A fully integrated sensor interface for a wide operational temperature range is presented. It translates the sensor signal into a pulse width modulated (PWM) signal that is then converted into a 12-bit digital output. The sensor interface is based on a pair of injection locked oscillators used to implement a differential time-domain architecture with low sensitivity to temperature variations. A prototype has been fabricated using a 180 nm partially depleted silicon-on-insulator (SOI) technology. Experimental results demonstrate a thermal stability as low as 65 ppm/°C over a large temperature range from −20 °C up to 220 °C. An increasing demand for electronic systems working at temperature up and even beyond 200 °C has appeared over the last years for critical applications such as oil drilling, automotive and/or aeronautic uses ,2,3. In Considering the constraint of thermally stable performance, time-domain sensor interfaces have appeared that are more competitive than classical analog sensor interfaces ,7,8,9. TFrequency-based time-domain architectures are based on voltage controlled oscillators (VCOs). They usually suffer from the high non-linearity of the oscillator frequency with respect to the tuning voltage . RecentlOriginally, PWM time-domain sensor interfaces were introduced to generate quasi-digital output signals which are less sensitive to noise coupling when transmitted compared to analog signals. Usually, PWM readout circuits are based on a periodic ramp generation whose output is compared to the analog quantity to be converted. The duration of the generated PWM equals the time difference between the ramp beginning and the comparator decision time, which is in turn proportional to the voltage to be converted. However, thermal stability of PWM-based readout circuits is affected by the thermal stability of the offset voltage of the comparator and of the ramp slope. What’s more, in typical PWM techniques, the degradation of the non-linearity of the ramp slope over the operation temperature range degrades the overall performance of the so-obtained PWM signal. De Smedt et al. in , proposeIn this paper, a new PWM-based sensor interface architecture that is able to operate over a wide temperature range is presented. It is based on the use of two injection locked relaxation oscillators to convert the transducer analog output into a PWM signal whose pulse width is defined by the difference of phase between both oscillators. Contrary to previous published works, where the PWM signal is transmitted into an ambient temperature environment for performing the signal processing , the sigThe paper is organised as follows: The proposed voltage to PWM conversion is based on ILOs used as phase shifters. The so-obtained pulse width is proportional to the phase shift of the ILO with respect to a reference signal. This section briefly recalls the ILO-based voltage to PWM conversion which is behind the principle of the sensor interface architecture.ILOΦ is the ILO phase shift , SV0 is the voltage magnitude of the locking signal and I0 the output current magnitude. FE is a called compliance factor (|FE| is its amplitude and β is its phase) which is the ratio of the variation of the oscillator frequency with respect to the impedance variation. syncf is the locking signal frequency and f0 is the oscillator free running frequency. It is well known that an oscillator can be locked on a parasitic signal if its frequency is close to the oscillator free running frequency  Figure . ILOs arOnce locked, the ILO output tracks the locking signal phase variation and Equation (1) could be rewritten as:Noting that cosinus function is lower than 1 and greater than −1, the locking range is easily obtained as:SV0, the oscillator output current magnitude I0 and the compliance factor FE which depends only on the oscillator topology [Thus, according to Huntoon and Weiss, the ILO locking range depends on the amplitude of the locking signal topology .From Equation (2), the ILO phase shift, once the ILO is locked, is extracted:Therefore, once locked, the ILO phase shift only depends on the difference between the locking and the oscillator free running frequencies and on the locking range. This property is very interesting as it allows the use of ILOs as phase shifters by keeping the locking frequency fixed and tuning the ILO free running frequency with an analog command as it is done for voltage or current controlled oscillators ,19. ThusSV is used to control the free running frequency of the ILO f0. Then, if a fixed locking frequency is used, the obtained phase shift ILOΦ is a function of the free running frequency and thus, the obtained phase shift is a function of the input voltage SV.The proposed PWM circuit is based on the previously mentioned properties of ILOs. The sensor voltage pwt between the locking signal syncV and the ILO output ILOO is linked to the ILO phase shift by Equation (5) and it is hence a function of SV tpw=ϕcounterT) is syncT/M (M is the PLL (Phase Locked Loop) frequency multiplication factor), the TDC output is given by:Since the counter resolution  and (6) is written as:Based on Equations (3) and (4) from Huntoon and Weiss theory, the digital output of the sensor interface is expressed as:syncf has the same temperature dependency as the ILO free running oscillator f0. Hence, their difference (syncf − f0) will be insensitive to temperature variations. What is more, the ratio between |SV0| and |I0|  can be made insensitive to temperature variations if they have both the same temperature coefficient. This can be achieved if, for example, SV0 is derived from the same biasing circuit as that of the oscillator. Moreover, the frequency multiplication factor M is temperature independent. In fact, the frequency multiplier  is designed to be always locked whatever temperature is; thus, it realizes the same frequency multiplication factor all over the operation temperature range. In addition to that, the compliance factor FE depends on the ILO passive components (capacitances for example) which have a low temperature coefficient; hence FE has a low thermal variation. As a consequence, a low temperature dependence could be expected for the digital output of such sensor interface architecture.The locking signal is generated from an oscillator having identical topology as that of the ILO free running oscillator, thus, the locking frequency syncf and the ILO free running frequency f0 (Equation (8)). Indeed, the linear behaviour of the acos function is limited to a phase shift range of π/2. Therefore, the linear range of the harmonic ILO-based PWM sensor interface will be limited to half of its dynamic range (the full dynamic range corresponds to a phase shift range of π).This architecture principle is adapted to any kind of ILOs and it leads to low temperature sensitivity. Nevertheless, in the case of harmonic locking signal, the overall architecture is limited by the non-linearity of the acos function that links the digital output to the frequency difference between the locking frequency In this paper, we introduce an ILO having an extended linear range which is based on a relaxation oscillator and a non-harmonic injection scheme . An ILO The chosen ILO is based on a relaxation oscillator as depicted in ILO is equal to zero, meaning that the D-flip-flop (DFF) output Q is at logic “1”, M1 is on while M0 is off. C2 is shorted to ground through M1 while C1 is charged by a bias current I0. When the voltage across C1 reaches the threshold voltage of the inverter inv1 thV, the DFF is reset  and ILOO is equal to the supply voltage Vdd. Hence, M1 is turned off and M0 is turned on, then C1 is rapidly discharged while the capacitor C2 is charged by the same bias current I0 until the voltage across C2 reaches the threshold voltage of the inverter inv2 thV. Consequently, a rising edge appears on the clock input of the flip-flop and it switches the DFF output to Vdd and ILOO to zero. The same cycle is then repeated and the frequency of oscillation depends on I0, thV, C1 and C2. Each ILO is composed of a free running oscillator and a sub-circuit for locking this oscillator with the locking signal as depicted in C for C1 and C2. The free running oscillation frequency is expressed as follows:C = C1 = C2. A change in the value of I0 can easily and linearly modify the free running oscillation frequency.Inverters inv1 and inv2 are used to ensure a square waveform signal at the DFF clock and reset inputs. The output of the ILO achieves a 50% duty cycle by adopting the same value syncf. The locking process uses a synchronization current syncI that is either pulled from or pushed into the capacitors of the ILRO. This current is subtracted or added to the bias current I0 according to the value of the locking signal syncV. For example, in addition to I0, a current −syncI flows into C2 at high level of syncV, while at low level of syncV, a current +syncI is added to the charging current of C2. Knowing that C2 can be charged only when the ILO output is at high level, a delay is created between syncV and ILOO as described in The locking process is performed by periodically modifying the charging current of the capacitors at the locking frequency rate, in such a way that the average charging current on a locking period equals the current which makes the oscillator run at the locking frequency dt, syncI and I0 as expressed in:The average charging current of the capacitors is a function of this delay averageI equal to the current necessary to get an oscillation frequency which is the same as the locking frequency (syncf):As explained before, the so-obtained delay is adjusted in order to make the average charging current of the capacitors ILOΦ, representing the delay between syncV and ILOO, can be expressed as:Using Equations (9)–(11), the ILO phase shift syncf − f0) is obtained, which is a clear benefit compared to harmonic ILOs.Equation (12) shows that a perfect linear relationship between the ILO phase shift and the frequency difference between the locking frequency and the ILRO free running frequency  which is in accordance with the theory. A goodness-of-fit of linear regression (R2) of 0.999 is obtained.I0:Combining Equations (9) and (12), the phase shift of the ILRO is a linear function of the ILO bias current I0 is linear with respect to the sensor output voltage, the relation between the ILRO phase shift and the sensor output is linear.Assuming that the current The proposed sensor interface, depicted in I01 − I02. The OTA output currents I01 and I02 are then used to control the free running frequencies of ILO1 and ILO2 respectively and thus to control their phase shifts . The differential architecture adopted for this interface has the advantage of rejecting the effects of temperature, process variations and common mode noise. As the output of the Wheatstone bridge is a differential voltage, a transconductance amplifier (OTA) is used to convert the sensor output voltage into a differential current SV is equal to zero, both output currents of the OTA are the same and both ILOs have the same free running oscillation frequency, and hence the same phase shift . Then, when SV is different from zero, the output currents of the OTA are fed into the ILOs, thus, obtaining a simultaneous and opposite variation of their free running oscillation frequencies f01 and f02 (f01 and f02 are respectively the free running frequency of ILO1 and ILO2) while their locking frequency is kept constant. This makes their phase shifts, ILOΦ1 and ILOΦ2, vary symmetrically as a function of the sensor output voltage SV. The difference between the two ILOs phase shifts, i.e., ∆Φout = ILOΦ2 − ILOΦ1, defines the time-domain output of the sensor interface.When the sensor output voltage syncV is up, a PWM signal is obtained whose pulse width is defined by ∆Φout. Connecting the two ILOs outputs to a simple Exclusive-OR logic gate that is active only when the locking signal counterf is, the higher the resolution of the digital output is. Equation (14) expresses the resolution of the sensor interface:The obtained PWM signal is then quantized by means of a simple digital counter in order to obtain a digital output value of the sensor output voltage ,21. The syncV and the counter clock counterf.A high frequency reference oscillator, implemented on the same chip, is used to generate both the locking signal The counter frequency is generated from this reference oscillator by means of a PLL that realizes a multiplication factor of 256. The same reference oscillator is used to generate the locking signal by means of a frequency divider having a division factor of 16. This choice has been adopted in order to obtain a 11-bit resolution.syncf and a PLL realizing a multiplication factor of 4096 that generates the counter clock. In fact, it was decided to lower the PLL multiplication factor to 256 for the sake of its bandwidth. The intermediate reference oscillator runs at counterf/256. That’s why, the frequency divider must realize a division factor of 16 so that the ratio counterf/syncf equals 4096.The choice of using an intermediate reference oscillator has been adopted as an alternative to the use of a reference oscillator running at SV by detecting which ILO output is in phase advance. For example, when SV is positive, the output of the first ILO1 is in phase advance with respect to ILO2 output , an additional bit is used to detect the polarity of the sensor output voltage 2 output b.syncI. It is based on a bandgap voltage reference as shown in BiasR is the bias resistance of the biasing block and BGV is the bandgap voltage reference.The biasing block generates the synchronisation current of the ILO GMI, which is the bias current of the OTA, is generated from the synchronisation current by means of a current mirror.The current SV into two currents with symmetrical variations, I01 and I02, which are the bias currents of ILO1 and ILO2 respectively. As the first block encountered in the sensor interface, the linearity of the OTA is an essential specification so that the sensor interface achieves a good linearity. A degenerated OTA with local feedback is adopted to reach the linearity requirement [The transconductance amplifier (OTA) converts the sensor output voltage uirement ,23. Figuuirement .GMR is the resistance of the OTA  and (16), the difference between the two ILOs phase shifts, Using Equations (15) and (19) can be written as:Then the digital output of the sensor interface is:In this interface, the Wheatstone bridge is biased by the bandgap voltage reference used for the biasing current generation as depicted in SV is expressed as:In this condition, the sensor output voltage BGV is eliminated. Hence, the sensor interface output depends only on a ratio of two resistances and a ratio of two frequencies as written below:Consequently, by combining Equations (21) and (22), the contribution of counterf/syncf is temperature independent because the PLL and frequency divider use the same reference frequency. Moreover, all the resistors embedded in the resistive Wheatstone bridge are of the same nature so that the ratio of resistances is also independent of the temperature variations. Furthermore, using the same kind of resistance for BiasR and GMR, their temperature coefficient is the same and their ratio  is then insensitive to temperature variations. For these reasons, the thermal dependency of the digital output should be low.Therefore, a low temperature dependency is achieved. Indeed, the ratio The sensor interface is initially designed to interface sensors with an output voltage having a dynamic range of ±60 mV. In fact, the ILO phase shifter has been designed so that the 60 mV input range corresponds to the maximum π phase shift. However, the simulations and experimental results presented in this paper are limited to a ±40 mV input dynamic range because better performances are obtained on this input range compared to the performances obtained on the overall ±60 mV input dynamic range .SV.The sensor interface is simulated as a function of an input voltage having a ±40 mV full scale which emulates the sensor differential output voltage N as a function of SV) is represented in The characteristic function the sensor interface .A zero thermal variation is obtained at zero Simulation results show also the good linearity of the sensor interface. The simulated INL, which is defined as the ratio of the difference between the simulated value and the linear fitted value over the linear fitted value, is lower than 0.15% over the wide operation temperature range . This goProcess variation and mismatch may increase the temperature dependence of the sensor interface. SV of 20 mV, the average thermal variation over process and mismatch is close to that obtained in the simulation, while for a SV of 40 mV, the average thermal variation over process and mismatch is much higher than that obtained in typical simulation. It can be concluded that for a higher sensor output voltage SV, the effect of process variation and mismatch is more pronounced.Thermal stability of the sensor interface over process and mismatch has been assessed with the help of Monte Carlo simulations. The obtained results are presented in The wide-temperature-range sensor interface has been fabricated using the 0.18 μm Partially-Depleted Silicon on Insulator (PD-SOI) technology from XFAB France , .For experimental measurements, the circuit has been packaged in a DIL-40 package and it has been tested on a high temperature printed circuit board (PCB). The sensor output voltage is emulated through an on-board differential signal generator (with no temperature dependence) and the prototype is placed under the nozzle of a thermal conditioner  to vary its temperature from −20 °C to 220 °C, which are the minimum and maximum temperatures of the thermal conditioner .SV for different temperatures from −20 °C to 220 °C.SV. Nevertheless, the sign of SV is given by the available lead/lag bit  that permits to discriminate negative values of SV from positive by detecting which ILO output is in phase advance. This lead/lag bit, not shown in SV and at 0 logic level for a negative one.It is worth mentioning that no calibration circuit is used either to compensate the thermal variation of the sensor interface output or to calibrate the gain error and offset. From the measured characteristic function of the fabricated prototype presented on SV has a non-zero thermal variation. This is because the fabricated sensor interface exhibits a certain output offset which is mainly due to mismatches and which is sensitive to temperature variations.Unlike what is obtained by simulations, the sensor interface output at zero Precisely, the obtained offset is due to the mismatches inside the OTA which create a dissymmetry between its output currents. These mismatches could be reduced by using transistors with larger size.SV into a digital output N with goodness-of-fit of linear regression higher than 0.998 (R2). Over this wide operation temperature range, the fabricated sensor interface converts the differential input voltage As a conclusion, the performances of the fabricated sensor interface are similar to that obtained in both typical and Monte Carlo simulations . Neverthf0(I0) (where f0 is its free running oscillation frequency and I0 is its bias current). On the other hand, the OTA linearity may be degraded by process variations. Since it is the first block of the sensor interface, this degradation could be at the origin of the high measured INL of the sensor interface. Moreover, the sensor interface has an open loop architecture. Then, a closed loop calibration could be considered in order to improve the linearity of the sensor interface. In order to better understand the origin of the high measured INL, further investigations are required.The fabricated sensor interface does not however achieve the expected linearity; the measured INL is higher than simulated one. This may be explained by the effect of process variations. On one hand, process variations could degrade the linearity of the ILO transfer function However, it is not possible to bypass the use of OTA because the sensor output voltage conversion into a current is required in order to use current controled oscillators (CCOs)  and to benefit from their high linear behaviour. The use of voltage controlled oscillators (VCOs) instead of CCOs could allow one to overcome the OTA imperfections. However, VCOs generally suffer from a reduced linearity compared to CCOs and this would degrade the INL of the sensor interface.A time-domain differential sensor interface with a very large range of operating temperatures has been proposed. The concept is based on a fully differential architecture of the analog chain that leads to a very high immunity to temperature variations. Indeed, the digital output of the circuit depends only on the relative variation of few parameters and then only mismatches between identical components may induce some temperature dependence. A proof-of-concept has been designed and fabricated using a 0.18 µm partially-depleted SOI technology with 1.8 V power supply. Experimental results show that the sensor interface has an excellent temperature stability over a wide temperature range extending from −20 °C to 220 °C. The obtained result (−65 ppm/°C over an input range of ±40 mV) is, to our knowledge, the lowest temperature coefficient ever reported for a bit more than 11-bit resolution. An analysis based on experimental and Monte Carlo simulation results showed that the residual temperature dependence may be explained by mismatches. The use of larger area devices should permit to reduce this effect and thus to improve the level of performance.


The onset of bathing disability among older people is critical for a decline in functioning and has implications for both the individuals’ quality of life and societal costs. The aim of this study was to evaluate long-term cost effectiveness of an intervention targeting bathing disability among older people. For hypothetical cohorts of community-dwelling older people with bathing disability, transitions between states of dependency and death were modelled over 8 years including societal costs. A five-state Markov model based on states of dependency was used to evaluate Quality-adjusted life years (QALYs) and costs from a societal perspective. An intervention group was compared with a no intervention control group. The intervention focused on promoting safe and independent performance of bathing-related tasks. The intervention effect, based on previously published trials, was applied in the model as a 1.4 increased probability of recovery during the first year. Over the full follow-up period, the intervention resulted in QALY gains and reduced societal cost. After 8 years, the intervention resulted in 0.052 QALYs gained and reduced societal costs by €2410 per person. In comparison to the intervention cost, the intervention effect was a more important factor for the magnitude of QALY gains and long-term societal costs. The intervention cost had only minor impact on societal costs. The conclusion was that an intervention targeting bathing disability among older people presents a cost-effective use of resources and leads to both QALY gains and reduced societal costs over 8 years. Bathing disability is common among people older than 80 years  to allow analysis of long-term cost effectiveness. The design and reporting of the trial were based on the Consolidated Health Economic Evaluation Reporting Standards (CHEERS) statement  , is dependent in no more than a single instrumental activity of daily living (IADL)  and needs help no more than one time per week. Moderate dependency refers to a state in which a person is independent in PADL, is regularly dependent in more than one IADL and needs help more than one time per week. Severe dependency refers to a state in which a person is dependent in at least one PADL and more than one IADL and needs help one or several times per day. Total dependency refers to a state in which a person is dependent in PADLs and IADLs, needs extensive help throughout the day and lives in ordinary or special housing. The final state was death  (Jagger et al. ath Fig. . Althougath Fig. . In our ath Fig.  of help In order to extrapolate transitions in the levels of dependency in a cohort of older people, the best longitudinal data we identified were from a Canadian study by Raîche et al. including participants 75 years or older from the general population who were identified as being at risk for functional decline (Raîche et al. mild dependency, we used unpublished baseline data from an ongoing trial including 177 well older people (Zingmark et al. moderate dependency, we made an approximation reflecting a decline in ADL and IADL (Fusco et al. severe dependency and total dependency, respectively (Table Previous studies indicate that a decline in ADL (Fusco et al. ly Table . The QoLly Table . For exaTo estimate costs for each state, we used data from a Swedish cohort study demonstrating that the levels of dependency in ADL and IADL have a strong impact on total costs (Lindholm et al. in our model, we applied an intervention effect of 1.4 (Table The intervention modelled included rehabilitation that focused on improving a person’s ability to perform self-care tasks related to bathing. Based on previous trials, the content of the intervention included practical training sessions in the person’s home in which therapists focused on encouraging the person to gradually increase her/his ability and self-efficacy to perform bathing-related tasks (Lewin et al. .4 Table , indicatThe intervention cost included salaries and the cost for technical aids. The main analysis was based on an occupational therapy intervention (Zingmark and Bernspång ® Excel software (Menn and Holle >55,000 € as a high cost/QALY (The National Board of Health and Welfare We applied MicrosoftTo acknowledge uncertainty in parameter estimates, we conducted a sensitivity analysis. Firstly, we hypothesized that a reduced intervention effect and an increased intervention cost would reflect real-world variation that could affect cost effectiveness. Instead of a 1.4 increase in the probability of recovery from severe dependency to moderate dependency as an effect of the intervention, as assumed in the main analysis, we assumed a 1.2 increase of recovery in the sensitivity analysis. Secondly, we assumed that the intervention cost was higher reflecting the multi-professional intervention. We performed the analysis for each of the assumptions separately and both assumptions combined.In hypothetical cohorts of 100 people in each group, 17 in the intervention group and 12 in the control group recovered to moderate dependency by the end of the first year as a result of the intervention. The intervention had no direct impact on transitions after the first year. All transition probabilities from the second year were equal in both groups, as presented in Table The sensitivity analysis showed that the size of the intervention effect was a more critical parameter than the intervention cost. When the intervention effect decreased, both QALYs gained and cost savings were reduced, but the intervention still resulted in QALY gains and was cost saving compared to no intervention. Although the intervention costs were more than 4 times as high with the multi-professional intervention, the costs for the intervention were still small compared to other societal costs.In both the main analysis and the sensitivity analysis, the intervention resulted in more QALYs gained and lower societal costs compared to no intervention Table . The intThis study showed that an intervention implemented to reduce bathing disability results in QALYs gained and cost savings for up to 8 years compared to no intervention. In a hypothetical cohort of 100 people with bathing disability, the intervention resulted in 5.2 QALYs gained and approximately 240,000 € in reduced societal costs. Considering that bathing disability is common among older people (Gill et al. The results must be interpreted based on the modelling approach used. Any modelling approach is a simplification of a real-world scenario, and the validity of the results is dependent on the fit between the model and the real world (Pouryamout et al. While some studies indicate that older people with limited dependency in IADL or ADL have a high probability of remaining in the same state or recover over time (Hardy and Gill Our findings are consistent with recent studies that have demonstrated that an intervention that promotes independence in ADL has a significant impact on the use and costs of health and social care (Cook et al. The QALY gains estimated in this study can be considered low based on the follow-up period of 8 years, but is consistent with the findings from a review of cost–utility analysis in which the median QALY gain was 0.06 (Wisløff et al. We identified four studies in which interventions had been implemented that were occupation-based Fisher  and focuThe results also indicate that the intervention indirectly may have an impact on mortality. It is known that mortality is related to the degree of disability (Cook et al. The sensitivity analysis showed that the cost for the intervention minimally impacted the overall cost effectiveness, whereas intervention effectiveness seems to have had a more significant impact. Although the results indicate that the intervention was cost saving independent of time, it is relevant to consider the content of the intervention and how it is delivered. The low intervention cost supports the notion that the intervention could be expanded if additional effects were to be obtained. The tendency that the intervention effects decline after 3 months calls for further research to explore if the initial intervention effect could be sustained. According to our knowledge, no previous trials focusing on disability in bathing or personal care have implemented interventions beyond 3 months. However, considering the low cost for the intervention, practically negligible in relation to other societal costs, any additional gain in intervention efficacy is likely to further improve cost effectiveness.This study demonstrates that an intervention that supports recovery from bathing disability is very cost effective over both the short and long term. The intervention leads to QALY gains and saves costs at any follow-up until 8 years, and thus resources can be used to implement other interventions. The most important factor for the magnitude of QALY gains and cost savings is the intervention effect. In contrast to the societal cost for elderly care and accommodation, the cost for the intervention is very small, indicating that it is worthwhile to explore if additional intervention content, such as follow-up sessions, could further enhance the intervention effect. Although our model was based on empirical evidence, we acknowledge that further refinement of the model parameters could enhance the precision of estimates of QALYs gained and cost savings.


The statistical screening of pharmacovigilance databases containing spontaneously reported adverse drug reactions (ADRs) is mainly based on disproportionality analysis. The aim of this study was to improve the efficiency of full database screening using a prediction model‐based approach.A logistic regression‐based prediction model containing 5 candidate predictors was developed and internally validated using the Summary of Product Characteristics as the gold standard for the outcome. All drug‐ADR associations, with the exception of those related to vaccines, with a minimum of 3 reports formed the training data for the model. Performance was based on the area under the receiver operating characteristic curve (AUC). Results were compared with the current method of database screening based on the number of previously analyzed associations.A total of 25 026 unique drug‐ADR associations formed the training data for the model. The final model contained all 5 candidate predictors . The AUC for the full model was 0.740 . The internal validity was good based on the calibration curve and bootstrapping analysis (AUC after bootstrapping = 0.739). Compared with the old method, the AUC increased from 0.649 to 0.740, and the proportion of potential signals increased by approximately 50% (from 12.3% to 19.4%).A prediction model‐based approach can be a useful tool to create priority‐based listings for signal detection in databases consisting of spontaneous ADRs. The main aim of spontaneous reporting is the early detection of previously unrecognized adverse drug reactions (ADRs). In addition, spontaneous reporting can also be useful for obtaining information on new aspects of known associations between drugs and ADRs.Lareb has criteria in place for assessors to determine which reports should be discussed at the weekly scientific meeting. However, because multiple assessors are involved in this process and the selection of reports for the weekly scientific is prone to some level of subjectivity, a computer‐assisted database screening tool is in place as an additional approach to reduce the risk for missing potential signals.The computer‐assisted database screening tool used in the Netherlands relies on the number of reports of drug‐ADR associations and disproportionality based on the reporting odds ratio (ROR). With the disproportionality analyses, the observed rate of a drug and ADR together is compared with an expected value based on their relative frequencies reported individually in the spontaneous reporting database.The Uppsala Monitoring Centre, WHO Collaborating Centre for International Drug Monitoring, has developed a data‐driven screening algorithm for emerging drug safety signals that accounts for report quality and content, called vigiRank.The primary aim of this study was to develop a new prediction model‐based screening tool in order to improve statistical signal detection. Secondary aim was to compare this new model to the old screening tool, which is based on the number of reports and the ROR025.Current methods for full database screening of ADRs are mainly based on disproportionality, which has its limits due to its sensitivity for several types of selection bias.We developed a prediction model‐based approach to generate a priority list of drug‐ADR associations to be analyzed.The performance of the model and the comparison with the current method showed that the prediction model‐based approach is to be preferred over the current method.22.1In this study, we developed a logistic regression‐based prediction model for drug‐ADR associations present in the Lareb spontaneous reporting database. Using the linear predictor of this model, a prioritized list of associations not present in the SPC was made for comparison with the current method. The data for this study were derived from the database of the Netherlands Pharmacovigilance Centre Lareb. This database consists of spontaneous reports of suspected ADRs reported to Lareb directly by both HCP and consumers. Additionally, reports from MAHs regarding events that occurred in The Netherlands are imported into our database from the European Medicines Agency database Eudravigilance. Each report contains 1 or more drug‐ADR associations. For the development of the prediction model, all drug‐ADR associations were extracted from each report. ADRs were coded using the preferred terms from the Medical Dictionary for Regulatory Activities.2.2The outcome of the model was defined as the presence in the SPC of each unique drug‐ADR association at the time of the analysis. Although the use of the SPC to determine if an association is actually an ADR  has its limitations, it has been used in several studies aimed at statistical signal detection.2.3All reports received until 12‐May‐2016 were considered eligible for inclusion with the exception of reports related to vaccines. For these reports, a method other than Naranjo is used to determine causality. Because that particular method lacks information about the presence in the SPC, reports related to vaccines were excluded. For statistical considerations, only associations with a minimum of 3 reports were selected, because this was deemed to be the minimum number of reports needed for a reliable ROR estimation.2.4The number of ICSRs.The lower limit of the 2‐sided 95%CI of the ROR (ROR025).The percentage of ICSRs derived from health care professionals (HCP). This variable was selected because HCP reports differ from consumer reports.The percentage of ICSRs derived from MAHs. This variable was selected because it is our experience that MAH reports differ from reports received directly from HPCs / consumers, most likely due to regulatory obligations for MAHs. This is confirmed by the fact that only 0.2% of the reports from MAHs are included in signals published by Lareb .For each association, the following variables were selected as candidate predictors in the model:2.5P < 0.05  were fitted into the model. Due to non‐linearity of the predictors, they were converted to categorical variables with equally sized categories. For all candidate predictors, the generalized variance inflation factor, a measure of variance for categorical variables, was calculated to investigate collinearity, using 4 as a conservative cut‐off value.A multivariable logistic regression model was developed using backward step‐wise selection. The training data consisted of all drug‐ADR associations with a minimum of 3 reports. The candidate predictors with 2.6Internal validation of the model was performed by means of a calibration curve of the observed versus predicted probabilities, Hosmer‐Lemeshow goodness of fit testing, and bootstrap resampling. For the latter, the validate function from the R package “rms” was used . The performance of the model was based on the area under the receiver operating characteristic curve (AUC).Because our prediction model was developed to be used specifically for the Lareb database, external validation was not considered to be relevant. Additionally, previous signal detection research showed that there are substantial differences among different pharmacovigilance databases,2.7Although the current method of screening at Lareb is not based on a prediction model, we considered it of interest to compare the current model with a model containing only the number of reports and the ROR025, which are the basis for the current screening method. The comparison consisted of 2 elements: First, the performance in terms of the AUC was compared between both methods. Second, we constructed priority lists of associations not present in the SPC, containing the first 10% and 20% of the associations, respectively. The priority list was based on the value of the linear predictor from the old and new model, respectively. With the list, we determined the (relative) number of associations that had been previously analyzed in depth (mainly triggered by case‐by‐case assessment), as a proxy for a possible signal, for both methods. This second method was performed to investigate whether a theoretical difference in performance, based on the AUC, also resulted in a different amount of potentially interesting signals in practice.33.1A total of 151 033 ICSRs, containing 120 171 unique drug‐ADR associations were extracted from the database. After the selection of associations with a minimum of 3 ICSRs, 25 026 associations remained as the training data for fitting of the model. Of these, 17 071 associations (68.2%) were present in the SPC. Additional information is presented in Table Prior to the regression analysis, all candidate predictors were divided into 4 categories of equal sizes due to non‐linearity. After the backward step‐wise selection procedure, all candidate predictors were included into the final model. VIF values for the assessment of multicollinearity were below the pre‐defined threshold (4) for all predictors in the model. The proportion of associations present in the SPC increased with increasing numbers of reports and an increasing proportion of HCP reports. For ROR025, Naranjo score and proportion of MAH reports the direction of the effect was less consistent. For ROR025, an increase in category was associated with increasing coefficients except for the highest category. For both Naranjo and MAH reports, the lower categories were associated with a higher coefficient  and 44.2% (from 9.6% to 13.9%) depending on the number of associations used . Additional information is present in Table 4P < 0.001), indicating a poor goodness of fit, is most likely explained by the large sample size and should be interpreted with caution.In this study, we developed a prediction model‐based screening tool aimed at improving statistical signal detection of our spontaneous ADR reports. Five relevant characteristics  were chosen as potential predictors in the model. For Naranjo, we considered to use the scoring  for categorization. However, this would result in a skewed distribution of observations due to the (very) low numbers of associations with outcome “definite”. Our choice to set the Naranjo score for all MAH reports to +2 was based on the assumption that the ADR occurred after the suspect drug was given, which gives a score of +2. Because no case‐by‐case assessment is performed for MAH reports at our centre, other items from the Naranjo algorithm could not be answered. This approach could lead to less diversity in the Naranjo scores, and as a result impact the performance of the model. However, a recent pilot study performed at our centre investigating case‐by‐case analysis of MAH reports showed that the documentation level of the reports was often poor.We found little differences in AUC values among individual predictors, although disproportionality ROR025) seems to have the lowest predictive value. This may be explained by the fact that disproportionality is sensitive to selective reporting and other types of bias. seems toWithin subgroups of predictors, we found some noteworthy results regarding the regression coefficients. The predictors “number of reports” and “percentage of HCP reports” showed a consistent increase in coefficients with increasing categories, which was as expected. For ROR025 and Naranjo, we anticipated similar results, which was not the case though (see Table Although one can debate the validity of the use of the SPC as the gold standard for causality, we considered it to be the most comprehensive and up‐to‐date data source with information regarding ADRs that is publicly available. A different approach could have been the method used for vigiRank, where a set of historical safety signals was used as a reference set of positive controls.The linear predictor‐based priority lists comparing the old and new model showed a substantial increase in potential signals among the most highly ranked drug‐ADR combinations not present in the SPC. In this context, the increase in potential signals should be seen in terms or earlier detection due to prioritization and not in terms of signals that would, or would not be picked up by either method.Previous research suggests that results obtained from signal detection algorithms depend on the database the algorithm is applied to.One of the limitations of our study is the risk of bias due to selective reporting. Because the database contains well‐established associations, it is reasonable to assume that these associations are reported more frequently than unknown associations, therewith influencing the predictors in the model. In an alternative approach, the values of the predictors immediately prior to the recognition of the association could be used in the model. However, recovering the date of recognition for several thousand associations may prove to be infeasible.In conclusion, this study shows that a prediction model‐based screening tool can be used to generate priority‐based listings of drug‐ADR associations for signal detection. Additionally, as seen in other studies,The authors state that no ethical approval was needed.The authors declare no conflict of interest related to this work


This article has been retracted at the request of the University of Cape Town and the Cureus Editor-in-Chief. Cureus editorial staff detected several irregularities with this article and contacted the submitting author and his corresponding department heads. While the submitting author did not respond to this initial query, the University of Cape Town initiated a full investigation. After a comprehensive investigation by a Special Investigation Committee at UCT, it was determined that all authors associated with this article are guilty of both plagiarism and falsification of images.Figure 3 in the article purports to depict human brain histology to complement the content of the article but, in fact, is a picture of mouse brain histology ) taken from an open access database. The image is clearly plagiarised. It also is a false picture that does not represent the content of the article.The hyperlink to the relevant image is "https://www.askjpc.org/wsco/wsc_showcase2.php?id=523"The authors responded to the preliminary report variously denying culpability, knowledge of improper use of images or failure to acknowledge sources. However, these denials are not relevant to whether plagiarism exists in the article. The allegation of fabrication or falsification can also be established without difficulty. The article states that the image came from GSH databases and represents human brain histology of the patient concerned – it does not.  A key condition of article submission is that authors must explicitly declare that their work is original and has not appeared in a publication elsewhere. Re-use of any data or images must be appropriately cited. As such this article represents a severe abuse of the scientific publishing system. The Cureus Journal of Medical Science takes a very strong view on this matter and we apologize that this was not detected during the submission process. The institutions of all authors have been notified and all authors are hereby banned from submitting further work to The Cureus Journal of Medical Science.


Northern Ireland has been and continues to be deeply divided on the basis of religion. This paper examines and compares contemporary fertility in the two communities given the sharp declines that have occurred in recent decades. The data are drawn from the Northern Ireland Longitudinal Study and cover 108,000 women aged 16–44 in the period 1997–2007. A logit analysis of births in the period is undertaken based on individual demographic data and also the characteristics of the locality in which the woman is resident. The effect of religion is measured by its individual marginal effect averaged over the total sample, over time and by the age of the woman. The estimated average marginal effect is 4 % of the probability of a woman having a birth over the entire period. The effect peaks when the woman is between 29 and 30 years and is stable over time. When the fertility behaviour of each religious group is compared separately with those women that came from the same background but had lost their religion, it is found to differ substantially. Thus, community background is rejected as a possible explanation of the difference in fertility between declared Catholics and Protestants. Although the fertility rates of former Catholics and Protestants appear to be converging, the size of these groups is relatively small. There is no evidence to suggest that the small but distinct difference in the fertility rates of the two religious communities is likely to change in the immediate future.The online version of this article (doi:10.1007/s10680-016-9399-8) contains supplementary material, which is available to authorized users. The state of Northern Ireland was formed in 1921 and comprised six of the thirty-two counties of Ireland. The division of the island was an attempt to accommodate violently contradictory unionist and nationalist aspirations. In the South of Ireland, the abandonment of the six northern counties precipitated a civil war in which the Republican forces were defeated. In the North, a Protestant state was formed excluding a substantial Catholic minority. In 1926, when the first Census of Northern Ireland was undertaken, one-third of the population of one and a quarter million was Catholic and overwhelmingly nationalist. Politically, they were committed to a single state on the island of Ireland  was undertaken and its findings published in a book by Compton and Coward . NortherThis paper seeks to determine the contribution of religion to fertility in contemporary Northern Ireland, based on self-designated religion in the 2001 Census. The different fertility regimes associated with self-defined Protestants and Catholics are of central interest. In the 2001 Census, 40.3 % of the population stated their religion to be Catholic versus 45.6 % Protestant and 13.9 % either had no religion or declined to state it. In this last group, 43.8 % have a Catholic background (referred to as former Catholics further) and 53.1 % are former Protestants NISRA . While tIn the three decades since the NIFS was undertaken, union and family formation have changed. For example, the role of marriage considerably lost importance. In 2010, 40 % of births in Northern Ireland occurred outside marriage compared to 9 % in 1983. Over a similar period, the total period fertility rate (TPFR) decreased from 2.79 in 1980 to 1.75 in 2000 though in 2008 it rebounded to 2.05  of Catholics (Protestants) classed themselves as either ‘extremely’ or ‘very religious’ according to the Life and Times Survey (NILTS). Equivalent figures exist for 2008 (12 vs. 17 %). Those who considered themselves ‘somewhat religious’ grew from 56 % (42 %) to 60 % (44 %) in the same period  effect of religion to be established; comparing those who have lost the Protestant or Catholic religion of their upbringing gives an important measure of the extent of secularization in Northern Ireland. Across Western Europe this has been associated with the decline of religion  is used. In this study, 2001 and 1991 Census returns and birth registrations can be linked at the individual level. This results in annual fertility data of a panel of over 108,000 women covering the years 1997–2007. The construction of these data, referred to hereafter as the fertility panel, is central for addressing the research questions outlined above.The Northern Ireland Longitudinal Survey provides the individual data that are used in the construction of the fertility panel. The NILS does not conduct any population surveys itself but rather anonymizes the individual returns used in the construction of the official, aggregate data. The official data on birth registrations and the Censuses are reviewed in the first two subsections which are then followed by a subsection that outlines how these data are combined by the NILS. The final two subsections are devoted to the statistical nature of the study.Birth registrations are a legal obligation and fall under the responsibility of the General Register Office (GRO). The data derived from the registrations (and mid-year population projections based on the Census) are aggregated and summarized in tables that accompany the Annual Report of the Registrar General .The enumeration form of the Census asks whether the individual belongs to any particular religion. For those respondents answering ‘yes’, religious affiliation can be aggregated into Catholic, Protestant (and other Christian) and Other. In the statistical analysis, Catholics and Protestants are represented by dummy variables. If respondents answered ‘no’, then and only then, the respondent is asked what religion he or she was brought up in (which can be aggregated as mentioned before). This information permits former religion also to be included as dummy variables.It is important in this work that the Census information on religion is unbiased. In 1981, 18.5 % of respondents declined to state their religion. In 2001, ‘no religion or not stated’ amounted to 13.5 % of the enumerated population. Unfortunately, the two groups were combined during processing of the Census. In an analysis of the raw data, approximately 10 % stated ‘no religion’ and 4 % left the question unanswered  of which there were 890 in 2001. The rotated principal components (RPC) of eleven relevant socio-economic variables from the 2001 Census provided four components, named RPC1–4, that explain 91 % of the variation in the data. Details can be found  in the online Appendix 1*.Published Census data relating to the locality that an individual resided in was employed as an indicator of determinants relevant to individual fertility decisions (such as income) but which are not available at an individual level. The proportion of persons from a Catholic community background, RPC1 which is the only rotated variable where the Census education variables load substantially. It may thus be considered as inversely related to potential economic well-being. It accounts for a third of the variance in the locality variables. RPC2 is the only other rotated component that is significant in the regression analysis   model is frequently employed  the explanatory variables and so the estimated coefficients for the variables The key concept in attempting to quantify the effect of religion is the marginal effect .The variables employed in the statistical model were  defined in Table CATHOLIC dummy variable. The results are presented on the left-hand side of Table PERIOD and LOCALITY sets and predominantly relate to the Catholic subset (period and cohort variables were only dropped if the entire set was insignificant). The discussion below centres first on the variables that were dropped and then interprets the remaining ones.Equation  was estiPERIOD variables is an important result as it demonstrates that the two communities responded in similar ways to shocks suffered by the Northern Ireland economy. It thus suggests that the forces that stimulated the revival of fertility early in the twenty-first century affected religious groups in a similar fashion. The proportion of A8 migrants in a locality did affect domestic fertility but in a similar fashion in both communities.The insignificance of specifically the Catholic set of Secondly, the Northern Ireland economy changed appreciably in the period 1997–2007, but this development had a similar effect on the two communities given that the period effects did not differ. The correlation between the estimated period effects and the female activity rate is positive and strong (the correlation coefficient between the two series is 0.82).PP, the proportion of Protestants in the locality if the woman herself is a Protestant. Its effect on the latent index is negative which suggests that the more numerous Protestants are in a locality, the lower is their fertility. CATHOLIC, the religion dummy variable, on its own was insignificant and thus dropped. This implies that the constant in the parsimonious model is the same for Catholics and Protestants. Thus, there is no general increase in Catholic fertility, but rather it is restricted to those variables that are significant in the final column of Table It is possible that a woman’s religiosity would be influenced by the proportion constituted by her co-religionists in her particular locality. The only variable that is significant is In contrast to the above variables where the Catholic dummy was insignificant, the cohort variables were found to be highly significant and indicate that differential decline in Catholic cohort effects increased for women born between 1958 and 1967 and then plateaued before increasing again for those born 1983–1992. That the demographic profile differs between the two communities is clearly demonstrated by the highly significant differentials for Catholics across all the variables. The effect of this can be best viewed through considering the marginal effects.MECatholic, is reported in Table MECatholic is 0.0051 which occurs when the woman is 29. Except for a slight decline at ages 20 and 21, the marginal effect steadily increases to 29 and then declines to near zero by age 44. Thus, the fertility differences between the two communities follow their demographic profiles with the Catholic one being slightly above the Protestant one.The individual marginal effect is defined as the difference in the predicted probabilities of a woman with a particular set of characteristics having a child in a particular year when her religion is changed from Protestant to Catholic. The average marginal effect of being a Catholic, Further evidence on the extent of convergence in fertility between the two religious groups is provided in Figs. MECatholic is averaged by year and graphed, showing little variation. Catholic fertility is slightly but distinctly higher than that of Protestants, and this differential is stable in the new millennium.Again, the graph suggests that there was very limited convergence in fertility rates between 1997 and 2007. In Fig. The methodology employed in the previous two sections has also been applied to test differences in fertility between current and former Catholics and Protestants. First, those who declare themselves as Catholics are compared to former Catholics. The equality of coefficients between the two logits is firmly rejected by the Likelihood Ratio Test, and it is possible to reduce the full model from 69 to 36 variables (full results can be found  in online Appendix 2*).The mean marginal effect for the panel is −0.0033, which is greater in absolute value than that between self-declared Protestants and Catholics. Figure The differences between Protestants and former Protestants are more marked compared to the Catholic case. The Likelihood Ratio Test rejects the equality of coefficients, although the reduction process leads to only 13 variables being dropped. The mean marginal effect is −0.0017, though the median is 0.0010. Figure The final part of the analyses compares the fertility of former Protestants and Catholics. Secularization is considered an important element of the second demographic transformation (van de Kaa L01) and another which combines the higher groups 4 and 5 (L45). This is reproduced at the individual level by the dummy variables DL01 and DL45.Table 2 is almost six times greater, the logit explaining former Catholics is considerably better than that explaining former Protestants. According to the 2001 Census, 14 % of Protestants by background declared they had no current religious affiliation compared to 8 % of Catholics. The second result of note is that the greater the proportion of the population of the neighbourhood made up of people with the same community background, the less likely a woman loses her religious affiliation. The final point relates to the role of education. For both Protestants and Catholics, the signs of the locality effects are negative and thus the larger the proportion of poorly or highly qualified women in it makes it less likely that the woman concerned will lose her religion. On the other hand, if a particular woman herself is lower or higher educated, then she is more likely to lose her religion. The marginal effect sheds light on this apparent contradiction.There are three striking results of these analyses Table . FirstlyThe definition of the marginal effect of education on the probability of losing a religious affiliation has to take into account that there are three educational categories. The average change of a Protestant woman as she moves from the lowest educational attainment to the middle one (groups 0 and 1 to groups 2 and 3) is −0.0274 while moving to the highest groups, 4 and 5, from the middle has an average change of 0.0801. Thus, those with middling education are likely to be the most religious, while those at the extremes, with little or higher education, are more likely to lose their religious affiliation. For Catholics also, those with middling education are least likely to lose their religious affiliation with the marginal effects being −0.0466 moving up to middling education and 0.0604 moving beyond it. Over time, the increase in higher education is likely to have discouraged religious affiliation.The central issue tackled in this paper is the contribution of religion to fertility in contemporary Northern Ireland. To address this, the Northern Ireland Longitudinal Study has been employed which in this case matches the records of women from a sample of the Census and the Birth Registration Data. This results in the construction of a panel consisting of over one hundred thousand women in the period 1997–2007. Using these data has two major benefits. Firstly, the difference between groups in the population can be expressed quantitatively by the marginal effect estimated from regression analysis where the latter controls for differences in demographic and socio-economic structure between groups. The marginal effect thus expresses the differential fertility of subgroups of the population as a statistic. This can be disaggregated over time so that the extent of convergence between groups in the period considered can be assessed. Secondly, the NILS allows the definition of groups to be developed. This allows the effect of religion on fertility to be compared not just between Protestants and Catholics but also, to highlight contribution of religion by itself, by comparing Protestants with former Protestants and Catholics with former Catholics. Finally, comparing the fertility of former Protestants and Catholics provides insight into the extent of secularization in Northern Ireland.The results show that the marginal effect of a being a Catholic woman is a 4 % higher fertility compared to a Protestant. This difference is small but significant though it is likely to fall in the future because there has been a marked decline in the fertility across older Catholic cohorts and these will drop out with the passage of time. Among younger cohorts, the difference between Catholic and Protestant fertility is less marked. Against this, there is no evidence of convergence for the panel period. No significant difference between the period effects of Catholics and Protestants is found. This suggests that economic and social change during the time examined impacted both communities in a similar way. Changes in the trade-off between childbearing and labour market participation have been put forward as an explanation of the recent fertility revival Kalwij . The picMarginal effects are particularly informative when comparing those with religion to those without it. The magnitude of the marginal effect comparing Catholics with former Catholics is larger than that between Catholics and Protestants. This suggests that the pure fertility impact of religion in this case is considerable since both groups would have a similar background. When such an analysis is carried out on Protestants, the results are similar but less robust. Of particular interest then is the fertility behaviour of former Protestants and former Catholics. The marginal effect in this case is the smallest of the four comparisons though it is still just significant at the 5 % level. Over time the marginal effect declines and gives a firm indication of convergence.The overall picture of fertility in contemporary Northern Ireland by these statistical results can be presented in terms of the groups concerned. Protestants and Catholics form the religious groups, and these are distinctive in a small but definite fashion. It is arguable when considering former Protestants and Catholics that they together comprise one group. While the marginal effect is just significant between the two sets, its magnitude is the smallest of the four sets considered. Moreover, over the period considered, the two birth rates show definite convergence. If a single group is designated, then it can be considered as secular. Secularism though is not a central element within the future of fertility in Northern Ireland. The group is small as it comprises only 13 % of the population in 2001. Moreover, the Northern Ireland Life and Times Survey gives no impression of a fall in religious commitment in the period considered. Given the higher birth rate of the religious groups, if anything secularism is under demographic pressure. In this it reflects a general European trend Below is the link to the electronic supplementary material.


We have demonstrated experimentally the existence of a giant frequency down-conversion of the translational oscillatory motion of individual submillimeter acoustic bubbles in water in the presence of a high frequency (500 kHz) ultrasonic standing wave. The frequency of the translational oscillations (~170 Hz) is more than three orders of magnitude smaller than that of the driving acoustic wave. We elucidate the mechanism of this very slow oscillation with an analytical model leading to an equation of translational motion of a bubble taking the form of Mathieu’s equation. This equation illuminates the origin of the giant down conversion in frequency as arising from an unstable equilibrium. We also show that bubbles that form chains along the direction of the acoustic standing wave due to radiation interaction forces exhibit also translation oscillations that form a spectral band. This band extends approximately from 130 Hz up to nearly 370 Hz, a frequency range that is still at least three orders of magnitude lower than the frequency of the driving acoustic wave. The complex behavior of bubbles in acoustic fields has fascinated generations of professional and amateur scientists. Acoustic bubbles can produce sonochemical reactions268910131415x(t), of individual bubbles as well as of bubbles in chains  water saturated with air at pH 5.8 subjected to an acoustic standing wave field of 500 kHz. The bubbles formed during sonication are therefore air bubbles. The typical diameter of bubbles characterized for translation motion is ~0.35 mm. These bubbles are about 25-fold larger than the resonant bubbles (diameter 0.015 mm) at 500 kHz excitation frequency, which ensures that the bubbles exhibit only small amplitude non-resonant radial oscillations at the driving frequency. The submillimeter-size bubbles localize at the antinodes of the standing wave due to first-order Bjerkness forces6ains See .x(t), normalized to half the standing wave wavelength, λ/2, exhibits what appears to be oscillatory behavior. To reduce the effect of possible random displacements of the bubble, we calculate the normalized position time-autocorrelation function which when fast Fourier transformed produces the bubble vibrational power spectrum. The most significant feature of the power spectrum of the single bubble is the existence of a well-defined peak at approximately 170 Hz. The very low frequency feature in the spectrum is assigned to the erratic behavior of the bubble. Indeed, we have verified that numerically generated random walks constrained by the experimental velocity of the bubble and the experimentally observed amplitude of the oscillation generate only power spectra features with frequency lower than 100 Hz. Five other submillimeter-size single bubbles that were studied showed qualitatively the same behavior and semi-quantitatively the same features in their power spectrum. The observed peak at 170 Hz is therefore characteristic of a translation oscillatory motion of the bubble trapped and driven by the standing wave. Variability in the position of the translational oscillation peak is observed with frequency ranging between 150–200 Hz. The frequency of this oscillatory motion is nearly 3000 times lower than the frequency of the driving acoustic wave. It was shown theoretically that bubble levitation during single-bubble sonoluminescence (SBSL) conditions is accompanied by translational oscillationsThe conditions of our experiments are far from SBSL conditions. Based on our high resolution imaging, we note that the radial dimension of the submillimeter bubble in our system appears not to vary during the translational oscillations. The bubbles do oscillate radially as shown indirectly by the presence of chains of bubbles. Indeed, chains of bubbles will form due to secondary Bjerknes bubble-to-bubble forces resulting from secondary sound fields emitted by the bubbles radial oscillations. However, the amplitude of these oscillations for sub-millimeter bubbles is small in contrast to that observed in SBL experiments. The frequency of the radial oscillations of sub-millimeter bubbles is also expected to be that of the driving acoustic field. Because of their high frequency and small amplitude, these radial oscillations are therefore not directly observable with the high speed camera we used . In contrast to SBSL experiments, the submillimeter bubbles of our experiments undergo radial oscillations with very small amplitude compared to the amplitude of a sonoluminescence bubble during its periodic collapse. Therefore, coupling between the translational motion and weak radial oscillations cannot explain the observed frequency-down converted translational oscillations. Furthermore, all our experiments are conducted in pure water and the giant frequency down-conversion in the translational motion of the bubble that we observe cannot be attributed to mass transport and/or reaction processes as is the case in ref. x(t)/λ, exhibits a well-defined oscillatory behavior which is also clearly apparent in the time-autocorrelation function. In contrast to the isolated bubble, the vibrational power spectrum of a bubble in a chain now exhibits translational oscillatory motion with a range of frequencies. This range extends approximately from 130 Hz up to nearly 370 Hz. Other submillimeter-size bubbles in chains that were studied showed qualitatively a similar behavior and a quantitatively similar frequency range. This range is characteristic of a band of translation oscillatory modes that results from the periodicity of the chain and of the interactions between bubbles and their associated secondary acoustic fields. The frequency of this band is still at least three orders of magnitude lower than the frequency of the acoustic wave. This behavior was verified for two bubbles in two different chains.In ω in a fluid can be described by an equation that takes the form of Mathieu’s equationρ is the density of the fluid and λ being the wavelength). For a bubble in a chain R0 is the average radius of the bubble and p refers to the order of interaction with neighboring bubbles . We have assumed that the radial oscillations of bubbles in a chain are in phase. This assumption results from our experimental observation of the formation of chains of bubbles which indicates that the radiation force between bubbles is attractive. It is well known that attractive radiation forces between two bubbles of similar size arise when their radial oscillations are in phaseQ cos 2z in Mathieu’s equation is a trigonometric periodic function that drives the translational dynamics of the bubble. The realm of application of Mathieu’s equation is quite broad. The prototypical examples of mechanical systems that obey Mathieu’s equation are the inverted pendulumπ) or twice the period (2π) of the driving trigonometric function. To support the experimental observation of giant frequency down-conversion of translational oscillation motion of bubbles, the present study focuses on solutions that have not been appreciated in the literature, namely vibrational modes with frequencies that are significantly lower than that of the driving trigonometric function. While x(t) = 0 is a stable solution, we show, in the 3, the longitudinal speed of sound is v ~ 1500 m/s, and with ω = 500 kHz, we determine q ~ 3.55 × 10−9 Pa. We have measured in our experimental set up a pressure amplitude of 2.3 atm leading to q ~ 8.16 × 10−4 and a frequency for the translational oscillation of i.e. the periodicity of the standing wave. The long-range acoustic interaction forces between bubbles that act as secondary sources of sound are at the origin of the broadening of the frequency band and dispersion arises from the lifting of the degeneracy of the oscillatory mode of non-interacting bubbles. In the case of a finite chain of bubbles, the band is replaced by a series of discrete non-degenerate modes whose frequency range depends on the number of bubbles in the chain i.e., the range of interaction between bubbles. Unlike the well-known elastic harmonic chain composed of masses and springs, the band supported by a chain of bubbles possesses a lower bound for the frequency of the long wavelength modes. Bubbles in a chain do not behave like point masses interacting via linear forces but behave like particles interacting nonlinearly through their secondary sound fields.We show in the We have demonstrated experimentally the existence of a giant frequency down-conversion of the translational oscillatory motion of submillimeter bubbles in water in the presence of a high frequency ultrasonic standing wave. The frequency of the translational oscillations is more than three orders of magnitude less than that of the driving acoustic wave. This surprising phenomenon, which requires an initial bubble velocity, can be understood by placing oneself in the bubble inertial reference frame. Recalling that a standing wave is composed of two waves traveling in opposite directions, relative to its reference frame, a moving bubble experiences frequency up-shifted and frequency down-shifted acoustic waves. In the case of a single bubble, the acoustic radiation forces (Bjerkness forces) resulting from the two frequency shifted waves and acting on the bubble do not balance each other and lead to an effective acceleration. The time scale of this acceleration is much longer than that of the driving acoustic wave, thus leading to a low frequency rhythmic dance of the acoustic bubble.2. The schematic of the tank with transducer is provided in A custom designed rectangular stainless steel sonochemical reactor affixed with 500 kHz transducer on one of the side walls was used for the experimental work. The size of the sonochemical tank was 23 × 23 × 23 cm with transducer area of 73 cmHow to cite this article: Deymier, P. A. et al. Giant frequency down-conversion of the dancing acoustic bubble. Sci. Rep. 6, 37385; doi: 10.1038/srep37385 (2016).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Biofilms are found at the inner surfaces of drinking water pipes and, therefore, it is essential to understand biofilm processes to control their formation. Hydrodynamics play a crucial role in shaping biofilms. Thus, knowing how biofilms form, develop and disperse under different flow conditions is critical in the successful management of these systems. Here, the development of biofilms after 4 weeks, the initial formation of biofilms within 10 h and finally, the response of already established biofilms within 24-h intervals in which the flow regime was changed, were studied using a rotating annular reactor under three different flow regimes: turbulent, transition and laminar. Using fluorescence microscopy, information about the number of microcolonies on the reactor slides, the surface area of biofilms and of extracellular polymeric substances and the biofilm structures was acquired. Gravimetric measurements were conducted to characterise the thickness and density of biofilms, and spatial statistics were used to characterise the heterogeneity and spatial correlation of biofilm structures. Contrary to the prevailing view, it was shown that turbulent flow did not correlate with a reduction in biofilms; turbulence was found to enhance both the initial formation and the development of biofilms on the accessible surfaces. Additionally, after 24-h changes of the flow regime it was indicated that biofilms responded to the quick changes of the flow regime. Overall, this work suggests that different flow conditions can cause substantial changes in biofilm morphology and growth and specifically that turbulent flow can accelerate biofilm growth in drinking water. The provision of safe drinking water is a top priority in all societies. Managing biofilms that are formed on the inside surface of drinking water pipes is a concern of water utilities around the world as these biofilms can affect the aesthetics of drinking water –3. HydroThere is a wealth of literature that supports the fact that biofilm structure is intimately linked with hydrodynamics –15. ThesHydrodynamics are found to affect biofilm thickness and density. High detachment forces, caused by increased shear stresses, have been shown to lead to denser biofilms that are mechanically more stable , 20. As This unexpected result of the development of thick biofilms in turbulent flow might be attributed to several other factors. The change in the substrate flux is one of those factors. High shear stress conditions are found to cause a double effect on mass transfer properties; on one hand, turbulence facilitates high substrate diffusion in biofilms and on the other hand, the resulting denser biofilm reduces the diffusivity of substrate . AnotherLittle is known regarding the initial colonisation of bacteria, which is a precursor to the formation of biofilms , 27, andFrom the engineering view, the study of flow conditions can contribute to the successful management and control of biofilm formation to avoid biocorrosion that leads to pipe material deterioration and subsequent reduced life of the pipe , 29. ThuBiofilms were grown in a jacketed rotating annular reactor . The main advantage of this reactor is that the shear stress conditions can be easily controlled by its motor device, and the flow rate can be controlled independently of the shear stress. It has been suggested that reactors cannot accurately simulate the flow conditions of real drinking water distribution systems due to their geometry , 31. HowThe reactor held 20 removable polycarbonate slides that were attached to its inner drum. The polycarbonate material was chosen as one of the plastic materials used in drinking water systems, which does not have a rough surface of corroded material . The jac2 in laminar flow, average velocity of 0.07 m/s and shear stress at the wall of 0.02 N/m2 in transition flow, and average velocity of 0.25 m/s and shear stress at the wall of 0.07 N/m2 in turbulent flow [This reactor was used to simulate flow conditions similar to those in a pipe with a radius equal to the gap between the two cylinders of the reactor, and mean velocity equal to the mean velocity of the reactor. The inner drum of the reactor was rotated at three different speeds to induce Taylor–Couette flows –35; at 3ent flow –38.The choice of the diameter of the pipe at 30.3 mm corresponds to the extremities of drinking water pipes where the service lines start –41. In tThe medium that the reactor was filled with consisted of 150 ml of nutrient medium and 850 ml of drinking water that was sampled from a domestic tap in Glasgow. The drinking water, which was used to feed the reactor, was taken from a tap that was fed from an internal plumbing system. The drinking water treatment plant, which supplies water to the location from which the water was sampled, uses surface water as its source. The treatment steps that are followed in this treatment plant are: coagulation, rapid gravity filtration, chlorine disinfection and orthophosphate dosing. The concentrations for mineral salts of the reactor medium were: ammonium sulphate 1.2 mg/l), ammonium chloride (0.9 mg/l), magnesium sulphate heptahydrate (0.3 mg/l), manganese chloride tetrahydrate (0.003 mg/l), copper sulphate pentahydrate (0.002 mg/l), cobalt sulphate heptahydrate (0.001 mg/l), sodium molybdate dehydrate (0.001 mg/l), zinc sulphate heptahydrate (0.01 mg/l), and boric acid 0.75 mg/l) , and the mg/l, am5 mg/l , 5 cells/ml and (7.6 ± 0.1) × 103 microcolonies/ml, respectively [The concentration of total chlorine of the drinking water, that was sampled from the tap, was measured immediately after its sampling using the USEPA DPD Method 8167  and a coectively .Three experiments were conducted, which are described here as “A”, “B” and “C” experiments. In each experiment, the same processes were followed. The first process, which is described here as “development”, is the process in which biofilm development was studied after 4 weeks of reactor operation Table . During The second process, which is described here as “formation”, is the process in which the biofilm initial formation was studied after 10 h Table . The reaThe last process, which is described here as “changes of flow regime”, lasted 72 h for A and C experiments and 96 h for B experiment. The aim of this process was to test how the already established biofilms after the 4 weeks of the reactor operation responded to changes in the shear stress conditions each of which lasted only 24 h. During this process, the reactor was operating under recirculation mode. One litre of a similar medium that initially filled the reactor was recycled; the differences being that distilled water was used instead of drinking water and the recycling medium here was 10 times more diluted. This meant that bulk liquid initially contained few planktonic bacteria and the bacteria that did appear were primarily derived from eroding biofilms on the surfaces. That medium was recirculated with flow rate at 22 ml/min and retention time at 45 min, to minimise suspended cell growth and enhance biofilm growth on the reactor surfaces [In Table Three reactor slides were used to characterise the thickness and density of biofilms in each of the three experiments at the end of the development process . In brieTwo slides were used to count the microcolonies on the reactor slides of each of the three experiments in each of the three processes. The biomaterial attached to each reactor slide was gently scraped from it using a sterile cell scraper , and diluted in 5 ml distilled water. Then, the 5 ml samples were fixed with 0.5 ml of 2% formaldehyde  and filt5 cells/cm2. Finally, the measurements for the calculation of the concentration of microcolonies and cells on the reactor slides were also conducted prior to the onset of each of the three experiments to ensure that the reactor slides were sterile.The concentration of cells on the reactor slides was also calculated following the same process as that described for the calculation of the concentration of microcolonies. The only difference is that after the biomaterial attached to the reactor slides was scraped from them, then it was homogenised in vortex for 2 min in 5 ml distilled water. Additionally, the membrane filters were covered with 1 ml of 0.1% Triton X-100 solution  to evenly disperse the cells before DAPI staining was applied. Cells were finally visualised using the oil immersion UPlanFLN objective lens  with 100× magnification/1.30 numerical aperture and their concentration was calculated at (5.4 ± 0.6) × 10For the biofilm structure measurements two slides were used for the development process, three slides were used for the formation process and three slides were used for the changes of flow regime process of each of the three experiments. The biofilms on the reactor slides were firstly fixed with 0.5 ml of 4% paraformaldehyde . The samThe surface area of both cells and EPS glycoconjugates on the reactor surfaces was then calculated. Additionally, the surface area that only the EPS glycoconjugates occupied on the reactor surfaces was calculated. These surface areas were calculated in Matlab by processing the microscopic fields of view obtained. Again, the coefficient of variation of the measurements was less than 0.30. The composite microscopic images of biofilms (from the cells and EPS glycoconjugates) were created using the Matlab command called “imfuse”. The original microscopic images were firstly converted to grayscale images using the Matlab command called “rgb2gray” and then to binary images using the Matlab command called “im2bw” to separate the biomaterial (the biofilms in one case and only the EPS glycoconjugates in the other case) from the background of the microscopic image. After the surface area for all the microscopic images obtained was calculated, it was divided to the total surface area of the microscopic image to finally calculate the percentage of the surface area (%). The measurements for the calculation of the surface area of biofilms on the reactor slides were also conducted using phase contrast microscopy and the percentages of surface area of biofilms were found to be in agreement with those found from the images obtained using fluorescence microscopy that were described here.P value lower than 0.05 was considered statistically significant.All measures were analysed in IBM SPSS Statistics using one of the following tests: (1) the one-way ANOVA test in conjunction with the Tukey’s and the Duncan-Waller’s tests, (2) the Kruskal–Wallis by ranks test, (3) the Jonckheere-Terpstra test and finally, (4) the Pearson’s chi-squared test in conjunction with the Phi and Cramer’s test, depending on the fitness of the data under comparison to the assumptions of the tests. All statistical calculations were based on the confidence level of 95%, which means that a Where the data sets were normally distributed and there was homogeneity of variances, then significant differences between data were tested using one-way ANOVA in conjunction with the Post hoc Tukey’s and Duncan-Waller’s tests that would further validate the statistical result of one-way ANOVA. Comparisons of the surface area of biofilms between the batch and recirculation mode of flow were tested using one-way ANOVA in conjunction with the Tukey’s and Duncan-Waller’s tests.Where the data sets were not normally distributed, then the Kruskal–Wallis test was used, in which the variances of the populations should be equal across the samples. Comparisons of the surface area of biofilms between the different flow regimes for the changes of flow regime process were made using this test.For the data in which the condition for the variances of the Kruskal–Wallis test was not met, the Jonckheere-Terpstra test was deployed, in which there should be a priori ordering of the populations. So, comparisons of the microcolonies that were attached to the reactor slides between the different flow regimes for the development process were made using this test. The same test was used for the comparisons of the surface area of EPS glycoconjugates between the different flow regimes for the formation process.In the case in which the data sets did not validate the assumptions of any of the previous tests, the Pearson’s chi-squared test in conjunction with the Phi and Cramer’s test were performed for large size and independent samples.Textural entropy was one of the measures used in this study to characterise the biofilm structures. It is used to describe the randomness of the components of a grayscale image by comparing the intensity of the image pixels. The higher the value of the entropy, the more heterogeneous the biofilm is. This means that more complex biofilm structures are demonstrated in the image , 54. EntSemi-variograms were used here as another measure to characterise the spatial variance of biofilm structures within grayscale images and quantify the spatial dependencies in the data sets. Their function relates the semi-variance of the data points to the distance that separates them. Large distance of the data points means more data pairs for estimation of the semi-variance, but less amount of detail in the semi-variogram. In other words, semi-variograms are a way of graphically capturing the spatial variance of points on a landscape as a function of their distance. All combinations of points at a distance are collated and their variance is determined for all possible separation distances , 56.An important part of a semi-variogram is the “origin”; the closest points of the diagram. Where values are co-located, for example, in clusters, the variances at short distances are low as the values are similar. At the characteristic cluster length, the variance will rapidly increase. Another important part of a semi-variogram is the “sill”; the variogram upper bound that is equal to the variance of the dataset and reflects the amount of variability. The sill is usually at large distances where there is no gradient in the diagram , 58. In Autocorrelation function (ACF) diagrams were used as the last measure to characterise the biofilm structures. The ACF diagrams are, in essence, a two-dimensional extension of the semi-variograms. They allow us to assess how the spatial autocorrelation changes with distance. They correlate pixel intensities within grayscale images and detect the repetitive structures within the images under consideration by combining together all parts of them. The ACF diagrams are real-space images, so that their dimensions have the same meaning as in the original images .In these diagrams, represented here as contour plots, the central element provides a measure of the size and shape of the basic element that dominates the original images. The rest of the contour lines reflect the size and shape of the neighbourhood elements of the original images. Finally, the bar on the right side of the diagrams provides a measure of the autocorrelation. The darker the colour of the bar, the less the autocorrelation value is with its lowest value to be zero and the highest value to be one . The ACF7–109 cells/cm2 [P < 0.05) in turbulent flow than in transition and laminar flow. No significant differences were found in these measures between the transition and laminar flow.The biofilm thickness Fig. a and theells/cm2 . AdditioThe measurements of the biofilm thickness and density, the concentration of microcolonies on the reactor surfaces, the percentage of surface area of biofilms and the entropy proved our hypothesis correct that turbulent flow was the flow regime in which biofilms were developed to a higher extent than the biofilms developed in transition and laminar flow. With the increase in shear stress associated with faster flows one might have expected biofilms to be smoother in the turbulent regime; where the biofilm protrudes into the flow the high stress could potentially shear off pieces of the biofilm eroding any lumps on the surface. However, this did not appear to be the case. The measure of roughness here is entropy and the entropy of biofilms was greatest in the turbulent regime. The increased number of microcolonies attached to the reactor slides and the increased growth of biofilms on the surfaces might mean that in turbulent flow more microcolonies actually come from the bulk liquid and land on the surfaces.Drinking water distribution networks are designed for liquid velocities of about 0.2–0.5 m/s. Flow conditions can range from laminar to turbulent flow but stagnant waters also occur in places in which the water consumption is low . In low-P < 0.05) in turbulent flow compared to the surface area and the entropy found in transition and laminar flow, respectively. Again, no significant differences in these measures were found between the transition and laminar flow. The surface area of EPS glycoconjugates  in turbulent flow compared to transition and laminar flow in the formation process. Again, no significant differences were found in the surface area of EPS glycoconjugates between the transition and laminar flow.In the formation process, the surface area of biofilms Fig.  and the P < 0.05) were found between 2–4, 2–6, 2–8, 4–8, 4–10, 6–8, 6–10 and 8–10 h. Finally, for the surface area of EPS glycoconjugates, significant differences (P < 0.05) were found between 2–4, 2–10, 4–6, 4–8 and 4–10 h.It was shown that in turbulent flow the entropy and surface area of biofilms peaked at 6 h, and the surface area of EPS glycoconjugates peaked at 4 h. So, again turbulence was found to be critical in shaping the structure of the biofilm with area and roughness being consistently higher than in the other flow regimes. The peak in those measures might show that in the early stage of formation, microcolonies that were already rich in EPS glycoconjugates were deposited on the slides. As the deposits grew the surface area of biofilms increased and so did the entropy. With increased roughness and surface area of biofilms became increased and more heterogeneous shear stresses and thus, erosion served to decrease both the entropy and the surface area of biofilms and subsequently that of EPS glycoconjugates over the latter part of the 10-h formation period. These changes in the structure of biofilms for the different time periods of the formation process were significant only in turbulent flow. For the entropy and the surface area of biofilms, significant differences (P < 0.05) were found in the surface area of biofilms between the different flow regimes in each of the three experiments  were found in the surface area of EPS glycoconjugates between the different flow regimes in each of the three experiments  Fig. a or lineThe exact structure of drinking water biofilms is still unclear and has not yet been described in detail due to difficulties in investigating such a small amount of biomass without disturbing it. This process is rendered even more complicated by the presence of debris, corrosion products and mineral deposits inside the pipe, which provide new niches for bacteria to colonise . OrganicThere are many types of biofilm heterogeneity –75. FirsBiofilms are found to form very complex structures, which are influenced by many factors. Hydrodynamic conditions are one of the most significant factors affecting biofilm structures because they influence important variables, such as substrate loading rate and developing shear stresses . The recThe semi-variograms of the development process for all three experiments are here demonstrated Fig. . The higThe gradient in the variance close to the origin was the highest in turbulent flow. This shows that the topography of the biofilm was the most heterogeneous in turbulent flow. Specifically, the gradient in variance dropped after about 20 μm, which shows that there was a prevalence of topographic structures with a characteristic radius  of approximately 20 μm. For the laminar and transition flows, the heterogeneity in the topography was much lower and there was a shallow linear gradient on the semi-variograms. This indicates a smoother surface potentially with features that extended over longer length scales than in the turbulent regime.For the formation and changes of flow regimes processes, the data are changing rapidly so the semi-variograms are less informative since the overall variance fluctuated between time points in a way that made it difficult to draw any further conclusions. The semi-variograms in the formation and changes of flow regimes processes indicate broadly similar patterns with those in the development process. The biofilm irregularity was the highest in the development process, after biofilms were established on the reactor surfaces for 4 weeks, as the variance was found to be higher in the development process that in the other two processes.The ACF diagrams of the development process for all three experiments are here demonstrated Fig. . In Fig.In transition Fig. b and lamThe ACF diagrams are most useful in determining the structures that have been established over the development phase, rather than the rapidly changing formation or changes of flow regime processes of the three experiments. In both these processes, the only spatial structure identified for all three experiments was that of microcolonies. Again, the autocorrelation of biofilm structures was the highest in turbulent flow.P < 0.05) in batch mode than in recirculation mode.Biofilms were studied for 4 weeks (development process) and for 10 h (formation process) while the reactor was operating under batch mode, which is not a typical condition for DWDS. The reason to do that was to emphasise the important differences that can be detected in biofilms under the different flow regimes in a closed well-controlled system. By the comparison between the batch mode at the end of 4 weeks of the development process and the recirculation mode at the end of the first 24 h of the changes of flow regimes process of each experiment, it was found that the surface area of biofilms, and the one of EPS were significantly higher  it is essential for engineers to understand how they form and develop and the role that the flow conditions play on them. From this study it is clear that the control of flow conditions is very important for DWDS as it was indicated that in turbulent flow, which occurs in most engineered systems, biofilms form and develop to the highest extent. Thus, it is essential that we found a way to carefully control turbulent flow (perhaps by reducing the shear stresses) in parts of DWDS if we are to control or even prevent biofilm formation.