Biomedical subjects

J G Li

Publications and source records attributed to J G Li.

At least 19 recordsLinked to original sources

PubMed2001

Role of beam orientation optimization in intensity-modulated radiation therapy.

PURPOSE: To investigate the role of beam orientation optimization in intensity-modulated radiation therapy (IMRT) and to examine the potential benefits of noncoplanar intensity-modulated beams. METHODS AND MATERIALS: A beam orientation optimization algorithm was implemented. For this purpose, system variables were divided into two groups: beam position (gantry and table angles) and beam profile (beamlet weights). Simulated annealing was used for beam orientation optimization and the simultaneous iterative inverse treatment planning algorithm (SIITP) for beam intensity profile optimization. Three clinical cases were studied: a localized prostate cancer, a nasopharyngeal cancer, and a paraspinal tumor. Nine fields were used for all treatments. For each case, 3 types of treatment plan optimization were performed: (1) beam intensity profiles were optimized for 9 equiangular spaced coplanar beams; (2) orientations and intensity profiles were optimized for 9 coplanar beams; (3) orientations and intensity profiles were optimized for 9 noncoplanar beams. RESULTS: For the localized prostate case, all 3 types of optimization described above resulted in dose distributions of a similar quality. For the nasopharynx case, optimized noncoplanar beams provided a significant gain in the gross tumor volume coverage. For the paraspinal case, orientation optimization using noncoplanar beams resulted in better kidney sparing and improved gross tumor volume coverage. CONCLUSION: The sensitivity of an IMRT treatment plan with respect to the selection of beam orientations varies from site to site. For some cases, the choice of beam orientations is important even when the number of beams is as large as 9. Noncoplanar beams provide an additional degree of freedom for IMRT treatment optimization and may allow for notable improvement in the quality of some complicated plans.

Algorithms↗

PubMed2001

[A study on breeding of "Ganzaoxian 47" from dry seeds of rice carried by recoverable satellite].

OBJECTIVE: To observe and investigate the variation and heredity of the offspring of dry seeds of rice carried by satellite, hence to select early maturing mutants, and to cultivate directly "Ganzaoxian 47" new varieties for production application. Isozymes analyses and studies of the new varieties and its original CK varieties were made. METHOD: Dry seeds of rice restorer line were carried to the space on board a recoverable satellite for 7 d in 1992. After recovery the seeds were planted in the field to study the agricultural characters, yield, disease resistance, rice quality and peroxidase isozymes change. RESULT: Its agricultural characters, yield, disease resistance, rice quality and peroxidase isozymes all showed distinct changes, and new varieties were cultivate directively for production application. CONCLUSION: It could be considered that certain variations of the rice seeds induced by the space conditions were heritable to the offspring's, and directive cultivation of new varieties is possible for production application. It could be used as a new method for mutagenic seed breeding.

Biomass↗

PubMed2001

[Study on induced mutation of sorghum seeds on recoverable satellites].

OBJECTIVE: To observe and investigate the variation and heredity of the offspring of dry seeds of sorghum carried by satellite hence to select excellent mutants and to cultivate directivity new varieties for production application. METHOD: Dry seeds of Tanghui 28, a sorghum restorer line, were carried to the space on board a recoverable satellite for 15 d. After recovery the seeds were planted in the field to study the growth dynamics and change of agricultural characters. RESULT: Variations of characters such as dwarfing of stalk, significant increase grain weight per spike etc were observed in SP1 generation. Wide separation occurred in SP2 generation. Regardless that only non-significant separation of disease resistance and a very little variation of glum color were observed, the other characters varied significantly, and a super large panicle type varied line was obtained. Its spike length was 4 cm longer, and grain weight per spike was 58.5 g more than the control. CONCLUSION: It may be considered that the variation of sorghum seeds induced by the space conditions was heritable to the offsprings. Therefore, exposure to the space environment could be used as a method for mutagenic seeds breeding.

Edible Grain↗

PubMed2000

Breast-conserving radiation therapy using combined electron and intensity-modulated radiotherapy technique.

BACKGROUND AND PURPOSE: To explore the feasibility of a multi-modality breast-conserving radiation therapy treatment technique to reduce high dose to the ipsilateral lung and the heart when compared with the conventional treatment technique using two tangential fields. MATERIALS AND METHODS: An electron beam with appropriate energy was combined with four intensity modulated photon beams. The direction of the electron beam was chosen to be tilted 10-20 degrees laterally from the anteroposterior direction. Two of the intensity-modulated photon beams had the same gantry angles as the conventional tangential fields, whereas the other two beams were rotated 15-25 degrees toward the anteroposterior directions from the first two photon beams. An iterative algorithm was developed which optimizes the weight of the electron beam as well as the fluence profiles of the photon beams for a given patient. Two breast cancer patients with early-stage breast tumors were planned with the new technique and the results were compared with those from 3D planning using tangential fields as well as 9-field intensity-modulated radiotherapy (IMRT) techniques. RESULTS: The combined electron and IMRT plans showed better dose conformity to the target with significantly reduced dose to the ipsilateral lung and, in the case of the left-breast patient, reduced dose to the heart, than the tangential field plans. In both the right-sided and left-sided breast plans, the dose to other normal structures was similar to that from conventional plans and was much smaller than that from the 9-field IMRT plans. The optimized electron beam provided between 70 to 80% of the prescribed dose at the depth of maximum dose of the electron beam. CONCLUSIONS: The combined electron and IMRT technique showed improvement over the conventional treatment technique using tangential fields with reduced dose to the ipsilateral lung and the heart. The customized beam directions of the four IMRT fields also kept the dose to other critical structures to a minimum.

Breast Neoplasms↗

PubMed2000

Monitor unit calculation for an intensity modulated photon field by a simple scatter-summation algorithm.

An important issue in intensity modulated radiation therapy (IMRT) is the verification of the monitor unit (MU) calculation of the planning system using an independent procedure. Because of the intensity modulation and the dynamic nature of the delivery process, the problem becomes much more involved than that in conventional radiation therapy. In this work, a closed formula for MU calculation is derived. The approach is independent of the specific form of leaf sequence algorithms. It is straightforward to implement the procedure using a simple computer program. The approach is illustrated by a simplified example and is demonstrated by a few CORVUS (NOMOS Corporation, Sewickley, PA) treatment plans. The results indicate that it is robust and suitable for IMRT MU verification.

Algorithms↗

PubMed2000

Computer verification of fluence map for intensity modulated radiation therapy.

In a treatment planning system for intensity modulated radiation therapy (IMRT), the time sequence of multileaf collimator (MLC) settings are derived from an optimal fluence map as a postoptimization process using a software module called a "leaf sequencer." The dosimetric accuracy of the dynamic delivery depends on the functionality of the module and it is important to verify independently the correctness of the leaf sequences for each field of a patient treatment. This verification is unique to the IMRT treatment and has been done using radiographic film, electronic portal imaging device (EPID) or electronic imaging system (BIS). The measurement tests both the leaf sequencer and the dynamic multileaf collimator (MLC) delivery system, providing a reliable assurance of clinical IMRT treatment. However, this process is labor intensive and time consuming. In this paper, we propose to separate quality assurance (QA) of the leaf sequencer from the dynamic MLC delivery system. We describe a simple computer algorithm for the verification of the leaf sequences. The software reads in the leaf sequences and simulates the motion of the MLC leaves. The generated fluence map is then compared quantitatively with the reference map from the treatment planning system. A set of pre-defined QA indices is introduced to measure the "closeness" between the computed and the reference maps. The approach has been used to validate the CORVUS (NOMOS Co., Sewickley, PA) treatment plans. The results indicate that the proposed approach is robust and suitable to support the complex IMRT QA process.

Algorithms↗

PubMed2000

Inverse planning incorporating organ motion.

Accurate targeting is important in intensity-modulated radiation therapy (IMRT). The positional uncertainties of structures with respect to the external beams arise in part from random organ motion and patient setup errors. While it is important to improve immobilization and reduce the influence of organ motion, the residual effects should be included in the IMRT plan design. Current inverse planning algorithms follow the conventional approach and include uncertainties by assuming population-based margins to the target and sensitive structures. Margin around a structure represents a "hard boundary" and the fact that a structure has a spatial probability distribution has been completely ignored. With increasing understanding of spatial uncertainties of structures and the technical capability of fine-tuning the dose distribution on an individual beamlet level in IMRT, it seems timely and important to fully utilize the information in the planning process. This will reduce the "effective" margins of the structures and facilitate dose escalation. Instead of specifying a "hard margin," we describe an inverse planning algorithm which takes into consideration positional uncertainty in terms of spatial probability distribution. The algorithm was demonstrated by assuming that the random organ motion can be represented by a three-dimensional Gaussian distribution function. Other probability distributions can be dealt with similarly. In particular, the commonly used "hard margin" is a special case of the current approach with a uniform probability distribution within a specified range. The algorithm was applied to plan treatment for a prostate case and a pancreatic case. The results were compared with those obtained by adding a margin to the clinical target volume. Better sparing of the sensitive structures were obtained in both cases using the proposed method for approximately the same target coverage.

Algorithms↗

PubMed2000

Analgesic effect of electric stimulation of peripheral nerves with different electric frequencies using the formalin test.

Although electroacupuncture (EA) has been widely used to treat pain, the optimal frequency of EA therapy remains unclear. The study sought to determine the effect of different EA frequencies in a Sprague-Dawley (SD) rat model of pain. Electric stimulation (ES) at frequencies of 2 Hz, 15 Hz or 100 Hz was applied to the ipsilateral or contralateral sciatic nerve of the injected hindpaw of SD rats. Formalin (50 microl, 5%) was subcutaneously injected into the plantar surface of the left hindpaw to induce a nociceptive response. Behavior, including licking and biting, was observed to have two distinct periods, an early phase during the first 5 mins and a late phase from 21-35 mins after injection. The total biting or licking count served as an Indicator of nociceptive response. Our results indicate that ES of the ipsilateral sciatic nerve at a frequency of 2 Hz or 15 Hz reduced the nociceptive responses in both the early and the late phases of the formalin test, whereas ES at 2 Hz had greater antinociceptive effect than ES at 15 Hz in the early phase. No similar analgesic effect in the early phase was observed for ES at 100 Hz. Both pretreatment with ES at 2 Hz and naloxone (3 mg/kg, s.c.) produced a greater antinociceptive response in the late phase than when ES at 2 Hz was delivered immediately after formalin administration. In addition, ES of the neck muscle or contralateral sciatic nerve at a frequency of 2 Hz also decreased licking and biting activity in both phases. The results of this study indicate that different analgesic mechanisms are involved in the response to ES at frequencies of 2 Hz, 15 Hz and 100 Hz, and that ES at 2 Hz has a greater analgesic effect on formalin-induced nociceptive response, especially when it is delivered prior to the onset of pain. The analgesic effect of ES may be mediated via a central origin in the supraspinal level. These findings suggest that 2 Hz may be a good frequency selection for clinical EA applications in analgesia, and that pretreatment with EA at 2 Hz may be an effective method to treat post-operative pain.

Analgesia↗

PubMed2000

Mechanisms of agonist-induced down-regulation of the human kappa-opioid receptor: internalization is required for down-regulation.

Previously, we showed that the human kappa-opioid receptor (hkor) stably expressed in Chinese hamster ovary (CHO) cells underwent down-regulation after prolonged U50,488H treatment. In the present study, we determined the mechanisms underlying this process. U50, 488H caused a significant down-regulation of the hkor, although etorphine did not. Neither U50,488H nor etorphine caused down-regulation of the rat kappa-opioid receptor. Thus, similar to internalization, there are agonist and species differences in down-regulation of kappa-opioid receptors. Expression of the dominant negative mutants arrestin-2(319-418) or dynamin I-K44A significantly reduced U50,488H-induced down-regulation of the hkor. Coexpression of GRK2 or GRK2 and arrestin-2 permitted etorphine to induce down-regulation of the hkor, although expression of arrestin-2 or dynamin I alone did not. Expression of the dominant negative mutants rab5A-N133I or rab7-N125I blunted U50,488H-induced down-regulation. Pretreatment with lysosomal enzyme inhibitors [(2S, 3S)trans-epoxysuccinyl-L-leucylamido-3-methylbutane ethyl ester or chloroquine] or proteasome inhibitors (proteasome inhibitor I, MG-132, or lactacystin) decreased the extent of U50,488H-induced down-regulation. A combination of chloroquine and proteasome inhibitor I abolished U50,488H-induced down-regulation. These results indicate that U50,488H-induced down-regulation of the hkor involves GRK-, arrestin-2-, dynamin-, rab5-, and rab7-dependent mechanisms and receptors seem to be trafficked to lysosomes and proteasomes for degradation. Thus, U50,488H-induced internalization and down-regulation of the hkor share initial common mechanisms. To the best of our knowledge, these results represent the first report on the involvement of both rab5 and rab7 in agonist-induced down-regulation of a G protein-coupled receptor. In addition, this study is among the first to show the involvement of proteasomes in agonist-induced down-regulation of a G protein-coupled receptor.

3,4-Dichloro-N-methyl-N-(2-(1-pyrrolidinyl)-cycloh↗

PubMed2000

[Effects of space conditions on mutation and inheritance of tomato].

OBJECTIVE: To study the effects of space conditions on mutation and inheritance of tomato. METHOD: Air-dried seeds of tomato were carried by a satellite for 7-15 d. These seeds were planted after returning. The mutagenic effects of space conditions on some of their variations of the botanical characteristics were studied. RESULT: Tomato dry seeds were carried to the outer space by satellite. After returned to the earth it was found that SP1 generation was of their germination percentage lower than the control. This physiological damage returned to normal in SP2 generation. Seeding isoenzyme, plant growth, resistance, and output, showed variation, and profitable variation had been expressed in later generations. The characters were expressed in the progenies. By observation and screen, promising line of tomato TF873, was obtained. CONCLUSION: It was suggested that space conditions induce profitable mutation of crop and it a possible way for plant mutation breeding.

Germination↗

PubMed2000

[Molecular analysis of space mutant line of kidney bean].

Objective. To identify the occurrence of gene mutant in mutant lines in the offspring of Kidney bean seeds under space flight condition. Method. Kidney bean seeds were carried onboard a recoverable satellite for 15 days in space and were planted on the ground after recovery. Five mutant lines showing variation in the form of leaf blade and their parents were analyzed with RAPD technique. Result. 50 random 10-mer primers were used in this study, among which 20 primers generated 180 polymorphic DNA bands, their size ranged from 200 bp to 2000 bp. 3 primers amplified obviously different bands in the DNA of mutant lines in comparison with that of the control. Conclusion. This is the first molecular analysis of the mutant lines of Kidney bean generated by space mutagenesis at DNA level. The result of RAPD analysis indicated that distinct variations were demonstrated in the DNA of mutant lines as compared with that of the original control.

Base Sequence↗

PubMed1999

Nucleoside diphosphate kinase associated with membranes modulates mu-opioid receptor-mediated [35S]GTPgammaS binding and agonist binding to mu-opioid receptor.

The role of nucleoside diphosphate kinase (NDKP), which converts GDP to GTP, in the coupling of mu-opioid receptors to G protein was investigated in membranes of Chinese hamster ovary cells stably transfected with the cloned rat mu-opioid receptor (rmor). Endogenous NDPK activity in membranes was determined to be 0.60+/-0.02 micromol/mg protein/30 min UDP (at 10 mM), a competitive substrate of NDPK for GDP with no effect on guanine nucleotide binding to G proteins, reduced basal [35S]GTPgammaS binding and unmasked morphine-stimulated [35S]GTPgammaS binding to pertussis toxin-sensitive G proteins, indicating that [35S]GTPgammaS binding to NDPK accounts for part of its high basal binding. UDP increased the extent of morphine-induced increase in [35S]GTPgammaS binding in the presence of GDP, most likely by reducing basal binding and inhibiting conversion of GDP to GTP. ATP greatly reduced morphine-induced increase in [35S]GTPgammaS binding, whereas AMP-PCP (adenylyl-(beta,gamma-methylene)-diphosphoate tetralithium salt), which cannot serve as the phosphate donor for NDPK, did not, demonstrating that effects of ATP is mediated by the NDPK product GTP. In addition, GDP and ATP increased the Kd and lowered the Bmax of the agonist [3H]DAMGO ([D-Ala2,N-Me-Phe4,Gly5ol]-Enkephalin) for the mu-opioid receptor and GDP alone increased Kd, most likely through their conversion to GTP by NDPK. Addition of exogenous NDPK enhanced the inhibitory effects of GDP and combined GDP and ATP on [3H]DAMGO binding. Thus, NDPK appears to play a role in modulating signal transduction of and agonist binding to mu-opioid receptors.

Adenosine Triphosphate↗

PubMed1999

U50,488H-induced internalization of the human kappa opioid receptor involves a beta-arrestin- and dynamin-dependent mechanism. Kappa receptor internalization is not required for mitogen-activated protein kinase activation.

Agonist-promoted internalization of some G protein-coupled receptors has been shown to mediate receptor desensitization, resensitization, and down-regulation. In this study, we investigated whether opioids induced internalization of the human and rat kappa opioid receptors stably expressed in Chinese hamster ovary cells, the potential mechanisms involved in this process and its possible role in activation of mitogen-activated protein (MAP) kinase. Exposure of the human kappa receptor to the agonists U50,488H, U69,593, ethylketocyclazocine, or tifluadom, but not etorphine, promoted receptor internalization. However, none of these agonists induced significant internalization of the rat kappa opioid receptor. U50, 488H-induced human kappa receptor internalization was time- and concentration-dependent, with 30-40% of the receptors internalized following a 30-min exposure to 1 microM U50,488H. Agonist removal resulted in the receptors gradually returning to the cell surface over a 60-min period. The antagonist naloxone blocked U50, 488H-induced internalization without affecting internalization itself, while pretreatment with pertussis toxin had no effect on U50, 488H-induced internalization. In contrast, incubation with sucrose (0.4-0.8 M) significantly reduced U50,488H-induced internalization of the kappa receptor. While co-expression of the wild type GRK2, beta-arrestin, or dynamin I had no effect on kappa receptor internalization, co-expression of the dominant negative mutants GRK2-K220R, beta-arrestin (319-418), or dynamin I-K44A significantly inhibited receptor internalization. Whether receptor internalization is critical for MAP kinase activation was next investigated. Co-expression of dominant negative mutants of beta-arrestin or dynamin I, which greatly reduced U50,488H-induced internalization, did not affect MAP kinase activation by the agonist. In addition, etorphine, which did not promote human kappa receptor internalization, was able to fully activate MAP kinase. Moreover, U50,488H or etorphine stimulation of the rat kappa receptor, which did not undergo internalization, also effectively activated MAP kinase. Thus, U50,488H-induced internalization of the human kappa opioid receptor in Chinese hamster ovary cells occurs via a GRK-, beta-arrestin-, and dynamin I-dependent process that likely involves clathrin-coated pits. In addition, internalization of the kappa receptor is not required for activation of MAP kinase.

3,4-Dichloro-N-methyl-N-(2-(1-pyrrolidinyl)-cycloh↗

PubMed1999

Functional role of the spatial proximity of Asp114(2.50) in TMH 2 and Asn332(7.49) in TMH 7 of the mu opioid receptor.

We examined whether a proposed spatial proximity between Asp114(2.50) and Asn332(7.49) affected the functional properties of the mu opioid receptor. The D114(2.50)N mutant had reduced binding affinities for morphine, DAMGO and CTAP, but not for naloxone and [3H]diprenorphine; this mutation also abolished agonist-induced increase in [35S]GTPgammaS binding. The N332(7.49)D mutation eliminated detectable binding of either [3H]diprenorphine or [3H]DAMGO. The combined D114(2.50)N-N332(7.49)D mutation restored high affinity binding for [3H]diprenorphine, CTAP and naloxone, and restored partially the binding affinities, potencies and efficacies of morphine and DAMGO. Thus, reciprocal mutations of Asp114(2.50) and Asn332(7.49) compensate for the detrimental effects of the single mutations, indicating that the residues are adjacent in space and that their chemical functionalities are important for ligand binding and receptor activation.

Animals↗

PubMed1999

ASP147 in the third transmembrane helix of the rat mu opioid receptor forms ion-pairing with morphine and naltrexone.

We tested the hypotheses that the carboxylate side chain of Asp147 of the mu opioid receptor interacts with the protonated nitrogen of naltrexone and morphine and that this interaction is important for pharmacological properties of the two compounds. Mutation of Asp147 to Ala or Asn substantially reduced the affinity of naltrexone and the affinity, potency and efficacy of morphine, while the Glu mutant had similar properties as the wildtype, indicating the significant role of the carboxylate group of Asp147 in receptor binding and activation. This role could be due to its direct interaction with ligands or involvement in interhelical interactions. The unprotonated analogs of naltrexone and morphine, cyclopropylcarbonyl noroxymorphone (CPCNOM) and N-formylnormorphine (NFNM), respectively, were used to discriminate between these mechanisms. CPCNOM was much less potent as an antagonist and had substantially lower affinity for the mu receptor than naltrexone. Similarly, NFNM was unable to activate the mu receptor and had much lower affinity than morphine. These results indicate the importance of the protonated nitrogen. Notably, the D147A and D147N mutations did not appreciably affect the binding affinities of CPCNOM and NFNM. In addition, the D147E mutant had similar affinities for CPCNOM and NFNM as the D147A and D147N mu receptors. Thus, the carboxylate group of Asp147 is not important for binding of the two unprotonated compounds. These results indicate that the carboxylate group of Asp147 of the mu receptor interacts directly with the protonated nitrogen of naltrexone and morphine and this interaction is important for binding and receptor activation.

Animals↗

PubMed1999

Clinical implementation of wedge filter optimization in three-dimensional radiotherapy treatment planning.

BACKGROUND AND PURPOSE: To describe a wedge filter optimization technique which automatically chooses the beam weights and wedge filters and to demonstrate the implementation of the algorithm in clinical three-dimensional (3D) radiotherapy treatment planning. MATERIAL AND METHODS: Given the incident directions and beam energies of J beams, the dose distribution is a function of the beam weights, wedge angles, and wedge orientations. Instead of decomposing an incident field into a superposition of an open and two nominal wedged fields and then optimizing their weights, the algorithm optimizes the objective function with respect to the beam weights, wedge angles and wedge orientations directly. A salient feature of the algorithm is that no planner intervention was required in the selection of wedge filters during the optimization process. A dose-based objective function which incorporated the relative importance of structures was adopted in this work. The objective function was minimized by the method of simulated annealing. The technique was demonstrated by using a phantom study and two clinical cases. RESULTS: For the phantom case, the classical wedge pair result was obtained, providing a useful test of the algorithm. Dose distributions and dose volume histograms for the target and surrounding organs were presented for the two clinical cases. It was also shown that dose homogeneity to the target could be compromised by increasing the relative importance factors to the surrounding organs. CONCLUSIONS: A 3D wedge filter optimization algorithm has been developed. The technique has the potential to fully automate the 3D radiotherapy treatment planning process. In addition, treatment planning time and efforts were significantly reduced.

Algorithms↗

PubMed1999

Optimization of importance factors in inverse planning.

Inverse treatment planning starts with a treatment objective and obtains the solution by optimizing an objective function. The clinical objectives are usually multifaceted and potentially incompatible with one another. A set of importance factors is often incorporated in the objective function to parametrize trade-off strategies and to prioritize the dose conformality in different anatomical structures. Whereas the general formalism remains the same, different sets of importance factors characterize plans of obviously different flavour and thus critically determine the final plan. Up to now, the determination of these parameters has been a 'guessing' game based on empirical knowledge because the final dose distribution depends on the parameters in a complex and implicit way. The influence of these parameters is not known until the plan optimization is completed. In order to compromise properly the conflicting requirements of the target and sensitive structures, the parameters are usually adjusted through a trial-and-error process. In this paper, a method to estimate these parameters computationally is proposed and an iterative computer algorithm is described to determine these parameters numerically. The treatment plan selection is done in two steps. First, a set of importance factors are chosen and the corresponding beam parameters (e.g. beam profiles) are optimized under the guidance of a quadratic objective function using an iterative algorithm reported earlier. The 'optimal' plan is then evaluated by an additional scoring function. The importance factors in the objective function are accordingly adjusted to improve the ranking of the plan. For every change in the importance factors, the beam parameters need to be re-optimized. This process continues in an iterative fashion until the scoring function is saturated. The algorithm was applied to two clinical cases and the results demonstrated that it has the potential to improve significantly the existing method of inverse planning. It was noticed that near the final solution the plan became insensitive to small variations of the importance factors.

Algorithms↗

PubMed1999

Estimation theory and model parameter selection for therapeutic treatment plan optimization.

Treatment optimization is usually formulated as an inverse problem, which starts with a prescribed dose distribution and obtains an optimized solution under the guidance of an objective function. The solution is a compromise between the conflicting requirements of the target and sensitive structures. In this paper, the treatment plan optimization is formulated as an estimation problem of a discrete and possibly nonconvex system. The concept of preference function is introduced. Instead of prescribing a dose to a structure (or a set of voxels), the approach prioritizes the doses with different preference levels and reduces the problem into selecting a solution with a suitable estimator. The preference function provides a foundation for statistical analysis of the system and allows us to apply various techniques developed in statistical analysis to plan optimization. It is shown that an optimization based on a quadratic objective function is a special case of the formalism. A general two-step method for using a computer to determine the values of the model parameters is proposed. The approach provides an efficient way to include prior knowledge into the optimization process. The method is illustrated using a simplified two-pixel system as well as two clinical cases. The generality of the approach, coupled with promising demonstrations, indicates that the method has broad implications for radiotherapy treatment plan optimization.

Algorithms↗