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Hagrot, E., Oddsdóttir, H. Æ., Mäkinen, M., Forsgren, A. & Chotteau, V. (2019). Novel column generation-based optimization approach for poly-pathway kinetic model applied to CHO cell culture. Metabolic Engineering Communications, 8, Article ID e00083.
Open this publication in new window or tab >>Novel column generation-based optimization approach for poly-pathway kinetic model applied to CHO cell culture
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2019 (English)In: Metabolic Engineering Communications, ISSN 2214-0301, Vol. 8, article id e00083Article in journal (Refereed) Published
Abstract [en]

Mathematical modelling can provide precious tools for bioprocess simulation, prediction, control and optimization of mammalian cell-based cultures. In this paper we present a novel method to generate kinetic models of such cultures, rendering complex metabolic networks in a poly-pathway kinetic model. The model is based on subsets of elementary flux modes (EFMs) to generate macro-reactions. Thanks to our column generation-based optimization algorithm, the experimental data are used to identify the EFMs, which are relevant to the data. Here the systematic enumeration of all the EFMs is eliminated and a network including a large number of reactions can be considered. In particular, the poly-pathway model can simulate multiple metabolic behaviors in response to changes in the culture conditions. We apply the method to a network of 126 metabolic reactions describing cultures of antibody-producing Chinese hamster ovary cells, and generate a poly-pathway model that simulates multiple experimental conditions obtained in response to variations in amino acid availability. A good fit between simulated and experimental data is obtained, rendering the variations in the growth, product, and metabolite uptake/secretion rates. The intracellular reaction fluxes simulated by the model are explored, linking variations in metabolic behavior to adaptations of the intracellular metabolism.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Amino acid, Chinese hamster ovary cell, Column generation, Elementary flux mode, Kinetic modelling, Metabolic flux analysis, Optimization, Poly-pathway model
National Category
Bioinformatics (Computational Biology)
Identifiers
urn:nbn:se:kth:diva-246415 (URN)10.1016/j.mec.2018.e00083 (DOI)2-s2.0-85061356952 (Scopus ID)
Note

QC 20190402

Available from: 2019-04-02 Created: 2019-04-02 Last updated: 2019-11-19Bibliographically approved
Forsgren, A. & Wang, F. (2019). On the existence of a short pivoting sequence for a linear program.
Open this publication in new window or tab >>On the existence of a short pivoting sequence for a linear program
2019 (English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-256539 (URN)
Note

QCR 20190828

Available from: 2019-08-27 Created: 2019-08-27 Last updated: 2019-08-28Bibliographically approved
Böck, M., Eriksson, K. & Forsgren, A. (2019). On the interplay between robustness and dynamic planning for adaptive radiation therapy. BIOMEDICAL PHYSICS & ENGINEERING EXPRESS, 5(4)
Open this publication in new window or tab >>On the interplay between robustness and dynamic planning for adaptive radiation therapy
2019 (English)In: BIOMEDICAL PHYSICS & ENGINEERING EXPRESS, Vol. 5, no 4Article in journal (Refereed) Published
Abstract [en]

Interfractional geometric uncertainties can lead to deviations of the actual delivered dose from the prescribed dose distribution. To better handle these uncertainties during the course of treatment, the authors propose a dynamic framework for robust adaptive radiation therapy in which a variety of robust adaptive treatment strategies are introduced and evaluated. This variety is a result of optimization variables with various degrees of freedom within robust optimization models that vary in their grade of conservativeness. The different degrees of freedom in the optimization variables are expressed through either time-and-uncertainty-scenario-independence, time-dependence or time-and-uncertainty-scenario-dependence, while the robust models are either based on expected value-, worst-case- or conditional value-at-risk-optimization. The goal of this study is to understand which mathematical properties of the proposed robust adaptive strategies are relevant such that the accumulated dose can be steered as close as possible to the prescribed dose as the treatment progresses. We apply a result from convex analysis to show that the robust non-adaptive approach under conditions of convexity and permutation-invariance is at least as good as the time-dependent robust adaptive approach, which implies that the time-dependent problem can be solved by dynamically solving the corresponding time-independent problem. According to the computational study, non-adaptive robust strategies may provide sufficient target coverage comparable to robust adaptive strategies if the occurring uncertainties follow the same distribution as those included in the robust model. Moreover, the results indicate that time-and-uncertainty-scenario-dependent optimization variables are most compatible with worst-case-optimization, while time-and-uncertainty-scenario-independent find their best match with expected value optimization. In conclusion, the authors introduced a novel framework for robust adaptive radiation therapy and identified mathematical requirements to further develop robust adaptive strategies in order to improve treatment outcome in the presence of interfractional uncertainties.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2019
Keywords
optimization, adaptive radiation therapy, robust optimization, model predictive control
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-251454 (URN)10.1088/2057-1976/ab1bfc (DOI)000468299400004 ()2-s2.0-85070547198 (Scopus ID)
Note

QC 20190625

Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2020-03-09Bibliographically approved
Engberg, L., Eriksson, K. & Forsgren, A. (2018). Increased accuracy of planning tools for optimization of dynamic multileaf collimator delivery of radiotherapy through reformulated objective functions. Physics in Medicine and Biology, 63(12), Article ID 125012.
Open this publication in new window or tab >>Increased accuracy of planning tools for optimization of dynamic multileaf collimator delivery of radiotherapy through reformulated objective functions
2018 (English)In: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 63, no 12, article id 125012Article in journal (Refereed) Published
Abstract [en]

The purpose of this study is to examine in a clinical setting a novel formulation of objective functions for intensity-modulated radiotherapy treatment plan multicriteria optimization (MCO) that we suggested in a recent study. The proposed objective functions are extended with dynamic multileaf collimator (DMLC) delivery constraints from the literature, and a tailored interior point method is described to efficiently solve the resulting optimization formulation. In a numerical planning study involving three patient cases, DMLC plans Pareto optimal to the MCO formulation with the proposed objective functions are generated. Evaluated based on pre-defined plan quality indices, these DMLC plans are compared to conventionally generated DMLC plans. Comparable or superior plan quality is observed. Supported by these results, the proposed objective functions are argued to have a potential to streamline the planning process, since they are designed to overcome the methodological shortcomings associated with the conventional penalty-based objective functions assumed to cause the current need for time-consuming trial-and-error parameter tuning. In particular, the increased accuracy of the planning tools imposed by the proposed objective functions has the potential to make the planning process less complicated. These conclusions position the proposed formulation as an alternative to existing methods for automated planning.

Place, publisher, year, edition, pages
IOP PUBLISHING LTD, 2018
Keywords
automated treatment planning, multicriteria optimization, mean-tail-dose, objective functions
National Category
Production Engineering, Human Work Science and Ergonomics
Identifiers
urn:nbn:se:kth:diva-231728 (URN)10.1088/1361-6560/aac70a (DOI)000435199900002 ()29786611 (PubMedID)2-s2.0-85049372120 (Scopus ID)
Note

QC 20180814

Available from: 2018-08-14 Created: 2018-08-14 Last updated: 2019-08-20Bibliographically approved
Forsgren, A. & Odland, T. (2018). On exact linesearch quasi-Newton methods for minimizing a quadratic function. Computational optimization and applications, 69(1), 225-241
Open this publication in new window or tab >>On exact linesearch quasi-Newton methods for minimizing a quadratic function
2018 (English)In: Computational optimization and applications, ISSN 0926-6003, E-ISSN 1573-2894, Vol. 69, no 1, p. 225-241Article in journal (Refereed) Published
Abstract [en]

This paper concerns exact linesearch quasi-Newton methods for minimizing a quadratic function whose Hessian is positive definite. We show that by interpreting the method of conjugate gradients as a particular exact linesearch quasi-Newton method, necessary and sufficient conditions can be given for an exact linesearch quasi-Newton method to generate a search direction which is parallel to that of the method of conjugate gradients. We also analyze update matrices and give a complete description of the rank-one update matrices that give search direction parallel to those of the method of conjugate gradients. In particular, we characterize the family of such symmetric rank-one update matrices that preserve positive definiteness of the quasi-Newton matrix. This is in contrast to the classical symmetric-rank-one update where there is no freedom in choosing the matrix, and positive definiteness cannot be preserved. The analysis is extended to search directions that are parallel to those of the preconditioned method of conjugate gradients in a straightforward manner.

Place, publisher, year, edition, pages
Springer, 2018
Keywords
Method of conjugate gradients, Quasi-Newton method, Unconstrained quadratic program, Exact linesearch method
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-221353 (URN)10.1007/s10589-017-9940-7 (DOI)000419346400009 ()2-s2.0-85047629692 (Scopus ID)
Funder
Swedish Research Council, 621-2014-4772
Note

QC 20180117

Available from: 2018-01-17 Created: 2018-01-17 Last updated: 2018-06-12Bibliographically approved
Engberg, L., Forsgren, A., Eriksson, K. & Hardemark, B. (2017). Explicit optimization of plan quality measures in intensity-modulated radiation therapy treatment planning. Medical physics (Lancaster), 44(6), 2045-2053
Open this publication in new window or tab >>Explicit optimization of plan quality measures in intensity-modulated radiation therapy treatment planning
2017 (English)In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 44, no 6, p. 2045-2053Article in journal (Refereed) Published
Abstract [en]

Purpose: To formulate convex planning objectives of treatment plan multicriteria optimization with explicit relationships to the dose-volume histogram (DVH) statistics used in plan quality evaluation. Methods: Conventional planning objectives are designed to minimize the violation of DVH statistics thresholds using penalty functions. Although successful in guiding the DVH curve towards these thresholds, conventional planning objectives offer limited control of the individual points on the DVH curve (doses-at-volume) used to evaluate plan quality. In this study, we abandon the usual penalty-function framework and propose planning objectives that more closely relate to DVH statistics. The proposed planning objectives are based on mean-tail-dose, resulting in convex optimization. We also demonstrate how to adapt a standard optimization method to the proposed formulation in order to obtain a substantial reduction in computational cost. Results: We investigated the potential of the proposed planning objectives as tools for optimizing DVH statistics through juxtaposition with the conventional planning objectives on two patient cases. Sets of treatment plans with differently balanced planning objectives were generated using either the proposed or the conventional approach. Dominance in the sense of better distributed doses-at-volume was observed in plans optimized within the proposed framework. Conclusion: The initial computational study indicates that the DVH statistics are better optimized and more efficiently balanced using the proposed planning objectives than using the conventional approach.

Place, publisher, year, edition, pages
WILEY, 2017
Keywords
convex optimization, mean-tail-dose, planning objectives
National Category
Radiology, Nuclear Medicine and Medical Imaging
Identifiers
urn:nbn:se:kth:diva-213816 (URN)10.1002/mp.12146 (DOI)000408033400003 ()28160520 (PubMedID)2-s2.0-85024484606 (Scopus ID)
Note

QC 20170911

Available from: 2017-09-11 Created: 2017-09-11 Last updated: 2018-10-24Bibliographically approved
Böck, M., Eriksson, K., Forsgren, A. & Hardemark, B. (2017). Toward robust adaptive radiation therapy strategies. Medical physics (Lancaster), 44(6), 2054-2065
Open this publication in new window or tab >>Toward robust adaptive radiation therapy strategies
2017 (English)In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 44, no 6, p. 2054-2065Article in journal (Refereed) Published
Abstract [en]

Purpose: To set up a framework combining robust treatment planning with adaptive re-optimization in order to maintain high treatment quality, to respond to interfractional geometric variations and to identify those patients who will benefit the most from an adaptive fractionation schedule. Methods: The authors propose robust adaptive strategies based on stochastic minimax optimization for a series of simulated treatments on a one-dimensional patient phantom. The plan applied during the first fractions should be able to handle anticipated systematic and random errors. Information on the individual geometric variations is gathered at each fraction. At scheduled fractions, the impact of the measured errors on the delivered dose distribution is evaluated. For a patient having received a dose that does not satisfy specified plan quality criteria, the plan is re-optimized based on these individually measured errors. The re-optimized plan is then applied during subsequent fractions until a new scheduled adaptation becomes necessary. In this study, three different adaptive strategies are introduced and investigated. (a) In the first adaptive strategy, the measured systematic and random error scenarios and their assigned probabilities are updated to guide the robust re-optimization. (b) In the second strategy, the degree of conservativeness is adapted in response to the measured dose delivery errors. (c) In the third strategy, the uncertainty margins around the target are recalculated based on the measured errors. The simulated treatments are subjected to systematic and random errors that are either similar to the anticipated errors or unpredictably larger in order to critically evaluate the performance of these three adaptive strategies. Results: According to the simulations, robustly optimized treatment plans provide sufficient treatment quality for those treatment error scenarios similar to the anticipated error scenarios. Moreover, combining robust planning with adaptation leads to improved organ-at-risk protection. In case of unpredictably larger treatment errors, the first strategy in combination with at most weekly adaptation performs best at notably improving treatment quality in terms of target coverage and organ-at-risk protection in comparison with a non-adaptive approach and the other adaptive strategies. Conclusion: The authors present a framework that provides robust plan re-optimization or margin adaptation of a treatment plan in response to interfractional geometric errors throughout the fractionated treatment. According to the simulations, these robust adaptive treatment strategies are able to identify candidates for an adaptive treatment, thus giving the opportunity to provide individualized plans, and improve their treatment quality through adaptation. The simulated robust adaptive framework is a guide for further development of optimally controlled robust adaptive therapy models.

Place, publisher, year, edition, pages
WILEY, 2017
Keywords
adaptive radiation therapy, robust optimization, treatment planning, uncertainty
National Category
Radiology, Nuclear Medicine and Medical Imaging
Identifiers
urn:nbn:se:kth:diva-213817 (URN)10.1002/mp.12226 (DOI)000408033400004 ()28317129 (PubMedID)2-s2.0-85024370829 (Scopus ID)
Note

QC 20170911

Available from: 2017-09-11 Created: 2017-09-11 Last updated: 2019-05-14Bibliographically approved
Forsgren, A., Gill, P. E. & Wong, E. (2016). Primal and dual active-set methods for convex quadratic programming. Mathematical programming, 159(1-2), 469-508
Open this publication in new window or tab >>Primal and dual active-set methods for convex quadratic programming
2016 (English)In: Mathematical programming, ISSN 0025-5610, E-ISSN 1436-4646, Vol. 159, no 1-2, p. 469-508Article in journal (Refereed) Published
Abstract [en]

Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bounds on the variables. In the first part of the paper, two methods are proposed, one primal and one dual. These methods generate a sequence of iterates that are feasible with respect to the equality constraints associated with the optimality conditions of the primal-dual form. The primal method maintains feasibility of the primal inequalities while driving the infeasibilities of the dual inequalities to zero. The dual method maintains feasibility of the dual inequalities while moving to satisfy the primal inequalities. In each of these methods, the search directions satisfy a KKT system of equations formed from Hessian and constraint components associated with an appropriate column basis. The composition of the basis is specified by an active-set strategy that guarantees the nonsingularity of each set of KKT equations. Each of the proposed methods is a conventional active-set method in the sense that an initial primal- or dual-feasible point is required. In the second part of the paper, it is shown how the quadratic program may be solved as a coupled pair of primal and dual quadratic programs created from the original by simultaneously shifting the simple-bound constraints and adding a penalty term to the objective function. Any conventional column basis may be made optimal for such a primal-dual pair of shifted-penalized problems. The shifts are then updated using the solution of either the primal or the dual shifted problem. An obvious application of this approach is to solve a shifted dual QP to define an initial feasible point for the primal (or vice versa). The computational performance of each of the proposed methods is evaluated on a set of convex problems from the CUTEst test collection.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2016
Keywords
Quadratic programming, Active-set methods, Convex quadratic programming, Primal active-set methods, Dual active-set methods
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-193822 (URN)10.1007/s10107-015-0966-2 (DOI)000382053900015 ()2-s2.0-84949941906 (Scopus ID)
Note

QC 20161019

Available from: 2016-10-19 Created: 2016-10-11 Last updated: 2017-11-29Bibliographically approved
Oddsdottir, H. A., Hagrot, E., Chotteau, V. & Forsgren, A. (2016). Robustness analysis of elementary flux modes generated by column generation. Mathematical Biosciences, 273, 45-56
Open this publication in new window or tab >>Robustness analysis of elementary flux modes generated by column generation
2016 (English)In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 273, p. 45-56Article in journal (Refereed) Published
Abstract [en]

Elementary flux modes (EFMs) are vectors defined from a metabolic reaction network, giving the connections between substrates and products. EFMs-based metabolic flux analysis (MFA) estimates the flux over each EFM from external flux measurements through least-squares data fitting. The measurements used in the data fitting are subject to errors. A robust optimization problem includes information on errors and gives a way to examine the sensitivity of the solution of the EFMs-based MFA to these errors. In general, formulating a robust optimization problem may make the problem significantly harder. We show that in the case of the EFMs-based MFA, when the errors are only in measurements and bounded by an interval, the robust problem can be stated as a convex quadratic programming (QP) problem. We have previously shown how the data fitting problem may be solved in a column-generation framework. In this paper, we show how column generation may be applied also to the robust problem, thereby avoiding explicit enumeration of EFMs. Furthermore, the option to indicate intervals on metabolites that are not measured is introduced in this column generation framework. The robustness of the data is evaluated in a case-study, which indicates that the solutions of our non-robust problems are in fact near-optimal also when robustness is considered, implying that the errors in measurement do not have a large impact on the optimal solution. Furthermore, we showed that the addition of intervals on unmeasured metabolites resulted in a change in the optimal solution.

Place, publisher, year, edition, pages
Elsevier, 2016
Keywords
Metabolic network, Robust optimization, Least-squares, Elementary flux mode, Chinese hamster ovary cell
National Category
Bioinformatics (Computational Biology)
Identifiers
urn:nbn:se:kth:diva-184008 (URN)10.1016/j.mbs.2015.12.009 (DOI)000370908500004 ()26748294 (PubMedID)2-s2.0-84960376800 (Scopus ID)
Note

QC 20160330

Available from: 2016-03-30 Created: 2016-03-22 Last updated: 2018-01-10Bibliographically approved
Fredriksson, A., Forsgren, A. & Hardemark, B. (2015). Maximizing the probability of satisfying the clinical goals in radiation therapy treatment planning under setup uncertainty. Medical physics (Lancaster), 42(7), 3992-3999
Open this publication in new window or tab >>Maximizing the probability of satisfying the clinical goals in radiation therapy treatment planning under setup uncertainty
2015 (English)In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 42, no 7, p. 3992-3999Article in journal (Refereed) Published
Abstract [en]

Purpose: This paper introduces a method that maximizes the probability of satisfying the clinical goals in intensity-modulated radiation therapy treatments subject to setup uncertainty. Methods: The authors perform robust optimization in which the clinical goals are constrained to be satisfied whenever the setup error falls within an uncertainty set. The shape of the uncertainty set is included as a variable in the optimization. The goal of the optimization is to modify the shape of the uncertainty set in order to maximize the probability that the setup error will fall within the modified set. Because the constraints enforce the clinical goals to be satisfied under all setup errors within the uncertainty set, this is equivalent to maximizing the probability of satisfying the clinical goals. This type of robust optimization is studied with respect to photon and proton therapy applied to a prostate case and compared to robust optimization using an a priori defined uncertainty set. Results: Slight reductions of the uncertainty sets resulted in plans that satisfied a larger number of clinical goals than optimization with respect to a priori defined uncertainty sets, both within the reduced uncertainty sets and within the a priori, nonreduced, uncertainty sets. For the prostate case, the plans taking reduced uncertainty sets into account satisfied 1.4 (photons) and 1.5 (protons) times as many clinical goals over the scenarios as the method taking a priori uncertainty sets into account. Conclusions: Reducing the uncertainty sets enabled the optimization to find better solutions with respect to the errors within the reduced as well as the nonreduced uncertainty sets and thereby achieve higher probability of satisfying the clinical goals. This shows that asking for a little less in the optimization sometimes leads to better overall plan quality.

Keywords
IMRT, IMPT, optimization, robustness, uncertainty
National Category
Other Medical Sciences
Identifiers
urn:nbn:se:kth:diva-171901 (URN)10.1118/1.4921998 (DOI)000357686400020 ()26133599 (PubMedID)2-s2.0-84935005101 (Scopus ID)
Note

QC 20150812

Available from: 2015-08-12 Created: 2015-08-10 Last updated: 2017-12-04Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-6252-7815

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