Biological Objective Function Research Articles

NGA-Inspired Nanorobots-Assisted Detection of Multifocal Cancer.

We propose a new framework of computing-inspired multifocal cancer detection procedure (MCDP). Under the rubric of MCDP, the tumor foci to be detected are regarded as solutions of the objective function, the tissue region around the cancer areas represents the parameter space, and the nanorobots loaded with contrast medium molecules for cancer detection correspond to the optimization agents. The process that the nanorobots detect tumors by swimming in the high-risk tissue region can be regarded as the process that the agents search for the solutions of an objective function in the parameter space with some constraints. For multimodal optimization (MMO) aiming to locate multiple optimal solutions in a single simulation run, the niche technology has been widely used. Specifically, the niche genetic algorithm (NGA) has been shown to be particularly effective in solving MMO. It can be used to identify the global optima of multiple hump functions in a running, effectively keep the diversity of the population, and prematurely avoid the genetic algorithm. Learning from the optimization procedure of NGA, we propose the NGA-inspired MCDP in order to locate the tumor targets efficiently while taking into account realistic in vivo propagation and controlling of nanorobots, which is different from the use scenario of the standard NGA. To improve the performance of the MCDP, we also modify the crossover operator of the original NGA from crossing within a population to crossing between two populations. Finally, we present comprehensive numerical examples to demonstrate the effectiveness of the NGA-inspired MCDP when the biological objective function is associated with the blood flow velocity profile caused by tumor-induced angiogenesis.

Optimal fishing mortality assignment for southern hake Merluccius australis in Chile

Since 1979, southern hake (Merluccius australis) has been exploited in Chile from the Bio Bio to the Magallanes regions, between the parallels 41°28.6'S and 57°S. There is evidence of a constant fishing effort and a sustained reduction of the fish population, consistent with a progressive decrease in total annual catches. Management strategies based on the maximum sustainable yield (MSY) and quota assignment/ distribution criteria have not been able to sustain acceptable biomass levels. A non-linear optimization model with two objective functions was proposed to determine an optimal total catch quota for more sustainable exploitation of this fishery. The first function maximizes the total catch over time in response to an optimal assignment of fishing mortality rates per fleet; the second function maximizes the total economic benefit associated with the total catch. The dynamics of the fish population were represented with the equations of a predictive age-structured model. Decision variables were fishing mortality rates and annual catch quotas per fleet, subject to constraints that guarantee a minimum level of biomass escape over a long-term period. The input parameters were obtained from the last stock evaluation report carried out by the Instituto de Fomento Pesquero (IFOP) of Chile. The historical background data of the fishery and the regulatory framework were relevant aspects of the methodology. Five scenarios were evaluated with the two objective functions, including a base scenario, which considered the referential mortality rate as input data as the average mortality rate per fleet from 2007 to 2012. Total economic benefits fluctuate between 102 and USD 442 million for total catches in the range of 108 to 421 thousand tons, which were obtained from maximizing the economic and biological objective functions. Economic benefit/catch ratios were reduced for scenarios with higher constraints on catch limits, and they were more efficient from a biological point of view. Situations with lighter constraints showed in general higher economic benefits and better performance ratios than those with stronger restrictions. The use of optimization models may provide a useful tool to evaluate the effect of regulations for adequate conservation and economical utilization of a limited resource.

MOOMIN - Mathematical explOration of 'Omics data on a MetabolIc Network.

Analysis of differential expression of genes is often performed to understand how the metabolic activity of an organism is impacted by a perturbation. However, because the system of metabolic regulation is complex and all changes are not directly reflected in the expression levels, interpreting these data can be difficult. In this work, we present a new algorithm and computational tool that uses a genome-scale metabolic reconstruction to infer metabolic changes from differential expression data. Using the framework of constraint-based analysis, our method produces a qualitative hypothesis of a change in metabolic activity. In other words, each reaction of the network is inferred to have increased, decreased, or remained unchanged in flux. In contrast to similar previous approaches, our method does not require a biological objective function and does not assign on/off activity states to genes. An implementation is provided and it is available online. We apply the method to three published datasets to show that it successfully accomplishes its two main goals: confirming or rejecting metabolic changes suggested by differentially expressed genes based on how well they fit in as parts of a coordinated metabolic change, as well as inferring changes in reactions whose genes did not undergo differential expression. github.com/htpusa/moomin. Supplementary data are available at Bioinformatics online.

A systematic approach for finding the objective function and active constraints for dynamic flux balance analysis.

Dynamic flux balance analysis (DFBA) has become an instrumental modeling tool for describing the dynamic behavior of bioprocesses. DFBA involves the maximization of a biologically meaningful objective subject to kinetic constraints on the rate of consumption/production of metabolites. In this paper, we propose a systematic data-based approach for finding both the biological objective function and a minimum set of active constraints necessary for matching the model predictions to the experimental data. The proposed algorithm accounts for the errors in the experiments and eliminates the need for ad hoc choices of objective function and constraints as done in previous studies. The method is illustrated for two cases: (1) for in silico (simulated) data generated by a mathematical model for Escherichia coli and (2) for actual experimental data collected from the batch fermentation of Bordetella Pertussis (whooping cough).

EUD-based biological optimization for carbon ion therapy.

Treatment planning for carbon ion therapy requires an accurate modeling of the biological response of each tissue to estimate the clinical outcome of a treatment. The relative biological effectiveness (RBE) accounts for this biological response on a cellular level but does not refer to the actual impact on the organ as a whole. For photon therapy, the concept of equivalent uniform dose (EUD) represents a simple model to take the organ response into account, yet so far no formulation of EUD has been reported that is suitable to carbon ion therapy. The authors introduce the concept of an equivalent uniform effect (EUE) that is directly applicable to both ion and photon therapies and exemplarily implemented it as a basis for biological treatment plan optimization for carbon ion therapy. In addition to a classical EUD concept, which calculates a generalized mean over the RBE-weighted dose distribution, the authors propose the EUE to simplify the optimization process of carbon ion therapy plans. The EUE is defined as the biologically equivalent uniform effect that yields the same probability of injury as the inhomogeneous effect distribution in an organ. Its mathematical formulation is based on the generalized mean effect using an effect-volume parameter to account for different organ architectures and is thus independent of a reference radiation. For both EUD concepts, quadratic and logistic objective functions are implemented into a research treatment planning system. A flexible implementation allows choosing for each structure between biological effect constraints per voxel and EUD constraints per structure. Exemplary treatment plans are calculated for a head-and-neck patient for multiple combinations of objective functions and optimization parameters. Treatment plans optimized using an EUE-based objective function were comparable to those optimized with an RBE-weighted EUD-based approach. In agreement with previous results from photon therapy, the optimization by biological objective functions resulted in slightly superior treatment plans in terms of final EUD for the organs at risk (OARs) compared to voxel-based optimization approaches. This observation was made independent of the underlying objective function metric. An absolute gain in OAR sparing was observed for quadratic objective functions, whereas intersecting DVHs were found for logistic approaches. Even for considerable under- or overestimations of the used effect- or dose-volume parameters during the optimization, treatment plans were obtained that were of similar quality as the results of a voxel-based optimization. EUD-based optimization with either of the presented concepts can successfully be applied to treatment plan optimization. This makes EUE-based optimization for carbon ion therapy a useful tool to optimize more specifically in the sense of biological outcome while voxel-to-voxel variations of the biological effectiveness are still properly accounted for. This may be advantageous in terms of computational cost during treatment plan optimization but also enables a straight forward comparison of different fractionation schemes or treatment modalities.

Location Isn't Everything: Timing of Spawning Aggregations Optimizes Larval Replenishment.

Many species of reef fishes form large spawning aggregations that are highly predictable in space and time. Prior research has suggested that aggregating fish derive fitness benefits not just from mating at high density but, also, from oceanographic features of the spatial locations where aggregations occur. Using a probabilistic biophysical model of larval dispersal coupled to a fine resolution hydrodynamic model of the Florida Straits, we develop a stochastic landscape of larval fitness. Tracking virtual larvae from release to settlement and incorporating changes in larval behavior through ontogeny, we found that larval success was sensitive to the timing of spawning. Indeed, propagules released during the observed spawning period had higher larval success rates than those released outside the observed spawning period. In contrast, larval success rates were relatively insensitive to the spatial position of the release site. In addition, minimum (rather than mean) larval survival was maximized during the observed spawning period, indicating a reproductive strategy that minimizes the probability of recruitment failure. Given this landscape of larval fitness, we take an inverse optimization approach to define a biological objective function that reflects a tradeoff between the mean and variance of larval success in a temporally variable environment. Using this objective function, we suggest that the length of the spawning period can provide insight into the tradeoff between reproductive risk and reward.

Investigation of the effects of human body stability on joint angles’ prediction

Loosing stability control in elderly or paralyzed has motivated researchers to study how a stability control system works and how to determine its state at every time instant. Studying the stability of a human body is not only an important problem from a scientific viewpoint, but also finally leads to new designs of prostheses and orthoses and rehabilitation methods. Computer modeling enables researchers to study and describe the reactions and propose a suitable and optimized motion pattern to strengthen the neuromus- cular system and helps a human body maintain its stability. A perturbation as a tilting is exposed to an underfoot plate of a musculoskeletal model of the body to study the stability. The studied model of a human body included four links and three degrees of freedom with eight muscles in the sagittal plane. Lagrangian dynamics was used for deriving equations of motion and muscles were modeled using Hill's model. Using experimental data of joint trajectories for a human body under tilting perturbation, forward dynamics has been applied to predict joint trajectories and muscle activation. This study investigated the effects of sta- bility on predicting body joints' motion. A new stability function for a human body, based on the zero moment point, has been employed in a forward dynamics procedure using a direct collocation method. A multi-objective optimization based on genetic algorithm has been proposed to employ stability as a robotic objective function along with muscle stresses as a biological objective function. The obtained results for joints' motion were compared to experimental data. The results show that, for this type of perturbations, muscle stresses are in conflict with body stability. This means that more body stability requires more stresses

Identification of Metabolic Engineering Targets through Analysis of Optimal and Sub-Optimal Routes

Identification of optimal genetic manipulation strategies for redirecting substrate uptake towards a desired product is a challenging task owing to the complexity of metabolic networks, esp. in terms of large number of routes leading to the desired product. Algorithms that can exploit the whole range of optimal and suboptimal routes for product formation while respecting the biological objective of the cell are therefore much needed. Towards addressing this need, we here introduce the notion of structural flux, which is derived from the enumeration of all pathways in the metabolic network in question and accounts for the contribution towards a given biological objective function. We show that the theoretically estimated structural fluxes are good predictors of experimentally measured intra-cellular fluxes in two model organisms, namely, Escherichia coli and Saccharomyces cerevisiae. For a small number of fluxes for which the predictions were poor, the corresponding enzyme-coding transcripts were also found to be distinctly regulated, showing the ability of structural fluxes in capturing the underlying regulatory principles. Exploiting the observed correspondence between in vivo fluxes and structural fluxes, we propose an in silico metabolic engineering approach, iStruF, which enables the identification of gene deletion strategies that couple the cellular biological objective with the product flux while considering optimal as well as sub-optimal routes and their efficiency.

Risk-Adaptive Volumetric Modulated Arc Therapy Using Biological Objective Functions for Subvolume Boosting in Radiotherapy

Objectives. Simultaneous integrated boost (SIB) for prostate cancer allows increases in tumor control probability while respecting normal tissue dose constraints. Biological optimization functions that optimize based on treatment outcome can be used to create SIB prostate plans. This study investigates the feasibility of biologically optimized volumetric modulated arc therapy (VMAT) for SIB prostate radiotherapy. Methods. Five prostate cancer patients with diffusion-weighted MR images were selected for analysis. A two-step VMAT optimization was performed, which consisted of an initial biological optimization of a static gantry angle delivery followed by conversion of the static delivery to a single arc VMAT plan. A dosimetric analysis was performed on the resulting plans. Results. The VMAT plans resulted in a ΔEUD between the prostate and the boost volume of between 15.1 Gy and 20.3 Gy. Rectal volumes receiving 75.6 Gy ranged from 4.5 to 9.9%. Expected rectal normal tissue complication probabilities were between 8.6% and 21.4%. Maximum bladder doses ranged from 73.6 Gy to 75.8 Gy. Estimated treatment time was 120 s or less. Conclusions. The presented biological optimization method resulted in deliverable VMAT plans that achieved sufficient modulation for SIB without violating rectal and bladder dose constraints. Advances in knowledge. This study presents a method for creating simultaneous integrated boost VMAT treatments using biological outcome objective functions.

Advantage of biological over physical optimization in prostate cancer?

The biological effects of an applied dose can be accounted for by using biological objective functions with IMRT. A commonly used concept is the generalized equivalent uniform dose (gEUD), developed by Niemierko. Unlike the equivalent uniform dose (EUD) which is defined for tumor only, the gEUD can be used for both target volume and organs-at-risk (OAR). In this study, the gEUD has been integrated in our in-house inverse treatment planning system DMCO. DMCO is based on an inverse kernel concept and maintains full Monte-Carlo precision. The system applies direct aperture optimization by means of simulated annealing. Thereby DMCO is per se predestined for the optimization of non-quadratic biological objective functions. In this work, the feasibility of gEUD-based optimization with DMCO is investigated and compared to modified physical optimization. A ‘pseudo’ Pareto study is performed in order to derive the gEUD-parameters ‘ a’ for the volumes-of-interest of a prostate case. The best biological plan is compared to a physically optimized plan, based on dose-volume objectives (DVO). Furthermore, a hybrid objective function (OF) was developed. It consists of both a biological OF for the OARs and a physical OF for the PTV. The plans are compared to another physically optimized plan, which includes additional zero-DVOs in order to further improve OAR-sparing. As a result of the comparisons it turns out, that the biological OF may improve plan quality with regard to the OARs, but at the price of a degradation of the PTV. This disadvantage can be overcome by a hybrid OF, by which the advantages of both biological and physical OF can be combined. With the application of the physical OF with properly set zero-DVOs, a similar or even superior plan quality may be achieved. The physical OFs do not need the time consuming stochastic optimization, which is mandatory in biological optimization and which is included in DMCO. Furthermore, biological evaluation leaves plan quality rather similar compared to physical optimization, but it cares automatically for the target and the OARs.

Improved vanillin production in baker's yeast through in silico design

BackgroundVanillin is one of the most widely used flavouring agents, originally obtained from cured seed pods of the vanilla orchid Vanilla planifolia. Currently vanillin is mostly produced via chemical synthesis. A de novo synthetic pathway for heterologous vanillin production from glucose has recently been implemented in baker's yeast, Saccharamyces cerevisiae. In this study we aimed at engineering this vanillin cell factory towards improved productivity and thereby at developing an attractive alternative to chemical synthesis.ResultsExpression of a glycosyltransferase from Arabidopsis thaliana in the vanillin producing S. cerevisiae strain served to decrease product toxicity. An in silico metabolic engineering strategy of this vanillin glucoside producing strain was designed using a set of stoichiometric modelling tools applied to the yeast genome-scale metabolic network. Two targets (PDC1 and GDH1) were selected for experimental verification resulting in four engineered strains. Three of the mutants showed up to 1.5 fold higher vanillin β-D-glucoside yield in batch mode, while continuous culture of the Δpdc1 mutant showed a 2-fold productivity improvement. This mutant presented a 5-fold improvement in free vanillin production compared to the previous work on de novo vanillin biosynthesis in baker's yeast.ConclusionUse of constraints corresponding to different physiological states was found to greatly influence the target predictions given minimization of metabolic adjustment (MOMA) as biological objective function. In vivo verification of the targets, selected based on their predicted metabolic adjustment, successfully led to overproducing strains. Overall, we propose and demonstrate a framework for in silico design and target selection for improving microbial cell factories.

SU‐GG‐J‐02: Dose Painting by Numbers Based on SUV Data for Advanced Lung Tumors

Purpose: to develop a plugin with user interface for the Pinnacle TPS (Philips Medical Systems) to directly integrate SUV data obtained by PET‐scanning into the optimization process for lung tumor IMRT plans. Method and Materials: A plugin generating a grid with the prescribed dose per voxel was developed. The prescribed dose values are based on the underlying SUV data per voxel, not on contours. Various user‐defined functions can be used to give the relation between SUV data and prescribed dose. New objective functions were generated to calculate a cost based on the voxel‐by‐voxel difference between the actual dose distribution and the prescribed dose distribution. During the IMRT optimization these (biological) objective functions are used in conjunction with conventional dose volume objectives process. Further tools were developed to create a SUV‐Volume Histogram, showing the SUV distribution in any ROI, and to visualize the quality of the resulting plan by showing the distribution of the voxel‐by‐voxel differences between prescribed and actual dose distribution. Results: With the plugin SUV‐based dose prescriptions were made. After optimization with the plugin, which took only several minutes per plan, plans were evaluated with the newly devised tools. Optimization resulted in doses to regions with high SUV of typically 130% – 200% of the current clinical dose. Mean lung dose and other dose objectives, which were unaltered from standard IMRT optimization, were met for all plans. Conclusion: A plugin was developed enabling us to steer the dose within the lung GTV based on the underlying SUV distribution. Using these tools we were able to boost voxels with high SUV up to a dose level of up to 200% of the current clinical dose with only very limited dose increase to the normal structures as lung and spine.Conflict of Interest: Research sponsored by Philips Medical Systems

Dose-painting IMRT optimization using biological parameters

Purpose. Our work on dose-painting based on the possible risk characteristics for local recurrence in tumor subvolumes and the optimization of treatment plans using biological objective functions that are region-specific are reviewed. Materials and methods. A series of intensity modulated dose-painting techniques are compared to their corresponding intensity modulated plans in which the entire PTV is treated to a single dose level, delivering the same equivalent uniform dose (EUD) to the entire PTV. Iso-TCP and iso-NTCP maps are introduced as a tool to aid the planner in the evaluation of the resulting non-uniform dose distributions. Iso-TCP and iso-NTCP maps are akin to iso-dose maps in 3D conformal radiotherapy. The impact of the currently limited diagnostic accuracy of functional imaging on a series of dose-painting techniques is also discussed. Results. Utilizing biological parameters (risk-adaptive optimization) in the generation of dose-painting plans results in an increase in the therapeutic ratio as compared to conventional dose-painting plans in which optimization techniques based on physical dose are employed. Conclusion. Dose-painting employing biological parameters appears to be a promising approach for individualized patient- and disease-specific radiotherapy.

TU‐EE‐A2‐01: Comparison of HDR Brachytherapy Optimization Using Physical Dose and Biological Response Models

Purpose: Comparison of optimized HDR treatment plans using biological and physical objective functions. Methods and Materials: For a gynecological cancer case, treatment plans were generated using physical and biological optimization models. Optimization was done using adaptive simulated annealing. The target and critical structure volumes were determined from CT images. Target volumes were planned to receive 80Gy using a uniform external beam dose of 0 or 45Gy. The physical model objective function uses a least square fitting. The biological model objective function uses EUD to maximize the target and minimize critical structures dose. Plan evaluation is done by comparing the isodose distribution and calculating tumor control probability (TCP), normal tissue complication probability (NTCP), equivalent uniform dose (EUD), coverage index (CI), homogeneity index (HI), and overdose index (OI). Results: The physical model produced excellent dose uniformity and target coverage. The biological model was able to increase EUD to the target, lower EUD to the rectum and sigmoid, but increased EUD to the bladder. When external beam dose is added, the differences in EUD were in the same direction, but smaller. The biological plan was less uniform (lower HI and higher OI) with the same CI as the physical model, but when an external beam was added, CI was the same, HI became smaller, and OI was larger compared to the physical model. TCP was larger for the biological model. NTCP are zero for plans without external beam dose. When external beam dose was added, TCP and NTCP increased for both plans. TCP became higher for the physical model and NTCP followed the same trend as the EUD calculations. Conclusion: The biological model is able to spare dose to critical structures, but has less homogeneity and greater overdose than the physical model. When an external beam dose is included, plans look almost identical.

Effective beam directions using radiobiologically optimized IMRT of node positive breast cancer

The purpose of this study was to investigate the optimal coplanar beam directions when treating an early breast cancer with locoregional lymphatic spread with a few radiobiologically optimized intensity modulated beams. Also to determine the increase in the probability of complication-free cure with the number of beam portals and the smallest number required to perform a close to optimal treatment for this tumour site. Four test patients with stage II left-sided breast cancer were studied with heart, lung and contralateral breast as principal organs at risk. The clinical target volume consisted of the breast tissue remaining after surgery, the axillary, the internal mammary as well as the supraclavicular lymph nodes. Through an exhaustive search of all possible beam directions the most effective coplanar beams with one to four intensity modulated photon beam portals were investigated. Comparisons with uniform beam treatment techniques and up to 12 intensity modulated beams were also made. The different plans were optimized using the probability of complication-free tumour cure, P +, as biological objective function. When using two intensity modulated beam directions three major sets of suitable directions were identified denoted by A, P and T. A corresponds to an anterior oblique pair of beams around 25° and 325°, P is a perpendicular lateral pair at around 50° and 130° whereas T is a more conventional tangential pair at around 155° and 300°. Interestingly, these configurations identify simply three major effective beam directions namely at 30°±20°, 145°±20° and 310°±15°. For the three intensity modulated beam technique a combination of these three effective beam directions generally covered the global maximum of the probability of complication-free tumour control. The improvement in complication-free cure probability with two optimally selected intensity modulated beams is around 10% when compared to a uniform beam technique with three to four beam portals. This increase is mainly due to a reduction by almost 1% in the probability of injury to the heart and an increase of 6% in the probability of local tumour control. When three or four biologically optimized beam portals are used a further increase in the probability of complication-free cure of about 6% can often be obtained. This improvement is caused by a small decrease in the probability of injury to the heart, left lung and other surrounding normal tissue, as well as a slight further increase in the probability of tumour control. The increase in the treatment outcome is minimal when more than four intensity modulated beams are employed. A small increase in dose homogeneity in the target volume and a slight decrease in the normal tissue volume receiving high dose may be seen, but without appreciably improving the complication-free cure probability. For a stage II breast cancer, three and in more complex cases four optimally oriented beams are sufficient to reach close to the maximum probability of complication-free tumour control when biologically optimized intensity modulated dose delivery is used. Angle of incidence optimization may then be advantageous starting from the given most effective three beam directions.

Optimization of radiobiological effects in intensity modulated proton therapy

Today, inverse treatment planning for intensity modulated proton therapy (IMPT) usually employs a constant relative biological effectiveness (RBE). In this paper, the potential clinical relevance of RBE variations for scanning techniques in IMPT is investigated, and a new strategy to include the RBE into the inverse planning process is presented. Three-dimensional RBE distributions are calculated based on a phenomenological model that describes the RBE as a function of dose, linear energy transfer (LET) and tissue type in the framework of the linear-quadratic model. This RBE model is integrated into the optimization loop of inverse planning by using a modified version of the standard quadratic objective function, where the physical dose is replaced by the biological effect. This system for "biological optimization" was implemented into a research version of the inverse planning software KonRad and allows the direct optimization of the product of RBE and physical dose. Several treatment plans for a prostate case are presented, which compare the biological with the conventional physical dose optimization for IMPT scanning techniques, in particular distal edge tracking (DET) and the full three-dimensional (3D) modulation of beam spots. Mainly due to their different LET distributions, the RBE effects for these two techniques are quite different: while the RBE distribution was more or less homogeneous in the planning target volume (PTV) for 3D modulation, considerable RBE variations within the PTV were observed for DET. These unfavorable effects could be compensated for by employing the new biological objective function, which led to a more homogeneous distribution of the product of RBE and physical dose in the PTV. The computation time increased by a factor of 2 compared to the optimization of the physical dose. In conclusion, the proposed method allows the simultaneous multifield optimization of the biological effect in a reasonable time, and is therefore well suited for studying the influence of a variable RBE in IMPT as well as for minimizing potentially adverse effects.

175 oral Deterministic and stochastic optimisation of physical and biological objective functions by means of the inverse Monte Carlo based TPS IKO

175 oral Deterministic and stochastic optimisation of physical and biological objective functions by means of the inverse Monte Carlo based TPS IKO

Comparison of conformal radiation therapy techniques within the dynamicradiotherapy project `Dynarad'

The objective of the dynamic radiotherapy project `Dynarad' within theEuropean Community has been to compare and grade treatment techniques that arecurrently applied or being developed at the participating institutions.Cervical cancer was selected as the tumour site on the grounds that theinvolved organs at risk, mainly the rectum and the bladder, are very close tothe tumour and partly located inside the internal target volume. In this work,a solid phantom simulating the pelvic anatomy was used by institutions inBelgium, France, Greece, Holland, Italy, Sweden and the United Kingdom. Theresults were evaluated using both biological and physical criteria. The mainpurpose of this parallel evaluation is to test the value of biological andphysical evaluations in comparing treatment techniques. It is demonstratedthat the biological objective functions allow a much higher conformality and amore clinically relevant scoring of the outcome. Often external beam treatmenttechniques have to be combined with intracavitary therapy to give clinicallyacceptable results. However, recent developments can reduce or even eliminatethis need by delivering more conformal dose distributions using intensitymodulated external dose delivery. In these cases the reliability of thepatient set-up procedure becomes critical for the effectiveness of the treatment.

Radiotherapy of prostate cancer with or without intensity modulated beams: a planning comparison

Purpose: To evaluate whether intensity modulated radiotherapy (IMRT) by static segmented beams allows the dose to the main portion of the prostate target to escalate while keeping the maximal dose at the anterior rectal wall at 72 Gy. The value of such IMRT plans was analyzed by comparison with non-IMRT plans using the same beam incidences. Methods and Materials: We performed a planning study on the CT data of 32 consecutive patients with localized adenocarcinoma of the prostate. Three fields in the transverse plane with gantry angles of 0°, 116°, and 244° were isocentered at the center of gravity of the target volume (prostate and seminal vesicles). The geometry of the beams was determined by beam’s eye view autocontouring of the target volume with a margin of 1.5 cm. In study 1, the beam weights were determined by a human planner ( 3D-man) or by computer optimization using a biological objective function with ( 3D-optim-lim) or without ( 3D-optim-unlim) a physical term to limit target dose inhomogeneity. In study 2, the 3 beam incidences mentioned above were used and in-field uniform segments were added to allow IMRT. Plans with ( IMRT-lim) or without ( IMRT-unlim) constraints on target dose inhomogeneity were compared. In the IMRT-lim plan, target dose inhomogeneity was constrained between 15% and 20%. After optimization, plans in both studies were normalized to a maximal rectal dose of 72 Gy. Biological (tumor control probability [TCP], normal tissue complication probability [NTCP]) and physical indices for tumor control and normal tissue complication probabilities were computed, as well as the probability of the uncomplicated local control (P+). Results: The IMRT-lim plan was superior to all other plans concerning TCP ( p < 0.0001). The IMRT-unlim plan had the worst TCP. Within the 3D plans, the 3D-optim-unlim had the best TCP, which was significantly different from the 3D-optim-lim plan ( p = 0.0003). For rectal NTCP, both IMRT plans were superior to all other plans ( p < 0.0001). The IMRT-unlim plan was significantly better than the IMRT-lim plan ( p < 0.0001). Again, 3D-optim-unlim was superior to the other 3D plans ( p < 0.0007). Physical endpoints for target showed the mean minimal target dose to be the lowest in the IMRT-unlim plan, caused by a large target dose inhomogeneity (TDI). Medial target dose, 90th percentile, and maximal target dose were significantly higher in both IMRT plans. Physical endpoints for the rectum showed the IMRT-unlim plan to be superior compared to all other plans. There was a strong correlation between the 65th percentile (Rp65) and rectal NTCP (correlation coefficient ≥89%). For bladder, maximal bladder dose was significantly higher in the IMRT-unlim plan compared to all other plans ( p ≤ 0.0001). P+ was significantly higher in both IMRT-plans than in all other plans. The 3D-optim-unlim plan was significantly better than the two other 3D plans ( p < 0.0001). Conclusion: IMRT significantly increases the ratio of TCP over NTCP of the rectum in the treatment of prostate cancer. However, constraints for TDI are needed, because a high degree of TDI reduced minimal target dose. IMRT improved uncomplicated local control probability. In our department, IMRT by static segmented beams is planned and delivered in a cost-effective way. IMRT-lim has replaced non-modulated conformal radiotherapy as the standard treatment for prostate cancer.

Inhomogeneous target-dose distributions: a dimension more for optimization?

Purpose: To evaluate if the use of inhomogeneous target-dose distributions, obtained by 3D conformal radiotherapy plans with or without beam intensity modulation, offers the possibility to decrease indices of toxicity to normal tissues and/or increase indices of tumor control stage III non-small cell lung cancer (NSCLC). Methods and Materials: Ten patients with stage III NSCLC were planned using a conventional 3D technique and a technique involving noncoplanar beam intensity modulation (BIM). Two planning target volumes (PTVs) were defined: PTV1 included macroscopic tumor volume and PTV2 included macroscopic and microscopic tumor volume. Virtual simulation defined the beam shapes and incidences as well as the wedge orientations (3D) and segment outlines (BIM). Weights of wedged beams, unwedged beams, and segments were determined by optimization using an objective function with a biological and a physical component. The biological component included tumor control probability (TCP) for PTV1 (TCP1), PTV2 (TCP2), and normal tissue complication probability (NTCP) for lung, spinal cord, and heart. The physical component included the maximum and minimum dose as well as the standard deviation of the dose at PTV1. The most inhomogeneous target-dose distributions were obtained by using only the biological component of the objective function (biological optimization). By enabling the physical component in addition to the biological component, PTV1 inhomogeneity was reduced (biophysical optimization). As indices for toxicity to normal tissues, NTCP-values as well as maximum doses or dose levels to relevant fractions of the organ’s volume were used. As indices for tumor control, TCP-values as well as minimum doses to the PTVs were used. Results: When optimization was performed with the biophysical as compared to the biological objective function, the PTV1 inhomogeneity decreased from 13 (8–23)% to 4 (2–9)% for the 3D-( p = 0.00009) and from 44 (33–56)% to 20 (9–34)% for the BIM plans ( p < 0.00001). Minimum PTV1 doses (expressed as the lowest voxel-dose) were similar for both objective functions. The mean and maximum target doses were significantly higher with biological optimization for 3D as well as for BIM (all p values < 0.001). Tumor control probability (estimated by TCP1 × TCP2) was 4.7% (3D) and 6.2% (BIM) higher for biological optimization ( p = 0.01 and p = 0.00002 respectively). NTCP lung as well as the percentage of lung volume exceeding 20 Gy was higher with the use of the biophysical objective function. NTCP heart was also higher with the use of the biophysical objective function. The percentage of heart volume exceeding 40 Gy tended to be higher but the difference was not significant. For spinal cord, the maximum dose as well as NTCP cord were similar for 3D plans ( D max : p = 0.04; NTCP: p = 0.2) but were significantly lower for BIM ( D max : p = 0.002; NTCP: p = 0.008) if the biophysical objective function was used. Conclusions: When using conventional 3D techniques, inhomogeneous dose distributions offer the potential to further increase the probability of uncomplicated local control. When using techniques as BIM that would lead to large escalation of the median and maximum target doses, it seems indicated to limit target-dose inhomogeneity to avoid dose levels that are so high that the safety becomes questionable.