A patient-specific respiratory model of anatomical motion for radiation treatment planning

Qinghui Zhang; Alex Pevsner; Agung Hertanto; Yu-Chi Hu; Kenneth E. Rosenzweig; C. Clifton Ling; Gig S Mageras

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A patient-specific respiratory model of anatomical motion for radiation treatment planning

Qinghui Zhang, Alex Pevsner, Agung Hertanto, Yu-Chi Hu, Kenneth E. Rosenzweig, C. Clifton Ling, Gig S Mageras

arXiv:0712.1783v1Dec 11, 2007physics.med-ph

TL;DR

Respiration-induced anatomical motion can limit radiotherapy dose accuracy. This paper develops a patient-specific, nonrepeating-breath model parameterized by diaphragm motion, finding that two principal components sufficiently model 3D organ motion in four patients.

Problem
Respiration-induced anatomical motion can limit the accuracy of radiotherapy dose assessment in the thorax and abdomen.
Method
The model adapts to individual patients and estimates three-dimensional organ motion without assuming repeatable breath cycles, using diaphragm motion as its parameterization.
Results
Two principal components appear sufficient to accurately model three-dimensional organ motion in the evaluated patients.
Takeaways & Limitations
The model provides a basis for estimating patient-specific respiration-induced organ motion for radiotherapy applications.
Takeaways & Limitations
Validation of interfraction motion states was limited to four cases.

Abstract

from arXiv · show

Modeling of respiratory motion is important for a more accurate understanding and accounting of its effect on dose to cancers in the thorax and abdomen by radiotherapy. We have developed a model of respiration-induced organ motion in the thorax, without the commonly adopted assumption of repeatable breath cycles. The model describes the motion of a volume of interest within the patient, based on a reference 3-dimensional image (at end-expiration), and the diaphragm positions at different time points. The input data are respiration-correlated CT images of patients treated for nonsmall cell lung cancer, consisting of 3D images, including the diaphragm positions, at 10 phases of the respiratory cycle. A deformable image registration algorithm calculates the deformation field that maps each 3D image to the reference 3D image. A principle component analysis is performed to parameterize the 3D deformation field in terms of the diaphragm motion. We show that the first two principal components are adequate to accurately and completely describe the organ motion in the data of 4 patients. Artifacts in the RCCT images that commonly occur at the mid-respiration states are reduced in the model-generated images. Further validation of the model is demonstrated in the successful application of the parameterized 3D deformation field to RCCT data of the same patient but acquired several days later. We have developed a method for predicting respiration-induced organ motion in patients that has potential for improving the accuracy of dose calculation in radiotherapy.

I. INTRODUCTION

Respiration-induced anatomical motion can reduce radiotherapy dose-calculation and delivery accuracy, while irregular breathing and limited internal-motion measurements challenge periodic motion models. This work develops and validates a patient-specific 3D model of thoracic tumor and lung motion without assuming repeatable breathing patterns.

Respiration-induced anatomical motion can limit the accuracy of radiotherapy dose calculation and delivery for thoracic and abdominal cancers.
Many patients breathe irregularly, making periodic functions inadequate for describing organ motion.
Fluoroscopy and respiration monitors measure breathing variability but do not provide adequate information about internal 3D motion, while interfractional anatomical variation introduces uncertainty.
The proposed model estimates thoracic tumor and normal-lung motion without repeatable breathing assumptions by parameterizing 3D voxel trajectories using diaphragm motion.
The model was validated by predicting anatomical changes in lung-cancer patients’ RCCT images acquired on different days and was reported accurate and potentially useful for improving radiotherapy dose calculation and delivery.

II. METHODS

The method adapts a high-dimensional respiratory motion model to patient-specific RCCT data, then uses deformable registration and PCA to predict 3D anatomical deformation from diaphragm-based surrogate signals. RCCT scans from four patients provide the respiratory-phase images for model construction and later validation.

Overall approach: The approach adapts the model to a particular patient using RCCT images and applies the improved model to predict 3D deformation in that patient’s anatomy.The model uses high-dimensional, voxel-level deformations to accommodate complex respiratory movement in the thorax.
Deformable registration: Deformable registration maps each respiratory-phase image to the end-expiration reference, producing voxel-dependent displacement fields that represent tissue motion over the respiratory cycle.The displacement fields deform the end-expiration reference image into the other 9 time points.
Principal component analysis: PCA reduces noise, redundancy, and registration-related inconsistencies in the high-dimensional displacement data by retaining a small set of principal components.The method assumes that high-variance components represent the main lung motion, whereas low-variance components reflect noise from imperfect deformable registration.
Surrogate-signal modeling: The model connects time-varying displacement fields with diaphragm-based surrogate signals to determine the relationship between measured respiratory motion and model parameters.The surrogate signals include the diaphragm top along the patient longitudinal axis and its precursor.

a) Deformable registration algorithm

The analysis uses a fast free-form deformable registration algorithm. The algorithm minimizes a specified objective function.

Deformable registration algorithm: The analysis uses a deformable registration algorithm.The passage identifies this algorithm as the registration method used for the analysis.
Deformable registration algorithm: The registration algorithm is fast and free-form.These properties are explicitly stated for the algorithm used in the analysis.
Deformable registration algorithm: The registration algorithm minimizes a specified objective function.The passage introduces the function minimized by the algorithm, but does not provide its form here.

b) Model adaptation using principal components analysis

The model parameterizes respiratory organ motion with centered voxel-displacement vectors and principal components obtained from their covariance matrix. With 10 respiratory measurements, at most 9 components can have nonzero eigenvalues, and arbitrary motion states are approximated by weighted eigenvector sums.

Vector construction: Voxel-displacement vectors are constructed for each time point, then centered by subtracting the respiration-averaged motion state.Each vector contains the three displacement components for every voxel.
Principal-component extraction: A covariance matrix is formed from the centered vectors, and eigenvectors with the largest eigenvalues serve as the model’s principal components.The covariance matrix is positive semi-definite, so its eigenvalues are non-negative.
Model scale: The displacement parameter vector can contain approximately 9 million voxel-related values.M, the total number of voxels, has a typical value around 9 million.
Dimensionality reduction: 10 respiratory measurements provide at most 9 eigenvectors with nonzero eigenvalues.The centered measurements sum to zero, leaving J-1 independent measurements when J=10.
Motion-state representation: An arbitrary motion state p(t) is represented as a weighted sum of K principal eigenvectors.The model expresses possible motion at an arbitrary time point using weights w_k and eigenvectors e_k.

c) Relating surrogate signals to model parameters

The model replaces unknown eigenvector weights with surrogate signals through a matrix relation between displacement fields and measured diaphragm motion. It uses current and precursor diaphragm positions to capture temporal respiratory correlations, including inspiration–expiration differences.

c) Relating surrogate signals to model parameters: The displacement field is expressed from surrogate signals by eliminating eigenvector weights and applying the inverse of the surrogate matrix.The relation is established under the assumption that the surrogate matrix is invertible.
c) Relating surrogate signals to model parameters: The surrogate matrix requires at least one surrogate signal for each eigenvector used in the motion model.Invertibility implies that the number of surrogate-signal rows must be at least the number of eigenvector columns.
c) Relating surrogate signals to model parameters: Diaphragm position is measured as the diaphragm top along the patient’s longitudinal axis in the CT coordinate system.The respiratory time index t ranges from 1 to J, and position uncertainty is estimated as one half of the slice thickness.

III. RESULTS

The results show that the first two eigenvalues capture most of the cumulative eigenvalue sum. Across four patients, they account for approximately 83%, 83%, 90%, and 89%, respectively.

Figure 1 shows the eigenvalue spectrum for one patient.
83% of the cumulative eigenvalue sum is accounted for by the first two eigenvalues in one patient.
83%, 90%, and 89% of the cumulative system eigenvalue sum are accounted for by the first two eigenvalues in the other three patients, respectively.

b) Model prediction within a single RCCT session

Within a single RCCT session, two principal components accurately predict respiratory motion across the cycle and closely reproduce observed tumor and lung geometry. The model also reduces mid-respiratory image artifacts while maintaining discrepancies comparable to observer variability.

Motion prediction: Two principal components accurately predict 3-D changes from end expiration to end inspiration and throughout the respiratory cycle.Model-reconstructed and actual images show almost entirely eliminated density mismatch at end inspiration and good agreement at mid-inspiration and mid-expiration.
GTV position accuracy: Mean discrepancy is less than 1 mm in LR and AP directions, about 1 mm in SI, and less than 2 mm at maximum.The slightly larger SI discrepancy is attributed to coarser CT resolution from 2.5 mm thick CT slices.
GTV shape accuracy: The 95% confidence limit differences for model-observer and interobserver GTV comparisons were comparable, with values of 0.22cm, 0.26cm, 0.32cm and 0.21 cm.These values correspond to Figures 4A, 4B, 4C and 4D, respectively.
Lung shape accuracy: Most 90% CL differences between model-predicted and actual delineated lung surfaces are 2 mm or less, with a largest discrepancy of 3mm.For the highlighted case, the mean discrepancy is 1 mm and the largest discrepancy is 4 mm in the superior lung region.

application of the model to remove artifacts in RCCT images.

The patient-specific model predicted respiratory motion on a different acquisition day using diaphragm positions as surrogate signals. Predicted and actual images showed good spatial agreement, and centroid displacement errors remained small across four patients and two motion states.

Model prediction for different sessions: Using diaphragm positions from a second RCCT as surrogate signals, the model predicted motion on a different day from calibration.The second RCCT was registered to the first by vertebral-body alignment.
Model prediction for different sessions: Predicted and actual end-inspiration images showed good spatial agreement for the GTV, consistent with the second RCCT’s 5 mm slice spacing.The comparison used axial and coronal overlays for two patients.
Model prediction for different sessions: 1.1 ± 0.6 mm LR, 1.8 ± 1.0 mm AP, and 1.6 ± 1.4 mm SI were the predicted-versus-observed GTV centroid displacement differences across 4 patients and 2 motion states.The motion states were end-expiration and end-inspiration.
Model prediction for different sessions: For patient 4, the model accurately predicted a between-session GTV shift of 1 cm AP and 1.5 cm SI at the same end-expiration state.The results support applicability of a simulation-derived, patient-specific model for anatomy near the diaphragm.

IV. DISCUSSION AND CONCLUSIONS

The proposed patient-specific model predicts 3D respiration-induced organ motion from temporal diaphragm-position variation without assuming repeatable breath cycles. Results support its potential for modeling interfraction variation and improving treatment planning, delivery evaluation, and dose calculation, while highlighting validation and calibration limitations.

Model contribution: The model estimates 3D thoracic motion from diaphragm-position variation without assuming repeatable breath cycles, including cycle-to-cycle and interfraction changes.It addresses breathing variability and interfraction variations that prior phase-parameterized models did not consider.
Model results: Two principal components appear sufficient to accurately model 3D respiration-induced thoracic motion, parameterized by voxel location and two surrogate signals.Preliminary results identify current diaphragm position and its position approximately one-third of a respiratory period earlier as appropriate surrogate signals.
Validation and limitations: Comparison of RCCT images acquired on different days suggests applicability to interfractional organ variations, but the evidence is limited to four cases and tumors near the diaphragm.The second RCCT covered a 9 cm region including the diaphragm, so validity for more superiorly situated tumors remains untested.
Validation and limitations: Model recalibration may be needed at approximately weekly intervals because tumor or tissue changes can alter tumor position relative to the surrogate.The model may be accurate over several days, but deeper breathing outside the calibration motion range is another unresolved limitation.
Clinical applications: The method could support treatment planning and delivery evaluation by reducing RCCT artifacts, testing plan sensitivity to breathing variations, and improving dose calculation for moving organs.Monitored diaphragm position combined with the model could provide a record of tumor and normal-organ motion throughout treatment.

36M. Turk and A. Pentland, “Eigenfaces for

The model uses principal components to represent respiration-induced organ motion and reconstruct patient-specific images from diaphragm-linked respiratory states. Two principal components reduce image artifacts, reproduce observed motion, and generalize to RCCT acquired on another day.

Motion validation: Model-predicted and observed GTV centroid displacements are compared across four patients and three respiratory time points in LR, AP, and SI directions.The plotted time points are end inspiration, mid-expiration, and mid-inspiration, with differences reported in millimeters.
Surface validation: The model evaluates lung-surface differences between predicted and actual delineations at end inspiration, mid-inspiration, and mid-expiration.The figure reports 90% confidence-limit differences using 3D vector length and includes a 2D polar map for patient 2 at the end-inspiration state.
Model representation: Two principal components predict lung-voxel displacement from end expiration to end inspiration similarly to deformable image registration.The comparison displays predicted displacement from deformable registration alongside the two-component model prediction.
Image reconstruction: Model-generated images at mid-inspiration reduce artifacts present in original respiration-correlated CT images for three patients.Arrows identify artifacts caused by respiration-correlated CT slice sorting in the original images.
Interfraction validation: A model-predicted end-inspiration image is compared with an actual image from a second RCCT acquired on a different day for two patients.The second RCCT was acquired on a different day from the first RCCT used to calibrate the model.