×

zbMATH — the first resource for mathematics

Intensity modulated radiation therapy treatment plan optimization. With comments and rejoinder. (English) Zbl 1154.90019
Summary: We provide an overview of the state-of-the-art of optimization models for static radiation therapy treatment planning, focusing in particular on intensity modulated radiation therapy (IMRT) by (i) establishing a novel connection between risk management and radiation therapy treatment planning, and (ii) unifying and contrasting two different modeling approaches. In addition, we discussion recent and ongoing technological developments which show that this area of research is a lively and promising one that can continue to help patients by improving the clinical practice of radiation therapy.

MSC:
90C90 Applications of mathematical programming
90B50 Management decision making, including multiple objectives
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Agazaryan N, Solberg TD (2003) Segmental and dynamic intensity-modulated radiotherapy delivery techniques for micro-multileaf collimator. Med Phys 30(7):1758–1765
[2] Ahuja RK, Hamacher HW (2005) A network flow algorithm to minimize beam-on-time for unconstrained multileaf collimator problems in cancer radiation therapy. Networks 45(1):36–41 · Zbl 1061.92033
[3] Alber M, Nüsslin F (2001) A representation of an NTCP function for local complication mechanisms. Phys Med Biol 46:439–447
[4] Aleman DM, Kumar A, Ahuja RK, Romeijn HE, Dempsey JF (2007a) Neighborhood search approaches to beam orientation optimization in intensity modulated radiation therapy treatment planning. Technical report, Department of Industrial and Systems Engineering, University of Florida. J Glob Optim (forthcoming) · Zbl 1177.90436
[5] Aleman DM, Romeijn HE, Dempsey JF (2007b) A response surface approach to beam orientation optimization in intensity modulated radiation therapy treatment planning. Technical report, Department of Industrial and Systems Engineering, University of Florida. INFORMS J Comput (forthcoming)
[6] Aleman DM, Romeijn HE, Dempsey JF (2008) Beam orientation optimization methods in intensity modulated radiation therapy treatment planning. In: Lim G, Lee EK (eds) Optimization in medicine and biology. Taylor and Francis, London, pp 223–251
[7] American Cancer Society (2008) Cancer facts & figures. Report. http://www.cancer.org/
[8] Baatar D, Hamacher HW, Ehrgott M, Woeginger GJ (2005) Decomposition of integer matrices and multileaf collimator sequencing. Discrete Appl Math 152(1):6–34 · Zbl 1084.15014
[9] Bednarz G, Michalski D, Houser C, Huq MS, Xiao Y, Anne PR, Galvin JM (2002) The use of mixed-integer programming for inverse treatment planning with pre-defined field segments. Phys Med Biol 47(13):2235–2245
[10] Boland N, Hamacher HW, Lenzen F (2004) Minimizing beam-on time in cancer radiation treatment using multileaf collimators. Networks 43(4):226–240 · Zbl 1044.92030
[11] Bortfeld T (1999) Optimized planning using physical objectives and constraints. Semin Radiat Oncol 19(1):20–34
[12] Bortfeld T, Burkelbach J, Boesecke R, Schlegel W (1990) Methods of image reconstruction from projections applied to conformal radiotherapy. Phys Med Biol 25(4):435–443
[13] Bortfeld TR, Kahler DL, Waldron TJ, Boyer AL (1994) X-ray field compensation with multileaf collimators. Int J Radiat Oncol Biol Phys 28:723–370
[14] Bortfeld T, Chan TCY, Trofimov A, Tsitsiklis JN (2008a) Robust management of motion uncertainty in intensity-modulated radiation therapy. Technical report, Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts. Operat Res (forthcoming) · Zbl 1167.90582
[15] Bortfeld T, Craft D, Dempsey JF, Halabi T, Romeijn HE (2008b) Evaluating target cold spots by use of tail EUDs. Phys Med Biol 71(3):880–889
[16] Brahme A (1995) Treatment optimization using physical and radiobiological objective functions. In: Smith AR (ed) Radiation therapy physics. Springer, Berlin, pp 209–246
[17] Brahme A (2001) Individualizing cancer treatment: biological optimization models in treatment planning and delivery. Int J Radiat Oncol Biol Phys 49(2):327–337
[18] Brahme A, Ågren AK (1987) Optimal dose distribution for eradication of heterogeneous tumours. Acta Oncol 26:377–385
[19] Carlsson F (2008) Combining segment generation with direct step-and-shoot optimization in intensity-modulated radiation therapy. Med Phys 35(9):3828–3838
[20] Carlsson F, Forsgren A (2006) Iterative regularization in intensity-modulated radiation therapy optimization. Med Phys 33(1):225–234
[21] Carlsson F, Forsgren A (2008) A conjugate-gradient based approach for approximate solutions to quadratic programs. Technical report, Royal Institute of Technology (KTH), Stockholm, Sweden
[22] Carlsson F, Forsgren A, Rehbinder H, Eriksson K (2006) Using eigenstructure of the Hessian to reduce the dimension of the intensity modulated radiation therapy optimization problem. Ann Operat Res 148:81–94 · Zbl 1104.92030
[23] Chan TCY, Bortfeld T, Tsitsiklis JN (2006) A robust approach to IMRT optimization. Phys Med Biol 51:2567–2583
[24] Chao KSC, Deasy JO, Markman J, Haynie J, Perez CA, Purdy JA (2001) A prospective study of salivary function sparing in patients with head-and-neck cancers receiving intensity modulated or three-dimensional radiation therapy: initial results. Int J Radiat Oncol Biol Phys 49(4):907–916
[25] Choi B, Deasy JO (2002) The generalized equivalent uniform dose function as a basis for intensity-modulated treatment planning. Phys Med Biol 47:3579–3589
[26] Chu M, Zinchenko Y, Henderson SG, Sharpe MB (2005) Robust optimization for intensity modulated radiation therapy treatment planning under uncertainty. Phys Med Biol 50:5463–5477
[27] Craft D, Bortfeld T (2008) How many plans are needed in an IMRT multi-objective plan database? Phys Med Biol 53(11):2785–2796
[28] Craft D, Halabi T, Bortfeld T (2005) Exploration of tradeoffs in intensity-modulated radiotherapy. Phys Med Biol 50(24):5857–5868
[29] Dai J, Zhu Y (2001) Minimizing the number of segments in a delivery sequence for intensity-modulated radiation therapy with a multileaf collimator. Med Phys 28(10):2113–2120
[30] Das SK, Marks LB (1997) Selection of coplanar or noncoplanar beams using three-dimensional optimization based on maximum beam separation and minimized nontarget irradiation. Int J Radiat Oncol Biol Phys 38:643–655
[31] Dempsey JF, Romeijn HE, Li JG, Low DA, Palta JR (2005) A Fourier analysis of the dose grid resolution required for accurate IMRT fluence map optimization. Med Phys 32(2):380–388
[32] Engel K (2005) A new algorithm for optimal multileaf collimator field segmentation. Discrete Appl Math 152(1):35–51 · Zbl 1076.92026
[33] Fallone G, Carlone M, Murray B, Rathee S, Steciw S (2007) Investigations in the design of a novel linac-MRI system. Int J Radiat Oncol Biol Phys 69(3, Suppl. 1):S19. Abstract, 49th annual meeting of the American Society for Therapeutic Radiology and Oncology
[34] Ferris MC, Voelker MM (2004) Fractionation in radiation treatment planning. Math Program 101:387–413 · Zbl 1055.92023
[35] Fowler JF (1989) The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol 62:679–694
[36] Fraass B, Balter J, Ten Haken R, McShan D (2003) Margins, errors and plan optimization. Radiother Oncol 68(Suppl. 1):S34
[37] Goitein M (1987) Tumour control probability for an inhomogeneously irradiated target volume. In: Evaluation of treatment planning for particle beam radiotherapy. National Cancer Institute
[38] Haas OC, Burnham KJ, Mills J (1998) Optimization of beam orientation in radiotherapy using planar geometry. Phys Med Biol 43:2179–2193
[39] Hall EJ (1993) Radiobiology for the radiologist, 4th edn. Lippincott Williams & Wilkins Publishers, Hagerstown
[40] Hamacher HW, Küfer K-H (2002) Inverse radiation therapy planning–a multiple objective optimization approach. Discrete Appl Math 118:145–161 · Zbl 0995.92024
[41] Hardy GH, Littlewood JE, Pólya G (1952) Inequalities. Cambridge University Press, Cambridge
[42] Hoffmann AL, Siem AYD, den Hertog D, Kaanders JHAM, Huizenga H (2006) Derivative-free generation and interpolation of convex Pareto optimal IMRT plans. Phys Med Biol 51(24):6349–6369
[43] Hoffmann AL, den Hertog D, Siem AYD, Kaanders JHAM, Huizenga H (2008) Convex reformulation of biologically-based multi-criteria IMRT optimisation including fractionation effects. Phys Med Biol 53(22):6345–6362
[44] Holmes T, Mackie TR (1994) A filtered backprojection dose calculation method for inverse treatment planning. Med Phys 21:321–333
[45] Hutchinson Encyclopaedia (2000) Helicon Publishing
[46] ICRU (International Commission on Radiation Units and Measurements) (1993) Prescribing, recording and reporting photon beam therapy. Report 50
[47] ICRU (International Commission on Radiation Units and Measurements) (1999) Prescribing, recording and reporting photon beam therapy. Supplement to report 50
[48] Jackson A (2001) Partial irradiation of the rectum. Semin Radiat Oncol 11:215–223
[49] Jackson A, Kutcher GJ, Yorke ED (1993) Probability of radiation-induced complications for normal tissues with parallel architecture subject to non-uniform irradiation. Med Phys 20:613–625
[50] Kalinowski T (2004) The algorithmic complexity of the minimization of the number of segments in multileaf collimator field segmentation. Technical report, Fachbereich Mathematik, Universität Rostock, Rostock, Germany, August 2004
[51] Kalinowski T (2005) A duality based algorithm for multileaf collimator field segmentation with interleaf collision constraint. Discrete Appl Math 152(1):52–88 · Zbl 1078.92035
[52] Kamath S, Sahni S, Li J, Palta J, Ranka S (2003) Leaf sequencing algorithms for segmented multileaf collimation. Phys Med Biol 48(3):307–324 · Zbl 1341.92028
[53] Kamath S, Sahni S, Palta J, Ranka S (2004a) Algorithms for optimal sequencing of dynamic multileaf collimators. Phys Med Biol 49(1):33–54 · Zbl 1341.92028
[54] Kamath S, Sahni S, Palta J, Ranka S, Li J (2004b) Optimal leaf sequencing with elimination of tongue-and-groove underdosage. Phys Med Biol 49(3):N7–N19
[55] Kamath S, Sahni S, Ranka S, Li J, Palta J (2004c) A comparison of step-and-shoot leaf sequencing algorithms that eliminate tongue-and-groove effects. Phys Med Biol 49(14):3137–3143
[56] Kamath S, Sahni S, Ranka S, Li J, Palta J (2004d) Optimal field splitting for large intensity-modulated fields. Med Phys 31(12):3314–3323
[57] Küfer K-H, Hamacher HW, Bortfeld TR (2000) A multicriteria optimization approach for inverse radiotherapy planning. In Bortfeld TR, Schlegel W (eds) Proceedings of the XIIIth ICCR, Heidelberg, Germany, pp 26–29
[58] Küfer K-H, Monz M, Scherrer A, Trinkhaus HL, Bortfeld T, Thieke C (2003) Intensity modulated radiotherapy–a large scale multi-criteria programming problem. OR Spektrum 25:223–249 · Zbl 1018.92015
[59] Kutcher GJ, Burman C (1989) Calculation of complication probability factors for non-uniform normal tissue irradiation: the effective volume method. Int J Radiat Oncol Biol Phys 16:1623–1630
[60] Lagendijk JJ, Raaymakers BW, Raaijmakers AJ, Overweg J, Brown KJ, Kerkhof EM, van der Put RW, Hårdemark B, van Vulpen M, van der Heide UA (2008) MRI/linac integration. Radiat Oncol 86(1):25–29
[61] Lahanas M, Schreibmann E, Baltas D (2003) Multiobjective inverse planning for intensity modulated radiotherapy with constraint-free gradient-based optimization algorithms. Phys Med Biol 48:2843–2871 · Zbl 1036.90544
[62] Langen KM, Jones DTL (2001) Organ motion and its management. Med Phys 50(1):265–278
[63] Langer M, Brown R, Urie M, Leong J, Stracher M, Shapiro J (1990) Large-scale optimization of beam weights under dose-volume restrictions. Int J Radiat Oncol Biol Phys 18(4):887–893
[64] Langer M, Thai V, Papiez L (2001) Improved leaf sequencing reduces segments or monitor units needed to deliver IMRT using multileaf collimators. Med Phys 28(12):2450–2458
[65] Lee EK, Fox T, Crocker I (2000) Optimization of radiosurgery treatment planning via mixed integer programming. Med Phys 27(5):995–1004
[66] Lee EK, Fox T, Crocker I (2003) Integer programming applied to intensity-modulated radiation treatment planning. Ann Operat Res 119:165–181 · Zbl 1046.90050
[67] Lenzen F (2000) An integer programming approach to the multileaf collimator problem. Master’s thesis, University of Kaiserslautern, Department of Mathematics, Kaiserslautern, Germany, June 2000
[68] Lim GJ, Choi J (2006) A two-stage integer programming approach for optimizing leaf sequence in IMRT. Technical report, Department of Industrial Engineering, University of Houston, Houston, Texas
[69] Lim GJ, Choi J, Mohan R (2008) Iterative solution methods for beam angle and fluence map optimization in intensity modulated radiation therapy treatment planning. OR Spectrum 30(2):289–309 · Zbl 1132.92009
[70] Lyman JT (1985) Complication probability as assessed from dose-volume histograms. Res Rep 8:S13–19
[71] Lyman JT, Wolbarst AB (1987a) Optimization of radiation therapy III: a method of assessing complication probabilities from dose-volume histograms. Int J Radiat Oncol Biol Phys 13:103–109
[72] Lyman JT, Wolbarst AB (1987b) Optimization of radiation therapy IV: a dose-volume histogram reduction algorithm. Int J Radiat Oncol Biol Phys 13:103–109
[73] Mageras GS, Mohan R (1993) Application of fast simulated annealing to optimization of conformal radiation treatments. Med Phys 20:639–647
[74] Maguire PD, Sibley GS, Zhou S-M, Jamieson TA, Light KL, Antoine PA, Herndon JE, Anscher MS, Marks LB (1999) Clinical and dosimetric predictors of radiation-induced esophageal toxicity. Int J Radiat Oncol Biol Phys 45:97–103
[75] McGary JE, Grant W III, Woo SY (2000) Applying the equivalent uniform dose formulation based on the linear-quadratic model to inhomogeneous tumor dose distribution: caution for analyzing and reporting. J Appl Clin Med Phys 1(4):126–137
[76] Men C, Romeijn HE, Taşkın ZC, Dempsey JF (2007) An exact approach to direct aperture optimization in IMRT treatment planning. Phys Med Biol 52(24):7333–7352
[77] Men C, Romeijn HE, Saito A, Dempsey JF (2008) A new stochastic programming approach to incorporating interfraction motion in IMRT treatment planning. Working paper
[78] Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer Academic, Boston · Zbl 0949.90082
[79] Munro TR, Gilbert CW (1961) The relation between tumour lethal doses and the radiosensitivity of tumour cells. Br J Radiol 34:246–251
[80] Murphy GP, Lawrence WL, Lenlard RE (eds) (1995) American cancer society textbook on clinical oncology. The American Cancer Society, Atlanta
[81] Niemierko A (1997) Reporting and analyzing dose distributions: a concept of equivalent uniform dose. Med Phys 24(1):103–110
[82] Niemierko A (1999) A generalized concept of equivalent uniform dose. Med Phys 26(6):1100
[83] Niemierko A, Goitein M (1991) Calculation of normal tissue complication probability and dose-volume histogram reduction schemes for tissues with a critical element architecture. Radiat Oncol 20:166–176
[84] Niemierko A, Goitein M (1993) Modeling of normal tissue response to radiation: the critical volume model. Int J Radiat Oncol Biol Phys 25:135–145
[85] Pareto V (1971) Manual of political economy. AM Kelley, New York. Translation of Manuale di economia politica (1906)
[86] Perez CA, Brady LW (1998) Principles and practice of radiotherapy, 3rd edn. Lippincott-Raven, Philadelphia
[87] Preciado-Walters F, Langer M, Rardin R, Thai V (2004) A coupled column generation, mixed integer approach to optimal planning of intensity modulated radiation therapy for cancer. Math Program 101(2):319–338 · Zbl 1055.92029
[88] Preciado-Walters F, Rardin R, Langer M, Thai V (2006) Column generation for IMRT cancer therapy optimization with implementable segments. Ann Operat Res 148:65–79 · Zbl 1106.92039
[89] Que W (1999) Comparison of algorithms for multileaf collimator field segmentation. Med Phys 26(11):2390–2396
[90] Que W, Kung J, Dai J (2004) ”Tongue-and-groove” effect in intensity modulated radiotherapy with static multileaf collimator fields. Phys Med Biol 49(3):399–405
[91] Romeijn HE, Ahuja RK, Dempsey JF, Kumar A, Li JG (2003) A novel linear programming approach to fluence map optimization for intensity modulated radiation therapy treatment planning. Phys Med Biol 48(21):3521–3542
[92] Romeijn HE, Dempsey JF, Li JG (2004) A unifying framework for multi-criteria fluence map optimization models. Phys Med Biol 49:1991–2013
[93] Romeijn HE, Ahuja RK, Dempsey JF, Kumar A (2005) A column generation approach to radiation therapy treatment planning using aperture modulation. SIAM J Optim 15(3):838–862 · Zbl 1077.90084
[94] Romeijn HE, Ahuja RK, Dempsey JF, Kumar A (2006) A new linear programming approach to radiation therapy treatment planning problems. Operat Res 54(2):201–216 · Zbl 1167.90587
[95] Rosen I, Lam KS, Lane RG, Langer M, Morrill SM (1995) Comparison of simulated annealing algorithms for conformal therapy treatment planning. Int J Radiat Oncol Biol Phys 33(5):1091–1099
[96] Schreibmann E, Lahanas M, Xing L, Baltas D (2004) Multiobjective evolutionary optimization of the number of beams, their orientations and weights for intensity-modulated radiation therapy. Phys Med Biol 49:747–770
[97] Schultheiss TE, Orton CG, Peck RA (1983) Models in radiotherapy: volume effects. Med Phys 10:410–415
[98] Shepard DM, Ferris MC, Olivera GH, Mackie TR (1999) Optimizing the delivery of radiation therapy to cancer patients. SIAM Rev 41(4):721–744 · Zbl 0955.90089
[99] Shepard DM, Ferris MC, Reckwerdt PJ, Mackie TR (2000) Iterative approaches to dose optimization in tomotherapy. Phys Med Biol 45:69–90
[100] Shepard DM, Earl MA, Li XA, Naqvi S, Yu C (2002) Direct aperture optimization: a turnkey solution for step-and-shoot IMRT. Med Phys 29(6):1007–1018
[101] Siebers JV, Lauterbach M, Keall PJ, Mohan R (2002) Incorporating multi-leaf collimator leaf sequencing into iterative IMRT optimization. Med Phys 29(6):952–959
[102] Siochi RAC (1999) Minimizing static intensity modulation delivery time using an intensity solid paradigm. Int J Radiat Oncol Biol Phys 43(43):671–689
[103] Siochi RAC (2004) Modifications to the IMFAST leaf sequencing optimization algorithm. Med Phys 31(12):3267–3278
[104] Siochi RAC (2007) Variable depth recursion algorithm for leaf sequencing. Med Phys 34(2):664–672
[105] Sir MY, Pollock SM, Epelman MA, Lam KL, Ten Haken RK (2008) Ideal spatial radiotherapy dose distributions subject to positional uncertainties. Phys Med Biol 51(24):6329–6347
[106] Stavrev P, Hristov D, Warkentin B, Sham E, Stavreva N, Fallone BG (2003) Inverse treatment planning by physically constrained minimization of a biological objective function. Med Phys 30(11):2948–2958
[107] Stavreva NA, Stavrev P, Warkentin B, Fallone BG (2003) Investigating the effect of cell repopulation on the tumor response to fractionated external radiotherapy. Med Phys 30(5):735–742
[108] Steel GG (2002) Basic clinical radiobiology, 3rd edn. Arnold, Sevenoaks
[109] Steuer R (1986) Multicriteria optimization: theory, computation and applications. Wiley, New York · Zbl 0663.90085
[110] Stroom JC, Heijmen BJM (2003) Usefulness of margins for normal structures. Radiother Oncol 68(Suppl. 1):S34
[111] Taşkın ZC, Smith JC, Romeijn HE, Dempsey JF (2008) Optimal multileaf collimator leaf sequencing in IMRT treatment planning. Technical report, Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida · Zbl 1228.90171
[112] Thieke C, Bortfeld T, Küfer KH (2003a) New optimization concepts in inverse treatment planning. Radiat Oncol 68(Suppl. 1):S2. Abstract, pre-meeting workshop on ”optimization of IMRT”, 7th biennial ESTRO meeting on physics and radiation technology for clinical radiotherapy, Geneva, Switzerland
[113] Thieke C, Bortfeld T, Niemierko A, Küfer KH, Nill S (2003b) Multicriteria optimization in inverse radiotherapy planning. Radiat Oncol 68(Suppl. 1):S44. Abstract, 7th biennial ESTRO meeting on physics and radiation technology for clinical radiotherapy, Geneva, Switzerland
[114] Thieke C, Bortfeld T, Niemierko A, Nill S (2003) From physical dose constraints to equivalent uniform dose constraints in inverse radiotherapy planning. Med Phys 30(9):2332–2339
[115] Tsien C, Eisbruch A, McShan D, Kessler M, Marsh R, Fraass B (2003) Intensity-modulated radiation therapy (IMRT) for locally advanced paranasal sinus tumors: Incorporating clinical decisions in the optimization process. Int J Radiat Oncol Biol Phys 55(3):776–784
[116] Van Santvoort JPC, Heijmen BJM (1996) Dynamic multileaf collimation without ’tongue-and-groove’ underdosage effects. Phys Med Biol 41(10):2091–2105
[117] Webb S (1989) Optimization of conformal radiotherapy dose distributions by simulated annealing. Phys Med Biol 34:1349–1370
[118] Webb S (1992) Optimization by simulated annealing of three-dimensional conformal treatment planning for radiation fields defined by multiple collimator. II. Inclusion of two-dimensional modulation of X-ray intensity. Phys Med Biol 37:1689–1704
[119] Webb S, Lomax T (2001) There is no IMRT? Phys Med Biol 46:L7–L8
[120] Withers HR, Taylor JMG, Maciejewski B (1988) Treatment volume and tissue tolerance. Int J Radiat Oncol Biol Phys 15:751–759
[121] Withers HR, McBride WH (1998) Biologic basis of radiation therapy. In: Perez CA, Brady LW (eds) Principles and practice of radiotherapy. Lippincott-Raven, Philadelphia, pp 79–118, chap 2
[122] Wolbarst AB (1984) Optimization of radiation therapy II: the critical-voxel method. Int J Radiat Oncol Biol Phys 10:741–745
[123] Wu Q, Mohan R, Niemierko A, Schmidt-Ullrich R (2002) Optimization of intensity-modulated radiotherapy plans based on the equivalent uniform dose. Int J Radiat Oncol Biol Phys 52(1):224–235
[124] Xia P, Verhey LJ (1998) Multileaf collimator leaf sequencing algorithm for intensity modulated beams with multiple static segments. Med Phys 25(8):1424–1434
[125] Xing L, Chen GTY (1996) Iterative methods for inverse treatment planning. Phys Med Biol 41:2107–2123
[126] Yang Y, Xing L (2004) Inverse treatment planning with adaptively evolving voxel-dependent penalty scheme. Med Phys 31(10):2839–2844
[127] Yorke ED, Jackson A, Kutcher GJ, Ling CC (1993) Probability of radiation-induced complications in normal tissues with parallel architecture under conditions of uniform whole or partial organ irradiation. Radiother Oncol 26:226–237
[128] Yu CX, Jaffray DA, Wong JW (1998) The effects of intra-fraction organ motion on the delivery of dynamic intensity modulation. Phys Med Biol 43:91–104
[129] Zaider M, Minerbo GN (2000) Tumour control probability: a formulation applicable to any temporal protocol of dose delivery. Phys Med Biol 45:279–293
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.