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Title: Beam Selection in Radiotherapy Design
Author: M. Ehrgott, A. Holder and J. Reese
URL:
http://lagrange.math.trinity.edu/tumath/research/reports/report95.pdf
The optimal design of a radiotherapy treatment depends on the collection of directions from which radiation is focused on the patient. These directions are manually selected by a physician and are typically based on the physician's previous experiences. Once the angles are chosen, there are numerous optimization models that decide a fluency pattern (exposure times) that best treats a patient. So, while optimization techniques are often used to decide the length of time a patient is exposed to a high-energy particle beam, the directions themselves are not optimized. The problem with optimally selecting directions is that the underlying mixed integer models are well beyond our current solution capability. We present a rigorous mathematical development of the beam selection problem that provides a unified framework for the problem of selecting beam directions. This presentation provides insights into the techniques suggested in the literature and highlights the difficulty of the problem. We also compare several techniques head-to-head on clinically relevant, two-dimensional problems.
Title: Fast Simultaneous Angle, Wedge, and Beam Intensity
Optimization in Inverse Radiotherapy Planning
Author:
Konrad Engel and Eckhard Tabbert
URL: ftp://ftp.math.uni-rostock.de/pub/preprint/2003/pre03_06.pdf
We present a new fast radiotherapy planning algorithm which determines approximatively optimal gantry and table angles, kinds of wedges, leaf positions and intensities simultaneously in a global way. Other parameters are optimized only independently of each other. The algorithm uses an elaborate field management and field reduction. Beam intensities are determined via a variant of a projected Newton method of Bertsekas. The objective function is a standard piecewise quadratic penalty function, but it is built with efficient upper bounds which are calculated during the optimization process. Instead of pencil beams, basic leaf positions are included. The algorithm is implemented in the new beam modelling and dose optimization module Homo OptiS.
Title: Continuous optimization of beamlet intensities
for photon and proton radiotherapy
Author: R. Reemtsen and M. Alber
URL:
http://www.math.tu-cottbus.de/INSTITUT/lsing1/publications/reemtsen_e.html
Inverse approaches and, in particular, intensity modulated radiotherapy (IMRT), in combination with the development of new technologies such as multi-leaf collimators (MLCs), have enabled new potentialities of radiotherapy for cancer treatment. The main mathematical tool needed in this connection is numerical optimization. In this article, the variety of continuous optimization approaches, which have been proposed for the computation of optimal beam and beamlet intensities respectively, is surveyed and discussed. The discussion includes a nonlinear optimization model for IMRT with biologically motivated goals, which has recently been presented by the authors and is accompanied by a sensitivity analysis proposed by Alber et al.. At last, new developments in intensity modulated proton therapy (IMPT) are considered. It is shown by a clinical case example that the algorithm introduced earlier by the authors is also capable to solve, within a few minutes of computation times, the much larger problems of treatment planning for the IMPT spot-scanning technique.
Title: Decomposition of Integer Matrices and
Multileaf Collimator Sequencing
Author: Davaatseren Baatar, Matthias Ehrgott, Horst W. Hamacher,
Gerhard J. Woeginger
URL:
http://kluedo.ub.uni-kl.de/frontdoor.php?source_opus=1786
In this paper we consider the problem of decomposing an integer matrix into a weighted sum of binary matrices that have the strict consecutive ones property. This problem is motivated by an application in cancer radiotherapy planning, namely the sequencing of multileaf collimators to realize a given intensity matrix. In addition we also mention another application in the design of public transportation. We are interested in two versions of the problem, minimizing the sum of the coeffients in the decomposition (decomposition time) and minimizing the number of matrices used in the decomposition (decomposition cardinality). We present combinatorial, polynomial time algorithms for unconstrained and constrained versions of the decomposition time problem and prove that the (unconstrained) decomposition time problem is strongly NP-hard. For the decomposition cardinality problem, some polynomially solvable special cases are considered and heuristics are proposed for the general case.
Title: Multileaf collimator field segmentation
without tongue-and-groove effect
Author: Thomas Kalinowski
URL:
ftp://ftp.math.uni-rostock.de/pub/preprint/2004/pre04_03.pdf
We present an algorithm for optimal step--and--shoot intensity modulated radiation therapy without interleaf collision and with elimination of tongue--and--groove effects. Adapting the concepts of {Kal03a} we characterize the minimal number of monitor units as the maximal weight of a path in a properly constructed weighted digraph. We also show that this number of monitor units can be realized by an unidirectional plan, thus proving that the algorithm of Kamath et al. {Kam04a} is monitor unit optimal in general and not only for unidirectional leaf movement. Our characterization of the minimal number of monitor units has the advantage that it can be used to derive a heuristic for the reduction of the number of segments following the ideas of {Kal03b}.
Title: The algorithmic complexity of the
minimization of the number of segments in multileaf collimator
field segmentation
Author: Thomas Kalinowski
URL:
ftp://ftp.math.uni-rostock.de/pub/preprint/2004/pre04_01.pdf
Intensity maps are nonnegative matrices describing the intensity modulation of beams in radiotherapy. In order to use a multileaf collimator in the static mode for the realization of the intensity modulation one has to determine a segmentation, i.e. a representation of an intensity map as a positive combination of special matrices corresponding to fixed positions of the multileaf collimator, called segments. We consider the problem to construct segmentations with the minimal total number of monitor units and the minimal number of segments. Neglecting machine-- dependent constraints like the interleaf collision constraint and assuming that the entries of the intensity map are bounded by a constant, we prove that a segmentation with minimal number of segments under the condition that the number of monitor units is minimal, can be determined in time polynomial in the matrix dimensions. The results of our algorithm are compared with Engel's \cite{Eng02} heuristic for the reduction of the number of segments.
Title: Reducing the number of monitor units in
multileaf collimator field segmentation
Author: Thomas Kalinowski
URL:
ftp://ftp.math.uni-rostock.de/pub/preprint/2004/pre04_02.pdf
Multileaf collimators (MLCs) are the prevailing tool for the realization of radiation fields in intensity modulated radiation therapy (IMRT). One step in the treatment planning is to determine a set of leaf positions realizing a certain intensity modulated radiation field. In this paper we suggest two extensions in the use of the MLC that lead to considerable savings in terms of monitor units, thus potentially increasing the treatment quality. We test our method with random and with clinical sample matrices.
Title: Inherent smoothness of intensity patterns for
intensity modulated radiation therapy generated by simultaneous
projection algorithms
Author: Y. Xiao, D. Michalski, Y. Censor and J.M. Galvin
URL:
http://math.haifa.ac.il/yair/smoothPMBaccepted280504.pdf
The efficient delivery of intensity modulated radiation therapy (IMRT) depends on finding optimized beam intensity patterns that produce dose distributions, which meet given constraints for the tumor as well as any critical organs to be spared. Many optimization algorithms that are used for beamlet-based inverse planning are susceptible to large variations of neighboring intensities. Accurately delivering an intensity pattern with a large number of extrema can prove impossible given the mechanical limitations of standard MLC delivery systems. In this study, we apply Cimmino's simultaneous projection algorithm to the beamlet-based inverse planning problem, modeled mathematically as a system of linear inequalities.
We show that using this method allows us to arrive at a smoother intensity pattern. Including non-linear terms in the simultaneous projection algorithm to deal with dose-volume histogram (DVH) constraints does not compromise this property from our experimental observation. The smoothness properties are compared with those from other optimization algorithms which include simulated annealing and gradient descent method. The simultaneous property of these algorithms is ideally suited to parallel computing technologies.
Title: A unifying framework for multi-criteria fluence map
optimization models
Author: H Edwin Romeijn, James F Dempsey and Jonathan G Li
URL:
http://www.iop.org/EJ/abstract/0031-9155/49/10/011
Models for finding treatment plans for intensity modulated radiation therapy are usually based on a number of structure-based treatment plan evaluation criteria, which are often conflicting. Rather than formulating a model that a priori quantifies the trade-offs between these criteria, we consider a multi-criteria optimization approach that aims at finding the so-called undominated treatment plans. We present a unifying framework for studying multi-criteria optimization problems for treatment planning that establishes conditions under which treatment plan evaluation criteria can be transformed into convex criteria while preserving the set of undominated treatment plans. Such transformations are identified for many of the criteria that have been proposed to date, establishing equivalences between these criteria. In addition, it is shown that the use of a nonconvex criterion can often be avoided by transformation to an equivalent convex criterion. In particular, we show that models employing criteria such as tumour control probability, normal tissue complication probability, probability of uncomplicated tumour control, as well as sigmoidal transformations of (generalized) equivalent uniform dose are equivalent to models formulated in terms of separable voxel-based criteria that penalize dose in individual voxels.
Title: A novel linear programming approach to
fluence map optimization for intensity modulated radiation
therapy treatment planning.
Author: Romeijn HE, Ahuja RK, Dempsey JF, Kumar A, and Li JG.
URL: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=14653560
We present a novel linear programming (LP) based approach for efficiently solving the intensity modulated radiation therapy (IMRT) fluence-map optimization (FMO) problem to global optimality. Our model overcomes the apparent limitations of a linear-programming approach by approximating any convex objective function by a piecewise linear convex function. This approach allows us to retain the flexibility offered by general convex objective functions, while allowing us to formulate the FMO problem as a LP problem. In addition, a novel type of partial-volume constraint that bounds the tail averages of the differential dose-volume histograms of structures is imposed while retaining linearity as an alternative approach to improve dose homogeneity in the target volumes, and to attempt to spare as many critical structures as possible. The goal of this work is to develop a very rapid global optimization approach that finds high quality dose distributions. Implementation of this model has demonstrated excellent results. We found globally optimal solutions for eight 7-beam head-and-neck cases in less than 3 min of computational time on a single processor personal computer without the use of partial-volume constraints. Adding such constraints increased the running times by a factor of 2-3, but improved the sparing of critical structures. All cases demonstrated excellent target coverage (> 95%), target homogeneity (< 10% overdosing and < 7% underdosing) and organ sparing using at least one of the two models.
Title: A Tutorial on Radiation Oncology and Optimization
Author: A. Holder and B. Salter
URL:
http://lagrange.math.trinity.edu/tumath/research/reports/report86.pdf
Designing radiotherapy treatments is a complicated and important task that affects patient care, and modern delivery systems enable a physician more flexibility than can be considered. Consequently, treatment design is increasingly automated by techniques of optimization, and many of the advances in the design process are accomplished by a collaboration among medical physicists, radiation oncologists, and experts in optimization. This tutorial is meant to aid those with a background in optimization in learning about treatment design. Besides discussing several optimization models, we include a clinical perspective so that readers understand the clinical issues that are often ignored in the optimization literature. Moreover, we discuss many new challenges so that new researchers can quickly begin to work on meaningful problems.
Title: The Relationship Between the Number of Shots and the
Quality of Gamma Knife Radiosurgeries
Author: D. Cheek, A. Holder, B. Salter, and M. Fuss
URL:
http://lagrange.math.trinity.edu/tumath/research/reports/report84.pdf
Radiosurgery is a non-invasive alternative to brain surgery that uses a single focused application of high radiation to destroy intracerebral target tissues. A Gamma Knife delivers such treatments by using 201 cylindrically collimated cobalt-60 sources that are arranged in a hemispherical pattern and aimed to a common focal point. The accumulation of radiation at the focal point, called a ``shot" due to the spherical nature of the dose distribution, is used to ablate (or destroy) target tissue in the brain. If the target is small and spherical, it is easily treated by choosing one of four available collimators (4, 8, 14, or 18 mm). For large, irregular targets, multiple shots are typically required to treat the entire lesion, and the process of determining the optimal arrangement and number of shots is complex.
In this research, fast simulated annealing and a novel objective function are used to investigate the relationship between the number of shots and the quality of the resulting treatment. Sets of 5, 10, 25, 50, and an unrestricted number of shots are studied for an arteriovenous malformation (AVM).
Title: The dose-volume constraint satisfaction problem for
inverse treatment planning with field segments
Author: D. Michalski, Y. Xiao, Y. Censor and J.M. Galvin
URL:
http://www.optimization-online.org/DB_HTML/2003/12/802.html
The prescribed goals of radiation treatment planning are often expressed in terms of dose{volume constraints. We present a novel formulation of a dose-volume constraint satisfaction search for the discretized radiation therapy model. This approach does not rely on any explicit cost function. The inverse treatment planning uses the aperture based approach with predefined, according to geometric rules, segmental fields. The solver utilizes the simultaneous version of the cyclic subgradient projection algorithm. This is a deterministic iterative method designed for solving the convex feasibility problems. A prescription is expressed with the set of inequalities imposed on the dose at the voxel resolution. Additional constraint functions control the compliance with selected points of the expected cumulative dose-volume histograms. The performance of this method is tested on prostate and head-and-neck cases. The relationships with other models and algorithms of similar conceptual origin are discussed. The demonstrated advantages of the method are: the equivalence of the algorithmic and prescription parameters, the intuitive setup of free parameters, the improved speed of the method as compared to similar iterative as well as other techniques. The technique reported here will deliver an approximate solutions for inconsistent prescriptions.
Title: An algorithm for optimal collimator field
segmentation with interleaf collision constraint 2
Author: Thomas Kalinowski
URL:
ftp://ftp.math.uni-rostock.de/pub/preprint/2003/pre03_08.pdf
Multileaf collimators are widely used in radiotherapy to realize intensity modulated fields as superpositions of homogeneous fields, so called segments. One important step in the planning process is the decomposition of the modulated field into a small number of segments such that the total number of monitor units is also small. In this paper we present an algorithm that is based on the results of Kalnowski and constructs a segmentation with minimal total number of monitor units and a small number of segments, taking into account a machine--dependent constraint, that forbids leaf overtravel in adjacent rows of the multileaf collimator.
Keywords: leaf sequencing, radiation therapy optimization, intensity modulation, multileaf collimator, IMRT
Title: Mathematical optimization for the inverse problem of
intensity modulated radiation therapy
Author: Y. Censor
URL:
http://math.haifa.ac.il/yair/coloradofinal.pdf
A superb tutorial that appeared in: J.R. Palta and T.R. Mackie (Editors), Intensity-Modulated Radiation Therapy: The State of The Art, American Association of Physicists in Medicine, Medical Physics Monograph No. 29, Medical Physics Publishing, Madison, Wisconsin, USA, 2003, pp. 25-49.
Title: An algorithm for optimal multileaf collimator field
segmentation with interleaf collision constraint
Author: Thomas Kalinowski
URL:
ftp://ftp.math.uni-rostock.de/pub/preprint/2003/pre03_02.pdf
Intensity maps are nonnegative matrices describing the intensity modulation of beams in radiotherapy. An important step in the planning process is to determine a segmentation, that is a representation of an intensity map as a positive combination of special matrices corresponding to fixed positions of the multileaf collimator, called segments. We consider the problem of constructing segmentations with small total numbers of monitor units and segments. Generalizing the approach of \cite{Eng02} so that it applies to the segmentation problem with interleaf collision constraint, we show that the minimal number of monitor units in this case can be interpreted as the length of a longest path in a layered digraph. In addition we derive an efficient algorithm that constructs a segmentation with this minimal number of monitor units.
Title: A new algorithm for optimal multileaf collimator field
segmentation
Author: Konrad Engel
URL:
ftp://ftp.math.uni-rostock.de/pub/preprint/2003/pre03_05.pdf
We present a new efficient leaf sequencing algorithm for the generation of intensity maps by a nonnegative combination of segments. Intensity maps describe the intensity modulation of beams in radiotherapy. We only study the static case (stop and shoot) an optimize the total number of monitor units and the number of segments. We will present a short exact proof for a formula giving the smallest total number of monitor units and describe a class of algorithms yielding this minimal value. A special member of this class provides in addition a solution with a very small number of segments.
Title: Optimization of Gamma Knife Treatment Plans
Author: Vira Chankong, Suradet Jitprapaikulsarn, Q. Jackie Wu
Physicians usually spend a great amount of time planning a Gamma Knife treatment by trial-and-error. In this study, we propose a very flexible and robust system to automate the treatment planning. The system consists of (1) a selection of the number of shots, shot locations, and shot sizes by the process of skeletonization and sphere packing, and (2) an adjustment of the weights by minimizing the dose to normal tissue in the target boundary. Not only the system eliminates the need to guess the number of shots a prior, it also allows the fine-tuning of relative dosages through optimization. We illustrate very encouraging results of our approach when applied to an ellipsoid target and three targets from actual patients.
Title: Multiobjective inverse planning for intensity modulated
radiotherapy with constrained-free gradient based optimization algorithms
Author: Michael Lahanas, Eduard Schreibmann and Dimos Baltas
URL:
http://www.mlahanas.de/Papers/preprint/IMRT_LBFGS.pdf
We consider the behavior of the limited memory L-BFGS algorithm as a representative constrained-free gradient-based algorithm which is used for multiobjective (MO) dose optimization for intensity modulated radiotherapy (IMRT). Using a parameter transformation, the positivity constraint problem of negative beam fluences is entirely eliminated: a feature which to date has not been fully understood by all investigators. We analyze the global convergence of L-BFGS by searching for the existence and the influence of possible local mininma. With a fast simulated annealing algorithm FSA we examine whether the L-BFGS solutions are globally optimal. The three examples used in our analysis are a brain tumor, a prostate tumor and a test case with a C-shaped PTV. In one percent of the optimizations global convergence is violated. A simple mechanism practically eliminates the influence of local minima and the obtained solutions are gloablly optimal. A single-objective dose optimization requires less than 4 seconds for 5400 parameters and 40000 sampling points. The elimination of the problem of negative beam fluences and the high computational speed permits constraint-free gradient-based optimization algorithms to be used for MO dose optimization. In this situation, a representative spectrum of possible solutions is obtained which contains information such as trade-off between the objectives and range of dose values. Using simple decision making tools the best of all the possible solutions can be choosen. We perform MO dose optimization for the three examples and compare the spectra of solutions, firstly using recommended critical dose values for the organs at risk and secondly, setting these dose values to zero.
Title: Radiotherapy Treatment Design and Linear Programming
Author: Allen Holder
URL:
http://lagrange.math.trinity.edu/tumath/research/reports/report70.pdf
Intensity modulated radiotherapy treatment (IMRT) design is the process of choosing how beams of radiation will travel through a cancer patient to treat the disease, and although optimization techniques have been suggested since the 1960s, they are still not widely used. Instead, the vast majority of treatment plans are designed by clinicians through trial-and-error. Modern treatment facilities have the technology to treat patients with extremely complicated plans, and designing plans that take full advantage of the technology is tedious. The increased technology found in modern treatment facilities makes the use of optimization paramount in the design of successful treatment plans. The goals of this work are to 1) present a concise description of the linear models that are under current investigation, 2) develop the analysis certificates that these models allow, and 3) foreshadow future research avenues.
Title: Neuro-Dynamic Programming for Radiation
Treatment Planning
Author: Michael C. Ferris and Meta M. Voelker
URL:
http://web.comlab.ox.ac.uk/oucl/publications/natr/na-02-06.html
In many cases a radiotherapy treatment is delivered as a series of smaller dosages over a period of time. Currently, it is difficult to determine the actual dose that has been delivered at each stage, precluding the use of adaptive treatment plans. However, new generations of machines will give more accurate information of actual dose delivered, allowing a planner to compensate for errors in delivery. We formulate a model of the day-to-day planning problem as a stochastic linear program and exhibit the gains that can be achieved by incorporating uncertainty about errors during treatment into the planning process. Due to size and time restrictions, the model becomes intractable for realistic instances. We show how neuro-dynamic programming can be used to approximate the stochastic solution, and derive results from our models for realistic time periods. These results allow us to generate practical rules of thumb that can be immediately implemented in current planning technologies.
Title: Minimizing Beam-On Time in Cancer Radiation Treatment Using
Author: Boland, N., Hamacher, H.W., and Lenzen, F.
URL:
http://kluedo.ub.uni-kl.de/Mathematik/Metadaten/gelb_78.html
In this paper the modulation of intensity matrices arising incancer radiation therapy using multileaf collimators (MLC) is investigated. It is shown that the problem is equivalent to decomposing a given integer matrix into a positive linear combination of (0,1) matrices. These matrices, called shape matrices, must have the strict consecutive-1-property, together with another property derived from the technological restrictions of the MLC equipment. Various decompositions can be evaluated by their beam-on-time (time in which radiation is applied to the patient) or the treatment time (beam-on-time plus time for set-ups). We focus on the former, and develop a nonlinear mixed integer programming formulation of the problem. This formulation can be decomposed to yield a column generation formulation: a linear program with a large number of variables that can be priced out by solving a subproblem. We then develop a network model in which paths in the network correspond to feasible shape matrices. As a consequence, we deduce that the column generation subproblem can be solved as a shortest path problem, and so obtain our main theoretical result that the problem is solvable in polynomial time. Furthermore, we are able to develop two alternative models of the problem as side-constrained network flow formulations. Finally, a numerical comparison of our exact solutions with those of well-known heuristic methods shows that the beam-on time can be reduced by a considerable margin.
Title: The Least-Intensity Feasible Solution for Aperture-Based
Inverse Planning in Radiation Therapy.
Author: Y. Xiao, Y. Censor, D. Michalski and J.M. Galvin
URL:
http://math.haifa.ac.il/yair/censor-recent-pubs.html
Aperture-based inverse planning (ABIP) for intensity modulated radiation therapy (IMRT) treatment planning starts with external radiation fields (beams) that fully conform to the target(s) and then superimposes sub-fields called segments to achieve complex shaping of 3D dose distributions. The segments' intensities are determined by solving a feasibility problem. The least-intensity feasible (LIF) solution, proposed and studied here, seeks a feasible solution closest to the origin, thus being of least intensity or least energy. We present a new iterative, primal-dual, algorithm for finding the LIF solution and explain our experimental observation that Cimmino's algorithm for feasibility actually converges to a close approximation of the LIF solution. Comparison with linear programming shows that Cimmino's algorithm has the additional advantage of generating much smoother solutions.
Title: Radiosurgery Treatment Planning via Nonlinear Programming
Author: Michael C. Ferris, Jin-Ho Lim and David M. Shepard
URL:
ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/01-01.pdf
The Gamma Knife is a highly specialized treatment unit that provides an advanced stereotactic approach to the treatment of tumors, vascular malformations, and pain disorders within the head. Inside a shielded treatment unit, multiple beams of radiation are focussed into an approximately spherical volume, generating a high dose shot of radiation. The treatment planning process determines where to center the shots, how long to expose them for, and what size focussing helmets should be used, in order to cover the target with sufficient dosage without overdosing normal tissue or surrounding sensitive structures. We outline a new approach that models the dose distribution nonlinearly, and uses a smoothing approach to treat discrete problem choices. The resulting nonlinear program is not convex and several heuristic approaches are used to improve solution time and quality. The overall approach is fast and reliable; we give several results obtained from use in a clinical setting.
Title: An Optimization Approach for Radiosurgery Treatment Planning
Author: Michael C. Ferris, Jin-Ho Lim and David M. Shepard
URL:
ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/01-12.pdf
We outline a new approach for radiosurgery treatment planning, based on solving a series of optimization problems. We consider a specific treatment planning problem for a specialized device known as the Gamma Knife, that provides an advanced stereotactic approach to the treatment of tumors, vascular malformations, and pain disorders within the head. The sequence of optimization problems involves nonlinear and mixed integer programs whose solution is required in a given planning time (typically less than 30 minutes). This paper outlines several modeling decisions that result in more efficient and robust solution. Furthermore, it outlines a new approach for determining starting points for the nonlinear programs, based on a skeletonization of the target volume. Treatment plans are generated for real patient data that show the efficiency of the approach.
Title: Inverse Radiation Therapy Planning - A multiple objective
optimisation approach
Author: Hamacher, Horst W. and Karl-Heinz Kuefer
URL:
http://www.itwm.fhg.de/zentral/berichte/bericht12.pdf
In order to tackle the dilemma of high dosages in the target and low dosages in risk organs, a multiple criteria approach is used. The paper has been accepted in Annals of Discrete Applied Mathematics and should appear in late 2001.
Title: Radiation Therapy Planning by Multicriteria Optimisation
Author: Matthias Ehrgott, Mena Burjony
URL:
http://www.mang.canterbury.ac.nz/orsnz/conf2001/papers/Ehrgott.pdf
Radiation is one of the major forms of treatment in cancer therapy besides chemotherapy and surgery. The determination of a treatment plan is a complex task that involves finding directions of beams, beam intensities and a realisation of optimal intensities on the equipment. In this talk we focus on determination of beam intensities. Dose distributions must satisfy the conflicting goals of effectively destroying the tumour while at the same time avoiding dangerous overdosing in surrounding tissue and organs at risk. We present a multicriteria model of the problem and show how to find a solution in which deviations from prescribed dose levels is balanced for all organs under consideration. Such a solution can serve as a starting point for the search for a best treatment plan among a pre-computed representative set of "efficient" solutions in an on-line database environment.
Title: Mobile Triage Support System for Pediatric Emergencies
Author: W. Michalowski, S. Rubin, R. Slowinski, Sz. Wilk
URL:
http://www.admin.uottawa.ca/wojtek/mobile_triage.pdf
This paper describes the process and methodology of designing and developing a mobile support system to triage abdominal pain in the emergency room of a hospital. Application of rough sets theory and fuzzy measures to data collected at Children’s Hospital of Eastern Ontario allows us to identify the most relevant clinical symptoms and signs while evaluating an abdominal pain patient. This information was used to develop a multi-level clinical algorithm that forms the reasoning module of a triage support system. We describe a front-end system called MAT that is installed on Palm handheld and that can be used to triage a child irrespective of the available information. We present MAT’s functions allowing for the electronic data capture and wireless data transfer. Such a system’s design and implementation supports triage at a bed side and facilitates fast and reliable patients’ record transfer and storage.
Title: Partitioning Multiple Objective Optimal Solutions with
Applications in Radiotherapy Design
Author: Allen Holder
URL:
http://lagrange.math.trinity.edu/aholder/research/papers/MOLPpartition.pdf
The optimal partition for linear programming is induced by any strictly complementary solution, and this partition is important because it characterizes the optimal set. However, constructing a strictly complementary solution in the presence of degeneracy was not practical until interior point algorithms became viable alternatives to the simplex algorithm. We develop analogs of the optimal partition for linear programming in the case of multiple objectives and show that these new partitions provide insight into the optimal set (both pareto optimality and lexicographic ordering are considered). Techniques to produce these optimal partitions are provided, and examples from the design of radiotherapy plans show that these new partitions are useful.
Title: Designing Radiotherapy Plans with Elastic Constraints and
Interior Point Methods
Author: Allen Holder
URL:
http://lagrange.math.trinity.edu/aholder/research/papers/rad.pdf
A new linear programming model used to aid in the design of radiotherapy plans is introduced. This model incorporates elastic constraints, and when solved with a path following interior point method, produces favorable plans. A sound mathematical analysis shows how to interpret the solution, and hence, the treatment planner receives meaningful knowledge about the radiotherapy plan being developed. Preliminary experiments are conducted.