In order to reduce the sensitivity of radiotherapy treatments to organ motion, compensation methods are being investigated such as gating of treatment delivery, tracking of tumour position, 4D scanning and planning of the treatment, etc. An outstanding problem that would occur with all these methods is the assumption that breathing motion is reproducible throughout the planning and delivery process of treatment. This is obviously not a realistic assumption and is one that will introduce errors. A dynamic internal margin model (DIM) is presented that is designed to follow the tumour trajectory and account for the variability in respiratory motion. The model statistically describes the variation of the breathing cycle over time, i.e. the uncertainty in motion amplitude and phase reproducibility, in a polar coordinate system from which margins can be derived. This allows accounting for an additional gating window parameter for gated treatment delivery as well as minimizing the area of normal tissue irradiated. The model was illustrated with abdominal motion for a patient with liver cancer and tested with internal 3D lung tumour trajectories. The results confirm that the respiratory phases around exhale are most reproducible and have the smallest variation in motion amplitude and phase (approximately 2 mm). More importantly, the margin area covering normal tissue is significantly reduced by using trajectory-specific margins (as opposed to conventional margins) as the angular component is by far the largest contributor to the margin area. The statistical approach to margin calculation, in addition, offers the possibility for advanced online verification and updating of breathing variation as more data become available.

HDR monotherapy for prostate cancer consists of four fractions. The first fraction is delivered with online TRUS-based treatment planning. For the last three fractions the treatment plan is based on a CT-scan acquired in between fractions 1 and 2. The patient position (high lithotomy, rectal US probe) during TRUS-guided catheter implantation and first fraction differs from the patient position in the CT-scan and the remaining three fractions (lowered legs, no TRUS probe). This study describes the effect of posture changes on dose distributions when a plan designed for the TRUS anatomy is applied to the CT-scan anatomy. The aim is to quantify dosimetrical errors that would result from skipping the use of a planning CT-scan, and rely for all fractions on the TRUS plan. Such a procedure would substantially reduce the involved workload, and would increase patient comfort. For three prostate cancer patients, images were acquired during TRUS-guided catheter implantation. Furthermore, a CT-scan (no US probe in rectum, different position of legs) was acquired and matched with the TRUS set. On both TRUS and CT, prostate, urethra and rectum were delineated and all catheters were traced. For each patient, an optimized treatment plan was designed using TRUS images and contours. Catheters with obtained dwell positions of the TRUS plan were transferred individually to the catheter positions in the CT. Changes in dose distribution due to relocation of catheters were evaluated using DVHs. For all patients the dose distributions changed significantly due to rearrangement of the catheters, having most impact on the urethra (maximum observed change: 32% volume receiving 120% of the prescribed dose) and a reduction of PTV coverage (6-28%). Implant deformation when changing from TRUS patient set-up to CT set-up affected negatively the quality of optimized treatment plans. Inclusion of more patients in this study was planned, but because of the observed strong negative effects it is already concluded that the TRUS plan cannot be used for the last three fractions with a deviating patient set-up.

The Synchrony Respiratory Tracking System (RTS) is a treatment option of the CyberKnife robotic treatment device to irradiate extra-cranial tumors that move due to respiration. Advantages of RTS are that patients can breath normally and that there is no loss of linac duty cycle such as with gated therapy. Tracking is based on a measured correspondence model (linear or polynomial) between internal tumor motion and external (chest/abdominal) marker motion. The radiation beam follows the tumor movement via the continuously measured external marker motion. To establish the correspondence model at the start of treatment, the 3D internal tumor position is determined at 15 discrete time points by automatic detection of implanted gold fiducials in two orthogonal x-ray images; simultaneously, the positions of the external markers are measured. During the treatment, the relationship between internal and external marker positions is continuously accounted for and is regularly checked and updated. Here we use computer simulations based on continuously and simultaneously recorded internal and external marker positions to investigate the effectiveness of tumor tracking by the RTS. The Cyberknife does not allow continuous acquisition of x-ray images to follow the moving internal markers (typical imaging frequency is once per minute). Therefore, for the simulations, we have used data for eight lung cancer patients treated with respiratory gating. All of these patients had simultaneous and continuous recordings of both internal tumor motion and external abdominal motion. The available continuous relationship between internal and external markers for these patients allowed investigation of the consequences of the lower acquisition frequency of the RTS. With the use of the RTS, simulated treatment errors due to breathing motion were reduced largely and consistently over treatment time for all studied patients. A considerable part of the maximum reduction in treatment error could already be reached with a simple linear model. In case of hysteresis, a polynomial model added some extra reduction. More frequent updating of the correspondence model resulted in slightly smaller errors only for the few recordings with a time trend that was fast, relative to the current x-ray update frequency. In general, the simulations suggest that the applied combined use of internal and external markers allow the robot to accurately follow tumor motion even in the case of irregularities in breathing patterns.

The contribution of organ and tumour motion to the degradation of planned dose distributions during radiotherapy to the breathing lung has been experimentally investigated and quantified. An anthropomorphic, tissue-equivalent breathing phantom with deformable lungs has been built, in which the lung tumour can be driven in any arbitrary 3D trajectory. The trajectory is programmed into a motion controller connected to a high-precision moving platform that is connected to the tumour. The motion controller is connected to the accelerator's dose counter and the speed of motion is scaled to the dose rate. This ensures consistent delivery despite variation in either the dose rate or inter-segment timing. For this study, the phantom was made to breathe by a set of periodic equations representing respiratory motion by an asymmetric, trigonometric function. Several motion amplitudes were selected to be applied in the primary axis of motion. Five three-dimensional, geometrically conformal (3DCRT) fractions with different starting phases (spaced uniformly in the breathing cycle) were delivered to the phantom and compared to a delivery where the phantom was static at the end-expiration position. A set of intensity-modulated radiotherapy plans (IMRT) was subsequently delivered in the same manner. Bigger amplitudes of motion resulted in a higher degree of dose blurring. Severe underdosages were observed when deliberately selecting the PTV wrongly, their extent being correlated with the degree of margin error. IMRT motion-averaged dose distributions exhibited areas of high dose in the gross tumour volume (GTV) which were not present in the static irradiations, arising from booster segments that the optimizer was creating to achieve planning target volume (PTV) homogeneity during the inverse-planning process. 3DCRT, on the other hand, did not demonstrate such effects. It has been concluded that care should be taken to control the delivered fluence when delivering IMRT to the breathing lung, even when the PTV margin has been adequately chosen to include the extent of the breathing motion.

The aim of this study has been to explicitly include the functional heterogeneity of an organ as a factor that contributes to the probability of complication of normal tissues following radiotherapy. Situations for which the inclusion of this information can be advantageous to the design of treatment plans are then investigated. A Java program has been implemented for this purpose. This makes use of a voxelated model of a patient, which is based on registered anatomical and functional data in order to enable functional voxel weighting. Using this model, the functional dose-volume histogram (fDVH) and the functional normal tissue complication probability (fNTCP) are then introduced as extensions to the conventional dose-volume histogram (DVH) and normal tissue complication probability (NTCP). In the presence of functional heterogeneity, these tools are physically more meaningful for plan evaluation than the traditional indices, as they incorporate additional information and are anticipated to show a better correlation with outcome. New parameters m(f), n(f) and TD(50f) are required to replace the m, n and TD(50) parameters. A range of plausible values was investigated, awaiting fitting of these new parameters to patient outcomes where functional data have been measured. As an example, the model is applied to two lung datasets utilizing accurately registered computed tomography (CT) and single photon emission computed tomography (SPECT) perfusion scans. Assuming a linear perfusion-function relationship, the biological index mean perfusion weighted lung dose (MPWLD) has been extracted from integration over outlined regions of interest. In agreement with the MPWLD ranking, the fNTCP predictions reveal that incorporation of functional imaging in radiotherapy treatment planning is most beneficial for organs with a large volume effect and large focal areas of dysfunction. There is, however, no additional advantage in cases presenting with homogeneous function. Although presented for lung radiotherapy, this model is general. It can also be applied to positron emission tomography (PET)-CT or functional magnetic resonance imaging (fMRI)-CT registered data and extended to the functional description of tumour control probability.

The purpose of this work was to determine a segmentation protocol for the treatment of localized non-small-cell lung cancer (NSCLC) with intensity-modulated radiotherapy (IMRT) that is as effective as possible while practically simple and hence robust to known practical inaccuracies. This study focused on the stratification of continuous profiles into a discrete number of intensity levels. The selection of the segmentation parameters for the delivery of the fluence profiles using multiple static fields has been considered. Five-field equispaced IMRT treatment plans of five patients with NSCLC were selected. The study comprised nine treatment plans for each patient, starting from a conformal plan, optimizing it for IMRT and then segmenting it utilizing different numbers of segments in each case and optimizing for segment weights separately. A conformal plan, optimized for beam directions, collimator and wedge angles, was also used for comparison with the IMRT plans, so as to consider the best coplanar conformal case. A dose objective for the PTV and the organs-at-risk plus a constraint for the spinal cord were set for all inverse plans. All stages were compared with the aid of dose-volume histograms, dose distributions at the plane of the isocenter, intensity maps for key beams and plots of PTV homogeneity and overall conformality versus complexity. The unsegmented IMRT plans gave the best results but cannot be realized in practice with an MLC. They were best approximated by plans that needed 106-167 segments to deliver, but did not deteriorate significantly when approximated by plans which required 26-40 segments in total. All segmented IMRT plans gave a better lung sparing than the conformal plans, indicating that the deterioration of IMRT plans following segmentation is not equivalent to that of unmodulated, conformal plans. However, optimized conformal plans have the potential to approach the lung sparing achieved by segmented IMRT plans. Among the IMRT situations examined, five-field treatment plans for the lung, utilizing a maximum of 40 segments in total, have proven to give a good approximation of the IMRT plans with continuous modulation.

A common unwanted difficulty in treatment planning, especially in non-coplanar radiotherapy set-ups, is the potential collision of the rotating gantry with the couch and/or the patient's body. A technique and computer program that detects these and signals avoidance of such beam directions is presented. The problem was approached using analytical geometry. The separate components within the treatment room have either been measured and modelled for an Elekta linear accelerator, or read out from a Pinnacle3 treatment planning system and are represented as an integer grid of points in three-dimensional (3D) space. The module is attached to the treatment planning system and can provide rejection or acceptance of unwanted beam directions in a plan. In contrast to previous work that has only used patient models, each individual patient's outlines are considered here in their actual treatment position inclusive of any immobilization device. The extremities of the patient superiorly and inferiorly to the scanned region are simulated by an expanded version of the RANDO phantom. In this way,'potential' collisions can be detected in addition to the certain ones. Patient position is not a limiting factor for the accuracy of the collision detection anymore, as each set-up is always created around the isocentre. Maps of allowed and forbidden zones within the treatment suite have been created by running the code for all possible gantry and couch angles for three commonly arising cases: a head and neck plan utilizing a small stereotactic collimator, a prostate plan with multileaf collimators and an abdominal plan with the lead tray attached. In the last case, the 3D map permitted significantly fewer set-up combinations. Good agreement between prediction and experiment confirmed the capability of the program and introduces a promising add-on for treatment planning.

In most healthy people morning awakening is associated with a burst of cortisol secretion: the cortisol awakening response (CAR). It is argued that the CAR is subject to a range physiological regulatory influences that facilitate this rapid increase in cortisol secretion. Evidence is presented for reduced adrenal sensitivity to rising levels of ACTH in the pre-awakening period, mediated by an extra-pituitary pathway to the adrenal from the suprachiasmatic nucleus (SCN). A role for the hippocampus in this pre-awakening regulation of cortisol secretion is considered. Attainment of consciousness is associated with 'flip flop' switching of regional brain activation, which, it is argued, initiates a combination of processes: 1) activation of the hypothalamic adrenal (HPA) axis; 2) release of pre-awakening reduced adrenal sensitivity to ACTH; 3) increased post awakening adrenal sensitivity to ACTH in response to light, mediated by a SCN extra-pituitary pathway. An association between the CAR and the ending of sleep inertia is discussed.

Advanced radiation techniques such as intensity-modulated radiotherapy (IMRT) for complex geometries in which targets are close to organs at risk have been introduced in radiation therapy, creating a need for procedures that allow easy three-dimensional (3-D) measurement of dose for verification purposes. Polymer gels that change their material properties when irradiated have been suggested for such use. For example, the change in their magnetic properties has been thoroughly investigated with magnetic resonance imaging (MRI). Also, we have previously shown that the mechanical stiffness, i.e., Young's modulus, of these gels changes with dose. This finding prompted us to assess whether we can image a radiation-induced stiffness distribution with quantitative ultrasound elastography and whether the stiffness distribution is correlated with the dose distribution. A methacrylic-acid-based gel was loaded with scatterers to create an ultrasound echoic signal. It was irradiated to create a rod-like region of increased stiffness with a 10 x 10 mm(2) cross-section. The gel block was compressed in a frame that restricted the movement of the gel to planes orthogonal to the long axis of the irradiated region and ultrasonic echo data were acquired in the central plane during compression. This simplified irradiation pattern and experimental set-up were designed to approximate plane-strain conditions and was chosen for proof of concept. The movement of the gel was tracked from ultrasound images of a different compressional state using cross-correlation, enabling a displacement map to be created. The shear modulus was reconstructed using an inverse algorithm. The role of the magnitude of the regularization parameter in the inverse problem and the boundary conditions in influencing the spatial distribution of stiffness and, thus, final dose contrast was investigated through parametric studies. These parameters were adjusted using prior knowledge about the stiffness in parts of the material, e.g., the background was not irradiated and therefore its stiffness was homogeneous. It was observed that a suitable choice for these reconstruction parameters was essential for a quantitative application of stiffness measurement such as dosimetry. The dose contrast and distribution found with the optimal parameters were close to those obtained with MRI. Initial results reported in this article are encouraging and indicate that with ongoing refinement of ultrasound elastography techniques and accompanying inverse algorithms, this approach could play an important role in gel dosimetry.(jeff.bamber@icr.ac.uk).

Several methods can be used to achieve multi-criteria optimization of radiation therapy treatment planning, which strive for Pareto-optimality. The property of the solution being Pareto optimal is desired, because it guarantees that no criteria can be improved without deteriorating another criteria. The most widely used methods are the weighted-sum method, in which the different treatment objectives are weighted, and constrained optimization methods, in which treatment goals are set and the algorithm has to find the best plan fulfilling these goals. The constrained method used in this paper, the 2pc (2-phase -constraint) method is based on the -constraint method, which generates Pareto-optimal solutions. Both approaches are uniquely related to each other. In this paper, we will show that it is possible to switch from the constrained method to the weighted-sum method by using the Lagrange multipliers from the constrained optimization problem, and vice versa by setting the appropriate constraints. In general, the theory presented in this paper can be useful in cases where a new situation is slightly different from the original situation, e.g. in online treatment planning, with deformations of the volumes of interest, or in automated treatment planning, where changes to the automated plan have to be made. An example of the latter is given where the planner is not satisfied with the result from the constrained method and wishes to decrease the dose in a structure. By using the Lagrange multipliers, a weighted-sum optimization problem is constructed, which generates a Pareto-optimal solution in the neighbourhood of the original plan, but fulfills the new treatment objectives.

Dose-rate-regulated tracking (DRRT) is a novel tumor-tracking technique based on a preprogrammed multileaf-collimator (MLC) sequence and dose-rate modulation. We have performed a parametric study on how limitations of the DRRT system and breathing irregularities affect the tracking error and the duty cycle of DRRT. The time delay and the allowed dose-rate increment (continuous-, discrete-increment or beam switching) were used as two parameters for the DRRT system limitation. The breathing irregularity was quantified in terms of three variables, namely, breathing period variation, variation of peak-to-peak amplitude and baseline drift. DRRT treatments were simulated using 2126 breathing cycles obtained from 24 lung-cancer patients. Tracking errors and duty cycles from all 24 patients were combined to evaluate their dependence on each parameter or variable. The tracking error and the duty cycle show a modest difference among the three dose-rate-increment cases. Time delay, breathing peak-to-peak variation and baseline drift are the main factors affecting tracking error. The duty cycle is affected mostly by the allowed dose-rate increment, peak-to-peak variation and baseline drift.

BACKGROUND. Respiration-induced tumor motion compensation using a treatment couch requires moving the patient at non-trivial speeds. The purpose of this work was to investigate motion sickness and stability of the patient's external surface due to a moving couch with respiration-comparable velocities and accelerations. MATERIAL AND METHODS. A couch was designed to move with a peak-peak displacement of 5 cm and 1 cm in the S-I and A-P directions, respectively, and a period of 3.6 s. Fifty patients completed a 16-question motion sickness assessment questionnaire (MSAQ) prior to, during, and after the study. Seven optical reflectors affixed to the abdomen of each patient were monitored by infrared cameras. The relationship between reflector positions under stationary and moving conditions was evaluated to assess the stability of the patient's external surface. RESULTS AND DISCUSSION. Among the 4800 responses, 95% were 1 (no discomfort) of 9, and there were no scores of 6 or higher. Mild discomfort (scores of 4-5) was similar during couch motion and before couch motion (p = 0.39). Mild discomfort was less common after couch motion (p = 0.039) than before or during couch movement. There was a near 1:1 correspondence between marker-pair regression coefficients and phase offset values during couch-stationary and couch-moving conditions. Our results show that patients do not suffer motion sickness or external surface instability on a moving couch.

Recent work in the area of thoracic treatment planning has been focused on trying to explicitly incorporate patient-specific organ motion in the calculation of dose. Four-dimensional (4D) dose calculation algorithms have been developed and incorporated in a research version of a commercial treatment planning system (Pinnacle3, Philips Medical Systems, Milpitas, CA). Before these 4D dose calculations can be used clinically, it is necessary to verify their accuracy with measurements. The primary purpose of this study therefore was to evaluate and validate the accuracy of a 4D dose calculation algorithm with phantom measurements. A secondary objective was to determine whether the performance of the 4D dose calculation algorithm varied between different motion patterns and treatment plans. Measurements were made using two phantoms: A rigid moving phantom and a deformable phantom. The rigid moving phantom consisted of an anthropomorphic thoracic phantom that rested on a programmable motion platform. The deformable phantom used the same anthropomorphic thoracic phantom with a deformable insert for one of the lungs. Two motion patterns were investigated for each phantom: A sinusoidal motion pattern and an irregular motion pattern extracted from a patient breathing profile. A single-beam plan, a multiple-beam plan, and an intensity-modulated radiation therapy plan were created. Doses were calculated in the treatment planning system using the 4D dose calculation algorithm. Then each plan was delivered to the phantoms and delivered doses were measured using thermoluminescent dosimeters (TLDs) and film. The measured doses were compared to the 4D-calculated doses using a measured-to-calculated TLD ratio and a gamma analysis. A relevant passing criteria (3% for the TLD and 5%/3 mm for the gamma metric) was applied to determine if the 4D dose calculations were accurate to within clinical standards. All the TLD measurements in both phantoms satisfied the passing criteria. Furthermore, 42 of the 48 evaluated films fulfilled the passing criteria. All films that did not pass the criteria were from the rigid phantom moving with irregular motion. The author concluded that if patient breathing is reproducible, the 4D dose calculations are accurate to within clinically acceptable standards. Furthermore, they found no statistically significant differences in the performance of the 4D dose calculation algorithm between treatment plans.

PURPOSE: To assess the effect of audio coaching on the time-dependent behavior of the correlation between abdominal motion and lung tumor motion and the corresponding lung tumor position mismatches. METHODS AND MATERIALS: Six patients who had a lung tumor with a motion range >8 mm were enrolled in the present study. Breathing-synchronized fluoroscopy was performed initially without audio coaching, followed by fluoroscopy with recorded audio coaching for multiple days. Two different measurements, anteroposterior abdominal displacement using the real-time positioning management system and superoinferior (SI) lung tumor motion by X-ray fluoroscopy, were performed simultaneously. Their sequential images were recorded using one display system. The lung tumor position was automatically detected with a template matching technique. The relationship between the abdominal and lung tumor motion was analyzed with and without audio coaching. RESULTS: The mean SI tumor displacement was 10.4 mm without audio coaching and increased to 23.0 mm with audio coaching (p <.01). The correlation coefficients ranged from 0.89 to 0.97 with free breathing. Applying audio coaching, the correlation coefficients improved significantly (range, 0.93-0.99; p <.01), and the SI lung tumor position mismatches became larger in 75% of all sessions. CONCLUSION: Audio coaching served to increase the degree of correlation and make it more reproducible. In addition, the phase shifts between tumor motion and abdominal displacement were improved; however, all patients breathed more deeply, and the SI lung tumor position mismatches became slightly larger with audio coaching than without audio coaching.

Intra-fraction tumor tracking methods can improve radiation delivery during radiotherapy sessions. Image acquisition for tumor tracking and subsequent adjustment of the treatment beam with gating or beam tracking introduces time latency and necessitates predicting the future position of the tumor. This study evaluates the use of multi-dimensional linear adaptive filters and support vector regression to predict the motion of lung tumors tracked at 30 Hz. We expand on the prior work of other groups who have looked at adaptive filters by using a general framework of a multiple-input single-output (MISO) adaptive system that uses multiple correlated signals to predict the motion of a tumor. We compare the performance of these two novel methods to conventional methods like linear regression and single-input, single-output adaptive filters. At 400 ms latency the average root-mean-square-errors (RMSEs) for the 14 treatment sessions studied using no prediction, linear regression, single-output adaptive filter, MISO and support vector regression are 2.58, 1.60, 1.58, 1.71 and 1.26 mm, respectively. At 1 s, the RMSEs are 4.40, 2.61, 3.34, 2.66 and 1.93 mm, respectively. We find that support vector regression most accurately predicts the future tumor position of the methods studied and can provide a RMSE of less than 2 mm at 1 s latency. Also, a multi-dimensional adaptive filter framework provides improved performance over single-dimension adaptive filters. Work is underway to combine these two frameworks to improve performance.

Treatment delivery with active beam scanning in proton radiation therapy introduces the problem of interplay effects when pencil beam motion occurs on a similar time scale as intra-fractional tumor motion. In situations where fractionation may not provide enough repetition to blur the effects of interplay, repeated delivery or 'repainting' of each field several times within a fraction has been suggested. The purpose of this work was to investigate the effectiveness of different repainting strategies in proton beam scanning. To assess the dosimetric impact of interplay effects, we performed a series of simulations considering the following parameters: tumor motion amplitude, breathing period, asymmetry in the motion trajectory for the target and time required to change the beam energy for the delivery system. Several repainting strategies were compared in terms of potential vulnerability to a dose delivery error. Breathing motion perpendicular to the beam direction (representing superior-inferior type tumor motion in patients) was considered and modeled as an asymmetric sine function with a peak-to-peak amplitude of between 10 and 30 mm. The results show that motion effects cause a narrowing of the high-dose profile and widening of the penumbra. The 90% isodose area was reduced significantly when considering a large motion amplitude of 3 cm. The broadening of the penumbra appears to depend only on the amplitude of tumor motion (assuming harmonic motion). The delivered dose exhibits a shift of 10-15% of the tumor amplitude (or 1-5 mm) in the caudal direction due to breathing asymmetry observed for both sin(4)(x) and sin(6)(x) motion. Of the five repainting techniques studied, so-called 'breath sampling' turned out to be most effective in reducing dose errors with a minimal increase in treatment time. In this method, each energy level is repainted at several evenly spaced times within one breathing period. To keep dose delivery errors below 5% while minimizing treatment time, it is recommended that breath sampling repainting be employed using 5-10 paintings per field for an assumed tumor volume of 8.5 x 8.5 x 10 cm(3). For smaller tumor volumes more repaintings will be required, while for larger volumes five repaintings should be sufficient to achieve the required dose accuracy.

An analytical approach to predict respiratory diaphragm motion should have advantages over a correlation-based method, which cannot adapt to breathing pattern changes without re-calibration for a changing correlation and/or linear coefficient. To quantitatively calculate the diaphragm motion, a new expandable 'piston' respiratory (EPR) model was proposed and tested using 4DCT torso images of 14 patients. The EPR model allows two orthogonal lung motions (with a few volumetric constraints):(1) the lungs expand (DeltaV(EXP)) with the same anterior height variation as the thoracic surface, and (2) the lungs extend (DeltaV(EXT)) with the same inferior distance as the volumetrically equivalent 'piston' diaphragm. A volume conservation rule (VCR) established previously (Li et al 2009 Phys. Med. Biol. 54 1963-78) was applied to link the external torso volume change (TVC) to internal lung volume change (LVC) via lung air volume change (AVC). As the diaphragm moves inferiorly, the vacant space above the diaphragm inside the rib cage should be filled by lung tissue with a volume equal to DeltaV(EXT)(=LVC-DeltaV(EXP)), while the volume of non-lung tissues in the thoracic cavity should conserve. It was found that DeltaV(EXP) accounted for 3-24% of the LVC in these patients. The volumetric shape of the rib cage, characterized by the variation of cavity volume per slice over the piston motion range, deviated from a hollow cylinder by -1.1% to 6.0%, and correction was made iteratively if the variation is >3%. The predictions based on the LVC and TVC (with a conversion factor) were compared with measured diaphragm displacements (averaged from six pivot points), showing excellent agreements (0.2 +/- 0.7 mm and 0.2 +/- 1.2 mm, respectively), which are within clinically acceptable tolerance. Assuming motion synchronization between the piston and points of interest along the diaphragm, point motion was estimated but at higher uncertainty ( approximately 10%+/- 4%). This analytical approach provides a patient-independent technique to calculate the patient-specific diaphragm motion, using the anatomical and respiratory volumetric constraints.