Quantifying the accuracy of automated structure segmentation in 4D CT images using a deformable image registration algorithm

Four-dimensional (4D) radiotherapy is the explicit inclusion of the temporal changes in anatomy during the imaging, planning, and delivery of radiotherapy. One key component of 4D radiotherapy planning is the ability to automatically ("auto") create contours on all of the respiratory phase computed tomography (CT) datasets comprising a 4D CT scan, based on contours manually drawn on one CT image set from one phase. A tool that can be used to automatically propagate manually drawn contours to CT scans of other respiratory phases is deformable image registration. The purpose of the current study was to geometrically quantify the difference between automatically generated contours with manually drawn contours. Four-DCT data sets of 13 patients consisting of ten three-dimensional CT image sets acquired at different respiratory phases were used for this study. Tumor and normal tissue structures [gross tumor volume (GTV), esophagus, right lung, left lung, heart and cord] were manually drawn on each respiratory phase of each patient. Large deformable diffeomorphic image registration was performed to map each CT set from the peak-inhale respiration phase to the CT image sets corresponding with subsequent respiration phases. The calculated displacement vector fields were used to deform contours automatically drawn on the inhale phase to the other respiratory phase CT image sets. The code was interfaced to a treatment planning system to view the resulting images and to obtain the volumetric, displacement, and surface congruence information; 692 automatically generated structures were compared with 692 manually drawn structures. The auto- and manual methods showed similar trends, with a smaller difference observed between the GTVs than other structures. The auto-contoured structures agree with the manually drawn structures, especially in the case of the GTV, to within published interobserver variations. For the GTV, fractional volumes agree to within 0.2+/-0.1, center of mass displacements agree to within 0.5+/-1.5 mm, and agreement of surface congruence is 0.0+/-1.1 mm. The surface congruence between automatic and manual contours for the GTV, heart, left lung, right lung and esophagus was less than 5 mm in 99%, 94%, 94%, 91% and 89%, respectively. Careful assessment of the performance of automatic algorithms is needed in the presence of 4D CT artifacts.     

Validation of an accelerated 'demons' algorithm for deformable image registration in radiation therapy

A greyscale-based fully automatic deformable image registration algorithm, originally known as the 'demons' algorithm, was implemented for CT image-guided radiotherapy. We accelerated the algorithm by introducing an 'active force' along with an adaptive force strength adjustment during the iterative process. These improvements led to a 40% speed improvement over the original algorithm and a high tolerance of large organ deformations. We used three methods to evaluate the accuracy of the algorithm. First, we created a set of mathematical transformations for a series of patient's CT images. This provides a 'ground truth' solution for quantitatively validating the deformable image registration algorithm. Second, we used a physically deformable pelvic phantom, which can measure deformed objects under different conditions. The results of these two tests allowed us to quantify the accuracy of the deformable registration. Validation results showed that more than 96% of the voxels were within 2 mm of their intended shifts for a prostate and a head-and-neck patient case. The mean errors and standard deviations were 0.5 mm+/-1.5 mm and 0.2 mm+/-0.6 mm, respectively. Using the deformable pelvis phantom, the result showed a tracking accuracy of better than 1.5 mm for 23 seeds implanted in a phantom prostate that was deformed by inflation of a rectal balloon. Third, physician-drawn contours outlining the tumour volumes and certain anatomical structures in the original CT images were deformed along with the CT images acquired during subsequent treatments or during a different respiratory phase for a lung cancer case. Visual inspection of the positions and shapes of these deformed contours agreed well with human judgment. Together, these results suggest that the accelerated demons algorithm has significant potential for delineating and tracking doses in targets and critical structures during CT-guided radiotherapy.     

Quantification of accuracy of the automated nonlinear image matching and anatomical labeling (ANIMAL) nonlinear registration algorithm for 4D CT images of lung

The performance of the ANIMAL (Automated Nonlinear Image Matching and Anatomical Labeling) nonlinear registration algorithm for registration of thoracic 4D CT images was investigated. The algorithm was modified to minimize the incidence of deformation vector discontinuities that occur during the registration of lung images. Registrations were performed between the inhale and exhale phases for five patients. The registration accuracy was quantified by the cross-correlation of transformed and target images and distance to agreement (DTA) measured based on anatomical landmarks and triangulated surfaces constructed from manual contours. On average, the vector DTA between transformed and target landmarks was 1.6 mm. Comparing transformed and target 3D triangulated surfaces derived from planning contours, the average target volume (GTV) center-of-mass shift was 2.0 mm and the 3D DTA was 1.6 mm. An average DTA of 1.8 mm was obtained for all planning structures. All DTA metrics were comparable to inter observer uncertainties established for landmark identification and manual contouring.     

Simulation of four-dimensional CT images from deformable registration between inhale and exhale breath-hold CT scans

PURPOSE: We propose to simulate an artificial four-dimensional (4-D) CT image of the thorax during breathing. It is performed by deformable registration of two CT scans acquired at inhale and exhale breath-hold. MATERIALS AND METHODS: Breath-hold images were acquired with the ABC (Active Breathing Coordinator) system. Dense deformable registrations were performed. The method was a minimization of the sum of squared differences (SSD) using an approximated second-order gradient. Gaussian and linear-elastic vector field regularizations were compared. A new preprocessing step, called a priori lung density modification (APLDM), was proposed to take into account lung density changes due to inspiration. It consisted of modulating the lung densities in one image according to the densities in the other, in order to make them comparable. Simulated 4-D images were then built by vector field interpolation and image resampling of the two initial CT images. A variation in the lung density was taken into account to generate intermediate artificial CT images. The Jacobian of the deformation was used to compute voxel values in Hounsfield units. The accuracy of the deformable registration was assessed by the spatial correspondence of anatomic landmarks located by experts. RESULTS: APLDM produced statistically significantly better results than the reference method (registration without APLDM preprocessing). The mean (and standard deviation) of distances between automatically found landmark positions and landmarks set by experts were 2.7(1.1) mm with APLDM, and 6.3(3.8) mm without. Interexpert variability was 2.3(1.2) mm. The differences between Gaussian and linear elastic regularizations were not statistically significant. In the second experiment using 4-D images, the mean difference between automatic and manual landmark positions for intermediate CT images was 2.6(2.0) mm. CONCLUSION: The generation of 4-D CT images by deformable registration of inhale and exhale CT images is feasible. This can lower the dose needed for 4-D CT acquisitions or can help to correct 4-D acquisition artifacts. The 4-D CT model can be used to propagate contours, to compute a 4-D dose map, or to simulate CT acquisitions with an irregular breathing signal. It could serve as a basis for 4-D radiation therapy planning. Further work is needed to make the simulation more realistic by taking into account hysteresis and more complex voxel trajectories.     

A general methodology for three-dimensional analysis of variation in target volume delineation.

A generic method for three-dimensional (3-D) evaluation of target volume delineation in multiple imaging modalities is presented. The evaluation includes geometrical and statistical methods to estimate observer differences and variability in defining the Gross Tumor Volume (GTV) in relation to the diagnostic CT and MRI modalities. The geometrical method is based on mapping the 3-D shape of the target volume to a scalar representation, thus enabling a one-dimensional statistical analysis. The statistical method distinguishes observer and modality related uncertainties, which are expressed in terms of three error components: random observer deviations, systematic observer differences, and systematic modality differences. Monte Carlo simulations demonstrate that the standard errors of each of the three model parameters are inversely proportional to the square root of the product of the patient group size and the number of observers and proportional to the intraobserver variation. For 18 patients and 3 observers the standard errors of the estimated systematic modality and observer differences are 19% and 14% of the intraobserver standard deviation, respectively. A scalar representation of the shape of the prostate, delineated by 3 observers for 18 patients, was obtained by sampling the distance between the average center of gravity of the prostate in CT and the prostate surface for a large number of directions (2500), using polar coordinates. Observer variability and differences were obtained by applying the statistical method to the samples independently. The intraobserver variation for CT was largest in regions near the seminal vesicles (s.d: 3 mm) and the apex (s.d: 3 mm). The systematic observer variation in CT was largest in a region near the plexus Santorini, at the caudal-anterior side of the prostate (s.d.: 2 mm). The sensitivity for the choice of origin was tested by using the average center of gravity from axial MRI instead of CT. The results were almost identical. The polar map measures distances in the scanning directions. A correction procedure to get the variability in directions perpendicular to the surface of the prostate yielded variations that were a factor of 0.85 smaller for all directions. It is concluded that by separating the shape evaluation in a geometrical and a statistical part, the complexity of the analysis of 3-D shape differences can be significantly reduced. The method was successfully applied to a group of prostate patients, where we demonstrated that delineation variability is nonhomogeneous, with the largest variations occurring near the seminal vesicles and the apex.     

Variability of Semiautomated Lung Nodule Volumetry on Ultralow-Dose CT: Comparison with Nodule Volumetry on Standard-Dose CT

The study investigates the effect of a substantial dose reduction on the variability of lung nodule volume measurements by assessing and comparing nodule volumes using a dedicated semiautomated segmentation software on ultralow-dose computed tomography (ULD-CT) and standard-dose computed tomography (SD-CT) data. In 20 patients, thin-slice chest CT datasets (1 mm slice thickness; 20% reconstruction overlap) were acquired at ultralow-dose (120 kV, 5 mAs) and at standard-dose (120 kV, 75 mAs), respectively, and analyzed using the segmentation software OncoTREAT (MeVis, Bremen, Germany; version 1.3). Interobserver variability of volume measurements of 202 solid pulmonary nodules (mean diameter 11 mm, range 3.2–44.5 mm) was calculated for SD-CT and ULD-CT. With respect to interobserver variability, the 95% confidence interval for the relative differences in nodule volume in the intrascan analysis was measured with −9.7% to 8.3% (mean difference −0.7%) for SD-CT and with −12.6% to 12.4% (mean difference −0.2%) for ULD-CT. In the interscan analysis, the 95% confidence intervals for the differences in nodule volume ranged with −25.1% to −23.4% and 26.2% to 28.9% (mean difference 1.4% to 2.1%) dependent on the combination of readers and scans. Intrascan interobserver variability of volume measurements was comparable for ULD-CT and SD-CT data. The calculated variability of volume measurements in the interscan analysis was similar to the data reported in the literature for CT data acquired with equal radiation dose. Thus, the evaluated segmentation software provides nodule volumetry that appears to be independent of the dose level with which the CT source dataset is acquired.     

Investigating the low-dose limits of multidetector CT in lung nodule surveillance

The purpose of this study was to evaluate the factors limiting nodule detection in thoracic computed tomography (CT) and to determine whether prior knowledge of nodule size and attenuation, available from a baseline CT study, influences the minimum radiation dose at which nodule surveillance CT scans can be performed while maintaining current levels of nodule detectability. Multiple nodules varying in attenuation (-509 to + 110 HU) and diameter (1.6 to 9.5 mm) were layered in random and ordered sequences within 2 lung cylinders made of Rando lung material and suspended within a custom-built CT phantom. Multiple CT scans were performed at varying kVp (120, 100, and 80), mA (200, 150, 100, 50, 20, and 10), and beam collimation (5, 2.5, and 1.25 mm) on a four-row multidetector scanner (Lightspeed, General Electric, Milwaukee, WI) using 0.8 s gantry rotation. The corresponding range of radiation dose over which images were acquired was 0.3-26.4 mGy. Nine observers independently performed three specific tasks, namely: (1) To detect a 3.2 mm nodule of 23 HU; (2) To detect 3.2 mm nodules of varying attenuation (-509 to -154 HU); and (3) To detect nodules varying in size (1.6-9 mm) and attenuation (-509 to 110 HU). A two-alternative forced-choice test was used in order to determine the limits of nodule detection in terms of the proportion of correct responses (Pcorr, related to the area under the ROC curve) as a summary metric of observer performance. The radiation dose levels for detection of 99% of nodules in each task were as follows: Task 1 (1 mGy); Task 2 (5 mGy); and Task 3 (7 mGy). The corresponding interobserver confidence limits were 1, 5, and 10 mGy for Tasks 1, 2, and 3, respectively. There was a fivefold increase in the radiation dose required for detection of lower-density nodules (Tasks 1 to 2). Absence of prior knowledge of the nodule size and density (Task 3) corresponds to a significant increase in the minimum required radiation dose. Significant image degradation and reduction in observer performance for all tasks occur at a dose of < or = 1 mGy. It is concluded that the size and attenuation of a nodule strongly influence the radiation dose required for confident evaluation with a minimum threshold value of 1-2 mGy (minimum dose CT). A prior knowledge of nodule size and attenuation is available from the baseline CT scan and is an important consideration in minimizing the radiation exposure required for nodule detection with surveillance CT.     

How does CT image noise affect 3D deformable image registration for image-guided radiotherapy planning?

PURPOSE: To measure the sensitivity of deformable image registration to image noise. Deformable image registration can be used to map organ contours and other treatment planning data from one CT to another. These CT studies can be acquired with either conventional fan-beam CT systems or more novel cone-beam CT techniques. However, cone-beam CT images can have higher noise levels than fan-beam CT, which might reduce registration accuracy. We have investigated the effect of image quality differences on the deformable registration of fan-beam CTs and CTs with simulated cone-beam noise. METHOD: Our study used three CT studies for each of five prostate patients. Each CT was contoured by three experienced radiation oncologists. For each patient, one CT was designated the source image and the other two were target images. A deformable image registration process was used to register each source CT to each target CT and then transfer the manually drawn treatment planning contours from the source CT to the target CTs. The accuracy of the automatically transferred contours (and thus of the deformable registration process) was assessed by comparing them to the manual contours on the target CTs, with the differences evaluated with respect to interobserver variability in the manual contours. Then each of the target CTs was modified to include increased noise characteristic of cone-beam CT and the tests were repeated. Changes in registration accuracy due to increased noise were detected by monitoring changes in the automatically transferred contours. RESULTS: We found that the additional noise caused no significant loss of registration accuracy at magnitudes that exceeded what would normally be found in an actual cone-beam CT. SUMMARY: We conclude that noise levels in cone-beam CTs that might reduce manual contouring accuracy do not reduce image registration and automatic contouring accuracy.     

胸中段食管癌复位前后靶区移位和剂量学变化的初步研究

目的:分析胸中段食管癌放疗复位前后靶区和剂量学变化,探讨胸中段食管癌放疗复位的必要性和可行性。方法:回顾性分析10例接受三维适形放疗的食管癌患者,食管靶区长度平均为11.7 cm。对患者行CT扫描并勾画靶区(GTV1),放疗40 Gy后行CT复位模拟定位,并且重新勾画靶区(GTV2)。制定两套计划,治疗计划1(Plan1)按前半程追加处方剂量至60 Gy;治疗计划2(Plan2)将后半程与前半程进行图像刚性配准,总处方60 Gy,比较分析两次计划靶区几何位移和剂量学变化。结果:复位后的靶区(PTV)体积明显小于复位前(P=0.036)。在同一横断面上x轴相差最大4 mm,y轴相差最大2.3 mm,z轴相差最大6.0 mm。PTV达到处方剂量的体积平均分别为97.45%±0.73%和95.19%±2.37%;靶区最大剂量、最小剂量和平均剂量差异均没有统计学意义。危及器官心脏、左肺和全肺的平均剂量以及脊髓最大点剂量复位后的计划均小于复位前计划(P>0.05);右肺平均剂量复位后显著小于复位前(t=3.172,P=0.025)。结论:胸中段食管癌放疗过程中靶区体积及解剖位置的变化等因素可能导致的靶区低剂量和正常组织的超量照射,实施CT重新扫描定位和调整治疗计划可以修正靶区剂量,减少不必要的正常组织的照射。     

Estimation of the delivered patient dose in lung IMRT treatment based on deformable registration of 4D-CT data and Monte Carlo simulations

The purpose of this study is to accurately estimate the difference between the planned and the delivered dose due to respiratory motion and free breathing helical CT artefacts for lung IMRT treatments, and to estimate the impact of this difference on clinical outcome. Six patients with representative tumour motion, size and position were selected for this retrospective study. For each patient, we had acquired both a free breathing helical CT and a ten-phase 4D-CT scan. A commercial treatment planning system was used to create four IMRT plans for each patient. The first two plans were based on the GTV as contoured on the free breathing helical CT set, with a GTV to PTV expansion of 1.5 cm and 2.0 cm, respectively. The third plan was based on the ITV, a composite volume formed by the union of the CTV volumes contoured on free breathing helical CT, end-of-inhale (EOI) and end-of-exhale (EOE) 4D-CT. The fourth plan was based on GTV contoured on the EOE 4D-CT. The prescribed dose was 60 Gy for all four plans. Fluence maps and beam setup parameters of the IMRT plans were used by the Monte Carlo dose calculation engine MCSIM for absolute dose calculation on both the free breathing CT and 4D-CT data. CT deformable registration between the breathing phases was performed to estimate the motion trajectory for both the tumour and healthy tissue. Then, a composite dose distribution over the whole breathing cycle was calculated as a final estimate of the delivered dose. EUD values were computed on the basis of the composite dose for all four plans. For the patient with the largest motion effect, the difference in the EUD of CTV between the planed and the delivered doses was 33, 11, 1 and 0 Gy for the first, second, third and fourth plan, respectively. The number of breathing phases required for accurate dose prediction was also investigated. With the advent of 4D-CT, deformable registration and Monte Carlo simulations, it is feasible to perform an accurate calculation of the delivered dose, and compare our delivered dose with doses estimated using prior techniques.     

Automatic registration of the prostate for computed-tomography-guided radiotherapy

The recent development of integrated computed tomography (CT)/linear accelerator (LINAC) combinations, where the CT scanner and the LINAC use the same patient couch, and of kilovoltage cone-beam CT systems attached to the LINAC gantry, means that suitable hardware is now available for CT-guided localization of the prostate. Clinical implementation is, however, currently impeded by the lack of robust and accurate software tools to compare the position of the prostate in the CT images used for the treatment plan with its position in the daily CT images. Manual registration of the planning CT images with the daily CT images can be slow and can introduce significant inter-user variations. We have developed an automatic registration technique that is not adversely influenced by changes in prostate shape, size or orientation, presence of rectal gas, or bladder filling. The cost function used in the registration is the mean absolute difference in CT numbers voxel-by-voxel between the daily CT image and the planning CT image for a volume extracted from the planning CT images using the original physician-drawn gross tumor volume contours. To enhance soft tissue contrast in the prostate region and to reduce the impact of rectal gas calcifications and bone on the registration, voxels with CT numbers that represent gas or bone are filtered out from the calculation. The results of the automatic registration agreed with the mean results of seven human observers, with standard deviations of 0.5 mm, 0.5 mm, and 1.0 mm in the left/right (RL), anterior/posterior (AP), and superior/inferior (SI) directions, respectively, for a patient that was relatively easy to localize. Agreement (one standard deviation) for a patient that was difficult to localize was 0.6 mm, 1.4 mm, and 1.9 mm in the RL, AP, and SI directions, respectively. These results are better than the interuser uncertainties reported for a manual alignment technique and are close to the reported intrauser uncertainties. The results are independent of the shape of contours in the original treatment plan, reducing the impact of interobserver variations in contouring the prostate. The algorithm is fast and reliable, allowing the entire CT localization process to take place in 5-9 minutes. In 120 CT image sets from seven patients, the failure rate was found to be less than 1%. The use of this algorithm will facilitate the clinical implementation of CT-guided localization of the prostate.     

Dynamic ventilation imaging from four-dimensional computed tomography

A novel method for dynamic ventilation imaging of the full respiratory cycle from four-dimensional computed tomography (4D CT) acquired without added contrast is presented. Three cases with 4D CT images obtained with respiratory gated acquisition for radiotherapy treatment planning were selected. Each of the 4D CT data sets was acquired during resting tidal breathing. A deformable image registration algorithm mapped each (voxel) corresponding tissue element across the 4D CT data set. From local average CT values, the change in fraction of air per voxel (i.e. local ventilation) was calculated. A 4D ventilation image set was calculated using pairs formed with the maximum expiration image volume, first the exhalation then the inhalation phases representing a complete breath cycle. A preliminary validation using manually determined lung volumes was performed. The calculated total ventilation was compared to the change in contoured lung volumes between the CT pairs (measured volume). A linear regression resulted in a slope of 1.01 and a correlation coefficient of 0.984 for the ventilation images. The spatial distribution of ventilation was found to be case specific and a 30% difference in mass-specific ventilation between the lower and upper lung halves was found. These images may be useful in radiotherapy planning.     

基于4D-CT和Mimics软件模拟分析肺癌肿瘤的呼吸运动规律

目的：利用Mimics10.01软件和4D-CT10个呼吸时相的肺部三维模型,研究肺部肿瘤的呼吸运动规律。方法：选择1例左上肺癌患者,在肿瘤上、中、下部植入3个金标,间隔为6 mm,4D-CT扫描相位排序后重建10个呼吸时相的CT图像。将10个时相的CT图像依次导入Mimics10.01软件中,采用阈值分割、区域生长的方法提取肺部区域,重建左右肺的三维模型。测量10个呼吸时相的左右肺体积和表面积;吸气末与呼气末时相之间左肺三维模型之间的偏差也进行了分析。在每个时相的CT图像上读取植入3个金标的位置坐标,求出金标在X、Y、Z方向上质心的坐标。结果：从吸气末到呼气末左、右肺体积的变化范围分别为12.8%和12.4%,左、右肺表面积的变化范围为6.6%和6.7%。3个金标的质心变化幅度在左右、头脚、前后方向分别为2 mm,1mm和2.7 mm。结论：利用4D-CT的图像和Mimics软件重建得出的肺模型可以方便地计算肺体积以及靶区的运动范围,有利于根据患者的靶区运动特征实现个体化治疗。     

基于4DCT和形变配准技术评估呼吸运动对肺癌立体定向放射治疗过程中剂量的影响

目的:探讨肺下叶肿瘤患者立体定向放射治疗（SBRT）治疗时,呼吸运动对肿瘤和正常器官受量的影响。方法:选取14例肺下叶肿瘤患者,均行平扫CT和四维CT（4DCT）扫描定位,获得平扫及10个呼吸时相的序列图像,同时记录患者放疗时的呼吸曲线,并得到各呼吸时相维持时间占比。利用MIM工作站勾画肿瘤和正常器官,基于平扫CT制定放疗计划,将3DCT计划移植到各呼吸时相的序列图像中并计算剂量,按照时间占比叠加各个时相的剂量。结果:比较平扫CT计划剂量分布和叠加剂量分布,得出相比平扫CT计划剂量。叠加剂量中,PTV平均剂量、患侧肺V20、患侧肺平均剂量、健侧肺平均剂量和全肺平均剂量的4D加权叠加均小于3D剂量,分别减小了2.37%、5.08%、5.19%、3.61%和3.46%,差异均有统计学意义（P<0.05）。结论:患者的呼吸运动导致肿瘤和肺受量的降低,但在较小的变化范围内。利用4DCT和形变配准技术,引入患者各呼吸时相维持时间占比的因素,可更合理评估呼吸运动对肺下叶肿瘤SBRT放射治疗过程中剂量的影响。     

4D-CT motion estimation using deformable image registration and 5D respiratory motion modeling

Four-dimensional computed tomography (4D-CT) imaging technology has been developed for radiation therapy to provide tumor and organ images at the different breathing phases. In this work, a procedure is proposed for estimating and modeling the respiratory motion field from acquired 4D-CT imaging data and predicting tissue motion at the different breathing phases. The 4D-CT image data consist of series of multislice CT volume segments acquired in ciné mode. A modified optical flow deformable image registration algorithm is used to compute the image motion from the CT segments to a common full volume 3D-CT reference. This reference volume is reconstructed using the acquired 4D-CT data at the end-of-exhalation phase. The segments are optimally aligned to the reference volume according to a proposed a priori alignment procedure. The registration is applied using a multigrid approach and a feature-preserving image downsampling maxfilter to achieve better computational speed and higher registration accuracy. The registration accuracy is about 1.1 +/- 0.8 mm for the lung region according to our verification using manually selected landmarks and artificially deformed CT volumes. The estimated motion fields are fitted to two 5D (spatial 3D+tidal volume+airflow rate) motion models: forward model and inverse model. The forward model predicts tissue movements and the inverse model predicts CT density changes as a function of tidal volume and airflow rate. A leave-one-out procedure is used to validate these motion models. The estimated modeling prediction errors are about 0.3 mm for the forward model and 0.4 mm for the inverse model.     

Technical note: A novel boundary condition using contact elements for finite element based deformable image registration

Deformable image registration is an important tool for image-guided radiotherapy. Physics-model-based deformable image registration using finite element analysis is one of the methods currently being investigated. The calculation accuracy of finite element analysis is dependent on given boundary conditions, which are usually based on the surface matching of the organ in two images. Such a surface matching, however, is hard to obtain from medical images. In this study, we developed a new boundary condition to circumvent the traditional difficulties. Finite element contact-impact analysis was employed to simulate the interaction between the organ of interest and the surrounding body. The displacement loading is not necessarily specified. The algorithm automatically deforms the organ model into the minimum internal energy state. The analysis was performed on CT images of the lung at two different breathing phases (exhalation and full inhalation). The result gave the displacement vector map inside the lung. Validation of the result showed satisfactory agreement in most parts of the lung. This approach is simple, operator independent and may provide improved accuracy of the prediction of organ deformation.