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PubMed2003

Optimization of biochemical systems by linear programming and general mass action model representations.

A new method is proposed for the optimization of biochemical systems. The method, based on the separation of the stoichiometric and kinetic aspects of the system, follows the general approach used in the previously presented indirect optimization method (IOM) developed within biochemical systems theory. It is called GMA-IOM because it makes use of the generalized mass action (GMA) as the model system representation form. The GMA representation avoids flux aggregation and thus prevents possible stoichiometric errors. The optimization of a system is used to illustrate and compare the features, advantages and shortcomings of both versions of the IOM method as a general strategy for designing improved microbial strains of biotechnological interest. Special attention has been paid to practical problems for the actual implementation of the new proposed strategy, such as the total protein content of the engineered strain or the deviation from the original steady state and its influence on cell viability.

Biochemical Phenomena↗
PubMed1990

Linear programming and pediatric dietetics.

The composition of 500 foods has been stored in a computer in order to analyse a child's diet. The methodology of operations research is applied to a very simple problem: a diet with only two foods. The geometrical representation of the 'feasible region' and of the 'objective function' is illustrated. One of the analytical methods employable with many variables (foods) is considered. This method was used in trying to find diets allowing for the preferential use of selected foods while respecting recommended dietary allowances, the tastes of the child and other constraints. The theoretical difficulty of transferring this methodology to pediatric dietetics was examined. We solved a simple case utilizing this procedure.

Child↗
PubMed2004

Optimal robust non-unique probe selection using Integer Linear Programming.

MOTIVATION: Besides their prevalent use for analyzing gene expression, microarrays are an efficient tool for biological, medical and industrial applications due to their ability to assess the presence or absence of biological agents, the targets, in a sample. Given a collection of genetic sequences of targets one faces the challenge of finding short oligonucleotides, the probes, which allow detection of targets in a sample. Each hybridization experiment determines whether the probe binds to its corresponding sequence in the target. Depending on the problem, the experiments are conducted using either unique or non-unique probes and usually assume that only one target is present in the sample. The problem at hand is to compute a design, i.e. a minimal set of probes that allows to infer the targets in the sample from the result of the hybridization experiment. If we allow to test for more than one target in the sample, the design of the probe set becomes difficult in the case of non-unique probes. RESULTS: Building upon previous work on group testing for microarrays, we describe the first approach to select a minimal probe set for the case of non-unique probes in the presence of a small number of multiple targets in the sample. The approach is based on an ILP formulation and a branch-and-cut algorithm. Our preliminary implementation greatly reduces the number of probes needed while preserving the decoding capabilities. AVAILABILITY: http://www.inf.fu-berlin.de/inst/ag-bio

Algorithms↗
PubMed2004

A linear programming approach to limited angle 3D reconstruction from DSA projections.

OBJECTIVES: We investigate the feasibility of binary-valued 3D tomographic reconstruction using only a small number of projections acquired over a limited range of angles. METHODS: Regularization of this strongly ill-posed problem is achieved by (i) confining the reconstruction to binary vessel/non-vessel decisions, and (ii) by minimizing a global functional involving a smoothness prior. RESULTS: Our approach successfully reconstructs volumetric vessel structures from three projections taken within 90 degrees. The percentage of reconstructed voxels differing from ground truth is below 1%. CONCLUSION: We demonstrate that for particular applications--like Digital Subtraction Angiography--3D reconstructions are possible where conventional methods must fail, due to a severely limited imaging geometry. This could play an important role for dose reduction and 3D reconstruction using non-conventional technical setups.

Angiography, Digital Subtraction↗
PubMed2003

A novel linear programming approach to fluence map optimization for intensity modulated radiation therapy treatment planning.

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.

Algorithms↗
PubMed2005

[Application of linear programming in the allocation of environmental capacity resources].

This paper analyzes the application of optimization approaches, particularly the application types of the linear programming (LP) model in environmental planning and management; put forwards the objective function models and their constraint conditions. Based on the formulation of linear programming model related to environmental planning the paper develops the allocation model of environmental purification capacity (EPC), and identifies the constraints to EPC allocation and their parameters or co-efficiencies. It is proved that LP approach is a practical and scientific tool for allocating EPC in specific region.

Conservation of Natural Resources↗
PubMed2003

Protein threading by linear programming.

Protein three-dimensional structure prediction through threading approach has been extensively studied and various models and algorithms have been proposed. In order to further explore ways to improve accuracy and efficiency of the threading process, this paper investigates the effectiveness of a new method: protein threading via linear programming. Based on the contact map model of protein 3D structure, we formulate the protein threading problem as a large scale integer programming problem, then relax to a linear programming problem, and finally solve the integer program by a branch-and-bound method. The final solution is optimal with respect to energy functions incorporating pairwise interaction and allowing variable gaps. The algorithm has been implemented as software package RAPTOR--RApid Protein Threading predictOR. Experimental results for fold recognition show that RAPTOR significantly outperforms other programs at the fold similarity level. The RAPTOR webserver is at http://www.cs.uwaterloo.ca/-j3xu/RAPTOR_form.htm.

Algorithms↗
PubMed2006

Breast cancer detection by Michaelis-Menten constants via linear programming.

The Michaelis-Menten constants (K(m) and V(max)) operated by linear programming, were employed for detection of breast cancer. The rate of enzymatic hydrolysis of fluorescein diacetate (FDA) in living peripheral blood mononuclear cells (PBMC), derived from healthy subjects and breast cancer (BC) patients, was assessed by measuring the fluorescence intensity (FI) in individual cells under incubation with either the mitogen phytohemagglutinin (PHA) or with tumor tissue, as compared to control. The suggested model diagnoses three conditions: (1) the subject is diseased, (2) the diagnosis is uncertain, and (3) the subject is not diseased. Out of 50 subjects tested, 44 were diagnosed correctly, in 5 cases the diagnosis was not certain, and 1 subject was diagnosed incorrectly.

Breast Neoplasms↗
PubMed2004

[Study on the 3D mathematical mode of the muscle groups applied to human mandible by a linear programming method].

Four types of 3D mathematical mode of the muscle groups applied to the human mandible have been developed. One is based on electromyography (EMG) and the others are based on linear programming with different objective function. Each model contains 26 muscle forces and two joint forces, allowing simulation of static bite forces and concomitant joint reaction forces for various bite point locations and mandibular positions. In this paper, the method of image processing to measure the position and direction of muscle forces according to 3D CAD model was built with CT data. Matlab optimization toolbox is applied to solve the three modes based on linear programming. Results show that the model with an objective function requiring a minimum sum of the tensions in the muscles is reasonable and agrees very well with the normal physiology activity.

Bite Force↗
PubMed2003

Optimization of operating room allocation using linear programming techniques.

BACKGROUND: New and innovative approaches must be used to rationally allocate scarce resources such as operating room time while simultaneously optimizing the associated financial return. In this article we use the technique of linear programming to optimize allocation of OR time among a group of surgeons based on professional fee generation. STUDY DESIGN: For the period of December 1, 2000, to July 31, 2002, the following individualized data were obtained for the Division of General Surgery at Duke University Medical Center: allocated OR time (hours), case mix as determined by CPT codes, total OR time used, and normalized professional charges and receipts. Inpatient, outpatient, and emergency cases were included. The Solver linear programming routine in Microsoft Excel (Microsoft Corp.) was used to determine the optimal mix of surgical OR time allocation to maximize professional receipts. RESULTS: Our model of optimized OR allocation would maximize weekly professional revenues at 237,523 US dollars, a potential increase of 15% over the historical value of 207,700 US dollars or an annualized increase of approximately 1.5 million US dollars. CONCLUSIONS: Our results suggest that mathematical modeling techniques used in operations research, management science, or decision science may rationally optimize OR allocation to maximize revenue or to minimize costs. These techniques may optimize allocation of scarce resources in the context of the goals specific to individual academic departments of surgery.

Fees, Medical↗
PubMed2003

Assessment of RAPTOR's linear programming approach in CAFASP3.

We have developed a new algorithm based on the mathematical theory of linear programming (LP) and implemented it in our program RAPTOR. Our new approach provides an elegant formulation of the protein-threading problem, overcomes the intractability problem of protein threading, in practice, and allows us to use existing powerful linear programming software to obtain optimal protein threading solutions. CASP5 and CAFASP3 gave us the first chance to test RAPTOR in an unbiased way. RAPTOR was ranked as the top individual (automatic) server for fold recognition by the CAFASP3 organizers. In this short article, we describe RAPTOR's LP formulation, assess RAPTOR's performance in CAFASP3/CASP5, explain why it has superceded other existing automatic individual methods, and point out its strengths, limitations, extensions, and prospects for improvement.

Algorithms↗
PubMedDate not supplied

Short-term case mix management with linear programming.

One short-term economic incentive created by a prospective payment system based on diagnosis-related groups (DRGs) is for hospital managers to optimally and efficiently use the hospital's current mix of services to maximize net contribution. DRGs provide a managerial definition of the hospital's product by determining the number of patients discharged within each of the 467 groupings. Thus, the DRG case mix can be thought of as the hospital's product mix. As in major industry, linear programming models may prove useful in determining the hospital's financially optimal case mix. This article provides a framework for applying the linear programming concept to case mix planning in the hospital setting. It also presents an illustration and interpretation of a linear programming model that provides information about the short-term optimal case mix.

Costs and Cost Analysis↗