David Craft
Harvard University, Harvard Medical School, Faculty Member
ABSTRACT Purpose: Dose‐volume histogram (DVH) constraints are frequently used in IMRT planning. For example, a DVH constraint may state that 5% (but no more) of the voxels in the planning target volume may receive a dose below the... more
ABSTRACT Purpose: Dose‐volume histogram (DVH) constraints are frequently used in IMRT planning. For example, a DVH constraint may state that 5% (but no more) of the voxels in the planning target volume may receive a dose below the prescription level. We want to find out if the percentage of violating voxels can be reduced. We are also interested in the “price” of this reduction of violating voxels, in terms of dose to other voxels and other structures. Methods and Materials: We introduce DVH objectives into IMRT planning. Here the objective is to minimize the number of voxels that violate a given dose constraint. We then integrate DVH objectives into a multi‐criteria optimization (MCO) framework, to analyze the trade offs between DVH objectives and other planning objectives. Relaxation of mixed integer programs (MIPs) used to produce the trade off curve yields a good approximation. This is contrary to relaxation of an MIP with DVH constraints in the conventional framework. A heuristic then fine tunes the relaxation results. Results: Our methods are applied to two clinical cases with both a dose‐volume objective on the tumor and a maximum dose objective on OAR. The trade off curve between those two objectives is calculated in around 20 minutes with the relaxed MIPs compared to 40 hours with the nominal MIPs. The two techniques differ on average by only .77% tumor volume coverage and the heuristic reduces this difference to .35%. Conclusion: The use of DVH objectives (instead of DVH constraints) has the potential to lead to better trade offs in IMRT treatment planning. Surprisingly, DVH objectives simplify the numerical handling of the problem and reduce calculation times.
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We examined the potential risk of tuberculosis transmission if we modified our policy for release of patients from the "airborne precautions" category from three negative acid-fast bacillus (AFB) smears to two, or even one. Over... more
We examined the potential risk of tuberculosis transmission if we modified our policy for release of patients from the "airborne precautions" category from three negative acid-fast bacillus (AFB) smears to two, or even one. Over a 4-year period, respiratory cultures from 42 patients grew Mycobacterium tuberculosis. Of these, 36 patients (81%) had a positive AFB smear result on the first submitted specimen. One additional patient (2%) had a first smear-positive finding on the second submitted specimen, and no patients had a first smear-positive result on the third submitted specimen. Respiratory cultures from five patients (12%) grew M. tuberculosis without ever having a positive AFB smear result. These data indicate that in our institution, reducing the number of negative smears required before removal of patients from the airborne precautions category would pose little, if any, increase in the risk of spreading tuberculosis.
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ABSTRACT Purpose: To evaluate automated multicriteria optimization (MCO)-- designed for intensity modulated radiation therapy (IMRT), but invoked with limited segmentation -- to efficiently produce high quality 3D conformal treatment... more
ABSTRACT Purpose: To evaluate automated multicriteria optimization (MCO)-- designed for intensity modulated radiation therapy (IMRT), but invoked with limited segmentation -- to efficiently produce high quality 3D conformal treatment (3D-CRT) plans. Methods: Ten patients previously planned with 3D-CRT were replanned with a low-segment inverse multicriteria optimized technique. The MCO-3D plans used the same number of beams, beam geometry and machine parameters of the corresponding 3D plans, but were limited to an energy of 6 MV. The MCO-3D plans were optimized using a fluence-based MCO IMRT algorithm and then, after MCO navigation, segmented with a low number of segments. The 3D and MCO-3D plans were compared by evaluating mean doses to individual organs at risk (OARs), mean doses to combined OARs, homogeneity indexes (HI), monitor units (MUs), physician preference, and qualitative assessments of planning time and plan customizability. Results: The MCO-3D plans significantly reduced the OAR mean doses and monitor units while maintaining good coverage and homogeneity of target volumes. MCO allows for more streamlined plan customization. All MCO-3D plans were preferred by physicians over their corresponding 3D plans. Conclusion: High quality 3D plans can be produced using IMRT optimization technology, resulting in automated field-in-field type plans with good monitor unit efficiency. Adopting this technology in a clinic could streamline treatment plan production.
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The purpose of this study was to evaluate automated multicriteria optimization (MCO), which is designed for intensity modulated radiation therapy (IMRT) but invoked with limited segmentation, to efficiently produce high-quality... more
The purpose of this study was to evaluate automated multicriteria optimization (MCO), which is designed for intensity modulated radiation therapy (IMRT) but invoked with limited segmentation, to efficiently produce high-quality 3-dimensional (3D) conformal radiation therapy (3D-CRT) plans. Treatment for 10 patients previously planned with 3D-CRT to various disease sites (brain, breast, lung, abdomen, pelvis) was replanned with a low-segment inverse MCO technique. The MCO-3D plans used the same beam geometry of the original 3D plans but were limited to an energy of 6 MV. The MCO-3D plans were optimized with fluence-based MCO IMRT and then, after MCO navigation, segmented with a low number of segments. The 3D and MCO-3D plans were compared by evaluating mean dose for all structures, D95 (dose that 95% of the structure receives) and homogeneity indexes for targets, D1 and clinically appropriate dose-volume objectives for individual organs at risk (OARs), monitor units, and physician preference. The MCO-3D plans reduced the mean doses to OARs (41 of a total of 45 OARs had a mean dose reduction; P < .01) and monitor units (7 of 10 plans had reduced monitor units; the average reduction was 17% [P = .08]) while maintaining clinical standards for coverage and homogeneity of target volumes. All MCO-3D plans were preferred by physicians over their corresponding 3D plans. High-quality 3D plans can be produced by use of MCO-IMRT optimization, resulting in automated field-in-field-type plans with good monitor unit efficiency. Adoption of this technology in a clinic could improve plan quality and streamline treatment plan production by using a single system applicable to both IMRT and 3D planning.
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In the event of a smallpox bioterrorist attack in a large U.S. city, the interim response policy is to isolate symptomatic cases, trace and vaccinate their contacts, quarantine febrile contacts, but vaccinate more broadly if the outbreak... more
In the event of a smallpox bioterrorist attack in a large U.S. city, the interim response policy is to isolate symptomatic cases, trace and vaccinate their contacts, quarantine febrile contacts, but vaccinate more broadly if the outbreak cannot be contained by these measures. We embed this traced vaccination policy in a smallpox disease transmission model to estimate the number of cases and deaths that would result from an attack in a large urban area. Comparing the results to mass vaccination from the moment an attack is recognized, we find that mass vaccination results in both far fewer deaths and much faster epidemic eradication over a wide range of disease and intervention policy parameters, including those believed most likely, and that mass vaccination similarly outperforms the existing policy of starting with traced vaccination and switching to mass vaccination only if required.
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We present a method for improving the delivery efficiency of VMAT by extending the recently published VMAT treatment planning algorithm vmerge to automatically generate optimal partial-arc plans. A high-quality initial plan is created by... more
We present a method for improving the delivery efficiency of VMAT by extending the recently published VMAT treatment planning algorithm vmerge to automatically generate optimal partial-arc plans. A high-quality initial plan is created by solving a convex multicriteria optimization problem using 180 equi-spaced beams. This initial plan is used to form a set of dose constraints, and a set of partial-arc plans is created by searching the space of all possible partial-arc plans that satisfy these constraints. For each partial-arc, an iterative fluence map merging and sequencing algorithm (vmerge) is used to improve the delivery efficiency. Merging continues as long as the dose quality is maintained above a user-defined threshold. The final plan is selected as the partial-arc with the lowest treatment time. The complete algorithm is called pmerge. Partial-arc plans are created using pmerge for a lung, liver and prostate case, with final treatment times of 127, 245 and 147 . Treatment times using full arcs with vmerge are 211, 357 and 178 s. The mean doses to the critical structures for the vmerge and pmerge plans are kept within 5% of those in the initial plan, and the target volume covered by the prescription isodose is maintained above 98% for the pmerge and vmerge plans. Additionally, we find that the angular distribution of fluence in the initial plans is predictive of the start and end angles of the optimal partial-arc. We conclude that VMAT delivery efficiency can be improved by employing partial-arcs without compromising dose quality, and that partial-arcs are most applicable to cases with non-centralized targets.
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We consider the fractionation problem in radiation therapy. Tumor sites in which the dose-limiting organ at risk (OAR) receives a substantially lower dose than the tumor, bear potential for hypofractionation even if the α/β-ratio of the... more
We consider the fractionation problem in radiation therapy. Tumor sites in which the dose-limiting organ at risk (OAR) receives a substantially lower dose than the tumor, bear potential for hypofractionation even if the α/β-ratio of the tumor is larger than the α/β-ratio of the OAR. In this work, we analyze the interdependence of the optimal fractionation scheme and the spatial dose distribution in the OAR. In particular, we derive a criterion under which a hypofractionation regimen is indicated for both a parallel and a serial OAR. The approach is based on the concept of the biologically effective dose (BED). For a hypothetical homogeneously irradiated OAR, it has been shown that hypofractionation is suggested by the BED model if the α/β-ratio of the OAR is larger than α/β-ratio of the tumor times the sparing factor, i.e. the ratio of the dose received by the tumor and the OAR. In this work, we generalize this result to inhomogeneous dose distributions in the OAR. For a parallel OAR, we determine the optimal fractionation scheme by minimizing the integral BED in the OAR for a fixed BED in the tumor. For a serial structure, we minimize the maximum BED in the OAR. This leads to analytical expressions for an effective sparing factor for the OAR, which provides a criterion for hypofractionation. The implications of the model are discussed for lung tumor treatments. It is shown that the model supports hypofractionation for small tumors treated with rotation therapy, i.e. highly conformal techniques where a large volume of lung tissue is exposed to low but nonzero dose. For larger tumors, the model suggests hyperfractionation. We further discuss several non-intuitive interdependencies between optimal fractionation and the spatial dose distribution. For instance, lowering the dose in the lung via proton therapy does not necessarily provide a biological rationale for hypofractionation.
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Unlike conventional optimization with dose-volume (DV) constraints, multi-criteria optimization (MCO) with DV objectives provides tradeoff information which we believe is necessary for choosing better treatment plans. We show that the MCO... more
Unlike conventional optimization with dose-volume (DV) constraints, multi-criteria optimization (MCO) with DV objectives provides tradeoff information which we believe is necessary for choosing better treatment plans. We show that the MCO formulation with DV objectives is better suited to convex approximation than conventional formulations with DV constraints. We provide a relaxation of the integer programming formulation which reduces the computation time for a single plan from over 5 h to about 2 min, without significantly compromising the results. We also derive a heuristic to improve on the relaxed solutions, adding only a few additional minutes of computation time. We apply these techniques to a skull based tumour case and a paraspinal tumour case. Based on a careful examination of the driving terms in the relaxed formulation and the heuristic, we argue that our techniques should apply more generally for DV objectives in multi-objective IMRT treatment planning.
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Multiobjective radiotherapy planning aims to capture all clinically relevant trade-offs between the various planning goals. This is accomplished by calculating a representative set of Pareto optimal solutions and storing them in a... more
Multiobjective radiotherapy planning aims to capture all clinically relevant trade-offs between the various planning goals. This is accomplished by calculating a representative set of Pareto optimal solutions and storing them in a database. The structure of these representative Pareto sets is still not fully investigated. We propose two methods for a systematic analysis of multiobjective databases: principal component analysis and the isomap method. Both methods are able to extract the key trade-offs from a database and provide information which can lead to a better understanding of the clinical case and intensity-modulated radiation therapy planning in general.
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To formulate and solve the fluence-map merging procedure of the recently-published VMAT treatment-plan optimization method, called VMERGE, as a bi-criteria optimization problem. Using an exact merging method rather than the... more
To formulate and solve the fluence-map merging procedure of the recently-published VMAT treatment-plan optimization method, called VMERGE, as a bi-criteria optimization problem. Using an exact merging method rather than the previously-used heuristic, we are able to better characterize the trade-off between the delivery efficiency and dose quality. VMERGE begins with a solution of the fluence-map optimization problem with 180 equi-spaced beams that yields the 'ideal' dose distribution. Neighboring fluence maps are then successively merged, meaning that they are added together and delivered as a single map. The merging process improves the delivery efficiency at the expense of deviating from the initial high-quality dose distribution. We replace the original merging heuristic by considering the merging problem as a discrete bi-criteria optimization problem with the objectives of maximizing the treatment efficiency and minimizing the deviation from the ideal dose. We formulate this using a network-flow model that represents the merging problem. Since the problem is discrete and thus non-convex, we employ a customized box algorithm to characterize the Pareto frontier. The Pareto frontier is then used as a benchmark to evaluate the performance of the standard VMERGE algorithm as well as two other similar heuristics. We test the exact and heuristic merging approaches on a pancreas and a prostate cancer case. For both cases, the shape of the Pareto frontier suggests that starting from a high-quality plan, we can obtain efficient VMAT plans through merging neighboring fluence maps without substantially deviating from the initial dose distribution. The trade-off curves obtained by the various heuristics are contrasted and shown to all be equally capable of initial plan simplifications, but to deviate in quality for more drastic efficiency improvements. This work presents a network optimization approach to the merging problem. Contrasting the trade-off curves of the merging heuristics against the Pareto approximation validates that heuristic approaches are capable of achieving high-quality merged plans that lie close to the Pareto frontier.
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Research Interests: Management Science, Probability, Biological Sciences, Time-Delay Systems, Disease Outbreaks, and 17 moreEmergency Response, Humans, Mathematical Sciences, Bioterrorism, Smallpox, Probabilistic reasoning, Capacity Planning, Vaccination, Probabilistic Analysis, Queueing, Spatial Distribution, Health Care Rationing, Animals and disease transmission, Disease Progression, Differential equation, Mathematical Biosciences, and Hospital Care
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Radiotherapy planning involves inherent tradeoffs: the primary mission, to treat the tumor with a high, uniform dose, is in conflict with normal tissue sparing. We seek to understand these tradeoffs on a case-to-case basis, by computing... more
Radiotherapy planning involves inherent tradeoffs: the primary mission, to treat the tumor with a high, uniform dose, is in conflict with normal tissue sparing. We seek to understand these tradeoffs on a case-to-case basis, by computing for each patient a database of Pareto optimal plans. A treatment plan is Pareto optimal if there does not exist another plan which is better in every measurable dimension. The set of all such plans is called the Pareto optimal surface. This article presents an algorithm for computing well distributed points on the (convex) Pareto optimal surface of a multiobjective programming problem. The algorithm is applied to intensity-modulated radiation therapy inverse planning problems, and results of a prostate case and a skull base case are presented, in three and four dimensions, investigating tradeoffs between tumor coverage and critical organ sparing.
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ABSTRACT Purpose: To solve the beam angle optimization (BAO) problem of IMPT to provable near‐global optimality. Global BAO, the selection of a given small number of beams from a large set of candidate beams, remains computationally hard... more
ABSTRACT Purpose: To solve the beam angle optimization (BAO) problem of IMPT to provable near‐global optimality. Global BAO, the selection of a given small number of beams from a large set of candidate beams, remains computationally hard due to the large scale and combinatorial nature of the problem. Exhaustive search is computationally prohibited. Stochastic optimization and local search have been used but confidence in global optimality cannot be established. Methods: We use a fast projection solver for the multi‐criteria robust IMPT optimization. Equally spaced 36 beams are optimized initially to generate a global optimal solution. The 36‐beam plan is then reduced to a 3‐beam plan by iteratively removing the beam with least average intensity and re‐optimizing subjected to 3% relaxation on the best objective value. The true optimal 3‐beam plan is also found by exhaustive search as a benchmark. Results: We apply the method to a chordoma case and an orbital rhabdomyosarcoma case. The optimal 3‐beam plan is only 3–5% worse than the optimal 36‐beam plan in terms of the objective value. The 3‐beam plan efficiently reduced from the 36‐beam optimal plan is almost as good as the optimal 3‐beam plan. There exist a large number of nearly optimal 3‐beam combinations. For these two cases our method finds near‐global optimal plan using 3 beams in a time scale of minutes. Exhaustive search would take on the order of days. Conclusion: We find that IMPT plans using 3 or 4 beams are only marginally improved by adding more beams. By exploiting the high degeneracy of the solution space, we present an efficient column reducing framework for global IMPT BAO. It first finds an optimal many‐beam plan and then uses the column reducing approach to produce a plan with a small number of beams at a user‐selected tolerance from the global optimal plan. This work was supported in part by NCI Grant P01 CA21239 Proton Radiation Therapy Research and NCI Grant R01 CA103904‐01A1 Multi‐criteria IMRT Optimization.