as the ratio of the maximum to the minimum local lung volume in a breathing cycle. LER is computed using deformable image registration. The end exhale (0EX) and the end inhale (100IN) phases of four-dimensional computed tomography (4DCT) are often used to estimate LER, which we refer to as LER3D. However, the lung may have out-of-phase ventilation, i.e., local lung volume change is out of phase with respect to global lung expansion and contraction. We propose the LER4D measure which estimates the LER measure using all phases of 4DCT. The purpose of this paper is to quantify the amount of out-of-phase ventilation of the lung. Out-of-phase ventilation is defined to occur when the LER4D measure is \(5\%\) or more than the LER3D measure. 4DCT scans of 14 human subjects were used in this study. Low-function (high-function) regions are defined as regions that have less (greater) than \(10\%\) expansion. Our results show that on average \(19.3\%\) of the lung had out-of-phase ventilation; \(3.8\%\) of the lung had out-of-phase ventilation and is labeled as low-function by both LER3D and LER4D; \(9.6\%\) of the lung is labeled as low-function by LER3D while high-function by LER4D; and \(5.9\%\) of the lung had out-of-phase ventilation and is labeled as high-function by both LER3D and LER4D. We conclude that out-of-phase ventilation is common in all 14 human subjects we have investigated.

Quantifying ventilation change due to radiation therapy using 4DCT Jacobian calculations

Purpose Regional ventilation and its response to radiation dose can be estimated using four‐dimensional computed tomography (4DCT) and image registration. This study investigated the impact of radiation therapy (RT) on ventilation and the dependence of radiation‐induced ventilation change on pre‐RT ventilation derived from 4DCT. Methods and materials Three 4DCT scans were acquired from each of 12 subjects: two scans before RT and one scan 3 months after RT. The 4DCT datasets were used to generate the pre‐RT and post‐RT ventilation maps by registering the inhale phase image to the exhale phase image and computing the Jacobian determinant of the resulting transformation. The ventilation change between pre‐RT and post‐RT was calculated by taking a ratio of the post‐RT Jacobian map to the pre‐RT Jacobian map. The voxel‐wise ventilation change between pre‐ and post‐RT was investigated as a function of dose and pre‐RT ventilation. Results Lung regions receiving over 20 Gy exhibited a significant decrease in function (3.3%, P < 0.01) compared to those receiving less than 20 Gy. When the voxels were stratified into high and low pre‐RT function by thresholding the Jacobian map at 10% volume expansion (Jacobian = 1.1), high‐function voxels exhibited 4.8% reduction in function for voxels receiving over 20 Gy, a significantly greater decline (P = 0.037) than the 2.4% reduction in function for low‐function voxels. Ventilation decreased linearly with dose in both high‐function and low‐function regions. High‐function regions showed a significantly larger decline in ventilation (P ≪ 0.001) as dose increased (1.4% ventilation reduction/10 Gy) compared to low‐function regions (0.3% ventilation reduction/10 Gy). With further stratification of pre‐RT ventilation, voxels exhibited increasing dose‐dependent ventilation reduction with increasing pre‐RT ventilation, with the largest pre‐RT Jacobian bin (pre‐RT Jacobian between 1.5 and 1.6) exhibiting a ventilation reduction of 4.8% per 10 Gy. Conclusions Significant ventilation reductions were measured after radiation therapy treatments, and were dependent on the dose delivered to the tissue and the pre‐RT ventilation of the tissue. For a fixed radiation dose, lung tissue with high pre‐RT ventilation experienced larger decreases in post‐RT ventilation than lung tissue with low pre‐RT ventilation.

SU‐F‐J‐219: Predicting Ventilation Change Due to Radiation Therapy: Dependency On Pre‐RT Ventilation and Effort Correction

PURPOSE Ventilation change caused by radiation therapy (RT) can be predicted using four-dimensional computed tomography (4DCT) and image registration. This study tested the dependency of predicted post-RT ventilation on effort correction and pre-RT lung function. METHODS Pre-RT and 3 month post-RT 4DCT images were obtained for 13 patients. The 4DCT images were used to create ventilation maps using a deformable image registration based Jacobian expansion calculation. The post-RT ventilation maps were predicted in four different ways using the dose delivered, pre-RT ventilation, and effort correction. The pre-RT ventilation and effort correction were toggled to determine dependency. The four different predicted ventilation maps were compared to the post-RT ventilation map calculated from image registration to establish the best prediction method. Gamma pass rates were used to compare the different maps with the criteria of 2mm distance-to-agreement and 6% ventilation difference. Paired t-tests of gamma pass rates were used to determine significant differences between the maps. Additional gamma pass rates were calculated using only voxels receiving over 20 Gy. RESULTS The predicted post-RT ventilation maps were in agreement with the actual post-RT maps in the following percentage of voxels averaged over all subjects: 71% with pre-RT ventilation and effort correction, 69% with no pre-RT ventilation and effort correction, 60% with pre-RT ventilation and no effort correction, and 58% with no pre-RT ventilation and no effort correction. When analyzing only voxels receiving over 20 Gy, the gamma pass rates were respectively 74%, 69%, 65%, and 55%. The prediction including both pre- RT ventilation and effort correction was the only prediction with significant improvement over using no prediction (p<0.02). CONCLUSION Post-RT ventilation is best predicted using both pre-RT ventilation and effort correction. This is the only prediction that provided a significant improvement on agreement. Research support from NIH grants CA166119 and CA166703, a gift from Roger Koch, and a Pilot Grant from University of Iowa Carver College of Medicine.

WE-AB-202-06: Correlating Lung CT HU with Transformation-Based and Xe-CT Derived Ventilation

PURPOSE Regional lung ventilation is useful to reduce radiation-induced function damage during lung cancer radiation therapy. Recently a new direct HU (Hounsfield unit)-based method was proposed to estimate the ventilation potential without image registration. The purpose of this study is to examine if there is a functional dependence between HU values and transformation-based or Xe-CT derived ventilation. METHODS 4DCT images acquired from 13 patients prior to radiation therapy and 4 mechanically ventilated sheep subjects which also have associated Xe-CT images were used for this analysis. Transformation-based ventilation was computed using Jacobian determinant of the transformation field between peak-exhale and peak-inhale 4DCT images. Both transformation and Xe-CT derived ventilation was computed for each HU bin. Color scatter plot and cumulative histogram were used to compare and validate the direct HU-based method. RESULTS There was little change of the center and shape of the HU histograms between free breathing CT and 4DCT average, with or without smoothing, and between the repeated 4DCT scans. HU of -750 and -630 were found to have the greatest transformation-based ventilation for human and sheep subjects, respectively. Maximum Xe-CT derived ventilation was found to locate at HU of -600 in sheep subjects. The curve between Xe-CT ventilation and HU was noisy for tissue above HU -400, possibly due to less intensity change of Xe gas during wash-out and wash-in phases. CONCLUSION Both transformation-based and Xe-CT ventilation demonstrated that lung tissues with HU values in the range of (-750, -600) HU have the maximum ventilation potential. The correlation between HU and ventilation suggests that HU might be used to help guide the ventilation calculation and make it more robust to noise and image registration errors. Research support from NIH grants CA166703 and CA166119 and a gift from Roger Koch.

WE-AB-202-03: Quantifying Ventilation Change Due to Radiation Therapy Using 4DCT Jacobian Calculations.

PURPOSE Four-dimensional computed tomography (4DCT) and image registration can be used to determine regional lung ventilation changes after radiation therapy (RT). This study aimed to determine if lung ventilation change following radiation therapy was affected by the pre-RT ventilation of the lung. METHODS 13 subjects had three 4DCT scans: two repeat scans acquired before RT and one three months after RT. Regional ventilation was computed using Jacobian determinant calculations on the registered 4DCT images. The post-RT ventilation map was divided by the pre-RT ventilation map to get a voxel-by-voxel Jacobian ratio map depicting ventilation change over the course of RT. Jacobian ratio change was compared over the range of delivered doses. The first pre-RT ventilation image was divided by the second to establish a control for Jacobian ratio change without radiation delivered. The functional change between scans was assessed using histograms of the Jacobian ratios. RESULTS There were significantly (p < 0.05) more voxels that had a large decrease in Jacobian ratio in the post-RT divided by pre-RT map (15.6%) than the control (13.2%). There were also significantly (p < .01) more voxels that had a large increase in Jacobian ratio (16.2%) when compared to control (13.3%). Lung regions with low function (<10% expansion by Jacobian) showed a slight linear reduction in expansion (0.2%/10 Gy delivered), while high function regions (>10% expansion) showed a greater response (1.2% reduction/10 Gy). Contiguous high function regions > 1 liter occurred in 11 of 13 subjects. CONCLUSION There is a significant change in regional ventilation following a course of radiation therapy. The change in Jacobian following RT is dependent both on the delivered dose and the initial ventilation of the lung tissue: high functioning lung has greater ventilation loss for equivalent radiation doses. Substantial regions of high function lung tissue are prevalent. Research support from NIH grants CA166119 and CA166703, a gift from Roger Koch, and a Pilot Grant from University of Iowa Carver College of Medicine.

TU-G-BRA-03: Predicting Radiation Therapy Induced Ventilation Changes Using 4DCT Jacobian Calculations

Purpose: Longitudinal changes in lung ventilation following radiation therapy can be mapped using four-dimensional computed tomography(4DCT) and image registration. This study aimed to predict ventilation changes caused by radiation therapy(RT) as a function of pre-RT ventilation and delivered dose. Methods: 4DCT images were acquired before and 3 months after radiation therapy for 13 subjects. Jacobian ventilation maps were calculated from the 4DCT images, warped to a common coordinate system, and a Jacobian ratio map was computed voxel-by-voxel as the ratio of post-RT to pre-RT Jacobian calculations. A leave-one-out method was used to build a response model for each subject: post-RT to pre-RT Jacobian ratio data and dose distributions of 12 subjects were applied to the subject’s pre-RT Jacobian map to predict the post-RT Jacobian. The predicted Jacobian map was compared to the actual post-RT Jacobian map to evaluate efficacy. Within this cohort, 8 subjects had repeat pre-RT scans that were compared as a reference for no ventilation change. Maps were compared using gamma pass rate criteria of 2mm distance-to-agreement and 6% ventilation difference. Gamma pass rates were compared using paired t-tests to determine significant differences. Further analysis masked non-radiation induced changes by excluding voxels below specified dose thresholds. Results: Visual inspection demonstrates the predicted post-RT ventilation map is similar to the actual map in magnitude and distribution. Quantitatively, the percentage of voxels in agreement when excluding voxels receiving below specified doses are: 74%/20Gy, 73%/10Gy, 73%/5Gy, and 71%/0Gy. By comparison, repeat scans produced 73% of voxels within the 6%/2mm criteria. The agreement of the actual post-RT maps with the predicted maps was significantly better than agreement with pre-RT maps (p<0.02). Conclusion: This work validates that significant changes to ventilation post-RT can be predicted. The differences between the predicted and actual outcome are similar to differences between repeat scans with equivalent ventilation. This work was supported by NIH grant CA166703 and a Pilot Grant from University of Iowa Carver College of Medicine

TU-A-12A-01: Consistency of Lung Expansion and Contraction During Respiration: Implications for Quantitative Imaging

PURPOSE Four-dimensional computed tomography (4DCT) can be used to evaluate longitudinal changes in pulmonary function. The sensitivity of such measurements to identify function change may be improved with reproducible breathing patterns. The purpose of this study was to determine if inhale was more consistent than exhale, i.e., lung expansion during inhalation compared to lung contraction during exhalation. METHODS Repeat 4DCT image data acquired within a short time interval from 8 patients. Using a tissue volume preserving deformable image registration algorithm, Jacobian ventilation maps in two scanning sessions were computed and compared on the same coordinate for reproducibility analysis. Equivalent lung volumes (ELV) were used for 5 subjects and equivalent title volumes (ETV) for the 3 subjects who experienced a baseline shift between scans. In addition, gamma pass rate was calculated from a modified gamma index evaluation between two ventilation maps, using acceptance criterions of 2mm distance-to-agreement and 5% ventilation difference. The gamma pass rates were then compared using paired t-test to determine if there was a significant difference. RESULTS Inhalation was more reproducible than exhalation. In the 5 ELV subjects 78.5% of the lung voxels met the gamma criteria for expansion during inhalation when comparing the two scans, while significantly fewer (70.9% of the lung voxels) met the gamma criteria for contraction during exhalation (p = .027). In the 8 total subjects analyzed the average gamma pass rate for expansion during inhalation was 75.2% while for contraction during exhalation it was 70.3%; which trended towards significant (p = .064). CONCLUSION This work implies inhalation is more reproducible than exhalation, when equivalent respiratory volumes are considered. The reason for this difference is unknown. Longitudinal investigation of pulmonary function change based on inhalation images appears appropriate for Jacobian-based measure of lung tissue expansion. NIH Grant: R01 CA166703.