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Designing radiotherapy plans with elastic constraints and interior point methods.

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.

Data Interpretation, Statistical↗

Selective minimum-norm solution of the biomagnetic inverse problem.

A new multidipole estimation method which gives a sparse solution of the biomagnetic inverse problem is proposed. This solution is extracted from the basic feasible solutions of linearly independent data equations. These feasible solutions are obtained by selecting exactly as many dipole-moments as the number of magnetic sensors. By changing the selection, we search for the minimum-norm vector of selected moments. As a result, a practically sparse solution is obtained; computer-simulated solutions for Lp-norm (p = 2, 1, 0.5, 0.2) have a small number of significant moments around the real source-dipoles. In particular, the solution for L1-norm is equivalent to the minimum-L1-norm solution of the original inverse problem. This solution can be uniquely computed by using Linear Programming.

Animals↗

An algorithm for generation of implant plans for high-dose-rate irradiators.

An algorithm is described for generating a treatment plan with minimal input from the user for a remote high-dose-rate afterloading irradiator. The algorithm generates a plan after locating all catheters involved and an area of interest on each catheter, and two additional numbers are specified: a radial distance and a target dose. The treatment volume becomes the locus of all points that are within the specified radial distance from any point within the area of interest on any catheter (except for the end points). For a single catheter, the volume may be alternately outlined on an x-ray film of the implant. The routine uses a linear programming formulism to compute which dwell positions are to be used, as well as the dwell time at each position, to irradiate the treatment volume to the target dose while minimizing the total volume integrated dose to the patient.

Algorithms↗

PRIMA: peptide robust identification from MS/MS spectra.

In proteomics, tandem mass spectrometry is the key technology for peptide sequencing. However, partially due to the deficiency of peptide identification software, a large portion of the tandem mass spectra are discarded in almost all proteomics centers because they are not interpretable. The problem is more acute with the lower quality data from low end but more popular devices such as the ion trap instruments. In order to deal with the noisy and low quality data, this paper develops a systematic machine learning approach to construct a robust linear scoring function, whose coefficients are determined by a linear programming. A prototype, PRIMA, was implemented. When tested with large benchmarks of varying qualities, PRIMA consistently has higher accuracy than commonly used software MASCOT, SEQUEST and X! Tandem.

Amino Acid Sequence↗

On the inference of parsimonious indel evolutionary scenarios.

Given a multiple alignment of orthologous DNA sequences and a phylogenetic tree for these sequences, we investigate the problem of reconstructing a most parsimonious scenario of insertions and deletions capable of explaining the gaps observed in the alignment. This problem, called the Indel Parsimony Problem, is a crucial component of the problem of ancestral genome reconstruction, and its solution provides valuable information to many genome functional annotation approaches. We first show that the problem is NP-complete. Second, we provide an algorithm, based on the fractional relaxation of an integer linear programming formulation. The algorithm is fast in practice, and the solutions it produces are, in most cases, provably optimal. We describe a divide-and-conquer approach that makes it possible to solve very large instances on a simple desktop machine, while retaining guaranteed optimality. Our algorithms are tested and shown efficient and accurate on a set of 1.8 Mb mammalian orthologous sequences in the CFTR region.

Algorithms↗

Precise formulation and evidence-based application of resource-constrained triage.

OBJECTIVES: To develop a precise mathematical formulation of resource-constrained triage, denoted the Sacco triage method (STM), to develop an evidence-based application to blunt trauma, and to compare the STM with the simple triage and rapid treatment (START) method. METHODS: Resource-constrained triage is modeled mathematically as a classic resource allocation problem. The objective is to maximize expected survivors given constraints on the timing and availability of resources. The model incorporates estimates of time-dependent victim survival probabilities based on an initial assessment and expected deterioration. For application to blunt trauma, an "RPM" score, based on respiratory rate, pulse rate, and motor response, was used to predict survivability. Logistic function-generated survival probability estimates for scene values of RPM were determined from 76,459 blunt-injured patients from the Pennsylvania Trauma Outcome Study (PTOS). The Delphi method provided expert consensus on victim deterioration rates, and the model was solved using linear programming. STM was compared with START across various criteria of process and outcome. Outcome was measured by expected number of survivors in simulated resource-constrained casualty incidents. RESULTS: In this mathematical simulation, RPM was a more accurate predictor of survivability from blunt trauma than the Injury Severity Score and the Revised Trauma Score, as measured by calibration and discrimination statistics. STM resulted in greater expected survivorship than START in all simulations. CONCLUSIONS: Resource-constrained triage is modeled precisely as an evidence-based, outcome-driven method that maximizes expected survivors in consideration of resources. The lifesaving potential and operational advantages over current methods warrant scrutiny and further research.

Delphi Technique↗

E-approximations for multidimensional weighted location problems.

This paper considers the multidimensional weighted minimax location problem, namely, finding a facility location that minimizes the maximal weighted distance to n points. General distance norms are used. An epsilon-approximate solution is obtained by applying a variant of the Russian method for the solution of Linear Programming. The algorithm has a time complexity of O(n log epsilon) for fixed dimensionality k. Computational results are presented.

Catchment Area, Health↗

Whole-herd optimization with the Cornell Net Carbohydrate and Protein System. II. Allocating homegrown feeds across the herd for optimum nutrient use.

The objective of this paper was to develop a linear optimization procedure for allocating homegrown feeds across the herd to optimize use of their nutrients in whole farm nutrient management planning. The first step involved developing an optimal diet for each group by a linear programming (LP) procedure developed for the Cornell Net Carbohydrate and Protein System (CNCPS). Information (feed biological values, nutrient requirements, animal and environmental factors, nutrient excretion, and the optimal diet) for each group was exported to a whole farm worksheet, where another LP procedure was used to optimize the allocation of homegrown crops by satisfying the set requirements of each animal group while optimizing return over feed costs and nutrient excretion constraints. A sample evaluation shows how this model was used to reduce N, P, and K excretion by changing feeding strategies while maintaining return over feed costs.

Animal Feed↗

Whole-herd optimization with the Cornell Net Carbohydrate and Protein System. III. Application of an optimization model to evaluate alternatives to reduce nitrogen and phosphorus mass balance.

The objectives of this paper were to use a linear programming model previously described to evaluate different alternatives for reducing excess nutrients that may influence water quality on a case study farm (300 lactating cows on 430 ha of cropland growing alfalfa, grass, and corn). Several alternatives perceived to influence farm nutrient balance were evaluated for their potential to reduce N and P mass balance. Dividing lactating cow diets into three groups according to their level of milk production versus a one-group total mixed ration decreased mass balance (tonne/yr) from 51.7 to 44.7 for N, from 6.7 to 6.1 for P and from 16.2 to 14.8 for K with little influence on return over feed costs. Increasing forage quality (lower neutral detergent fiber and higher crude protein) did not improve N balance because of the increased N fixation from the air to the soil, but it increased returns over feed costs by $31,385. Improving yields to the maximum potential for the farm reduced mass balance by 29, 51, and 100% for N, P, and K, respectively, and increased returns over feed costs by $70,579. Changing the crop hectare proportions to more corn and less alfalfa reduced N and K balances by 19 and 29%, respectively, and increased returns over feed costs $39,383. Increasing annual milk production 10% by increasing milk production per head 10% compared with increasing animal numbers at the current average milk production per cow until total milk increased 10% gave $34,132 more return over feed costs with less N, P, and K retained on the farm.

Agriculture↗

Measuring efficiency of physician practices using data envelopment analysis.

PURPOSE: Medical-group practices are becoming increasingly common-place, with more than a third of licensed physicians in the United States currently working in this mode. While previous studies have focused on physician practices, little attention has been focused specifically on the contribution of internal organizational factors to overall physician practice efficiency. This paper develops a model to help determine best practices of efficient physician offices while allowing for choices between inputs. Measuring how efficient practices provide services yields useful information to help improve performance of less efficient practices. DESIGN: Data for this study were obtained from the 1999 Medical Group Management Association (MGMA) Cost Report. In this study, 115 primary care physician practices are analyzed. Outputs are defined as gross charges; inputs include square footage and medical, technical, and administrative support personnel. METHODOLOGY: Data envelopment analysis (DEA) is used in this study to develop a model of practice outputs and inputs to help identify the most efficient medical groups. DEA is a linear programming technique that converts multiple input and output measures to a single comprehensive measure of efficiency. These practices are used as a reference set for comparisons with less efficient ones. CONCLUSION: The overall results indicate that size of physician practice does not increase efficiency. There does not appear to be extensive substitution among inputs. Compared to other practices, efficient practices seem to manage each input well.

Benchmarking↗

MetMAP: an integrated Matlab package for analysis and optimization of metabolic systems.

In previous works we have presented and applied a method to predict the parameter profile that optimizes biochemical systems regarding either a single or a set of metabolic responses within physiological constraints [Vera et al., 2003a]. This optimization technique requires a previous model definition and a translation to S-system form and the use of widely available linear programming packages. However, in dealing with these issues the interested researcher has to confront additional difficulties because of a lack of connectivity among available software packages or routines specifically designed to perform different tasks. In addition to this difficulty is the unavailability of any automated package which is capable of performing such optimizations and the previous required analysis. This situation prompted us to develop an integrated software package able to deal with these tasks in a single program environment. In this paper we present a software package for the model definition, analysis and optimization of a biochemical system. It starts with a given model definition that is directly translated to its equivalent S-system form. Once the model quality assessment is performed (stability and sensitivity analysis) the program determines the parameter profile that yields the optimized response compatible with a predefined set of constraints. Moreover the package finds the set of solutions obtained when more than one system's responses are to be optimized (multiobjective optimization).

Algorithms↗

[Optimization of the intracavitary irradiation of patients with cancer of the endometrium].

Twelve variants of uterine cavity structure were defined on analysis of 52 hysterocervicograms performed in patients with cancer of the uterine body. Using the method of linear programming, the most effective schemes for the location of radiation sources were proposed to ensure optimum dose distribution in intracavitary irradiation. Sources I and II were the main contributors to dose distribution. The use of sequential radiation sources was appropriate in considerable sizes of the uterine cavity. In a spherically shaped uterine cavity dose distribution could be ensured by using only one source, located in the center.

Brachytherapy↗

Transportation or CT scanners: a theory and method of health resources allocation.

Cost containment and access to appropriate care are the two most frequently discussed issues in contemporary health policy. Conceiving of the health services available in specific regions as "packages" of diverse items, the authors of this article consider the economic trade-offs among the various resources needed for appropriate care. In the discussion that follows, we examine the trade-offs between two divergent offering of the health care system: high technology medicine and support services. Specifically, we examine several strategies designed to achieve an optimal mix of investments in CT scanners and transportation resources in the South Chicago region. Using linear programming as a method for examining these options, the authors found that 1) the proper location of CT scanners is as important for cost containment as optimal number, and 2) excess capacity in the utilization of a single resource--CT scanners--need not imply inefficiency in the overall delivery of the service. These findings help demonstrate the importance of viewing health care as a package of interrelated services, both for achieving cost containment and for providing access to appropriate care.

Catchment Area, Health↗

[Stability of the optimal solution to the problem of determining optimal physicotechnical irradiation conditions].

The problem of determination of optimum physical and technical plans of irradiation often amounts to the problems of linear programming. To solve such a problem, it is necessary to calculate a matrix of conditions (dose rate in the system of distributed control points in the body during irradiation in different present directions). The purpose was to study the influence of errors of the calculation of dose rates upon the optimum irradiation plans. It has been established that though the task of determining optimum plans is a correct one, convergence of the solution of a disturbed problem to an initial one occurs extremely slowly. The optimum values of the functionals of a disturbed problem converge more rapidly to the functional of an initial problem. The comparison of optimum irradiation plans or optimum and traditional irradiation plans seems difficult. To compare different irradiation plans, it is more convenient to use the values of a specific function (optimum criteria).

Humans↗

[Data envelopment analysis: its use to assess efficiency of hospital preventive medicine services of Andalusia].

BACKGROUND: The evaluation of hospital units efficiency is a major matter of health services management. Among the techniques to measure efficiency. The Data Envelopment Analysis (DEA) can be used in multiple resources units (inputs) obtaining multiple products (outputs). The objective of this study is the evaluation of Hospital Preventive Medicine Services in Andalucia, using the technique DEA. METHODS: The Preventive Medicine Services from seven hospitals of Andalucia were selected. DEA is technique, based on a linear programming, which finds the weights, which make a Service efficient in relation with the rest. The relative efficiency of seven units was calculated. The unit with the best practice was found by means of cross efficiency matrixes. With regard to the inefficient services, their necessity of increasing activities to achieve efficiency was identified. RESULTS: Two efficiency assumptions were elaborated. In the first one, 4 services were efficient (Efficiency = 1) in relation with the rest. In the second one, the Service S.1 was inefficient. Among the efficient units, S.2 shown the highest average efficiency in both assumptions and appeared as the reference unit for all the inefficient ones. CONCLUSIONS: In the evaluation of Preventive Medicine Services efficiency, at least, three of them shown some kind of inefficiency. The Service S.2 was the point of reference for inputs and outputs selected.

Efficiency, Organizational↗

Probabilistic constraint satisfaction: application to radiosurgery.

Although quite successful in a variety of settings, standard optimization approaches can have drawbacks within medical applications. For example, they often provide a single solution which is difficult to explain, or which can not be incrementally modified using secondary "soft" constrains that are difficult to encode within the optimization. In order to address these issues, we have developed a probabilistic optimization technique that allows the user to enter prior probability distributions (Gaussian) for the parameters to be optimized as well as for the constraints on the parameters. Our technique combines the prior distributions with the constraints using Bayes' rule. The algorithm produces not only a set of parameter values, but variances on these values and covariances showing the correlations between parameters. We have applied this method to the problem of planning a radiosurgical ablation of brain tumors. The radiation plan should maximize dose to tumor, minimize dose to surrounding areas, and provide an even distribution of dosage across the tumor. It also should be explainable to and modifiable by the expert physicians based on external considerations. We have compared the results of our method with the standard linear programming approach.

Humans↗

A staff allocation model for mental health facilities.

This article describes a model for allocating staff within a large psychiatric hospital. The model provides an objective framework within which one can test alternative staff operating policies before making critical decisions concerning the employment of one category of personnel as opposed to another. It is based on objective data describing patient needs and staff functioning patterns, rather than subjective opinions concerning staff deployment. Besides being useful for the short-term deployment of staff and budgetary resources, it can also be used as a long-range planning tool for testing modifications in policy decisions and budget proposals. The algorithm employed, mixed-integer linear programming, is readily available; computer costs and running time are relatively minimal.

Hospitals, Psychiatric↗

A user's experience with a standard non-linear regression program (BMDP3R).

A study was made to test and compare the behavior of a standard non-linear regression program (BMDP3R) in fitting data from six classical least-squares problems. The use of three program control parameters is discussed and four measures of regression failure are utilized to give a quantitative reference of success. Recommendations are given to aid the user of packaged programs in the parameter estimation of non-linear regression models.

Computers↗