This mosquito cannot breed in Wales, or anywhere else in the UK, because the winters are too cold, so it is not possible for the virus to become established.The first comprehensive definition and detailed discussion of herd immunity appeared in 1929 in the first edition of the classic text, Topley and Wilson’s ‘The Principles of Bacteriology and Immunity’ [Homo sapiens. Presciently, he also discussed the subherd of antivaccinationists. “They form a very difficult administrative problem. They are perfectly honest in their convictions, but their power of dissociation and rationalization is so great that they often seem to the saner members of the herd to be absolutely unscrupulous and dishonest, whereas really they are only completely inaccessible to logic… making the most absurd accusations against those who dare to differ from them.”As soon as it was coined, the use of the term ‘herd’ to designate human communities was criticized. Dudley  mounted 0 to <1, so that the virus will not be able to maintain itself and continue to spread, a situation which should eventually result in its elimination. The calculation underpinning this view is [Considerations this year about COVID-19 control have in general used the term ‘herd immunity’ with a much narrower meaning than Topley’s and Wilson’s. They carry the implication of a level of specific immunity against the virus that will reduce the effective reproductive rate R view is :(Eq. 1)pc is the proportion of the population that is immune, either as a consequence of an infection or by immunization with a vaccine or both [You will want to protect those at risk groups so that they basically do not catch the disease and by the time that they come out of their cocooning, herd immunity has been achieved in the rest of the population.” This strategy has been endorsed by the Great Barrington Declaration signed on 4 October 2020 by some infectious disease epidemiologists and public health scientists [We know that all populations will eventually reach herd immunity, in other words, the point at which the rate of new infections is stable and that this can be assisted by (but is not dependent upon) a vaccine. Our goal should, therefore, be to minimize mortality and social harm until we reach herd immunity. The most compassionate approach that balances the risks and benefits of reaching herd immunity, is to allow those who are at minimal risk of death to live their lives normally to build up immunity to the virus through natural infection, while better protecting those who are at highest risk.” Other scientists and healthcare professionals disagree profoundly with this strategy. Their views have been outlined in the John Snow Memorandum, first published on 14 October 2020 [The arrival of a second wave and the realization of the challenges ahead has led to renewed interest in a so-called herd immunity approach, which suggests allowing a large uncontrolled outbreak in the low-risk population, while protecting the vulnerable. Proponents suggest this would lead to the development of infection-acquired population immunity in the low-risk population, which will eventually protect the vulnerable. This is a dangerous fallacy unsupported by scientific evidence…uncontrolled transmission in younger people risks significant morbidity and mortality across the whole population, furthermore, there is no evidence for lasting protective immunity to SARS-CoV-2 following natural infection.”In which p or both . It is rientists : “We knober 2020 : “The arA wide range of estimates of the herd immunity threshold for COVID-19 have been published. Formula (1) above assumes that everyone in the population is equally likely to become infected. However, there is abundant evidence that this is not the case. Social activity levels and age-related effects mean that the population is heterogeneous regarding the likelihood of becoming infected. Together with the large number of asymptomatic cases, these things make estimating the threshold a difficult task at this time ,8.Too many of the putative facts known to public health planners rest on enthusiastic retelling of plausible tales, rather than on controlled experiments or careful analysis of data.” On the basis of estimated values of its effective reproductive rate they calculated the degree of herd immunity required for smallpox eradication(pc) to be 70–80%. Before 1967, the WHO smallpox eradication programe was defined in terms of the number of vaccinations performed: “It has been demonstrated that eradication of smallpox from an endemic area can be accomplished by vaccinating 80% of a population within a period of 4–5 years.” However, it was found that outbreaks still occurred in districts where the 80% goal had been reached; in 1973 the goal had been achieved in India, but in that year it had 88,114 cases. Continued virus transmission in mass vaccinated communities was strongly associated with high population densities [It is often claimed that the eradication of smallpox testifies to the success of a herd immunity policy. It does not. The comment of Anderson and May  in this would involve an interference with the course of trade at variance with our national habits; and it would demand sacrifices from large numbers of people, who are removed from the presence of the disease.” Legislation giving effect to control measures was hurried through the House of Commons in a manner that was described as savoring of despotism [To date, rinderpest is the only infectious disease that has been eradicated by engendering herd immunity sufficient to lead to its extinction in the wild. Related to measles, it causes a disease in cattle and buffalo often with high morbidity and mortality. Historically, attempts to control it in Britain have an uncanny similarity to current events. Imported from Europe in 1865, it killed at least 420,000 cows . Expertsespotism .The UN Food and Agriculture Organization and the World Organization for Animal Health declared the global eradication of rinderpest in 2011. Absolutely central to this success was TRCV, the tissue culture rinderpest vaccine, which protected against all rinderpest variants, provided life-long immunity, was never associated with any adverse reactions, gave immunity after a single dose and in its ThermoVax form was thermostable, with a shelf life of 30 days outside the cold-chain, holding a maximum titre for 14 days at 45°C .o of between 2.5 and 3.5, the level of herd immunity needed to block virus transmission is about 60–72% [It is too early to tell whether any of the COVID-19 vaccines under development will possess all or even just some, of these properties. To block the transmission of SARS-CoV-2 by creating the necessary levels of herd immunity, much depends on vaccine efficacy and the duration of vaccine protection. For a vaccine with 100% efficacy that gives life-long protection, and taking into account prelockdown values of Rt 60–72% . Less efHowever effective COVID-19 vaccines turn out to be, it is likely in most countries that the first batches will be mainly used to protect groups of individuals with the highest case fatality rates, in other words, those older than 70 years. It seems likely that herd immunity strategies will have to wait, giving time, perhaps, to counter the influence of the antivax sub herd and to address the issues that cause vaccine hesitancy.


The assessment of CASP models for utility in molecular replacement is a measure of their use in a valuable real‐world application. In CASP7, the metric for molecular replacement assessment involved full likelihood‐based molecular replacement searches; however, this restricted the assessable targets to crystal structures with only one copy of the target in the asymmetric unit, and to those where the search found the correct pose. In CASP10, full molecular replacement searches were replaced by likelihood‐based rigid‐body refinement of models superimposed on the target using the LGA algorithm, with the metric being the refined log‐likelihood‐gain (LLG) score. This enabled multi‐copy targets and very poor models to be evaluated, but a significant further issue remained: the requirement of diffraction data for assessment. We introduce here the relative‐expected‐LLG (reLLG), which is independent of diffraction data. This reLLG is also independent of any crystal form, and can be calculated regardless of the source of the target, be it X‐ray, NMR or cryo‐EM. We calibrate the reLLG against the LLG for targets in CASP14, showing that it is a robust measure of both model and group ranking. Like the LLG, the reLLG shows that accurate coordinate error estimates add substantial value to predicted models. We find that refinement by CASP groups can often convert an inadequate initial model into a successful MR search model. Consistent with findings from others, we show that the AlphaFold2 models are sufficiently good, and reliably so, to surpass other current model generation strategies for attempting molecular replacement phasing. It is also clear that protein structure prediction will accelerate the experimental determination of 3D structures, by improving the models for molecular replacement (MR).MR is the most commonly used method to determine the unmeasured phases needed to compute an electron density map from a diffraction pattern. This is carried out, typically, by determining the orientation angles and translation vector (together referred to as the “pose”) required to superimpose the model generated by prediction with the coordinates of the atoms in the crystal. Models generated by structure prediction supplement the models that can be derived from previously determined structures of homologues in the worldwide Protein Data Bank (wwPDB),As recently as 20 years ago, it would have been fair to say that even template‐based protein models were rarely more useful for MR than the templates on which they were based, because it was too difficult to distinguish the few ways in which they could be improved from the vast number of ways in which they could be degraded. Since then, modeling methods have turned a corner and are becoming progressively more useful. A test for utility in MR was introduced for CASP7,When model accuracy was low, a useful score could only be generated if the model was sufficiently good to identify the correct pose in the full search. This problem was circumvented later by the use of rigid‐body refinement starting from a structural superposition instead of the full MR search, judging the models by the log‐likelihood‐gain (LLG) score of the refined model instead of by whether or not the model could be placed. This also had the benefit of dramatically reducing the CPU time required to explore many incorrect solutions with poor models that lack useful signal, and ensuring that the LLG scores corresponded with models in the correct pose. Although the success‐or‐failure aspect of the MR searches was lost, the LLG scores could still be interpreted in the knowledge that MR searches yielding LLG values above 60 are usually correct.A second problem arose in MR scoring when there are multiple copies in the asymmetric unit, or more than one type of component. With the full MR approach, the MR scoring was restricted to those cases for which there was a single copy of a single protein component in the asymmetric unit of the crystal. However, the rigid body refinement approach allowed these more complicated targets to be scored by placing all copies of the tested model within a background that includes the deposited structure for all other components of the crystal; the increase in the LLG obtained when adding the tested model to the background structure alone was the measure of model quality.Phaser script to carry out rigid‐body refinement calculations, written by Gábor Bunkóczi, was used by other assessors in the refinement category of CASP10,A Problems remain with the rigid‐body refinement approach, not least the fact that it requires diffraction data to be made available to assessors; not all crystallographers contributing targets are able to share these data in advance of publication. A substantial number of targets and domain evaluation units (EUs) derived from them now arise from cryo‐EM structure determinations  that requires only the coordinates of the target to rank the suitability of a model for MR. Most significantly, it is a crystal‐form independent measure. We test the reLLG against the LLG score as a ranking measure and demonstrate its utility as a more convenient and robust measure, which should supersede the use of the LLG for this purpose. We find that the ability of refinement groups to improve reLLG values correlates well with their ability to improve the performance of refinement targets in actual MR experiments. Finally, our results provide another metric by which the superiority of the AlphaFold222.1In CASP, structures contributed for the prediction season are examined and divided into smaller pieces  that usually have a relatively compact structure. These are referred to as “evaluation units” or EUs. For CASP14, a total of 96 EUs were selected for evaluation of structure prediction. Prior to the CASP14 meeting, diffraction data were made available by the experimentalists who contributed 32 crystal structures, from which 54 EUs were drawn. These EUs were therefore able to be included in the MR assessment, which used the previously described diffraction data‐dependent LLG score. Diffraction data were not available at the time of assessment for the remaining 17 EUs drawn from other crystal structures, nor of course for the EUs drawn from cryo‐EM or NMR structures.In the refinement round, a total of 49 prediction targets were selected. These included seven “extended” targets and seven “double‐barrelled” targets used to conduct additional experiments in CASP14. For the extended targets, refined models were collected after the initial 3‐week period and again after an additional 6 weeks, during which more extensive computations may have been performed (denoted with an “x” in the target name). For the double‐barrelled targets, two starting models were chosen for refinement, one typically chosen from the server models and the other from models submitted by the AlphaFold2 group . Thirty‐four of the 49 total targets were derived from structures determined by X‐ray crystallography, of which 20 had diffraction data available at the time of assessment and could therefore be used for LLG calculations.2.2For the double‐barrelled refinement targets, one group recognized correctly that one of the two starting models  was superior to the other, and they submitted the better model as a refinement model for the poorer one. While the ability to recognize good models is laudable, it does not reveal anything about the ability of the group to carry out refinement, so the Alphafold2 models provided by this group were excluded from consideration. All other models for both structure prediction and refinement were evaluated.2.32.3.1Phaser, using the rest of the final crystal structure as a fixed background for the calculation. The initial superposition of the evaluation unit on the target was carried out using the sequence‐independent structure alignment program TM‐align.As in the case of CASP13, the LLG for each model of each EU was computed by rigid‐body refinement in y axis taken as the null‐model‐LLG. All models with an LLG below the corresponding null‐model‐LLG were assigned a score of zero. This can happen if the entries in the B‐factor field for a model are all too large to correspond to sensible root‐mean‐square displacement (RMSD) estimates and effectively downweight the contributions of the atoms to zero. The likelihood calculations can also fail for computational reasons, such as if the model represents an unfolded protein and extends over such a large volume that memory limits are exceeded in the FFT calculations of structure factors. Models leading to such failures are also assigned a score of zero.To calculate the EU‐specific null‐model‐LLG, for each EU, the models were binned into 100 equally spaced GDT_HA bins and the average LLG value for each bin taken. This average was computed iteratively, removing at each iteration those data points with an LLG 1σ below the average until no more data points were excluded. Out of these bins, the first 35% (bottom 35% GDT_HA) were considered further, and the average of their average LLG taken. Those bins with an average LLG within 3σ the average over all bottom 35% were sorted by their average LLG and the middle 80% taken. A linear model was fitted to the averages of these bins and the intersection in the We refer to the difference LLG score as the dLLG for short.2.3.2As discussed above, there are substantial advantages to a likelihood score that measures suitability for MR independent of crystal form or structure determination method.σA value used in crystallographic likelihood targets, such as the log‐likelihood gain on intensities (LLGI) used for MR.σA and the score expected to be obtained in likelihood‐based MR. The expected log‐likelihood‐gain (eLLG) can be approximatedσA4/2, allowing valuable optimizations of the MR strategy depending on the qualities of the model and the data.By the correlation theorem of Fourier transforms, the correlation between electron densities is proportional to the complex correlation between structure factors calculated from those electron densities. In turn, the complex correlation in a resolution shell is equivalent to the resolution‐dependent phasertng, which is under development to replace and enhance the functionality of Phaser.E values for which the mean‐squared value is one. In this case, the off‐diagonal complex covariance term of the covariance matrix becomes the complex correlation, σA:σA is a real number because, if a systematic phase shift were known between the two structures, that would imply the existence of a known relative translation vector, which could be corrected instead.Superposition of model and target with an algorithm such as that in the LGA programσA is zero, that is, when the model is uncorrelated to the target and is thus uninformative. The contribution of a single Fourier term to the total LLG is given in the following:σA for each structure factor pair. The orientation is defined in terms of three rotation angles specifying rotations of the pre‐oriented model around axes parallel to x, y and z running through the center of the model. Because the perturbations of the initial orientation will be small, these rotations will be nearly orthogonal and will therefore behave well in the optimization. The position is defined in terms of translations along the x, y, and z axes, which are orthogonal and are essentially independent of the rotations applied around the center of the model. The σA values are a function of the resolution of the relevant structure factors and are defined in terms of the radial RMSD for coordinate errors drawn from a single 3D Gaussian. The value of σA is given, as a function of resolution, by the Fourier transform of that Gaussian:fp is the fraction of the target explained by the model, assumed to be one for the calculations reported here, rmsd is the refined parameter and s is the magnitude of the diffraction vector (the inverse of the resolution).The likelihood target is the conditional probability of the target structure factors given the known model structure factors. This is derived from the joint distribution by standard manipulations to obtain the conditional variance of the target E‐value given the model and its expected value:EtEmcosΔϕ is equivalent, by the correlation theorem, to the contribution of a Fourier term to the density correlation. The variance term in the phased log‐likelihood‐gain is controlled by the rmsd parameter, which will be optimal when the σA values computed as a function of resolution from that rmsd match the mean values of EtEmcosΔϕ in resolution shells.The refinement against the phased log‐likelihood‐gain can be seen to optimize the electron density overlap: FSC4/2, weighted by the number of Fourier terms in each shell. This eLLG varies with the number of Fourier terms, determined by crystal lattice volume (size of the target), so normalization to a relative eLLG (reLLG) is required to put the scores on a common scale for all target‐model pairs. The normalization cannot be carried out simply by comparing the eLLG to what one would expect for a perfect model, because the conditional probability for a perfect model with perfect data is a delta function, which would yield an infinite LLG. We resolve this problem by introducing an “ideally imperfect model”, that is, the best model one could reasonably expect to get from a high‐resolution structure determination of the same protein in a different crystal form, given the inevitable errors in any experimental structure and the differing influence of crystal packing and other environmental effects. By comparing structures of the same protein in different crystal formsrmsd of about 0.4 Å. The reLLG is therefore computed by dividing the eLLG for the model being tested by the eLLG that would be obtained for σA values computed for a complete model with rmsd set to 0.4 Å.Once an optimal superposition is obtained, structure factors from the target and the superimposed model are compared in resolution shells to obtain an FSC curve. The eLLG is then calculated by accumulating the sum of The reLLG calculation also requires making a choice for the high resolution limit. A calculation carried out to a higher resolution limit would be more sensitive to model errors, whereas the use of lower resolution would be more forgiving. In principle, one could define scores based on different resolution limits, analogous to the way that the GDT_TS score is more forgiving than the GDT_HA score.σA curve defined by the refined rmsd parameter, and this could even be done analytically. The advantage of using the actual FSC curve from the comparison of structure factors is that no assumptions are made about the distribution of coordinate errors in the model. The use of a single rmsd requires that all the coordinate errors are drawn from the same 3D Gaussian distribution, whereas models have locally varying errors. It is further assumed that the coordinate errors and the atomic scattering factors are uncorrelated, whereas atoms on the surface of a protein both tend to have higher B‐factors and are modeled less accurately.We note that it would be possible to compute an eLLG from the 2.3.3For a number of years, predictors submitting models for CASP have been asked to provide estimated RMS positional errors in the B‐factor field of the PDB files containing the models, on the principle that knowing how confident you should be in a model is as useful, in practice, as the model itself. By CASP13, most predictors in the template‐based modeling category included error estimatesSuch error estimates are extremely valuable for MR models. If the B‐factors of the models are increased by an amount that effectively smears each atom's density over its probability distribution of true positions using the following equation, the electron density overlap, and therefore the LLG score, is optimized.To measure the utility of the error predictions numerically, each model was evaluated two times. In the primary calculation, the number in the B‐factor field of the model was transformed using the equation above from a coordinate error estimate into a B‐factor providing an error weight; in the secondary calculation the B‐factor was substituted with a constant value set to 25 Å.2.4For all the evaluation measures, Z‐scores were computed using an algorithm that has frequently been applied in other rounds of CASP. The primary ranking was based on model #1 of up to five models submitted for each target; this choice implicitly rewards the ability of groups to assess the relative quality of their models. Z‐scores were computed in two steps: a set of initial scores was calculated based on the mean and standard deviation (SD) of all models under consideration. All models yielding a Z‐score below −2 in the first pass were considered as outliers and the Z‐scores recomputed using the mean and SD obtained when the outliers were excluded. At the end, the minimum Z‐score was set to −2 to avoid excessively penalizing outliers. For ranking, all Z‐scores were summed and a penalty of −2 introduced per target for which a method did not produce a model, effectively treating missing models as outliers.For rankings based on either the conventional LLG or the new reLLG score, the primary ranking was based on interpreting the B‐factor field as an estimate of the RMS error in that atomic position, as requested in the submission instructions provided by the CASP organizers. The difference between this LLG or reLLG for error‐weighted models and the value computed setting all B‐factors to a constant value was used to measure the value added by the coordinate error estimate.2.5https://github.com/clacri/CASP14_MR_evaluation. The Jupyter notebooks have been prepared to be run in the cloud environment of Google Collaboratory,The tables with the reLLG calculations as well as the Jupyter notebooksphaser_voyager (manuscript in preparation), a structural biology computing framework that exploits phasertngphaser_voyager strategy “CASP_rel_eLLG” is distributed in recent builds of PhenixComputation of the reLLG was implemented in 33.1The statistical analysis and ranking calculations were carried out as described in Materials and Methods. Briefly, the primary ranking was based on the sum of the Z‐scores for the #1 predictions when the B‐factor field was interpreted as an error estimate, and including the penalty of assigning a Z‐score of −2 for missing models.3.1.1Conventional dLLG scores were calculated for 54 evaluation units that correspond to the 32 targets for which the experimental diffraction data were available to us at the time of assessment. We calculated the scores with and without using the error estimates that were intended to be encoded in the B‐factor field, thus assessing the impact of the error estimates. The resulting rankings are shown in Figure 3.1.2One hundred and forty‐six groups presented models for at least some of the 96 EUs. While calculation of the dLLG score requires diffraction data (limited at the time of assessment to 54 EUs), the calculation of the reLLG does not, and so allows all 96 EUs to be included in the statistics. This includes 71 EUs derived from structures determined by X‐ray crystallography, 22 from cryo‐EM structures and three from NMR structures.In order to compare and assess the novel reLLG score against the traditional CASP dLLG score, we addressed three questions. First, do the dLLG and reLLG yield similar rankings of models for a specific target? Second, do the dLLG and reLLG yield similar group rankings? Third, do the reLLG calculations obtained from cryo‐EM or NMR experiments also yield correlated group rankings?Phaser calculations with some models. To avoid these complications, we chose to compare the reLLG and dLLG values obtained when setting the B‐factors constant. Figure We compared reLLG scores with dLLG scores for the targets for which diffraction data were available at the time of assessment. We do not expect these measures to be linearly related to each other, because the dLLG score is affected non‐linearly by factors such as model quality (which has different effects for different resolution limits) or the fraction of the asymmetric unit of the crystal accounted for by the model. Because the reLLG calculation has been designed to cope better with numerical issues caused by the large estimated RMS errors found in some CASP models, comparisons of the scores obtained interpreting the B‐factor field as an estimated error can be complicated by the relative instability of the Next, we examined whether the group ranking on the subset of targets for which diffraction data were available was similar. Figure To verify that there are no systematic differences in how reLLG would score models of structures determined by other methods, we compared the group ranking scores that would have been achieved using only cryo‐EM targets or NMR targets with those achieved using X‐ray targets. The scatter plots in Figure Given that rankings on common targets are very similar using either dLLG or reLLG, that reLLG rankings on sets of targets derived by different methods  are similar, and that the use of the reLLG allows the use of a much larger data set (96 EUs rather than 54), we expect the ranking based on reLLG to be closer to what would be achieved for dLLG if diffraction data were available for all 96 EUs than the dLLG ranking based on only 54 EUs. The ranking based on reLLG is more robust, and we take it as the authoritative ranking for this study.The ranking for all targets by reLLG Z‐score Figure  is againWe note that the top three groups are the same in this ranking as in the rankings using just targets for which diffraction data are available, but there are substantial differences in other methods near the top. Based on the comparisons discussed above, we believe that these differences reflect sampling error rather than a systematic difference between targets with and without diffraction data. Such sampling error should be reduced for the larger set of targets, further supporting the decision to use the reLLG Z‐score as the primary ranking measure in this study.3.1.3CASP participants are asked to contribute error estimates for their predicted models in the B‐factor field of submitted PDB files. While the group ranking analysis in this study has been done using the information from those estimates, we also computed the reLLG scores substituting those estimates by a constant value. We then computed the difference between the sum of the reLLG scores for each group, either using or not using the error estimates. As can be observed in Figure 3.1.4The ability of the groups to identify their best models and rank them is an important aspect for prospective users, as many users will focus on the top model. Arguably, this is somewhat less important for MR models, as it is reasonably common  to test a number of alternative models. One metric that can be used to score the accuracy of self‐ranking is a rank correlation. We chose instead to use the fraction of the time that the #1 model is also the best of the five models submitted, because it is easy to understand and corresponds to one of the possible MR scenarios where only the best model is tested.A scatter plot comparing the percentage of #1 models ranked correctly with the reLLG ranking score Figure  shows th3.23.2.1In this category, 36 groups contributed to 44 targets. Group rankings were computed in the same way as for the prediction round. To assess whether starting models were generally improved or degraded by refinement, we included in the ranking calculations a “naïve predictor”, who returns the starting model unchanged. One complication in scoring the naïve predictor was that the B‐factor field of the PDB files containing the starting models did not typically contain estimated RMS coordinate errors; for consistency we evaluated the starting models by computing the reLLG score with all B‐factors set to a constant. For this reason, even if a refinement group had left the coordinates unchanged but provided useful error estimates, they would have surpassed the naïve predictor.Figure 3.2.2The effect of including the coordinate error estimates in the reLLG scoring was evaluated as for the prediction category. Figure 3.2.3There is a weak positive correlation (correlation coefficient of 0.31) between the ranking scores for different groups and their ability to correctly rank their best model as #1 Figures . One wou3.2.4We performed MR using search models generated in the refinement category for those cases where diffraction data were made available. There were 13 targets that fulfilled this requirement. Four of these included extended submissions benefitting from 6 weeks of refinement in addition to the standard 3‐week refinement submissions . Further to this, T1053, T1067, and T1074 were double‐barrelled cases with refinement performed on two initial starting models. In each of these cases one of the starting models was an AlphaFold2 prediction. This gave a total of 20 sets of refined models to be tested in MR. Refined models from 36 different groups were included with each group producing up to five models per target. Starting models were also used in MR for comparison. The full set of target details is provided in Table PhaserPhaser requires an estimate of the effective RMS coordinate error for the search model, which we set to 1.2 Å for all search models. For all of the refined models used, the B‐factor field of the coordinate file was interpreted as an estimated RMS error, as discussed in Materials and Methods. To test if the solution in each trial was correct, we used phenix.famos from PhenixThe MrBUMP automated pipelineFigure An example of a successful refinement by the FEIG‐S group of a starting model unsuitable as a search model in MR, for the target T1090, is shown in Figure For two of the four targets subjected to the extra 3 weeks of refinement time, groups MUFOLD, Jones‐UCL, GLoSA, FOLDYNE, and UNRES‐template were able to exploit the extra time to improve some of their models sufficiently to be suitable as search models for MR. Other groups including BAKER and FEIG were able to increase their success rate with the extra time. However, the overall results were mixed. For three of the four targets, the total number of models succeeding in MR declined following the extra refinement Table . Only inThere were only four refinement targets for which none of the starting models or refined models succeeded in these MR tests: R1052‐D2, R1053v1, R1082, and R1091‐D2. However, in each of these cases either the Ample MR pipeline3.3As seen with many other CASP metrics, the quality of the AlphaFold2 models for MR represents a step change in what can be achieved. It is difficult to attach a numerical value to quantify progress in MR, but there is strong qualitative evidence. In previous rounds of CASP, the quality of models for MR was only measured for the easy and hard subsets of template‐based‐modeling (TBM), but not for the most difficult free‐modeling (FM) and borderline FM/TBM categories, because almost none of the FM and FM/TBM models were judged to bear sufficient resemblance to the targets to make that a meaningful exercise. In addition, this is the first occasion in which targets contributed to CASP were actually solved using submitted models.Target difficulty in CASP has traditionally been measured using the mean of target rankings by sequence coverage and sequence identity to the closest homologue of known structure.The relatively poor correlation between the traditional difficulty score and performance suggests that improved difficulty measures are required for the newer prediction methods, which depend more on multiple sequence alignments but less on identifying and improving the best template or templates. In addition to the increased difficulty of predicting structures of proteins in multimers or domains in multi‐domain proteins, Kinch et al.Methods of similar power to AlphaFold2, when they become readily available to the structural biology community, can be expected to play an increasing role in structure determination. We note that the development of the RoseTTAFold algorithm, inspired in part by features of AlphaFold2, has already enabled the determination of several structures that evaded previous efforts.4Crystallographers have a great deal of experience carrying out MR with models derived from homologues with different levels of sequence identity. Although success in MR involves a combination of factors , a commonly used rule of thumb is that MR is likely to succeed if there is a homologue with at least 30% sequence identity (for 100% sequence coverage). It is useful to also relate the reLLG directly to solvability.Phaser, which is an important parameter in LLG calculations in the MR search. The VRMS can be estimated from sequence identity, taking into account perturbations introduced by molecule size.Sequence identity correlates with solvability because there is a relationship between sequence identity and the effective RMS error, termed the VRMS in In this study, we have not validated whether or not a reLLG over 0.1 is sufficient to solve the structures for which diffraction data are available. However, MR trials have been carried out as part of the high‐accuracy assessment,4.1The CASP refinement category was instigated to encourage the development  of expensive computational methods, ones for which most groups do not have the resources to apply to the large number of targets in the prediction round. However, there has been a trend for methods pioneered by refinement groups to be incorporated into the initial models in subsequent CASP rounds, raising the bar for current refinement groups. In this category, a number of server‐generated models are traditionally provided for further improvement. In CASP14, this pool of models was supplemented with seven (non‐server) AlphaFold2 models. Although the best refinement groups were consistently able to improve the server‐generated refinement targets, most refinement methods degrade the AlphaFold2 models, as seen here for MR as well as for other CASP assessment measures.In conclusion, we have shown that the reLLG is a useful addition to the assessment metrics for CASP and should replace the metrics based on dLLG used in previous rounds. Although developed in the context of MR, it can be evaluated for models of structures determined by NMR, cryo‐EM or with other structural restraints. It has a broad advantage over other metrics by combining assessment of coordinate accuracy with the assessment of the accuracy of the estimates of RMSD in coordinates. To further improve the reLLG of predicted models (and thus their utility in MR), groups should target estimates of individual atomic accuracy rather than grouped residue accuracy. It should also be understood by predictors that optimization of the reLLG ideally requires optimization as well of the predicted atomic B‐factors. To optimize the reLLG for a nearly perfect model, the B‐factor field of the PDB file should be equal to the B‐factor in the target structure, whereas for a model with errors the optimal B‐factor should add to that the B‐factor equivalent of the predicted RMSD. Optimizing reLLG in the current format, where there is one B‐factor field in the submitted PDB file, would actually require submitting “error” values that, when translated into B‐factors, produce the sum of the actual B‐factor of the atom and the B‐factor corresponding to the coordinate error. Since this would conflate more than one phenomenon in one number, CASP should facilitate the submission of separate B‐factor and error estimates, by replacing the current PDB submission format with the flexible and extensible mmCIF format.The authors declare no conflict of interest.https://publons.com/publon/10.1002/prot.26214.The peer review history for this article is available at APPENDIX S1: Supporting informationClick here for additional data file.


Based on the literature research, it was found that the design was the smallest among the same type of implanted antenna. The antenna is optimized and loaded with a defective slotted structure, which improves the efficiency of the overall performance of the antenna and thus the gain thereof. The antenna maintains good impedance matching in the ISM frequency band, covering the entire ISM frequency band. The actual bandwidth of the antenna is 22%, with the peak gain of − 24.9 dBi. The antenna is processed and manufactured in such a manner that the simulation keeps consistent with the actual measurement. In addition, the specific absorption rate of the antenna is also evaluated and analyzed. The result shows that this kind of antenna is the best choice to realize the wireless biological telemetry communication in the extremely compact space of the wireless cardiac pacemaker system.A tiny and compact implantable antenna for wireless cardiac pacemaker systems is designed. The antenna works in the Industrial Scientific Medical (ISM) frequency band (2.4–2.48 GHz). The size of the antenna is greatly reduced with the adoption of a high dielectric constant medium and a folded meander structure. The volume of the antenna is 4.5 mm The pacemaker system realizes the function of wireless communication, which could improve the comfort of the patient and power supply safety of the device.The rapid development of electronic technology has promoted the birth of a new generation of pacemakers and embedded cardioverter defibrillators. As a communication carrier for wireless electronic medical equipment, antennas are playing an increasingly important role. At present, nearly 3 million people in the world are using pacemakers2. Therefore, the design and research of implantable antennas used in wireless cardiac pacemaker systems is still an important research topic.As shown in Fig. With the dedicated frequency resources for medical electronics and radio information transmission allocated bythe International Telecommunication Union (ITU), the radio transmission of medical implants is granted with a reliable spectrum resource. There are mainly three frequently used operating frequency bands for implantable antennas, namely the medical implantable communication service frequency band , the wireless medical telemetry service frequency band , and the industrial, scientific, and medical frequency bands . In addition, some foreign regions have also authorized ultra-wideband frequency bands for high-quality transmission .3. designed an implantable antenna that serves the MICS frequency band for cardiac pacemakers. The antenna adopts a conformal meander structure with a radius of 4.73 mm and a length of 20.5 mm. The antenna works in the MICS frequency band with a gain of − 32 dBi. In4, an implantable conformal antenna loaded with an open loop resonator (CSRR) was designed for use in a leadless pacing system. The design has a compact design and works at 2.45 GHz. The antenna has a peak gain of − 35 dBi, but it is too large in size. Literature5 designed a miniaturized broadband implantable antenna, which realized the miniaturization of the antenna by opening several different slots on the radiation patch and introducing short-circuit pins. In6, a coplanar waveguide fed (CPW) patch implanted antenna with a size of 24 × 22 × 0.07 mm3 was designed. The antenna gain designed in this research was − 19.7 dBi, with a bandwidth of 24%. Although it had a wider bandwidth and greater gain, it was at the expense of the size7. introduced a broadband implantable antenna suitable for implantable medical devices. The antenna adopteda symmetrical geometric structure as the radiation patch, which has good radiation performance. In8, the author realized the miniaturization of the antenna by using the meandering radiation patch and loaded short-circuit pin, and slotted the antenna ground plane. The antenna was small in size and worked in multiple frequency bands. Recently, an ultra-small implantable antenna was proposed in9. The antenna was used in the pacemaker system to serve the ISM frequency band with the size of 3 × 4 × 0.5 mm3. The simplified structural design of the antenna was easy for system integration. However, the peak gain of the antenna was only − 25.95 dBi.Research teams around the world have conducted researches on miniaturized implantable antennas. The implantable antennas issued in public prints are developing towards diversification, functionalization, convenience and miniaturization. The most important thing about the antenna used in the pacemaker system is how to make it smaller in size and volume. The smaller the device is, the better it can alleviate the rejection of implants and relieve the pain of patients3, and 3 mm × 3 mm × 0.5 mm in size. Through literature review, it is found that the antenna designed in this paper is the smallest among the implanted antennas of the same type and structure, which is consistent with the popularity of miniaturization of implanted electronic devices. In this paper, through optimization analysis of the antenna's reflection coefficient, current distribution, radiation efficiency, specific absorption rate (SAR) and other performances, it is verified that the designed antenna meets the requirements of radiation performance, design and effect while being very small in size. The paper introduces the methodology in “This paper introduces an ultra-compact implantable antenna, which serves biomedical telemetry and is applicable to wireless cardiac pacemaker systems. The volume of the proposed antenna is only 4.5 mmThe planar antenna with a zigzag structure has the advantages of compact structure, small size, light weight, and easy processing. Combined with the spatial structure of the implantable electronic device, the implanted antenna with a flat zigzag structure is a good choice.In the antenna design process, the length of the bus will affect its resonance characteristics. The increase in length will extend the path of the current, so that the resonance frequency will shift to low frequencies. The antenna bus calculation formula is shown in :1\documeIn formula , L is thThe working environment of the implantable antenna is in a mixed medium, not a free space. After implantation in biological tissue, the effective dielectric constant will change to a certain extent. According to the Lichtenecker formula (formula ), the efmentclass2pt{minimIn the formula , \docume9. The overall structure of the antenna designed in this paper is simple. Figure In the process of designing a wireless cardiac pacemaker system, antennas with the simple meander structure are usually selected for the convenience of manufacturing. The complex structure of the antenna form will cause greater trouble in processing3 in size. The size of this design is the smallest among similar antennas in accordance with the existing literature. The radiating layer of the antenna adopts the patch with a zigzag structure to expand the current path, so as to achieve miniaturization. The short branches of the radiating patch play the role of guiding current and optimizing impedance matching. In addition, the antenna employs a high dielectric constant substrate to further reduce its size. The ground plane is loaded with a slotted structure, which is equivalent to the effect of capacitive loading. The ground plane is slotted to enhance the electric field strength of the antenna, thereby improving its radiation efficiency thereof. In order to protect the radiation safety of the human body and prevent the high dielectric properties of the biological tissue structure from damaging the performance of the antenna, this design uses the dielectric plate which is consistent with the base as the covering layer of the radiation patch, so as to have a good protective effect10. The dielectric constant (εr) of the antenna substrate is 10.2, and the loss tangent (tan δ) is 0.0023. We selected the Rogers 3010 owing to its high permittivity. This paper mainly focuses on the angle of antenna design. Antennas are usually embedded in implantable electronic medical equipment during application. More biocompatibility issues should be considered at the level of electronic systems. Usually, the electronic equipment used in the antenna will add a layer of biocompatible material film. Such considerations can meet the needs of biocompatibility. In addition, in order to prevent the occurrence of biocompatibility incidents in the antenna design, some treatments are also done to prevent harm to the human body. In order to meet the requirements of biocompatibility, the processed antenna is coated with a ceramic aluminum oxide film on the surface of its structure. The thickness of the antenna substrate is reduced as much as possible to 0.25 mm. The antenna is coaxial-fed with the position of the feeding point is x = 2.7 mm and y = 0.25 mm. The specific parameter size of the antenna structure is shown in Table To meet the needs of miniaturized antenna structure and the rational use of the limited space of the pacemaker system, the antenna is designed to be 3 × 3 × 0.5 mm11. The implanted antenna is modeled and optimized in the equivalent model of the typical human heart. The conductivity of the heart tissue at 2.45 GHz is 2.215 and the dielectric constant is 54.918. Antenna implantation depth is 3 mm. The schematic diagram of the antenna implanted heart tissue model and its structure information are shown in Fig. Human tissue has characteristics of dispersion, and the dielectric change of the human body has little effect on the performance of the implanted antenna12. The antenna S parameter test adopts the E5063A vector network analyzer (VNA). The radiation characteristics of the antenna were tested in the minced pork. The designed antenna is compared with a standard horn antenna to obtain the best gain.The actual test scenario and the processed antenna and its system are shown in Fig. S11 of the antenna is obtained in this paper by adjusting the coaxial-fed position and optimizing the structure of the implanted antenna. This paper refers to the physical design and simulates the structure of a pacemaker system to test the interference of the system to the antenna. The 3D-printed imitation pacemaker system tries its best to recreate the actual working environment so as to better test the performance of the antenna and make the test results more accurate. The antenna simulation and actual test results with or without pacemaker system equipment are shown in Fig. According to the comparison in Fig. The bus length of the antenna determines the resonant frequency of the antenna. Figure The electric field distribution of the slotted and unslotted antenna grounding plane is shown in Fig. 5 V/m without treatment. Figure 5 V/m after optimizing the slotting of the ground plane. The designed antenna has a low operating frequency and works in an environment with large dielectric loss. The gap magnitude of the slot is small relative to the frequency band, and the gap will not increase its backward radiation. On the contrary, it can be seen from the electric field strength that the space field superimposition effect of the two-layer structure is significant. The designed ground slot can form a leaky wave radiator, which helps to improve the overall performance of the antenna. It can be verified that the slotted structure of the ground plane improves the radiation performance of the antenna and increases the electric field strength of the antenna.The antenna obtains an optimal radiation effect by optimizing the slot width, spacing and number of slots. Figure Figure The antenna measurement is carried out by using radio frequency cables. Considering that the coaxial cable may interfere with the performance of the antenna, we set three scenarios in the simulation model  of the human body cannot exceed 1.6 W/kg and 2 W/kg in 1 g tissue and 10 g tissue respectivelyDue to the presence of the device circuitry close to the antenna, there is a coupling between the device and the antenna. The battery and electronic components consider the use of perfect electrical conductor (PEC) materials, and the circuit PCB is manufactured on Roger 3010. We build a model, set the gap between the antenna and the electronic device as D, analyze and determine the best gap. Finally, we get an optimum gap through simulation analysis. As shown in Fig. Due to the loss of human tissue, the gain of the antenna is very low, which results in the short communication distance of the implanted antenna. In order to determine the communication performance of the designed antenna, its communication link needs to be analyzed. In calculating the link power budget, the designed implanted antenna is used as the transmitter (Tx), and the linearly polarized monopole antenna in free space is used as the receiver (Rx). In the communication process, the impedance matching of the transmitting and receiving antenna is good, ignoring the loss caused by the antenna mismatch. Table 17. The detailed link margin is shown in Fig. The communication link margin (LM) can be calculated using the relationship given inThe antenna designed in this paper satisfies the needs of miniaturization and performance improvement. Table 3. The SAR of this ultra-small antenna meets the requirements defined by IEEE C95.1-1999. Miniaturization has always been the eternal pursuit of implantable antennas. This design adheres to the principle of ultra-small and compact structure and the original aspiration of meeting the antenna's radiation performance, providing a better reference solution for the antenna design of wireless cardiac pacemaker systems.This paper introduces a compact and micro-implanted antenna used in wireless cardiac pacemaker systems. The miniaturized design of the antenna is realized by selecting a dielectric substrate with a high dielectric constant and a folded serpentine structure, and the size is controlled within a very small space. The use of the ground slot method further improves the antenna's radiation characteristics and optimizes the antenna's impedance matching. The antenna is ultra-small in structure with a volume of 4.5 mm


However, other imaging parameters are the same as those used for the signal image acquisition. The SNR is calculated from the mean signal intensity in the region of interest (ROI) of the signal image divided by the signal standard deviation in the ROI of the noise image after the required corrections. We compared SNRs determined using the COMBET and double echo with the longest second echo time (DELSET) methods for single‐shot echo‐planar imaging and fast spin‐echo sequences in white mineral oil phantom, purified water phantom, human head, and upper abdomen. We used the subtraction method as the reference standard.In the COMBET method, we first obtain a signal image using the objective pulse sequence. Then, we obtain the noise image of this sequence using the diffusion gradient with the largest 2 signal in the purified water phantom, cerebrospinal fluid, and digestive fluid. Therefore, the DELSET method afforded incorrect results for the long T2 regions in the noise and SNR maps, while the COMBET method enabled the in vivo evaluation of the SNR even in the long T2 regions.The COMBET method could obtain the optimal noise image, whereas the DELSET method could not sufficiently suppress the long T2 relaxation time.The COMBET method allows simple and practical SNR measurement, which is applicable to tissues with long T However, the DELSET method can generate errors in the noise estimation owing to residual signals in the noise image. These residual signals originate from long T2 tissues  due to the limit on the maximum available TE in MRI systems.In a recent study, a novel method for simply and accurately measuring the SNR was developed called double echo with the longest second echo time (DELSET).2 tissue on SNR measurement, which we termed combined maximum b‐value and echo time (COMBET).The aim of this study was to develop a novel method that combines the DELSET method with a diffusion gradient to address the effect of long T22.1b‐value and longest TE  is defined as follows:The COMBET method is based on pulse sequences in which the diffusion gradient can be applied. We obtained a signal image using the objective pulse sequence and noise image utilizing the diffusion gradient with the largest E Figure . Imaging2.2By the DELSET method, we obtained the noise image using the longest TE but without the diffusion gradient. The mean signal intensity and SD of signals were determined in the ROIs in the signal and noise images, respectively, in the same manner as for the COMBET method. An appropriate correction was applied to the SD as with the COMBET method. Then, the SNR was calculated by dividing the mean signal intensity by the corrected SD.2.3sub) was determined in the same manner as in the COMBET and DELSET methods. Then, the noise was estimated by dividing the noise SD by an appropriate correction factor, given as follows2 is the correction factor for the bias caused by the image subtraction process. The SNR was calculated by dividing the mean signal intensity in the ROIs in the two signal images by the estimated noise.We used the subtraction method as the reference standard for determining the SNR. The difference image was obtained by subtraction of two signal images obtained under identical imaging conditions. The SD of the signals in the ROI in the difference image  and the other filled with purified water . The T1 and T2 of the phantoms were determined using a multi‐echo spin‐echo interleaved with a multi‐echo inversion recovery sequence.b‐values of 0 and 1000 s/mm2. The imaging parameters are summarized in Table t‐test with Bonferroni correction for five multiple comparisons. We used the subtraction method as the reference standard. Significance was set at a p‐value < 0.05. Moreover, coefficient of variation (CV) of the SNR in the white mineral oil phantom was calculated by dividing the SD of the measured SNR by the mean of 20 consecutive SSEPI scans to evaluate variability and to perform comparisons among the COMBET, DELSET, and subtraction methods.We conducted phantom experiments using a 3.0‐T MRI system with a 16‐channel phased‐array head‐neck coil . We prepared two types of uniform cylindrical phantoms: One filled with white mineral oil  standard phantom, which is the international standard for the measurement of effective slice thickness.2.5The head and upper abdomen of a healthy volunteer were scanned to demonstrate the validity of the COMBET method in vivo. This study was approved by the appropriate institutional review board. The purpose and procedures of the study were fully explained to the subject, who provided written informed consent before the scans. Head scans of the subject were performed using the same MRI system and sequences (SSEPI and FSE) with the identical parameters used for the phantom experiments Table . For the3p‐values after correction for multiple comparison = 4.8 × 10−5 and 4.7 × 10−7 for the bottom and right ROIs, respectively). In the long T2 purified water phantom, the SNRs obtained using the COMBET method were higher than those obtained using the subtraction method, whereas those obtained using the DELSET method were substantially lower, with statistical significances observed in all ROIs . Figure 2 phantom especially in the purified water phantom, which resulted in an erroneous decrease in the SNR.Figure Figure 2 tissues, including the CSF and digestive fluid in the stomach, where the signal was present. Consequently, the SNR erroneously decreased in such tissues.Figures 42 values. Therefore, the aim of this study was to develop the COMBET method to address this issue and evaluate this method's feasibility in the phantom and in vivo experiments.Using the DELSET method is a simple and accurate way of measuring the SNR for MRI.2 value of the white mineral oil phantom (75 ms) owing to the limited maximum TE available in the MRI system.2 value (2390 ms) in the FSE sequence. This indicates that the signals in the noise image were sufficiently attenuated so that noise was the dominant effect even in the long T2 phantom owing to the diffusion and T2 relaxation processes. However, the COMBET and subtraction methods exhibited slightly different SNRs in the purified water phantom using the SSEPI sequence. These results might be explained as follows. Purified water can result in stronger fluid convection in the phantom due to its lower viscosity compared with the mineral oil phantom. In addition, the SSEPI sequence might be more sensitive to the effect of fluid convection because of the very rapid acquisition compared with the FSE sequence in which the effect can be averaged out over a longer scan time. Consequently, the residual signals due to fluid convection in the phantom might overestimate the noise estimate in the subtraction method. Namely, the subtraction method may not be applicable to the SNR measurement in fluid phantoms with low viscosity using the SSEPI sequence. In contrast, the COMBET method is immune to the effects of fluid convection given that the signals from the purified water phantom are completely suppressed when both the diffusion gradient with the largest b‐value and the longest TE are used. In addition, the DELSET method resulted in substantially lower SNRs, especially using the SSEPI sequence because the T2 value of the phantom was longer than the longest TE, which caused the residual signals in the noise image. These results demonstrate the major advantage of the COMBET method over the DELSET method for long T2 tissues or materials. On the other hand, the much lower SNR using the FSE sequence compared to that obtained with the SSEPI sequence can be attributed to the fourfold higher spatial resolution (1 × 1 × 5 mm3 for the FSE vs. 2 × 2 × 5 mm3 for the SSEPI). Moreover, in the purified water phantom, the DELSET method appeared to be more closely comparable to the other methods using the FSE sequence compared to the SSPEI sequence, this finding might be explained by the above‐mentioned smaller residual signals in the noise image obtained using the DELSET because of the lower SNR of the FSE sequence. When the COMBET method is used, the signal intensity for the real part of the noise image of the purified water phantom was theoretically 3.11 × 10−17% for the SSEPI sequence and 3.41 × 10−17% for the FSE sequence under the imaging conditions used in the present study. These values are sufficiently below the signed 16‐bit quantization limit  and thus support the validity of the noise image obtained using the COMBET method. Furthermore, the COMBET method resulted in no obvious differences in the SNRs between the diffusion gradient directions, indicating that the SNR is independent of the diffusion gradient axis. However, it should be noted that since these results pertain to the particular MRI system used in the present study and further validation of our findings in different MRI systems is warranted. The CVs of the SNR were generally comparable between the COMBET, DELSET, and subtraction methods. These results indicate that the repeatability of the SNR in the COMBET method is comparable with those in the other methods. Moreover, the SNR when the COMBET method was used had a stronger positive correlation with the effective slice thickness than the DELSET and subtraction methods, which indicates that the COMBET method may offer more robust SNR measurement than the other methods.In the experiments involving the white mineral oil phantom, the SNRs obtained using the COMBET method were comparable with those obtained using the subtraction method, which is considered the reference standard for SNR measurements.2 tissues, including the CSF and digestive fluid, because of the limited maximum TE available for the MRI systems. Compared with these methods, the COMBET method is more practical because it allows for simple and reliable SNR estimation even in long T2 tissues and does not require a specialized pulse sequence. As demonstrated in the present study, the COMBET method successfully addresses the main limitation of the DELSET method.It was possible to obtain adequate noise and SNR maps in the head and upper abdomen using the COMBET method. The subtraction method is difficult to apply for SNR measurement of abdominal MRI because it requires two identical scans; thus, it is susceptible to image misregistration caused by motion. Moreover, the DELSET method is not applicable to SNR measurement of long Tb‐value differs depending on the MRI systems. Although a larger b‐value can sufficiently attenuate signals in the noise image to reach the noise level, the optimal combination of b‐values and TEs for the COMBET method needs to be validated for different MRI systems and pulse sequences in future studies.There were some limitations to this study. First, the COMBET method is only applicable to pulse sequences to which a diffusion gradient can be applied. Therefore, a feasible clinical application is the measurement of SNRs in diffusion imaging. Second, the largest available 52 tissues.The COMBET method, which is suitable for pulse sequences to which a diffusion gradient can be applied, offers a simple and practical approach to SNR measurement that is applicable to long TNaoki Ohno: Conceptualization, methodology, software, validation, formal analysis, investigation, data curation, visualization, and writing‐original draft. Tosiaki Miyati: Conceptualization, methodology, and writing–review and editing. Hirotaka Oyabu: Conceptualization, methodology, formal analysis, investigation, data curation, visualization, and writing–original draft. Toshifumi Gabata: Supervision. Satoshi Kobayashi: Supervision.The authors declare no conflict of interest.


Modern dentistry commonly uses a variety of imaging methods to support diagnosis and treatment. Among them, cone beam computed tomography (CBCT) is particularly useful in presenting head structures, such as the temporomandibular joint (TMJ). The determination of the morphology of the joint is an important part of the diagnosis as well as the monitoring of the treatment results. It can be accomplished by measurement of the TMJ gap width at three selected places, taken at a specific cross-section. This study presents a new approach to these measurements. First, the CBCT images are denoised using curvilinear methods, and the volume of interest is determined. Then, the orientation of the vertical cross-section plane is computed based on segmented axial sections of the TMJ head. Finally, the cross-section plane is used to determine the standardized locations, at which the width of the gap between condyle and fossa is measured. The elaborated method was tested on selected TMJ CBCT scans with satisfactory results. The proposed solution lays the basis for the development of an autonomous method of TMJ index identification. Imaging techniques in modern dentistry are increasingly based not only on classic radiology but also on magnetic resonance imaging (MR), conventional computed tomography (CT), cone-beam computed tomography (CBCT), and ultrasonography (USG). In the diagnosis of disorders involving the temporomandibular joint, cone-beam computer tomography, also known as volumetric tomography, plays a significant role because it allows a three-dimensional image to be obtained of nearly all of the head and neck calcified structures ,2. The cDespite unquestionable advantages of CBCT and its ability to depict the tiny details of the human body, the most important and most challenging part—the image interpretation—lies in the hands of experts. The interpretation task, as well as the visualization of particular structures in the volumetric data can be tedious and error prone. Therefore, suitable methods are being developed to address this issue. Among them, image processing constitutes one of the most promising ones. Image processing and further image analysis have found many applications in a variety of disciplines. Their numerous applications in industry ,9, qualiAttempts were made to use CBCT for measurement of the temporomandibular joint (TMJ) parameters. The position of the TMJ head, which can be determined by analyzing the space between the TMJ head and the fossa, is recognized as being most important . There hThe aim of this research was to develop a method for determining the TMJ parameters on the CBCT scans. The proposed method allows the measurements to be performed in an almost fully automated way. The only part of the measurements, which has to be done manually is the selection of the volume of interest (VOI). Once the VOI is determined, all other operations can be performed automatically. As TMJ parameters are used in dentistry and orthodontics, increasing accuracy and consistency of their determination affect the effectiveness and comfort of treatment. The parameters sought are the measurements of the TMJ gap width with radiological fossa tomography in three locations: upper, frontal, and dorsal and evaluation of the condylar position in subjects with signs and symptoms of functional disorders of the temporomandibular joint through images made with cone-beam computed tomography on the sagittal plane . RadioloPresented retrospective research used the data gathered during the medical treatment of patients at the dental clinic at the Medical University of Silesia. All the data were anonymized before usage. The data are available for retrospective research for the University scientists.The input data for the TMJ parameters consisted of 36 tomographic images. The scans were taken while ensuring that the patient’s head was in the Natural Head Position (NHP) , which iTMJDP, TMJh,P and TMJFP are shown in TMJhP is the highest point of the TMJ head. The Cr is measured between it and that placed vertically above the point of the acetabulum, TMJaP. The Cr is perpendicular to the Frankfurt Plane (FHP) [The TMJ can be characterized by measurements of the parameters of the radiological gap between the ossified  structures including bones and in some cases during the inflammation process of cartilage. As is known from the literature, it is sufficient to measure the gap width in three carefully selected points . The locne (FHP) ,29.Dr = Fr = TMJDP and TMJFP which are defined as the points where the lines Dl, Fl passing through TMJaP are tangent to the TMJ head outer shape. The perpendicular lines exposed at TMJDP and TMJFP intersect the acetabulum at TMJaDP and TMJaFP. However, it is significant in knowing how the section presented in The other two distances are measured on both sides of the TMJ head, one in the dorsal  identification. The VOI is a cuboid containing the TMJ. All further steps are limited to the VOI. The essence of determining the width of the TMJ gap is to ensure that the points at which this width is determined are unambiguously located. The most important thing is to eliminate the variability always present when the measurements are done by the physician. The proposed method deals with this problem by calculation of the TMJ cross-sectional plane, in which the measurements are then carried out, as well as determining the measurement points. The calculations are composed of set of well-defined steps, which are described in detail in the following sections.Cr, Dr, and Fr distances are obtained. The detailed descriptions of the proposed algorithm steps are presented in the following sections.The position of the section plane on which the measurements are made is characterized by the following conditions . The plane is vertical and is perpendicular to the plane containing a segment connecting the most distant points of the TMJ head. The plain containing the longest segment contained in the TMJ head also contains its horizontal projection, and the projection is normal to the sought reference plane. Determination of the reference plane should therefore start with identification of the projection of the longest segment contained in the TMJ head on the vertical plane. Therefore, the TMJ head is segmented on the CBCT using axial slices of the VOI. Once the TMJ head is segmented, the projection of the cross-section is determined, upon which the placement of the reference plane is calculated. In the next step, the vertical reference slice is determined and the z coordinate was determined. The highest z value should allow containment of the slice depicting the bone right above the TMJ acetabulum. The lowest point is the point where the analysis of the TMJ head should stop. The ranges of the x and y coordinates should be selected so that the TMJ head can be completely included inside the VOI leaving a little space on each size. The example of VOI selection is presented in The CT scans produced by cone-beam tomography are known for their relatively high noise levels . TherefoThe pseudo-HU values in the vicinity of the TMJ are more representative of the voids (air) than the bones, hardly exceeding 200.The values differ significantly from pixel to pixel. However, the gradient at the edge of the fossa opening is significantly larger than within the bone or soft tissue.There are many voids visible which are separated by thin bone walls. They differ from the acetabulum in shape and size.The identification of the TMJ head is based on a series of visualizations showing the patient’s skull in axial cross-section. The research was limited to the previously determined VOI region (becoming the Region of Interest—ROI on each slice). A series of views of consecutive cross-sections through the ROI containing the TMJ is presented in The observations allowed formulation of the TMJ head segmentation method. iS denote the ith slice in the VOI. The slices are numbered from the superior towards the inferior and are perpendicular to the z-axis. Considering the histogram ih of the voxel values within the iS, it can be noticed that there is no apparent voxel value at which the image can be thresholded to achieve the requested segmentation. It can also be seen that the image after smoothing has a more compact histogram—almost all values within the range are present. In the histogram, one can observe a single big peak, resembling the Gaussian curve. The peak starts from the lowest values and spreads until approximately −100. The part of the histogram to the right of this value is rather flat, with two or three faintly visible peaks. The pattern can be observed in the vast majority of the analyzed slices. Only the slices showing the bone just above the acetabulum  have more uniform histograms, although the left-most peak is still clearly visible on them. The idea of segmentation is based on using the Gaussian Mixture Model [Let re Model ,40. The re Model ,42. The It is apparent that the visible parts of bone tissue were correctly recognized. Despite that, some problems still need to be resolved. First, the TMJ head is not the only object made of bone tissue segmented in the image, which influences further steps of the analysis. On the other hand, the TMJ head is not segmented perfectly, i.e., there is a hole visible inside the TMJ head ; in some of the slices, the outer shape is not closed. Both of these drawbacks can be eliminated by further processing.The elimination of head structures other than TMJ can be performed considering two insights. The other bone structures are placed at the borders of VOI and the condyle is the largest object placed in the central part of each slice image. The filling of the gaps in the middle of the TMJ head or closing its contours results from the assumption that its shape is not significantly different from its convex hull. Such an approximation does not affect the further analysis process. Therefore, this part of post-processing includes three steps. First, all segmented parts adjacent to the edges of the image are removed using morphological operations . Second,iS, containing the images of the segmented TMJ head, a minimal rectangle comprising the segmented area is constructed. Then, the shorter edges of the rectangle are considered. For each of the edges, the common points between them and the segmented area are identified. If there is more than one point common to the edge, the mean is used as the selected common point. For each slice iS, there are two points determined in that way. The comparison of the points along with the slices allows the ones most spread out to be selected. The section connecting them is the sought after longest section. Once the section is determined, its perpendicular bisector defines the section plane orientation. As the section plane is vertical, the knowledge of the bisector is sufficient for appropriate TMJ slicing. The formal description of the algorithm is presented in Algorithm 1.In order to obtain repeatability of measurements with maximum accuracy, the authors propose a reference cross-section, which is the cross-section of the mandibular head along its long axis. This cross-section is considered along the axis close to the sagittal axis. This is because the mandible head is turned towards the center of the head. As a result of segmentation, a collection of slices  of the condyle is obtained. The next step involves finding the direction of the vertical section used for the determination of the TMJ parameters. The idea behind it is to find the longest section connecting the opposite points in the volume of the TMJ head. The projection of the section on an axial plane determines the orientation of the slicing vertical plane. The algorithm is constructed as follows: for each axial slice P0, P1 are defined in a 2D space. They are the ends of the longest section projection on the axial plane. The sought cross-section plane VS represents the base slice for estimating TMJ parameters.Algorithm 1. The longest section search algorithmi = i0 # i0 is the index of the first slice containing the TMJ headp0_max_lst =  # list, beginning point of the sectionp1_max_lst =  # list, ending point of the sectionwhile i < MAX_I:      TMJ_head_contour = findTMJContour(Si)      rect = find_min_area_rectangle(TMJ_head_contour)      # get list of rect’s shorter sides coordinates      sides = get_shorter_sides(rect)      # find mid points of all sections where rect’s side passes      # through the TMJ head slice. p0_lst, p1_lst are list.      p0_lst = get_mids_of_sections      p1_lst = get_mids_of_sections      # find the longest section connecting both sides of the TMJ head      p0, p1 = find_longest_segment      p0_max_lst.append(p0)      p1_max_lst.append(p1)      i = i + 1 # find the longest of the connecting sections # p0, p1 contain the coordinates of beginning and ending # of the longest sectionp0, p1 = find_longest_segmentMAX_I = height(VOI) #search is performed within VOI onlyThe points Cr, Dr, Fr requires the data contained in the slice, defined in the previous section. The image analysis starts with the determination of the highest temporal fossa point coordinates. Since the cross-cutting vertical plane is placed at an arbitrary angle, usually it is neither parallel to the coordinate system planes nor to voxels directions. Therefore, obtaining VS is almost always connected with resampling. Segmentation of the bone tissue should be repeated for the slice. However, this time, no hole filling is necessary.The determination of the TMJ parameters TMJaP point starts with the determination of the top of the TMJ head. It is easily done as the TMJ head is already segmented. The highest (first) slice TMJhP, the coordinates of the top of the TMJ head, on the cross-section slice defined by the cutting plane TMJaP as the first point (and in practice voxel) assigned to bone tissue lying on a vertical line contained in TMJhP. The knowledge of TMJaP and TMJhP coordinates allows the Cr parameter to be calculated, as it is the length of the The determination of the Fr and Dr requires finding of the lines passing through the TMJaP and tangent to the TMJ head . Let us define the lines D’l and F’l as the lines lying on the plane Vπ defined by the vertical slice and passing through the point TMJaP. Let the lines be different from line Cl and different from each other. Let the θD and θF be the angles between D’l and C’l and F’l and C’l, respectively . Similarly, the direction of the Dl depends on the selected value of the θD, D = lD (lθD). Let TMJDP and TMJFP denote the points where lines Dl and Fl are tangent to the TMJ head. Next, let TMJDP’ and TMJFP’ be the points where the lines Dl and Fl cross the TMJ head , and F (lθFi+1). Then, let each of the profiles be limited to the section contained in ROI. In another step, a derivative for each profile should be calculated. Depending on the angle θF, the line F (lθF) crosses the boundary between bone and the soft tissues at least once. Therefore, the derivative should contain at least one peak in the places where the profile passes between the gap in the acetabulum and the bone. The first peak is placed in the TMJaP. If the θFi is small enough, the second peak is located at the point where Fl crosses the TMJ head (TMJFP’). The third (and further) peak can be observed if Fl crosses the TMJ head boundary once again, going from bone to soft tissues. At least one of the peaks has a negative value, while the most interesting one, if present, has values greater than zero . With the increase of the θFi, the length of the section also increases, as the Fl approaches the tangent to the TMJ head. Let θFT denote the angle at which the line Fl is tangent to the TMJ head. As the θF becomes greater than θFT, the line Fl no longer crosses the TMJ head (consider the lines F = f(lFi)θ and F = f(lFi+1)θ as shown in F = f(lθFT). It is also possible that there is no soft tissue to bone crossing within the ROI. Observing the distance between first and second peaks visible on the profile derivative as the function of θF, the discontinuity (step) can be noticed as θF exceeds θFT. Once such a step is detected, its placement reveals the θFi for which the line Fl becomes tangent to the TMJ head. The placement of a derivative peak on the profile determined for such an angle shows the placement of the sought point TMJFP. Because the numeric algorithm assumes that θF is incremented with step ΔθF, further refinement of the TMJFP position is possible. For that, it is suggested that binary search within the angle values section <θFi, θFi+1> should be performed. Alternatively, ΔθF can be chosen small enough to ensure the requested precision.Let us consider the length of the section TMJFP is determined, the Fr value can be easily calculated. At the point defined by the peak (TMJFP), a line placed on the plane Vπ and perpendicular to the tangent F(lθFT) can be drawn. Let the point TMJFP be the origin on this line and the coordinate system be directed towards the acetabulum. The distance between point TMJFP and the crossing point is the sought Fr. The analogous procedure should be performed for the other side of the Cl, resulting in the determination of Dr. The tuple  forms the parameters describing uniquely the TMJ.Once x, y, and z coordinate ranges. After the VOI was identified, the noise level was limited by the application of the curvature flow filter. The best results were obtained when the time step for the filter was equal to 0.01 and 10 iterations were performed. After this, the preprocessed images with defined VOIs were ready for further processing.The assessment of the proposed method was twofold. First, the ability of appropriate identification of the objects sought at each step was checked. Second, the comparison with the results achieved by experts was carried out. The first stage involves the testing of the robustness of the algorithm itself. What kind of difficulties occur during the process is investigated. Therefore, the used input data (CBCT images) were collected using various devices (CBCT tomographs). The experiments were carried out as follows. First, the preprocessing stage was performed. All values in the DICOM files were transformed into HU units. The VOI for each TMJ was manually determined, as described in the previous section. The VOI was remembered as the An exemplary set of axial slices images is presented in y axis of the coordinate system. Knowing the position of the said section, one can easily find this angle. Determining the cross-section given by this plane requires finding of all the voxels it cuts through and interpolating their values. In practice, it turned out to be more convenient to rotate the entire scan by this angle so that the This plane creates a certain angle with the TMJaP point. First, the highest set of voxels on the TMJ head is determined. The vertical line is constructed in the middle of the identified voxels. The TMJaP is found as the first voxel on the segmented bone tissue lying on the constructed line. Once it is determined, the iterations start to find the tangent to the TMJ head. The procedure used was divided into two steps. In the first one, a rough scan of the profiles was performed. The θ angles were changed from 0° to 50° with 5° steps. Next, the angle interval was limited to the vicinity of the tangent placement, and the step was reduced to 0.5°. For each line orientation, a line profile and its first derivative were calculated. The results for the example data are presented in θ. The function is presented in Cr as the Rθ increases. An abrupt step is clearly visible between Rθ = 31° and Rθ = 31.5°. The θRT can be taken as the mean of the two values yielding 31.25°. The analogous procedure performed for the left side of the reference slice gives θLT = −32.75°. The determination of distances Rr and Lr are straightforward as well as the lines perpendicular to the found Rl and Ll at points TMJRP and TMJLP. The profiles reveal the placement of the ends of Rr and Lr. The distances calculated for the presented example data gave the following values:All further analyses are performed on the reference slice. Determining the TMJ parameters requires finding the Lr = 2.1 mm, Cr = 3 mm, Rr = 1.5 mm.The reference points determined by the method are based on the method described by Ikeda and Kawamura . The proented in ,44, an aented in ,46, the The presented method assumes, that the patient’s head during the CBCT data acquisition is in NHP. Despite the stabilization of the patient’s head and performing the CBCT scan by experienced personnel, some deviation from the NHP can be detected. The proposed method will be influenced by it, regardless of the type of deviation. The usage of the large field of view, which is typical for TMJ scans, allows visualization of the points in the skull which can be used for the determination of the orientation of the Frankfurt plane , and canThe presented procedure proved to be successful in the determination of TMJ parameters. The method is deterministic and therefore tabulated and repeatable measurement results are obtained. The same set of CBCT scans lead to the same results, which is advantageous for the manually performed assessment. Once the VOI is determined, the method leaves no space for subjectivity. the procedure also opens up the possibility of determining the parameters independently of the doctor’s qualifications and predispositions. The good head position and determination of VOI seem to be the most important for the presented method. As the TMJ gap width measurement points are oriented to the highest point of the fossa, the incorrect position of the patient’s head will affect the robustness of the method. Once the VOI is properly established, the method will give consistent and reliable results. However, the VOI determination is not always obvious. The perfect VOI should contain both condyle and the fossa while including as few other adjacent bone structures as possible. Therefore, further research should aim at developing methods for an automatic assessment of the TMJ including VOI.The article presents a method for determining the parameters of the temporomandibular joint based on CBCT scans. The joint is characterized by the values of the width of the gap between the condyle and the acetabulum, measured at three selected characteristic points. The proposed method enables the determination of these parameters in an automated manner, which has a positive effect on the consistency, repeatability, and reliability of measurements. The crucial steps of the method include segmentation of the condyle on the axial slices of the VOI and the determination of the reference plane. The reference plane defines the vertical cross-section used further for the TMJ gap widths. The well-defined algorithm for the reference plane determination and the identification of the measurements points forms a common foundation for measurements. Formalizing the process allowed for its automation. The presented algorithm is a new proposition for dental practice. However, the method can still be improved. For example, it can be enhanced with automatic VOI determination or head position correction. Despite this, the improvement in the time of measurements and the precision are readily detectable.