Penetration enhancement of metformin hydrochloride via its molecular dispersion in sorbitan monostearate microparticles is reported. This represents basic philosophy to maximize its entrapment for maximum penetration effect. Drug dispersion in sorbitan monostearate with different theoretical drug contents (TDC) were prepared. Products showed excellent micromeritics and actual drug content (ADC) increased by increasing TDC. The partition coefficient of the drug products showed huge improvement. This indicates the drug entrapped in the polar part of sorbitan monostearate as a special image which effects on the drug release. The drug permeation profiles from the different products are overlapped with nearly equal permeation parameters. The permeation results suggested the main driving force for improving the drug paracellular pathway is its dispersion in sorbitan monostearate and is independent of ADC. Pharmacodynamic of the products showed a significant improvement than the drug alone at p ˂ 0.05. ANOVA test indicated the insignificant pharmacodynamic difference between the low, middle, and high ADC of the products. An excellent correlation founded between the drug permeation and pharmacodynamic precents. Drug permeation driving force via the paracellular pathway is its entrapment in sorbitan monostearate and independent on ADC. The technique is simple and the products had excellent micromeritics. It has some drawbacks concerned with gastro-intestinal disorders especially with an older patient2. The marketed doses of the drug are 3 doses, 500, 850, and 1000 mg per tablet with low bioavailability3. The biopharmaceutical classification system classifies metformin hydrochloride as a class III drug4. This group of drugs has high solubility but low intestinal permeability4. Then, it can understand the low bioavailability of the drug and consequently the high dose used in addition to the abdominal side effect.Metformin Hydrochloride is one of the worldwide drugs used for the treatment of diabetic II patients. The drug is considered safe and does not produce a hypoglycemic effect6. The high solubility of the drug and its Paracellular pathway absorption suggested a rapid and complete drug absorption. But the absorption of metformin hydrochloride is limited. It was reported that the addition of tween 80 to the drug led to an increase in all drug permeation parameters8. That is due to the role of non-ionic surfactants on enhancing metformin absorption via the paracellular pathway8. There is a significant saturable component of the paracellular pathway that limited the absorption of the highly water-soluble drug. The presence of tween 80 reduces the saturable paracellular pathway by electrostatic interactions between. the opposite charges of diffused substances (drug and tween 80) and the anionic residues of the lateral space and or tight junctions10. A novel “sponge” hypothesis was formulated to explain how metformin could be absorbed across human intestinal through the predominantly paracellular mechanism10.Metformin hydrochloride was found to be absorbed (about 90%) via the Paracellular pathway7 succeed to prepare sorbitan monostearate as microparticles containing metformin in the molecular state by using the rapid congealing technique. The molecular state of the drug in sorbitan monostearate was proved by different instrumental analyses. The authors suggested and used a modified non-everted sac technique in the discussion of the in-vitro drug permeation mechanism. They found that the addition of tween enhanced the drug permeation from the rabbit intestinal sac. The drug permeation enhancement was more pronounced from sorbitan monostearate entrapped drugs. The permeation parameters  are markedly increased from sorbitan monostearate microparticles encapsulating drug. The authors concluded that, as a result of the drug polarity, the drug is encapsulated in the polar part of the surfactant which led to a huge increasing the encapsulated drug partition coefficient. Emulsification of sorbitan monostearate microparticles encapsulated drug in phosphate buffer pH 6.8 by using tween 80 indicated the change of the surface again to hydrophilic. This image may be responsible for the above permeation parameters as a result of the correction of the HLP value  of the image, which could be easily diffused through the paracellular pathway7.Mady et al.7. Then studying the relationship between increasing the actual drug content on the penetration effect to achieve the maximum drug dispersed in sorbitan monostearate for maximum penetration effect and consequently maximum pharmacodynamic effect. The pharmacodynamic study would be tested in diabetic rats. The micromeritics properties of the prepared products should be also studied, which are essential in the manufacture processing. At the end trying to find a correlation between the two normally related parameters for a drug, drug permeation enhancement percent and the drug pharmacodynamic enhancement percent.Accordingly, the aim of this work is trying to investigate the penetration driving force of the drug via the paracellular pathway based on the previously reported by the author that, the drug dispersion in sorbitan monostearate has higher paracellular pathway penetrationMetformin hydrochloride (HCl), was purchased from El-Nasr Pharmaceutical Chemical Co (Egypt), Sorbitan monostearate of research-grade was purchased from Altas Chemie, IC GmbH (Germany). All other chemicals were of analytical grade and used as received.11. The prepared physical mixtures were melted at 60 °C ± 5 while stirring until clear molten solutions were obtained to assure from molecular dispersion of the drug in the carrier. The molten solutions were slowly cooled at room temperature while stirring to form sold masses. The products obtained were grinding, sieving, and stored at room temperature. The product particles, which passed from sieve size 600 µm was used for further studies11.Metformin HCl is dispersed in sorbitan monostearate by using the melting method. The required amounts of metformin HCl and sorbitan monostearate to prepare the solid dispersions of 25%, 33.33%, 50%, 66.66% and 75% theoretical drug content (TDC) in sorbitan monostearate were weight and physically mixed12.An accurate amount of each solid dispersion product containing 20 mg as TDC was weighed and then dissolved in 100 ml of 0.1 N HCl at 60 °C. The solution may be filtered if necessary and measure spectrophotometry at 232 λ max using 0.1 HCl as a blank. Sometimes dilutions may be carried out and the procedure was repeated in triplicate. The mean actual drug content and encapsulation % were calculated using Eqs. (14. The angle of repose (ɵ) was calculated by using Eq.  was measured cm317. The densities parameters of the granules were calculated according to Eq.  was measured in cmg to Eq. 18, Eq.  to the aqueous was measured spectrophotometrically at 232 λ max. using Eq. 7,207\doc21. The release solution was 900 ml of 0.1 N HCl with a maintained temperature at 37 ± 0.5 °C. The stirring rate was 100 rpm. The samples of 5 ml were taken at predetermined time intervals for determining the cumulative drug release. A new release medium was added to replenish each sample withdrawn. Sometimes dilutions may be carried out and the resulting solutions were measured at 232 λ max using 0.1 HCl as a blank. The procedure is carried out in triplicate7.To the USP paddle dissolution apparatus, an accurate weight of the product containing 500 mg of Metformin HCl [calculated according to the determined actual drug content] was added25.Preparation of non-everted intestinal sacs:26, and adequate care was taken to minimize pain and discomfort for animals. Upon confirmation of loss of the pain reflex, the animal was sacrificed. A midline longitudinal incision of 3–4 cm was made, and the small intestine was located. A 14 cm segment of the intestine was used to prepare the sac. The lumen of the intestinal segment was washed with buffer to remove any solid material. Using a surgical thread, a side of the segment of the small intestine could be tied. The fresh intestinal sac was then filled with buffer, tied to the other side with surgical thread, and checked for leaks. The prepared segments after each step were placed in continuous aerated phosphate buffer and used for studying the drug permeation after filling with the perfusion solution7.The animal used in this study was a Male albino rabbit with a weight of 2 kg obtained from the Tanta animal house. All procedures were approved and regularly controlled by the Animal Ethics Committee of Faculty of Pharmacy Tanta University (No: 2212018) and all experiments were performed by the guidelines and regulations of this committee. All the procedures were also carried out in full accordance with the ARRIVE guidelines 20207.An amount of Sorbitan monostearate product containing 50 mg of Metformin HCl as an actual drug content was accurately weighed and dispersed in 4 ml of pH 6.8 phosphate buffer. One ml of tween 80 added. The fresh intestinal sac segment was then emptied from the buffer solution. The intestinal sac was then filled with prepared perfusion solution, tied with surgical thread, and tested for leaks. The segment length and diameter were measured for surface area determinationDrug permeation profile study7.The prepared segment was suspended on the shaft of the USP dissolution apparatus. The outside of the sac medium (permeation medium) was 900 ml of phosphate buffer (pH 6.8) with continuous aeration and maintained the temperature at 37 ± 0.5 °C. The stirring rate was 50 rpm. Samples of 5 ml were taken at predetermined time intervals and the new release medium was added to replenish each sample taken. The amount of drug permeated from the segment to the medium was determined spectrophotometrically at 232 λ maxDetermination of permeability coefficient28. A simplified equation could be written as Eq. (The use of Fick`s law for the determination of the permeability coefficient (apparent permeability) of the drug across the isolated rat intestine was previously reportedThe method steps employed to evaluate the drug permeability profile from the modified non-everted sac method are modified experimental procedures described by references30.The variables M and Cd could be determined by analysis of mucosal fluid. The surface area [S] could be calculated by considering the intestinal sac a cylinder. Then, M/SCd could be calculated and plotted against time. The slope of the linear part of the plot is the permeability coefficient (P), which has the units of velocity (cm/s). The slope of the linear part of the curve was determined by linear regressionAnimals26, and adequate care was taken to minimize pain and discomfort for animals. The housing of the animal was at an ambient temperature of 25 ± 1 °C and relative humidity of 45–55% with a 12 h each of dark and light cycles. They fed was pellet diet and water ad libitum.The animal used in this study was the male albino Wister rats aged 7–8 weeks with a weight of 150–200 g. All procedures were approved and regularly controlled by the Animal Ethics Committee of Faculty of Pharmacy Tanta University (No: 2212018) and all experiments were performed by the guidelines and regulations of this committee. All the procedures were also carried out in full accordance with the ARRIVE guidelines 2020Induction of the experimental diabetes32. The animals were allowed to drink 5% glucose solution as a solution for the hypoglycaemic effect of the drug33. On the third day of streptozotocin injection, the rats fasted for 6 h and blood was withdrawn from the tail vein. The blood glucose level was measured by using Accu-Chek active (Accu-chek active test strip). Rats that had fasting blood glucose levels > 250 mg/dl were considered to be diabetic and were used to monitor the efficacy of metformin formulations34.After overnight fasting of the animals, diabetes was induced by a single intraperitoneal injection of a freshly prepared solution of streptozotocin (50 mg/kg body weight) in 0.1 M citrate buffer (pH 4.5)Determination of the hypoglycaemic effect of metformin HCl35.For only 15 min on the day of the experiment, the rats were given free access to the pellet. To provide a stable blood glucose level, the food was restricted but the rats were given free access to water for 2 h. Then, the formulations were dispersed in water at a concertation of 30 mg/ml, and 0.125 ml tween 80 was added for each ml. From the prepared tested dispersion, 1 ml was administered orally to each rat. At time intervals of  hours, blood samples were withdrawn from the tail vein. The blood glucose was measured by using Accu-Chek active (Accu-chek active test strip). The blood glucose level was plotted as a function of time. The area above the curve was determined and used for monitoring the efficacy of different formulations. The amount of reduction in blood glucose level was also calculated and plotted as a function of timeStatistical analysisStatistical analysis of the in-vivo data was carried out by applying the ANOVA test. The data were analyzed by one-way analyses of variance (ANOVA) with blood glucose level as an independent factor.26.All procedures of animal study were approved and regularly controlled by the Animal Ethics Committee of Faculty of Pharmacy Tanta University (No: 2212018) and all experiments were performed in accordance with the guidelines and regulations of this committee. All the procedures were also carried out in full accordance with the ARRIVE guidelines 20207. In that work, it was proved the molecular dispersion of the drug led to improving its Paracellular pathway permeation. To be assured from complete dispersion of the drug molecules and sorbitan monostearate, the solid dispersion is prepared by melting the physical mixture of the required amounts of the drug and the carrier. In addition, it could be expected there is no loss in both components of the solid dispersion as a result of the absence of a third component, which can dissolve either of the components or both. This led to assurance from nearly remaining the ratios of the components.The work aims to determine the drug permeation driving force through the Paracellular pathway reported by the authors from sorbitan monostearate microparticles encapsulated the drug36.The effect of drug dispersion in the wax matrix on the drug processing could be noticed from the Table Since metformin-sorbitan monostearate solid dispersions were prepared by using melting technique, this led to supposes that there is no loss for both drug and matrix and the actual drug content should be equal to theoretical drug content. On the determination of the actual drug content, from a Table Po/w is again increased and remains constant on increasing the drug percentage in the solid dispersion products. Since the drug-sorbitan monostearate solid dispersion is prepared by the melting method to produce a melt clear solution and the partition coefficient value depends on the lipophilicity of the drug, it can be concluded that the melting of the drug led to its dispersion in the polar part of the carrier. In this case, the polar part of the carrier could be only the polar part of an image of the surfactant which is, maybe, the surfactant micelle. This conclusion was also previously reported by the author7.The partition coefficient of the pure drug and all drug solid dispersion products with different ratios were studied. Figure The drug release profile from different matrices prepared with different metformin-span ratios was studied. From Fig. 38. The benefits of the application of the intestinal sac would be increased after solving the critical points facing its application by the author. Mady et al.7 succeed to solve the critical points of the technique by suspension the sac to the dissolution shaft in the dissolution media of the dissolution apparatus. This modification led to creating instead of drug release profile to drug permeation profile on using standard dissolution apparatus. The author discussed the critical points about the suggested solution, which may increase the value of the application of the technique as a modified non-everted sac.The intestinal sacs for assaying the permeability are a quick and sensitive technique for determining the overall intestinal integrity or comparative transport of a specific molecule, with the added benefit of intestinal site-specificity. The apparent permeability [Papp] or permeation coefficient of a molecule through the intestinal barrier could be calculated10 These effects would be more pronounced from the different solid dispersion products of the drug in sorbitan monostearate. The drug permeation profiles from the different drug-sorbitan monostearate solid dispersion products showed an overlap profile style concerning the initial, rate, and the total amount of drug released. This may be due to the drug dispersion in the carrier matrix and the use of an amount of the products containing the same actual drug concentration. Mady et al.7 discussed the essential of metformin HCL encapsulation in the molecular state in the carrier to improve its permeability. The conclusion of the author about the essential molecular dispersion of the drug in sorbitan monostearate as a carrier represents the basic philosophy to maximize its entrapment in the matrix. Increasing the initial drug permeated and total drug permeated leads to expecting improving the onset of action and decreasing the drug reported dose. Although metformin is reported to be safe from producing a hypoglycemic effect, decreasing the dose leads to decreasing the GIT side effect especially in older patients.Figure 2, in each case, are high enough to consider a good fitting of the calculated permeation data. In every case, there is no lag time. In the case of metformin HCl, the absences of lag time may be due to its high-water solubility which may be responsible for the presence of intercept values with y abscissa in concentration. The presence of an intercept value represents, in this case, the rapid saturation of the Paracellular pathway tissues of the intestinal wall with the drug before drug transport7. This finding is reinforced by the fact that about 90% of metformin HCl is absorbed via the Paracellular pathway6, and the absence of lag time. The addition of tween 80 to the drug led to increasing of all permeation parameters by different reported mechanisms10. The permeation parameters of the drug from its different molecular dispersion products in sorbitan monostearate are markedly increased than that from drug-tween although the intercept values are nearly the same. In addition, the permeation parameters of the drug from its solid dispersion products prepared with different ratios are nearly equal which is reflected in the drug absorption enhancement (DAE %). The drug absorption enhancement percent was calculated according to Eq. . Entrapment of the drug in sorbitan monostearate led to a huge increasing its partition coefficient indicating the entrapment of the drug occurred in the polar part of the surfactant. This led to the change of the drug from hydrophilic to the lipophilic entrapped image in sorbitan monostearate. The formed image led to the previously reported increasing the partition coefficient and decreasing the drug release. Emulsification of the image by tween 80, led to a marked increasing the apparent permeability and consequently the total permeability of the drug. Emulsification of the image by tween 80 may be changed the image surface from lipophilic to hydrophilic and that may explain the absence of the lag time and the presence of the intercept with y abscissa in concentration. Changing the formed image surface to hydrophilic by adding tween 80 may be led to increasing the Paracellular pathway of the image-encapsulated drug. The similarity of the intercept values to the drug-tween indicating the same permeation mechanism of the image to the drug itself (paracellular pathway). These results could be also confirmed from the histogram representation of the total drug permeation Fig. The similarity of the drug permeation profiles, the permeability coefficient, total permeation percent, and drug absorption enhancement percent from its different solid dispersion products prepared with different ratios suggesting that the role of sorbitan monostearate is only entrapment of the drug in its polar part as an image. This image entrapment process represents the drug permeation driving force, which is responsible for the paracellular permeation enhancement effect and this effect does not affect all drug-matrix ratios.Evaluation of the in-vivo effect of metformin hydrochloride is monitored by using its pharmacodynamics marker parameter . The blood glucose level was measured before the drug administration, which represents the glucose level at zero time. After the drug administration, the plasma glucose level is monitored as a function of time. The blood glucose level would be expressed as a percent and the profile of drug glucose concentration is plotted as a function of time Fig. A drop in the blood glucose level could be noticed from the first hour after oral drug administration. The effect of the high-water solubility of the drug and its paracellular pathway could be also reported as a result of the beginning of dropping of the blood glucose level after 15 min. The maximum and rate of blood glucose level from drug-tween are higher than that from drug alone which confirms the results of the drug permeation through the modified permeation non everted sac test. Expected results could be noticed from the glucose dropping level as a result of administration of drug dispersed in sorbitan monostearate matrix. A clear significant difference between the pharmacodynamic effect of the pure drug and the dropping of glucose level after administration of lower, middle, or higher drug entrapped in sorbitan monostearate at p ˂ 0.05 on applying ANOVA test was found.From Fig. The area above the curves (AAC) was calculated from Fig. From Table 42. FDA guidance described 4 levels for IVIVC which are A, B, C, and multiple C40. In this study, level A was selected because of its highest category of correlation since it correlates a point-to-point relationship42.FDA defined in-vitro-in-vivo correlation (IVIVC) as “a predictive mathematical model describing the relationship between an in vitro property of a dosage form and a relevant in vivo response”. In general, the in vitro property is the rate or extent of drug dissolution or release while the in vivo response is the plasma drug concentration or amount of drug absorbedThe pharmacodynamic marker of metformin is its dropping effect on the blood glucose level. Therefore, it was tried to correlate (point-to-point correlation) the percentage of drug permeated and its dropping of blood glucose level percentage. From Fig. Since Level A correlation is a linear relationship between two variables, it was tried to create a mathematic line correlation between the drug permeation enhancing percent and its pharmacodynamics enhancing percent (dropping of glucose level) as a point-to-point correlation. Table 1. the drug permeation profiles from all drug molecular dispersed products in sorbitan monostearate  are found to be overlapped to each other. 2. The drug pharmacodynamic effect of the prepared products is intersecting at more than one point to the degree of congruence. 3. Applying the ANOA test showed there is no significant difference between the pharmacodynamic effect (dropping of glucose level) of the three-drug molecular dispersed products at p ˂ 0.05. 4. The mean drug absorption (permeation) percent is equal to the mean pharmacodynamic percent. Accordingly, it can be reported that the paracellular enhancement of sorbitan monostearate to metformin is based on its dispersion in the matrix, which is confirmed by the author before7, and the enhancement does not depend on the drug–matrix ratio. This conclusion is supported by the results of the ANOVA test, which shows no significant difference between the drug products' pharmacodynamic effects. Accordingly, the mean pharmacodynamic effect of the low, middle and high drug molecular dispersed in the matrix was calculated and is represented in Fig. From the above study, it was found the following: From this study, it can be concluded that the permeability problem facing metformin, as an example for the class III drugs according to BSC classification, may be solved by its dispersion in sorbitan monostearate. Sorbitan monostearate is widely used in food industries and its uses in pharmaceutical technology would be harmless. The high hydrophilicity property of the Class III drug solubilizes them in the polar part of sorbitan monostearate in a special image, which may be theoretically micelle form. The image suggested by the authors (micelle) represents the penetration driving force of class III group drugs via the paracellular pathway. This image, which needs more investigation, does not depend on the drug-matrix ratio. Permeability enhancement could also test by using the author's suggested modified non-everted sac technique. This conclusion is based on an excellent relationship found between the drug permeation percent and its pharmacodynamic effect percent. Improving drug permeability leads to improving the drug bioavailability and consequently leads to decreasing the drug dose and side effects to the patient. At the same time decreasing the cost for the pharmaceutical industry as a result of decreasing the raw materials required, in addition to the simplicity and reproducibility of the technique used, encourage to suggest the technique for its dual effects.


Performing optimal Bayesian design for discriminating between competing models is computationally intensive as it involves estimating posterior model probabilities for thousands of simulated data sets. This issue is compounded further when the likelihood functions for the rival models are computationally expensive. A new approach using supervised classification methods is developed to perform Bayesian optimal model discrimination design. This approach requires considerably fewer simulations from the candidate models than previous approaches using approximate Bayesian computation. Further, it is easy to assess the performance of the optimal design through the misclassification error rate. The approach is particularly useful in the presence of models with intractable likelihoods but can also provide computational advantages when the likelihoods are manageable.The online version contains supplementary material available at 10.1007/s11222-022-10078-2. In many applications, finding the most appropriate model among a class of possible models is an important goal of statistical inference. In the classical literature, these decisions are commonly based on model selection criteria such as the Akaike information criterion or related criteria  information gain of the experiment with respect to the desired statistical objective . This is achieved by applying the principles and methods of optimal experimental design  to each model such that marginal likelihood, evidence, or prior predictive distribution for model m; marginal likelihood or prior predictive distribution; and posterior model probability of model m.We assume there are l that quantifies the loss of an experiment needs to be specified, see, e.g. Overstall et al. .One disadvantage of trees is their high variance. Slight changes in the data might lead to widely different trees. To reduce the variance, Breiman  proposesout-of-bag class predictions  algorithm , E(t), and I(t) denote the number of susceptible, exposed, and infected individuals at time t in a closed population of size t. The possible transitions in an infinitesimal time a priori.An example involving four competing continuous-time Markov process models for the spread of an infectious disease is considered in Dehideniya et al. . Let S m simulations in the retained sample, where the retained sample is composed of those simulations from the reference table which are ‘closest’ to the process realisation Dehideniya et al.  develop d et al.  is used a et al.  for morea et al.  improve For each of the classification methods from machine learning, we use a sample of 5K simulations from each model to train the classifier and to estimate the expected loss at each new design. For the classification trees, we use tenfold cross-validation to estimate the expected loss functions. When using random forests, we employ out-of-bag class predictions. As a criterion, we use expected 0–1 loss as well as expected multinomial deviance loss. When computing the expected multinomial deviance loss, we set the posterior model probability of the correct model to 0.001 whenever it is estimated to be 0, see Sect. 1 of Online Resource 1 for more information. We could follow the ABC method and draw the simulations from a large bank of prior predictive process realisations simulated at the whole design grid to reduce the computing time. However, since the machine learning classification method requires significantly fewer simulations, we find that it is still fast to draw a fresh process realisation for each proposed design. For the ABC approach, the reference table contains 100K stored prior predictive simulations for each model. To compute the expected loss, we average the estimated loss over 500 ‘outer’ draws from Figure The optimal designs obtained by the machine learning and ABC approaches are shown in Table As our next step, we compare the optimal designs found under the different approaches using a random forest classifier. For each of the optimal designs, we train a random forest with 100 trees based on 10K simulations from each model. The misclassification error rates and the misclassification matrices are estimated from a fresh set of 10K simulations from each model. This is repeated 100 times to be able to quantify the random error in estimating the misclassification error rates. The results for all the optimal designs as well as for the equispaced designs are shown in Table Finally, we compare the optimal designs obtained by the different methods based on approximate posterior model probabilities estimated using ABC, as described in Sect. A more detailed investigation of the classification performance at the optimal designs can be found in Sect. 4.3 of Online Resource 1.For the example in this section, we use the same infectious disease model set-up as in Sect. Another aim of this example is to demonstrate that the classification approach can easily cope with higher-dimensional designs, where other methods would fail to produce reasonable results in an acceptable amount of time. For the epidemiological example with four models in Sect. q realisations, then the total number of observations and therefore the design dimension is For simplicity, we assume that the same number of observations, The prior distributions for the parameters are In this example, we will only consider designs based on using the misclassification error rate as the design criterion. In order to compute the misclassification error rates based on the likelihoods, it is necessary to compute the marginal likelihoods for both models. When searching for the optimum design, we employ a relatively fast Laplace-type approximation to the marginal likelihood. For validating the resulting designs using the likelihood-based approach, we use a more expensive Gauss–Hermite quadrature scheme to obtain the marginal likelihoods. Details on both integral approximation methods can be found in Sect. 5.2 of Online Resource 1.When searching for the optimal designs, we employ trees with cross-validation as well as random forests using out-of-bag class predictions for our supervised classification approach. For both classification approaches, we use simulated samples of size 10K (5K per model).For the likelihood-based approach, the expected 0–1 loss (= misclassification error rate) is estimated by averaging the computed 0–1 loss over a sample of size 400 (200 per model) from the prior predictive distribution. The size of this prior predictive sample is considerably smaller than for the two supervised classification approaches due to computational limitations. Therefore, the volatility of our likelihood-based misclassification error rate estimates is much higher than for the supervised classification methods, so we expect our optimisation procedure to be less stable. The expected loss surface for the one-dimensional design is depicted in Fig. 3 of Online Resource 1.However, setting the prior predictive sample size for the likelihood-based approach to 10K as well would have made it infeasible to find an optimal design in a reasonable amount of time. Running the classification methods is still much more time-efficient than evaluating the likelihood function many times, especially for the SI model in high dimensions, see also Sect. 3 of Online Resource 1. Therefore, we only used the likelihood-based approach to find designs up to a total design dimension of q, and the number of observations per realisation, q and We consider various combinations of the number of realisations, The optimal designs found with the different methods are validated in two ways. Firstly, for each observation from a sample of size 2K (1K per model) from the prior predictive distribution, the posterior model probabilities are computed using the generalised Gauss–Hermite quadrature approximation to the marginal likelihood with n, and each line within each plot displays the results for a particular setting of We can also use the estimates for the posterior model probabilities to compute estimates of the misclassification error rates for each of the methods and dimension settings. These estimates are provided in the plots on the right-hand side of Figure n are very similar for both validation methods. This suggests that for this example random forests are suitable to validate and compare the efficiency of the resulting designs. In addition, it is reasonable to expect that the designs which are optimal for the random forest classification approach are close to the true optimal designs.From Figure One can also see from Fig. Salmonella enterica serovar Typhimurium (S. Typhimurium)—with human phagocytes, inside which they can replicate. The experiments assessed the effect of a number of different human immunoglobulin subclasses on the intracellular dynamics of infection by combining observed numbers of bacteria per phagocyte with a mathematical model representing a range of different plausible scenarios. These models were fit to experimental data corresponding to each human immunoglobulin subclass in order to determine the underlying nature of the interactions between the antibodies and bacteria. In these experiments, the data demonstrated bimodal distributions in the number of intracellular bacteria per phagocytic cell. The aim was to identify the source of the unobserved heterogeneity in the system that caused the observed patterns. Specifically, is there underlying heterogeneity in the bacteria’s ability to divide inside phagocytes, or is it the phagocyte population which is heterogeneous in its ability to control bacterial division? In this context, the classification approach allows us to find the experimental design which best enables us to discriminate between these competing hypotheses—(1) unobserved heterogeneity in the bacteria, (2) in the cells, or (3) no heterogeneity.A common challenge in experimental biology is identifying the unobserved heterogeneity in a system. Consider for example the experimental system in Restif et al. . In thisAfter bacterial opsonisation (i.e. the process by which bacteria are coated by antibodies), the bacteria are exposed to the phagocytic cells for a total of Next, the cells are treated with gentamicin, an antibiotic that kills extracellular bacteria, so that phagocytosis stops.n observation times S cells each are taken from the overall population of cells: one sample to count the proportion of infected cells (under a low-magnification microscope), and one sample of infected cells to determine the distribution of bacterial counts per infected cell (at higher magnification).At each of the That is, a design is composed of We give a brief account of the experimental procedure:f et al. .For the purpose of our example, we consider a realistic scenario where we have the resources to count a fixed number of cells, q of being refractory, in which case it only contains non-replicating bacteria, and a probability We consider three mathematical models, based on Restif et al. , to reprSimulations from the models are based on simulations of bacterial counts for the individual macrophages. As for our infectious disease examples, we can use the efficient Gillespie algorithm  with respect to the misclassification error rate. It is assumed Similar to the other examples, we assess each design by producing 10K new simulations under each model at that design and using these to train a random forest with 100 trees. A further 10K new simulations per model are then used to estimate the misclassification error rate. This is repeated 100 times for each design. The estimated misclassification error rates for the designs found under the tree and random forest classification approaches are shown in Table We are also interested in the posterior model probabilities at the different optimal designs. At each optimal design, we simulate 20 process realisations under the prior predictive distribution of each model. For each process realisation, we approximate the posterior model probability of the model that generated the data using importance sampling Below is the link to the electronic supplementary material.


Blue-enriched white light at night has the potential to delay the circadian rhythm in daily life. This study was conducted to determine whether the use of high correlated color temperature (CCT) light at home at night is associated with delay of sleep timing in university students.The survey was conducted in 2014–2015 in 447 university students in Japan and 327 students in China. Habitual sleep timing and type of CCT light at home were investigated by using a self-administered questionnaire. The Japanese students were significantly later than the Chinese students in bedtime, wake time, and midpoint of sleep. They were asked whether the lighting in the room where they spend most of their time at night was closer to warm color (low CCT) or daylight color (high CCT). The amount of light exposure level during daily life was measured for at least 1 week by the use of a light sensor in 60 students in each country.The percentages of participants who used high CCT lighting at night were 61.6% for Japanese students and 80.8% for Chinese students. Bedtime and sleep onset time on school days and free days were significantly later in the high CCT group than in the low CCT group in Japan. The midpoint of sleep in the high CCT group was significantly later than that in the low CCT group on free days but not on school days. On the other hand, none of the sleep measurements on school days and free days were significantly different between the high CCT and low CCT groups in China. Illuminance level of light exposure during the night was significantly higher in Japanese than in Chinese, but that in the morning was significantly higher in China than in Japan.The use of high CCT light at night is associated with delay of sleep timing in Japanese university students but not in Chinese university students. The effects of light at night on sleep timing and circadian rhythm may be complicated by other lifestyle factors depending on the country.The online version contains supplementary material available at 10.1186/s40101-021-00257-x. Light is a strong synchronizing agent (zeitgeber) for the circadian system. Light exposure in the morning has an important role in resetting the circadian rhythm to a 24-h cycle in humans. On the other hand, evening light exposure delays the phase of circadian rhythms. This relationship between the timing of light exposure and phase shift of circadian rhythms is known as a phase-response curve , 2. In aThe non-visual effects of light depend on the intensity of light, the spectrum of light, and the duration of exposure. The light intensity of even general home lighting is known to affect circadian rhythms and melatonin secretion , 10. RegHowever, many of those studies were conducted in a laboratory, and there have been few studies in which the influence of CCT of home lighting in real life was examined. We previously reported that there were significant correlations between CCT of lighting at home and phase of the circadian rhythm in middle-aged adults and primary school children in Japan . The resFurthermore, the survey was conducted in Japan and China. Our previous study conducted in Japan showed that the CCT of lighting used in the home correlates with circadian rhythms . HoweverThe purpose of this study was to determine the differences between light environments in China and Japan and to clarify the relationship between light environments at night and sleep habits in university students in Japan and China.The study was conducted in mid-December 2014 and mid-January 2015. The year-end and New Year holidays were excluded from the survey period. The participants included 470 Japanese university students and 397 Chinese university students. All participants provided informed written consent. The study was approved by the Institutional Ethics Committee of Kyushu University; the protocol and all the procedures were in agreement with the Declaration of Helsinki. After excluding participants whose data included typographical errors or for whom data were missing, we finally analyzed data for 447 Japanese students (average age of 21.5 ± 1.6 years) and 327 Chinese students (average age of 23.3 ± 2.7 years). The ratio of males in the Japanese students (62.8%) was significantly higher than that in the Chinese students (53.4%).The survey was conducted in Fukuoka City in Japan and Shanghai City in China. The latitudes of Fukuoka and Shanghai are 33° 36′ north latitude and 31° 11′ north latitude, respectively. The time difference between Japan and China is 1 h. The local times at sunrise on December 1st in Fukuoka and Shanghai were 7:04 and 6:34, respectively, and the local times at sunset were 17:10 and 16:51, respectively.We investigated the habitual bedtime (lights off time), subjective sleep latency, and wake time on school days and free days using a self-administered questionnaire. The sleep onset time was calculated by adding the sleep latency to the bedtime, and the sleep period time was calculated by the time from the sleep onset time to the wake time. The sleep midpoint was calculated by adding 1/2 of the sleep period time to the sleep onset time. Social jet lag was calculated as the absolute difference between midpoint of sleep on free days and midpoint on school days .p < 0.001). Sleep period time was also significantly shorter in Japanese students than in Chinese students  (p < 0.001). Subjective sleep latency   was not significantly different between the two groups. Social jet lag was significantly larger in Japanese students than in Chinese students (p < 0.001).Table To the best of our knowledge, this study is the first study in which the type of CCT light used at home was investigated for a large sample using a questionnaire. Therefore, we originally made a simple two-choice question. The participants were asked whether the lighting in the room where they spend most of their time at night was closer to warm color (low CCT) or daylight color (high CCT). Color photographs were used to help participants make accurate selections. The participants looked at two photographs of lighting in the questionnaire and chose one of them. The photographs used in the questionnaire in this study are not allowed to be shown here due to copyright issues, but almost the same pictures are shown as a supplemental file  and illuminance was continuously measured for about 2 weeks at 2-min intervals. After exclusion of subjects due to missing data, data for 54 Japanese students  and 58 Chinese students  were used for analysis. Sleep timing was significantly later in Japanese students than in Chinese students . Sleep habits were compared in the high CCT group and the low CCT group for both Japanese students and Chinese students after adjusting for sex and age. In the Japanese students, bedtime and sleep onset time in the high CCT group were significantly later than those in the low CCT group on school days (p < 0.05) and free days (p < 0.01) (Table p < 0.01)  and social jet lag (p = 0.051) tended to be larger in the high CCT group than in the low CCT group. On the other hand, in the Chinese students, there was no significant difference in sleep measurements between the high CCT group and the low CCT group on school days or free days  Table . Also, t01) Fig. . The wakys Table .Fig. 1Pp < 0.001). The average illuminance was significantly higher for the Japanese students than for the Chinese students during the period from midnight to early morning (0:00–6:00) including sleeping time . On the other hand, the average illuminance in the morning (6:00–12:00) was significantly higher for the Chinese students than for the Japanese students . There was no significant difference between illuminance levels in the afternoon (12:00–18:00) for the Japanese students and Chinese students. The average illuminance level for 2 h before habitual bedtime was significantly higher for the Japanese students (74.8 lx ± 56.5 lx) than for the Chinese students (59.9 lx ± 64.8 lx) . Correlation analysis was conducted for illuminance level for 2 h before habitual bedtime at night and sleep habits. There was no significant correlation between illuminance level and any of the sleep measurements for both the Japanese students and Chinese students.Figure The results of investigation of the relation between the CCT of lighting and sleep habits in each country showed that bedtime and sleep onset time of the students who used high CCT lighting was significantly later on school days and free days for the Japanese students. Previous laboratory studies showed that high CCT lighting (blue-enriched white lighting) has a greater impact on arousal level and melatonin suppression –18. The The difference between sleep habits of students in the high CCT group and the low CCT group in Japan was more pronounced on free days than on school days. The midpoint of sleep on free days was significantly later in the high CCT group than in the low CCT group Fig. . Also, wIn the present study, significant differences in sleep habits between lighting conditions were found in Japanese students but not in Chinese students. One of the reasons for this difference may be the difference in illuminance level. Illuminance level after sunset for the Japanese students was significantly higher than that for the Chinese students. It is known that the effects of light also depend on the illuminance . TherefoFurthermore, the effects of light at night on sleep timing may be complicated by other lifestyle factors depending on the country. For example, in this study, about 80% of the Chinese students lived in dormitories and about 70% of the Japanese students lived alone. Chinese students lived with quite regular timetables for classes. Weak social pressure for a sleep/wake schedule is considered to be related to the delay of sleep pattern in Japanese students. This means that Japanese students are exposed to artificial lighting for a longer period of time before going to bed, which might be a cause of the delay of circadian rhythm as shown in a previous study . In otheIn this study, more than half of the Japanese and Chinese students used high CCT lighting at night. This result reflects the fact that it is common to use white and high CCT fluorescent lighting at night at home in some Asian countries including Japan and China. The percentage of students using high CCT lighting was significantly higher in Chinese students. The exact reason why white fluorescent lights are often used at home at night in Asia is not known. White fluorescent lighting began to become popular in Japan after the 1950s, and white fluorescent lighting becomes the preferred alternative to incandescent light in ordinary households. In the 1980s, fluorescent lamps with low CCT began to be sold, and it is thought that low CCT lighting has gradually become widespread in Japan. On the other hand, in China, low CCT fluorescent lights are not widely sold in stores and are not widely used at home. This may be one of the reasons for the differences between Japan and China. Currently, LED lighting is rapidly becoming widespread in both Japan and China. Since the CCT of LEDs can be easily adjusted, the lighting environment at home may be changing. Further research is needed because the lighting environment can be influenced by culture and technology.For the survey of CCT light environments, we did not test its validity since it was a simple question. When the survey was conducted in 2014–2015, daylight color and warm color fluorescent lamps or incandescent lamps were generally used at home in Japan and China. Today, however, LED lighting with continuous color adjustment functions is widespread, and we may therefore need to be more careful about a survey of  CCT  of light using a questionnaire.There were no significant correlations between illuminance level at night and sleep habits in this study. One reason may be that this study was a field study that included some uncontrolled factors affecting sleep habits other than the lighting condition at night. Although the purpose of this study was not to investigate the cause of differences in sleep habits of Chinese students and Japanese students, it is necessary to consider these factors that influence sleep habits. The low reliability of measurements of illuminance level using the pendant sensor is also a possible cause. For example, the problems with pendant-type sensors are that they may be hidden by clothing and the orientation of the sensor is not stable. Reliable measurements of illuminance level are needed to evaluate the relationships between individual sleep habits and illuminance levels at home. In addition, only 60 of the 447 Japanese and 60 of the 327 Chinese participants had their illuminance measured. Unfortunately, due to the small sample size in this study, we were also unable to examine the interaction between CCT and illuminance level.OPN4) are associated with both the non-visual effects of light and the timing of sleep in Japanese university students [Furthermore, the relationship between illuminance level and sleep habits may be complicated by individual differences in circadian photosensitivity –40. In ostudents . It woulIn conclusion, the use of blue-enriched white light (high CCT light) at night is associated with delay of sleep timing in Japanese university students but not in Chinese university students. Although the effects of light at night on sleep timing and circadian rhythm may be complicated by other lifestyle factors depending on the country, use of low CCT light at home at night is recommended to prevent delay of sleep timing and the circadian rhythm.Additional file 1: Figure S1. The pictures used in the questionnaire in this study are not allowed to be shown due to copyright issues, but almost the same pictures are shown as additional files.Additional file 2: Table S1. Demographic data and sleep habits in Japanese and Chinese students whose illuminance was measured.


In this study we present a novel method for re‐calculating a treatment plan on different respiratory phases by accurately modeling the panning and tilting beam motion during DTT (the “rotation method”). This method is used to re‐calculate the dose distribution of a plan on multiple breathing phases to accurately assess the dosimetry.exhale) for 10 previous liver stereotactic ablative radiotherapy patients. Our method was used to re‐calculate the plan on the inhale (0%) and exhale (50%) phases of the four‐dimensional CT (4DCT) image set. The dose distributions were deformed to the BHexhale CT and summed together with proper weighting calculated from the patient’s breathing trace. Subsequently, the plan was re‐calculated on all ten phases using our method and the dose distributions were deformed to the BHexhale CT and accumulated together. The maximum dose for certain organs at risk (OARs) was compared between calculating on two phases and all ten phases.sIMRT plans were optimized on a breath hold computed tomography (CT) image taken at exhale  and weighting them properly provides accurate results while requiring less time. This approach should be used to confirm the safety of a DTT treatment plan prior to delivery. Since the TPS cannot pan/tilt the beam on these other phases, they have either simplified the beam motion as a translation within the TPSIn this paper, we describe the rotation method for re‐calculating a dose distribution on any respiratory phase. The advantage of our rotation method is that the user stays in the TPS to perform the calculation. The procedure is more efficient and streamlined and uses clinically commissioned beam data to perform the dose calculation. It also minimizes errors that may arise from transferring data to another application. To our knowledge, this is the first time such an approach has been mentioned in the literature for a gimballed linac. This rotation method is demonstrated here for dose calculations with the Vero, but the ideas and concepts can be applied to any other system that pans/tilts the beam during tracking.2A retrospective study was conducted to compare the dose to OARs when the dose distribution is calculated on different respiratory phases using two different methods  and to demonstrate how the calculation method can affect clinical decisions. This study also investigated the temporal resolution required to retrieve accurate dosimetric information.2.1RPM system during their 4DCT scan and thereafter retrospectively binned into ten respiratory phases in external software . Clinical plans are generated on breath‐hold images taken at exhale . This study uses a patient’s 4DCT data to evaluate doses from a plan optimized on the BHexhale CT on multiple breathing phases.Patients treated with liver SABR at our center have three or more gold fiducials implanted near their tumor prior to a planning CT simulation scan. A patient’s respiratory trace is recorded using Varian’s 2.2exhale CT is transferred to the inhale (0%) phase of the 4DCT based on this registration and the dose distribution is re‐calculated. This models tumor tracking as a translation of the beam, and all beams are shifted by the same amount.The translation method used in this study is described by Depuydt et al.2.3This novel method re‐creates the beam’s path through the patient when it pans and tilts by changing the gantry, ring, and collimator angles of the Vero, as well as the location of each beam's isocenter, within the TPS. Figure A script was written within the RayStation TPS to perform this calculation for each beam in the original plan and copy the new beams to a plan on a different respiratory phase. The dose distribution is then re‐calculated. This allows the dosimetry for a plan to be verified on a different respiratory phase than what it was originally optimized for while modeling the appropriate beam geometry. This process was tested on a cylindrical phantom with a cylindrically shaped target that was moved 1–2 cm in one, two, and three dimensions in the TPS to simulate different complexities of respiratory motion.2.4exhale CT were rigidly propagated to all other phases of their 4DCT and reviewed and adjusted as necessary by oncologists. A sIMRT plan was optimized on the BHexhale CT in the RayStation TPS following clinical protocols, meeting the prescription and dose limit requirements for each patient.A retrospective analysis was performed with the CT data of 10 patients previously treated with liver SABR with fiducial markers implanted in the liver adjacent to the target. OARs of interest previously delineated on the BH2.4.1These plans were transferred to the inhale (0%) phase CT using both the translation and rotation methods outlined above. The maximum dose to OARs of interest on the inhale phase, as calculated by each method, was reported. The schematic in Fig. 2.4.2exhale CT using the ANACONDA deformable image registration (DIR) algorithmDuring a DTT treatment, the plan is not delivered statically in the exhale or inhale position, so the next step was to model the plan being delivered throughout the breathing cycle and incorporate a temporal element. Dose distributions calculated on other breathing phases were transferred back to the BHexhale CT image. In this study the BHexhale CT image was always the reference image for dose accumulation. The patient’s breathing trace, taken at the time of their 4DCT, was divided into the “inhale” and “exhale” halves of their breathing cycle based on their breathing amplitude. The percentage of their total breathing time spent in either phase was calculated, and the “inhale” and “exhale” phase weightings were used to weight the dose distributions from the inhale (0%) and exhale (50%) CT images after they were deformed to the BHexhale CT and summed together. Figure First, the plan was re‐calculated on the inhale (0%) and exhale (50%) breathing phases from the 4DCT using only the rotation method. These dose distributions were then deformed back to the BHexhale CT and summed together with equal weightings since each image phase represents the same duration of time. As such, the proper phase weighting is inherently included in this approach.Second, the plan was re‐calculated on all 10 breathing phases of the 4DCT and these were deformed to the BHTo summarize, we have four different scenarios that re‐calculate the dose to organs at risk during DTT. Table 33.1G2), ring (R2), and collimator (C2) angles, and patient shift , are given by eqs.  in Fig. Δfidx,Δfidy,Δfidz given by eq.  and the new respiratory phase the position of the fiducial markers on the original respiratory phase the location of the center of the PTV on the original image used for planning : G1 and R1.the original gantry and ring angles for each beam: Testing the script on a sIMRT plan optimized for a cylindrical phantom produced the new beam parameters shown in Table 3.2trans), 13 out of 26 OARs had a higher maximum dose than from the original plan . When the plan was re‐calculated on the inhale phase using the rotation method , 14 out of 26 OARs had a higher maximum dose than on the original plan . In both cases , three OARs exceeded their dose constraint after meeting their dose limit with OriginalBH. However, the maximum dose calculated between the two methods differed significantly for many of the 26 OARs, as shown in the second and third columns for each OAR plot in Fig. When the plan was re‐calculated on the inhale phase using the translation method  among the ten patients. When re‐calculating a dose distribution with Sum2Phases, six OARs exceeded their dose constraint. Sum10Phases uses the rotation method on all 10 phases of the 4DCT scan. When the dose distribution was re‐calculated using this method, five OARs exceeded their dose constraint. These results are shown in the fourth and fifth columns of each OAR plot in Fig. Sum4exhale CT only provides dosimetric information representing the entire plan being delivered during that phase of the respiratory cycle. During DTT the plan is delivered throughout the entire respiratory cycle, thus it is important to gather dosimetric information during other phases. Checking the maximum dose to OARs on another respiratory phase can be used to conservatively identify plans that would not be safe for DTT. Clinically at our center, the Inhaletrans method is used to check if a plan could be unsafe for DTT prior to treatment.Optimizing and calculating a treatment plan on the BHThe translation method is simple to implement but its representation of the beam's path through the body can give inaccurate dosimetric results. The rotation method is more complex but using the scripting environment in the TPS makes the calculation easily accessible. The rotation method accurately models the beam’s path through the body as well as the correct source‐to‐surface and source‐to‐target distances to provide more accurate dosimetry. Using DIR to sum the dose contributions from different respiratory phases gives a more accurate representation of the real dose distribution than assessing the dosimetry on each phase separately . If regions of high dose on multiple phases align, the maximum dose to an OAR will remain high. However, if the high dose regions do not overlap, they may sum to a lower dose than either phase alone would predict. This could influence clinical decisions regarding whether a plan is safe for tracking.2Phases uses the breathing trace data acquired during the 4DCT to properly determine the weighting for each extreme phase of the breathing cycle . Sum10Phases is the most accurate method available to us within the TPS. It also properly models the time spent in each breathing phase by using ten images representing equal segments in time over the entire breathing cycle. However, in order to create accurate image registrations between each phase and the BHexhale image to deform the dose distribution, it requires contouring the OARs of interest on each image. In this study that included 286 contours for all 10 patient’s 26 OARs on 11 images . This extra time may not be feasible for a clinical workflow. Therefore, based on the results from this study, Sum2Phases is the suggested procedure to follow as it provides results most similar to Sum10Phases  phase, but the Sum10phases method (the most accurate method) shows this OAR would in fact exceed its limit. Even the Inhalerot method, which models the proper beam geometry, would not indicate to a clinician that an OAR will exceed its dose constraint in these cases. This demonstrates the importance of adequately accumulating dose between different breathing phases when making clinical decisions.Figure Planning on a mid‐ventilation phase of a 4DCT, rather than an extreme end of the respiratory cycle , may provide more consistent dosimetric results among all respiratory phases. At this center, planning is done on a breath hold exhale phase CT with contrast to improve tumor visualization. The timing between contrast injection and when the image is taken must be precise. This is more difficult to time with mid‐ventilation during a 4DCT scan than on a breath hold CT, but if contrast is not being used planning on mid‐ventilation is a viable option.Several other groups have also acknowledged the need for better dosimetry for DTT plans with the Vero and have developed solutions to model the beam motion during treatment. One group uses the translation method by aligning the fiducial markers near the target on each phase of a 4DCT before transferring and re‐calculating the dose distribution on each phase. Then, using deformable image registration they accumulated the dose to one reference respiratory phase for a final total dose distribution.et al. developed a 4D Monte Carlo algorithm to calculate the dose distribution during tumour tracking on the Vero from a ten phase 4DCT.et al. model gimbal rotation by rotating each phase’s CT image from a 4DCT outside the TPS based on the gantry, ring, and pan and tilt angles that would occur during that respiratory phase. The rotated CT was then brought back into the TPS for a dose calculation.Other groups properly model the beam motion as a rotation around a pivot point but are required to leave the TPS to perform this dose calculation. Ishihara 10phases method was the most accurate and time consuming. However, it also has a limited temporal resolution that is dependent on the amount of phases in the 4DCT. It has been shown that accumulating dose distributions with a temporal resolution of 500 ms is adequate for an accurate dose reconstruction.In this study, the SumUsing a 4DCT to calculate the dose on other phases is a limitation of our technique because it assumes the patient’s breathing is the same during treatment as it was for their 4DCT. One could use the motion of the fiducial markers during treatment in the calculations above to check if a daily fraction’s dose distribution is consistent with the dose distribution calculated using the 4DCT images. This could identify instances when adaptive offline re‐planning is necessary. Future work will include developing appropriate treatment planning strategies to ensure a plan is safe for tracking and take advantage of respiratory motion to create a more optimal plan. This will incorporate multiple respiratory phases during plan creation and optimization and will require the proper panning/tilting beam geometry to be modeled.10Phases method is the most accurate for calculating dose to an OAR, the time it takes to contour on all phases of the 4DCT can make this method clinically infeasible. The Sum2Phases method is a useful compromise as it still produces accurate results and requires less time to implement. Clinical decisions as to whether a treatment plan is safe for DTT are made by checking the dose on other respiratory phases, therefore it is imperative that the dosimetry is as accurate as possible while still being easily accessible.The script that automates the calculation for our rotation method in the TPS makes it easily accessible for clinical use. The correct beam geometry of the rotation method provides more accurate dosimetry than the translation method. While the Sum5We have developed a method for re‐calculating the dose distribution of sIMRT plans on different respiratory phases that correctly models the pan/tilt beam geometry during DTT while staying within the TPS. The same method can be used for 3DCRT plans. Correctly modelling DTT beam motion as a rotation when re‐calculating the maximum dose to OARs on a different respiratory phase can provide different outcomes than when the beam motion is simplified to a translation. Accumulating the dose distributions from multiple respiratory phases onto one reference phase and summing them together gives a more accurate calculation of the maximum dose to an OAR. While accumulating the dose from all 10 phases of a 4DCT is the most accurate, it takes a considerable amount of time. Therefore, accumulating the dose from the exhale and inhale phases only, and weighting them according to a patient’s breathing trace, should be used to confirm the safety of a sIMRT plan intended for DTT prior to delivery.All authors on this manuscript contributed to the conception of this work or the acquisition, analysis, and interpretation of the data. Everyone was either involved in drafting the work or made critical revisions prior to submission. All authors approved this final version being submitted and agree to be accountable to the work presented.


ViewDEX  is an image viewer compatible with Digital Imaging and Communications in Medicine (DICOM) that has been especially designed to facilitate image perception and observer performance studies within medical imaging. The software was first released in 2004 and since then a continuous development has been ongoing. One of the major drawbacks of previous versions of ViewDEX has been that they have lacked functionality enabling the possibility to evaluate multiple images and/or image stacks simultaneously. This functionality is especially requested by researchers working with modalities, where an image acquisition can result in multiple image stacks . In ViewDEX 3.0 this functionality has been added and it is now possible to perform image evaluations of multiple images and/or image stacks simultaneously, by using multiple monitors and/or multiple image canvases in monitors. Additionally, some of the previously available functionality has been updated and improved. This paper describes the recent developments of ViewDEX 3.0. The software was first released in 2004 and the prerequisites for the development were that the software should be DICOM compatible, easy to use, freely available and be suitable for both imaging research and clinical optimisation. Since the first release of the software, continuous development has been ongoing and additional papers describing the developments have been published. The ViewDEX software can be downloaded free of charge from www.vgregion.se/sas/viewdex, and in the end of October 2020 ViewDEX had been downloaded from over 40 countries and had received over 230 citations in scientific publications. ViewDEX has for example been used for studies in conventional projection radiography, tomosynthesis, computed tomography (CT), mammography, magnetic resonance imaging (MRI), nuclear medicine imaging, interventional imaging and ultrasound.The introduction of digital radiography in the late 1900s resulted in new challenges regarding the optimization of image quality and radiation dose. Digital technology enables the possibility to change the appearance of a collected radiograph not only by changing the acquisition parameters, but also by adjusting the image processing. Hence, the task of optimising the examinations became more challenging as more variables were added to the equation. At many radiological departments one limiting factor in the optimization process is finding time for the radiologists to review and evaluate the radiological images. In order to facilitate the image evaluation process, the software ViewDEX  was developed is cumbersome, as each set of images has to be manually created before the study is configured in ViewDEX. Other limitations with ViewDEX 2.0 include that the log file may be difficult to work with and that data from physical measurements cannot automatically be saved in the log file.The development of ViewDEX has always been focused on keeping up with the technological progress within the field of medical imaging. The goal of the development is to create a software that enables the observers to review study images in a surrounding that resembles the real clinical situation. The largest limitation with previous versions of ViewDEX is that they only support the possibility to include one single image or image stack in each case. Hence, the clinical benefits obtained by e.g. multi-planar reconstructions (MPRs) cannot be fully utilised during image review using ViewDEX, as the different reconstructions cannot be shown to the observer side-by-side. Additionally, performing alternative forced choice (AFC) studiesIn this paper, ViewDEX 3.0 will be presented. This new version of the software has been adapted to modern medical imaging, e.g. by the development of a new architecture that enables the possibility to simultaneously review multiple images/image stacks. the history of the development of ViewDEX since the first release in 2004 is presented, together with a detailed description of the available functionality of ViewDEX 2.0. To summarise, ViewDEX 2.0 can handle DICOM images from different modalities, for example conventional projection radiography, CT, single-photon emission CT, positron emission tomography, MRI and ultrasound. The cases included in a study can be displayed in a unique randomised order for each observer. During image review the observers are able to alter the image display properties e.g. by changing the window settings or zoom and pan the images. The observers can also perform physical measurements in the images, such as distance measurements, area measurements and measurements of mean pixel value in specific locations of an image. If a study is based on localisation of pathology the observers can make localization markings in the images and also answer questions connected to the markings made. It is also possible for the observer to write general notes regarding specific cases included in the study. The person responsible for study setup has full control over the conditions for image review and also has the possibility to log into a study and review (‘show mode’) or edit (‘edit mode’) the responses from each specific observer.In Svalkvist et al.ViewDEX 3.0 is written in the Java programming language version 8  and the code can run on any desktop system. The software is compatible with Windows 64, Linux 64 and MacOS 64. Compared to ViewDEX 2.0, version 3.0 is optimised with respect to performance, leading to for example shorter execution times.In the previous version of ViewDEX only one image/image stack at a time could be displayed to the observer. As a consequence, each case included in a study could only consist of one image/image stack . AlreadyIn order to facilitate the possibility to review multiple images simultaneously in ViewDEX, the architecture of the software has been changed. In ViewDEX 3.0, it is possible to review images using up to four different monitors. Additionally, each monitor can be divided into four separate image canvases, which means that a total of 16 different images/image stacks can be included in each case and reviewed simultaneously. Possible canvas setup on each monitor is 1 × 1 (full-screen), 1 × 2 or 2 × 1  or 2 × 2 (four canvases). If three image/image stacks are included in each study and only one monitor is used, the canvas setup is 2 × 2 with one of the four canvases empty (black). Each image canvas will function as a separate display, which means that all functionality that was available in ViewDEX 2.0 is implemented in each canvas separately in ViewDEX 3.0. This means that the observer for example can change window settings and use zoom, pan and cine-loop individually in each image canvas. Additionally, the observers can mark two or more canvases, i.e. perform a multi-select of canvases. If more than one canvas is selected the scroll function (if image stacks are reviewed) and all changes of image properties  are altered in the selected canvases simultaneously.During the setup of a study the default configuration of number of monitors and number of canvases in each monitor is determined. During image review the observer has the possibility to temporarily change the image setup, e.g. to review one image/image stack in full-scale format on one of the monitors (1 × 1) or to review two out of four images on one monitor side-by-side (i.e. in canvas setup 1 × 2 or 2 × 1 instead of 2 × 2). In During study setup, the person responsible for study design specifies the location at which each image series should be displayed (monitor and canvas). However, it is also possible to choose that the location of each image series included in a case is randomised for each case and observer. This functionality enables the possibility to conduct AFC studies without any need to process the images in advance.. However, the fact that it is not possible to automatically store the results from physical measurements performed in ViewDEX 2.0 limits the usefulness of the functionality. Up until now, the only way to store results from physical measurements in ViewDEX has been to manually type the result in the notes panel. This solution comes with a number of disadvantages. For example, the risk for incorrect registration due to typing errors increases and if several different measurements are performed in each case, it may be difficult to distinguish the registered measurements from each other.Functionality enabling the possibility to perform physical measurements in images is a valuable tool in many image evaluation studies. Also in the clinic, measurements of different kinds are valuable in order to make a correct diagnosis. Already in ViewDEX 2.0 measurements such as distance, area and mean pixel values were enabled. This functionality has been used in many studies conducted using ViewDEX2) and the mean pixel value will be given. The actual locations of the stored measurements can be reviewed in retrospect by logging in to the study in show mode.In ViewDEX 3.0, the observers can choose which measurements should be stored in the log file. A physical measurement is made by holding down specific buttons on the keyboard while clicking and dragging the mouse pointer over the image. By using keyboard short commando, the result from the measurement is stored and incorporated into the log file. For a distance measurement the distance will be stored in millimetres (mm). Additionally, the coordinates for the starting point and end point of the measured line will be given. For area measurements using a circular ROI or an ROI of variable shape, the measured area will be stored in cubic millimetres  study with single images is reviewed with a rate of ~150 cases/hour, whereas a free-response ROC study with image stacks of 60 images/case is reviewed with a rate of ~20 cases/hour. One reason for the relatively high image review rates is the fact that both image display and the registration of answers are made using the same software. The observer can concentrate solely on image evaluation, while the software automatically logs the answers connected to the current case. If separate systems would be used for image display and for recording answers, the observers themselves would need to keep track of the recorded answers in order to certify that the answers are registered for the correct case.It is difficult to determine the reading times using ViewDEX as these are affected by e.g. type of study, number of images in each case (single images or image stacks) and number of tasks for the observer. In an estimation of reviewing times using ViewDEX, Håkansson et al.Even though the development of ViewDEX 3.0 has led to a more modern and general software, there is still room for further improvements. The development of ViewDEX has been focused on reducing the effort needed by the observers reviewing a study, because one of the most common limiting factors for conducting image review studies is finding time for the observers to review the images. However, study setup in ViewDEX is still quite cumbersome. Technically, study setup is easy, as it only requires editing of the property files that are simple text files. Nevertheless, as more and more functionality is added to the software the property files become longer and study setup more time consuming. Also, small errors in e.g. spelling or data that accidentally was left out in the editing of the property files might lead to the fact that the study cannot be run in ViewDEX. Finding the error in order to correct the input in the property file is time consuming and often leads to frustration. Future releases of ViewDEX 3.0 will include the development of a semi-automatic configuration menu in which the details concerning the study setup can be customised. The configuration menu will require less manual texting in order to edit the property file. Instead, the menu will consist of different headings under which available editing alternatives are presented, e.g. as check boxes. Another future development may include making the software even more general regarding the configuration of monitors and canvases in each monitor. In the current release of ViewDEX 3.0, there is a limitation regarding the maximum number of simultaneous monitors and canvases/monitor (maximum four monitors and four canvases/monitor), leading to a maximum of 16 images/image stacks that can be reviewed simultaneously.The fact that ViewDEX is not server based leads to limitations regarding the possibilities to easily conduct a ViewDEX study with observers from different sites. Today, the only solution in this situation is to distribute one copy of the study to each site. Another limitation is that ViewDEX cannot communicate with the Picture archiving and communication system (PACS), which means that the person designing the study needs to copy the images that should be included in the study from the PACS system and insert them into a separate folder, which will be working as the image database for the study. This work can be quite cumbersome and time consuming. There are, however, several reasons why the development of ViewDEX has not been focused on creating a server-based software. For example, such a solution might require a higher level of data security in order to follow the recommendations of the General Data Protection Regulation. Additionally, if a study can be reviewed online, the observers have full access to the study from an arbitrary number of locations. This might limit the possibilities for the person responsible for the study to control the image reading conditions, e.g. type of monitor, monitor calibration and surrounding light environment, which also might lead to biases in the results from a study.ViewDEX 3.0 is a more modern version of the well-established and frequently used image evaluation software ViewDEX. The software has now been configured to facilitate review of multiple images/image stacks simultaneously, enabling the possibility to use ViewDEX for evaluations of more complex imaging modalities.This work was supported by grants from the Swedish state under the agreement between the Swedish government and the county councils, the ALF-agreement [ALFGBG-718111]; The Healthcare Committee, Region Västra Götaland (Hälso- och sjukvårdsstyrelsen) [VGFOUREG-932018]; and the Euratom research and training programme 2014–18 under grant agreement No. 755523 (MEDIRAD).


The function of non-coding RNA sequences is largely determined by their spatial conformation, namely the secondary structure of the molecule, formed by Watson–Crick interactions between nucleotides. Hence, modern RNA alignment algorithms routinely take structural information into account. In order to discover yet unknown RNA families and infer their possible functions, the structural alignment of RNAs is an essential task. This task demands a lot of computational resources, especially for aligning many long sequences, and it therefore requires efficient algorithms that utilize modern hardware when available. A subset of the secondary structures contains overlapping interactions , which add additional complexity to the problem and are often ignored in available software.We present the SeqAn-based software LaRA 2 that is significantly faster than comparable software for accurate pairwise and multiple alignments of structured RNA sequences. In contrast to other programs our approach can handle arbitrary pseudoknots. As an improved re-implementation of the LaRA tool for structural alignments, LaRA 2 uses multi-threading and vectorization for parallel execution and a new heuristic for computing a lower boundary of the solution. Our algorithmic improvements yield a program that is up to 130 times faster than the previous version.With LaRA 2 we provide a tool to analyse large sets of RNA secondary structures in relatively short time, based on structural alignment. The produced alignments can be used to derive structural motifs for the search in genomic databases. Non-coding RNAs (ncRNAs) are RNA molecules that do not translate into proteins, but instead have various functions, e.g. they participate in splicing or gene regulation. Analysing ncRNA molecules by comparison to functionally related RNA molecules requires more than sequence information, because their function is primarily determined by their structure, which is often better conserved than the primary sequence. Hence, sequence–structure alignment rewards the conservation of structural interactions of the ncRNA molecules, which is a key property for many applications, e.g. finding homologous structures of known ncRNA families , phylogeIt is now well-established that ncRNA molecules introduce an additional layer in genetic information processing. They play a significant, active role in cell and developmental biology and carry out many tasks that were previously attributed exclusively to proteins. However, only a small fraction of ncRNA families have been identified so far and many more can still be discovered . StructuOwing to the importance of ncRNA molecules, there has been a steady stream of developments for analysing the molecules computationally. Specific rules govern RNA structure formation, therefore structured RNAs provide clear patterns of selection with base pairing patterns directly reflecting structural conservation . In othen. The tool LocARNA [Considering structural information unfortunately adds complexity to the problem of aligning two or several sequences. The original algorithm for simultaneous alignment and folding by Sankoff  has the  LocARNA  reduces al {O}}n^$$\end{doldAlignM  and LaRAldAlignM .Fig. 1ThIt is estimated that about udoknots , which amentclass2pt{minimudoknots  that hasudoknots . In pseuudoknots . In factudoknots –26.A short run time in relation to the problem size is an important aspect. Given the current rapid increase of the size of data sets it is essential to have efficient implementations available that solve the structural alignment problem in reasonable time, while securing a sufficient quality of the results. Some programs already allow to distribute the work on several cores for parallel execution through multi-threading. We go a step further and combine multi-threading and vectorization with SIMD instructions: By storing the data of 4 or 8 alignments in vectors we compute a vector of alignments simultaneously on each core. For example, with 16 cores and vector length 8, we process 128 alignments simultaneously.Previous work has been done on the vectorization of the pairwise alignment computation using the wavefront approach , 28 and In 2007 and 2008 the tools LaRA and T-LaRA , 30 intrWe present an improved and parallelized version of the LaRA program for RNA sequence–structure alignment, which is up to n. The paper demonstrates besides RNAmountAlign also good performance for LocARNA [For a complete overview of all tools related to sequence–structure alignment we refer to the review paper by Lalwani et al. . A recen LocARNA . LocARNAl Pankov , which hThe general workflow for LaRA is as follows: For given entclass1pt{minimaKatoh and Toh  presenteThe following paragraphs introduce how LaRA solves pairwise sequence–structure alignments, however for the mathematical background we refer to the LaRA paper .Vertical alignment edges exist between each combination of a node from the first sequence and a node from the second sequence. For distinction, we use the term line for this type of edge. If a line l is active, i.e. the connected nodes are aligned, the flag Horizontal interaction edges represent structural alignment. Let l which is incident to the left interaction partners and line m which is incident to the right interaction partners. We draw two directed edges  and  between those two lines and assign weights l, m) is active and 0 otherwise.In order to represent a valid alignment, the graph needs to satisfy the following constraints:All active lines must be conflict-free, i.e. any two lines with Each line is incident to at most 1 interaction edge.An interaction edge can only be active if the line at its origin is active.l, m) the reverse edge must also be active: For any active interaction edge  of the sequences to be aligned by using the RNAfold tool , a widelrelaxed solution, because it may violate the last constraint. Its score valid solution, because the computed alignment is optimal with respect to fewer constraints.The problem can be solved by applying Lagrange relaxation on the last constraint: The maximum profit that a line can contribute is the weight of the maximum weighted outgoing edge plus the line weight itself, minus a penalty if the last constraint has been violated. The maximum score for each line is interpreted as a value in a position-specific score matrix, which is then used by a global alignment algorithm, e.g. Needleman and Wunsch . As a rel and m the equation valid structural alignment and its score If for all pairs of lines Overall, LaRA iteratively solves the relaxed problem, where the penalty for violating the constraint is incorporated in the scoring matrix. In each iteration after the alignment a new lower bound is computed by finding the best structural interactions of this alignment. The solutions get increasingly better through the iterations and the bounds entclass1pt{minimaThe following subsections describe algorithmic and implementation details of the LaRA 2 program and point out the differences from the old version.LaRA 2 consists of five main steps as can be seen in Fig. The second step computes and validates the alignment graph, which we introduced in the previous section, ensuring that the constraints are satisfied. The application of a sequence alignment algorithm ensures that aligned base pairs are mutually conflict-free: in Fig. Step three formalizes the constraints as an integer linear program (ILP) with an objective function designed to maximize the weighted sum of sequence and structure scores, as introduced in the previous section.In the fourth step we solve the ILP with Lagrangian Relaxation. The solution to the relaxed ILP can be computed via a sequence alignment with position-specific scores, and it serves as an upper boundary of the optimal solution. It is based on the Needleman-Wunsch algorithm in which we allow choosing among three different gap scoring models: Linear , DynamicStep five combines the pairwise alignments progressively according to the pairwise similarity. We use the multiple sequence alignment program T-Coffee or the MAFFT X-INS-i framework to combine all pairwise alignments into one multiple alignment.In the following subsections we describe deeply some of the most important optimizations implemented in LaRA 2 for improving both performances and quality of produced alignments.structure annotation. An RNA sequence is a string of n characters over the RNA alphabet n is given as an i and nucleotide j forming a pair in the secondary structure of the RNA molecule.LaRA 2 works on a set of at least two RNA sequences with RNAfold tool [If the structure information is not available, LaRA 2 can internally compute it with the old tool , which cThe first implementation of the LaRA algorithm  computesTo make the LaRA algorithm amenable for acceleration via vectorization, we changed the internal logic. In the LaRA algorithm each individual, pairwise sequence–structure alignment is solved using a Lagrange relaxation approach which in essence computes a series of interleaved standard sequence alignments with position dependent scores and a matching routine to adapt the Lagrange multipliers. In Algorithm 1 the code in line 3 shows the inner loop which computes per iteration one alignment followed by a general matching to update weights for the alignment in the next iteration. all pairwise sequence alignments followed by a parallelized version of the matchings. This can be seen in Algorithm 2. This parallelized computation of the first iteration step is then followed by the second iteration of sequence alignments and matchings. We measured that the sequence alignment step is about 200 times faster on a 16 core standard Xeon processor with 256 bit SIMD registers  position-specific score matrix A valid solution  of the original alignment problem is computed by applying a maximum weighted matching (MWM) algorithm on the interaction graph that is depicted in Fig. We have tested two different heuristics for MWM: The Blossom algorithm by Edmonds , which iThe main idea of the Blossom algorithm is to search for cycles consisting of an odd number of edges and contract each such cycle into a single node, which is called a blossom. The search is then continued in the reduced graph.k edges from the beginning of this list and perform an exhaustive search on the maximum weighting combination. The selected edges become part of the resulting matching and all incident edges are excluded from the list. We repeat this process with the next k heaviest edges from the list until the list is empty.In our greedy approach we generate a list of all edges sorted by their weight. Then we consider the heaviest We find that using the greedy approach with The score for the lower bound of the current LaRA 2 iteration is the sum of the weights of the edges that are part of the computed matching, plus the sequence alignment score. The highest score over all iterations together with the corresponding alignment is reported as the valid solution of the pairwise sequence–structure alignment problem.LaRA 2 can produce two different output formats, which can be selected with a parameter: MSA library for T-Coffee  and pairThe MSA library is a data structure that stores the base pairings with their individual scores for each of the T-Coffee  algorithThe pairwise alignment output is designed to be parsed by the MAFFT framework and contains three lines per pairwise alignment: The first line is a header line similar to the FastA format containing both sequence identifiers, and the other two lines consist of the first and the second aligned sequence. The aligned sequences possibly contain gap symbols and have equal length. Through the four-way-consistency score in MAFFT it incorporates the structural information not only through the (here unweighted) base pairs in the pairwise alignments but additionally from the initial base pair probabilities resulting from the McCaskill algorithm.In case We implemented the algorithm for pairwise structural alignments in a new C++ program with the name LaRA 2, which computes structural alignments with pseudoknots in high quality. It is capable of processing large data sets because of its enormous speed-up thanks to its implementation optimized for multi-threading and vectorization. The name reflects that the underlying model is the one of LaRA  that hashttps://seqan.github.io/lara/ provides assistance for using LaRA 2 with T-Coffee or MAFFT for multiple structural alignments and demonstrates the supported input and output formats.Alongside the program we develop an interactive iPython manual that serves as a template for getting started and provides practical use cases. Furthermore, the manual on ® Xeon® CPU E5-2650 v3 with 2.30 GHz and 126 GB RAM. We compiled with GCC version 9 and where applicable, we used up to 16 threads and AVX2 instructions. For the benchmarks we have used the program versions and parameters displayed in Table In order to demonstrate the performance of LaRA 2 compared to relevant existing software, we evaluate three different benchmarks with focus on multiple alignment with conserved structure, run time on a large data set, and the detection of pseudoknots. All benchmarks have been performed on a Linux server using an x86_64 architecture with IntelIn this benchmark we show the performance across several RNA families dependent on the sequence similarity. We took the BRAliBase 2.1 data set, which consists of 388 reference alignments of 5 sequences each. For RNAmountAlign we excluded 46 sequences that contain the character ‘N’, because the program does not accept wildcard symbols.In order to evaluate the resulting multiple structural alignments we use two metrics: SPS and MCC. The sum-of-pairs (SPS) score is a measure of similarity between the test alignment and the curated reference alignment that is available in the Rfam database . Values RNAalifold from the ViennaRNA package [PETfold [i in the test alignment and i in the reference. Based on these sets we define the confusion matrix and calculate the MCC. Note that the true negative (tn) value contains the number of all possible base pairs that are contained in neither the test nor the reference set.In order to compute the MCC Eq. , we foll package . We have[PETfold  as well,[PETfold . In the RAliBase , we diviThe results demonstrate that LaRA 2 performs as good as LocARNA and LaRA 1, and better than RNAmountAlign and MAFFT. In the alignments with more than Another question that has concerned us is the performance drop of all programs around the s et al.  have poiFor the structure evaluation with Matthews correlation coefficient we find again that LaRA 2 has the same performance as LocARNA and LaRA 1, while outperforming RNAmountAlign and MAFFT. An interesting observation is the decline of the reference curve for high sequence similarity, which is mainly represented by alignments of the tRNA family. For the reference curve we computed the optimal structures of the BRAliBase reference alignments with RNAalifold  , which is impressive in the light of its non-parallel execution, but shadowed by its performance in the benchmark. LaRA 2 with MAFFT runs in less than 13 min, LocARNA takes almost 35 min and the single-threaded LaRA requires more than 1 h to compute the test alignments. MAFFT is the fastest among all tested tools, however this is expected because sequence alignment is a less complex problem. As there are only five sequences aligned at a time, parallel execution has just a minor effect compared to the benchmark in the following subsection.In addition, we examined the time and memory consumption of LaRA 2 with respect to the average sequence length. As the BRAliBase data set contains rather short sequences (up to 300 bases) we extended the set with two additional RNA families from the RNAStrAlign database : TelomerIn order to demonstrate the ability of LaRA 2 to process large data sets in reasonable time, we use the plastids data set from the 5SrRNAdb  databaseThe speed-up of LaRA 2 with MAFFT using 16 threads is about 9 which is much better than the other tools. With T-Coffee it reduces to a factor of 3 due to the non-parallel implementation of T-Coffee. Still this is the same speed-up as LocARNA. Taking a look at the peak memory allocation in Table In addition, we use the Plasmids data set to demonstrate the scaling of the run time of pairwise structural alignments with LaRA 2 in the light of SIMD instruction sets and multi-threading. Figure RNAfold, which takes constantly 25 seconds. An additional effect has a larger memory allocation, e.g. for AVX2 instructions and 16 threads the program needs to allocate 128 alignments.The effect of SIMD instructions is a speed-up of Although it is estimated that eudoknot  the mostWe show with SPS values of some pseudoknotted RNAs from Rfam and in a graphical example that LaRA 2 actually detects pseudoknots. SPS scores express the similarity to the reference alignment and therefore a high score indicates that the pseudoknot is aligned properly, however a low score can result from a different location and is not sufficient to prove the absence of the pseudoknot in the test alignment.The scores in Table We have chosen a structure for the graphical example where the pseudoknot interactions are biologically essential: Athanasopoulos et al.  describeWe computed the structural multiple alignment from the seed sequences with all the tools. Based on these alignments we ran IPknot  Any restrictions to use by non-academics: None