| 11. | Quantifying the contribution of NHL player types to team performance Journal Article T. C. Y. Chan, J. A. Cho, D. C. Novati In: Interfaces, vol. 42, pp. 131-145, 2012. @article{ChanTCY.J007,
title = {Quantifying the contribution of NHL player types to team performance},
author = {T. C. Y. Chan and J. A. Cho and D. C. Novati},
doi = {10.1287/inte.1110.0612},
year = {2012},
date = {2012-03-01},
journal = {Interfaces},
volume = {42},
pages = {131-145},
abstract = {In this paper, we use k-means clustering to define distinct player types for each of the three positions on a National Hockey League (NHL) team and then use regression to determine a quantitative relationship between team performance and the player types identified in the clustering. Using NHL regular-season data from 2005–2010, we identify four forward types, four defensemen types, and three goalie types. Goalies tend to contribute the most to team performance, followed by forwards and then defensemen. We also show that once we account for salary cap and playing-time information, the value of different player types may become similar. Lastly, we illustrate how to use the regression results to analyze trades and their impact on team performance.},
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In this paper, we use k-means clustering to define distinct player types for each of the three positions on a National Hockey League (NHL) team and then use regression to determine a quantitative relationship between team performance and the player types identified in the clustering. Using NHL regular-season data from 2005–2010, we identify four forward types, four defensemen types, and three goalie types. Goalies tend to contribute the most to team performance, followed by forwards and then defensemen. We also show that once we account for salary cap and playing-time information, the value of different player types may become similar. Lastly, we illustrate how to use the regression results to analyze trades and their impact on team performance. |
| 10. | Split personalities of NHL players: Using clustering, projection and regression to measure individual point shares Proceedings Article T. C. Y. Chan, D. C. Novati In: Proceedings of the 6th Annual MIT Sloan Sports Analytics Conference, 2012. @inproceedings{ChanTCY.Oth003c,
title = {Split personalities of NHL players: Using clustering, projection and regression to measure individual point shares},
author = {T. C. Y. Chan and D. C. Novati},
url = {http://www.sloansportsconference.com/wp-content/uploads/2012/02/59-Chan_Novati_Split-personalities-of-NHL-players.pdf},
year = {2012},
date = {2012-03-01},
booktitle = {Proceedings of the 6th Annual MIT Sloan Sports Analytics Conference},
abstract = {Recent literature in hockey analytics has considered the use of clustering to determine specific categories or types of NHL players. Regression analysis has then been used to measure the contribution of each of these player types to team performance. This paper uses a combination of clustering, projection and regression methods to individualize the classification of NHL players. Instead of assigning each player to only one type, the overall "personality" of the player is split into fractional components representing different player types. The result is a unique make-up for each player, which is used to quantify his individual contributions to his team's performance, a metric known as "point shares". Top ranked players in terms of point shares tend to be winners of major NHL awards, are leaders in scoring, and have the highest salaries. High point shares in a contract year may also factor into salary increases. Overall, a better understanding of individual NHL player characteristics may provide a foundation for deeper, data-driven player analysis.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
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Recent literature in hockey analytics has considered the use of clustering to determine specific categories or types of NHL players. Regression analysis has then been used to measure the contribution of each of these player types to team performance. This paper uses a combination of clustering, projection and regression methods to individualize the classification of NHL players. Instead of assigning each player to only one type, the overall "personality" of the player is split into fractional components representing different player types. The result is a unique make-up for each player, which is used to quantify his individual contributions to his team's performance, a metric known as "point shares". Top ranked players in terms of point shares tend to be winners of major NHL awards, are leaders in scoring, and have the highest salaries. High point shares in a contract year may also factor into salary increases. Overall, a better understanding of individual NHL player characteristics may provide a foundation for deeper, data-driven player analysis. |
| 9. | Optimal margin and edge-enhanced intensity maps in the presence of motion and uncertainty Journal Article T. C. Y. Chan, J. N. Tsitsiklis, T. Bortfeld In: Physics in Medicine and Biology, vol. 55, pp. 515-533, 2010. @article{ChanTCY.J006,
title = {Optimal margin and edge-enhanced intensity maps in the presence of motion and uncertainty},
author = {T. C. Y. Chan and J. N. Tsitsiklis and T. Bortfeld},
doi = {10.1088/0031-9155/55/2/012},
year = {2010},
date = {2010-01-01},
journal = {Physics in Medicine and Biology},
volume = {55},
pages = {515-533},
abstract = {In radiation therapy, intensity maps involving margins have long been used to counteract the effects of dose blurring arising from motion. More recently, intensity maps with increased intensity near the edge of the tumour (edge enhancements) have been studied to evaluate their ability to offset similar effects that affect tumour coverage. In this paper, we present a mathematical methodology to derive margin and edge-enhanced intensity maps that aim to provide tumour coverage while delivering minimum total dose. We show that if the tumour is at most about twice as large as the standard deviation of the blurring distribution, the optimal intensity map is a pure scaling increase of the static intensity map without any margins or edge enhancements. Otherwise, if the tumour size is roughly twice (or more) the standard deviation of motion, then margins and edge enhancements are preferred, and we present formulae to calculate the exact dimensions of these intensity maps. Furthermore, we extend our analysis to include scenarios where the parameters of the motion distribution are not known with certainty, but rather can take any value in some range. In these cases, we derive a similar threshold to determine the structure of an optimal margin intensity map.},
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In radiation therapy, intensity maps involving margins have long been used to counteract the effects of dose blurring arising from motion. More recently, intensity maps with increased intensity near the edge of the tumour (edge enhancements) have been studied to evaluate their ability to offset similar effects that affect tumour coverage. In this paper, we present a mathematical methodology to derive margin and edge-enhanced intensity maps that aim to provide tumour coverage while delivering minimum total dose. We show that if the tumour is at most about twice as large as the standard deviation of the blurring distribution, the optimal intensity map is a pure scaling increase of the static intensity map without any margins or edge enhancements. Otherwise, if the tumour size is roughly twice (or more) the standard deviation of motion, then margins and edge enhancements are preferred, and we present formulae to calculate the exact dimensions of these intensity maps. Furthermore, we extend our analysis to include scenarios where the parameters of the motion distribution are not known with certainty, but rather can take any value in some range. In these cases, we derive a similar threshold to determine the structure of an optimal margin intensity map. |
| 8. | Experimental evaluation of a robust optimization method for IMRT of moving targets Journal Article C. Vrančić, A. Trofimov, T. C. Y. Chan, G. C. Sharp, T. Bortfeld In: Physics in Medicine and Biology, vol. 54, pp. 2901-2914, 2009. @article{ChanTCY.J005,
title = {Experimental evaluation of a robust optimization method for IMRT of moving targets},
author = {C. Vrančić and A. Trofimov and T. C. Y. Chan and G. C. Sharp and T. Bortfeld},
doi = {10.1088/0031-9155/54/9/021},
year = {2009},
date = {2009-03-25},
journal = {Physics in Medicine and Biology},
volume = {54},
pages = {2901-2914},
abstract = {Internal organ motion during radiation therapy, if not considered appropriately in the planning process, has been shown to reduce target coverage and increase the dose to healthy tissues. Standard planning approaches, which use safety margins to handle intrafractional movement of the tumor, are typically designed based on the maximum amplitude of motion, and are often overly conservative. Comparable coverage and reduced dose to healthy organs appear achievable with robust motion-adaptive treatment planning, which considers the expected probability distribution of the average target position and the uncertainty of its realization during treatment delivery. A dosimetric test of a robust optimization method for IMRT was performed, using patient breathing data. External marker motion data acquired from respiratory-gated radiotherapy patients were used to build and test the framework for robust optimization. The motion trajectories recorded during radiation treatment itself are not strictly necessary to generate the initial version of a robust treatment plan, but can be used to adapt the plan during the course of treatment. Single-field IMRT plans were optimized to deliver a uniform dose to a rectangular area. During delivery on a linear accelerator, a computer-driven motion phantom reproduced the patients' breathing patterns and a two-dimensional ionization detector array measured the dose delivered. The dose distributions from robust-optimized plans were compared to those from standard plans, which used a margin expansion. Dosimetric tests confirmed the improved sparing of the non-target area with robust planning, which was achieved without compromising the target coverage. The maximum dose in robust plans did not exceed 110% of the prescription, while the minimum target doses were comparable in standard and robust plans. In test courses, optimized for a simplified target geometry, and delivered to a phantom that moved in one dimension with an average amplitude of 17 mm, the robust treatment design produced a reduction of more than 12% of the integral dose to non-target areas, compared to the standard plan using 10 mm margin expansion.},
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Internal organ motion during radiation therapy, if not considered appropriately in the planning process, has been shown to reduce target coverage and increase the dose to healthy tissues. Standard planning approaches, which use safety margins to handle intrafractional movement of the tumor, are typically designed based on the maximum amplitude of motion, and are often overly conservative. Comparable coverage and reduced dose to healthy organs appear achievable with robust motion-adaptive treatment planning, which considers the expected probability distribution of the average target position and the uncertainty of its realization during treatment delivery. A dosimetric test of a robust optimization method for IMRT was performed, using patient breathing data. External marker motion data acquired from respiratory-gated radiotherapy patients were used to build and test the framework for robust optimization. The motion trajectories recorded during radiation treatment itself are not strictly necessary to generate the initial version of a robust treatment plan, but can be used to adapt the plan during the course of treatment. Single-field IMRT plans were optimized to deliver a uniform dose to a rectangular area. During delivery on a linear accelerator, a computer-driven motion phantom reproduced the patients' breathing patterns and a two-dimensional ionization detector array measured the dose delivered. The dose distributions from robust-optimized plans were compared to those from standard plans, which used a margin expansion. Dosimetric tests confirmed the improved sparing of the non-target area with robust planning, which was achieved without compromising the target coverage. The maximum dose in robust plans did not exceed 110% of the prescription, while the minimum target doses were comparable in standard and robust plans. In test courses, optimized for a simplified target geometry, and delivered to a phantom that moved in one dimension with an average amplitude of 17 mm, the robust treatment design produced a reduction of more than 12% of the integral dose to non-target areas, compared to the standard plan using 10 mm margin expansion. |
| 7. | Robust management of motion uncertainty in intensity modulated radiation therapy Journal Article T. Bortfeld, T. C. Y. Chan, A. Trofimov, J. N. Tsitsiklis In: Operations Research, vol. 56, pp. 1461-1473, 2008. @article{ChanTCY.J004,
title = {Robust management of motion uncertainty in intensity modulated radiation therapy},
author = {T. Bortfeld and T. C. Y. Chan and A. Trofimov and J. N. Tsitsiklis},
doi = {10.1287/opre.1070.0484},
year = {2008},
date = {2008-04-01},
journal = {Operations Research},
volume = {56},
pages = {1461-1473},
abstract = {Radiation therapy is subject to uncertainties that need to be accounted for when determining a suitable treatment plan for a cancer patient. For lung and liver tumors, the presence of breathing motion during treatment is a challenge to the effective and reliable delivery of the radiation. In this paper, we build a model of motion uncertainty using probability density functions that describe breathing motion, and provide a robust formulation of the problem of optimizing intensity-modulated radiation therapy. We populate our model with real patient data and measure the robustness of the resulting solutions on a clinical lung example. Our robust framework generalizes current mathematical programming formulations that account for motion, and gives insight into the trade-off between sparing the healthy tissues and ensuring that the tumor receives sufficient dose. For comparison, we also compute solutions to a nominal (no uncertainty) and margin (worst-case) formulation. In our experiments, we found that the nominal solution typically underdosed the tumor in the unacceptable range of 6% to 11%, whereas the robust solution underdosed by only 1% to 2% in the worst case. In addition, the robust solution reduced the total dose delivered to the main organ-at-risk (the left lung) by roughly 11% on average, as compared to the margin solution.},
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Radiation therapy is subject to uncertainties that need to be accounted for when determining a suitable treatment plan for a cancer patient. For lung and liver tumors, the presence of breathing motion during treatment is a challenge to the effective and reliable delivery of the radiation. In this paper, we build a model of motion uncertainty using probability density functions that describe breathing motion, and provide a robust formulation of the problem of optimizing intensity-modulated radiation therapy. We populate our model with real patient data and measure the robustness of the resulting solutions on a clinical lung example. Our robust framework generalizes current mathematical programming formulations that account for motion, and gives insight into the trade-off between sparing the healthy tissues and ensuring that the tumor receives sufficient dose. For comparison, we also compute solutions to a nominal (no uncertainty) and margin (worst-case) formulation. In our experiments, we found that the nominal solution typically underdosed the tumor in the unacceptable range of 6% to 11%, whereas the robust solution underdosed by only 1% to 2% in the worst case. In addition, the robust solution reduced the total dose delivered to the main organ-at-risk (the left lung) by roughly 11% on average, as compared to the margin solution. |
| 6. | Tumor trailing strategy for intensity-modulated radiation therapy of moving targets Journal Article A. Trofimov, C. Vrancic, T. C. Y. Chan, G. C. Sharp, T. Bortfeld In: Medical Physics, vol. 35, pp. 1718-1733, 2008. @article{ChanTCY.J003,
title = {Tumor trailing strategy for intensity-modulated radiation therapy of moving targets},
author = {A. Trofimov and C. Vrancic and T. C. Y. Chan and G. C. Sharp and T. Bortfeld},
doi = {10.1118/1.2900108},
year = {2008},
date = {2008-02-22},
journal = {Medical Physics},
volume = {35},
pages = {1718-1733},
abstract = {Internal organ motion during the course of radiation therapy of cancer affects the distribution of the delivered dose and, generally, reduces its conformality to the targeted volume. Previously proposed approaches aimed at mitigating the effect of internal motion in intensity-modulated radiation therapy (IMRT) included expansion of the target margins, motion-correlated delivery (e.g., respiratory gating, tumor tracking), and adaptive treatment plan optimization employing a probabilistic description of motion. We describe and test the tumor trailing strategy, which utilizes the synergy of motion-adaptive treatment planning and delivery methods. We regard the (rigid) target motion as a superposition of a relatively fast cyclic component (e.g., respiratory) and slow aperiodic trends (e.g., the drift of exhalation baseline). In the trailing approach, these two components of motion are decoupled and dealt with separately. Real-time motion monitoring is employed to identify the 'slow' shifts, which are then corrected by applying setup adjustments. The delivery does not track the target position exactly, but trails the systematic trend due to the delay between the time a shift occurs, is reliably detected, and, subsequently, corrected. The 'fast' cyclic motion is accounted for with a robust motion-adaptive treatment planning, which allows for variability in motion parameters (e.g., mean and extrema of the tidal volume, variable period of respiration, and expiratory duration). Motion-surrogate data from gated IMRT treatments were used to provide probability distribution data for motion-adaptive planning and to test algorithms that identified systematic trends in the character of motion. Sample IMRT fields were delivered on a clinical linear accelerator to a programmable moving phantom. Dose measurements were performed with a commercial two-dimensional ion-chamber array. The results indicate that by reducing intrafractional motion variability, the trailing strategy enhances relevance and applicability of motion-adaptive planning methods, and improves conformality of the delivered dose to the target in the presence of irregular motion. Trailing strategy can be applied to respiratory-gated treatments, in which the correction for the slow motion can increase the duty cycle, while robust probabilistic planning can improve management of the residual motion within the gate window. Similarly, trailing may improve the dose conformality in treatment of patients who exhibit detectable target motion of low amplitude, which is considered insufficient to provide a clinical indication for the use of respiratory-gated treatment (e.g., peak-to-peak motion of less than 10 mm). The mechanical limitations of implementing tumor trailing are less rigorous than those of real-time tracking, and the same technology could be used for both.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Internal organ motion during the course of radiation therapy of cancer affects the distribution of the delivered dose and, generally, reduces its conformality to the targeted volume. Previously proposed approaches aimed at mitigating the effect of internal motion in intensity-modulated radiation therapy (IMRT) included expansion of the target margins, motion-correlated delivery (e.g., respiratory gating, tumor tracking), and adaptive treatment plan optimization employing a probabilistic description of motion. We describe and test the tumor trailing strategy, which utilizes the synergy of motion-adaptive treatment planning and delivery methods. We regard the (rigid) target motion as a superposition of a relatively fast cyclic component (e.g., respiratory) and slow aperiodic trends (e.g., the drift of exhalation baseline). In the trailing approach, these two components of motion are decoupled and dealt with separately. Real-time motion monitoring is employed to identify the 'slow' shifts, which are then corrected by applying setup adjustments. The delivery does not track the target position exactly, but trails the systematic trend due to the delay between the time a shift occurs, is reliably detected, and, subsequently, corrected. The 'fast' cyclic motion is accounted for with a robust motion-adaptive treatment planning, which allows for variability in motion parameters (e.g., mean and extrema of the tidal volume, variable period of respiration, and expiratory duration). Motion-surrogate data from gated IMRT treatments were used to provide probability distribution data for motion-adaptive planning and to test algorithms that identified systematic trends in the character of motion. Sample IMRT fields were delivered on a clinical linear accelerator to a programmable moving phantom. Dose measurements were performed with a commercial two-dimensional ion-chamber array. The results indicate that by reducing intrafractional motion variability, the trailing strategy enhances relevance and applicability of motion-adaptive planning methods, and improves conformality of the delivered dose to the target in the presence of irregular motion. Trailing strategy can be applied to respiratory-gated treatments, in which the correction for the slow motion can increase the duty cycle, while robust probabilistic planning can improve management of the residual motion within the gate window. Similarly, trailing may improve the dose conformality in treatment of patients who exhibit detectable target motion of low amplitude, which is considered insufficient to provide a clinical indication for the use of respiratory-gated treatment (e.g., peak-to-peak motion of less than 10 mm). The mechanical limitations of implementing tumor trailing are less rigorous than those of real-time tracking, and the same technology could be used for both. |
| 5. | Optimization under uncertainty in radiation therapy PhD Thesis T. C. Y. Chan Sloan School of Management, MIT, 2007. @phdthesis{Chan2007,
title = {Optimization under uncertainty in radiation therapy},
author = {T. C. Y. Chan},
url = {https://dspace.mit.edu/handle/1721.1/40302},
year = {2007},
date = {2007-06-01},
address = {Operations Research Center},
school = {Sloan School of Management, MIT},
abstract = {In the context of patient care for life-threatening illnesses, the presence of uncertainty may compromise the quality of a treatment. In this thesis, we investigate robust approaches to managing uncertainty in radiation therapy treatments for cancer. In the first part of the thesis, we study the effect of breathing motion uncertainty on intensity-modulated radiation therapy treatments of a lung tumor. We construct a robust framework that generalizes current mathematical programming formulations that account for motion. This framework gives insight into the trade-off between sparing the healthy tissues and ensuring that the tumor receives sufficient dose. With this trade-off in mind, we show that our robust solution outperforms a nominal (no uncertainty) solution and a margin (worst-case) solution on a clinical case. Next, we perform an in-depth study into the structure of different intensity maps that were witnessed in the first part of the thesis. We consider parameterized intensity maps and investigate their ability to deliver a sufficient dose to the tumor in the presence of motion that follows a Gaussian distribution. We characterize the structure of optimal intensity maps in terms of certain conditions on the problem parameters. Finally, in the last part of the thesis, we study intensity-modulated proton therapy under uncertainty in the location of maximum dose deposited by the beamlets of radiation. We provide a robust formulation for the optimization of proton-based treatments and show that it outperforms traditional formulations in the face of uncertainty. In our computational experiments, we see evidence that optimal robust solutions use the physical characteristics of the proton beam to create dose distributions that are far less sensitive to the underlying uncertainty.},
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In the context of patient care for life-threatening illnesses, the presence of uncertainty may compromise the quality of a treatment. In this thesis, we investigate robust approaches to managing uncertainty in radiation therapy treatments for cancer. In the first part of the thesis, we study the effect of breathing motion uncertainty on intensity-modulated radiation therapy treatments of a lung tumor. We construct a robust framework that generalizes current mathematical programming formulations that account for motion. This framework gives insight into the trade-off between sparing the healthy tissues and ensuring that the tumor receives sufficient dose. With this trade-off in mind, we show that our robust solution outperforms a nominal (no uncertainty) solution and a margin (worst-case) solution on a clinical case. Next, we perform an in-depth study into the structure of different intensity maps that were witnessed in the first part of the thesis. We consider parameterized intensity maps and investigate their ability to deliver a sufficient dose to the tumor in the presence of motion that follows a Gaussian distribution. We characterize the structure of optimal intensity maps in terms of certain conditions on the problem parameters. Finally, in the last part of the thesis, we study intensity-modulated proton therapy under uncertainty in the location of maximum dose deposited by the beamlets of radiation. We provide a robust formulation for the optimization of proton-based treatments and show that it outperforms traditional formulations in the face of uncertainty. In our computational experiments, we see evidence that optimal robust solutions use the physical characteristics of the proton beam to create dose distributions that are far less sensitive to the underlying uncertainty. |
| 4. | Accounting for range uncertainties in the optimization of intensity modulated proton therapy Journal Article J. Unkelbach, T. C. Y. Chan, T. Bortfeld In: Physics in Medicine and Biology, vol. 52, pp. 2755-2773, 2007. @article{ChanTCY.J002,
title = {Accounting for range uncertainties in the optimization of intensity modulated proton therapy},
author = {J. Unkelbach and T. C. Y. Chan and T. Bortfeld},
doi = {10.1088/0031-9155/52/10/009},
year = {2007},
date = {2007-03-08},
journal = {Physics in Medicine and Biology},
volume = {52},
pages = {2755-2773},
abstract = {Treatment plans optimized for intensity modulated proton therapy (IMPT) may be sensitive to range variations. The dose distribution may deteriorate substantially when the actual range of a pencil beam does not match the assumed range. We present two treatment planning concepts for IMPT which incorporate range uncertainties into the optimization. The first method is a probabilistic approach. The range of a pencil beam is assumed to be a random variable, which makes the delivered dose and the value of the objective function a random variable too. We then propose to optimize the expectation value of the objective function. The second approach is a robust formulation that applies methods developed in the field of robust linear programming. This approach optimizes the worst case dose distribution that may occur, assuming that the ranges of the pencil beams may vary within some interval. Both methods yield treatment plans that are considerably less sensitive to range variations compared to conventional treatment plans optimized without accounting for range uncertainties. In addition, both approaches—although conceptually different—yield very similar results on a qualitative level.},
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Treatment plans optimized for intensity modulated proton therapy (IMPT) may be sensitive to range variations. The dose distribution may deteriorate substantially when the actual range of a pencil beam does not match the assumed range. We present two treatment planning concepts for IMPT which incorporate range uncertainties into the optimization. The first method is a probabilistic approach. The range of a pencil beam is assumed to be a random variable, which makes the delivered dose and the value of the objective function a random variable too. We then propose to optimize the expectation value of the objective function. The second approach is a robust formulation that applies methods developed in the field of robust linear programming. This approach optimizes the worst case dose distribution that may occur, assuming that the ranges of the pencil beams may vary within some interval. Both methods yield treatment plans that are considerably less sensitive to range variations compared to conventional treatment plans optimized without accounting for range uncertainties. In addition, both approaches—although conceptually different—yield very similar results on a qualitative level. |
| 3. | A robust approach to IMRT optimization Journal Article T. C. Y. Chan, T. Bortfeld, J. N. Tsitsiklis In: Physics in Medicine and Biology, vol. 51, pp. 2567-2583, 2006. @article{ChanTCY.J001,
title = {A robust approach to IMRT optimization},
author = {T. C. Y. Chan and T. Bortfeld and J. N. Tsitsiklis},
doi = {10.1088/0031-9155/51/10/014},
year = {2006},
date = {2006-01-26},
journal = {Physics in Medicine and Biology},
volume = {51},
pages = {2567-2583},
abstract = {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.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
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. |
| 2. | Single and multi-agent exploration of a Markov decision process Proceedings Article T. C. Y. Chan, E. Feron In: Proceedings of the 42nd Allerton Conference on Communication, Control, and Computing, 2004. @inproceedings{ChanTCY.Oth002c,
title = {Single and multi-agent exploration of a Markov decision process},
author = {T. C. Y. Chan and E. Feron},
year = {2004},
date = {2004-10-02},
booktitle = {Proceedings of the 42nd Allerton Conference on Communication, Control, and Computing},
abstract = {In this paper, we investigate the problem of efficiently visiting every state of a Birth-Death Markov Decision Process (BDP). In the single-agent case, we consider two different BDPs and derive their corresponding optimal policies - one being a pure greedy policy, and the other being a threshold policy based on greedy actions. We then generalize to a multi-agent setting and prove the optimality of a greedy policy in a related problem},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
In this paper, we investigate the problem of efficiently visiting every state of a Birth-Death Markov Decision Process (BDP). In the single-agent case, we consider two different BDPs and derive their corresponding optimal policies - one being a pure greedy policy, and the other being a threshold policy based on greedy actions. We then generalize to a multi-agent setting and prove the optimality of a greedy policy in a related problem |
