The learning policy favoured by our simulations and experiments gives rise to a compression of values that is routinely observed in psychophysics and behavioural economics. In other words, a seemingly biased learning strategy that yields well-known cognitive distortions can be beneficial for transitive inferential judgements.Humans and other animals are capable of inferring never-experienced relations  from other relational observations . The processes behind such transitive inference are subject to intense research. Here we demonstrate a new aspect of relational learning, building on previous evidence that transitive inference can be accomplished through simple reinforcement learning mechanisms. We show in simulations that inference of novel relations benefits from an asymmetric learning policy, where observers update only their belief about the winner (or loser) in a pair. Across four experiments ( Ciranka, Linde-Domingo et al. show that inference of transitive orderings from pairwise relations benefits from a seemingly biased learning strategy, where observers update their belief about one of the pair members but not the other. Transitive inference is not a uniquely human capacity5 but can also be observed in non-human primates8, rats9 and birds12.Humans routinely infer relational structure from local comparisons. For instance, learning that boxer Muhammad Ali defeated George Foreman can let us infer that Ali would probably win against other boxers that Foreman had defeated. More formally, generalizing from relational observations to new, unobserved relations  is commonly referred to as transitive inference14. Alternatively, transitive inference could be accomplished through more explicit, hippocampus-based memory processes18, which we will return to below.In the laboratory, transitive inference can be observed after teaching participants the relations between neighbouring elements from an ordered set of arbitrary stimuli Fig. . The neiQ-learning; Q) of item A and decrease that of item B  applied to the winner and loser in a pair  learns worse than the symmetric model (Q1) where α+ = α−  than elements with greater ordinal distance21.Before turning to transitive inference, we consider relational learning in a full-feedback scenario Fig.  where ch α− Fig. . Implici3. However, the model can easily be adapted to performing transitive inference when extending it with a simple assumption: value updates should scale with the difference between the estimated item values, Q(A) − Q(B) . More specifically, to the extent that A is already higher valued than B, observing the expected outcome A > B should induce weaker value updates, whereas the unexpected outcome A < B should induce stronger updates. To illustrate, observing an unknown amateur boxer win against a world champion should induce stronger changes in belief than the opposite, less surprising result (champion > amateur). When we incorporate this simple assumption into our model (Model Q1*), it learns orderly structured values, Q(A) > Q(B) > … > Q(H), and thus accomplishes transitive inferences for all pairs of items . We also observe a symbolic distance effect with this type of learning under partial feedback, similar to what we observed with simple RL under full feedback  under partial feedback is strikingly different from what we observed with full feedback. Under partial feedback, optimal performance is achieved with a strongly asymmetric learning policy (α+ ≫ α− or α+ ≪ α−), where only the winner (or loser) in a pair is updated confirmatory outcomes28. A noteworthy aspect of our Model Q2* is that the superior, asymmetric learning policy results in a compression of the observer’s latent value structure , Q(B), Q(C), … ; item-level learning). An alternative strategy is to more directly learn response preferences for each individual item pairing  through associative recall35 or spreading activation36 to infer a transitive preference  with an implicit value (n = 145) where we varied whether feedback was full or partial and whether it was probabilistic or deterministic , probabilistic choice feedback  was identical to that of Exp. 1. Experiment 3 (n = 48) was an online replication of Exp. 2, where the pair items on each trial were shown side by side instead of sequentially. Experiment 4 (n = 49) was similar to Exp. 3, but the feedback was made deterministic (100% truthful), as in previous studies of transitive inference  to study transitive inference. In these experiments, we increased the frequency at which the participants were shown neighbouring pairs relative to non-neighbouring pairs to provide more learning opportunities, since the task is inherently harder. We verified that our simulation results were invariant to this modification , 0.29 to 0.63). However, we found no evidence that pair-level memory contributed to transitive inference in our experiments. Incorporating associative recall of ‘linking’ neighbour pairs (+Pi) worsened the model fits, in terms of both pxp  and BIC , which is in line with the absence of an ‘inverse’ symbolic distance effect  incorporated pair-level learning in addition to the value estimates of the individual items. This pair-level memory +P; ‘’ accountFigure 37. Given above-chance performance, the chosen item will statistically be more likely to be the winning item. To test this alternative explanation, we repeated our modelling analyses using separate learning rates (α+/α−) for chosen/unchosen items instead of for the winning/losing item , corroborating our interpretation that transitive inference learning was better characterized by asymmetries between winners and losers. Previous RL studies have also highlighted potential differences in learning from positive (confirmatory) as opposed to negative (disconfirmatory) feedback28. Extending our winning model to incorporate such confirmation bias , which is consistent with previous findings in other learning contexts28. However, the addition of confirmation bias left the finding of winner/loser asymmetries unchanged . This a21 and a more recent model based on ranking algorithms used in competitive sports such as chess (RL-ELO)22. Both VAT and RL-ELO were outperformed by our winning model Q2* + P when fitted to our partial-feedback data . This held true even when we modified VAT and RL-ELO to include pair-level learning (+P) and separate learning rates for winners and losers  were indeed characterized by extreme asymmetry towards winners (with α− near zero). However, another subgroup (n = 15) showed the opposite, an extreme asymmetry towards losers (with α+ near zero). In other words, in the partial-feedback setting, most individuals showed an extreme bias towards winners or losers, either of which proved to be an optimal policy in our model simulations  compared with Exp. 1 (n = 17): P = 0.007; z = −2.69; r = 0.22; 95% CI, 0.04 to 0.39; Our model simulations Fig.  indicateons Fig. , right. α+ and/or α− yielded a small but significant improvement in model fit . More specifically, in the n = 64 participants who selectively updated winners , α− estimates were weakly negative . Memory confusions may thus explain the systematically false inferences about certain item pairs , human learning was characterized by an asymmetric outcome attribution to either winners or losers, which proved to be surprisingly optimal in model simulations. In contrast, a symmetric attribution of relational outcomes emerged in a setting where all pair relations could be directly experienced (Exp. 1), and for which our simulations identified symmetric updating to be the most efficient.Reasoning about the relationships between arbitrary pairings of items is a key component of human intelligence. Through simulations, we showed how different learning regimes perform better in full- and partial-feedback contexts. Under full feedback, the best learning model used symmetric learning to update the value estimates for the winning and losing items in opposite directions, with the same magnitude. However, under partial feedback (only for neighbouring items), the best learning model used asymmetric learning to only update the value representations for either the winner or the loser. Across four experiments, we found robust evidence that human learners used the best learning rule to match their feedback context. The participants used symmetric learning under full feedback (Exp. 1) and asymmetric learning under partial feedback (Exps. 2–4). While our asymmetric models allowed for a wide range of possible learning rate combinations, a majority of the participants showed one-sided learning, where value representations were only updated for either winners or losers.29, where sensitivity to stimulus differences diminishes with increasing magnitude . While there exist alternative theoretical accounts for this ubiquitous phenomenon39, our findings add a new perspective: compressed representations of magnitude emerge naturally from a learning policy that is optimized for inferring global relationships from local comparisons. From this perspective, subjective compression might not only reflect an efficient adaptation to the distribution of stimuli in the environment42 but could also result from learning policies that enhance transfer to novel relationships.An important feature found both in our model simulations and participant behaviour is a compression of the emerging implicit value structure, which results in a systematic decrease in discriminability of higher-valued items Fig. . This re25 or confirmatory and disconfirmatory outcomes28. The one-sided learning policy highlighted here in the context of transitive inference is orthogonal to these other asymmetries but may play a similar role in leveraging a biased but advantageous learning strategy . Unlike with ‘optimal’ cognitive biases reported previously49, we did not find the benefit of the present learning asymmetries to emerge from general limitations (noise) in decision-making  can be sufficient for performing transitive inference and for accurately describing human learners.Previous theories have proposed richer and more complex cognitive mechanisms for transitive inference, often with an emphasis on the key role of the hippocampus in representing relational knowledge55 or the possibility that participants develop direct action policies for each pairing56 after learning progress. A related question for future work is to what extent learning from relational feedback may transfer to comparisons with new items that were not contained in the learning set.While our model explains transitive inference via learning of individual item values, our findings do not preclude the emergence of a more explicit  mental model of the items’ relational structureTo summarize, we report evidence for pronounced asymmetries in transitive relational learning, where observers selectively update their beliefs only about the winner (or the loser) in a pair. Although asymmetric learning yields distorted value representations, it proves beneficial for generalization to new, more distant relationships. This biased learning regime thus seems well adapted for navigating environments with relational structure on the basis of only sparse and local feedback.n = 20 participated in Exp. 1 , and n = 35 participated in Exp. 2 . The participants in Exps. 3 and 4 were recruited online via Prolific Academic (www.prolific.co), with n = 76 completing Exp. 3  and n = 60 completing Exp. 4 . The participants in Exps. 1 and 2 received compensation of €10 per hour and a bonus of €5 depending on performance. Payment in Exps. 3 and 4 was £4.87 (£1.46 bonus) and £3.75 (£1.12 bonus), respectively. We obtained written informed consent from all participants, and all experiments were approved by the ethics committee of the Max Planck Institute for Human Development.The participants in Exps. 1 and 2 were recruited from a participant pool at the Max Planck Institute for Human Development. Of these, P < 0.01 compared with chance level (50%). After exclusion, n = 17 (Exp. 1), n = 31 (Exp. 2), n = 48 (Exp. 3) and n = 49 (Exp. 4) participants remained for analysis.Participants who did not reach above-chance learning levels were excluded from analysis. The threshold for inclusion was set to 60% correct judgements in the last two blocks of the experiment, which corresponds to a binomial test probability of 57, with the original white background removed.In Exps. 1 and 2, eight pictures of everyday objects and common animals were used as stimuli Fig. . In ExpsAll experiments involved learning the latent relations between the eight stimuli (A > B > C > D > E > F > G > H) through pairwise choice feedback, where the latent value structure was pseudo-randomly assigned to the pictures for each participant. On each trial, a pair of pictures was presented, and the observers were asked to choose the higher-valued stimulus . All possible stimulus pairings (7 neighbouring and 21 non-neighbouring) were randomly intermixed across trials, with randomized ordering of the elements in a pair . Prior to all experiments, the participants were given written instructions and were asked to complete two brief practice blocks to become familiar with the task.n = 56) presented in each of eight consecutive blocks. Experiments 1 and 2 were conducted in lab, using Psychophysics Toolbox Version 3 (ref. 58) running in MATLAB 2017a (MathWorks).On each trial in Exp. 1, two items were presented one after the other at fixation (0.5 s per item) with an inter-stimulus interval of 2–3 s (randomized). After the second item, Arabic digits ‘1’ and ‘2’ were displayed to the left and right of fixation , and the participants were asked to choose the higher-valued item by pressing the corresponding arrow key (left or right) within 2 s. A written feedback message  was shown after each choice (neighbouring and non-neighbouring pairs). The items’ latent values in Exp. 1 were probabilistic (with a Gaussian distribution) and designed such that feedback was truthful on approximately 80% of neighbour trials (probabilistic feedback). Each participant performed 448 learning trials with all possible stimulus pairings , resulting in 616 trials (presented in 8 blocks of 77). In Exp. 2, we additionally recorded EEG, and the participants performed a brief picture-viewing task before the experiment. These data were collected for the purpose of a different research question and are not reported here.59) and conducted online (pavlovia.org), with intermittent attention checks.The basic design of Exp. 3 was identical to that of Exp. 2, except for the following changes. Both pair items were displayed simultaneously on the screen for 2.5 s, one to the left and the other to the right of a centred fixation cross. The participants were instructed to quickly select the higher-valued item using the left or right arrow key. After neighbouring pairs, a feedback message (‘win’ or ‘loss’) was presented. After non-neighbouring pairs, no feedback message was shown. Experiments 3 and 4 were programmed in PsychoPy v.2020.1.3 . As learning expectedly proceeds faster with deterministic feedback, neighbouring pairs were presented only two times as often as non-neighbours, and we reduced the number of trials to 420 .i and the losing item j after relational feedback, we assume a simple delta rule60 (Model Q1):Qt is the estimated item value at time t, and α is the learning rate.To model how observers update their value estimates about the winning item 22) based on the relative difference dt between the value estimates for the winner i and the loser j in a pair:η is a scaling factor. Value updating is then moderated by the extent to which feedback is consistent (or inconsistent) with dt (Model Q1*):i and the losing item j, respectively. Note that equation (η = 0.Transitive inference is enabled by a modified updating rule (similar to refs. mentclass2pt{minimα+ and α− (Models Q2 and Q2*):i is updated via α+, and the losing item j is updated via α−.We can allow asymmetric updating of winners and losers by introducing separate learning rates, i and j, we use a logistic choice function to define the probability of choosing i > j on the basis of the difference between the estimated item values:τitem is the (inverse) temperature parameter controlling the level of decision noise in choices based on item-level learning.To convert the value estimates from item-level learning into pairwise choice probabilities for any two items n (1…7), we can describe the preference between its members  probabilistically in terms of a beta distribution:For the partial-feedback scenario, we also define an alternative learning model (Model P) that learns pairwise preferences between neighbouring items . For each neighbouring pair γ acting as a learning rate. We can thus define the learned neighbour preference at time t on the basis of the expectation of the beta distribution (Model P):pn,t = 0.5 reflects indifference, and values of pn,t larger  than 0.5 reflect a preference for the higher (or lower) ranking pair member. While this mechanism can learn the relations between neighbouring items under partial feedback, it fails to learn the relations between non-neighbouring items, for which there is no direct feedback signal. However, transitive inference of preferences between non-neighbouring items is possible through associative recall of those neighbour preferences that ‘link’ the two non-neighbour items in question. To allow for this possibility, we define the inferred preference between any two items i and j via the set M of intermediate neighbour preferences i and j (Model Pi):i − j| is the rank distance between the items’ true values, and λ is a free parameter reflecting failure to retrieve linking pair preferences in the range . If λ = 0, preferences between non-neighbours will be a lossless average of all intermediate neighbour preferences . As λ grows, the preference between non-neighbours will shrink to indifference with increasing distance between j and i. In other words, this model performs perfect transitive inference if λ = 0 and no transitive inference as λ → ∞. Note that for neighbour pairs (where |i − j| = 1), equation , the upper value of the beta distribution is updated, increasing the preference in favour of the higher-ranking pair member:i over j on the basis of pair preference pi>j,t subject to decision noise τpair:We again use a logistic choice rule to define the probability of choosing item λ is fixed at a large value) and pair-level transitive inference .From equations –9), we , we 9), item) if:pair) if:To combine item-level (equations –5)) and) and5)) This effectively implements a mixture of item- and pair-level learning.γ = 0 yields Model Q2*, or α+ = α− yields symmetric updating).From equations –10), we, we10), Q1(i) = 0—that is, the first choice was always a random guess with CP1 = 0.5). As in the human experiments, choice feedback was provided either for all pairs (full feedback) or only for neighbour pairs . We simulated model performance over a range of learning rates . Relational difference-weighting (η) was set to either 0 (Models Q1 and Q2) or 8 (Models Q1* and Q2*), and decision noise (τitem) was set to 0.2 and 0.04 , which resembles the noise levels estimated in our human observers in the respective experiments. Mean choice probabilities  in tasks akin to those used in the human experiments, with full and partial feedback , η, τitem, γ, λ, τpair, with a uniform prior). The best-fitting parameter estimates are shown in Extended Data Fig. 61). Minimization was performed using a differential evolution algorithm62 with 200 iterations. We then computed the BIC of each model for each participant and evaluated the models’ probability of describing the majority of participants best (pxp)63. In Fig. R2 computed as R2 = 1 − (BICmodel/BICnull), which quantifies goodness of fit relative to a null model of the data, with larger values indicating better fit (similar to ref. 64). Model comparisons for Exp. 1 (full feedback) were restricted to item-level learning models, as the availability of direct feedback for every pairing would equate pair-level learning models (P and Pi) to homogenous learning of all pairs, obviating contributions from transitive inferences.Model parameters were estimated by minimizing the negative log-likelihood of the model given each observer’s single-trial responses  across values of the model’s free parameters : A = (α+ − α−)/|(α+ + α−)|, which ranges from −1 (updating of losers only) to 1 (updating of winners only), with A = 0 indicating symmetric updating. For comparison between full- and partial-feedback experiments, we contrasted the absolute |A| estimated from the winning model in Exps. 2–4 ). However, a metric more critical for evaluating our empirical results is p(gen|fit), which is the probability that the data was generated by a specific model, given that the model was observed as providing the best fit to the generated data65. We compute this probability using Bayes’s theorem, with a uniform prior over models (p(gen)):To establish whether the individual models can be distinguished in model comparison, we simulated, for each participant and model, 100 experiment runs using the individuals’ empirical parameter estimates under the respective model. We then fitted the generated datasets  with each model and evaluated how often it provided the best fit (in terms of BIC). This way, we estimated the conditional probability that a model fits best given the true generative model (p(fit|gen) and p(gen|fit) on the experiment level, on the basis of full simulations of all participants in Exp. 1 (full feedback) and Exp. 2 . Critically, under partial feedback (Exps. 2–4), all our models were robustly recovered with this approach , even when both learning rates were free parameters . We likewise enforced difference-weighted updating (η > 0) when simulating Model Q2*, by setting η to similar levels as empirically observed in the partial-feedback experiments (µ = 3 and σ = 0.5). With this, the model recovery for Exp. 1 successfully distinguished between symmetric (Q1 and Q1*) and asymmetric learning models , human participant behaviour was best characterized by symmetric learning rates  is reported in the main text, while the individual test results are detailed in Supplementary Tables The behavioural and modelling results were analysed using non-parametric tests (two-sided), as detailed in the Further information on research design is available in the Supplementary InformationSupplementary Tables 1–4 and Methods.Reporting Summary.Supplementary VideoQ-learning under partial feedback for models Q1 (left) and Q1* (centre) with the same learning rate for winning and losing items, and for model Q2* (right) with asymmetric learning about winners only (α− set to 0). The coloured dots indicate the momentary Q-values for items A–H. Simulations are shown for a trial sequence with deterministic feedback for illustration purposes. The video first plays 200 learning trials (top) and then repeats the same trials more slowly (bottom). Non-neighbour trials (on which no feedback is given) are fast forwarded. The green and red discs indicate the winning and losing items on every trial. Model Q1 (left) effectively learns only about the extreme items (A and H), while intermediate item values fluctuate unsystematically around the pre-experiment baseline. In models with difference-weighted updating , value differences propagate through the item series, which leads to a more monotonic value structure that enables transitive inferences about intermediate items (B–G). In model Q1* (centre), with symmetric learning, propagation can occur in both directions, which results in partly conflicting updates for mid-range items . This induces residual non-monotonicity in the evolving value structure, which can compromise transitive inference. In model Q2* (right), with asymmetric learning, conflicting updates are reduced, leading to a more strictly monotonic value structure that enables superior transitive inference.Simulations of Peer Review Information.


Due to strong NIR absorbance, arising from the heavy hole−doping (copper cation deficiency), the Cu2−xS/PI composite film exhibited great promise for use in the filtration of the NIR spectrum. By monitoring Cu2−xS densities, its NIR−shielding efficiency reached 69.4%, with hundred−percent UV blocking and consistent performance within the reliability (85 °C/85%RH) tests over one week as well as 5000 bending cycles. The integration of the films into model cars and building windows exhibited excellent thermal−shielding performance upon exposure to direct sunlight. Moreover, benefiting from the distinctive distribution of Cu2−xS, the additional thermal energy (holes) generated in NIR absorption was successfully utilized. The densely surface−confined hollow structure of Cu2−xS on PI significantly endowed good formaldehyde catalytic capacity, with removal efficiency reaching approximately 72% within 60 min and a negligible decline after quartic reuse. These integration methodologies enable the promising fabrication of a high−performance, bifunctional window film combining thermal shielding and indoor organic pollutant removal.Window−film−integrated, near−infrared (NIR) absorption−based nanomaterials are of great interest in terms of numerous demands to reduce energy consumption, especially in buildings and vehicles. However, the question of how to effectively manage thermal energy generated from NIR harvesting in light−absorbing materials, rather than being wasted or causing negative effects, remains challenging. Herein, hollow copper sulfide (Cu Excessive energy consumption for cooling and heating (air−conditioning) leads to explosive negative effects such as serious environment pollution and global warming ,2. In coO4, etc. ,12,13,14 dopants ,20,21,22 dopants ,24, NIR− dopants . However2, etc., which probably exist in indoor air [2, CeO2, Co3O4, and so forth [In addition to thermal shielding, environmental quality management is another important prerequisite to enable individuals to stay indoors for a long time, considering the variety of organic pollutants, especially air pollutants such as second−hand smoke, formaldehyde (HCHO), and harmful substances such as CO, SOdoor air ,27,28. Adoor air . Among vso forth ,35,36,372−xS), was employed, and it is of interest in numerous fields such as energy and biotechnology [2S) possesses a tendency to lose cations because of oxidation, and copper has high mobility [2−xS owns a high hole density (1021 cm−3) which enables the strong NIR harvesting of localized surface plasmon resonance (LSPR), which gives them great promise in the NIR harvesting of solar radiation for thermal shielding [2−xS is a potential candidate for use in building SPR−enhanced composite photocatalysts, making successful use of the vis−NIR region of the solar spectrum [2−xS into flexible substrates for high−efficiency NIR shielding and utilizing the additional thermal energy from NIR harvesting for indoor HCHO removal for use in dual−function window films is very promising.Alternatively, the development of nanomaterials that can utilize the energy generated in NIR harvesting for photocatalysis is preferred. Here, the nontoxic material, copper sulfide  film and the in situ growth method were employed in this work. As an ultraviolet (UV) cutoff, PI film is a kind of special material with good thermal stability and flame resistance, which has been extensively employed in many fields [2−xS on a PI surface to form a thermal−shielding film. The direct growth of nanostructures from the molecular chain would increase the adhesion between the two. Moreover, the main benefit of the in situ fabrication technique is the controllable dispersion capability of the surface−confined nanostructures. As a result, hollow Cu2−xS was successfully integrated into PI via in situ growth fabrication. These Cu2−xS/PI films exhibited high visual transparency and excellent blocking efficiency in both the UV and NIR regions. Benefiting from the distinctive distribution and hollow structure of Cu2−xS, the additional thermal energy from their NIR harvesting was successfully utilized for efficient photocatalysis, and a good HCHO catalytic efficiency was achieved by monitoring the Cu2−xS densities, indicating that the facile integration method provides a promising fabrication of reliable thermal−shielding and organic−pollutant−removal bifunctional window films.To take good advantage of the additional generated heat from NIR absorption for pollutants’ photodegradation, it is necessary to ensure enough nanomaterials are exposed to the surface of a film, so as to offer a sufficient contact area with pollutants for efficient catalytic degradation. Commonly used fabrication procedures for NIR−absorbing materials for window films, which disperse the nanomaterials into a prepared polymeric precursor solution and use surface coating on substrates, or magnetron−sputtered metals and other materials on a flexible substrate with high tension , are noty fields ; it was 3)2) aqueous solution to undergo Cu cation exchange for 1 h. Subsequently, the Cu ions were chemically reduced into metallic Cu with a dimethylamine borane (DMAB) aqueous solution (10 mM) for 5 h. After each step, the samples were rinsed with abundant DI water and dried with nitrogen gas for later use.The in situ growth of metallic Cu on PI films was achieved as in previous work ; typical2−xS composite film was obtained using the Kirkendall method [The Cul method ,53. Typi2−xS/PI composite film, Rhodamine (RhB) was first selected as a tentative organic material. In each test, the composite film  was immersed in the glass bottle with 15 mL of RhB aqueous solution, and then, 200 µL of hydrogen peroxide (30 wt%) was added. Sequentially, 2 mL of the RhB solution was extracted every 10 min after the light was irradiated. The absorbance of the extracted solution was collected using a UV−vis−NIR spectrophotometer to estimate the rate of photodegradation.To assess the photocatalytic capacities of the prepared Cu2, cylindrical ring) was placed in 7 of the same little bottles (5 mL) containing 3 mg of HCHO aqueous solution. Each bottle was taken out after 10 min of irradiation (avoiding direct exposure to HCHO in samples that were extracted midway), adsorbed with a 50 ppm MBTH aqueous solution for 10 min, and subsequently reacted with 1% ammonium iron (III) sulfate dodecahydrate at 35 °C for 20 min. The absorbance of the resulting solutions was also collected. The HCHO removal was calculated using the following formula:C0 and Ct are the HCHO concentrations which refer to absorbance before and after the catalytic reaction within 60 min, respectively.Similarly, the indoor HCHO removal capacity was preceded as follows: the synthesized composite film , high−resolution transmission electron microscopy , and FE−SEM . Note: To prepare the TEM samples, the PI substrate had to be dissolved away because of the robust adhesion between the Cu2−xS and PI, which was too strong to be obtained simply through ultrasonication within a short time. A UV−vis−NIR spectrophotometer  was adopted to monitor the NIR−shielding efficiency. To confirm the changes during the nanostructure growth process, FT−IR  and XPS  were employed. The cyclic bending test was conducted using a homemade reciprocating extensometer to explore the durability of Cu2−xS/PI films. After 5000 bending cycles, the NIR−shielding performance and haze factor values were collected. The light source (100 mW∙cm−2) was utilized via a 300 W xenon lamp  coupled with an AM 1.5 G filter.The crystallinity and morphology of the Cu2−xS nanoparticles (NPs) to PI films. As presented in 2+ with DMAB , led to enhanced Cu2−xS densities, making a darker surface due to the densely configured NPs, with a tendency toward black  are necessary for thermal−shielding window films in buildings or vehicles to satisfy the comfort and visibility of the human eye. To estimate the heat−insulating performance of the composite films, the shielding efficiencies in visible and NIR regions were calculated using [Tvis and SNIR are the visible light transparency and NIR shielding values, and T(λ) refers to the optical transmittance acquired from UV−vis−NIR spectrums  and a low haze factor (1.60%).rd black . Figure te films . As the smission , is an eed using :(2)Tvis=pectrums b. Table 2−xS NPs results from the Cu vacancies, caused by the decreasing Cu stoichiometry and presence on top of the valence band, thus leading to absorption changes. It can be seen that the absorbance spectra of the Cu2−xS/PI film in 2−xS density. The LSPR absorption peak of Cu2−xS NPs was located at 1238 nm after 120 min of KOH processing. As the resonance NIR absorption is correlated with the free carrier concentration, the free carrier density of Cu2−xS NPs could be calculated with Mie’s theory using the following equation [To assess the catalytic potential of the selected film, the carrier concentration was calculated. The level of free carrier density in Cuequation :(4)ω=12πω refers to the LSPR frequency, N is the free carrier density, e is the electron charge, em is the free carrier effective mass, ε0 is the permittivity of free space, ε∞ is the high−frequency dielectric constant (assumed to be 9) [mε is the dielectric constant of the surrounding medium (εm of PI = 2.49). From Equation (4) and N of Cu2−xS NPs was estimated to be 1.02 × 1022 cm−3, which closely matched that in previously reported work [2−xS/PI films are promising candidates for LSPR−enhanced photocatalysts, especially in the vis−NIR region.Here, to be 9) , and εm ted work . Therefo2−xS/PI can be estimated with the hole density value N by the Drude–Lorentz model, as follows [c and inω are the incident light speed and frequency, τ presents the mean time between two charge carrier scattering events, and n is the refractive index of Cu2−xS. Formula (4) demonstrates an exactly linear dependence between the absorption coefficient α with the hole density N. In this regard, the high hole concentration in Cu2−xS via in situ growth fabrication provides the foundation for its utilization in thermal shielding and pollutants’ photodegradation.In turn, the NIR−shielding performance of Cu follows ,59:(5)α=2−xS, the fabricated processes were monitored using ATR−FTIR spectra, as presented in −1 (symmetric) and 1710 cm−1 (antisymmetric) totally disappeared after KOH treatment. New bands were observed at 1650 and 1530 cm−1, which were ascribed to the amide bond including carbonyl stretching and N–H bending after ring cleavage, respectively. After copper cation exchange or reduction into metallic Cu, and even sulfur diffusion to Cu2−xS, the spectrum was nearly the same; the mild change around 1000 cm−1 implied that several corresponding states were substituted for the Cu2+ and Cu complexes. X−ray photoelectron spectroscopy (XPS) analysis was employed to monitor the surface change during the Cu2−xS growth process. As plotted in 2−xS nanostructure was probably formed. Scanning electron microscope (SEM) measurement was utilized to confirm the morphology and distribution of the NPs, as shown in 2−xS NPs were uniformly covered on the PI surface, and negligible change in morphology was observed after S2− diffusion. It was observed that the uniformly distributed Cu2−xS NPs on film undoubtedly facilitated the NIR absorption without the aggregation of particles. The corresponding SEM energy−dispersive spectrum (SEM−EDS) mapping of the composite film  was used. As plotted in 2−xS were 10–20 nm in thickness, and the average size slightly increased to 62.3 ± 1.20 nm , with significantly increased S elements located on the outer surface of NPs, which strongly confirmed the existence of hollow structures. It is speculated that the Kirkendall−type diffusion process [2−xS NPs. The CuS thin layer was firstly nucleated and formed on the outer surface of Cu seeds, which then acted as an interface and barrier with the inner Cu cations and outside S2− ions in the bulk solution, hindering the direct reaction of Cu with S2−. Then, atomic diffusion occurred through vacancy exchange, thus forming the hollow Cu2−xS structures as previously reported [To confirm the successful growth of Cuite film d–f demonite film f evenly ite film e after s 1.20 nm , and fro 1.20 nm h, shows  1.20 nm i and peaobserved . Moreove process  could exreported . Encoura2−xS/PI composites films, 2−xS/PI films onto the car window is shown in 2−xS/PI film (2−xS/PI film using a xenon lamp (simulated solar irradiation). In this test, the composite films and glass acted as window films, and the window was attached to the sealed dark acrylic box, as depicted in 2−xS/PI film attached slowly increased to 26.8 °C (ΔT = 4.9 °C). These results effectively demonstrate the potential of the composite films to perform heat−shielding functions to save energy. To determine their potential application as a window film, the reliability test for Cu2−xS/PI films was conducted by investigating transmittance and haze changes in extreme environments (85 °C temperature and 85% humidity). During the 7−day−long tests, no obvious change was monitored in the NIR−shielding performance and haze factor  existed after peeling, the overall regional particles were fully retained, which provide a guarantee for reaching catalytic stability. The catalytic capacities for organic pollutant removal were evaluated. The rate of Rhodamine (RhB) and HCHO catalytic oxidation with Cu2−xS/PI was measured  and 240 min in HCHO (98.7%), as shown in 2−xS/PI composite films demonstrated in the first−order reaction kinetics model (–ln(Ct/C0) = kt), and the kinetic constant (k) in RhB and HCHO was calculated to be 0.0292 and 0.0174 min−1. Expectedly, during the cycle test, the decline in catalytic efficiency was inevitable after catalyst re−collection and the washing process, whereas the robust adhesion between Cu2−xS and PI, without any collection, enabled the degradation rate of RhB to still reach 85% and nearly 60% in HCHO in 60 min after four cycles, which maintained a stable removal efficiency of 96.1% in RhB and 82.6% in HCHO with the composite films, as plotted in 2−xS/PI exhibited structural and chemical stability after four cycles, as evidenced by the results of the XRD analysis; the film had no obvious changes and still maintained good crystallinity  test as well as after 5000 cyclic bending cycles. The composite films with optimal densities of Cu2−xS demonstrated superior NIR−shielding efficiency (69.4%) and excellent heat−blocking when directly attached to the window of a model car and simulated building. Moreover, with the distinctive distribution and hollow structure of Cu2−xS, this enabled the successful utilization of the additional thermal energy from NIR harvesting and provided good HCHO removal efficiency (72%) within 60 min and high reusability after four cycles. These findings can provide a new method for the generation of thermal−shielding and indoor organic−pollutant−removal bifunctional window films.In summary, the hollow Cu


Introduction: Rodent models of cardiovascular disease have uncovered various types of lymphatic vessel dysfunction that occur in association with atherosclerosis, type II diabetes and obesity. Previously, we presented in vivo evidence for impaired lymphatic drainage in apolipoprotein E null (ApoE−/−) mice fed a high fat diet (HFD). Whether this impairment relates to the dysfunction of collecting lymphatics remains an open question. The ApoE−/− mouse is a well-established model of cardiovascular disease, in which a diet rich in fat and cholesterol on an ApoE deficient background accelerates the development of hypercholesteremia, atherosclerotic plaques and inflammation of the skin and other tissues. Here, we investigated various aspects of lymphatic function using ex vivo tests of collecting lymphatic vessels from ApoE+/+ or ApoE−/− mice fed a HFD.Methods: Popliteal collectors were excised from either strain and studied under defined conditions in which we could quantify changes in lymphatic contractile strength, lymph pump output, secondary valve function, and collecting vessel permeability.Results: Our results show that all these aspects of lymphatic vessel function are altered in deleterious ways in this model of hypercholesterolemia.Discussion: These findings extend previous in vivo observations suggesting significant dysfunction of lymphatic endothelial cells and smooth muscle cells from collecting vessels in association with a HFD on an ApoE-deficient background. An implication of our study is that collecting vessel dysfunction in this context may negatively impact the removal of cholesterol by the lymphatic system from the skin and the arterial wall and thereby exacerbate the progression and/or severity of atherosclerosis and associated inflammation. Active lymphatic pumping is a major component of lymph transport. Active pumping is achieved by the spontaneous contractions of collecting lymphatics, which propel lymph centrally and act in concert with 1-way lymphatic valves, spaced at regular intervals, to prevent backflow . Efficie2  mice fed a high fat diet (HFD)  . This iset (HFD) , in whicelopment  and inflelopment . Lim et elopment  showed tthe skin  and aortthe skin  was signcontrols . CollectApoE+/+ or ApoE−/− mice fed a HFD and studied under defined conditions ex vivo, in which we could quantify possible changes in lymphatic contractile strength, spontaneous contraction frequency, calculated and measured lymph pump output, secondary valve function, and collecting vessel permeability to albumin. Our results show that all of these aspects of lymphatic vessel function are compromised in ApoE−/− mice, compared to ApoE+/+ control mice, fed a HFD. These findings extend those of other groups (in vivo observations (ApoE deficiency. The combination of ApoE deficiency and HFD negatively impacts both lymphatic smooth muscle (LMC) and lymphatic endothelial cell (LEC) function, which may result in impaired removal of cholesterol by the lymphatic system from the skin and the arterial wall . Male and female mice were fed a diet rich in fat and cholesterol  from 6 weeks of age for 14–16 weeks, as described in our previous studies (ApoE−/− mice of both sexes fed a HFD developed hypercholesterolemia and atherosclerosis (ApoE+/+ mice had average weights of 28.2 ± 4.9 (SD) g, whereas ApoE−/− mice had average weights of 24.1 ± 1.5 (SD) g; these values were significantly different . Similar weight differences between these two strains have been reported in other studies .  studies . ApoE−clerosis . ApoE+ studies .2O, and further cleaned. The chamber, with associated micropipettes, pipette holders and micromanipulators, was transferred to the stage of an inverted microscope. The same pair of cannulation pipettes was used for all experiments in order to standardize valve function measurements. Polyethylene tubing connected the back of each micropipette to a low pressure transducer and analog pressure controller  and placed face down on a heated pad. Popliteal lymphatic vessels were exposed through a superficial incision in the back of the leg, removed and transferred to a dissection chamber filled with Krebs-albumin solution for further dissection. For mesenteric vessel isolation, the abdomen was opened and the entire small intestine was removed and pinned out, after which lymphatic collectors were excised from the duodenum. Individual vessels containing three to four valves were pinned to the base of a Sylgard chamber and partially cleaned of fat and connective tissue. A 1-valve vessel was then transferred to a 3-ml myograph chamber containing Krebs-albumin solution, cannulated at each end with a glass micropipette (40–50 μm OD), pressurized to 3 cmHntroller , allowinntroller . Digital2+-free Krebs buffer at 37°C to eliminate spontaneous contractions that otherwise would have interfered with the tests. Luminal pressure on the inflow side of the valve (Psn) was measured with a servo-null micropipette inserted through the wall. A sharply-tapered pilot micropipette was used to make an initial hole in the vessel wall upstream from the valve. That pipette was then removed and replaced with a less-tapered servo-null micropipette with a tip diameter of 3–5 μm. After insertion, the servo-null micropipette was advanced to seal the hole. The calibration of the servo-null pipette was checked, and adjusted as needed, after raising Pin and Pout simultaneously between .5 and 10 cmH2O and changing the gain/offset of the Psn amplifier signal.After a multi-valve segment was set up on the microscope, the segment was shortened to a single valve for valve function tests and the rest of the vessel was stored at room temperature for later re-cannulation. Valve tests were conducted in CaTo ensure accurate and consistent measurements of valve back-leak, 1) all three transducers  were calibrated before each experiment; 2) the pipettes were cleaned after each experiment and checked before and during each valve test to ensure that the tips were free of debris; 3) the lines were free of bubbles; 4) the Psn pipette calibration was rechecked at the end of the valve test.2O, and the valve open, Pout was raised, ramp-wise, to 10 cmH2O over ∼1 min period while Pin was held at .5 cmH2O. A normal valve closed as Pout exceeded ∼1 cmH2O and remained closed for the duration of the Pout ramp. Pressure back-leak through the closed valve was measured on the inflow side of the vessel using the servo-null micropipette, which could resolve changes as small as ∼.05 cmH2O. The value of Psn at Pout = 10 cmH2O was sometimes used as a representative index of back-leak, but additional values of Psn at intermediate Pout levels were determined offline using a LabView program after binning the Psn data in .5 cmH2O Pout intervals.The first test of valve function measured the back-leak of pressure through a closed valve. Starting with Pin and Pout = .5 cmH2O, which resulted in measurements over a range of diameters spanning ∼40%–100% of the maximal passive diameter. ΔP for closure was then plotted against Pin or normalized diameter. The highest ΔP that we could test was 30 cmH2O (equating to a maximum Pout of 40 cmH2O when Pin was 10 cmH2O) without exceeding the specified safety range the ultra-sensitive pressure sensor elements.The second test determined the adverse pressure gradient  required to close an initially open valve. Because this value increases with increasing vessel diameter , the meaex vivo contraction protocol, similar to that described previously (2O (some vessels had no contractions at .5 or 1 cmH2O), Pout was elevated ramp-wise, usually to 10 cmH2O, at a rate of ∼3 cmH2O/min, with Pin held constant, while monitoring the position of the outflow valve. Successful ejection during a contraction cycle was associated with opening of the outflow valve when the peak of the contraction-induced internal pressure spike transiently exceeded Pout  across the lymphatic wall was measured directly using microscope-based photometry on a Zeiss Axiovert microscope equipped with appropriate optics and filters for measuring FITC fluorescence. A mesenteric collecting lymphatic was excised and cannulated as described above. To control perfusion and pressure, each micropipette was connected to manual water manometers via polyethylene tubing. Two manometers were connected through a valve to each side of the dual-lumen perfusion micropipette, such that when the valve was turned, one side of the pipette or the other selectively perfused the lymphatic vessel without changing intraluminal hydrostatic pressure. This allowed controlled perfusion of either the unlabeled or fluorescent BSA. A fraction of the perfused albumin was labeled with a fluorescent dye (Alexa-488) and fluorescence intensity was measured within a rectangular region of interest defined by an adjustable window in front of a photometer  that sampled light from the vessel lumen and adjacent extravascular space. The photometer output was digitized using an analog-to-digital converter  and analyzed off-line. Based on pilot experiments, the vessels were pressurized to 9 cmH2O on the inlet side and 5 cmH2O on the outflow side to enable rapid changes in the perfusate. To make a measurement, unlabeled BSA was perfused first to obtain the background fluorescence intensity. Switching to perfusion of the fluorescent BSA caused a rapid, step-increase in fluorescence intensity (Io) on the photometer. Over time, the fluorescent BSA moved across the lymphatic vessel wall into the bath solution, which caused a gradual but linear increase in photometer voltage (dIf/dt). Changing the perfusate to the unlabeled BSA washed away all fluorescence, eventually returning the photometer signal to baseline, and allowed repeated measurements to be made. Albumin permeability  was then calculated from a rederived form of Fick’s first law relating albumin flux to a constant surface area  and concentration gradient :Albumin flux  was simultaneously tracked on a transmitted-light, near infrared image of the vessel displayed on a computer monitor to ensure that it did not change throughout each recording. There was no overlap between the near infrared light and the fluorescence emission of Alexa-488-BSA.Dissected popliteal collecting lymphatics were fixed with 2% paraformaldehyde and blocked with phosphate-buffered saline (PBS) containing .3% Triton X-100% and .5% bovine serum albumin. Samples were incubated with primary FITC-conjugated monoclonal anti-smooth muscle actin (Sigma-Aldrich). Samples were mounted on a slide with Dako fluorescent mounting medium and coverslip and then viewed with a confocal microscope  with LAS AF confocal software .2·2H2O, 1.2 mM MgSO4, 1.2 mM NaH2PO4·H2O, 3 mM NaHCO3, 1.5 mM Na-HEPES, and 5 mM d-glucose (pH = 7.4). An identical buffer (“Krebs-BSA”) also contained .5% bovine serum albumin. Krebs-BSA buffer was present both luminally and abluminally during cannulation, but the abluminal solution was constantly exchanged with plain Krebs during the experimental protocol. For Ca2+-free Krebs, 3 mM EGTA replaced CaCl2·2H2O. All chemicals were obtained from Sigma-Aldrich  except BSA , MgSO4 and Na-HEPES .Krebs buffer contained: 146.9 mM NaCl, 4.7 mM KCl, 2 mM CaCln refers to the number of vessels included per group. There were no obvious differences in lymphatic function between male and female mice in our protocols so data from both sexes were combined for statistical analyses. The normality of data sets was assessed using Kolmogorov-Smirnov tests. Statistical differences between normally distributed data sets were assessed via mixed-effects model ANOVAs with Geisser-Greenhouse correction  with Fisher’s or Sidak’s multiple comparisons tests, as specified in the individual figure legends. Mann-Whitney tests were used to compare differences in groups that were not normally distributed. Statistical analyses were performed using Prism9 (Graphpad). Data are plotted as mean ± SEM. Unless otherwise stated, the significance level was p < .05.The number ApoE−/− mice typically exhibited blunted contraction amplitudes compared to ApoE+/+ vessels (with both strains fed a HFD). Representative examples of spontaneous contractions as a function of pressure are shown in ApoE−/− vessel at all pressures studied as well as a lower frequency at pressure = .5 cmH2O  rose as the Pout ramp began until Pout reached ∼1.8 cmH2O when the valve snapped closed (arrow). After that time Psn stayed at a low level even as Pout reached 10 cmH2O. The ApoE−/− valve in 2O, Psn began to increase until it reached a value of 3.5 cmH2O at Pout = 10 cmH2O. The concomitant rise in D upstream from the valve during the Pout ramp confirms that the ApoE−/− valve was leaky. The pressure back-leak (Psn-Pin) at Pout = 10 cmH2O was 0 cmH2O for the ApoE+/+ valve and 3.0 for the ApoE−/− valve.Next, we conducted tests of lymphatic valve function using methods described previously . For the2O Pout intervals and an average value ±SEM for each bin was obtained using a LabView program. At Pout = 10 cmH2O, ApoE+/+ valves showed only very slight back-leak (.1 cmH2O), but back-leak was much more severe for ApoE−/− valves and the differences were statistically significant at Pout levels ≥4 cmH2O.Summary data sets for the two genotypes are shown in 2O, the ApoE+/+ valve closed when the Pout ramp reached ∼1.2 cmH2O . The value of ΔP at Dmax is somewhat higher than for other “control” mouse genotypes fed a normal diet , as shown in limit, was defined as the value of Pout (minus Pin) at the time of last successful ejection. In the representative examples shown in limit for ApoE+/+ vessel (panel A) was 6 cmH2O (after subtraction of Pin) and Plimit for the ApoE−/− vessel was 2.2 cmH2O (panel B). The pump test data are summarized in ApoE−/− mice have a significantly lower pump strength (1.2 vs. 4.8 cmH2O) than comparable vessels from ApoE+/+ mice, in agreement with the lower calculated pump flows for ApoE−/− vessels in For pump tests, a 2-valve segment  was used. Pin was held constant at a low value while Pout  was raised ramp-wise  ejection prior to outflow valve “lock”. This likely underestimated the actual Plimit, but a minimal estimate of Plimit could at least be made. An example of this behavior is shown in ApoE−/− vessel; in that case D increased gradually prior to ejection failure, probably due to back-leak . The near-uniform spacing suggests that the leakage was possibly occurring at valve sites. Because subsequent analysis of dye leakage would have been highly subjective, we quantified the permeability of popliteal collectors using ex vivo methods similar to those previously described in detail  compared with ApoE+/+ controls  that was statistically significant  and one with significantly elevated permeabilities (ApoE−/− High). The reasons for these differences are not clear but suggest that some ApoE−/− vessels may be more susceptible to damage by whatever combination of factors is mediating the hyperpermeability.For permeability measurements, a collecting lymphatic was dissected from the mesentery, taking advantage of the lack of strong spontaneous contractions of lymphatics in this tissue bed. After cannulation and cleaning, a vessel was perfused through a ‘theta’ micropipette that contained two identical solutions, one of which contained albumin tagged with a fluorophore. Initially, a washout solution was perfused to obtain a baseline recording on the photometer. Switching to the other half of the micropipette selectively perfused the fluorescent albumin without a change in intraluminal pressure. Over time, fluorescent albumin moved across the lymphatic wall. The photometer voltage increased rapidly after the solution change, followed by a slow increase due to albumin movement across the vessel wall. Permeability (Ps) could be determined from the slope of the steady-state portion of the recording, which was fit using linear regression. Measurement of mesenteric collecting lymphatic Ps revealed a loss of barrier function in nificant . Furtherin situ revealed that many valves in ApoE−/− mice also had reduced LMC coverage in their sinus regions. Three examples are shown in ApoE+/+ vessels, in which the green fluorescence signal denotes SMA staining to mark the locations of LMCs, with unusually large gaps occurring at valve sites; valves at those sites were identified based on CD31 staining (not shown).Subsequent imaging of the valve regions of popliteal collectors ApoE−/− mice, we demonstrate here that hypercholesterolemia significantly compromises the contractile, valve and barrier functions of collecting lymphatics.Despite existing evidence that hypercholesterolemia impairs lymphatic drainage, it was unknown whether functional alterations in collecting lymphatics contributed to this impairment. Through comprehensive analyses of collecting lymphatic function using vessels from hypercholesterolemic ApoE−/− mice . Like the effect of adipose tissue expansion on collecting lymphatics, hypercholesterolemia in ApoE−/− mice reduced the contractile function of collecting vessels . Thus, any acute effects of perivascular fat were eliminated. Vessels in which all perivascular fat remained intact would not have be amenable to tests of valve function, pump function or permeability. Although studies such as Harvey et al.  and nitric oxide (NO). Various ROS molecules, such as H2O2, are known to impair contractile activity (+ (KATP) channels in LMCs , MARCO (SR-A6), and CD36 on lymphatic endothelial cells . This raApoE−/− collectors is triggered. The loss of SMC coverage in the valve regions may explain some of the contractile amplitude impairment, but that seems unlikely to be the complete explanation as the LMC loss was highly localized. Interestingly, at least two other conditions are also associated with LMC loss from collecting lymphatics and impaired contractions, including overproduction of the cytokine TNFα (ApoE−/− mice on HFD, may be elevated cytokine and/or ROS production (ApoE−/− mice (Hypercholesterolemia may also compromise the function of collecting lymphatics by altering their structure. This idea is consistent with our observations of reduced LMC coverage in the valve sinus regions of collecting vessels  as well ine TNFα  and expoine TNFα . A commooduction . LMC los/− mice  may also/− mice . An incr/− mice . Consist/− mice .via lymphatics in ApoE−/− mice (Given the role of lymphatic vessels in immunity , the dys/− mice  as well /− mice .ApoE−/− mice may also facilitate the progression of atherosclerosis by interfering with the efficiency of reverse cholesterol transport, an atheroprotective mechanism dependent on lymphatic transport (Finally, lymphatic dysfunction in ransport . This coransport . Lymphatransport . Therefo


One major challenge in the design of highly multiplexed PCR primer sets is the large number of potential primer dimer species that grows quadratically with the number of primers to be designed. Simultaneously, there are exponentially many choices for multiplex primer sequence selection, resulting in systematic evaluation approaches being computationally intractable. Here, we present and experimentally validate Simulated Annealing Design using Dimer Likelihood Estimation (SADDLE), a stochastic algorithm for design of multiplex PCR primer sets that minimize primer dimer formation. In a 96-plex PCR primer set (192 primers), the fraction of primer dimers decreases from 90.7% in a naively designed primer set to 4.9% in our optimized primer set. Even when scaling to 384-plex (768 primers), the optimized primer set maintains low dimer fraction. In addition to NGS, SADDLE-designed primer sets can also be used in qPCR settings to allow highly multiplexed detection of gene fusions in cDNA, with a single-tube assay comprising 60 primers detecting 56 distinct gene fusions recurrently observed in lung cancer. The design of highly multiplex PCR primers to amplify and enrich many different DNA sequences is increasing in biomedical importance as new mutations and pathogens are identified. The authors present and experimentally validate Simulated Annealing Design using Dimer Likelihood Estimation (SADDLE), a stochastic algorithm for design of highly multiplex PCR primer sets that minimize primer dimer formation. For discovery applications, “shotgun” whole genome sequencing (WGS) is the preferred approach to identify novel DNA sequences of interest5. However, the human genome comprises over 3 billion nucleotides, and despite the lowering costs of high-throughput sequencing, it is not practical today to perform WGS to high depths necessary for identification of subclonal mutations, such as somatic mutations in cancer. For routine detection of disease-relevant DNA variants in known genes of interest, targeted sequencing or direct qPCR approaches are typically used7. Of the two dominant methods today for target enrichment, multiplex PCR tends to have shorter workflows and require less DNA input than hybrid-capture probes8. However, multiplex PCR struggles to scale to large panels covering hundreds of genes, due to the nonlinear increase of primer dimer species that reduce NGS mapping rates and increase effective cost9.The advance of high throughput sequencing has uncovered a large number of biomedically relevant DNA sequences, from driver mutations in cancer to new bacterial/viral pathogen DNA sequences to microbiome metagenomic profiles that affect mental disorders on the gut-brain axis8) primarily rely on (1) enzymatic digestion of modified bases in primers10 and (2) DNA size selection to preferentially remove short amplicon species likely to be primer dimers. However, both steps are labor-intensive and cannot be applied universally to all multiplexed PCR reactions. In contrast, relatively little systematic work has been reported on computational approaches to minimizing the formation of primer dimers in the first place. To the best of our knowledge, existing multiplex primer design algorithm never exceeded 70 primer pairs in one tube14. This is mainly due to the high computational cost when the number of primers increases15. The development of a robust multiplex primer set design algorithm that produces highly multiplexed primer sets with minimal primer dimer formation could allow further scaling of multiplex PCR target enrichment to even larger NGS panels when combined with enzymatic and size selection methods. Alternatively, it can simplify the workflow of moderate size NGS and qPCR assays by removing the need for strict contamination control from open-tube steps.Currently, multiplex PCR methods for NGS target enrichment  will not be effective.There are two primary challenges in designing highly multiplexed PCR primer sets: First, for an Here, we present Simulated Annealing Design using Dimer Likelihood Estimation (SADDLE), an algorithmic framework for designing highly multiplex PCR primer sets. Within this framework, we present an example multiplex primer design algorithm, comprising an algorithm for primer candidate generation and a rapidly computable Loss function for estimating primer dimers. Using the SADDLE, we designed and experimentally tested multiplex primer sets comprising 192 primers (96-plex) and 784 primers (384-plex), and show low primer dimer formation through NGS experiments. Building upon this success, we built a single-tube 60 primer qPCR and Sanger assay to detect and identify 56 gene fusions with clinical actionability for non-small cell lung cancer.Generation of forward primer (fP) and reverse primer (rP) candidates for each gene target.S0 from the primer candidates.Selection of an initial primer set S) on the initial primer set S0.Evaluation of the Loss function L(T based on set Sg (primer set from generation g) by randomly changing 1 or more primers.Generate a temporary primer set T), and set Sg+1 to either Sg (no change) or T, depending probabilistically on the relative values of L(Sg) and L(T).Evaluate L ranges for primers, were experimentally optimized and these are described below.The above abstract framework provides a basis for many potential multiplex primer design algorithms, depending on the specific details of primer candidate generation, form of Loss function, temporary set 1. Primer candidate generation. We begin our implementation of primer candidate generation through the selection of one or more “pivot” nucleotides on human genomic DNA around which we design the forward and reverse primers Fig. a. The piG° ≈ −11.5 kcal/mol have the best tradeoff between amplification efficiency/uniformity and nonspecific hybridization. Shorter primers may not bind consistently with high efficiency to their templates, resulting in variability in amplification efficiency and non-uniformity of amplicon on-target reads in the NGS library. Longer primers have increased likelihood of binding to other loci in human genome, and can result in non-specific amplicons. Based on this ΔG° goal, we next systematically constructed primer candidates from the proto-primers by truncating nucleotides from the 3′ end until the primer candidate has ΔG° between −10.5 kcal/mol and −12.5 kcal/mol . Optionally, one could implement additional filters here to remove undesirable prime candidates, such as based on G/C content. For our demonstration panels, we restrict the G/C content of primer candidates to be between 0.25 and 0.75, removing primer candidates with G/C content outside this range.From our past experiences and preliminary optimization experiments, primers that hybridize to their cognate templates with ΔIn the implementation of SADDLE, primer candidates can be treated as individual primers or as primer pairs. Our specific implementation treats primers as pairs, so we next combinatorially generate all candidate primer pairs for an DNA target, in order to better constrain the distribution of amplicon lengths. Any candidate primer pairs that generate amplicons with length exceeding our maximum amplicon length or below our minimum are removed.S0 selection. We randomly selected a primer pair candidate for every amplicon that we wish to design, and collectively the selected primers are known as the initial primer set S0.2. Initial primer set S) on S0. The Loss function L(S) is a rapidly computable function that aims to approximate the severity of primer dimer formation by a primer set S. L(S) sums the potential primer dimer interactions between every pair of primers in the primer set. To prevent confusion, we refer to the predicted formation of dimers for a particular pair of primers to be the Badness. Mathematically,pa and pb are the ath and bth primer in primer set S, respectively  can be calculated in advance during primer candidates generation. One can imagine the Badness function to be proportional to the amount of primer dimers formed by two primers. In an optimized primer set with a relatively low concentration of primer dimers compared to the concentration of on-target amplicons, the amount of primer dimers formed between primer pa and pb should not significantly impact the amount of dimers formed between pa and pc, so the Loss function being defined as the sum of the component Badness functions is justified.3. Evaluation of Loss function L reactions.The sum in the Badness definition is over all reverse complementary subsequences between primer 18, because there is significant uncertainty in the effective salinity of the PCR reaction buffer, and because our previous studies on DNA thermodynamics suggests that previously reported ΔH° and ΔS° parameters do not extrapolate well to higher temperatures19.For each complementary subsequence, its length (len) and its number of GC nucleotides in complementary subsequence (numGC) contribute exponentially to Badness. Thus, the exponential components of Badness roughly reflect the partition function of the complementarity interaction, with G/C base pairs roughly twice as strong as A/T base pairs. We chose to use these simplistic parameters, rather literature base stacking thermodynamics parameterspa and pb, denoted as d1 and d2, are known to significantly affect the likelihood of primer dimer formation. In our preliminary qPCR experiments, we observed that a primer pair with 10 nt of complementarity at the 5′ end will not result in observable primer dimer formation, but a primer pair with 5 nt of complementarity at the 3′ end would. Depending on whether the specific DNA polymerase used, different d1-based and d2-based attenuation of Badness may be optimal for minimizing primer dimers. Because high-fidelity DNA polymerases with d1-based and d2-based attenuation should be significantly weaker for high-fidelity DNA polymerases.The distances of the complementary subsequence to the 3′ ends of primers P3), where P is the length of each primer . Naively, evaluation of the Loss L(S) of the whole primer set would have time complexity of O(N2 × P2)  to calculate the hash value for each unique subsequence in the primer set, and the time complexity to evaluate the L(S) by stepping through all subsequences of all primers is also O(N × P) (Eq. S) is O(N × P) for all primers in S.The evaluation of the Badness function is single largest component of software runtime cost, due to the large number of times the Badness function will be evaluated. For a primer that is 25 nt in length, there are 22 subsequences of length 4, 21 subsequences of length 5, etc. Evaluation of Badness for a single primer pair would thus have time complexity of OP, where PT based on Sg. Step 4 begins the recursive optimization process. Based on the current primer set Sg at generation g, we first randomly select one primer pair to “mutate.” For that primer pair, we randomly select a different primer pair from the list of all candidate primer pairs generated in Step 1. Temporary primer set T is thus generated by combining this new primer pair with all remaining primers in set Sg. Optionally, multiple primer pairs can be replaced simultaneously in this step to allow faster and more efficient exploration of the primer set space. In our preliminary in silico evaluations, we found that simultaneously mutating multiple primer pairs generally caused a slowdown of the optimization process.4. Generate temporary primer set T) and set Sg+1 to be either T or Sg. The Loss of temporary primer set T can be evaluated significantly faster than the initial evaluation of L(S0), because the hash table only need to be modified based on the changed primers.5. Evaluate L(T) vs. L(Sg). If L(T) is smaller than L(Sg), then the primer pair change was an improvement and accepted, so Sg+1 is set to T. If L(T) is larger than L(Sg), the change was detrimental, but we will still accept the change with a certain probability, as part of the simulated annealing algorithm21. To clarify, “simulated annealing” here refers to a specific computer science algorithm, and not a literal simulation of a physical DNA thermal annealing process. If we never accept any detrimental primer pair changes, then the approach degenerates to become a stochastic gradient descent approach. In preliminary in silico evaluations, we confirmed that stochastic gradient descent produces final primer sets with significantly worse Loss, because it becomes too easy to get stuck in a local Loss minima.We next compare the value of L(T) − L(Sg)) and the generation g of the optimization. Worse changes with higher L(T) are accepted with lower probability, and later generations of the optimization (higher g) are less tolerant of detrimental changes. In our implementations, the probability of setting Sg+1 to be T when L(T) is greater than L(Sg) are as follows:e is Euler’s number and gt is a positive interger. C(g) is a function that is monotonically non-increasing in g, indicating decreasing tolerance to detrimental changes at later generations. The parameter gt indicates the generation in which simulated annealing terminates, and we switch over to stochastic gradient descent.The probability of accepting a detrimental change depends on both the magnitude of the detriment  is below a pre-determined threshold Lt. In our implementation, we typically run the optimization to about 1.5 × gt to ensure we reach local minima. To further improve the overall quality of the generated primer set, we recommend running multiple SADDLE optimization processes with different starting conditions  and selecting the best final primer set.6. Repeat steps 4 and 5. Steps 4 and 5 are repeated until either a pre-determined generation 25  at different generations g, and is representative of our typical optimization trajectory. We selected the designed primer sets at three different optimization generations for experimental testing: PS1 , PS2 (primer set with intermediate Loss optimization), and PS3 (primer set with saturating Loss optimization). The primer set Loss decreased roughly 24-fold from PS1 to PS3; after 40,000 generations, only very marginal improvements were observed. We chose the primer set at 40,000 generations as PS3, rather than the one at 60,000 generations, because we know that our Loss function is an imperfect predictor of primer dimers. Over-training on an imperfect Loss function can lead to worse experimental results. The optimization finished in about 10 min under a conventional laptop with MATLAB R2021b and Linux operating system.We first used SADDLE to optimize the design of a 96-plex primer set, each amplicon target one arbitrarily selected exon of a different cancer-related gene26. The remaining NGS reads were aligned separately to each forward and reverse primer sequence. Reads with insert length shorter than the sum of the two aligned primers are classified as Dimers, and reads with insert length longer than the sum of the two aligned primers are classified as Non-specific amplicons (amplifying unintended regions of the human genome).We applied each of the three primer sets individually to human genomic DNA  and amplified for 17 cycles. We next constructed NGS libraries from the amplicons generated using PS1, PS2, and PS3, using a standard adaptor ligation protocol  clinical tissue samples  and the Badness Threshold . The plotted Reads Threshold in Fig. rve Fig. b. The arrve Fig. c, but thWe next examined the top five most dominant Dimer reads in the library Fig. d and comBeyond the above observations, it is not clear why some dimers are observed at much higher reads experimentally than others. For example, the top observed dimer only has a 5 nt overlap at the 3′ end, compared to a 7 nt overlap at the 3′ end for the rank 4 dimer. This is not consistent with our understanding of DNA hybridization and polymerase extension kinetics, and implies that we may not be able to generate a perfect Badness function even ignoring computational resource constraints.30. Currently, gene fusions are detected either in single-plex by qPCR for known high-frequency fusions , or by NGS. A highly multiplexed qPCR assay that can detect tens of potential gene fusions relevant to a particular disease could greatly increase the accessibility of gene fusion testing.Gene fusions are therapeutic targets and attractive diagnostic biomarkers to guide treatmentALK, ROS1, RET, NRTK1, NTRK2, and NRTK3). The number of primers are lower than 56 × 2 because the same exon can be fused with multiple partner genes or exons. We detect the fusions in complementary DNA (cDNA) reverse transcribed from RNA, in order to limit the complexity and length of the detection targets. For each fusion of interest, the primer set includes a forward primer (fP) targets the upstream partner gene and a reverse primer (rP) targets the downstream partner gene  across six genes  and preimplantation genetic diagnosis (PGD) are also very limited, and require rapid turnaround for molecular diagnostics due to the time-sensitivity of clinical decisions33.The improvement of NGS library on-target rates through the reduction of primer dimers can allow significantly larger targeted panels to be possible using multiplex PCR library preparation. Because multiplex PCR generally requires less input DNA and are faster than ligation-based library preparation approaches34.Through our analyses of predicted vs. observed dimers, we found that the parameters in the Loss function used in SADDLE could be adjusted to optimize dimer prediction performance, particularly in the 335, qPCR assays will likely be the dominant tool for study of genomic variants. In qPCR, even single-plex primers can form significant dimers if poorly designed with Ct values below 30. Multiplex qPCR thus typically requires significant empirical optimization, even at around 4-plex11. SADDLE allowed us to successfully design a 60-primer qPCR panel targeting 56 gene fusions, and exact fusion identities can be determined through affordable Sanger sequencing. Thus, we envision that SADDLE can revolutionize the use of qPCR for highly multiplex molecular diagnostics.In medical and research applications where the cost of NGS cannot be economically justifiedAll procedures performed in studies involving human participants were approved by the ethics committees of Shanghai Pulmonary Hospital, Tongji University (protocol K19-155Y), and were in accordance with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. Informed consent was obtained from all participants.All primers were purchased as standard desalted DNA oligonucleotides (Integrated DNA Technologies), and stored at 4 °C.Synthetic DNA templates were purchased as desalted DNA oligonucleotides , and stored at −20 °C. Human cell-line gDNA sample NA18562 (Coriell Biorepository) was stored at −20 °C. The gDNA was mixed with synthetic DNA templates at various ratios to create samples containing different proportions of a specific variant sequence. Dilution of gDNA samples and synthetic DNA templates were made in 1× TE buffer with 0.1% Tween 20 (Sigma Aldrich).FFPE slides were purchased from Coriell Institute. FFPE DNA was extracted from GeneRead DNA FFPE Kit (Qiagen).™ IV First-Strand Synthesis System (ThermoFisher Scientific).Ten plasma samples from ten NSCLC patients in de-identified format were collected from Shanghai Pulmonary Hospital. RNA in extracellular vesicles was extracted with exoRNeasy Serum/Plasma Kit (Qiagen). cDNA was synthesized with SuperScriptMultiplex PCR was performed on a T100 Thermocycler or a C1000 Thermocycler (Bio-Rad). The total volume of each reaction was 50 µl. DNA sample input ranged from 10 to 100 ng per tube. PCR reagents including vent (exo-) polymerase, ThermoPol Reaction Buffer (10×), and dNTP (New England Biolabs) were used for enzymatic amplification. Thermal cycling started with a 3 min incubation step at 95 °C for polymerase activation, followed by 17 cycles of 30 s at 95 °C for DNA denaturing, 3 min at 60 °C for annealing, and 30 s at 72 °C for extension, followed by a final extension of 5 min at 72 °C. Detailed experiment protocol for the NGS library preparation can be found in Supplementary Section ™ II End Repair/dA-Tailing Module (New England Biolabs). Each reaction was a mixture of 3 μl NEBNext Ultra II End Prep Enzyme Mix, 7 μl NEBNext Ultra II End Prep Reaction Buffer, 20 μl multiplex PCR products, and 30 μl H2O. End repair was performed on a Eppendorf Mastercycler. Thermal cycling started with the incubation at 20 °C for 30 min and 65 °C for 30 min, with the heated lid set to 80 °C.Multiplex PCR product was end-repaired using NEBNext® Ultra™ II Ligation Module (New England Biolabs). Each reaction was a mixture of 30 μl NEBNext Ultra II Ligation Master Mix, 1 μl NEBNext Ligation Enhancer, 2.5 μl NEBNext Adaptor for Illumina, and 60 μl previous End repair mixture. Ligation was performed on a Mastercycler from Eppendorf. Thermocycling started with the incubation at 20 °C for 15 min with the heated lid off; after adding 3 μl USER™ enzyme to the ligation mixture, the reaction was incubated at 37 °C for 15 min with the heated lid set to 55 °C.End repair mixture was ligated with adapters using NEBNext® UltraFollowing adapter ligation, Index qPCR was performed on CFX96 Touch Deep Well Real-Time PCR Detection system (Bio-Rad). Quantification of different libraries was performed simultaneously in each well. Each reaction was a 10 μl mixture, with 1 μl i5 index, 1 μl i7 index, 1 μl ligation products, 2 μl Milli-Q, and 5 μl PowerUp SYBR Green Master Mix. Experiment was performed following a thermal cycling protocol with a 3 min incubation step at 95 °C for polymerase activation, followed by 40 cycles of 10 s at 95 °C for DNA denaturing and 30 s at 60 °C for annealing and extension. Ct values were obtained directly from the CFX96 system.Index PCR was performed on a T100 Thermocycler or a C1000 Thermocycler (Bio-Rad). Index primers used were NEBNext® Multiplex Oligos for Illumina® (New England Biolabs). Each reaction was a mixture of 2 μl each i5 and i7 index primers, 5 μl ligation products, and PCR reagents including vent (exo-) polymerase, ThermoPol Reaction Buffer (10×), and dNTP. The volume of each reaction was 52 μl. Thermal cycling started with a 3 min incubation step at 95 °C for polymerase activation, followed by various cycles of 30 s at 95 °C for DNA denaturing and 30 s at 60 °C for annealing, and 30 s at 72 °C for extension, followed by a final extension of 5 min at 72°.Multiplex PCR products and ligation products were all purified using DNA Clean & Concentrator Kits (ZYMO Research). The volume of DNA-binding buffer was 250 μl for multiplex PCR products clean-up, and 482.5 μl for ligation products clean-up; 25 μl Milli-Q water was used as elution buffer for each reaction.Index PCR product was purified using AMPure XP beads (Beckman Coulter). For each 50 μl reaction mixture, 90 μl of beads was added; 40 μl Milli-Q water was used as elution buffer.™ dsDNA HS Assay Kit (ThermoFisher Scientific).All the libraries were quantified using the QubitSizes of PCR products and libraries were measured using Bioanalyzer High Sensitivity DNA Assay (Agilent), and DNA chips were run on the Agilent 2100 Bioanalyzer system.All the libraries were loaded on a Miseq Reagent V2 for obtaining pair-end reads and were sequenced on a Miseq (Illumina).PCR products were purified and prepared using a BigDye Terminator v1.1 Cycle Sequencing Kit (Thermo Fisher Scientific) and were sequenced on a Thermo Fisher Scientific 3500 Series Genetic Analyzer. Detailed experiment protocol for Sanger Sequencing can be found in Supplementary Section Further information on research design is available in the Supplementary InformationReporting SummaryPeer Review FileDescription of Additional Supplementary FilesDataset 1Dataset 2Dataset 3


In the “after” group, two eyes (25%) developed iatrogenic retinal holes and one eye (12%) developed self-limited subretinal hemorrhage during external needle drainage. The duration of surgery was significantly shorter for the “before” group (mean 89 ± 16 min) compared to the “after” group (118 ± 20 min) (p = 0.008). The primary anatomic success rate was 100% for the “before” group and 75% for the “after” group (p = 0.233). Final VA was not significantly different between the groups or from baseline. In conclusion, while limited by our small sample size, this pilot study suggests that drainage of subretinal fluid before scleral buckle placement may be safer and more efficient compared to draining after buckle placement. Initial drainage may facilitate retinochoroid apposition to allow targeted cryopexy and precise buckle placement.In this retrospective comparative case series at a teaching hospital, we reviewed adult patients with rhegmatogenous retinal detachment who underwent scleral buckling surgery with external drainage of subretinal fluid performed before versus after placement of the scleral buckle. Eight eyes in each group were roughly matched for age, sex, baseline visual acuity (VA), and detachment characteristics. The complication rate was 0% for the “before” group and 37% for the “after” group ( Successful treatment of rhegmatogenous retinal detachment (RRD) requires closure of all retinal breaks, a principle first demonstrated by Jules Gonin in 1930 . Such scA typical scleral buckling procedure involves cryotherapy to retinal breaks followed by application of the buckle. The need for drainage of SRF has posed controversy ,5. FactoConventional drainage of SRF involves sclerotomy and external diathermy . An alteExternal drainage of subretinal fluid has often been performed after scleral buckle placement, out of concern that low intraocular pressure after drainage could make scleral buckle placement more difficult. In this small retrospective comparative study, we compare cases in which drainage was performed before versus after scleral buckle placement. We hypothesize that initial drainage before buckle placement could facilitate retinochoroid apposition and therefore improve the accuracy of cryotherapy and buckle placement. In draining before buckle placement, we also incorporate a less commonly used external needle drainage technique without simultaneous visualization of the fundus. We compare the outcomes between patients treated with these two approaches.This is a retrospective comparative study of adult patients with RRD who underwent scleral buckling by a team consisting of one attending vitreoretinal surgeon and one vitreoretinal surgery fellow. The same attending and fellow team performed all surgeries in this study. Institutional Review Board approval was obtained. Inclusion criteria included phakic lens status and the absence of PVD by optical coherence tomography . Patients were treated with drainage before buckle placement (the “before” approach) beginning February 2019. An equal number of similar patients treated with the “after” approach were retrospectively and consecutively selected. Variables reviewed in the medical record included past medical and ocular history; visual acuity (VA); detachment and break(s) features; surgical technique; and complications. Primary anatomic success was defined as retinal reattachment without any secondary retina-affecting surgery. The OCT was performed preoperatively and at postoperative week 1 and month 1 for all patients.https://tinyurl.com/5csb8php).Westcott scissors were used to create a conjunctival peritomy in proportion to the anticipated circumference of the buckle, and the appropriate rectus muscle(s) were isolated. In conjunction with the noncontact viewing system of the operating microscope, a light pipe or chandelier via a trocar-cannula system was used to inspect the retina for areas of detachment and breaks. A 25-gauge needle on a tuberculin (TB) syringe was introduced at an oblique angle into the subretinal space, transclerally, in the area that was to be covered by the buckle. See Surgical video: Intraoperative video of the restructured surgical approach to scleral buckling. Steps include stab incision drainage followed by cryotherapy and then buckle placement. Accessible via the following link: https://ucsf.box.com/s/uz1fmvly14t2vsixpmf04lk5pnsr74lv.Eight eyes of seven patients were treated with the “before” procedure. Eight eyes of eight patients were retrospectively and consecutively identified to demonstrate the “after” procedure (from September 2016 to February 2019). The most common “after” approach (37%) involved cryotherapy followed by buckle placement then needle drainage. Other sequences included cryotherapy-needle drainage-buckle placement (25%), buckle placement-cryotherapy-needle drainage (12%), and buckle placement-needle drainage-cryotherapy (12%). Needle drainage was performed under visualization and involved transcleral insertion of a 25-gauge short needle on a TB syringe.p = 0.133), sex (p = 1.000), and detachment characteristics. Median preoperative VA (Snellen) was 20/30 for the restructured group and 20/50 for the traditional group (p = 0.189). The median number of detached clock hours was three for the “before” group and four for the “after” group (p = 0.221). Most detachments were macula on . See The eight eyes in each group were roughly matched for age (p = 0.008). All eyes in the “before” group achieved primary anatomic success at a mean follow-up of nine months (range: 4–21). The primary anatomic success rate for the “after” group was 75% at a mean follow-up of 14 months (range: 2–24). One patient required buckle revision for progression of subretinal fluid, and the second patient required vitrectomy for recurrent detachment, both at postoperative month 1. Final VA was 20/25 for the “before” group and 20/30 for the “after” group (p = 0.202), which were not significantly different from baseline for either group . There were no complications in the “before” group. Two eyes (25%) in the “after” group developed iatrogenic retinal holes during external needle drainage which were successfully repaired with cryotherapy in one case and cryotherapy and a segmental buckle in the second case. One eye in the “after” group (12%) developed self-limited subretinal hemorrhage following external needle drainage. The duration of surgery was significantly shorter for the “before” group (mean 89 ± 16 min) compared to the “after” group (118 ± 20 min) , and allowing only a very short segment of the needle tip to enter the subretinal space. In this study, retinal holes occurred in 25% of the eyes treated with the “after” technique. This is higher than previous reports demonstrating a less than 2% incidence ,17,21,22Another potential concern could be the introduction of complications related to the relative hypotony induced by performing drainage at the beginning of the procedure, namely intraocular hemorrhage or difficulty passing scleral sutures. Neither materialized as a barrier. Rates of subretinal hemorrhage vary widely between techniques, from 0 to 28 percent, though direct comparison is limited by differences in case numbers and patient populations ,17,21,22Our technique utilizes endo-illumination and the noncontact viewing system of the operating microscope for intraoperative visualization of the retina. This method has previously been described by various authors ,22,23. AThis pilot study suggests that it may be reasonable to drain subretinal fluid early in the scleral buckle procedure, using a less commonly used external needle drainage technique via a stab incision followed by cryotherapy and buckle placement. While limited by the small sample size and retrospective design, the present study suggests that this technique may increase the safety, efficiency, and effectiveness of scleral buckling.


Angular pregnancy is a rare entity which is commonly confused with interstitial or cornual pregnancies. A lack of consensus about the specific ultrasound features of these 3 entities leads to inappropriate interchange between them among the literature. An angular pregnancy should be considered as a potentially viable intra-uterine eccentric pregnancy as it might be carried to term and result in a live-born baby whereas interstitial or cornual pregnancies should be considered as ectopic pregnancies which should be interrupted. We report here two cases of women at 8 weeks of pregnancy with an angular pregnancy diagnosed by vaginal 2D and 3D ultrasound and discuss about specific ultrasound features and alternative imaging modalities to distinguish it from interstitial and cornual pregnancies.The online version contains supplementary material available at 10.1007/s40477-022-00668-1. Angular pregnancy is a rare entity which was initially described in 1898 by Kelly as implantation of the embryo in the endometrial cavity at the superior and lateral angle of the uterine cavity and medially to the utero-tubal junction [Ectopic pregnancies correspond to pregnancies which are located outside of the endometrial cavity but inside the uterus such as interstitial, caesarean scar or cervical pregnancies. Interstitial pregnancies represent 2–4% of ectopic pregnancies . They ar“Cornual” pregnancy designs an intrauterine implantation in an abnormal unicornuate, bicornuate, or septate uterus  whereas A lack of consensus about the specific ultrasound features of these 3 entities leads to inappropriate interchange between them among the literature. Nonetheless, the recent 2020 ESHRE recommendation aims to standardize the terminology to describe embryo site implantation , 6.In this setting, the clinical challenge is to avoid managing an ectopic pregnancy , as an intrauterine pregnancy (such as angular pregnancy) –10. IndeWe report hereby two cases of women who had an 8-week angular pregnancy diagnosed by vaginal 2D and 3D ultrasound and discuss about specific ultrasound features and alternative imaging modalities to distinguish it from interstitial and pregnancies.A 38-year-old woman, G3P1, was referred to our center by her own practitioner for a second-look ultrasound for a suspicion of ectopic tubal pregnancy. In her history, she had a prior cesarean section eighteen years ago for an unexplained in utero fetal death at 28 weeks, and an early miscarriage in 2020. The current pregnancy was estimated at 8 weeks of gestational age according to the date of her last period. Clinically, she was paucisymptomatic, except for small vaginal bleeding for 3 days. The physical examination was normal. The blood pressure was 125/70 mmHg, the heart rate was 65 bpm and the oxygen saturation was 100%.Transvaginal pelvic sonography was performed and did not induce any pelvic pain. The transvaginal 2D revealed an anteverted uterus measuring 110 × 63 × 72 mm, with a 16 × 17 mm anterior intra-mural myoma, and no pelvic fluid in the Douglas’s pouch. There was an evolutive 8w0d-pregnancy with a crown rump length embryo of 16.3 mm and a normal heart activity of 135 bpm. The pregnancy was localized in the uterine upper left angle of the uterus and was fully surrounded by endometrium without any interstitial line sign. Around the gestational sac, a subchorionic hematoma of 25 × 22 × 20 mm was present  An empty uterine cavity, (2) A chorionic sac seen separately (> 1 cm) from the lateral edge of the uterine cavity, (3) A thin myometrial layer (< 5 mm) surrounding the chorionic sac. The combination of these 3 signs provided a specificity of 88–93% and a poor sensitivity of 40% . In addiIn a review of the literature, Lewiss et al. assessed the sonographic measurement of the endomyometrial mantle as a criterion for diagnosing an abnormal implantation location and concluded to a near-uniform acceptance of less than 5 mm as being highly suspicious for an interstitial pregnancy . By contRecently, the ESHRE society guidelines  suggesteIn a prospective cohort of 42 patients with angular pregnancy, Bollig and Schust suggested the following criteria: (1) Non anomalous uterus, (2) Implantation of the embryo in the lateral angle of the uterus, (3) < 10 mm of myometrial thickness from the gestational sac to the outer border of the uterus, (4) Completely circumferential endometrium surrounding the gestational sac, (5) Lack of the interstitial line sign . Main diIn case of unclear situation after performing a vaginal ultrasound, magnetic resonance imaging (MRI) appears to be a suitable alternative as second line exam , 23. MRIIn our two cases, the lack of the interstitial line sign and the fully surrounded endometrium sign were present. Although these both signs are rarely described in most of recent case-reports Table , they enDespite all these descriptions, diagnosis of angular pregnancy may remain difficult and repeated exams by experienced ultrasonographist and close follow up should be required before considering exploratory laparoscopy.Angular pregnancy is uncommon, and the eventuality of such unusual localization should be remembered to avoid confusing with cornual and interstitial topography. Those cases highlight the role of the 3D ultrasonography to help for diagnosing angular pregnancy which may be considered as a viable intra-endometrial eccentric pregnancy and may be managed to term.Supplementary file1 (MP4 5148 KB)Supplementary file2 (MP4 1146 KB)Below is the link to the electronic supplementary material.