The impact of parity on breastfeeding duration may be explained by physiological as well as psychosocial factors. The aim in the present study was to investigate the mediating influence of intention and self-efficacy on the association between the breastfeeding duration of the first and the following child.A 5-year Danish cohort study with data from online questionnaires was used. Data came from 1162 women, who participated in the “Ready for child” trial in 2006–7 and gave birth to their second child within 5 years in 2011–3. Analysis included multiple regression models with exclusive/any breastfeeding duration of first child as the exposure variables, intention and self-efficacy measured as mediators, and exclusive/any breastfeeding duration of the second child as the outcome variables.p <  0.001) and with the self-reported intention and self-efficacy in the ability to breastfeed the second child (p <  0.001). The exclusive breastfeeding period was slightly longer for the second child. Self-efficacy and intention mediated the association between breastfeeding duration in the first and second child. Together the two factors explained 48% of the association in exclusive breastfeeding and 27% of the association in any breastfeeding between the first and second child.Duration of exclusive breastfeeding of the first child was significantly associated with exclusive breastfeeding duration of the second child  contains supplementary material, which is available to authorized users. Breastfeeding rates are only increasing slowly in Western societies  even thoSeveral studies have reported how breastfeeding duration of the first child has been found to be predictive for breastfeeding duration in following child –18. The A cohort study design was used following Danish women who participated in the “Ready for child” trial over 5 years , 24. WomThe data were obtained from three questionnaires forwarded to the participating mothers at 6 weeks, 1 and 5 years after giving birth to their first child , 25. FurThe outcome variables were duration of exclusive breastfeeding and duration of any breastfeeding of the second child.The exposure variables were duration of exclusive breastfeeding and duration of any breastfeeding of the first child. All variables were collected according to indicators for assessing breastfeeding practices [ractices  by askinMediators addressing the psychosocial aspect of breastfeeding were collected by asking the mothers 1 year postpartum on intention and self-efficacy to breastfeed a potential second child. The variables were measured reflecting the conceptual framework of Fishbein and Ajzen’s Theory of Reasoned Action [d Action  and Bandd Action . IntentiCovariates included maternal socio-demographic characteristics at the time of the birth of the first child and the second child’s birth weight and gestational age as well as perinatal conditions and perceptions of postnatal care from the hospital and the health visitor. All variables with sub-categories appear from Table Bivariate associations between all variables and breastfeeding duration (exclusive and any) of the second child were assessed with one-way ANOVA for categorical variables and Pearson’s correlation coefficient for continuous variables Table . The assThe “Ready for child” trial was initiated in 2006–07 and 1980 women pregnant with their first child were invited to participate; 60% agreed to be included in the study. Between data collection at 6 weeks and 1 year after the birth of their first child, 31 participants were lost to follow-up, leaving 1162 women for the follow-up 5 years postpartum. The response rate at the 5-year follow-up was 79%. Among the respondents, 154 women who had not given birth to a second child during this 5-year period, eight women who had missing information on whether they had given birth to a second child, and 13 women who did not initiate breastfeeding of their second child were excluded. This resulted in a population of 738 women available for analysis  with a coefficient of 0.42 for exclusive breastfeeding and 0.60 for any breastfeeding. The intention and self-efficacy in relation to breastfeeding the second child reported when the first child was 1 year of age were significantly associated with the duration of exclusive and any breastfeeding of the second child (p <  0.001). Socio-demographic factors were not associated with breastfeeding duration, except for maternal educational level which was significantly correlated with the duration of any breastfeeding (p = 0.01). Among the perinatal factors, lower gestational age in the second child, undergoing a cesarean section or infants receiving formula supplement in hospital were significantly correlated with shorter duration of exclusive breastfeeding (p <  0.01) and shorter duration of any breastfeeding if the infant was delivered by cesarean section (p = 0.03) or had received formula supplement (p <  0.01). Gender and birth weight of the second child were not associated with breastfeeding duration. Maternal self-reported support received in relation to breastfeeding in the hospital was associated with breastfeeding duration (p = 0.01 for exclusive breastfeeding and p = 0.03 for any breastfeeding). However, the self-reported support received from the health visitor or the father was not significantly associated with breastfeeding duration.Table Table The linear regression coefficients in Table At the 5-year follow-up after the birth of their first child, 11 mothers were still exclusively breastfeeding their second child and 36 mothers were still partially breastfeeding their second child. These mothers were excluded from the main analysis. However, supplementary analyses were carried out including these mothers, first with the current number of weeks they had exclusively or partially breastfed their second child at the 5-year follow-up and subsequently adding 4 weeks to the current number of weeks. Results from these additional analyses were not found to differ noteworthy from the results of the main analysis.Data on breastfeeding duration of the first child were obtained from questionnaires at 6 weeks and 1 year postpartum. Thus, the duration of any breastfeeding of the first child was censored at 52 weeks. A total of 126 mothers were still partially breastfeeding their first child 1 year postpartum. Additional analyses were carried out to assess the impact of the censoring. The duration of any breastfeeding in the first child was coded in five levels  and included in the analysis as a continuous variable ranging from 1 through 5, or with 6 weeks added to the start of the interval . Results from these additional analyses without censoring did not differ significantly from the results of the main analysis.This study found breastfeeding duration of the first and second child was highly correlated. Breastfeeding intention and self-efficacy towards future breastfeeding reported after the first breastfeeding period played a significant role in explaining the relation between breastfeeding duration of the first and second child. Intention and self-efficacy combined explained 48% of the association between exclusive breastfeeding duration of the first and second child and 27% of the association between any breastfeeding duration of the first and second child.In the present study we used a prospective design and by collecting data at different time points we were able to disentangle the directions of the relations between the exposure, mediators and outcome variables. The reporting of the breastfeeding duration was collected retrospectively in the 5-year follow-up questionnaire, which may give risk of recall bias. On the other hand, breastfeeding duration is usually well recalled by the mothers  and the The correlations between the duration of exclusive or any breastfeeding of the first and the second child are consistent with earlier findings from Scandinavia , 21, 33,The psychosocial factors intention and self-efficacy  have earAnother interesting finding was that the proportion of mothers who had previously breastfed their first child for less than 4 months showed a tendency to breastfeed exclusively for a longer period (increase) whereas mothers who had exclusively breastfed their first child for more than 4 months showed a tendency to exclusively breastfeed for a shorter period (decrease) the second time. Similar patterns have earlier been found by Nagy et al.  among HuThis study was performed in Denmark, Scandinavia where the proportion of mothers who breastfeed is high compared to other western countries. Still, the influence of psychosocial factors on breastfeeding duration have been found to be consistent in western societies during the last decades , 13. ThePrevious breastfeeding duration, which may be an expression of earlier breastfeeding experience, is strongly associated with the intention and self-efficacy of breastfeeding a future child. The two psychosocial factors intention and self-efficacy explain nearly half of the association between the breastfeeding durations of the first and the second child and are therefore important to consider when planning and conducting future breastfeeding support.Additional file 1:Questions used in the study: the role of intention and self-efficacy on the association between breastfeeding of first and second child, a Danish cohort study. (DOCX 25 kb)


This process of elimination and compensation of disadvantage in flawed questions, as applied by the Institut für medizinische und pharmazeutische Prüfungsfragen (IMPP), can lead to This procedure is applied here to examinations containing items with partial credit scoring. A simple numerical rule can be applied which can be used to decide whether a flawed item has be taken into account in the grading procedure in order to achieve a pass or a particular grade for a candidate. This rule – as in the state examinations – must take account of the individual number of scores achieved in the flawed item and, if the relative pass threshold ("automatic adjustment clause") is applied, the average score achieved in the item by all candidates. In addition, however, it also includes the grade boundaries. An item such as this is considered to be "flawed" because, contrary to convention, it permits more than one single correct answer.Despite the careful review of examination items Those responsible for examinations within the faculties are therefore faced with the problem of needing to develop a legally sound procedure for dealing with flawed items. Study regulations and examination guidelines frequently contain insufficient directives regarding this aspect, which is why the approach of the Institut für medizinische und pharmazeutische Prüfungsfragen (IMPP), which is seen as legally sound, has been or is soon to be adopted by faculties for their own examinations in some places. correctly or incorrectly by the candidate.This is possible as long as the examination consists only of items in which no partial scores are awarded, i.e. in which an item can only be scored as having been answeredhttps://www.impp.de/internet/de/impp-aktuell.html], [This section presents a short description of the grading method in the written examinations within the German state examination and essentially is a summary and paraphrasing of the explanations given by the IMPP [l.html], .https://www.gesetze-im-internet.de/_appro_2002/]:On the decision regarding whether an examination has been passed and, if yes, how to grade this examination performance, the Ärztliche Approbationsordnung  sets out the following  and the detailed description of elimination and compensation of disadvantage [https://www.impp.de/internet/de/impp-aktuell.html], , the actual pass threshold is the smallest whole number which is greater than or equal to the mathematical threshold. If ceil(z) denotes the rounding up function , then the actual pass threshold is ceil(B) (for B=BS or BG). The mathematical grade boundaries are thenIt should be noted here that the mathematical pass thresholds thus defined are not necessarily whole numbers (in the licensing regulations the term "pass threshold" is Ng=ceil(B)+g x (M–ceil(B))(1) g=0 (pass threshold), the further boundaries for "satisfactory", "good" and "very good" result in g=0.25, 0.50 and 0.75. Note that these boundaries must be achieved or exceeded in each case, falling below the boundary even by only a minimal amount results in the poorer grade in each case. The grade boundaries are defined for both BS and BG, the lower of the two thresholds in each case is of significance for the students.Whereby the boundary between "fail" and "pass" for When partial credit scorig is used, it is not possible to define pass and grade boundaries based solely on the number of "correctly answered examination questions". It would be better to speak of "points" achieved, this formulation permits firstly the use of partial points as well as an unequal weighting of items, amongst other things.M describes the maximum number of points achievable , and XR describes the mean score achieved in the examination , then the absolute pass threshold BS and the relative pass threshold BG are determined in accordance with the automatic adjustment clause using two constants cS or cG.In most degree or examination regulations, absolute and relative pass thresholds ("automatic adjustment clause") are stipulated. If BS=cS x MBG=cG x XRcS is usually 0.6 in medical examinations ("anyone who achieves 60% of the maximum score passes the examination"), cG is often 0.78 as in the state examinations ("… anyone achieving not more than 22% … has failed"), for cG other values are also used, such as for example at the Medical Faculty of Heidelberg where the value 0.80 is used  sets out: Section 14 of the licensing regulations for doctors [(4) The examination items must […] be checked as to whether they are flawed, measured against the requirements of paragraph 2, sentence 1. If this check shows that individual examination items are flawed then these must not be taken into account when establishing the examination result. The prescribed number of items for the individual examinations […] is reduced accordingly. The evaluation of the written examination […] shall be based on the reduced number of examination items. The reduction in the number of examination items shall not have a negative impact on a candidate.The last sentence is interpreted in legal terms to mean that flawed items are still to be taken into account in individual cases and will only remain outside of consideration if this is not disadvantageous to the candidate. This means that for each candidate, flawed items are to be considered in such a way that the best possible result for the candidate is achieved, in other words a subset of flawed items is sought which achieves the best possible result for the candidate. This subset is generally not empty.In the case of the state examinations in which each item can only be marked as correct or incorrect, it can be shown that both for passing and for achieving particular grades, for a particular candidate the best possible result is achieved by the inclusion of all of those eliminated items in which he or she gave a correct answer whilst the other eliminated items are not taken into account.If the pass and grade boundaries, as defined in sections 2.2 and 2.3 by equation (2) or (4) are applied, it is easy to determine which items should be taken into account.m is the maximum score achievable, xR points were achieved at the mean (or the mean of the reference group in the item) and p points were achieved by a candidate, should be taken into account for that candidate.It must be determined whether an eliminated item in which S, we must also verify here whetherFor the grade boundaries derived from Bg x m+(1–g) x cS x m≤p(5) and for the grade boundaries of the automatic adjustment clause (with BG as the pass threshold)g x m+(1–g) x cG x xR≤p(6) If the inequality condition is met, the item must be taken into account in terms of the respective pass threshold and the grade boundaries derived from it, otherwise not.Note that the items used to determine the performance of the student thus depend on the grade boundary.Example 6: In an examination, 102 items are set each offering a maximum of 1 point, one of these items is eliminated due to a defect of form. A student achieves 0.75 points in this item. Depending on whether the student lies at the pass threshold or at the “good”/”very good” boundary, taking the eliminated item into account may be favourable or not for the student.If, for example, he achieves 60.50 points and thus just misses the mathematical pass threshold of 60.60, then taking into account the eliminated item has the result that he now has a score of 61.25 meaning that he now lies above the pass threshold of 61.20 points for 102 items . In the inequality (5) we would need to apply g=0.00, m=1, cS=0.60 and p=0.75 andg x m+(1–g) x cS x m=0.00x1+(1–0.00) x 0.6 x 1=0.60<0.75=pIf he has achieved 91.00 points in the marked items, thus gaining “very good” (the boundary is 90.90 points at 101 items) then taking into account the flawed item produces a total score of 91.75 which is not sufficient to achieve the boundary of 91.80 points for a “very good” at 102 items .The condition of the inequality (5) is in fact not met here:g x m+(1–g) x cS x m=0.75 x 1+(1–0.75) x 0.6 x 1=0.90>0.75=pi.e. the item shall not be included in the grading.Adopting the approach to elimination and compensation of disadvantage applied in the state examinations in examinations with unequally weighted items and items with partial credit scoring is not difficult to undertake with a similar definition of the pass and grade boundaries. More minor deviations from the definition of the pass and grade boundaries conditioned by the rounding functions in the setting out of the rules of the licensing regulations (see equation 1 vs. 3) are – as shown in example 3 – required to maintain the consistency of the grading scheme.For determining those eliminated items which must be individually taken into account for a particular candidate in order to achieve or exceed pass or grade boundaries, there are simple conditions which are dependent only on the number of points achieved in the item, the grade boundaries and – if the automatic adjustment clause is applied – the mean number of points achieved in the item. g in equations (2) or (4) are broken down finely enough, decimal grades can be awarded, for example.The procedure presented is also suitable for application to grading systems other than a division into four grades once the exam has been passed, which is the focus here. If the values for bonus points; nevertheless, even if bonus points are awarded, only the pass and grade boundaries derived from the correctly formulated items are applied. The "readjustment" of the pass threshold which takes place in the state examinations is not carried out, the same pass and grade boundaries apply for all candidates.In general, however, the negative consequences of different pass and grade boundaries in individual cases should be considered. The approach described may well be clear in form, but is not always easy for the students to follow. This is the reason, why, for example, in the grading regulations of the Medical Faculty of Heidelberg  it has bdirectly applicable to examinations containing differently weighted items and/or items for which partial scores are awarded  and a simple application of the grading scheme to examinations in which the pass thresholds are determined using the standard setting procedure and further grade boundaries are mathematically derived from it.In consideration of the introduction of innovative examination formats promoted in the Masterplan 2020, it would be welcomed if the rules of any future licensing regulations were formulated from the very beginning in such a way that they were se items ). This ased (see ), a geneKey to symbols used (see Table 2 This paper was created as part of the MERLIN II project (01PL17011C) funded by the Federal Ministry for Education and Research.I would like to express my particular thanks to Dr. H. Shahla of the Institut für medizinische und pharmazeutische Prüfungsfragen for the intensive and constructive discussions.The author declares that he has no competing interests.


High–harmonic generation (HHG) in gases has been the main enabling technology of attosecond science since its discovery. Recently, HHG from solids has been demonstrated, opening a lively area of research. In contrast, harmonic generation from liquids has so far remained restricted to low harmonics in the visible regime. Here, we report the observation and detailed characterization of extreme ultraviolet HHG from liquid water and several alcohols extending beyond 20 eV. This advance was enabled by the implementation of the recent liquid flat–microjet technology, which we show to facilitate the spatial separation of HHG from the bulk liquid and the surrounding gas phase. We observe striking differences between the HHG spectra of water and several alcohols. A comparison with a strongly–driven few–band model establishes the sensitivity of HHG to the electronic structure of liquids. Our results suggest liquid–phase high–harmonic spectroscopy as a new method for studying the electronic structure and ultrafast scattering processes in liquids. th order from the bulk of liquid water and different alcohols.While high–harmonic generation from gases, and more recently also from solids, has been extensively studied, there is little data on HHG from liquids. Here, Luu et al. experimentally demonstrate and study HHG up to 27 This technique not only provided a new source of coherent extreme ultraviolet (EUV) radiation but also enabled a variety of applications in spectroscopy and molecular imaging4 using single or multiple attosecond pulses. Recently, HHG from solids10 opened new possibilities for studying electronic dynamics15 and electronic structure18 in the bulk of solids. Extreme ultraviolet HHG from gases and solids has played a pivotal role in establishing and expanding real–time microscopic studies of electrons in matter. In the bulk of liquids, early efforts to observe HHG were limited to low–order harmonics in the visible domain19. EUV emission from water droplets has been observed20, however it was restricted to incoherent plasma radiation. Coherent HHG could only be observed after laser-induced expansion of the droplets to densities lying 1–2 orders of magnitude below that of liquid water22. In an entirely different class of experiments23, HHG was observed from the surface plasma and expanding high-pressure gas created by the interaction of an extremely intense laser pulse with a liquid jet. Therefore, EUV HHG from the bulk of liquids has not been reported so far.Studies of electronic dynamics on their natural time scale have tremendously benefited from HHG in gases25). The flat microjet provides an ultrathin , continuously renewed slab of liquid, which avoids the curvature of the interface inherent to spherical droplets and cylindrical microjets. These properties minimize the effect of reabsorption and phase mismatch, sample damage, as well as microfocussing of the infrared driver leading to divergence of the emitted harmonics, turning flat microjets into robust, reproducible and nearly flawless targets for HHG. This new approach enables us to isolate EUV high-harmonic emission from the bulk of liquids from that of the surrounding gas phase. Our detailed measurements moreover provide detailed information about the generation mechanism. We demonstrate a pronounced sensitivity of the HHG spectra of liquids to their electronic structure, especially to the widths of the bands and the band gaps. We further show that these spectral signatures are dominated by the microscopic non-linear response rather than by macroscopic propagation effects. Finally, we show that the ellipticity dependence of HHG from liquids is considerably broadened compared to that of gas-phase HHG. These combined results suggest liquid-phase high-harmonic spectroscopy as a potential avenue for studying the electronic structure and sub-femtosecond electron scattering processes in liquids.In this work, we investigate the properties of EUV HHG from the bulk of liquids for both scientific and practical purposes using a new experimental approach: the liquid flat–microjet method  onto a flat microjet made from two colliding cylindrical liquid microjets (~50 μm diameter) in high vacuum. The emitted spectra are recorded by a flat–field EUV spectrometer (see Methods). A key challenge, the separation of HHG from the liquid and the surrounding gas phase created by evaporation from the jet, is elegantly solved by making use of the wedge–like shape of the flat microjet, which converges from top to bottom24. This shape, combined with different refractive–index changes for the fundamental and high harmonics, results in a spatial separation of HHG from the bulk of liquids and the gas phase located behind the flat microjet (see Methods). We note that HHG from the gas phase located in front of the flat microjet is entirely absorbed by the jet because typical absorption lengths at our EUV energies are on the order of ~11 nm at 21 eV26. The simultaneously observed and spatially separated high–harmonic spectra from the liquid and gas phases are shown in Fig. Figure We chose water and various alcohols as liquid samples because of their relevance to chemistry and biology. Their balanced viscosity and vapor pressure supports the generation of optimal flat microjets while preserving a sufficient vacuum to operate multichannel–plate–based detectors. Figure Hcut-off ∝ E1.2). This linear dependence is similar to recent observations in solids5 and contrasts with the quadratic scaling observed in gases27. We proceed to study the dependence of the intensity of individual harmonics on the electric–field strength. Figure As a first step to elucidate the mechanism underlying liquid–phase HHG, we studied the high–harmonic spectral intensity dependence on the amplitude of the laser electric field. Figure 28 is sensitive to the spatial and temporal coherence properties of the emission. Our observation of a nearly identical contrast of the liquid–phase and gas–phase emission suggests that the liquid–phase harmonics are no less coherent than those from the gas phase.In the next step, we investigated the spatial coherence properties of HHG from liquids. Using a phase mask introduced into the driving laser beam, we created two spatially separated foci either inside the liquid or in the surrounding gas phase , the detected HHG originates mainly from the final ≈500 nm of the sample (see Methods). Future technological advances, including the application of mid–infrared drivers, might significantly increase the cut–off photon energy. Furthermore, since the absorption length increases monotonically for e.g., water from its minimum of ~11 nm at 21 eV26 to ~10 μm before the oxygen K-edge, extending the cut–off photon energy might considerably increase the photon flux of HHG from liquids.Having demonstrated the non–perturbative and highly coherent characteristics of EUV HHG from liquids, we furthermore determined its photon flux  extracted from state–of–the–art X–ray spectroscopy42, see Fig. 1 band in the DOS of water44. This difference led us to use a broader conduction band (labeled CB1(E)) in the case of ethanol.With the goal of understanding the origin of these characteristic spectra, we now turn to numerical simulations. We confine our theoretical study to liquid water and ethanol since the electronic-structure properties of ethanol are similar to those of the other two alcohols5. Second, it is generally accepted that water can be described as a very-large-band-gap semiconductor46 on one hand, and that its electronic properties can be approximated by an effective band structure47 due to the existence of local order on the other hand48.These bands were then used as input to quantum–mechanical calculations, i.e., the numerical solution of the semiconductor Bloch equations (SBE) in one dimension. In addition, to facilitate a direct comparison with the experimental spectra, we included an approximation of propagation and spatial integration across the laser beam profile (Methods). This theoretical approach is motivated by the following arguments  suggests the importance of these curvatures and therefore of intraband excitations in the HHG from liquid water. Furthermore, we found that the energetic position of the spectral minimum at H13 is also sensitive to the band gap as shown in Methods. We found that the minimum shifts linearly with the size of the band gap, therefore coinciding with the position of the odd harmonics when the band gap is modified by an even multiple of the fundamental photon energy.These results show that the dominant spectral features observed in EUV HHG from liquids can be explained by the width of the conduction and valence bands, the band gap, and the peak electric field strength, in each case. We further verified the influence of macroscopic effects by solving the coupled Maxwell-SBE problem (Methods). The results of these calculations are in good agreement with both the experiment and the SBE results discussed above, showing that macroscopic effects have a minor influence on the observed spectral features.49. Figure Finally, we discuss the ellipticity dependence of HHG in liquids. We exploited our ability to simultaneously record HHG spectra of the liquid and gas phases to directly compare their ellipticity dependences, as shown in Fig. =1) Fig.  without 8 are consistent with the following qualitative interpretation. In the gas phase, the continuum–electron wave packet has to return to the parent ion to emit high harmonics, specifically to the spatial region defined by the ionized orbital(s)  and the mean free path including all types of collisions (~4.0 nm), determined from experiments on amorphous ice55 at the relevant kinetic energies (~ 11eV). In the absence of experimental data on liquid water at these energies, and assuming that electron transport in liquid water is similar to that in ice57, we conclude that the number of collisions experienced by the strongly-driven electrons in our experiments amounts to one or less. Therefore, the spatial extension of the valence hole is likely to be the dominant effect in the observed broadening of the ellipticity dependence. Further extension of the theory described in ref. 58 may help in understanding this in more details.An additional effect that might contribute to a broadening of the ellipticity dependence in the liquid phase is electron scattering with neighboring molecules. These collisions would broaden the spatial extension of the continuum electron wave packet and cause partial decoherence, thereby suppressing the HHG amplitude. We estimate a maximal electron excursion length of 1.5 nm, i.e., a propagation length of 3 nm for the cut–off harmonic observed in our experiments (20 eV emitted in a 1.5 V/Å field). This is longer than most calculated elastic mean–free paths (EMFP) for liquid water18. However, it is much lower compared to the 35-eV cutoff photon energy of HHG from quartz18, which possesses long-range order. Considering that the effective band gap of water is very similar to the band gap of fused silica (and quartz), this suggests that the limited cutoff photon energy observed in the present experiments might be due to the lack of long-range order.Similar to the observation of EUV HHG from amorphous solids, our results may contribute to clarifying the role of short/long-range correlations in HHG from amorphous media. The EUV HHG from liquids observed in our experiments has a cutoff photon energy of about 20 eV, which is very similar to the maximum photon energy observed in fused silicaIn this work, we have demonstrated the generation and characterization of EUV high harmonics from liquids. This progress was enabled through the application of the innovative liquid flat–microjet technique, that elegantly separates high–harmonic emission from the liquid and gas phases. Intense, coherent HHG from four different liquids has been observed up to 20 eV, showing promise as an alternative source of coherent EUV radiation that combines the advantages of both gas and solid samples while alleviating their shortcomings . We also demonstrated the sensitivity of HHG to the electronic structure of liquids, especially their density of states and their band gaps by comparison with a quantum–mechanical strongly–driven few–band model. These results establish the potential of liquid–phase high–harmonic spectroscopy to investigate the electronic structure of liquids. Finally, we reported a broadened ellipticity dependence of HHG from liquids compared to the same molecules in the gas phase. Such measurements might shed new light on the spatial extension of valence–electron holes in liquids and sub–femtosecond electron scattering dynamics in liquids.f/45 to reach a peak-electric-field strength of ≈1.8 V/Å in vacuum as estimated from the calibration of the HHG cutoff in neon. The electric-field amplitude inside the liquid sample is then estimated using Fresnel’s formula for S and P polarizations and assuming that a normal incident geometry is used. The incident angle due to the wegde-like shape of the flat microjet is negligible for this calculation. The fields inside the sample are calculated to be ~0.86 times the field strengths outside (neglecting interference effects due to the thin flat microjet) for all liquids due to their similar refractive indices. Under operating conditions, the flat–microjet chamber displays a pressure of ≈1 × 10−3 mbar maintained by two liquid-nitrogen cold traps, while the spectrometer has a pressure of ≈1 × 10−5 mbar.We utilized a high-power Ti:Sapphire laser delivering 7 mJ, 1 kHz, 30 fs pulses at the carrier wavelength of 800 nm. The amplified laser pulses are sent to an optical parametric amplifier  to create signal pulses centered at 1500 nm with 1.2 mJ pulse energy. The signal pulses are focused onto the flat microjet inside a vacuum chamber with The generated EUV spectra are recorded using a spectrometer consisting of a flat-field abberation-corrected grating , a multichannel-plate detector coupled to a phosphor screen, and a charge-coupled device camera. All spectra reported in the main text are corrected for grating efficiency, multichannel-plate response, and conversion from wavelength to frequency domain.24. The liquid sample is pumped with a high-performance liquid chromatography (HPLC) pump through two cylindrical nozzles, creating two colliding microjets. For all experimental results presented in this paper two ≈50 μm nozzles have been used. We used white light interferometry to measure the thickness of our flat microjet. The thickness is in the range of ~1.2–1.9 μm depending on the flow rate, type of liquid, and position of the measurement with respect to the flat microjet. The flow rate for the creation of a stable flat microjet in turn depends on the nozzle size and the viscosity of the sample, which is in the range of 2 ml/min for alcohols and up to 6 ml/min for liquid water. Under the chosen flow rates and nozzle sizes, the speed of the liquid exiting the nozzles is ≈10 m/s. With the laser focus size of ≈120 μm and the repetition rate of 1 kHz, this corresponds to complete sample renewal between each laser shot. Millipor-purified water with around 18 MΩ of electrical resitivity and 99.8% ethanol, 99.7% iso–propanol, 99.8% methanol have been used as liquid samples in our experiments.Flat–microjet apparatus: We developed our own flat-microjet system with inspiration from the commercially available system59 that micro–droplets and small bubbles are produced upon interaction of intense laser pulses with liquids. The extreme energy of the laser pulse generates a vapor cloud immediately after  hitting the jet. The vapor cloud then expands with hypersonic speed and forms a shock wave, the sound of which can be heard when the laser–flat–microjet interaction takes place under atmospheric pressure. In our experiments, although each laser shot sees a new spot of the liquid slab, the vapor cloud does not have enough time to escape completely after each laser shot and therefore accumulates. Therefore, the green area shown in the main text  = S as the microscopic spectral intensity generated at a given position r in cylindrical coordinates, the spatially integrated spectral intensity on the detector Savg(ω) can be calculated as:A is the area of the effective laser focal spot size of radius rmax. Evidently, the above integration strongly depends on the shape of the laser focal spot, which is assumed to be Gaussian as supported by our measured beam profile at the focus. Considering that liquids possess a density similar to or even higher than solids, electron scattering with nearest neighbors happens on similar time scales, which led us to choose a dephasing time T2 ≈ 1 fs66. Finally, we have neglected Coulomb interactions in our calculations because they have been shown to play a significant role only in the weak–field regime63.For all simulations shown in the main text, we used the well-established formalism of SBEEg which is changed gradually from the starting value Eg0 with a step size of 2ħω0, where ω0 is the angular frequency of the carrier wave. For clarity of the main physical message, we turned off spatial integration and reduced the peak electric-field strength. The results demonstrate that the position of the intensity minimum shifts linearly with the size of the bandgap. Moreover, the position of the dip also depends on the intensity which is an expected behavior in strongly-driven systems. However, this effect is not apparent when the CB1(E) is used instead, suggesting that the formation of the plateau in HHG from water is collectively due to the size of the bandgap and the characteristic density of states of water.In the next step, we demonstrate the effect of the bandgap on the position of the intensity minimum and the shape of the HHG spectrum of water. The results of the simulations are shown in Fig. 67. This combination of the SBE as the microscopic nonlinear response and the first-order wave propagator in the frequency domain represents the state-of-the-art numerical treatment of HHG. This approach has been traditionally applied to gases, and its application to solids was suggested61, but to the best of our knowledge, it has not been performed for HHG from solids or liquids yet. The results of the simulation are shown in Figs. 68, we can unambiguously quantify multiple macroscopic effects.In the following, we investigate the effects of absorption and phase-velocity mismatch  on HHG from liquid water. Our propagation formalism is based on the slowly-varying-envelope approximationL) of propagation and then come back in phase after a longer distance (2L). This effect manifests itself as an oscillatory behavior of the intensities of H11 and H15 as shown in Fig. Phase–velocity mismatch: Since the imaginary part of the refractive index is associated with the absorption and the real part with the phase-velocity mismatch, we isolated the effect of phase-velocity mismatch by artificially turning off the absorption (setting the imaginary part to zero) before starting the propagation calculation. The results are shown in Fig. Absorption: We performed the complementary analysis by keeping the imaginary part unchanged while setting the real part to one. This keeps the absorption while artificially turning off any possible phase-velocity mismatch. The results are shown in Fig. By keeping the entire complex refractive index unchanged, our propagation simulations include the generation of new photons, the loss of photons due to absorption of liquid water, and the modulation of the photon flux caused by phase matching during propagation. The results are shown in Fig. Furthermore, our coupled Maxwell-SBE simulations also reveal the dominant role of the microscopic emission in shaping the final spectra. The effects due to propagation inside liquids are less important. The results are shown in Fig. Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Movie 1Supplementary Movie 2


This calculation is based solely on an individual’s family history. This APOE4 genotype estimation is then combined with a number of known factors that influence AD onset to produce a function that estimates the onset of AD as a function of age. We disseminated our Alzheimer’s predictive tool online at  Alzheimer’s disease (AD) is a devastating age-related neurodegenerative disease. Its devastation lies in its ability to impair the memory and cognitive function of people who have lived to an elderly age by having avoided or conquered many of the other mortal diseases such as cancer, cardio- and cerebro-vascular diseases, and respiratory infections. This cognitive impairment requires the allocation of extensive familial and societal resources to care for the afflicted individual . Many peA number of other reports have successfully demonstrated the use of various data to predict the onset of AD. Tierney et al used neuropsychological tests to predict AD with a sensitivity and specificity above 70% for predicting AD within 5 years . CallahaIn this work, we propose a theoretical framework to predicting AD onset by applying a hierarchical Bayesian model to a subject’s familial history to predict their APOE4 genotype, the major genetic risk factor for LOAD. Firstly, this model considers the familial history of the subject dating back two generations, i.e. parents and grandparents. Following the APOE4 genotype estimate, known hazard ratios are applied to determine a mathematical model of the probability of AD as a function of age correcting for covariates sex, race, diabetic history, traumatic brain injury, physical activity, diet, and education level. Important limitations of this approach are discussed in the discussion section of this report.http://www.alzheimerpredictor.com for general interest purposes.Our novel AD prediction model provides a theoretical predictive tool that corrects for various factors not considered in existing genetic tests without the costs associated with genetic tests. Our model is accessible online at In order to obtain the most information about the APOE4 genotype, we began by estimating the genotype of each grandparent using Bayes theorem  to deterThe conditional probability of an individual having a certain APOE genotype based on the age of AD onset, between 45 and 95 years of age, P(Genotype|AGE), was solved using Bayes theorem,++) is prior probability of an individual having an APOE4 +/+ genotype which is equal to the frequency of the APOE +/+ genotype in the population (i.e. 4.5%).For example, the conditional probability of a subject having an APOE4 +/+ genotype is given by the equation:g is the standard deviation of the age of onset, AGE is the age of onset, MeanOnsetAgeg is the mean age of AD onset. The subscript, g, is used to indicate generality of the genotype. To calculate the probability for a given genotype, the values for the genotype being calculated are used. For example, to calculate the probability for the APOE4 +/+ genotype, P(AGE|Genotype++), σ++ and MeanOnsetAge++ are used.Within the population, the mean age of onset for APOE4 +/+ individuals is 68±8.2; +/- 76±8.2, and 84±8.2 for -/- individuals ,16. AssuP(AGE) is given by the equation:We used a hierarchical Bayesian methodology to estimate the posterior probability of each genotype for each subsequent generation. The probability of each genotype for progeny was calculated by multiplying the probabilities of the genotypes of the parents by factors obtained from Mendelian statistics  ,18. The Pat” and “Mat” denote the previous generations’ posterior probabilities that the given allele was inherited from the paternal and maternal side respectively.For example, the prior probability of a subject who developed AD at a specific age having an APOE4 +/+ genotype, regardless of whether or not the parents had AD, is given by:Although we calculated the probability of the subject having any of the rare autosomal dominant genotypes , the very small genetic frequency of these genes resulted in a negligible posterior probability at most relevant ages and therefore the consideration of autosomal dominant genetics was omitted from further consideration for our model.A baseline hazard function was calculated by fitting the cumulative risk of AD to a Gompertz function which is a function known to fit well to AD onset probability . The Gom+/+ · P+/+ + A+/- · P+/- + A-/- · P-/-. Σ k · P and Σ x · P follow a similar pattern. P+/+, P+/-, P-/- is the probability of the respective genotype based on the Bayesian analysis (e.g. P+/+ = P(Genotype++ | Age)). Coefficients A, k, x are determined by fitting the cumulative AD symptom probability function to a Gompertz function . Correction for diet and exercise was excluded from the validation because these data were not available from the ADNI database. Only participants with a known APOE status and having sufficient data collected for analysis were included in the data analysis. The probability of AD symptoms was calculated using our tool from data supplied from AD participants (n = 250) and age-matched healthy controls (n = 1751). Mean “Risk of AD” at the current age was calculated for healthy controls and Mean “Risk of AD” at the time of AD onset was calculated for AD patients within the dataset.We begin our analysis by graphing the conditional probability function, P(AGE|Genotype), of a subject having a given APOE4 genotype based on their age of onset . The APOThe calculated estimated APOE4 genotype is noted in the bottom of the cell for each individual and is calculated in accordance with the methodology in the Methods section. Onset is the age of AD onset. If there is no history of AD, then the field is blank. Age is the current age of the individual or the age of death, although this variable is not used in the analysis.Once the APOE4 genotype is estimated, a “baseline” age of onset Gompertz function can be plotted based on the previously calculated parameters of A, k, and x weighted in accordance with the probability of the individual having each of the +/+, +/-, -/- genotypes .Finally, additional risk factors were added to modify the amplitude of the Gompertz AD risk function. In our example, the individual in the example above is a white male with a history of diabetes and no traumatic brain injury with a high school education. He exercises regularly and eats a typical “American” diet. His hazard ratios are shown in The Gompertz AD onset function is multiplied by a factor of 1.22 to obtain a factored AD onset risk function .Finally, we validated our theoretical model to actual data acquired from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset. AD patients  were age matched to healthy controls . Data from these patients were inputted into the AD prediction calculator and the probability of AD at the participants’ age  or the age of AD onset (for AD participants) was calculated. The mean theoretical probability of displaying AD symptoms for healthy controls was 12.2% whereas the mean theoretical probability of displaying AD symptoms for AD patients was 15.9%.In this work, we provide a theoretical framework based on a hierarchical Bayesian model for estimating an individual’s APOE4 genotype and further to estimate the probability of AD onset as a function of age based on a number of known factors that affect AD onset. AD is a progressive disease and is heavily dependent on APOE4 genotype ,16,22, hWe can apply this approach in a hierarchical manner to estimate the genotype of an individual based on the age of AD onset of his or her parents. In this case, the parents’ posterior probability of a given genotype is used as the prior probability for the subject’s genotype estimation. This methodology can then be applied to subsequent generations. In our model we only go back two generations from the subject to estimate the subject’s genotype. This is because it is rare for subjects to be familiar with the cognitive status of their great-grandparents. Additionally, cognitive history beyond two generations has little impact on the genotype estimation of a subject. It is worth noting that even if the subject is not familiar with an AD status of a parent or grandparent, the model simply assigns an APOE4 genotype estimation equal to the prior probability.The strength of our work is that it provides a low cost rough estimation of AD onset that is accessible to members of the general public and provides concerned individuals lifestyle modification factors that affect the risk of AD. Secondly, the Bayesian approach to determining APOE4 genotype is a novel method of determining a specific genotype and could be adapted to the prediction of other disease such as BRCA genotypes for individuals with breast cancer.In addition to the strengths of our work that we have identified, our work has a number of important limitations that must be identified:We added the hazard ratios from different factors  to obtain a cumulative hazard ratio. In reality, different hazards act in a confounding, not an additive, fashion. However, we found no individuals in our dataset that had the both of the greatest risk factors for AD (T2DM and TBI). The result of this limitation is that in the highly improbable case where an individual has a high probability of APOE4 +/+ genotype, low educational attainment, and a history of T2DM and TBI, the predicted AD onset would be in excess of 100% at a certain age. Whether a subject with multiple co-morbidities and such a poor prognosis would actually live to this theoretically certain age of AD onset would be the subject of conjecture.Because this model relies heavily on the APOE4 genotype prediction, this methodology only estimates AD onset, not the onset of dementia of different aetiologies such as vascular dementia.AD has overlapping diagnostic criteria with other aetiologies of dementia and differentiating AD is somewhat problematic. For this reason, an individual may have been incorrectly diagnosed with AD thereby influencing the APOE4 genotype estimation of his progeny.This model makes no prediction of EOAD onset.The difference between AD onset risk for healthy individuals (12.2%) vs the risk of AD for people who displayed AD symptoms (15.9%) highlights the highly sporadic nature of LOAD. Despite these limitations, this work can still serve as a theoretical framework for future studies with sufficient resources to conduct large scale clinical trials to validate the hazards for different factors and provide a more accurate tool for the prediction of AD onset.S1 File(XLSX)Click here for additional data file.


Crowding in the emergency department (ED) is associated with increased mortality, increased treatment cost, and reduced quality of care. Crowding arises when demand exceed resources in the ED and a first sign may be increasing waiting time. We aimed to quantify predictors for departure from the ED, and relate this to waiting time in the ED before departure.N = 17,520). We build a transition model for each time step using the number of past departures and pre-specified risk factors  to predict the expected number of departures and from this the expected waiting time in the ED. The model was validated with data from the same ED collected March through August 2014.We utilised administrative data from the ED and calculated number of arrivals, departures, and the resulting queue in 30 min time steps for all of 2013  corresponding to additional 7 min waiting time per new arrival in a 30 min time interval with an a priori time spend in the ED of two hours. The serial correlation of departures was present up to one and a half hour previous but had very little effect on the estimates of the risk factors. Boarding played a negligible role in the studied ED.We present a transition regression model with high predictive power to predict departures from the ED utilising only system level data. We use this to present estimates of expected waiting time and ultimately crowding in the ED. The model shows good internal validity though further studies are needed to determine generalisability to the performance in other settings.The online version of this article (10.1186/s12874-019-0710-3) contains supplementary material, which is available to authorized users. Crowding in the emergency department (ED) can be defined as a situation where demand exceed the resource supply  and is associated with increased mortality, increased treatment cost, and reduced quality of care –7. AspliWhile several studies –15 have https://www.strobe-statement.org).The aim of the present study was to model the probability of a departure from the ED dynamically as a function of the number of arrivals and the queue length given weekday or weekend and work shift  thus quantifying the effect of these previously identified risk factors for crowding in the ED . We willWe obtained data from the ED unit at Aarhus University Hospital, Denmark. The ED attends to approximately 40,000 patients per year from an uptake area of 330,000 inhabitants and receives all acute orthopaedic, trauma, and unstable medical patients from this area. Patients with other surgical and medical needs are also attended in the studied ED though not exclusively in this unit. Patient groups that are not received in the ED include medical paediatric and psychiatric patients as well as patients with cardiac arrest and myocardial infarction . When admitted to the ED unit patients are treated and discharged or admitted to the hospital. See Additional file We used an open cohort design including patients from 1. January 2013 to 31. December 2013. From the Electronic Health Records (EHR) we obtained data on arrivals to and departures from the ED including time stamps. The total number of arrivals was 41,693.N = 24 * 2 * 365 = 17,520). The queue length at the beginning of a new interval (t + 1) was calculated from the queue length, number of arrivals and departures in the previous interval (t):We created an aggregate data set with census of arrivals A(t) and departures D(t) in 30 min intervals  = 0.To mirror the clinical setting we defined a day as beginning with the day shift at 7 a.m. with each work shift lasting eight hours. To reduce the effect of the arbitrary choice of the initial queue length (Q(0) = 0) the first three shifts of the study period were excluded in the statistical analysis.| t-1) is the probability of a departure in time step t dependent on past values.We expected serial or lagged correlation of the departures  and thus utilised a transition model for each time step (present departures) with conditional analyses on past departures (as predictor variables) together with the pre-specified predictor variables (risk factors) to predict the expected number of present departures . The traIn binomial regression models it is standard to express the probability p for given values of the predictors through the logit function (as in logistic regression):In our setting we used this expression for each time step with predictors that include both the number of past departures to handle the time dependent transition step and the pre-specified predictor variablesDue to the logit model each regression parameter can be expressed as an odds ratio (OR) by exp(β(i)) = OR(i).The pre-specified predictor variables were new arrivals, weekday/weekend and shift  since these have been shown to be important risk factors for crowding . We alsoWe will use “waiting time” in the meaning of “waiting to leave the ED”, synonymously with the term “length-of-stay” (ED LOS), counting from the time of arrival until the time of departure from the ED disregarding the fact that much imperative work - such as assessment, treatment etc. - is being done during this time. Thus, here “waiting time” is a matter of queueing terminology and should not be taken literally.Assuming that the queue length is in steady state the number of departures will follow a geometric distribution and hence the expected time spend from arriving to the ED in a given 30 min time interval until leaving the ED (immediate waiting time) can be estimated in hours aswhere p is the probability of a departure. The ratio between waiting time in two scenarios with departure probabilities p(1) and p(0) isthat is, the inverse OR between the departure probabilities can be interpreted as the factor by which the expected waiting time changes.From the binomial model we calculated for each time step the expected number of departures (fitted) as E(t + 1) = E(D(t + 1)) = n(t + 1) * p(t + 1 | t), where p(t + 1 | t) is considered as the one-step-ahead prediction for the probability of departure and is estimated through the logit-expression given above. We plotted the standardised residuals against the fitted values to check for the assumptions of linearity, homoscedasticity, and independent errors Fig. . To confWe used a new dataset from the same ED but collected during 6 month of 2014 (March 1st to August 31st) to evaluate how well our final model captures the observed data. We evaluated the model fit the same way as for the model presented above but using parameter estimates from the original data . The code is available together with a constructed example of the dataset in the GitHub repository In the study period, approximately 3% of the patients stayed less than 30 min in the ED and 5% stayed longer than 5 h. The ED had 19 beds and was staffed with 4 to 8 nurses depending on time of day and week. A detailed description of the study population and site can be found in .The serial correlation on previous departures was present up to one and a half hour previous (OR = 1.008 to 1.012).New arrival (OR = 0.942) and change in queue length (OR = 0.978) had the greatest impact on lowering the odds of a departure. In a “standard scenario” of weekday day shift, with an empty queue for at least the past one and a half hour the waiting time for one patient arriving to the ED is given by the transition model asSee Table p <  0.0001) with a higher probability for a departure in weekends evening and night shift as compared to weekday day shift  and unpredictable (e.g. accidents and unrecognised epidemics) events. This number will, to a high degree, be random and hence hard to predict and to base any action upon. Contrary, a rise in the queue length as compared to the past 30 min time interval is easily monitored and is associated with a decreased probability of a departure as well. It indicates a vicious cycle beginning  and may very well be an early sign of crowding in the ED which can be countered. The Plan-Do-Study-Act tool could be utilised in implementing such intervention .The pre-determined predictors’ coefficients were nearly unchanged when we did not include the serial (departure) correlation in the model. This indicates that it is to a lesser degree the throughput processes that affects whether or not a patient is likely to spend a long time in the ED: The “internal system” (throughput processes) remains the same through 30 min intervals. This is in accordance with our previous results and other studies , 11 thouContrary to the conclusion of Bashkin et al.  we foundThe chosen binomial model assumes that the probability of departure is homogeneous across patients in a given time interval, but it seems likely, that heterogeneity in e.g. triage scores (red patients) can cause heterogeneity in the departure probabilities. Due to the number of missing values on the triage score this predictor could not be included in the model.All diagnostics as well as Fig. The EHR contains prospectively collected data to be used in a clinical setting. This makes EHR a secondary data source when used in research: We (the researchers) had no control over the data collection process, which might make EHR data questionable for research . The timWe present a regression model to predict departures from the ED in the absence of boarding. We use this to present estimates of expected waiting time and ultimately crowding in the ED. Our model follows the recommendations by McCarthy et al.  for measAdditional file 1:Table of characteristics of the emergency department and the patients. Friday and Saturday nights were considered part of the weekend. *The ED unit has two additional beds reserved for trauma call patients. Adapted from Eiset et al. (TIF 1490 kb)Additional file 2:Figure of diagnostic plot for the validation data (six month of 2014). See main text, Figs. Additional file 3:Figure of arrivals, departures (observed and expected), and queue length in the study period. The 12 days have been randomly chosen (one for each month in 2013) eight times. Departures are plotted as negative for visualisation. Abbreviations: obs., observations; expt., expected; arr., arrivals. (PDF 1111 kb)Additional file 4:Table of the expected waiting time in a scenario with few and many arrivals. Two examples of the number of arrivals and departures, the resulting queue length and probability of departure, and the waiting time estimate based on this data. The examples are chosen to show the contrast of a day with few arrivals and a day with many arrivals  of the waiting time on the 20th October and 5th September 2013. The median estimated waiting time was 1 h and 48 min (IQR = 27 min) on the 20th October and 2 h and 13 min (IQR = 40 min) on the 5th September. The notch indicates the estimated 95% confidence interval for the median. The individual observations are jittered. See Additional file


The objective of this study is to investigate the performance of a serpentine channel for acoustically driven selective particle filtering. The channel consists of sharp corners and straight sections, and the acoustic field is affecting the particles throughout the channel. A prototype of the separator channel is manufactured using 3D printing. Acoustic waves are generated by a piezoelectric transducer operating near 2 MHz. Computer simulations are carried out to explore and visualize the flow field and acoustic field in the separator. Selective particle trapping is aimed to be achieved in the hairpin sections, which is confirmed by experiments. Spherical polyethylene particles of 34 µm, 70 µm and 100 µm diameter are used to demonstrate selective trapping by adjusting the flow rate in the channel or voltage input to the transducer. In addition, wheat beer containing yeast up to 20 µm size is selectively filtered by adjusting the flow rate to the channel. Experiments demonstrate that selective particle filtering is possible in the serpentine channel as both methods yield clear separation thresholds. In the micrometer-scale, acoustophoresis is one of the methods for particle filtering in solid-liquid mixtures among inertial, gravitational, magnetic and optical methods6.Manipulation of particles by acoustics is known as “acoustophoresis”. Applications of acoustophoresis cover a wide range of applications, from centimeter-scale9. Particles are aggregated by virtue of the acoustic radiation force and sedimentation is thus enhanced. This method can be combined with flow fields to selectively retain viable cells13. Apart from enhanced sedimentation, most applications in acoustophoresis utilize a single acoustic node in the separator channel. Since the frequency is often high and the wavelength is therefore low, dimensions of such channels are in micrometer range. Hence, these are referred to as microchannels. Selective separation for model particles and bioparticles using microchannels are demonstrated in a number of studies18. Selective particle retention and fractionation can also be achieved with methods other than enhanced sedimentation and acoustophoresis. Examples are inclined sedimentation19, dielectrophoresis22, and flow manipulation25. Acoustic filtering can be an alternative for existing applications in food processing6. For example, in rough beer filtration processes, membranes recently offer a competitive alternative to traditional kieselguhr method28. The potential of acoustic filtration is yet to be explored for this application. Possible benefits include the absence of fouling, no addition of chemicals, not having internals and less cleaning requirement.Enhanced sedimentation is one of the common applications of acoustophoresis in particle-liquid separation29, but also by employing multiple nodes. To have multiple nodes in the resonator, the resonator dimensions must be around multiple wavelengths at the excitation frequency. In such systems, it is also possible to employ relative motion between the fluid flow and the acoustic field, by either pushing the flow against the acoustic field or creating a dynamic acoustic field30. Recently, multi-wavelength setups utilizing surface acoustic waves have been proposed31. A review on multiple wavelength resonators was done by Hawkes et al.32.A disadvantage of a single node channel is the relatively low throughput. The throughput can be increased by operating multiple set-ups in parallel33. Later, an expression for compressible particles in a generic acoustic field was developed by Gor’kov34. As compared to traveling wave fields standing wave acoustic fields have higher energy density, thus leading to higher time-averaged forces33. In acoustic standing wave separators particles are trapped in specific grid points , thus making it possible to separate particles from the suspension6.To understand acoustic particle filtering, it is crucial to know how the acoustic field affects particles. A body in an acoustic field experiences a force called acoustic radiation force. Expressions for the acoustic radiation forces on spherical particles were presented by King, for traveling and standing wave fields35. Interestingly, some particles are trapped with relatively lower effort compared to others as acoustic radiation force scales with particle properties such as volume, density and compressibility while drag force scales with particle size. Such diverse behavior can be used in selective filtering using acoustic fields.Depending on the particle properties, acoustically different particles can be forced to different locations in the same acoustic field. When a particle moves relative to the liquid, the particle will also experience a so-called drag force. If the liquid flow is characterized by a low Reynolds number, the drag force is typically modeled as Stokes drag force40. Thus, the dominant external forces on a particle in an acoustic field are drag force and acoustic radiation force. Being able to adjust those external forces enables the particles to be selectively trapped. If the particles are pushed relative to the acoustic field by the fluid flow, the drag force can be controlled by the fluid velocity whereas the acoustic force can be controlled by the voltage input to the system. A serpentine channel consisting of hairpins and linear sections can be used to control the fluid flow and acoustic input.Combining those external forces on particles, the equation of motion for a particle can be constructed, which is a second-order nonlinear ordinary differential equation. In general, particle trajectories can be calculated numerically, but under some assumptions analytical solutions are also possible. The solution of the equation of motion can be combined with the flow profile in the separator, leading to more complex modelingThe aim of this study is to investigate the possibility for selective filtering in an acoustophoretic serpentine channel and to demonstrate it on solid polyethylene particles and on wheat beer flocs. The width of the channel is such that multiple wavelengths at operating frequencies fit in the channel. Furthermore, the channel dimensions and shape are chosen such that particles are trapped in multiple nodal locations, while keeping the liquid flow inside the channel close to laminar. The serpentine structure has low velocity hairpin turns connected by straight sections. Drag force on the particles becomes weaker in the hairpins and the straight sections ensure that the flow becomes fully developed before entering the hairpins. This selective filtering ability is shown in computer simulations and in experiments using a 3D printed prototype, by adjusting the flow rate in the channel or voltage input to the system. Model polyethylene particles of 34 µm, 70 µm and 100 µm diameter are used to demonstrate the ability of selective particle separation in the prototype by either changing the input flow rate or voltage input to the transducer. The other test mixture, wheat beer, contains yeast up to 20 µm in size and has a more or less continuous size distribution of yeast particles. Wheat beer is used to demonstrate the ability to selectively separate compressible flocs by changing the input flow rate.The experimental set-up consists of a signal generator (Keysight Trueform 33512B), a custom-made amplifier, an oscilloscope (Tektronix TDS2024C), a syringe pump (Aitecs PRO SP-12S) and the separator prototype, Fig. Two particle mixtures were used in the experiments. Mixture (1) contains model spherical polyethylene particles with known dimensions and density. Mixture (2) is a commercially available wheat beer.−1 of the surfactant CTAB (Hexadecyltrimethylammonium bromide), 0.99 mM HCl and 0.02 g L−1 of each particle type, while multiple bottles of mixtures are consumed during the experiments. CTAB prevents the particles from aggregating and the PMMA cover whereas HCl prevents the particles from sticking to the PLA parts. Mixture (2), Hoegaarden wheat beer, contains dissolved carbon dioxide in very small bubbles and it produces foam when moved or shaken. To be able to remove all carbon dioxide the beer mixture was acidified. The acidification shifts the carbonate equilibrium towards carbonic acid and dissolved carbon dioxide. The gas was removed by keeping the solution under vacuum for 2.5 hours.The properties of particles of mixture 1) are listed in Table  are list41. Whether particles got trapped or not was first checked by observing the experiments live and later verified by analyzing the particle trajectories using ImageJ. Separation thresholds were adjusted by changing the voltage input or flow rate for mixture (1). Prior to operation, the admittance of the system, filled with degassed MilliQ water and particle mixtures, was measured with an impedance analyzer (HP 4194 A) between 1800–2000 kHz. Computer simulations were carried out to compute the acoustic field, where a frequency of 1979 kHz was selected as excitation frequency, since at 1979 kHz the acoustic field appeared to be the most favorable for trapping in the hairpins. Admittance calculations by computer simulation, with an isotropic structural loss factor of 0.1 included in the PLA material, suggested that there is more than one resonance in the frequency range of 1800–2000 kHz. The selected frequency of 1979 kHz coincided with the frequency of minimum imaginary admittance in the simulations. In the measurements the phase is closest to zero at 1924 kHz in mixture (1) and 1972 kHz in mixture (2) indicating the minimum imaginary admittance occurs there. Thus, excitation frequencies for both mixtures are chosen accordingly. For mixture (2), separation threshold was adjusted only by changing the flow rate. After separation, the particle size distributions were analyzed with a DIPA 2000 particle size analyzer.During the treatment of mixture (1), the selective separation thresholds were determined visually using a microscope with camera and ImageJThe dimensions of the acoustic separator allow for multiple wavelengths in the operating frequency range. Ideally, in this type of resonator the acoustic field is a one-dimensional standing acoustic plane wave field. The equation of motion for a spherical particle in such a field is given byr is the particle radius (m), y is the distance of particle from the source (m), ρ0 is the density of the medium (kg m−3), c0 is the speed of sound (m s−1) in the medium, P0 is the amplitude of the sound pressure (Pa), ω is the angular frequency of excitation (rad s−1), k is the wavenumber (m−1) and Φ is the acoustic contrast factor. The acoustic contrast factor is a measure on how much the particle differs from the surrounding media in terms of acoustics36. Particle density is denoted by ρ whereas c represents the speed of sound in the particle, μ is the dynamic viscosity (Pa s) of the medium, u is the velocity (m s−1) of the flow in the direction of acoustic radiation force. With a known acoustic field and particle properties, Eq.  area in Fig. In order to gain insight of the properties in the system, first computer simulations were carried out to calculate the resonance frequencies, the acoustic field and the flow field. Excitation frequency of the system was selected based on admittance measurements and simulations. A simulation plot of the acoustic field corresponding to 1979 kHz is given in Fig. −1 and (b) represents the flow for an input flow rate of 500 mL h−1. For a flow rate of 100 mL h−1 Reynolds number is around 5. The channel provides a fully developed flow in the middle sections and for a flow rate of 500 mL h−1 the Reynolds number is around 25, indicating that the flow inside the channels is indeed close to laminar. Higher Reynolds numbers affect the flow especially around the corners, resulting in leaning as can be seen in Fig. The flow field was computed in COMSOL Multiphysics and given in Fig. −1 flow rate  is pumped through the experimental flow cell with a constant flow rate of 100 mL hpp across the transducer. When increasing the voltage first the largest particles (blue) were retained in the system with 26% of the maximum voltage, followed by the largest and medium (orange and blue) particles with 48% of the maximum voltage. Lastly, all particles including the smallest (red) particles were retained with 96% of the maximum available voltage . Voltage input was set to 50% of the maximum available voltage and the flow rate is changed step-wise. Figure −1, 80 mL h−1, 50 mL h−1 and 20 mL h−1, respectively. Figure −1 filtered the particles larger than 17 μm and with 20 mL h−1 flow rate particles larger than 9 μm were filtered.While processing mixture (2), the wheat beer, the acoustic separator was operated at 1972 kHz and at the maximum voltage as the size of the particles are small and acoustic contrast factor is unknown. Flow rate in the syringe pump was adjusted to 100 mL hExperiments and simulations confirm that the particles are trapped at the hairpin sections. Acoustic forces are acting in the vertical direction and the flow speed in vertical direction is lower in the hairpin sections. The acoustic force experienced by particles is large enough to counter the drag force around the hairpins. Ideally the acoustic field is a plane acoustic wave field and therefore the peak acoustic pressure is similar throughout the field. If the acoustic force is large enough to trap a particle in the middle of the channel, it can also trap the particle at the hairpins due to a locally lower velocity in vertical direction Fig. . The aimThis study demonstrated the possibility for selective filtering in an acoustophoretic serpentine channel. Interplay of the acoustic and drag forces results in particle trapping in hairpin sections, and multiple hairpin sections provide multiple areas for particles to be retained. The acoustic field inside the prototype may be improved by changing the inside wall material with a material that provides stronger reflections than PLA. Ensuring that the flow will be laminar and fully developed before entering the hairpins, shortening the linear sections and therefore the distance between the source and reflector would also provide stronger acoustic field. With a stronger acoustic field, the separator can be operated more efficiently and with higher flow rates.A standing wave acoustic field is generated by a piezoelectric transducer and the resulting acoustic radiation force is able to selectively trap particles in the hairpin sections of the serpentine separator. Simulations confirm that particles are captured in the hairpins of the separator. A single hairpin does not capture all targeted particles, but as the system contains multiple hairpins, effective particle trapping is ensured. Selective separation is achieved by changing the voltage input or flow rate in the case of model polyethylene particles. For wheat beer, the separation threshold is tuned by changing the input flow rate only. Both types of experiments demonstrated clear separation thresholds. Decreasing the flow rate or increasing the power input moves the threshold towards smaller particle sizes while increasing the flow rate or decreasing the power input creates the opposite effect. The efficiency of the system can be improved by adjusting the channel dimensions and reducing the losses in the system; stronger acoustic field will result with higher throughput possibility.