WO2010083415A1 - Methods for tracking motion of internal organs and methods for radiation therapy using tracking methods - Google Patents

Abstract

The present invention relates to new methods for (1) predicting the dynamic tidal volume of a patient and (2) predicting the motion of the diaphragm and points of interest near the diaphragm by monitoring the external volume change of the patient's torso, thereby improving time-resolved computed tomography (4DCT) and motion- compensated radiation therapy (4DRT).

Description

METHODS FOR TRACKING MOTION OF INTERNAL ORGANS AND METHODS FOR RADIATION THERAPY USING SUCH TRACKING METHODS

This application claims the benefit of U.S. Provisional Application Serial No. 61/145,487 filed January 16, 2009, the teachings/contents of which are incorporated herein by reference in their entirety.

FIELD OF INVENTION

The present invention relates to methods for time-resolved computed tomography (4DCT), more particularly to methods for tracking internal organ motion, and yet more particularly to a motion-compensated radiation therapy (4DRT) using such methods for tracking internal organ motion. The present invention also relates to apparatuses for radiation therapy embodying such methods.

BACKGROUND OF THE INVENTION

Four-dimensional image-guided radiation therapy (4D IGRT or 4DRT) is an emerging field of clinical research that deals with the motion, deformation and change of a tumor (i.e., the treatment target) and surrounding normal tissues during the course of radiation therapy (Jaffray, D. et al., Expert Rev. Anticancer Ther. 7(l):89-103 (2007), Li, G. et al., Tech. Cancer Res. Treat. 7(1):67-81 (2008)). The ultimate objective is to spare the maximum volume of normal tissue, especially within critical structures, as well as to permit the escalation of the radiation dose delivered to the target; thereby improving the therapeutic ratio.

Such clinical gains, however, often come at the expense of additional radiation dose from those imaging studies required to localize and track the moving target. This can amount to as much as 3-8 cGy for a kilovoltage or megavoltage cone-beam CT (kV CBCT or MV CBCT) (Islam, M. K. et al., Med. Phys. 33(6): 1573-1582 (2006); Morin, O. et al., Med. Phys. 34(5):1819 (2007)) for IGRT patient setup prior to treatment. 4DCT imaging acquires images for multiple respiratory stages (Vedam, S. Phys. Med. Biol. 48:45-62 (2003); Low, D. A. et al., Med. Phys. 30(6): 1254-1263 (2003)) and generally requires approximately 10 times more radiation dose (Li, T. et al., Med. Phys. 32(12):3650-3660 (2005)) than conventional CT studies. Multiple imaging studies

(continuous or frequent) are often required for IGRT tumor motion tracking or gating during treatment (Shirato, H. et al., Int. J. Radiat. Oncol. Biol. Phys. 48(2):435-442 (2000); Schwelkard, A. et al., Med. Phys. 31(10):2738-2741 (2004)). Therefore, a significant dose will be delivered to the normal tissues within the field of view during imaging.

External respiratory surrogates have been studied and applied in radiation therapy, serving as correlative indicators for retrospective reconstruction of four- dimensional computed tomography (4DCT) (Ford, E C et al, Med. Phys. 30, 88-97 (2003); Vedam, S. et al, Phys. Med. Biol. 48, 45-62 (2003); Low, D. A. et al, Med. Phys. 30, 1254-1263 (2003); Keall, P. et al, Phys. Med. Biol. 49, 2053-2067 (2004);

Rietzel, E. et al, Med. Phys. 32, 874-889 (2005)), as well as for respiratory gating or motion tracking during 4D radiation therapy (4DRT) (e.g., Shirato, H. et al, Int. J. Radiat. Oncol. Biol. Phys. 48, 435-442 (2000); Ionascu, D. et al, Med. Phys. 34, 3893- 3903 (2007); Li, G. et al, Tech. Cancer Res. Treat. 1, 67-81 (2008)). They provide an attractive alternative to x-ray based imaging by minimizing the radiation dose from imaging to patients.

The foundation for such a working surrogate is the establishment of a correlation between the deformable motions of the external body and internal organs during respiration. Three external parameters have so far been utilized to establish such a clinically relevant correlation. These external parameters are: (1) the height variation of one or more fiducials on a patient's upper abdomen or lower thorax; (2) the tension variation of a bellows around the abdomen (due to circumference change); and (3) the dynamic airflow (volume) into and out of the lungs. These surrogates are currently employed in the clinic to varying extents depending upon their accuracy, simplicity and convenience. For quiet respiration, external fiducial markers have been used as surrogates for internal organ motion by establishing an external-internal correlation. An optical tracking system using a reflector placed on a patient' s upper abdomen or lower thorax has been used to predict organ motion due to diaphragmatic changes (Vedam, S. S. et al., Med. Phys. 30(4):505-513 (2003)). The Real-time Position Management™ (RPM) system (Varian Medical Systems, Inc., Palo Alto, CA) has been widely used for respiratory motion tracking or gating in the clinic (Jaffray, D. et al., Expert Rev. Anticancer ther. 7(l):89-103 (2007); Chi, P-C. M. et al., Med. Phys. 33(9):3116-3123 (2006)). In the presence of breathing irregularity, the correlation between respiratory phase and amplitude can be reduced dramatically, resulting in inadequate phase-based

4DCT reconstructions as high as 30-40% (Rietzel, E. and Chen, G. T. Y., Med. Phys. 32, 874-889 (2006); Lu et al, Med. Phys. 32, 2351-2357 (2005); Mutaf et al, Med. Phys. 34, 1615-1622 (2007)) and correlation coefficients as low as 0.39 when used for respiratory gated radiotherapy (Korreman et al., Acta Oncol. 45, 935-942 (2006); Ionascu et al, Med. Phys. 34, 3893-3903 (2007)). A linear relationship between lung air content and tidal volume measured with spirometry has been studied (Lu, W. et al., Med. Phys. 32(4):890-901 (2005)), in an attempt to use abdominal height as an external indicator for monitoring respiration (Lu, W. et al., Med. Phys. 32(7):2351-2357 (2005)).

The external-internal correlation and prediction of target position have been studied using implanted fiducial markers in both lung and abdominal cancer patients: in the former, the mismatch is usually less than 5 mm (Ionascu, D. et al., Med. Phys. 34(10):3893-3903 (2007)) while in the latter a relatively large mismatch may occur due to the non-cyclical nature of abdominal (digestive) motion (Gierga, D. P. et al., Int. J. Radiat. Oncol. Biol. Phys. 61(5):1551-1558 (2005)). The correlation-based target motion prediction requires a patient-based calibration to determine the patient-specific linear coefficient, since a high correlation indicates a synchronization of the external and internal motions but not their motion amplitudes. In addition, phase-shifts between the two motions have been observed in the fiducial-based surrogates (Hoisak, J. D. P et al., Int. J. Radiat. Oncol. Biol. Phys. 60:1298-1306 (2004); Korreman, S. et al., Acta Oncol. 45:935-942 (2006)). The quality of correlation may also depend upon the location of marker placement. Multiple external markers have been employed to enhance optical tracking systems, but it has been demonstrated that complexity also is introduced due to large variations among the markers, yielding marginal improvements (Yan, H. et al., Med. Phys. 33(11):4073-4084 (2006); Baroni, G. et al., /. Radiat. Res. 48 Suppl. A61-A74

(2007)).

It thus would be desirable to provide new devices, apparatuses and external- internal prediction methods for tracking organ or target motion. It would be particularly desirable to provide such devices, apparatuses and methods that would provide such motion tracking and that exhibits quantitative, reliable predictability of such motion.

Such methods preferably would minimize the need for users requiring more skill as compared to the skill of users utilizing conventional techniques.

SUMMARY OF THE INVENTION The present invention embodies two aspects or embodiments that improve time- resolved computed tomography (4DCT) and motion-compensated radiation therapy (4DRT). The first aspect/embodiment of the present invention relates to a novel method for predicting the dynamic tidal volume of a patient by monitoring the external volume change of the patient's torso. A hypothesis of volume conservation within the torso during quiet respiration was validated using 4DCT and spirometry data of fourteen patients.

It has been discovered that the torso volume change equals the tidal volume change of the lungs throughout the respiratory cycle, with an uncertainty of <5% on average. The tidal volume therefore can be measured indirectly. Compared with conventional surrogates based on the thoracic/abdominal skin height, abdominal tension, or spirometer measurement, this volumetric approach is advantageous from several respects, including the quantitative predictability without location-dependency and phase- shift. This approach also establishes the foundation for implementing a volumetric surrogate, which provides a more reliable and accurate measure of respiratory motion for 4DCT imaging and 4DRT treatment. The second aspect/embodiment of the present invention involves a novel method for predicting the motion of the diaphragm and points of interest near the diaphragm, based on the external torso volume change. A new expandable "piston" respiratory (EPR) model is developed and used to translate the volumetric variation of the lungs into the diaphragm displacement. This model considers the volume changes from both lung expansion (posterior-anterior) and lung extension (superior- inferior). The former is calculated by assuming that the height variation of the lungs equals that of thoracic skin, while the latter is used to predict diaphragm position within the patient-specific rib cage (cylindrically or conically shaped). The predicted diaphragm displacement agrees with the measured within 2 mm, which is clinically acceptable. The prediction of points of interest near the diaphragm has 8 + 2 % uncertainty, potentially useful in predicting the target motion in 4DCT simulation and 4DRT delivery.

According to another aspect/embodiment of the present invention, such methods include a method for tracking the motion of an anatomical feature within a body segment. Such a method includes determining an initial position of the anatomical feature and an initial external parameter associated with the anatomical feature and which can be correlated to a corresponding internal parameter, and measuring the external parameter at a time subsequent to the initial determination. Such a method further includes using the measured external parameter acquired at the subsequent time and the determined initial position of the anatomical feature to predict a new location of the anatomical feature.

In further embodiments, such a method includes establishing a reliable correlation between the external parameter and the internal parameter and using the established correlation and the measured external parameter to determine another internal parameter that correlates to the measured external parameter. Also, said using the measured external parameter includes using the determined another internal parameter and the initial position to determine said new location of the anatomical feature.

In yet further embodiments, for such a tracking method, the external parameter is measured at each of a plurality of times subsequent to the initial determination and the new location of the anatomical feature is determined at each of the plurality of times. The new location is determined using a currently measured external parameter and the previously determined location of the anatomical feature.

In yet further embodiments, such a tracking method further includes, establishing a correlation between the external parameter and the internal parameter and using the established correlation and each currently measured external parameter to determine another internal parameter that correlates to said each currently measured external parameter. In such a method, said using the measured external parameter includes using the determined another currently determined internal parameter and the previously determined location of the anatomical feature to determine said new location of the anatomical feature.

In such methods, the anatomical feature is one of an organ of the body, healthy tissue of the body or unhealthy tissue within the body. In more particular embodiments, the unhealthy tissue is a tumor.

According to yet another aspect/embodiment of the present invention, such methods include a method for treating an anatomical feature within a body using radiotherapy. Such a treating method includes determining an initial position of the anatomical feature and an initial external parameter associated with the anatomical feature and which can be correlated to a corresponding internal parameter; measuring the external parameter at a time subsequent to the initial determination; and using the measured external parameter measured at the subsequent time and the determined initial position of the anatomical feature to determine a new location of the anatomical feature. Such a method also includes irradiating the anatomical feature with ionizing radiation so that the radiation is adjusted to compensate for movement of the anatomical feature.

In yet further embodiments, such a method further includes establishing a correlation between the external parameter and the internal parameter and using the established correlation and the measured external parameter to determine another internal parameter that correlates to the measured external parameter. In such a method said using the measured external parameter includes using the determined another internal parameter and the initial position to determine said new location of the anatomical feature. In yet further embodiments, in such a treating method the external parameter is measured at each of a plurality of times subsequent to the initial determination and the new location of the anatomical feature is determined at each of the plurality of times, where the new location is determined using a currently measured external parameter and the previously determined location of the anatomical feature. Also, in such a method said irradiating the anatomical feature with ionizing radiation includes adjusting the radiation to compensate for movement of the anatomical feature between each of the determined new locations.

In yet further embodiments, such a treating method further includes establishing a correlation between the external parameter and the internal parameter and using the established correlation and each currently measured external parameter to determine another internal parameter that correlates to said each currently measured external parameter. Also with such a method, said using the measured external parameter includes using the determined another currently determined internal parameter and the previously determined location of the anatomical feature to determine said new location of the anatomical feature.

In such methods, the anatomical feature is unhealthy tissue within the body such as tumor.

In yet further embodiments of such tracking and treating methods, such measuring includes using an imaging technique to image an exterior surface of the body segment so as to determine that external parameter. In such methods, the body segment is the torso of the body. In yet further embodiments of such tracking and treating methods, the external parameter is an external volume of the body segment and the internal parameter is an internal volume within the body segment, where changes in the internal volume cause a corresponding change in the external volume.

Also featured is a computer readable medium on which is stored a program for tracking movement of anatomical feature within the body. Such a program includes, instructions, criteria and/or code segments for (a) determining an initial position of the anatomical feature and an initial external parameter associated with the anatomical feature and which can be correlated to a corresponding internal parameter; (b) measuring the external parameter at a time subsequent to the initial determination; and (c) using the measured external parameter measured at the subsequent time and the determined initial position of the anatomical feature to determine a new location of the anatomical feature.

In yet further embodiments, such a program further includes, instructions, criteria and/or code segments for: (d) establishing a correlation between the external parameter and the internal parameter; and (e) using the established correlation and the measured external parameter to determine another internal parameter that correlates to the measured external parameter. In such methods said using the measured external parameter includes using the determined another internal parameter and the initial position to determine said new location of the anatomical feature.

Yet also featured is a computer readable medium on which is stored a program for tracking movement of anatomical feature within the body and treating the anatomical feature using radiotherapy. Such a program includes, instructions, criteria and/or code segments for: (a) determining an initial position of the anatomical feature and an initial external parameter associated with the anatomical feature and which can be correlated to a corresponding internal parameter; (b) measuring the external parameter at a time subsequent to the initial determination; (c) using the measured external parameter measured at the subsequent time and the determined initial position of the anatomical feature to determine a new location of the anatomical feature; and (d) controlling the irradiation of the anatomical feature with ionizing radiation so that the radiation is adjusted (e.g., periodically adjusted) to compensate for movement of the anatomical feature.

In yet further embodiments, such a program further includes, instructions, criteria and/or code segments for: (e) establishing a correlation between the external parameter and the internal parameter and (f) using the established correlation and the measured external parameter to determine another internal parameter that correlates to the measured external parameter. In such a program, said using the measured external parameter includes using the determined another internal parameter and the initial position to determine said new location of the anatomical feature. As noted in the Background, a number of techniques have been used in attempts to predict organ motion due to movement of the thoracic diaphragm (hereafter "diaphragm") to improve targeting of radiation therapy. Unfortunately, these techniques have limited success to provide the ability to predict organ motion with clinically acceptable accuracy and/or reliability. The methods of the present invention on the other hand permit predicting diaphragm displacement quantitatively with a clinically acceptable accuracy.

Other aspects and embodiments of the invention are discussed below/herinafter.

DEFINITIONS

The instant invention is most clearly understood with reference to the following definitions:

As used in the specification and claims, the singular form "a", "an" and "the" include plural references unless the context clearly dictates otherwise. As used herein, the term "comprising" or "including" is intended to mean that the compositions, methods, devices, apparatuses and systems include the recited elements, but do not exclude other elements. "Consisting essentially of", when used to define compositions, devices, apparatuses, systems, and methods, shall mean excluding other elements of any essential significance to the combination. Embodiments defined by each of these transition terms are within the scope of this invention.

The term patient shall be understood to include mammalians including human beings as well as other members of the animal kingdom.

USP shall be understood to mean U.S. Patent Number, namely a U.S. patent granted by the U.S. Patent and Trademark Office. A computer readable medium shall be understood to mean any article of manufacture that contains data that can be read by a computer or a carrier wave signal carrying data that can be read by a computer. Such computer readable media includes but is not limited to magnetic media, such as a floppy disk, a flexible disk, a hard disk, reel-to-reel tape, cartridge tape, cassette tape or cards; optical media such as CD-ROM, DVD and writeable CD/DVD; magneto-optical media in disc, tape or card form; paper media, such as punched cards and paper tape; or on carrier wave signal received through a network, wireless network or modem, including radio-frequency signals and infrared signals. IGRT shall be understood to mean image-guided radiation therapy.

4DRT shall be understood to mean image-guided, motion compensated radiation therapy.

BRIEF DESCRIPTION OF THE DRAWING For a fuller understanding of the nature and desired objects of the present invention, reference is made to the following detailed description taken in conjunction with the accompanying drawing figures wherein like reference character denote corresponding parts throughout the several views and wherein:

Fig. 1 is a high level flow diagram illustrating the method(s) of the present invention.

Fig. 2A is an illustrative view of a patient torso image with an array of five anatomical sites for characterizing the breathing pattern: (1) mid-point of sternum; (2) end-point of sternum; (3) mid-point between point 2 and biblical point; (4) biblical point; and (5) mid-point between point 4 and the pubic bone. Figs. 2B and C are various graphical views. The volumetric descriptor BPV is defined in Equation 8.

Figs. 3 A and B are graphical views of linear regression analyses for all data in 14 patients: Fig. 3A - internal lung air volume change (AVC) vs. external torso volume change (TVC) and Fig. 3B the spirometric tidal volume vs. the TVC. The slopes (α = 0.950 and 1.053) are slightly off unity, largely due to patient #9 who has a unusually large maximum tidal volume in the fitting scale.

Figs. 4A-D are graphical views of four typical examples of the external and internal volume changes (the TVC and the AVC), spirometric tidal volume, and lung density as functions of respiratory stage. The GI gas volume change (GVC) does not correlate with the respiratory stage, unlike the TVC, the AVC and the dynamic tidal volume. A slight phase shift (0.1-0.4 stages) is shown for the spirometric curve relative to others.

Figs. 5A-D are graphical views of four typical examples of comparison of the lung air volume change (AVC) with thoracic and abdominal heights, which differ from each other. Most thoracic curves possess a phase shift larger than 1 stage.

Figs. 6 A and B are illustrative views that demonstrate the similarity between thoracic skin height variation and anterior lung height variation. Torso and lung contours in full-exhalation (red) and full-inhalation (yellow) stage CTs of a patient in supine position. Fig. 6A, an axial view, also shows that lateral width variations of the lung and body are small. Fig. 6B, the sagittal view, illustrates the unevenness of diaphragm motion, as well as three points (1, 2 and 3) that are used for calculating an average diaphragm position and displacement.

Figs. 7A-C are illustrative views, demonstrating and describing the expandable piston respiratory (EPR) model. Figs. 7A-B, the piston (equivalent diaphragm) moves ~2 cm (green) in the superior- inferior (SI) direction. The volumetric shape of this section is critical for calculating the volume of the vacant space above the diaphragm. Fig. 7C illustrates the procedure for calculating the diaphragm displacement using the EPR model.

Figs. 8A-F are various illustrative views of two examples of cylindrical and conical rib cages and segmentation (green) of thoracic cavity inside the rib cages. The top row of images (Figs. 8A-C) show a cylindrical rib cage (patient #8) and the bottom row of images (Figs. 8D-F) show a conical rib cage (patient #9). The axial images are at the top of the diaphragm interfaced with the right or left lungs.

Figs. 9A-D are graphical views of four examples of the diaphragm motion trajectory measured from 4DCT and predicted using the TVC and the LVC. The prediction, based on the LVC, is superior to that based on the TVC, in most cases.

Figs. 10A-D are graphical views for two patients of two examples of correlation of cone-shape rib cage. After the correction, the predicted diaphragm motion is improved, in comparison with the measured curve in both the LVC and the TVC methods.

Figs. 11A-B are residual error graphs between the prediction and the measurement for the LVC method (-0.2+1.2 mm) and the TVC (0.2+1.6 mm) method. The data of all stages of all patients are used in these two plots.

Fig. 12 is a tabulation of quantitative external and internal volumetric relationship and quantitative descriptors of breathing pattern. The maximum torso volume change (TVC) and lung air volume change (AVC) are in close agreement. The volume descriptor is defined as the ratio of maximum thoracic to torso volume change (tVC/TVC) ^Max, while the height descriptors are the maximum height variation at five anatomical sites, which are shown in Figs. 2A-C, and the height ratio (Hth_o/H_abd) ^Max-

Fig. 13 is a tabulation of linear regression and correlation coefficient analyses of external parameters vs. internal lung air volume change (AVC) obtained from the 4DCT images. The slopes are close to unity (α =1.027+0.061), and the intercepts are relatively small in comparison with the maximum AVC (-2.0%+3.7%). The torso volume change

(TVC), thoracic and abdominal heights are used against the AVC for calculating correlation coefficient, rχ_{; AVC}- The GI-gas volume change (GVC) apparently is independent of respiratory stages with relatively small variation (2.8%+1.9%).

Fig. 14 is a tabulation of correlation coefficient and linear regression analyses of spirometric tidal volume and the lung air volume change (AVC). The average correlation coefficient (r = 0.973+0.012 with p < 0.0001) and linear relationship (α = 1.030+0.092) provide a quantitative assessment on the agreement between the two sets of data. Experimental spirometry data for patients 4, 6 and 13 were not available for these analyses. Fig. 15 is a tabulation characterizing patient-specific, respiration-related features.

Characterization of patient-specific, respiration-related features. The breathing pattern is quantified using two ratios: the external ((TVC/TVC)Max) and the internal ((ΔVEXp/ΔVLungWx)- The stage-averaged conversion factor (<k>) is a constant across the patients. The rib cage shape at the equivalent "piston" position (0 mm) and its motion range (about 15 mm) is the region of interest. The volume variation ((V₁₅- Vo)/V_{7 5}) smaller than 3% is considered a cylindrical rib cage; three patients (#6, #9 and #11) have conically shaped rib cages (>3%), for which up to 30 mm motion range were evaluated, showing a linear volume increase. Equation 22 or 23 was used for calculating diaphragm displacement, depending on the shape.

Fig. 16 is a tabulation of a comparison of the predicted and measured diaphragm displacements in the respiratory cycle. The averaged difference over 12 stages, the standard deviation, and relative standard deviation are shown. Two methods of calculation were employed using the LVC in Equation 13 or using the TVC in Equation 15. The averaged conversion factor ( \*v = 1.11) was used (from Fig. 15). The averaged difference (<ΔZip -ΔZI_M>) from all stages (i = 1 to 12) and the standard deviation (σΔZp- ΔZm) show a close agreement between the predicted and the measured for both calculation methods.

Fig. 17 is a tabulation of a comparison of the predicted and measured displacements for four points at the diaphragm. The points are number 1 and 3 in the right and left side as shown in Fig. 6B, totally 56 points in 14 patients. The patient specific diaphragm motion curves are used to predict the motion of the four points using Equation 13. The stage-averaged difference (<dΔzp>), standard deviations (σ) and relative deviation (σ/Δz) between the predicted and the measured are shown. Three points (5%) have the discrepancy larger than 2 mm, and nine points (16%) have a standard deviation larger than 3. Overall, the relative error of the calculation is 6.8%+2.2%.

DESCRIPTION OF THE PREFERRED EMBODIMENT Referring now to the various figures of the drawing wherein like reference characters refer to like parts, there is shown in Fig. 1 a high level flow diagram/chart illustrating methods of the present invention for tracking movement of an anatomical feature within a body and treating such an anatomical feature, such as with ionizing radiation (e.g., x-ray/electron beam, proton beam, and heavy ion particle beams), while adjusting the therapy so as to compensate for such motion. Such a flow diagram/chart herein illustrates the structure of the logic of the different methodologies/inventions, which can be embodied in computer program software for execution on a computer, digital processor or microprocessor. Those skilled in the art will appreciate that the flow diagrams/charts illustrate the structures of the computer program code elements (e.g., instructions, criteria, and/or code segments), including logic circuits on an integrated circuit, that function according to the present inventions. As such, the present inventions are practiced in its essential embodiments by a machine component that renders the program code elements in a form that instructs a digital processing apparatus (e.g., computer) to perform a sequence of function step(s) corresponding to those shown in the flow diagrams/charts.

As set forth in more detail in the Examples described further herein, the studies underlying the present invention found that a highly correlated linear relationship exists during quiet breathing between the external torso volume change ("TVC") and the internal lung air volume change ("AVC"). It is called volume conservation rule (VCR). As a result, it is possible to predict internal anatomical change (volume) and motion during respiration through use of external volumetric surrogates. The lung volume compensation model (or the expandable piston respiratory (EPR) model) developed during the studies demonstrate a novel approach to monitor internal organ motion via external torso information in the quietly breathing patient, independent of the patient's breathing patterns. The prediction of internal motion can tolerate non-cyclical irregularities, since the periodical breathing is not required.

Previous attempts to correlate respiratory phase and height of upper abdomen (or lower thorax), used in such approaches as clinical respiratory motion gating devices, have been stymied due to the variety and complexity of the breathing motions, which cause deformation in the thorax as well as the abdomen. In addition, depending upon where the fiducial markers (or optical reflectors) are placed, a phase shift (delayed response) between external and internal motion may occur due to dynamic pressure imbalances within the lungs and trachea as well as deformation of the abdomen in response to the respiratory motion, limiting the reliability of such approaches. Thus, previous fiducial-point based motion monitoring systems have not provided for reliable, quantitative relationship between external and internal motions.

On the other hand, under quiet (or normal) respiratory conditions, the volumetric approach for motion tracking of the present invention produces a highly correlated, linear relationship between the TVC and the AVC. Torso volume conservation allows instant determination of internal anatomical change (volume) during respiration through observation of the external volumetric surrogate. Furthermore, based on the EPR model, the diaphragm displacement is predictable quantitatively with a clinically acceptable accuracy. Therefore, this volumetric study demonstrates a novel approach to monitor internal organ motion via external torso information independent of the patient's normal breathing patterns and non-cyclical irregularities.

Persons of skill in the art will recognize that lung expansion occurs in both the head to toe direction (cranial-caudal, or superior to inferior) and from sternum to spine (anterior to posterior), with the major movement being from superior to inferior as the diaphragm contracts and the thoracic cavity expands. The movement of the diaphragm during quiet breathing is typically about 1-3 cm.

The practitioner will recognize that the correlation noted in the studies refer to normal, or "quiet" breathing. As is well known, individuals can force themselves to inhale or exhale more deeply than normal. These voluntary actions engage more and different muscles than are engaged in normal respiration and place additional pressure on the internal organs. Forced breaths may therefore have a less precise correlation between external volume change and internal movement. Persons of skill in the art when preparing patients for radiation therapy are familiar with calming patients and asking them to breath normally during the procedure. Thus, such persons of skill when preparing patients for therapy in connection with the methods of the invention can educate the patients on the importance of normal, "quiet" breathing during the radiation session, and the 4DCT imaging session for 4D treatment simulation.

The processes for tracking movement of an anatomical feature or for treating such an anatomical feature begin with establishing a correlation between an external parameter and an internal parameter (Step 100) such that changes to the internal parameter can be determined using the correlation and a determined external parameter. In this way, one can reasonably predict the internal parameter with sufficient accuracy using the correlation and the comparatively easier determined external parameter.

In particular illustrative embodiments, the external parameter is the external volume of a body segment such as the torso of a body and the internal parameter is a volume within the body such a the volume formed by the respiratory system (e.g., lungs, etc.). As described herein, in an illustrative embodiment an internal-external correlation is established relating the external volume to the internal volume, whereby a determination of the internal volume can be made using a determination or measurement of the external volume. It should be recognized that it is well within the skill of those knowledgeable in the art to arrive at correlations between any number of external features or parameters of a body and a related internal feature of the body.

An advantageous effect of the present invention is that the internal-external correlation is a parameter that is not patient specific, whereas a number of conventional techniques require the development of patient specific input for the technique to be effective.

After the internal/external parameter correlation(s) have been established, the practitioner, such as a radiation oncologist, follows standard procedures to select the area to be irradiated and the treatment regimen. The patient is typically counseled on maintaining quiet breathing during treatment and positioned in a conventional manner

(the supine position) for administration of the radiation. Typically, the patient is positioned on a table adjacent to a linear accelerator and aligned using skin marks and in- room orthogonal and isocentric lasers. The cross-point of the three laser lines is the isocenter of the treatment gantry and table. More particularly, the patient is positioned in such way that the center of the tumor or anatomical feature is placed at the isocenter of the treatment system. A pair of orthogonal x-ray radiographs or a cone-beam CT (CBCT) is typically taken in an IGRT patient setup procedure to further align the patient and the machine as precisely as possible. Also, the patient is typically instructed not to move once positioned and sometimes immobilized to prevent voluntary movement causing deviation from the setup position.

After the internal/external parameter correlation(s) have been established, the practitioner initiates the tracking and/or treatment process according to the present invention thereby causing baseline information to be obtained (Step 110). Such baseline information as described further herein is obtained for purposes of determining an initial position of the anatomical feature and to establish internal and external parameters corresponding to the initial position. Such information is typically obtained using an imaging technique such as an x-ray imaging technique that can be used to image the internal volume of the body segment which provides a mechanism for determining the location of the anatomical feature and at the same time employing a technique for determining the related external parameter.

In an illustrative embodiment, the internal and external parameters are volume parameters. Thus, an appropriate technique is used to determine the volume of the body segment using externally acquired information. In more particular embodiments, any of a number of other imaging techniques are used which are adaptable for determining the volume of the body segment. In an illustrative embodiment, an imaging technique using reflected light is adapted for use in determining or measuring the volume of the body segment, an external volume, using externally obtained information of the body segment. In particular illustrative embodiments, the patient torso volume is calculated from surface images acquired using an optical camera system. Such optical camera systems have been reported useful in IGRT patient setup by aligning the surface image to the planning CT image or among the daily surface images (Djajaputra and Li, Med. Phys. 32(l):65-75 (2005) and Bert, C. et al., Int. J. Radiat. Oncol. Biol. Phys. 64(4): 1265- 1274 (2006)).

After the baseline information is acquired, the process continues with measuring or determining the external parameter at a time subsequent to acquiring the baseline information (Step 120). The external parameter is determined or measured using a technique such as that described above in connection with Step 110. After determining the external parameter, a determination is made using the internal-external correlation, of the corresponding internal parameter (Step 130). In illustrative embodiments, the external volume at the time is determined and using an appropriate internal-external correlation a corresponding internal volume is determined.

After determining the internal parameter or internal volume, a determination is made as to the new location of the anatomical feature (Step 140). The new location is determined using a previously determined position of the anatomical feature and the change(s), if any, between the previously determined internal parameter/volume and the currently determined internal parameter/volume. When determining the new location at the time following the acquisition of the baseline information, the previously determined position of the anatomical feature and the previously determined internal parameter/volume are those determined using the baseline information.

The methods of the present invention are particularly useful in radiation treatment such as radiation therapy of an organ or area in the thorax or abdomen which moves in relation to the position of the patient's diaphragm, more specifically, treatment of tumors near the diaphragm, which typically exhibit significant movement as the diaphragm moves during breathing. The methods are useful, for example, in connection with treatment of the lungs, liver and pancreas, and especially useful in connection with radiation treatment of the lower lung and upper liver.

Using the determined new location of the anatomical feature, the therapeutic technique is adjusted so as to compensate for the motion of the anatomical feature (Step

150). In particular embodiments, the therapeutic technique is a radiotherapy technique or radiation treatment. In such a radiation treatment and using the methods of the present invention, the emission of ionizing radiation is adjusted so as to compensate for the movement of the anatomical feature from the previously determine location/position to the currently determined location/position. This is particularly advantageous because it minimizes delivery of ionizing radiation to areas other than the anatomical feature and provides a mechanism for delivery of the ionizing radiation mainly to the anatomical feature.

After adjusting the therapy, a determination is made as to whether the process of tracking and/or delivering therapy is completed (Step 160). If therapy or tracking is to be continued (No, Step 160) then the process returns to Step 120 and another determination/measurement is made of the external parameter at another time. Thereafter the processes of Steps 130-160 are repeated until it is determined that the process of tracking and/or delivering therapy is completed (Yes, Step 160). When it is determined that the process is complete, the method process is stopped or ended (Step

170). In the case where the process is limited to tracking motion, step 150 is eliminated and the process goes from step 140 to step 160.

In the above described methods, an accelerator is operated by generating a high frequency pulse train of ionizing radiation that is directed to the patient area or anatomical feature being treated. The overall quantity of radiation administered to the patent is determined by an ionization chamber placed within the beam path before patient in real-time. The internal ion chamber is calibrated against an external standard, which is traceable back to the National Institute of Standards and Technology (NIST). As is well known in the art, during a treatment session, radiation fractions are usually administered along a series of paths to maximize radiation at the target while reducing the radiation exposure to normal tissue. In conventional techniques, the volume being irradiated is typically enlarged to account for setup uncertainty, as well as patient and organ movement both during the actual administration of radiation ("intra-fraction") and between each administration in a session ("inter-fraction"). In one conventional practice, respiratory-gated radiation therapy (RGRT), real time measurements of the patient's breathing are taken by measuring the height of the patient's abdomen, typically by reflecting infrared light off a reflector positioned on the patient's upper- abdomen. This permits the practitioner to determine when the patient inhales and when the patient exhales. Usually, the patient is irradiated during multi- phases around the full exhalation phase. This approach has several disadvantages, such as limiting radiation administration to less than 40% of the entire breath cycle, the presence of significant motion, and the fact that irregularities in the patient's breathing may cause the correlation to the radiation to be inaccurate.

The methods of the present invention on the other hand provide improved targeting of radiation administration, permits radiating the patient at any point during the breathing cycle, and significantly reduces the problem posed due to irregularities in the patient's breathing pattern. As a result of such improved targeting as well as compensation for movement of the anatomical feature, other areas proximal the target area are not irradiated to the extent as with conventional techniques thereby also reducing toxicity to surrounding tissues.

In the methods of the present invention, standard procedures are typically followed in counseling the patient on maintaining quiet breathing during treatment and in positioning the patient for radiation administration. As in conventional treatment, the patient is positioned on a table adjacent to the radiation source, such as a linear accelerator, and is aligned so that the radiation source will be aimed precisely on the area to be treated (the "target"), with the patient instructed not to move once positioned. For ease of reference, the radiation produced by the radiation source will be referred to as the "radiation beam".

The methods of the present invention are further exemplified from the following discussion, which is directed to an application where the internal and external parameters are appropriate volumes of a body segment for the patient. In such methods, once the patient is determined to be breathing normally (that is, to be engaged in quiet breathing), the patient's maximum torso volume or minimum torso volume is determined. In more particular embodiments, both of these volumes are determined and such patient torso volumes can be calculated using any method known in the art or hereinafter developed.

As indicated above, in particular illustrative embodiments, the patient torso volume or the change to such a volume is determined from surface images acquired using an optical camera system.

Once the patient's torso volume is determined, it is assigned to the patient's breathing cycle, with maximum volume correlating to peak inhalation, and minimum volume correlated to peak exhalation. The torso volume increase or change (TVC) from the minimum volume reflects the respiratory tidal volume (AVC). A reference CT image at peak exhalation is used to determine the absolute position of the diaphragm (an anatomical feature) as a reference for calculating its displacements, based on the EPR model and volume conservation rule (VCR). For calculating the motion of points of interest, methods of the present invention preferably require a second reference CT image at peak inhalation in order to determine the motion range of the points. Such reference CT images at a particular respiratory stage can be acquired using 4DCT imaging, respiratory-gated CT imaging, or breath-held CT imaging. These images are often used as the planning CT images for motion reconstruction.

Using the methods of the present invention, the patient's diaphragm movement is correlated to the patient's external torso volume. That is, as the patient breathes in from maximum exhalation to maximum inhalation, the torso volume will increase as the diaphragm contracts. For purposes of administering radiation, the excursion of the target (i.e., the target movement) is considered to move in sync with the contraction of the diaphragm. Further, the movement of the diaphragm is considered to be around 1-3 cm in the head-to-toe (superior to inferior) direction and approximately 0.5 cm in the sternum to spine. The studies underlying the present invention show a one-to-one linear relationship between a patient's external torso volume and a patient's internal volume. For example, if the patient's external torso volume is measured in real-time, the position of the target can be calculated based on the predicted displacement from the reference position. In other words, the movement of the target due to the patient's breathing at any point in the breathing cycle can be accounted for by simply determining the patient's external torso volume. The radiation beam can then be adjusted to keep it focused on the target area. Thus, the methods of the invention provide a straightforward way to adjust radiation treatment to account for changes in the position of a target due to a patient's breathing.

Example 1 This Example sets forth hypotheses and materials and methods used in volume conservation studies underlying the present invention. Volume Conservation Hypothesis

Tissues in the human body are composed with materials in solid, liquid and gaseous phases. Solids (bone and soft tissue) and liquids (blood and other bodily fluids) do not change in volume with physiological pressure variations. Gases can be contained in a closed system (such as the digestive tract) or an open system (such as the lung). The airflow (dynamic tidal volume) changes lung volume and density during respiration. However, the amount of air in the expiratory reserve and the residual volumes (hereafter, "reserve air volume") remains unchanged through a dynamic equilibrium, which can be regarded as a pseudo-closed system. Therefore, the gas volume in the closed and the pseudo-closed system should obey the ideal gas law:

PxV = H - R - T (1) where P, V, n, R, and T represent pressure, volume, the mole of the gas molecules, ideal gas constant, and temperature (in ⁰K), respectively.

Under quiet respiration, the lung pressure varies from -2 to +3 mmHg (Applegate, E. The anatomy and physiology learning system, 2nd Ed., W. B. Saunders

Co. (Philadelphia, Pennsylvania), (2000)), or <1% of the ambient atmosphere pressure. The gastric pressure variation during the respiratory cycle for a patient in the supine position is normally between 10 and 15 CmH₂O (Agostoni, E. et al., /. Appl. Physiol, 15(6): 1087-1092 (I960)), or 7.5 and 11 mmHg, < 2% of the ambient pressure. Hence, the volume change of the air "sealed" in these closed systems should be within 3%.

Therefore, a clinically relevant hypothesis of torso volume conservation was proposed as TVC = AVC, linking the lung AVC (ΔV_Air) to the external TVC (ΔV_Tθrso), which covers motions in both thorax and abdomen (Konno, K. et al., /. Appl. Physiol. 22(3):407-422 (1966)).

Patient 4DCT Images

4DCT torso images were acquired for 14 patients under quiet breathing conditions using a 16-slice CT scanner (Philips Medical Systems, Bothell, WA) operated under a special research protocol, which was described previously (Lu, W. et al., Med. Phys. 33(8):29642974 (2006)). In brief, twenty-five scans in cine mode were acquired at each abutting couch position (24 mm span) for 18 seconds, and the entire torso was scanned. Two respiratory surrogates, a bellows and a spirometer, were used to enhance the fidelity of respiratory measurement and the reliability of retrospective binning. The bellows (pressure transducer) was placed around each patient's upper abdomen for monitoring the expansion/contraction pressure change during respiration. The spirometer was used to measure the amount of air flowing into and out of the patient's lungs.

Both bellows displacement and spirometry were used as external surrogates for monitoring respiratory motion by determining the pseudo tidal volume using the dual surrogates (Lu, W. et al, Med. Phys. 33, 2964-2974 (2006)). Based on the amplitude of the tidal volume (and airflow direction) within the respiratory cycle, all image projections were sorted into 12 stage bins for retrospective 4D image reconstruction. Each of the 12- stage 4DCT images contained 464, 1.5mm thick slices. The pixel size in the 512x512 slices is 0.98x0.98 mm². The actual torso image volume used in this study was selected anatomically, from the clavicles to the pubic arch, including both the thoracic and the abdominal cavities.

Automatic Organ Segmentation and Quantitative Correlation Analysis

Two automatic threshold-based segmentation tools were applied using an edge- tracing algorithm and a voxel-counting algorithm. External contours were automatically generated across the entire torso using the edge-tracing algorithm: each slice contour was defined by up to 800 points, after 2-time smoothing with an erosion-dilation (size conservative) filter. Multiple thresholds were tested (-250 to -400 Hounsfield Units, or HU) for defining tissue/air and tissue/lung interfaces, and -350 HU was used in this study. Within the body contour, tissue volumes and densities could be calculated using the voxel-counting algorithm. Depending upon the threshold, body volume (all CT# inside body contour) and lung volume (CT# < -350 HU inside the thoracic body contours excluding GI gas) were obtained. This strategy does not need lung segmentation, reducing workload as well as gaining accuracy and reproducibility. The GI gas volume was calculated by subtracting the lung volume from the total air volume in the torso. The volume changes were calculated with reference to the full exhalation stage. Lung Air Volume Change (AVC) Based on Lung Density Correction

It is well known that lung density changes during respiration due to air dilution in the alveoli. Therefore, the lung volume change (LVC, AVtu_ng) does not fully reflect the AVC (ΔV_AJ>). The fraction of air content can be calculated as (Lu, W. et al., Med. Phys. 32(7):2351-2357 (2005)):

where CT _Lung , CT _Ti_ssue and CT _{Air are} the CT# of lung voxels and average CT# for tissue and air. Assuming that air density is negligible and the tidal volume is much smaller than the lung volume, the AVC at stage i can be calculated as:

AV Air = J f Air - V Lung - J f A⁰ir - V L⁰ung i \ (3)

- — ^ Ky Lung - [ VC^ ¹V Lung - V ^y Lung - C ^ ¹TL⁰uHg - V ^v L⁰ung I

where ΔV_A,> , ΔVtung , Vtung and CTtung are the AVC, the LVC, the lung volume and density. The superscripts refer to two respiratory stages (0 is the reference).

Lung Air Volume Change Using Spirometry Measurement Data

The pseudo tidal volume in a respiratory cycle was measured using a spirometer and a bellows with correction for instrumental drift (Lu, W. et al., Med. Phys. 33, 2964-

2974 (2006)). The rate of the AVC showed a linear relationship with the rate of airflow into the lungs through the spirometer. The conversion factor is expressed as (Lu, W. et al, Med. Phys. 32, 2351-2357 (2005)):

Δv AV_Spmm T₁ - (P₁ - P₁^)

where Ti, T_s, Pi, P_s, Pι,_wate_r and P_s,_Wate_r are the temperatures, total pressures and partial pressures of water vapor in lungs (1) and spirometer(s), respectively. Thus, the AVC (ΔV_AJ>) can be calculated from the spirometry data, with a theoretical correction factor of 1.11 (measured as 1.08) (Lu, W. et al, Med. Phys. 32, 2351-2357 (2005)). The volume increases as air enters the lungs due to increased temperature and humidity compared with ambient room conditions.

Lung Temperature Kinetics and Gastrointestinal Pressure Variation

Equation 4 assumes instant thermal equilibrium. This assumption can overestimate the air volume in the lungs by about 1%. When the reserve air volume is known (based on 4DCT), the temperature of the mixed air in the pseudo-closed lung system can be calculated based on Equation 1, assuming lung pressure variation (<1%) is negligible:

V ^γ Res + V

T = ' Re seerrvvee ^r TTiidal CK) (5)

(273 + 37)^{"1 •} V_Reserve + (273 + 22)^{"1 •} V^

where VR_eserve and V Vidai are the reserve air volume (assumed at -37⁰C) and inhaling tidal volume (assumed at -22⁰C) at inspiration stage i. In the expiration stages, the thermal equilibrium is gradually approached, resulting in an equilibrium temperature of 37⁰C at the end of exhalation. A linear temperature rise is assumed in the exhalation process, since the actual kinetics is likely location dependent and unknown, as well as the maximum temperature variation is estimated to be less than 1% in ⁰K (given estimated the VReserve/VTidal ratio of about 10 in Equation 5).

The lung air volume changes with the slight temperature variation, following Charles's Law (reduced from Equation 1) in a constant pressure (isobaric) process:

T V

-± = -± (6)

T ' V ' where the subscript i and 0 are any respiratory stage and the reference stage. Using this equation, the <1% temperature variation can be translated to <1% volume variation. Together with the variation of the partial pressure of vapor as the temperature changes in the lungs, this non-equilibrium correction provides a conversion factor of 1.10. The bowel gas would follow Boyle's Law (reduced from Equation 1) between two respiratory stages i and 0 in a constant temperature (isothermal) process:

P V

— = — (7)

P_n 0 V.

Namely, the pressure variation is reciprocal of the volume variation. So, a -2% of gastrointestinal (GI) pressure increase in the supine position should result in a -2% volume decrease of the GI gas, and vice versa.

Measurements of Thoracic and Abdominal Heights

Two skin areas (lower thorax and upper abdomen) are selected to track their heights in 4DCT, mimicking the RPM reflector placed on these two spots. Anatomically, the lower thoracic point is defined as 5 slices (0.75 cm) superior to the inferior end of the sternum body, while the upper abdominal skin point is selected as 10 slices (1.5 cm) inferior to the tip of the xiphoid process of the sternum. The "fiducial" height changes (AHxhorax and AHAbdomen) are calculated as the average skin height in five consecutive slices in the mid-sagittal plane for each of the 4DCT stage images. The measurement is performed manually based on body contours with a precision of about 0.5 mm.

Determination of breathing pattern can be subjective and lack of quantification, since most patients are combined (thoracic and abdominal) breathers, utilizing both costal muscle and diaphragm. To quantify the breathing pattern (BP), three approaches are introduced: a volume ratio, a point array and a height ratio. A ratio of the maximum volume changes in the thorax and the torso is introduced for assessment of thoracic involvement:

_ {thoracicVolumeChange)^Max _ (tVC)^Max (TorsoVolumeChange) "^* {JVC) ^∞

The separation of thorax and abdomen is at the inferior end of the xiphoid process of the sternum. The abdominal volumetric involvement can be estimated from (1.0 - Bpγ). An array of five points (B P₅) in the mid- sagittal plane, as shown in Fig. IA, is also used to monitor the breathing pattern using skin height variation: two points are on the thorax and three on the abdomen. Similarly, a ratio (BPH) of averaged heights is introduced to quantify the involvement of the thoracic over the abdomen:

ψbdominalHeightVariationj [H_abd )

Quantitative Correlation and Linear Regression Analyses

Correlation coefficient, linear regression and cross -correlation analyses were implemented using Matlab (The Math Works, Natick, MA) and Excel (Microsoft, Redmond, WA). Twelve pairs of data, x (AV_Tθrso, ΔV_Spιrθm, ΔV_GiG_as, ΔH_Thorax, or ΔH_Abdo_me_n) vs. y (ΔV_AJΓ), were analyzed for each patient to determine the correlation coefficient (r_{x> y}):

where cov(x,y) is a covariance matrix of x and y in the 12-stage respiratory cycle.

A linear relationship between external and internal volume changes based on the volume conservation hypothesis was assumed as:

Y = a - X + β (11) where the slope α provides a quantitative assessment of the hypothetical one-to-one relationship, and the intercept β provides an assessment of any systematic bias between the two quantities. Ideally, α should be close to unity and β should be close to null, independent of patients, including gender and breathing pattern.

The cross -correlation analysis was performed between x(ϊ) and y(ϊ) (as functions of respiratory stage i) to examine any phase shift by fitting the two curves for maximum overlap. A fractional phase shift could be obtained by analyzing linearly interpolated data between stages (i), making the discrete functions jc(i) and y(ϊ) continuous. Example 2

This Example sets forth the results of volume conservation studies conducted using the methods described above.

Assessments of Patient Breathing Patterns Based on 4DCT Images

A tabulation is provided in Fig. 12 that shows patients' gender, ranges of the TVC and AVC, as well as quantitative descriptors of breathing pattern based on volume and height variations on the thorax and abdomen. The volumetric descriptor (BPy) estimates that the thoracic involvement is 16%+11%, ranging from 3% to 46%. In parallel, the height descriptor (BP_H) shows that the ratio of thoracic height variation to abdominal variation is 16%+8%, ranging from 9% to 39%. Both descriptors suggest a large variation in the thoracic motion over the abdominal motion, and detailed height variations of the five skin points for all patients are plotted in Fig. 2B. Given the differences in patient's gender and breathing pattern, the maximum TVC and AVC are in a close agreement: on average the relative difference is -2.7%+7.3%.

Linear Regression and Correlation Analyses of the AVC and the TVC

A tabulation is provided in Fig. 13 that shows the linear regression results between the AVC and the TVC for all patients. The average slope is 1.027+0.061, supporting the hypothetical relationship. The apparent intercept of -11.9+25.3 cm³, or - 2.1%+3.8% relative to the maximum tidal volumes, indicates a small systematic bias between the two measures. A linear regression plot of the data from all patients is shown in Fig. 3A, which shows that the linear relationship holds sufficiently well across the patient spectrum. Figs. 4A-D shows four examples of the dynamic plot of internal and external volumetric variables versus respiratory stages. According to the tabulation provided in Fig. 13, these four patients are statistical representatives of the pool of 14 patients. Cross-correlation analysis and visual examination find no phase shift.

The tabulation in Fig. 13 shows correlation results for the TVC and AVC, together with the thoracic and abdominal heights versus the AVC. The TVC-AVC correlation coefficients are high (0.992+0.005) with a p-value of <0.0001, independent of patient gender and breathing pattern. In contrast, the correlation for abdominal height vs. the AVC (0.82+0.30) is higher than that of thoracic height (0.28+0.44), but inferior to that of the TVC. Figs. 5A-D show four examples, comparing the AVC with the point height measurements.

Volume and Pressure Variations of Gas in the Gastrointestinal Tract

The tabulation provided in Fig. 13 also shows that the bowel gas volumes (ranging from 95 to 1385 cm ) have very small changes during respiration. The average relative variation is 2.8%+1.9%. Figs. 4A-D show four examples of the minute GVC variation during respiration. Little correlation (r = -0.05+0.31) was found between the GVC and the TVC in the patients. Based on Equation 7, the small volume variation indicates a small pressure variation in the similar scale (-3%), consistent with measured values (-2%) (Agostoni, E. and Rahn, H., /. Appl. Physiol, 15, 1087-1092 (I960)). This indicates that the GI gas volume conserves during respiration within a tolerable range.

Linear Regression and Correlation Analyses of the AVC and Spirometry Data There is provided in Fig. 14 a tabulation that shows linear regression and correlation coefficient results of the AVC and the spirometric tidal volume. The close- to-unity slope (1.030+0.092) and small intercept (4.5%+5.0%) are similar to those in the TVC-AVC results. Fig. 3B shows the linear fitting of the spirometry data vs. the TVC across all patients. The tabulation in Fig. 14 also shows a high correlation (0.973+0.012) between the two data sets. Figs. 4A-D show four plots of the spirometic tidal volume vs. the other volumetric variables as a function of respiratory stage. An average phase shift of 0.3 stages in the spirometric tidal volumes comparing with the AVC data is observed based on cross-correlation analysis, possibly due to dynamic pressure imbalance between the bronchi and the alveoli (Lu, W. et al, Med. Phys. 33, 2964-2974 (2006)).

Comparison between the External Volumetric and Point-Fiducial Surrogates

As shown in the tabulation in Fig. 12, the patient-specific maximum TVC and AVC are quantitatively comparable with a relative difference of -3%, while the five point heights have very different motion ranges, depending upon anatomical locations (Figs. 2A, 2B). The dynamic curves of the TVC, the AVC and the tidal volume resemble to each other, indicated by the near-unity slope in the linear regression results (Figs. 3A, 3B) and illustrated in the four examples (Figs. 4A-D). No phase-shift is observed for the TVC-AVC curves. In contrast, the dynamic curves of the thoracic and abdominal heights differ from each other, including the shape, phase and amplitude. Most of the thoracic curves show a phase shift (>1 stage), as shown in Figs. 5A-D. Although the abdominal height can correlate well with the AVC, its curve can be dissimilar to the AVC curve. For instance, Fig. 5A shows a high correlation coefficient case (r = 0.973 for patient #3 in Table 2) with flatten inhalation stages (stages 6, 7, and 8) in the abdominal height curve, differing from the peaked inhalation in the AVC curve.

Example 3

This Example discusses the results obtained during the course of the volume conservation studies underlying the present invention.

Minimization of Residual Motions and Motion Artifacts in 4DCT Imaging

The validation of the volume conservation hypothesis is primarily based on 4DCT imaging with confirmation from the spirometry measurements. So the quality of the 4DCT imaging plays a significant role in determining the accuracy and reliability of the result. In summary, the following five efforts were devoted to minimize the residual motion artifacts in the 4DCT images (Lu et al. , Med. Phys. 33, 2964-2974 (2006)).

These are: (1) Dual surrogates (bellows and spirometer) were employed to monitor respiratory motions for higher accuracy and reliability (Mutaf et al., Med. Phys. 34, 1615-1622 (2007)); (2) Cine mode scanning was utilized with repetitive and redundant (25) scans in each couch position to minimize possible breathing irregularity (Pan, T., Med. Phys. 32, 627-634 (2005)); (3) Amplitude-based retrospective binning was used to further suppress residual motions in case of breathing irregularity (Lu et al., Med. Phys. 33, 2964-2974 (2006)); (4) Twelve-stage binning vs. ten was applied to have slightly better time resolution with reduced residual motion in each stage CT (1.5 mm slice thickness); and (5) Patients were pre-instructed on their control of breathing regularity, which was established prior to the image acquisitions.

The use of both spirometry and bellows combine their advantages and overcome their shortcomings enhancing the reliability and accuracy of the respiratory motion measurements. Although there are minor residual motions (between couch positions, mostly in the abdomen) and motion artifacts (diaphragm) due to breathing irregularity and fast motion, the 4DCT image quality is the best possible under the current technology scope. Therefore, these 4DCT images provide most reliable and accurate basis for the assessment on the volume conservation hypothesis.

Uncertainties in the Quantitative Volumetric Approach

It is worthwhile to emphasize that the torso coverage should be anatomically complete since the respiration-induced motion involves tissues in both thorax and abdomen [Konno, K. and Mead, J., /. Appl. Physiol. 22, 407-422 (1966)]; otherwise an underestimate of the volume change will lead to incorrect conclusion as tissues often deform and move out of the thoracic region. In the tabulation in Fig. 12 and Figs. 2A-B, the volume and height descriptors of breathing pattern show that the maximum thoracic volume change only accounts for a fraction (0.03 to 0.46) of the maximum TVC (~ AVC) and the respiratory motion extends all the way into the pelvis. By far, almost all 4DCT images reported in the literature cover only the thorax and upper abdomen [Jaffray et ciL, Expert Rev. Anticancer ther. 7, 89-103 (2007); Li et al, Tech. Cancer Res. Treat. 7, 67-81 (2008a)], and they cannot be used to study the external-internal volumetric relationship.

The TVC and LVC obtained from segmentation are highly reproducible (< +1 cm³). The edge-tracing algorithm is suitable to segment topologically simple anatomy, such as the torso, and the voxel-counting algorithm is utilized for calculation of the torso and lung volumes with different thresholds within the body contour. Inclusion of foreign objects in the torso contour, such as the bellows and body supports, could introduce some uncertainty (< +10 cm ) in the TVC calculation, although most of such noises are cancelled out in calculating the volume change to a reference stage. In addition, different residual motions in the 4DCT introduce different uncertainties in the TVC and AVC calculation. In the diaphragm region, residual motion blurring introduces uncertainty to the AVC, rather than the TVC. In abdominal regions, different residual motions between abutting cine sections introduce uncertainty in TVC, but not the AVC.

The volume conservation hypothesis is validated for quiet respiration. The negligible bowel gas pressure variation (-3%) is consistent with experimental results [Agostoni, E. and Rahn, H., /. Appl. Physiol, 15, 1087-1092 (I960)]. It is likely caused by a slight internal tension variation as the abdomen expands and contracts. For labored respiration, heavy muscular engagement can cause substantial pressure change, making the GVC a significant factor in the TVC. Hence, a quiet respiration is required, consistent with the current clinical practice. After all, the above uncertainties are responsible to the non-unity slope (1.027), standard deviations (-6%), and intercept (-2% relative to the maximum tidal volume) as shown in the tabulation in Fig. 13. This linear volumetric relationship is confirmed by the cross-verification from independent spirometric tidal volume measurement. To the best of our knowledge, it is the first time that the one-to-one volumetric relationship has been established between external and internal organ motions during respiration.

Volumetric Approaches vs. Fiducial Point(s) Approaches The correlation between respiratory phase and height of upper abdomen or lower thorax has been intensively studied [Vedam et al, Phys. Med. Biol. 48, 45-62 (2003a); Vedam et al, Med. Phys. 30, 505-513 (2003b); Vedam et al, Med. Phys. 31, 2274-2283 (2004); Hoisak et al, Int. J. Radiat. Oncol. Biol. Phys. 60, 1298-1306 (2004); Lu et al, Med. Phys. 32, 890-901 (2005a); Lu et al, Med. Phys. 32, 2351-2357 (2005b); Chi et al, Med. Phys. 33, 3116-3123 (2006); Ionascu et al, Med. Phys. 34, 3893-3903 (2007)] and widely utilized in clinical respiratory monitoring devices, such as the RPM. However, due to the diversity and complexity of breathing motions, which cause deformation in the thorax as well as the abdomen, point-fiducial-based motion monitoring systems may not provide a reliable, real-time signal for quantitative linking of external and internal motions [Chi et al, Med. Phys. 33, 3116-3123 (2006); Lu et al, Med. Phys. 32, 2351- 2357 (2005b); Ionascu et al, Med. Phys. 34, 3893-3903 (2007); Gierga et al, Int. J. Radiat. Oncol. Biol. Phys. 61, 15511558 (2005)], resulting in possible phase shifts and/or potential low correlative indications.

The sensitivity of fiducial placement that was reported previously is confirmed in this study with two different positions. These two positions were selected based on the commonality of RPM placement (lower thorax and upper abdomen) in the clinic, and the continuity of the adjacent neighboring cine sections in the 4DCT across all patients, avoiding potential residual motion artifacts. It was not our intention to simulate the RPM reflector's motion (an averaged height in a slightly larger area), but to demonstrate the location dependency of the surface height. As a matter of fact, the abdominal and thoracic heights in responses to the respiratory motion are dramatically different from each other due to body deformation, as shown in the tabulation provided in Fig. 13 and Figs. 5A-D. Although fiducial arrays were tried as an alternative, marginal improvements were demonstrated [Yan et al, Med. Phys. 33, 4073-4084 (2006); Baroni et al, J. Radiat. Res. 48S. A61-A74 (2007)]. Instead, the dissimilar, complex motion patterns among the individual points due to the torso deformation (as shown in Figs. IA- C) may complicate the signal processing.

The superiority of this volumetric approach (the TVC-AVC- spirometry linearity) over the fiducial height method discussed above is consistent with previous reports on the superiority of spirometric tidal volume over the fiducial height [Hoisak et al., Int. J.

Radiat. Oncol. Biol. Phys. 60, 1298-1306 (2004); Lu et al., Med. Phys. 33, 2964-2974 (2006)]. One or a few point fiducial(s) are fundamentally insufficient representation(s) of the deformable moving anatomy (the torso). In contrast, the volume conservation rule offers a predictable linear relationship, without phase shift. This volumetric approach also provides an advantage over spirometry, which is inconvenient, demands frequent calibration, and requires baseline drift correction [Lu et al., Med. Phys. 33, 2964-2974 (2006); Ha et al., Phys. Med. Biol. 53, 4269-4283 (2008)]. A Potential Volumetric Respiratory Surrogate

The physiological process of respiration involves tidal volume change due to airflow into and out of the lungs, driven by minute intrapulmonary pressure variations from the ambient atmospheric pressure. As shown in this study, the one-to-one relationship exists among all three volumetric quantities: the TVC, AVC and spirometric tidal volume. Therefore, the external-internal linear volumetric relationship is naturally one of the most direct and most straightforward assessments of respiratory process.

In order to apply this predictable volumetric relationship to establish a clinically useful respiratory surrogate, we are investigating the use of a commercially-available optical surface imaging system to acquire the external torso volume during respiration to replace the use of 4DCT imaging and spirometry. Such optical camera systems have been reportedly used for image-guided patient setup based on surface matching [Djajaputra, D. and Li, S., Med. Phys. 32, 65-75 (2005); Bert et al, Int. J. Radiat. Oncol. Biol. Phys. 64, 265-1274 (2006)]. The surface imaging resolution can reach 1280x1024 pixels with a speed of up to 15Hz [Schoffel et al. , Phys. Med. Biol. 52, 3949-3963

(2007)]. As the technology advances, the spatial and temporal resolutions of the surface imaging could soon become comparable to or even exceed those of 4DCT imaging in the coming years. On the other hand, computational techniques for real-time volumetric analysis of 3D multimodality images are available [Li et al., Int. J. Radiat. Oncol. Biol. Phys. 63, 261-273 (2005); Li et al, Tech. Cancer Res. Treat. 1, 67-81 (2008a); Li et al,

J. Appl Clin. Med. Phys., 9(4), 17-36 (2008)]. Although the implementation of the volumetric respiratory surrogate based on this fundamental study remain to be seen in the future, it is considered to be both desirable and feasible. Such a potential respiratory surrogate can provide more reliable guidance to 4DCT as well as 4DRT without ionizing radiation.

Conclusion

This study proposes and validates the volume conservation hypothesis within human torso during respiration. It demonstrates a new, one-to-one relationship between the volume changes of the external torso and the internal lung air content (the tidal volume). Based on this quantitative volumetric relationship, a potential torso respiratory surrogate can be implemented to provide an accurate and reliable guidance for 4DCT imaging as well as 4DRT treatment.

Example 4

This Example sets forth the expandable piston respiratory (EPR) model and materials and methods for internal motion prediction studies underlying the present invention.

Volume Conservation Rule (VCR) Linking External-internal Volumetric Changes The VCR rule, which was previously proposed and validated within the torso during quiet respiration in the studies reported above, indicates that the external torso volume change (TVC, or ΔVxorso) is the same as the lung air volume change (AVC, or ΔV_AIΓ), owing to airflow into and out of the lungs. Based on this rule, the external TVC predicts the internal AVC. AV_Torso ≡ AV_Air (12)

This is because the materials in solid, liquid and gas phases have negligible volume change under the respiratory pressure variation (-15 mmHg, or -2% of ambient room pressure) (Applegate, E., The anatomy and physiology learning system, W.B. Saunders Co., Philadelphia, Pennsylvania (2d ed., 2000); Agostoni, E. and Rahn, H., /. Appl. Physiol, 15:1087-1092 (I960)). Based on the ideal gas law, the -2% pressure variation can be translated to a -2% volume uncertainty, which can be tolerated and ignored assuming a constant body temperature.

The relationship between the AVC and the lung volume change (LVC, or ΔVLung) is established with a lung density correction between a respiratory stage X and the reference stage 0 (the full exhalation):

W_Lung = AV_Aιr + (CJt_ng ^■ V_L ^x _ung - CT_L°_ung ^■ V_L°_ung ) (13)

where CTmng and Vmng are the CT number and volume of the lung. The conversion factor (k) from the AVC to the LVC is respiratory stage dependent, but the variation is small and the stage-averaged conversion factor (<k>) is introduced:

Lung ^y Lung - C ^- ¹T Lung - V ' L

(k) == _ . V ^- ¹ ung

All respiratory stages are used except the two stages at the full exhalation. Little patient dependency is observed, so that the patient-averaged conversion factor (

) can be used to estimate the LVC from the TVC, using the following approximate equation:

AV_Lung →) - AV_Aιr ≡ (kj - AV_Torso (15)

This calculated LVC is slightly overestimated for stages near full-inhalation while slightly underestimated for stages near full-exhalation. It should be emphasized that the

LVC is the main quantity used in the EPR model, which will be discussed later herein. Two methods can be used to calculate LVC: one is obtained from image segmentation using Equation 13 and the other is estimated from the TVC using Equation 15. Both are used in the diaphragm displacement prediction.

Amplitude-based 4DCT Imaging, Reconstruction and Segmentation

Fourteen patients' torso 4DCT were acquired using Philips Big Bore 16-slice CT scanner with both the bellows and spirometry as respiratory surrogates using a special clinical imaging protocol (Lu, W. et al., Med. Phys., 33:2964-2974 (2006)). In brief, special efforts have been made to minimize the residual motions and motion artifacts in the 4DCT images, including (1) entire torso scan (-464 slices) with 1.5 mm slice thickness; (2) dual surrogates for measuring the pseudo tidal volume; (3) redundant (25) scans with low (40) mAs for abutting sections in cine mode; (4) amplitude-based retrospective sorting in 12-stage bins; and (5) patients were pre-instructed to keep a quiet breathing, which was established prior to image acquisition. All patients were in spine, arm-up position, the bellows was placed on the abdomen below the rib cage, and the spirometer was connected to a patient with a mouth piece with nose clipped. The image size was 512x512x464 voxels and the voxel size is 0.98x0.98x1.5 mm³. Detailed 4DCT imaging conditions could be found in Lu, W. et al., Med. Phys., 33:2964-2974 (2006); and as reported in Examples 1-3, above.

A self-developed treatment planning system software was used for image analysis. The external torso and internal lung volumes were calculated based on a voxel- counting algorithm with different thresholds (< -350 HU for lung and all HU for body) within the body contour, which was segmented using an edge-tracing algorithm with a threshold of -350 HU and two times of erosion-dilation smoothing, as shown in Figs. 6A- B. The torso (Figs. 7A, 7B) was defined anatomically from the clavicles to the pubic bones. The lung range was defined from the first to the last slices that contain segmented lungs. The diaphragm range was defined from the first superior slice, in which the apex of the diaphragm was segmented, to the inferior ends of the lungs. The right and left lungs were processed separately. The full-exhalation stage CT was used as the reference in calculating the lung volume changes and diaphragm displacements. To calculate thoracic cavity volume, excluding all tissues (lung and non-lung) inside the rib cage, a semi-automatic segmentation procedure was utilized. A paint-brush was used to temporarily assign non-lung tissues with the lung CT number at the interface with the rib cage, topologically isolating the chest wall from the interior. Then the thoracic cavity was automatically segmented, as shown in Figs. 8A-F. The thoracic cavity volume per slice was then calculated and averaged in three consecutive slices.

An Expandable "Piston" Respiratory (EPR) Model for Predicting Diaphragm Motion

An expandable "piston" respiratory (EPR) model is proposed to predict diaphragm displacement within the rib cage, as shown in Fig. 6. Two major orthogonal lung motions are allowed: (1) posterior- anterior (PA) expansion and (2) superior-inferior (SI) extension. The full-exhalation stage CT is used as the reference for calculation.

For lung expansion, our model assumes that the well-known thoracic skin height variation during respiration can be directly translated into the lung height variation in the PA direction. In other words, the tissue anterior to the lungs is assumed to have a constant thickness on average, as shown in Fig. 6A. Laterally, although there is a slight lung width change induced by respiration, it is negligibly small comparing to lung height change and so ignored. Therefore, the lung expansion volume (Δ VEXP) can be calculated based on the reference CT and external thoracic surface variation. The lung extension volume (ΔVEXT) is obtained by deducting the ΔVEXP from the lung volume change (LVC, ΔVLung) at a certain respiratory stage (X):

AV^ = AVl_ung - AV^ (X = 1, 2, ... , 12) (16)

For lung extension, it is assumed that the overall diaphragm position, equivalent to the "piston", could be estimated by the average of three points at the diaphragm, as shown in Fig. 5A. The piston moves 1 to 3 cm in SI direction, as shown in Figs. 7A-B. In reference to the full exhalation stage, the inferior displacement of the diaphragm generates empty space inside the rib cage above the piston with a volume that should be equal to the ΔVEXT. Therefore, the vertical thickness of the empty space would predict the diaphragm displacement.

ΔF^ = V^;^der - AZ^X (X = 1, 2, ... , 12) (17) Cylinder _γ where ^v cavity is cylindrical cavity volume per slice and ΔZ is the piston displacement.

It is worthwhile to mention that only lung tissues should be included to fill the empty cavity. Details in the EPR model (Fig. 7C) will be discussed in the following sections.

Lung Expansion and Extension Volume Calculation

Based on observation of fourteen torso 4DCT images, our model assumes that the averaged lung expansion in PA direction is the same as the averaged thoracic surface elevation in any lung-containing slice of the 4DCT images (as shown in Figs. 6A-B). In any respiratory stage (X), the average height variation ( ' ) in a slice (i) can be calculated by the area (Ai) divided by the maximum thoracic width

namely,

(18)

The lung expansion volume (Δ V;) can be estimated by the maximum width of the lungs (wi^Max = w_iL ^Max + w_iR ^Max) multiplied by the height variation ( ^Δ^ ) and slice thickness (t):

(AV₁ Y = [Ah₁ ) - W₁^ - t (X = 1, 2, ... , 12) (19)

So, the overall lung expansion volume (Δ VEXP) is the sum of all lung-containing slices (N) in reference to full exhalation CT image:

ΔF-_P = ∑(AVj = ∑ (Ah₁ f - _Wl ^Max - t (X = 1, 2, ... , 12) (20)

Then, the lung extension volume (ΔV_EXT) can be calculated using Equation 16.

Equivalent Diaphragm Position and Volumetric Shape of the Rib Cage

The diaphragm position is defined as the inferior lung boundary, which can be assessed quantitatively using a volume- weighted average (<Z>) in the region where the lungs co-exist with the diaphragm in the reference CT. Such average defines the piston position with the volume-equivalent, flat-bottomed lung in the rib cage cavity:

N Σ V , x Z

( Z ) ⁰ = n = \

N (21)

Σ n = \

where i, N, V; and Z; are slice index, the number of slices in the diaphragm range, lung volume and SI position, respectively. The left and right diaphragms were processed separately and averaged.

This equivalent diaphragm can move about 20 mm inferiorly during respiration. The volumetric shape of the rib cage ("cylindrical" or "conical") in the motion range from <Z> to <Z>+20 mm is critical, since the vacant space volume is a function of the thoracic cavity, as shown in Fig. 4. To determine the volumetric shape of the cavity, a plot of volume vs. position characterizes the cavity shape. The position range is from 10- 30 mm, covering the motion range of the diaphragm for all patients. A volume change of α = 3% was used as the criteria: cylindrical rib cage has a smaller change (α < 3%) while the conical rib cage has a larger change (α> 3%).

Volume Conservation for Non-lung Tissues inside the Thoracic Cavity

Both the respiratory and cardiac motions make non-lung tissues in the thoracic cavity move and deform with a conserved volume. Therefore, the volume of non-lung tissues is a constant regardless respiratory stage. The primary assumption is that there is a dynamic equilibrium of the blood flow in and out the thoracic cavity. Of course, it is also assumed that the patients are not swallowing anything, including air, and their esophagus is empty and no food passes and no reflux during scanning. Therefore, in the ERP model, the empty space generated by the "piston" SI motion inside the rib cage should be filled with lung tissues only, as the volume of all non-lung tissues conserves.

Diaphragm Displacement Prediction with the Rib-cage Volume Constraint

In case of cylindrical rib cage, the equation for calculating diaphragm displacement has been given by combining Equations 16 and 17. The predicted diaphragm displacement at a stage X can be rewritten as:

ΔZiU_** 1, 2, ... , 12) (22)

IT Cylinder where Δ_VEXT, ^Cav"y and t are the lung extension volume, the cylindrical cavity volume per slice inside the vacant space, and the slice thickness, respectively.

In case of conical rib cage, a numerical iterative approach was applied with the initial value taken from the above equation. As the cavity volume changes with the piston displacement, a linear volume increase rate (α = ΔV/ΔZ) was used to project the average cavity volume. The iterative equation (ΔZj₊i = f(ΔZj) can be expressed as:

ΔZ X AV Extension

P} eώcated ;+i (23)

^LS-^{y ?} I^Lns^ye^hrⁿU 'e^dd^er + 0 5 - a- AZ P^Λredicat ^•ied 1 J The denominator represents the adaptive volume to the conical rib cage at the previous piston position. The stopping criterion was set as (ΔZj₊i -ΔZj) < 1 mm.

Comparison of Predicted with Measured Diaphragm Displacements

Six points (three on each lateral side) were used to calculate the average diaphragm position and its displacement, as shown in Fig. 6B. This average position represents key points in the right-left and anterior-posterior sides, accounting for some deformation. The measured displacement (ΔZ_Measu_red) is the position difference in the SI direction (Z) between a stage (X) and the reference stage (0):

^ΔZ£_W = (j ^■

(ή + ή ) - « ⁺ 4 ) ^" <²⁴>

The predicted diaphragm displacements were compared with the measured values, and the residual differences and standard deviations provide an accuracy assessment:

d{AZ)^x = AZf_reΛcated - AZ*_easured (X = 1, 2, ... , 12) (25)

Comparison of Predicted and Measured Point Motion at the Diaphragm

Using the predicted diaphragm motion based on the EPR model, the motion of any point of interest at or near the diaphragm can be predicted if its motion range (Δz_Ma_x) is known, assuming that the two motions are in synchronization. The point displacement at any stage (X) in the respiratory cycle can be calculated as:

⁰^ Predicated ~ P ^^ Predicated ~ ^~T7y ^ZλZl Predicated V^{Z C}V

ΔZ " M, ax

This equation converts the diaphragm motion into the motion of a point of interest. Similarly, the discrepancy between the predicted and the measured indicates the quality of the motion prediction of a point of interest:

d{Az)^x = Azl_edwated - Δz_M ^x _easured (X = 1, 2, ... , 12) (27) Example 5

This Example sets forth the results of internal motion prediction studies underlying the present invention.

Compensating for Lung Expansion Volume in Posterior-anterior Direction Figs. 2A-B show a patient's thoracic height variation between two extreme respiratory stages. Anteriorially, the height difference on skin is roughly the same as that of the lungs. The lung area change in PA direction accounts for the primary difference in the axial image (Fig. 6A). Laterally, the lung shape difference is small and neglected. The tabulation provided in Fig. 15 shows the ratio of maximum ΔV_EXP over maximum ΔVmng, indicating how much the lung expansion contribution is in the lung tidal volume.

This is a more precise and accurate descriptor of breathing pattern than the estimation based on external volumes (tVC/TVC). The thoracic expansion in respiration among the 14 patients is diversified, ranging from 3% to 24%. In other words, the lung extension consumes 76% to 97% of the total lung tidal volume.

Cylindrically or Conically Shaped Rib Cages among Patients

The reference diaphragm position is calculated using the volume- weighted average, which provides a volumetrically equivalent "piston" position with a flat bottom in the full-exhalation CT. Figures 7A-B show the equivalent piston position and its 2 cm moving range, relative to the lungs. The tabulation provided in Fig. 15 shows three thoracic cavity volumes (per slice) at, and 7.5 and 15.0 mm inferior to, the equivalent piston position. The volume variation serves as an indicator about the shape of the rib cage within the motion range. Three patients (6, 9 and 11) show 6.0%, 4.0% and 5.2% volume increase, suggesting a conical rib cage, while all other patients show an approximately cylindrical rib cage (< 3%). A linear volume increase per slice (R₂ > 0.95) is shown for the three conically-shaped rib cages. Figs. 8A-F show a cylindrical and a conical rib cage, in axial and 3D views, together with the contours of the thoracic cavity. Comparison between the Predicted and Measured Diaphragm Motion

Fig. 7C shows the EPR model and procedure for calculating the diaphragm displacement. The tabulation provided in Fig. 16 shows the comparison between the measured and two predicted diaphragm displacements. The maximum displacements (from 8.5 to 29 mm) are in excellent agreement. The stage-averaged residual errors are ranging from -1.38 to 0.99 mm (0.2+1.0 mm) and from -1.95 to 1.57 mm (0.2+1.1 mm), based on the LVC and TVC, respectively. The

of 1.11 (in Fig. 15) was used to convert the TVC to the LVC. The relative errors are also small (6.6+3.2% and 7.6+3.1%, respectively). Figs. 9A-D show four examples with the predicted and the measured diaphragm motion trajectories in SI direction as the function of respiratory stage. These curves resemble to one another in shape and amplitude.

Figs. 10A-D show two examples of improved calculation of diaphragm displacement by adapting to the volume change in the conical rib cages. The residual error distributions of the LVC-based and TVC-based calculations are shown in Figs. 1 IA-B; the latter has a slightly broadened error distribution, due to the uncertainty in external-internal relationship and the approximation of using patient-averaged conversion factor in the TVC-based calculation. These residual errors are considered to be clinically acceptable.

Motion Prediction of Points of Interest with Known Motion Range Fig. 6B shows that the diaphragm moves differently from point to point with considerable deformation. Using Equation 15 with known motion range (ΔzMax), the point motion, Δz(i), is predicted and compared with measured from the 4DCT. The motion ranges and residual errors for 4 points at the diaphragm are shown in the tabulation provided in Fig. 17. Three out of 56 points showed a stage-averaged residual error larger than 2 mm, while nine points have a standard deviation larger than 3 mm.

Such discrepancy is a direct result of the imperfect synchronization between the diaphragm and the point of interest, deviating from the assumption. Dramatic tissue deformation is observed around the diaphragm, as shown in Fig. 6B. Nevertheless, accounting for the large motion range for these individual points (up to 63 mm), the relative error was found to be 6.7+2.2% across all points in all patients. If 4DCT is used clinically for 4D treatment planning, the potential phase shift between the piston motion and point motion can be calculated using the cross -correlation method. With the phase shift correction, the prediction of point motion around the diaphragm can be further improved.

Example 6

This Example discusses the internal motion prediction results reported in Example 5.

Accuracy of the Diaphragm Displacement Prediction

As demonstrated in the tabulation provided in Fig. 16 and Figs. 11A-B, the prediction uncertainty in diaphragm motion based on the TVC is <σ> = 1.1 mm (within 2 mm) over the 14 patient studied. Relatively, it is about 7%. This accuracy is within clinically acceptable tolerance, as it does not exceed the uncertainty (<+3 mm) of the current image-guided patient setup. Such accuracy relies on that in all steps of the process, including 4DCT imaging, image segmentation, volume calculation, the VCR rule, as well as the EPR model, translating the external volumetric information to the diaphragm displacement. Residual motions in the 4DCT, although minimized by using dual-surrogates

(Mutaf, Y.D. et al., Med. Phys., 34:1615-1622 (2007)), multi-scans in cine mode (Pan, T., Med. Phys., 32:627-634 (2005)), and amplitude-based sorting with 12 bins (Lu, W. et al., Med. Phys., 33:2964-2974 (2006)), was observed around the diaphragm and abutting section, due to patient' s breathing irregularity. The torso segmentation showed an uncertainty of <+l cm₃ and the inclusion of foreign objects (such as bed support) introduced an uncertainty of <+10 Cm₃. However, these uncertainties are small (-2-3%), provided the tidal volume of approximate 500 cm₃.

The VCR rule, which links the TVC to the LVC via the AVC, was estimated to have an uncertainty of about 2-3%, determined by the pressure variation inside the lungs and in the gastrointestinal tract. The averaged conversion factor over all respiratory stages and patients shows σ ~ 7% (in Fig. 15), primarily contributing to the difference between the LVC -based and TVC -based calculations and broadening the residual error distribution, as shown in Fig. 7. The EPR model translates the LVC into the diaphragm displacement during the respiratory cycle. This model is a first-order approximation of the real respiratory motion with four major assumptions: (1) the anterior expansion of the lungs can be estimated as the height variations of the thoracic skin on average; (2) the section of interest in the patient- specific rig cage shape can be estimated using an equivalent piston position in the moving range; (3) the non-lung tissues in the thoracic cavity can be regarded as volume conservative; and (4) the diaphragm position can be represented by the six key points on the right and left dome-like diaphragm.

A cylindrical rib cage in the diaphragm piston motion range appears mostly (Figs. 9A-D), while the cone-shaped rib cage can be taken into account using iteration approach (Figs. 1 OA-D). The average relative uncertainty for the results shown in the tabulation provided in Fig. 16 and Figs. 11A-B is within 8% for all patients, and the overall ~2 mm discrepancy of the predicted diaphragm motion is clinically acceptable.

Volumetric Approaches vs. Fiducial Point(s) Approaches

Several studies reported correlation between external fiducial and internal organ motions (Vedam, S.S. et al., Med. Phys., 30:505-513 (2003); Hoisak, J.D.P. et al., Int. J.

Radiat. Oncol. Biol. Phys., 60:1298-1306 (2004); Megeras, G.S. and Yorke, E., Semi. Rad. Oncol, 14:65-75 (2004); Lu, W. et al., Med. Phys., 32:2351-2357 (2005)). The respiratory response of these point- or line-based fiducials was location dependent and could contain a phase shift, due to anatomical deformation. A PRM reflector placement was reported to be in the mid-point between the umbilicus and the xyphoid (Vedam, S.S. et al., Med. Phys., 30:505-513 (2003)), while other places were also used, or even multiple fiducial placements on patient's lower thoracic or upper abdomen (Yan, H. et al., Med. Phys., 33:4073-4084 (2006); Baroni, G. et al., /. Radiat. Res., 48S:A61-A74 (2007)). Different responses were observed at different locations. Even if the marker location could be reproducibly repeated among fractions, the change in patient's breathing pattern (between thoracic and abdominal breathing) will likely change the abdominal height (Megeras, G.S. and Yorke, E., Semi. Rad. Oncol, 14:65-75 (2004)). Hence, the point-based correlation may be disrupted, producing unreliable prediction. In contrast, this volumetric approach eliminated the fiducial-location dependency and was free from the phase-shift, since a volumetric response of entire torso (both thorax and abdomen) accounts for tissue motion as well as deformation. In this study, no dependency on respiratory pattern was observed. Based on the EPR model, when a patient's breathing pattern changes, the contribution to the expansion and extension of the lungs will be changed accordingly. As a matter of fact, the EPR model accounts contributions from both thorax and abdomen, adaptive to any breathing pattern changes.

Vedam, S.S. et al., Med. Phys., 30:505-513 (2003) reported that the RPM was used for predicting diaphragm motion based on the strong correlation with internal diaphragm motion observed using x-ray fluoroscopic imaging. In multiple sessions of treatment of five patients, the first session was used to "calibrate" a linear predication model, which was subsequently used in the following sessions to predict diaphragm motion within an uncertainty of 1 mm (lσ) on average. In comparison, the volumetric approach predicted diaphragm motion trajectory with a similar range of uncertainty (<σ> = 1.0-1.2) and a clinically acceptable tolerance of ~2 mm. This volumetric approach does not require patient-based quality assurance, because all parameters in the EPR model can be measured from either the reference CT image or the torso surface, assuming the availability of an external volumetric surrogate. Hence, it is fair to say that the volumetric technique predicts the absolute organ motion, while the point fiducial predicts relative motion and requires a patient- specific calibration.

Target Motion Estimation Based on Diaphragm Displacement

This study showed preliminary result of a linear motion projection from the average diaphragm to points at the diaphragm. The linear assumption is the limitation of this approach, since the diaphragm moves with dramatic deformation, as shown in Fig. 6B. Although some of the results in the tabulation provided in Fig. 17 have a standard deviation larger than 3 mm, their motion ranges may also be significantly larger than that of the diaphragm (< 30 mm). As a matter of fact, more than half of the points R3 and L3 (as shown Fig. 6B) have larger motion range than 30 mm, up to 63 mm for patient #9 who has a dramatic tidal volume of -1700 cm . For points Rl and Ll, however, the averaged standard deviations are 1.5 mm and 1.3 mm, respectively, with the maximum of

2.2 mm. The different motion ranges between points 1 and 3 suggest different muscle engagements in different regions of the diaphragm. However, the relative errors are small for all points, ranging from 6.3+1.5% to 7.9+3.2%.

The results suggest a linear amplification of the residual error of the diaphragm (in mm), proportional to the motion range ratio of the point to the diaphragm. We anticipate similar results may apply to the points in the vicinity of the diaphragm, such as lower lobs of the lungs and upper portion of the liver, with a slightly increased margin, such as 5 mm motion margin (Ionascu, D. et al., Med. Phys., 34:3893-3903 (2007)). The root of the relatively larger uncertainty is the assumption of synchronization between the piston and the points. With 4DCT, the phase shift could be calculated through cross- correlation, so that the accuracy of the point motion prediction could be further improved.

Further away from the diaphragm, the target motion is likely also affected by other factors: (1) local structures, such as bronchi and blood vessels and (2) independent motions, such as cardiac and digestive motions. High rigidity of these anatomical structures hinders the target motion while the cardiac motion is known to cause more lateral motion than SI motion (Seppenwoolde, Y. et al., Int. J. Radiat. Oncol. Biol. Phys., 53:822-834 (2002)). So, the linear projection based on the assumed motion synchronization to the diaphragm only may not be applicable in these cases. This is consistent with previous reports, in which the prediction of the target motion was considered much more difficult than that of organ motion, such as diaphragm (Megeras, G.S. and Yorke, E., Semi. Rad. Oncol, 14:65-75 (2004); Ozhasoglu, C. and Murphy, M.J., Int. J. Radiat. Oncol. Biol. Phys., 52:1389-1399 (2002)).

As a consequence, a larger tolerance for the target motion prediction would be translated to a larger treatment margin. Nevertheless, the motion-compensated margin should be significantly reduced in comparison with those used in conventional 3D conformal radiotherapy. Recently, it was reported that an accurate (~1 mm) target localization technique using 4DCT based on lung vessel feature extraction and matching (Tashiro, M. et al., Med. Phys., 33:1747-1757 (2006)). Such deformable vector technique may be useful in future investigation.

Potential Clinical Implications of Diaphragm Displacement Prediction

In order to apply this volumetric technique to predict the organ motion in radiation therapy, an alternative volumetric surface imaging technique to the 4DCT must be developed to provide the external volumetric information of the entire torso in real time. An optical-based surface imaging technique could be adopted and adapted to volume calculations required by the volumetric method, as they were used for patient setup and respiratory gating in the clinic (Djajaputra, D. and Li, S., Med. Phys., 32:65-75 (2005); Bert, C. et al., Int. J. Radiat. Oncol. Biol. Phys., 64:265-1274 (2006); Schoffel, PJ. et al., Phys. Med. Biol, 52:3949-3963 (2007)). This study established a novel volumetric approach to predict the motion of the diaphragm and points of interest.

Conclusion

This study proposed an expandable "piston" respiratory (EPR) model to predict the diaphragm motion with the volumetric constraint. The expansion and extension of the lungs are both taken into account. The predicted and measured diaphragm motions agreed within 2 mm. The motion of a point of interest at or near the diaphragm can be calculated with the same relative accuracy given its motion range, assuming a synchronized motion behavior. If a phase-shift correction (out of sync) based on 4DCT planning image, the result could be further improved.

Although a preferred embodiment of the invention has been described using specific terms, such description is for illustrative purposes only, and it is to be understood that changes and variations may be made in light thereof will be suggested to persons skilled in the art without departing from the spirit or scope of the following claims. Incorporation by Reference

All patents, published patent applications and other references disclosed herein are hereby expressly incorporated by reference in their entireties by reference.

Equivalents

Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents of the specific embodiments of the invention described herein. Such equivalents are intended to be encompassed by the following claims.

Claims

What is claimed is:

1. A method for tracking the motion of an anatomical feature within a body segment, said tracking method comprising the step(s) of: determining an initial position of the anatomical feature and an initial external parameter associated with the anatomical feature and which can be correlated to a corresponding internal parameter; measuring the external parameter at a time subsequent to the initial determination; using the measured external parameter measured at the subsequent time and the determined initial position of the anatomical feature to determine a new location of the anatomical feature.

2. The tracking method of claim 1, further comprising the step(s) of: establishing a correlation between the external parameter and the internal parameter; using the established correlation and the measured external parameter to determine another internal parameter that correlates to the measured external parameter; and wherein said using the measured external parameter includes using the determined another internal parameter and the initial position to determine said new location of the anatomical feature.

3. The tracking method of claim 1, wherein the external parameter is measured at each of a plurality of times subsequent to the initial determination and the new location of the anatomical feature is determined at each of the plurality of times, where the new location is determined using a currently measured external parameter and the previously determined location of the anatomical feature.

4. The tracking method of claim 3, further comprising the step(s) of: establishing a correlation between the external parameter and the internal parameter; using the established correlation and each currently measured external parameter to determine another internal parameter that correlates to said each currently measured external parameter; and wherein said using the measured external parameter includes using the determined another currently determined internal parameter and the previously determined location of the anatomical feature to determine said new location of the anatomical feature.

5. The tracking method of any of claims 1-4, wherein said measuring includes using an imaging technique to image an exterior surface of the body segment so as to determine that external parameter.

6. The tracking method of any of claims 1-5, wherein the body segment is the torso of the body.

7. The tracking method of any of claims 1-6, wherein the external parameter is an external volume of the body segment and the internal parameter is an internal volume within the body segment, where changes in the internal volume cause a corresponding change in the external volume.

8. The tracking method of any of claims 1-7, wherein the anatomical feature is one of an organ of the body, healthy tissue of the body or unhealthy tissue within the body.

9. The tracking method of claim 8, wherein the unhealthy tissue comprises a tumor.

10. A method for treating an anatomical feature within a body using radiotherapy, said treating method comprising the step(s) of: determining an initial position of the anatomical feature and an initial external parameter associated with the anatomical feature and which can be correlated to a corresponding internal parameter; measuring the external parameter at a time subsequent to the initial determination; using the measured external parameter measured at the subsequent time and the determined initial position of the anatomical feature to determine a new location of the anatomical feature; and irradiating the anatomical feature with ionizing radiation so that the radiation is adjusted to compensate for movement of the anatomical feature.

11. The treating method of claim 10, further comprising the step(s) of: establishing a correlation between the external parameter and the internal parameter; using the established correlation and the measured external parameter to determine another internal parameter that correlates to the measured external parameter; and wherein said using the measured external parameter includes using the determined another internal parameter and the initial position to determine said new location of the anatomical feature.

12. The treating method of claim 10, wherein: the external parameter is measured at each of a plurality of times subsequent to the initial determination; the new location of the anatomical feature is determined at each of the plurality of times, where the new location is determined using a currently measured external parameter and the previously determined location of the anatomical feature. said irradiating the anatomical feature with ionizing radiation so that the radiation is adjusted to compensate for movement of the anatomical feature between each of the determined new locations.

13. The treating method of claim 12, further comprising the step(s) of: establishing a correlation between the external parameter and the internal parameter; using the established correlation and each currently measured external parameter to determine another internal parameter that correlates to said each currently measured external parameter; and wherein said using the measured external parameter includes using the determined another currently determined internal parameter and the previously determined location of the anatomical feature to determine said new location of the anatomical feature.

14. The treating method of any of claims 10-13, wherein said measuring includes using an imaging technique to image an exterior surface of the body segment so as to determine that external parameter.

15. The treating method of any of claims 10-14 wherein the body segment is the torso of the body.

16. The treating method of any of claims 10-15, wherein the external parameter is an external volume of the body segment and the internal parameter is an internal volume within the body segment, where changes in the internal volume cause a corresponding change in the external volume.

17. The treating method of any of claims 10-16, wherein the anatomical feature is unhealthy tissue within the body.

18. The treating method of claim 8, wherein the unhealthy tissue comprises a tumor.

19. A computer readable medium on which is stored a program for tracking movement of anatomical feature within the body, wherein the program includes, instructions, criteria and/or code segments for: determining an initial position of the anatomical feature and an initial external parameter associated with the anatomical feature and which can be correlated to a corresponding internal parameter; measuring the external parameter at a time subsequent to the initial determination; using the measured external parameter measured at the subsequent time and the determined initial position of the anatomical feature to determine a new location of the anatomical feature.

20. The computer readable medium of claim 19, wherein the program further includes, instructions, criteria and/or code segments for: establishing a correlation between the external parameter and the internal parameter; using the established correlation and the measured external parameter to determine another internal parameter that correlates to the measured external parameter; and wherein said using the measured external parameter includes using the determined another internal parameter and the initial position to determine said new location of the anatomical feature.

21. A computer readable medium on which is stored a program for tracking movement of anatomical feature within the body and treating the anatomical feature using radiotherapy, wherein the program includes, instructions, criteria and/or code segments for: determining an initial position of the anatomical feature and an initial external parameter associated with the anatomical feature and which can be correlated to a corresponding internal parameter; measuring the external parameter at a time subsequent to the initial determination; using the measured external parameter measured at the subsequent time and the determined initial position of the anatomical feature to determine a new location of the anatomical feature; and controlling the irradiation of the anatomical feature with ionizing radiation so that the radiation is periodically adjusted to compensate for movement of the anatomical feature.

22. The computer readable medium of claim 21, wherein the program further includes, instructions, criteria and/or code segments for: establishing a correlation between the external parameter and the internal parameter; using the established correlation and the measured external parameter to determine another internal parameter that correlates to the measured external parameter; and wherein said using the measured external parameter includes using the determined another internal parameter and the initial position to determine said new location of the anatomical feature.