Motion Probability Density Function Research Articles

A probability-based multi-cycle sorting method for 4D-MRI: A simulation study.

To develop a novel probability-based sorting method capable of generating multiple breathing cycles of 4D-MRI images and to evaluate performance of this new method by comparing with conventional phase-based methods in terms of image quality and tumor motion measurement. Based on previous findings that breathing motion probability density function (PDF) of a single breathing cycle is dramatically different from true stabilized PDF that resulted from many breathing cycles, it is expected that a probability-based sorting method capable of generating multiple breathing cycles of 4D images may capture breathing variation information missing from conventional single-cycle sorting methods. The overall idea is to identify a few main breathing cycles (and their corresponding weightings) that can best represent the main breathing patterns of the patient and then reconstruct a set of 4D images for each of the identified main breathing cycles. This method is implemented in three steps: (1) The breathing signal is decomposed into individual breathing cycles, characterized by amplitude, and period; (2) individual breathing cycles are grouped based on amplitude and period to determine the main breathing cycles. If a group contains more than 10% of all breathing cycles in a breathing signal, it is determined as a main breathing pattern group and is represented by the average of individual breathing cycles in the group; (3) for each main breathing cycle, a set of 4D images is reconstructed using a result-driven sorting method adapted from our previous study. The probability-based sorting method was first tested on 26 patients' breathing signals to evaluate its feasibility of improving target motion PDF. The new method was subsequently tested for a sequential image acquisition scheme on the 4D digital extended cardiac torso (XCAT) phantom. Performance of the probability-based and conventional sorting methods was evaluated in terms of target volume precision and accuracy as measured by the 4D images, and also the accuracy of average intensity projection (AIP) of 4D images. Probability-based sorting showed improved similarity of breathing motion PDF from 4D images to reference PDF compared to single cycle sorting, indicated by the significant increase in Dice similarity coefficient (DSC) (probability-based sorting, DSC = 0.89 ± 0.03, and single cycle sorting, DSC = 0.83 ± 0.05, p-value <0.001). Based on the simulation study on XCAT, the probability-based method outperforms the conventional phase-based methods in qualitative evaluation on motion artifacts and quantitative evaluation on tumor volume precision and accuracy and accuracy of AIP of the 4D images. In this paper the authors demonstrated the feasibility of a novel probability-based multicycle 4D image sorting method. The authors' preliminary results showed that the new method can improve the accuracy of tumor motion PDF and the AIP of 4D images, presenting potential advantages over the conventional phase-based sorting method for radiation therapy motion management.

SU‐E‐J‐158: A Phantom Study Based Simulation to Quantify the Motion and Tumor Volume Affected 18F‐FDG PET Uptake Distribution Within the Tumor

Purpose: Molecular imaging studies reveal tumor heterogeneity which may explain therapeutic resistance. Alternatively, variations observed in the SUV uptake may not be due to intrinsic heterogeneity of the tumor, but due to effects of position resolution (volume dependence) or tumor motion . The objective of this study is to evaluate motion artifacts on PET SUV uptake within tumors for different volumes. Methods: We conducted a phantom study: spheres of homogeneous18F‐FDG activity of motion amplitudes (0, 5, 10, 15, 20, 25, 30 mm) and volumes (internal diameter 10, 13, 17, 22, 28, 37 mm). Any variation observed in SUV uptake distribution with homogeneous activity spheres must be due to motion and volume effects. Therefore, we used this data to quantify uptake variations as a function of motion and volume. PET SUV uptake values for each tumor were fit with a Woods‐Saxon model with 2 parameters: radius and skin depth. When the ratio of radius to skin depth becomes small, this simplifies to a Gaussian. By using this parameterization for stationary phantoms, using the probability density function for motion, and using an image convolution technique we were able to simulate the SUV uptake distribution of moving tumor in the central 2D plane. Taking voxel by voxel SUV uptake distribution in 2D we quantified the accuracy of our simulation for motion affected, tumor volume affected SUV uptake heterogeneity within the phantom. Results: Phantom study for stationary spheres show motion has a high impact on SUV uptake distributions. Maximum percentage uptake variation across the phantoms was 22%. Convolution results confirm that motion is the largest contributor to the SUV heterogeneity of the tumors. Average difference between convolution and measurement is 6.7%. Conclusion: These results will impact the studies that utilize tumor heterogeneity such as tumor detection, planning with dose painting, and treatment response. UVA Radiation Oncology george Amarino Grant ‐ 2012

SU‐E‐T‐409: A Probability Density Function Based Dose Calculation for Gated Volumetric Modulated Arc Therapy in Lung Stereotactic Body Radiotherapy

Purpose: To evaluate the accuracy of probability density function based dose calculation for phase gated volumetric modulated arc therapy (VMAT) in lung stereotactic body radiotherapy, and to quantify the dose uncertainty induced by tumor motion. Methods: During VMAT gating delivery the tumor position, gantry, MLC leaves and dose rate change independently and continuously. To compute the accumulated dose, we convert the target motion into MLC motion for each control point by convolution of MLC leaf positions with target motion probability density function. The new VMAT plan file was imported back to treatment planning system (Eclipse) to reconstruct the dose distribution. The planar dose distribution was compared to a mobile phantom (QUASAR) measurement with the gating technique with an amplitude gating window of 5 mm. This method mentioned above was used to compute the gated VMAT dose distribution and evaluate the motion effect to the PTV and GTV coverage and normal tissues. Results: The probability density function based VMAT gated dose calculation can greatly simplify the dose calculation procedure since only the reference/planning image is used for the accumulated dose calculation. Our results show good agreement between the modified plan and measured dose distribution. Calculated results show that motion can greatly reduce the PTV coverage but its effect on GTV coverage is insignificant for the gated VMAT for the treatment of lung cancer. The gated dose distribution is comparable to the static plan for spinal cord and lung dose. Conclusion: The dose distribution comparison shows good agreement between the modified plan and the measured dose distribution. The VMAT gated dose distribution can be calculated using the probability density function so that the accumulated dose calculation procedure can be greatly simplified.

Respiratory motion sampling in 4DCT reconstruction for radiotherapy

Phase-based and amplitude-based sorting techniques are commonly used in four-dimensional CT (4DCT) reconstruction. However, effect of these sorting techniques on 4D dose calculation has not been explored. In this study, the authors investigated a candidate 4DCT sorting technique by comparing its 4D dose calculation accuracy with that for phase-based and amplitude-based sorting techniques. An optimization model was formed using organ motion probability density function (PDF) in the 4D dose convolution. The objective function for optimization was defined as the maximum difference between the expected 4D dose in organ of interest and the 4D dose calculated using a 4DCT sorted by a candidate sampling method. Sorting samples, as optimization variables, were selected on the respiratory motion PDF assessed during the CT scanning. Breathing curves obtained from patients' 4DCT scanning, as well as 3D dose distribution from treatment planning, were used in the study. Given the objective function, a residual error analysis was performed, and k-means clustering was found to be an effective sampling scheme to improve the 4D dose calculation accuracy and independent with the patient-specific dose distribution. Patient data analysis demonstrated that the k-means sampling was superior to the conventional phase-based and amplitude-based sorting and comparable to the optimal sampling results. For phase-based sorting, the residual error in 4D dose calculations may not be further reduced to an acceptable accuracy after a certain number of phases, while for amplitude-based sorting, k-means sampling, and the optimal sampling, the residual error in 4D dose calculations decreased rapidly as the number of 4DCT phases increased to 6. An innovative phase sorting method (k-means method) is presented in this study. The method is dependent only on tumor motion PDF. It could provide a way to refine the phase sorting in 4DCT reconstruction and is effective for 4D dose accumulation. Optimized sorting techniques could achieve acceptable residuals (less than 0.5% of the prescription dose) using 6 sorting samples, which is much better than amplitude-based or phase-based sorting. Further increase in sorting phase number exceeding 6 or more may not be necessary when using the k-means sampling or optimal sampling points.

Mitigation of motion artifacts in CBCT of lung tumors based on tracked tumor motion during CBCT acquisition

An algorithm capable of mitigating respiratory motion blurring artifacts in cone-beam computed tomography (CBCT) lung tumor images based on the motion of the tumor during the CBCT scan is developed. The tumor motion trajectory and probability density function (PDF) are reconstructed from the acquired CBCT projection images using a recently developed algorithm Lewis et al (2010 Phys. Med. Biol. 55 2505–22). Assuming that the effects of motion blurring can be represented by convolution of the static lung (or tumor) anatomy with the motion PDF, a cost function is defined, consisting of a data fidelity term and a total variation regularization term. Deconvolution is performed through iterative minimization of this cost function. The algorithm was tested on digital respiratory phantom, physical respiratory phantom and patient data. A clear qualitative improvement is evident in the deblurred images as compared to the motion-blurred images for all cases. Line profiles show that the tumor boundaries are more accurately and clearly represented in the deblurred images. The normalized root-mean-squared error between the images used as ground truth and the motion-blurred images are 0.29, 0.12 and 0.30 in the digital phantom, physical phantom and patient data, respectively. Deblurring reduces the corresponding values to 0.13, 0.07 and 0.19. Application of a −700 HU threshold to the digital phantom results in tumor dimension measurements along the superior–inferior axis of 2.8, 1.8 and 1.9 cm in the motion-blurred, ground truth and deblurred images, respectively. Corresponding values for the physical phantom are 3.4, 2.7 and 2.7 cm. A threshold of −500 HU applied to the patient case gives measurements of 3.1, 1.6 and 1.7 cm along the SI axis in the CBCT, 4DCT and deblurred images, respectively. This technique could provide more accurate information about a lung tumor's size and shape on the day of treatment.

SU‐GG‐J‐88: Evaluation of Phase Sampling Methods for 4D Dose Accumulation

Purpose: Simplifications and reductions in 4D dose accumulation can be achieved using the motion probability density function (PDF) with properly selected weighting and sampling. One scheme to select phase sampling and weighting scheme is to use k‐means clustering from motion PDF. In this study, we investigated the accuracy and feasibility of this method for 4D dose construction. Method and Materials: Respiration curves from 6 patients and 15 static dose profiles were used in the evaluation. Motion PDFs were constructed from respiration curves for dose convolution and phase sampling. Four sampling schemes were compared: (1) Equal phase sampling; (2) Equal amplitude sampling; (3) K‐means clustering based sampling; (4) PDF and dose profile specific optimal sampling. The cumulative 4D dose from different methods were compared to the expected 4D dose. A digital motion phantom was constructed with dose computed at various displacements for 3D dose evaluation on the above methods. Mid phase dose profile through isocenter was used for optimization in method 4. Results: For dose profiles analysis, the residual errors (normalized to the maximum dose) for the method 1 to 4 are: 1.9+1.4%, 2.2±0.59%, 0.88±0.70%, and 0.55%±0.48%. For phantom study, the maximum residual errors are 7.8%, 3.6%, 2.9%, and 3.5%. The 3D gamma analysis passing rates are (dose difference 2%, distance to agreement 2mm, and dose threshold 30% of maximum dose): 96.1%, 99.6%, 99.7%, and 99.6%. Conclusion: K‐means clustering sampling is effective in 4D dose accumulation. Method 4 will be most accurate sampling method for single dose profile analysis, with all the information included for optimization. K‐means sampling has slightly larger residual error in dose profile approximation, but it applies to multiple dose profiles for a given PDF. In 3D dose analysis, k‐means sampling is the most effective and accurate among the four methods.

WE‐C‐204B‐06: Tumor Specific Reconstruction of Motion Probability Density Function from 4DCT

Purpose: The actual delivered dose to a moving tumor can deviate from prescribed dose not only during each fraction, but during each IMRT field. This deviation can be anticipated and incorporated into a treatment plan if the tumor specific motion probability density function (PDF) is accurately identified. In this study, a novel technique in determining the actual, tumor specific PDF of a moving gross tumor volume (GTV) is described and confirmed through phantom experiments using a quantitative approach of 4DCT imaging. Methods and Materials: We hypothesize that a PDF of the GTV can be obtained through weighted sums of phase‐sorted 4DCT images. Experimental validation is performed using a lung phantom attached to a programmable motion platform. The ground truth motion PDF of the targets was calculated through convolution of the motion pattern and the GTV dimension along the direction of motion. These PDF convolutions are compared to the normalized, reconstructed CT numbers obtained from averaging ten phase sorted 4DCT images after background subtraction. Results: The PDF reconstructed from averaged, weighted sets of 4DCT images was almost identical to the ground truth PDF in all comparisons made. Through sums of phase sorted 4DCT images, the resulting CT number represents a relative probability of finding some portion of the GTV in each geometric location (or voxel). In physical phantom reconstructions, the Pearson correlation coefficient between CT‐based PDF and the ground truth PDF was greater than .97 in all cases considered. An actual patient PDF was also evaluated in frontal and sagittal planes. Conclusions: Combining phase sorted CT images is an effective method in obtaining the actual tumor PDF as seen by an IMRT field. With the patient specific PDF, treatment planning to ensure proper target coverage can be achieved through intra‐field modulation, dose rate, and monitoring initial beam‐on phase.

Four-dimensional targeting error analysis in image-guided radiotherapy

Image-guided therapy (IGT) involves acquisition and processing of biomedical images to actively guide medical interventions. The proliferation of IGT technologies has been particularly significant in image-guided radiotherapy (IGRT), as a way to increase the tumor targeting accuracy. When IGRT is applied to moving tumors, image guidance becomes challenging, as motion leads to increased uncertainty. Different strategies may be applied to mitigate the effects of motion: each technique is related to a different technological effort and complexity in treatment planning and delivery. The objective comparison of different motion mitigation strategies can be achieved by quantifying the residual uncertainties in tumor targeting, to be detected by means of IGRT technologies. Such quantification requires an extension of targeting error theory to a 4D space, where the 3D tumor trajectory as a function of time measured (4D Targeting Error, 4DTE). Accurate 4DTE analysis can be represented by a motion probability density function, describing the statistical fluctuations of tumor trajectory. We illustrate the application of 4DTE analysis through examples, including weekly variations in tumor trajectory as detected by 4DCT, respiratory gating via external surrogates and real-time tumor tracking.

WE-B-350-02: Patient Motion &amp; 4D Inverse Planning

Motion of the patient and inner organs does not substantially change the spatial dose distribution in photon therapy in the room coordinate system, aside from the build-up region. In other words, organs move within a static “dose cloud”. Using this approximation it is easy to understand the consequences of motion: systematic errors (lack of accuracy) lead to an offset of the dose distribution in the frame of the organs, and random errors (lack of precision) lead to dose blurring. Dose blurring can be described in a statistical way by use of a motion probability (density) function (PDF). The motion-blurred dose distribution is obtained by a convolution of the “sharp” (static case) dose distribution with the motion PDF. This holds true for both inter- and intra-fraction motions. If intra-fraction motion is present during an IMRT treatment, the dose distribution will also be affected by an “interplay” effect, in addition to the blurring. It has been shown that the interplay effect averages out during the course of a fractionated treatment, and that it is usually negligible after a typical number of fractions. The convolution model relies on the linear superimposition principle, which holds true for dose values but not for the biological effect. This issue has recently been addressed and will be discussed. Several investigations have now looked at the feasibility of un-doing the motion blur through the use if intensity-modulation. In principle it should indeed be possible to de-convolve the motion PDF from the intensity maps, to compensate for motion effects. This approach has been called 4D optimization or 4D inverse planning. Motion de-convolution cannot, however, compensate motion effects exactly and it cannot be applied in a naïve straight-forward way, because that would lead to undeliverable intensity maps with sharp spikes and negative values. The method of choice is rather to include the motion PDF in the IMRT optimization process. It has been shown that this can indeed yield a surprisingly high degree of motion compensation and it can even compete with other motion compensation methods such as gated delivery. However, this is only true if the motion characteristics (the PDF) are known with great precision. If the actually realized motion PDF deviates substantially from the planned PDF, the method becomes less useful and can, in principle, make things worse. More recently, uncertainties in the knowledge of the motion characteristics have been taken into account by use of robust optimization techniques. With these one can now compensate for motion effects in an approximate way for a large class of motion characteristics. In terms of the sparing of normal structures, the results are in between the use of conventional margins and the idealistic case of perfect motion compensation. The resulting intensity maps exhibit “horns”, which can shave off a few mm from the margins. Educational Objectives: 1. Understand the concepts of motion blur and PDF. 2. Understand the idea of de-blurring a dose distribution through “4D” motion optimization. 3. Be able to discuss the relative potential and limitations of 4D motion optimization in comparison with margins and gating.

SU-GG-T-113: Using Probability Density Functions of Respiratory Motion to Model Motion Effects On Dose Distributions and Optimize Treatment Planning for Lung Cancers

Purpose: Respiratory motion is an important factor potentially contributing to excessive normal tissue irradiation in radiotherapy of lungcancers. This study uses the motion probability density function (PDF) to model the motion effects on dose distributions and incorporates this information to optimize treatment planning for lungcancers.Method and Materials:PDFs were calculated from the respiratory motion signals of 10 representative patients. Motion effects were evaluated by convolving static dose distributions with various PDFs. Based on a differential dose prescription with relative lower dose to the clinical target volume (CTV) than to the gross tumor volume (GTV), two strategies were proposed to incorporate PDFs into optimization of treatment planning. The first strategy used the GTV‐based‐ITV to ensure full dose to the GTV, and utilized the motion induced dose gradient to cover the CTV. The second strategy was to find an intensity‐modulated static dose distribution to best match the prescription dose gradient. Results: Motion effect on dose distributions was minimal in the axial direction. A 10‐mm motion amplitude induced a 3% dose reduction in the peripheral zone of the target. The motion effect was remarkable in the cranial‐caudal direction. It varied with the motion amplitude, but tended to be similar for various respiratory patterns. We found that the motion‐induced gradients resulting from motion with amplitudes of 10–15 mm would adequately cover the CTV (60–70% of the GTV dose). For motions 15 mm, an intensity modulated static dose distribution was generated to decrease the dose to the normal tissue beyond the CTV without compromising the GTV coverage. Conclusion: The effect of respiratory motion on dose gradients can be utilized to individualize treatment planning and minimize the lungdose.

WE-B-350-01: Adaptive Management of Patient Motion in Radiotherapy

Patient‐specific target margin and 4D inverse planning are two typical methods to include treatment relevant patient motion in the treatment planning. Internal target volume (ITV) is probably the earliest technique in constructing patient‐specific target volume to compensate for target motion. However, this method only considers motion geometric information in the construction without utilizing inter‐patient heterogeneity of dose distribution, therefore the target margin has not been minimized. In contrast, a recent development in patient‐specific target margin construction includes motion probability density function (pdf) directly in the 4D dose evaluation; therefore individual dose distribution is included in the target margin design. Utilizing 4D dose calculation, treatment plan can also be optimized by modulating beam intensity with respect to a pre‐measured patient motion pdf. Concept of utilizing non‐uniform beam intensity to compensate for temporal displacements of target position has been pointed out long time ago, however it has not been implemented until recent years. Process of designing beam intensity by including patient geometric variation or motion pdf in the dose calculation and inverse planning has been called 4D inverse planning. Since this planning process is based on organ displacement information in a frequency domain, instead of the spatial domain used in the gating and tracking techniques, it is insensitive to the uncertainties in the motion phase. However, uncertainties in pdf characteristics could significantly detriment the treatment qualities. The most significant variation in motion pattern is the target position baseline variation. Study has shown that inter‐treatment target baseline variation can be minimized efficiently using daily free breathing cone beam CTimaging location and patient repositioning. However, the relative position variation between target and normal organs, the dose response related organ volume variation, as well as intra‐treatment motion pattern variation cannot be easily corrected by repositioning the patient. Therefore, treatment feedback and adaptive planning modification become necessary. In principle, 4D inverse planning is a central part of adaptive planning modification, however to fully accomplish an adaptive planning, the dose distribution in organs of interest which has been delivered previously and may be delivered in future is also important factor and needs to be included in the objective evaluation for 4D planning optimization. Educational Objectives: 1. Understand the options of 4D planning. 2. Understand the sensitivity of 4D planning to the motion uncertainties. 3. Understand the key components of adaptive treatment process and their functions. Research on adaptive management of patient motion is partially supported by Elekta and Philips Research Funds.

Quantifying the interplay effect in prostate IMRT delivery using a convolution-based method.

The authors present a segment-based convolution method to account for the interplay effect between intrafraction organ motion and the multileaf collimator position for each particular segment in intensity modulated radiation therapy (IMRT) delivered in a step-and-shoot manner. In this method, the static dose distribution attributed to each segment is convolved with the probability density function (PDF) of motion during delivery of the segment, whereas in the conventional convolution method ("average-based convolution"), the static dose distribution is convolved with the PDF averaged over an entire fraction, an entire treatment course, or even an entire patient population. In the case of IMRT delivered in a step-and-shoot manner, the average-based convolution method assumes that in each segment the target volume experiences the same motion pattern (PDF) as that of population. In the segment-based convolution method, the dose during each segment is calculated by convolving the static dose with the motion PDF specific to that segment, allowing both intrafraction motion and the interplay effect to be accounted for in the dose calculation. Intrafraction prostate motion data from a population of 35 patients tracked using the Calypso system (Calypso Medical Technologies, Inc., Seattle, WA) was used to generate motion PDFs. These were then convolved with dose distributions from clinical prostate IMRT plans. For a single segment with a small number of monitor units, the interplay effect introduced errors of up to 25.9% in the mean CTV dose compared against the planned dose evaluated by using the PDF of the entire fraction. In contrast, the interplay effect reduced the minimum CTV dose by 4.4%, and the CTV generalized equivalent uniform dose by 1.3%, in single fraction plans. For entire treatment courses delivered in either a hypofractionated (five fractions) or conventional (> 30 fractions) regimen, the discrepancy in total dose due to interplay effect was negligible.

WE‐B‐BRB‐02: Patient Motion: Adaptive RT

Organ motion blurs dose distributions. The blurring can be described in a statistical way by use of a motion probability (density) function (PDF). The motion‐blurred dose distribution is obtained by a convolution of the “sharp” (static case) dose distribution with the motion PDF. This holds true for both inter‐ and intra‐fraction motions. If intra‐fraction motion is present during an IMRT treatment, the dose distribution will also be affected by an “interplay” effect, in addition to the blurring. It has been shown that the interplay effect averages out during the course of a fractionated treatment, and that it is usually negligible after a typical number of fractions. The convolution model relies on the linear superimposition principle, which holds true for dose values but not for the biological effect. This issue has recently been addressed and will be discussed.Several investigations have now looked at the feasibility of un‐doing the motion blur through the use if intensity‐modulation. In principle it should indeed be possible to de‐convolve the motion PDF from the intensity maps, to compensate for motion effects. This approach has been called 4D optimization or 4D inverse planning. Motion de‐convolution cannot, however, compensate motion effects exactly and it cannot be applied in a naïve straight‐forward way, because that would lead to undeliverable intensity maps with sharp spikes and negative values. The method of choice is rather to include the motion PDF in the IMRT optimization process. It has been shown that this can indeed yield a surprisingly high degree of motion compensation and it can even compete with other motion compensation methods such as gated delivery. However, this is only true if the motion characteristics (the PDF) are known with great precision. If the actually realized motion PDF deviates substantially from the planned PDF, the method becomes less useful and can, in principle, make things worse.More recently, uncertainties in the knowledge of the motion characteristics have been taken into account by use of robust optimization techniques. With these one can now compensate for motion effects in an approximate way for a large class of motion characteristics. In terms of the sparing of normal structures, the results are in between the use of conventional margins and the idealistic case of perfect motion compensation. The resulting intensity maps exhibit “horns”, which can shave off a few mm from the margins.Educational Objectives:1. Understand the concepts of motion blur and PDF.2. Understand the idea of de‐blurring a dose distribution through “4D” motion optimization.3. Be able to discuss the relative potential and limitations of 4D motion optimization in comparison with margins and gating.

MO‐E‐BRA‐03: Application of Robust Optimization in Lung Cancer Treatment

For lung tumors, the presence of motion due to breathing is a key source of uncertainty. Motion essentially blurs the static dose distribution, which can be thought of mathematically as a convolution of the static dose distribution with a probability density function (PDF) describing the motion. The 4D IMRT optimization/inverse planning method tries to undo this blurring effect by taking the motion PDF into account during the optimization of the intensity map. Such an approach is effective as a motion compensation technique, but only when the motion is highly reproducible over the entire treatment course. In terms of the PDF, “reproducibility” corresponds to witnessing the same PDF over the course of treatment that was observed in the treatment planning stage. However, if the realized PDF during treatment differs from the planning PDF, the subsequent convolution of the static dose distribution with the realized PDF may produce undesirable hot and cold spots.Robust optimization is a concept that has gained prominence in the optimization community for its wide applicability to problems with uncertain data. Real‐world problems are rarely, if ever, accompanied by noiseless data, hence, there is a natural motivation to incorporate this uncertainty into any optimization process. The robust framework we present builds on the 4D approach by explicitly accounting for the uncertain motion represented by uncertainty in the motion PDF. Instead of basing the optimization on one PDF, robust optimization uses a family of PDFs to create a static dose distribution that is less sensitive to variations in the motion.The robust framework allows us to craft solutions in the entire spectrum between the idealized 4D method, and a conservative, ITV‐like margin approach. A given intensity map that results from the robust optimization method will balance intensity‐modulation with intensity‐homogeneity in order to effectively trade off the sparing of healthy tissues with ensuring sufficient tumor coverage. Accordingly, the robust optimization method implicitly performs multi‐objective optimization on these competing objectives.Educational Objectives:1. Understand the concept of robust optimization.2. Understand the construction of robust treatment plans based on breathing motion PDFs.3. Understand the mathematical and dosimetric differences between treatment plans of varying levels of robustness.4. Understand the multi‐objective viewpoint of robust optimization.

The use of spatial dose gradients and probability density function to evaluate the effect of internal organ motion for prostate IMRT treatment planning

The aim of this study is to investigate the effects of internal organ motion on IMRT treatment planning of prostate patients using a spatial dose gradient and probability density function. Spatial dose distributions were generated from a Pinnacle3 planning system using a co-planar, five-field intensity modulated radiation therapy (IMRT) technique. Five plans were created for each patient using equally spaced beams but shifting the angular displacement of the beam by 15° increments. Dose profiles taken through the isocentre in anterior–posterior (A–P), right–left (R–L) and superior–inferior (S–I) directions for IMRT plans were analysed by exporting RTOG file data from Pinnacle. The convolution of the ‘static’ dose distribution D0(x, y, z) and probability density function (PDF), denoted as P(x, y, z), was used to analyse the combined effect of repositioning error and internal organ motion. Organ motion leads to an enlarged beam penumbra. The amount of percentage mean dose deviation (PMDD) depends on the dose gradient and organ motion probability density function. Organ motion dose sensitivity was defined by the rate of change in PMDD with standard deviation of motion PDF and was found to increase with the maximum dose gradient in anterior, posterior, left and right directions. Due to common inferior and superior field borders of the field segments, the sharpest dose gradient will occur in the inferior or both superior and inferior penumbrae. Thus, prostate motion in the S–I direction produces the highest dose difference. The PMDD is within 2.5% when standard deviation is less than 5 mm, but the PMDD is over 2.5% in the inferior direction when standard deviation is higher than 5 mm in the inferior direction. Verification of prostate organ motion in the inferior directions is essential. The margin of the planning target volume (PTV) significantly impacts on the confidence of tumour control probability (TCP) and level of normal tissue complication probability (NTCP). Smaller margins help to reduce the dose to normal tissues, but may compromise the dose coverage of the PTV. Lower rectal NTCP can be achieved by either a smaller margin or a steeper dose gradient between PTV and rectum. With the same DVH control points, the rectum has lower complication in the seven-beam technique used in this study because of the steeper dose gradient between the target volume and rectum. The relationship between dose gradient and rectal complication can be used to evaluate IMRT treatment planning. The dose gradient analysis is a powerful tool to improve IMRT treatment plans and can be used for QA checking of treatment plans for prostate patients.

Novel lung IMRT planning algorithms with nonuniform dose delivery strategy to account for respiratory motion

To effectively deliver radiation dose to lung tumors, respiratory motion has to be considered in treatment planning. In this paper we first present a new lung IMRT planning algorithm, referred as the dose shaping (DS) method, that shapes the dose distribution according to the probability distribution of the tumor over the breathing cycle to account for respiratory motion. In IMRT planning a dose-based convolution method was generally adopted to compensate for random organ motion by performing 4-D dose calculations using a tumor motion probability density function. We modified the CON-DOSE method to a dose volume histogram based convolution method (CON-DVH) that allows nonuniform dose distribution to account for respiratory motion. We implemented the two new planning algorithms on an in-house IMRT planning system that uses the Eclipse (Varian, Palo Alto, CA) planning workstation as the dose calculation engine. The new algorithms were compared with (1) the conventional margin extension approach in which margin is generated based on the extreme positions of the tumor, (2) the dose-based convolution method, and (3) gating with 3 mm residual motion. Dose volume histogram, tumor control probability, normal tissue complication probability, and mean lung dose were calculated and used to evaluate the relative performance of these approaches at the end-exhale phase of the respiratory cycle. We recruited six patients in our treatment planning study. The study demonstrated that the two new methods could significantly reduce the ipsilateral normal lung dose and outperformed the margin extension method and the dose-based convolution method. Compared with the gated approach that has the best performance in the low dose region, the two methods we proposed have similar potential to escalate tumor dose, but could be more efficient because dose is delivered continuously.

MO‐D‐ValA‐03: Inverse Planning Optimization with Organ Motion Probability

Organ motion blurs dose distributions. The blurring can be described in a statistical way by use of a motion probability (density) function (PDF). The motion‐blurred dose distribution is obtained by a convolution of the “sharp” (static case) dose distribution with the motion PDF. This holds true for both inter‐ and intra‐fraction motions. In the case of intra‐fraction motions an “interplay” effect is superimposed on top of the blurring effect. It has been shown that the interplay effect averages out during the course of a fractionated treatment, and that it is usually negligible after a typical number of fractions. The convolution model relies on the linear superimposition principle, which holds true for dose values but not for the biological effect. This issue has recently been addressed and will be discussed.Several investigations have now looked at the feasibility of un‐doing the motion blur through the use if intensity‐modulation. In principle it should indeed be possible to de‐convolve the motion PDF from the intensity maps, in order to compensate motion effects. This approach has been called 4D optimization or 4D inverse planning. Motion de‐convolution cannot, however, compensate motion effects exactly and it cannot be applied in a naïve straight‐forward way, because that would lead to undeliverable intensity maps with sharp spikes and negative values. The method of choice is rather to include the motion PDF in the IMRT optimization process. It has been shown that this can indeed yield a surprisingly high degree of motion compensation and it can even compete with other motion compensation methods such as gated delivery. However, this is only true if the motion characteristics (the PDF) are known with great precision. If the actually realized motion PDF deviates substantially from the planned PDF, the method becomes less useful and can, in principle, make things worse. More recently, uncertainties in the knowledge of the motion characteristics have been taken into account by use of robust optimization techniques. With these one can now compensate for motion effects in an approximate way for a large class of motion characteristics. In terms of the sparing of normal structures, the results are in between the use of conventional margins and the idealistic case of perfect motion compensation. The resulting intensity maps exhibit “horns”, which can shave off a few mm from the margins.Educational Objectives:1. Understand the concepts of motion blur and PDF.2. Understand the idea of de‐blurring a dose distribution through “4D” motion optimization.3. Be able to discuss the relative potential and limitations of 4D motion optimization in comparison with margins and gating.

A robust approach to IMRT optimization

Managing uncertainty is a major challenge in radiation therapy treatment planning, including uncertainty induced by intrafraction motion, which is particularly important for tumours in the thorax and abdomen. Common methods to account for motion are to introduce a margin or to convolve the static dose distribution with a motion probability density function. Unlike previous work in this area, our development does not assume that the patient breathes according to a fixed distribution, nor is the patient required to breathe the same way throughout the treatment. Despite this generality, we create a robust optimization framework starting from the convolution method that is robust to fluctuations in breathing motion, yet spares healthy tissue better than a margin solution. We describe how to generate the data for our model using breathing motion data and we test our model on a computer phantom using data from real patients. In our numerical results, the robust solution delivers approximately 38% less dose to the healthy tissue than the margin solution, while providing the same level of protection against breathing uncertainty.

WE‐D‐T‐6E‐01: A New Lung IMRT Planning Algorithm with Dose Shaping Strategy to Compensate for Respiratory Motion

Purpose: To develop a new lung IMRT planning algorithm that shapes dose distributions to the probability distribution of the tumor over the breathing cycle in order to compensate for respiratory motion, thereby enabling tumor dose escalation. Method and Materials: We implemented a new optimization algorithm on an in‐house IMRT planning system on an Eclipse (r) workstation (Varian, Palo Alto). Our new dose shaping algorithm makes the dose of each voxel on the 3‐D dataset proportional to its probability of being inside the tumor over the respiratory cycle. The maximum dose is set to be the prescription dose multiplied by the ratio of the volume encompassed by the extreme positions of the tumor to the tumor volume. We also implemented two other popular approaches: (1) an optimal margin method in which the margin is generated based on the extreme positions of the tumor; and (2) a convolution method that performs 4‐D dose calculations using a modeled tumor motion probability density function. A simulated 4‐D CT dataset, which was generated by superimposing the patient's respiratory motion pattern onto one's 3‐D CT dataset, was used to evaluate the performance of these three approaches via DVH comparison for the inhale phase of the breathing. Results: Five‐field 6MV beams were used for all plans delivering a total dose of 63Gy in 35 fractions. Comparing to the IMRT plan with optimal margin, the convolution method reduced the mean dose to the ipsilateral lung by 5% while maintaining the same tumor coverage. Compared to the convolution method, our dose shaping method achieved the same lung sparing, but is much faster and has the extra ability to escalate tumor dose: 95% tumor received more than 72Gy. Conclusion: Dose shaping method is able to spare the healthy lung tissue, and has the capacity to further facilitate dose escalation.