Via questionnaire, subjects reported a decrease of ownership after the RHI manipulation; at the same time, tactile sensitivity thresholds were shown to increase in tactile evaluation using the Semmes-Weinstein monofilaments test. The tactile detection rate changes before and after the RHI were negatively correlated with the disownership-score changes. These results show that subjects’ sense of disownership, that their own hands did not belong to them, led to decreases in tactile sensitivity. The study findings also suggest that manipulating of illusory ownership can be a tool for estimating the degree of exacerbation of sensory impairment in patients. Consideration of new interventions that optimize the sense of body ownership may contribute to new rehabilitation strategies for post-stroke sensory impairment.The sense of body ownership, the feeling that one’s own body belongs to oneself, is generated from the integration of visual, tactile, and proprioceptive information. However, long-term non-use of parts of the body due to physical dysfunction caused by trauma or illness may disturb multisensory integration, resulting in a decreased sense of body ownership. The rubber hand illusion (RHI) is an experimental method of manipulating the sense of ownership (SoO). In this illusion, subjects feel as if the rubber hand in front of them were their own hand. The RHI elicits the disownership phenomenon; not only does the rubber hand feels like one’s own hand, but one’s own hand does not feel like one’s own hand. The decrease of ownership of one’s own body induced by the bodily illusion is accompanied by neurophysiological changes, such as attenuation of somatosensory evoked potential and decreases in skin temperature. If the loss of the SoO is associated with decreased neurophysiological function, the dysfunction of patients complaining of the loss of ownership can be exacerbated; appropriate rehabilitation prescriptions are urgently required. The present study attempted to induce a sense of disownership of subjects’ own hands using the RHI and investigated whether the tactile sensitivity threshold was altered by disownership.  Sense of ownership (SoO) is the feeling that parts of the body, or the entire body, belong to oneself . This suThe sense of body ownership can be altered selectively by stroke-induced brain damage, interfering with multisensory integration. Patients’ complaints like that I feel that this hand that I am now observing is not my own are occasionally reported in clinical cases. According to an observational study of stroke patients using the Visual Analog Scale (VAS) to investigate body disownership after brain damage, body disownership was also detected in cases with no obvious agnosia. Moreover, in patients with more severe impairment of motor and sensory function, more reduction in body ownership has been detected . In moreThe principal sources of these complaints from stroke patients include not only the primary factor, such as damage to the areas responsible for motor and sensory function, but also secondary factors, such as decreased frequency of use. Use-dependent plasticity is the brain’s ability to adapt to various changes in the surrounding environment ,b. When via RHI has been demonstrated to cause physiological changes, such as reduced skin temperature of the real hand , first reported by eal hand , and deceal hand .A significant amount of neurological evidence has been obtained through studying illusory ownership of the virtual body. However, it remains unclear whether the attribution of ownership to the virtual body is complementary to the disownership of the actual body. In a study with a psychometric approach to the RHI, subjects reported feeling that their own hands had been replaced with rubber hands, rather than that a new third hand had been added . A studyIn the present study, we hypothesized that the introspection on decreased body ownership in stroke patients has analogical properties to the decrease in body ownership caused by the bodily illusion. Observing changes in subjects’ ownership of their own hands during studies utilizing the RHI leads to an understanding of the relationship between the patient’s decrease of body ownership and the change of sensory function in clinical practice. To examine the effect of disownership on tactile sensation, this study investigated healthy subjects’ perceived changes in the ownership of their real hands due to the RHI as well as changes in the tactile pressure detection rate before and after the illusory manipulation. Clarifying the relationship between changes in ownership and tactile sensation can potentially contribute to the development of new rehabilitation strategies that improve sensory impairment by optimizing perceptions of body ownership of patients with post-stroke sensory impairment.Twenty-six healthy adults  were recruited by posting notices within the Tohoku University campus and at Tohoku University Hospital and by publishing the recruitment information on the Miyagi Occupational Therapists’ Association website. Handedness was assessed by way of the Edinburgh Handedness Inventory . All parThe series of experiments consisted of three components: the RHI, questionnaire and tactile evaluation. Each operation was carried out in the order shown in The study’s RHI manipulation procedure was based on the method of The experimenter stroked the subject’s palm and the palm of the rubber hand with two identical cosmetic brushes for 120 s, excluding the thumb, which was the test site of the subsequent tactile evaluation. The frequency of the brush stroking was set to 1 Hz and controlled by a metronome. This part of the experiment consisted of two conditions: the first in which the rubber hand and the subject’s hand were stroked simultaneously, wherein the illusion generally occurs (synchronous condition), and the second in which the rubber hand and the subject’s hand were stroked at different times, wherein the illusion generally does not occur (asynchronous condition). The order of the experimental conditions was counterbalanced among the subjects.To evaluate changes in the subjective sense of body ownership, subjects were asked to rate the following two statements, items modified from a questionnaire used by Q1. “I feel as if the rubber hand is my hand.”Q2. “I feel as if the real left hand is no longer mine.”Question 1 queried the amount of illusory body ownership of the rubber hand (ownership score). Question 2 queried the amount of ownership decrease of the real hand due to the illusion (disownership score). Responses were collected verbally on a 7-point numerical rating scale and ranged from “−3” (very strongly disagree) to “+3” (very strongly agree). Pre-evaluation in the observation phase of the rubber hand before the synchronous or asynchronous stimulation was defined as the baseline to derive the amount of change of subjective evaluation, and to investigate the correlation with the amount of change of other indicators. Thus, a total of four measurements were conducted before and after the illusion-induced operation in the synchronous and asynchronous conditions.The tactile pressure evaluation was conducted immediately after the questionnaire on body ownership; the evaluation was conducted four times, as with the questionnaire measurements. A modified version of the method from The Shapiro–Wilk test was used to examine the distribution of all datasets. As the results of the questionnaire and of the tactile pressure sensation assessment were datasets that were not normally distributed, the Wilcoxon signed-rank test was used to analyze the difference between the means of the two datasets before and after the intervention. Spearman’s rank correlation coefficient was then used to examine the relationship between the amount of change in the decrease of body ownership score and the amount of change in the justification rate of tactile pressure sensation.One of the participants who was recruited reported numbness in the arm during the experiment and ceased their participation. Therefore, data for 25 participants were obtained and analyzed.p < 0.0005), while in the asynchronous condition no significant change was revealed.The SoO scores (ownership score) from Q1 are shown in p < 0.0005), while in the asynchronous condition no significant change was revealed.The decrease of ownership scores (disownership score) from Q2 are shown in p < 0.0005). From these results, the RHI induction by the visuo-tactile stimulation has confirmed.Both the ownership score and the disownership score was significantly higher in the synchronous condition after the illusory manipulation (post-sync) than in the asynchronous condition (post-async) .The detection rate of the No. 2.36 filament in the tactile evaluation is shown in p < 0.0005) and asynchronous conditions (p = 0.030).The detection rate of the No. 2.44 filament is shown in p < 0.0005; p < 0.0005; To clarify the relationship between the decrease of the SoO and tactile detection ability, the correlation between subjective rating changes and detection-rate changes was investigated. The correlation between the amount of change in each score  is shown in In this study that synchronized visuo-tactile stimuli, subjects experienced feeling as if a rubber hand was part of their own body, while at the same time declaring a decrease of ownership toward their actual hand. There was a high correlation between the subjective ratings of Q1 and Q2. This correlation indicates deductively that embodiment of the rubber hand and disembodiment of the self-hand are complementary phenomena. In comparisons before and after presentation of the illusion stimulus, subjects’ filament-detection rates were significantly decreased after the illusion. Correlations were found between the disownership data obtained from the questionnaire and filament-detection rate changes; the greater the change in disownership, the greater the decrease in the filament-detection rate. These study results revealed that subjects’ tactile pressure thresholds increased when they felt a decrease of their sense of body ownership, induced by the illusion’s stimuli.Tactile information ascends primarily from the spinal thalamic tract and is detected when it reaches the primary somatosensory cortex (S1). From there, the information is further transmitted to higher association areas, such as the parietal and temporal lobes, resulting in more complex cognition, including renewal of body representation . A previAnother recent psychophysical experiment has shown the opposite effect of suppressing tactile detection and promoting visual detection after the RHI . This efvia the questionnaire, in all conditions regardless of the filament applied (No. 2.36 or No. 2.44). These correlations indicate that the tactile-pressure threshold increased relatively as feelings of ownership of their real hand decreased significantly because of the RHI, resulting in difficulty detecting the tactile stimuli.In the tactile-pressure evaluation test conducted before and after the visuo-tactile stimulation in this study, the filament-detection rate was significantly lower after stimulation than before stimulation under all conditions . In addition, negative correlations were observed between the amount of change in the filament-detection rate and the change in the disownership score, collected In a previous study investigating changes in tactile-detection performance after the presentation of illusion stimuli, the detection of vibration after synchronous conditions was significantly lower than detection after asynchronous conditions . AlthougPhysiological changes induced by illusory body ownership include less activation of motor-evoked potential of the corresponding body part , an atteIn the study’s experimental environment, the rubber hand was placed next to the subject’s own hand in a homologous orientation, which is generally prone to be under the illusion. Therefore, most subjects reported a change in ownership through the illusion manipulation of their non-dominant hands. The detection rate of thick (No. 2.44) filaments was significantly reduced in the study, even under asynchronous conditions. A previous study reported that visual information from a first-person perspective enabled the provision of illusory ownership even under asynchronous visuo-tactile stimulation . The curThe present study demonstrated that illusion-induced stimulation in healthy adults leads to a decrease in sensory detection as well as to a decrease in the SoO of the subjects’ own hands. In clinical cases, many stroke patients declaring disownership showed severe sensory and motor deficits , indicatA previous study using RHI with healthy subjects reported that the illusion had a greater effect on the non-dominant than on the dominant hand . AnotherResults of the present study revealed that the sense of disownership induced by the RHI is an inhibiting factor for sensory detection. Based on this finding, optimizing the SoO of limbs with sensory impairment and decreasing the occurrence of learned nonuse may contribute to the normalization of sensory function. These trials are expected to lead to innovations in rehabilitation strategies.First, the ownership and disownership scores in this study were obtained from questionnaires completed by healthy subjects only; similar results describing changes in the SoO due to illness or trauma are not guaranteed. The causal relationship between the loss of the sense of body ownership and sensory dysfunction in clinical cases remains unclear. Future studies will require the same questionnaire evaluations from clinical patients. Second, the tactile pressure evaluation’s examination region was limited to part of the left thumb; therefore, changes in sensory function throughout the entire hand or in other body parts are unknown. Future investigations that examine if the same physiological change extends to the whole body are necessary and should utilize other experimental set-ups, such as full body illusion.A sense of disownership invoked by inducing the RHI in healthy subjects led to an increase in those subjects’ tactile-pressure thresholds. This result suggests that decrease of body ownership is an important factor in changing the function of tactile sensation. Interventions that alter the sense of body ownership may contribute to the rehabilitation of sensory impairment after stroke.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.The studies involving human participants were reviewed and approved by the Ethics Committee of Tohoku University School of Medicine (registration number: 2020-1-47). The patients/participants provided their written informed consent to participate in this study.KA, TS, and S-II conceived and designed the experiment. KA developed the experimental system, conducted the experiment, and statistical analysis. TS, RO, and ES provided critical review of the experimental procedure and data analysis. KA and TS wrote the draft of the manuscript. All authors contributed to the discussion of the results and approved the final manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Measuring and monitoring health inequalities is key to achieving health equity. While disaggregated data are commonly used to assess differences in health between different population subgroups, summary measures of health inequality also play a vital role in monitoring health inequalities. Building on disaggregated data, they quantify the level of inequality in a single number and are useful to compare inequality over time and across different health indicators, programmes and settings. We provide a comprehensive overview of existing summary measures of health inequality, including their definition, calculation, interpretation and application. The use of these measures is illustrated based on an example from the WHO’s Health Equity Monitor database using the WHO’s Health Equity Assessment Toolkit (HEAT) software. We discuss the strengths and limitations of different measures and provide guidance for selecting suitable summary measures for analysing health inequalities and communicating results. Summary measures of health inequality should form an integral part of health inequality monitoring to inform equity-oriented policies and programmes. Measuring and monitoring health inequalities is essential for achieving health equity—a core commitment of the World Health Organization (WHO) and a central goal of the 2030 Agenda for Sustainable Development ,2. HealtA number of earlier works from the 1990s and 2000s have described existing summary measures of health inequality ,7,8,9,10The aim of this paper is to provide an updated and systematic overview of existing summary measures of health inequality, all of which are available via the WHO’s Health Equity Assessment Toolkit (HEAT) . The sofThere are a number of essential considerations that need to be considered when calculating summary measures of health inequality ,16,17. FHealth indicators may measure various aspects of health, including inputs and processes, outputs, outcomes and impact, as outlined in the WHO’s monitoring, evaluation and review framework ,19. The Dimensions of inequality refer to demographic, socioeconomic or geographic characteristics, based on which populations can be categorised into different subgroups ,22. IneqGenerally, summary measures of health inequality assess either absolute or relative inequality. While absolute measures indicate the magnitude of inequality between population subgroups and normally retain the unit of the health indicator, relative measures show proportional inequality between subgroups and have no unit. Furthermore, summary measures can be divided into simple and complex measures of inequality. Simple measures make pairwise comparisons between two population subgroups, such as the poorest and richest wealth quintile. Complex measures, on the other hand, consider the situation in all population subgroups  and they may also account for the population size of each subgroup. Many complex measures are weighted measures, i.e., weighting population subgroups according to their population size, whereas simple measures are unweighted measures, i.e., weighting all subgroups equally regardless of their size. There are two main types of complex measures: ordered measures, that can be calculated for ordered dimensions (such as economic status) and non-ordered measures, that can be calculated for non-ordered dimensions . An important consideration for non-ordered measures is the selection of a reference point against which the other subgroups are compared. The reference point may be a selected reference subgroup , a reference value , or a defined target. Impact measures are another type of complex measures that can be calculated for both ordered and non-ordered dimensions. These types of measures assess the impact of addressing inequality and estimate the possible improvement in setting average of a health indicator that could be achieved if inequality was eliminated.Simple measures compare the situation in two population subgroups. The selection of the two subgroups depends on the characteristics of the inequality dimension and the purpose of the analysis. For dimensions with two subgroups, such as place of residence , the selection is straightforward. For ordered dimensions, typically, the most-advantaged and most-disadvantaged subgroups are compared . For non-ordered dimensions, the subgroups with the lowest and highest indicator value can be used . Alternatively, it is possible to compare the situation between a defined reference subgroup  or a defined reference value  and another population subgroup. In some cases, it may also be appropriate to compare the situation between defined top and bottom percentiles .DifferenceDefinition: The difference (D) is an absolute measure of inequality that shows the difference in health indicator between two population subgroups.Calculation: D can be calculated as:Interpretation: If there is no inequality, D assumes the value of zero. Greater absolute values indicate higher levels of inequality.RatioDefinition: The ratio (R) is a relative measure of inequality that shows the ratio of two population subgroups.Calculation: R can be calculated as:Interpretation: If there is no inequality, R assumes the value of one. R assumes only positive values. The further the value of R from one, the higher the level of inequality. R is a multiplicative measure and has to be displayed on a logarithmic scale .Complex measures are calculated for inequality dimensions with more than two population subgroups. They consider the situation in all population subgroups and they may also account for the population share of each subgroup. We can differentiate between three types of complex measures as described below: ordered, non-ordered and impact measures.Ordered measures can be calculated for inequality dimension with subgroups that have a natural ordering, such as wealth quintiles. They can be grouped into two categories: disproportionality measures, which express inequality as a function of shares of the health indicator compared to shares of the population, and regression-based measures, which make use of an appropriate regression model to estimate the association between the rank of subgroups and the health indicator ,24.Disproportionality MeasuresAbsolute Concentration IndexDefinition: The absolute concentration index (ACI) is an absolute measure of inequality that shows the gradient across population subgroups. It indicates the extent to which an indicator is concentrated among disadvantaged or advantaged subgroups, on an absolute scale. Subgroups are weighted according to their population share.Calculation: j, j and j.The calculation of ACI is based on a ranking of the whole population from the most-disadvantaged subgroup (at rank 0) to the most-advantaged subgroup (at rank 1), which is inferred from the ranking and size of the subgroups. The relative rank of each subgroup is calculated as: Interpretation: If there is no inequality, ACI assumes the value of zero. Positive values indicate a concentration of the indicator among the advantaged, while negative values indicate a concentration of the indicator among the disadvantaged. The larger the absolute value of ACI, the higher the level of inequality.Relative Concentration IndexDefinition: The relative concentration index (RCI) is a relative measure of inequality that shows the gradient across population subgroups, on a relative scale. It indicates the extent to which an indicator is concentrated among disadvantaged or advantaged subgroups. Subgroups are weighted according to their population share.Calculation: RCI is calculated by dividing the absolute concentration index (ACI) by the setting average Interpretation: RCI is bounded between −1 and +1  and assumes the value of zero if there is no inequality. Positive values indicate a concentration of the indicator among the advantaged, while negative values indicate a concentration of the indicator among the disadvantaged. The greater the absolute value of RCI, the higher the level of inequality.Regression-Based MeasuresSlope Index of InequalityDefinition: The slope index of inequality (SII) is an absolute measure of inequality that represents the difference in estimated indicator values between the most-advantaged and most-disadvantaged subgroup, while taking into consideration the situation in all other subgroups—using an appropriate regression model. Subgroups are weighted according to their population share.Calculation: To calculate SII, a weighted sample of the whole population is ranked from the most-disadvantaged subgroup (at rank 0) to the most-advantaged subgroup (at rank 1). This ranking is weighted, accounting for the proportional distribution of the population within each subgroup. The population of each subgroup is then considered in terms of its range in the cumulative population distribution, and the midpoint of this range. The indicator of interest is then regressed against this midpoint value using an appropriate regression model , and the predicted values of the indicator are calculated for the two extremes (rank 1 and rank 0). The difference between the estimated values at rank 1  is a relative measure of inequality that represents the ratio of estimated indicator values of the most-advantaged to the most-disadvantaged subgroup, while taking into account the situation in all other subgroups—using an appropriate regression model. Subgroups are weighted according to their population share.Calculation: To calculate RII, a weighted sample of the whole population is ranked from the most-disadvantaged subgroup (at rank 0) to the most-advantaged subgroup (at rank 1). This ranking is weighted, accounting for the proportional distribution of the population within each subgroup. The population of each subgroup is then considered in terms of its range in the cumulative population distribution, and the midpoint of this range. The indicator of interest is then regressed against this midpoint value using an appropriate regression model , and the predicted values of the indicator are calculated for the two extremes (rank 1 and rank 0). The ratio of the estimated values at rank 1 .Non-ordered measures can be calculated for dimensions with subgroups that do not have a natural ordering, such as subnational regions. There are three main groups of non-ordered measures: variance measures, which are based on the variance that summarises the squared deviations from the setting average; mean difference measures, which show the mean difference from a reference point, such as the setting average or the best-performing subgroup, i.e., the subgroup with the highest value in the case of favourable health indicators and the subgroup with the lowest value in the case of adverse health indicators; and disproportionality measures, which express inequality as a function of shares of the health indicator compared to shares of the population ,25,26. VVariance MeasuresBetween-Group VarianceDefinition: The between-group variance (BGV) is an absolute measure of inequality that considers all population subgroups. Subgroups are weighted according to their population share.Calculation: BGV is calculated as the weighted average of squared differences between the subgroup estimates Interpretation: BGV obtains only positive values with larger values indicating higher levels of inequality. BGV is zero if there is no inequality. BGV is more sensitive to outlier estimates as it gives more weight to the estimates that are further from the setting average. It is reported as the squared unit of the health indicator.Between-Group Standard DeviationDefinition: The between-group standard deviation (BGSD) is an absolute measure of inequality that considers all population subgroups. Subgroups are weighted according to their population share.Calculation: BGSD is calculated as the square root of the weighted average of squared differences between the subgroup estimates Interpretation: BGSD assumes only positive values, with larger values indicating higher levels of inequality. BGSD is zero if there is no inequality. BGSD is more sensitive to outlier estimates as it gives more weight to the estimates that are further from the setting average. It has the same unit as the health indicator.Coefficient of VariationDefinition: The coefficient of variation (COV) is a relative measure of inequality that considers all population subgroups. Subgroups are weighted according to their population share.Calculation: COV is calculated by dividing the between-group standard deviation (BGSD) by the setting average Interpretation: COV assumes only positive values, with larger values indicating higher levels of inequality. COV is zero if there is no inequality.Mean Difference MeasuresMean Difference from MeanDefinition: The mean difference from mean (MDM) is an absolute measure of inequality that shows the mean difference between each subgroup and the setting average. MDM can be calculated as an unweighted or weighted measure. For the unweighted version, all subgroups are weighted equally. For the weighted version, subgroups are weighted according to their population share.Calculation: The unweighted version (MDMU) is calculated as the average of absolute differences between the subgroup estimates Interpretation: MDM assumes only positive values, with larger values indicating higher levels of inequality. MDM is zero if there is no inequality.Mean Difference from Best-Performing SubgroupDefinition: The mean difference from best-performing subgroup (MDB) is an absolute measure of inequality that shows the mean difference between each population subgroup and a reference subgroup. MDB can be calculated as an unweighted or weighted measure. For the unweighted version, all subgroups are weighted equally. For the weighted version, subgroups are weighted according to their population share.Calculation: The unweighted version (MDBU) is calculated as the average of absolute differences between the subgroup estimates The weighted version (MDBW) is calculated as the weighted average of absolute differences between the subgroup estimates Interpretation: MDB assumes only positive values, with larger values indicating higher levels of inequality. MDB is zero if there is no inequality.Index of DisparityDefinition: The index of disparity (IDIS) is a relative measure of inequality that shows the average difference between each population subgroup and the setting average, in relative terms. IDIS can be calculated as an unweighted or weighted measure. For the unweighted version, all subgroups are weighted equally. For the weighted version, subgroups are weighted according to their population share.Calculation: The unweighted version (IDISU) is calculated as the average of absolute differences between the subgroup estimates The weighted version (IDISW) is calculated as the weighted average of absolute differences between the subgroup estimates Interpretation: IDIS assumes only positive values, with larger values indicating higher levels of inequality. IDIS is zero if there is no inequality.Disproportionality MeasuresTheil IndexDefinition: The Theil index (TI) is a relative measure of inequality that considers all population subgroups. Subgroups are weighted according to their population share.Calculation: j, j and TI is calculated as the sum of products of the natural logarithm of the share of the indicator of each subgroup .Mean Log DeviationDefinition: The mean log deviation (MLD) is a relative measure of inequality that considers all population subgroups. Subgroups are weighted according to their population share.Calculation: j, j and MLD is calculated as the sum of products between the negative natural logarithm of the share of the indicator of each subgroup .Impact measures estimate the impact of addressing inequalities in a health indicator. They quantify the possible improvement in setting average of a health indicator that could be achieved if the entire population had the same level of the health indicator as a reference subgroup. Which subgroup is selected as the reference subgroup depends on the type of health indicator and inequality dimension. For ordered dimensions, the most-advantaged subgroup is used , regardless of the indicator type. For Non-ordered dimensions, such as subnational regions, usually the best-performing subgroup is used, i.e., the subgroup with the highest value in the case of favourable indicators and the subgroup with the lowest value in the case of adverse indicators. Alternatively, a defined reference subgroup can be used .Population Attributable RiskDefinition: The population attributable risk (PAR) is an absolute measure of inequality that shows the potential improvement in setting the average of a health indicator, in absolute terms, that could be achieved if all population subgroups had the same level of the indicator as a reference group.Calculation: μ:PAR is calculated as the difference between the estimate for the reference subgroup Given the setting average is the weighted average of all subgroup estimates (with subgroups being weighted by their population share), PAR considers all population subgroups. As described above, the selection of the reference subgroup depends on the characteristics of the inequality dimension and the indicator type. Please refer to Interpretation: PAR assumes positive values for favourable indicators and negative values for adverse indicators. The larger the absolute value of PAR, the higher the level of inequality. PAR is zero if no further improvement can be achieved, i.e., if all subgroups have reached the same level of the indicator as the reference subgroup or surpassed that level.Population Attributable FractionDefinition: The population attributable fraction (PAF) is a relative measure of inequality that shows the potential improvement in setting the average of a health indicator, in relative terms, that could be achieved if all population subgroups had the same level of the indicator as a reference group.Calculation: PAF is calculated by dividing the population attributable risk (PAR) by the setting average Interpretation: PAF assumes positive values for favourable indicators and negative values for adverse indicators. The larger the absolute value of PAF, the larger the level of inequality. PAF is zero if no further improvement can be achieved, i.e., if all subgroups have reached the same level of the indicator as the reference subgroup or surpassed that level.The summary measures described above were calculated based on disaggregated data from the WHO Health Equity Monitor database (2021 update) . The datFor the purpose of this paper, we used data from three rounds of DHS from Indonesia  to assess the latest situation of inequality and the change in inequality over time. In addition, we compared the situation in Indonesia with the situation in 15 other countries from the WHO South-East Asia and Western Pacific regions, using data from the latest available DHS and MICS from 2015–2019. We selected three RMNCH indicators, including births attended by skilled health personnel; demand for family planning satisfied ; and measles immunisation coverage among one-year-olds. All indicators were disaggregated by economic status and subnational region. Detailed information about the data sources, health indicators and inequality dimensions can be found in the indicator compendium of the Health Equity Monitor database .Summary measures of health inequality and corresponding 95% confidence intervals were calculated using the HEAT software .The latest available data for these three health indicators show that coverage in Indonesia also varied largely by subnational region . In 2017In comparison with 15 other countries from the WHO South-East Asia and Western Pacific regions, Indonesia performed well overall, both in terms of national average (91.6%) and absolute economic-related inequality (difference of 23.6 percentage points between the richest and poorest quintile) in births attended by skilled health personnel . CountriState of health inequality: Indonesia report provides a comprehensive assessment of the state of health inequality in Indonesia [Please refer to ndonesia .We have provided a systematic overview of existing summary measures of health inequality, including their definition, calculation and interpretation. The application of these measures based on an example from the WHO’s Health Equity Monitor database using the WHO’s Health Equity Assessment Toolkit demonstrates their usefulness for monitoring health inequalities in countries.The different summary measures presented in this paper have different strengths and limitations that are important to keep in mind when monitoring health inequalities. Simple measures can be calculated for all types of inequality dimensions and are easy to interpret. However, for dimensions with more than two population subgroups, they ignore the situation in the other subgroups, and they do not account for the population size of each subgroup . Complex measures overcome these two limitations. They consider all population subgroups and they may also account for the population share of each subgroup . However, complex measures are inherently more challenging to calculate and interpret. Whether to use simple or complex, unweighted or weighted measures, depends on the available data and purpose of the analysis. Similarly, the selection of a reference point for certain summary measures , is a normative decision that needs to be considered in the context of the research question at hand. Finally, while summary measures of health inequality are useful to quantify the magnitude and direction of inequality, they do not explain why inequalities exist. In order to identify the root causes of inequality, further in-depth research is required that makes use of additional quantitative and qualitative data and more sophisticated analysis methods.Software applications such as HEAT make it easy for users to calculate summary measures of health inequality, including complex measures . The chaSummary measures of health inequality quantify the level of inequality in a single number and facilitate the assessment of inequalities over time and across different indicators and settings. Software applications, such as the WHO’s Health Equity Assessment Toolkit, make it easy for users to calculate, interpret and communicate summary measures. Their use should be complementary with disaggregated data, and form an integral part of health inequality monitoring in order to design health policies and programmes that are equity oriented.


Goal: The importance of the main impeller design parameters in bearingless centrifugal pumps with respect to hemolysis for cardiopulmonary bypass (CPB) and extracorporeal membrane oxygenation (ECMO) applications are studied in this work. Methods: Impeller prototypes were designed based on theoretical principles. They were manufactured and their hydraulic and hemolytic performance were analyzed experimentally. The cell compatibility is benchmarked against commercially available centrifugal blood pumps BPX-80 (Medtronic) and FloPump 32 . Results: The developed prototypes outperform the BPX-80 and FloPump 32 with regard to hemocompatibility by more than a factor of 4.5. The implemented pump features reduced overall and priming volumes. A significant improvement of the cell compatibility is achieved by increasing the radial gap between the impeller and the pump head. The blade should be sufficiently high and a blade outlet angle of 90° provides favorable performance. No correlation between the hydraulic and hemolytic performance is observed. Conclusions: This work identified the most important geometrical parameters of the impeller for blood pumps with respect to cell compatibility. This provides valuable design guidelines for improving existing pumps. I.Extracorporeal life support (ECLS) is used during surgery and to support failing organ systems of the human body. During cardiac surgery, the cardiopulmonary bypass (CPB) technique is applied to temporarily take over the function of the heart and lungs. In case of acute respiratory diseases, a modified form of CPB, referred to as extracorporeal membrane oxygenation (ECMO) is used. Compared to CPB, where 100% of the blood flow is directed through the pump, the heart function is only supported and approximately 20% of the volume flow still passes through the heart and lung to prevent stagnation and clotting. Due to the lower stress on these organs, they are able to regenerate more quickly If both, the heart and lung function, must be supported, blood is drawn venously, filtered, oxygenated, tempered outside the body, and injected arterially (VA-ECMO). If only the lung has to be supported, blood is drawn venously and returned venously (VV-ECMO). During VV-ECMO, the heart continues its normal function. Thus, VA-ECMO is typically used in case of cardiac failure, while VV-ECMO is used in case of respiratory failure To provide a continuous blood flow through the extracorporeal circuit, specialized blood pumps that are designed to be hemocompatible are required. One of the complications arising from the use of such mechanical circulation is the rupture and destruction of red blood cells (hemolysis) caused by the severe stresses acting on the blood.The objective of this work is to analyze the importance of different geometrical parameters of the impeller in bearingless centrifugal pumps with respect to hydraulic efficiency and hemolysis by means of experiments. The results are intended to provide design guidelines for improving the cell compatibility of blood pumps and ultimately result in higher survival rates in future ECLS applications. The findings of this study are particularly relevant for bearingless centrifugal pumps. Their applicability to other pump and motor concepts with significantly different geometries, dimensions, and operating conditions needs to be carefully assessed. In vitro testing of newly developed pumps remains necessary.A.Until 2009, roller pumps were the predominant type of pump used in ECLS The Bio-Medicus vortex pump (presently Medtronic BPX-80) was the first centrifugal pump to be tested as an ECLS pump in 1975 and brought to the market in the same year In 2004, the CentriMag (Abbott) was the first pump featuring a completely magnetically suspended impeller that was clinically tested In the paper at hand, the same bearingless motor type is used. It combines the bearing and drive unit in a single magnetic circuit, thus resulting in a highly compact system. The rotor features a disk shape, which allows for passive stabilization in three degrees of freedom, namely with respect to axial displacements and tilting around the axis of magnetization and perpendicular to it. Only the two radial degrees of freedom have to be controlled actively to attain stable levitation B.Due to its complexity, the process of cell damage is still not entirely understood. However, a broad consensus in the literature exists that cell damage is related to shear forces Several studies exist that benchmark commercially available products and prototypes against each other In the study at hand, in vitro hemolysis experiments on selective impeller variations for a fully magnetically levitated pump for ECLS applications are conducted. To the authors' knowledge, this is the first in vitro study that considers impeller geometry variations for this type of pump.II.A.1)During VA-ECMO, the amount of flow that is taken over from the heart by the pump depends on the severity of the disease. The highest flow rates have to be provided for severe diseases and high oxygenation, as well as during CPB, where the entire flow of the human heart In centrifugal pumps, the pressure is generated by means of centrifugal forces. The fluid enters the impeller blade at the top opening around the axis of rotations in axial direction and exits the blade passage at the circumference of the impeller in radial direction towards the volute. 3)The optimal impeller diameter with respect to hydraulic efficiency for a given operating point  can be found based on an empirical study of industrially used turbomachinery 4)The outlet angle The lowest rotational speeds are obtained for low outlet angles and large outlet heights. However, the required speed is highly sensitive to the outlet height. For For the aforementioned calculations, a volumetric efficiency of 5)The circular opening at the inlet side of the impeller, referred to as the eye, is designed such that a minimal relative velocity between the fluid and the leading edge of the blade is achieved. Considering the velocity triangle at the inlet, the relative velocity 6)A conventional semi-volute design is chosen to reduce the radial thrust over the entire range of the flow-rate. This also prevents regions of high shear stress at the volute tongue. The radial distance from the impeller to the outer wall of the volute is chosen larger than in classical pump designs to reduce the circumferential velocity of the flow near the volute housing. These are typical design choices for slurry pumps The inlet and outlet are chosen to have an inner diameter of B.To identify the most important geometric parameters with respect to cell damage, the major design parameters, namely the blade outlet angle ent} see  were adjBetween designs B, BH−, and BH+, the blade height All impellers and housings were milled from polycarbonate with minimum possible surface roughness For the presented in vitro study, bovine blood was used as its hemolytic characteristics are similar to those of human blood 2)Each pump circuit, as shown in 3)Blood samples of To reduce the variation between different experiments caused by the blood sensitivity of different individuals, the industrial bearingless pump DCP-1.4 (Levitronix GmbH) was run simultaneously during all experiments, acting as an independent reference. The different designs can thus be compared to the reference value III.A.All impeller designs were tested hydraulically at their nominal operating speeds. The resulting pressure-flow curves, including the pump efficiencies Except for the design SO, all prototypes reach the operating conditions listed in B.To relate the cell compatibility of the developed prototype to state-of-the-art pumps, the standard impeller design was benchmarked against the commercially available BioPump BPX-80 (Medtronic) and the FloPump 32 , which is identical to the Maquet Rotaflow, using the test setup described in The base design B shows a statistically significant improvement of the hemocompatibility compared to the BPX-80 and FloPump 32 (C.All impeller variations were tested for their cell compatibility according to Each variation was tested 8 times. The base design was tested 16 times in total. IV.In the following, the results of the hemolysis tests are discussed in detail and interpreted.A.The impact of the blade height is assessed by comparing the mean values achieved by the designs B, BH−, and BH+ in B.In the designs D- and RG+, the radial gap between the impeller hub and the volute housing was increased with respect to the base design B. C.Compared to the initial design, no improvement of the hydraulic efficiency can be found for a blade angle of D.The semi-open blade of design SO results in a low hydraulic efficiency. This is likely due to the increased slip at the hub and shroud side of the open impeller part. Even though the rotational speed and, thus, the shear stress in the bottom part of this impeller are significantly reduced compared to the base design B, the hemolysis generation significantly increases (E.Design HH- only differs from design B by a reduced magnet and hub height. During hydraulic tests, this impeller performed best. However, it causes more hemolysis (F.Based on the obtained experimental results for the hydraulic efficiency and hemolytic performance, it can be observed that it is not sufficient to design the impeller blades for high hydraulic efficiency as only a weak correlation between these two parameters can be observed. For example, designs D- and RG+ both have an improved cell compatibility compared to B but exhibit similar efficiencies. Between the mean G.For the base design B a cell damage of less than 1/5 of that caused by the BPX-80 pump was observed during in vitro tests (V.A bearingless centrifugal pump was designed and implemented. Several impeller designs were tested hydraulically and with regard to hemolysis. An overall hydraulic efficiency between Impeller blades should not reach into the volute as this reduces the hydraulic efficiency and cell compatibility. No relevant correlation between the hydraulic efficiency and hemolysis was observed.The developed prototype outperforms the BPX-80 and FloPump 32 pumps in terms of hemolysis generation by a factor of 5.4 and 2.7, respectively and requires a priming volume of only


The recent development of 3D flash memories has promoted the widespread application of SSDs in modern storage systems by providing large storage capacity and low cost. Garbage collection (GC) as a time-consuming but necessary operation in flash memories largely affects the performance. In this paper, we perform a comprehensive experimental study on how garbage collection impacts the performance of flash-based SSDs, in the view of performance cliff that closely relates to Quality of Service (QoS). According to the study results using real-world workloads, we first observe that GC occasionally causes response time spikes, which we call the performance cliff problem. Then, we find that 3D SSDs exacerbate the situation by inducing a much higher number of page migrations during GC. To relieve the performance cliff problem, we propose PreGC to assist normal GC. The key idea is to distribute the page migrations into the period before normal GC, thus leading to a reduction in page migrations during the GC period. Comprehensive experiments with real-world workloads have been performed on the SSDsim simulator. Experimental results show that PreGC can efficiently relieve the performance cliff by reducing the tail latency from the 90th to 99.99th percentiles while inducing a little extra write amplification. Due to shock-resistance, high access speed, low energy consumption, and increased capacity, Solid-State Drives (SSDs) ,2,3 gradGarbage collection (GC) is responsible for reclaiming blocks with a large proportion of invalid pages. A GC operation consists of two main phases: valid page migration and block erase. GC often has a great impact on system performance. Paik et al.  and Wu eIn this paper, we perform a comprehensive experimental study on how garbage collection affects the system performance of SSDs in the view of performance cliff that closely relates to tail latency and affects Quality of Service (QoS). According to preliminary study results, we first observe that SSD response time shows occasional spikes. By comparing with 2D SSDs, these spikes in 3D SSDs have much higher values and occur more frequently, which makes the performance situation worse. We call this phenomenon of response time spikes the problem of “performance cliff”. This directly induces the sharp increase of tail latency that is often used as the evaluation of Quality of Service (QoS) by the industry.In order to study the cause of performance cliff, we collect some experimental results about garbage collection and obtain two extra observations. On the one hand, the number of page migrations during GC sharply increases, especially in 3D SSDs. On the other hand, page migration latency takes up the majority of GC latency while block erase only takes up a small proportion.According to the above observations, we propose a GC-assisting method, called PreGC to mitigate the GC latency and to optimize tail latency. The key idea of PreGC is to migrate part of valid pages in advance of normal GC, which can distribute heavy page migrations into the other system time. The challenge to implement PreGC is to decide when and how many pages to migrate. PreGC is invoked near by the normal GC and migrates valid pages during system idle time in a fine-grained incremental way. In this way, it can mitigate unnecessary migrations that overlap with page updates between PreGC and normal GC and reduces the effect of pre-migrations on normal requests.In order to evaluate the proposed PreGC, we perform a comprehensive experiment on the SSDsim simulator with real-world workloads. From the experimental results, we show that PreGC is effective in reducing page migrations and optimizing system performance with reduced 90th to 99.99th percentile tail latencies.We perform a preliminary experimental study on the response time and tail latency of SSDs and observe the performance cliff problem.We uncover that the main cause of the performance cliff problem is the significantly increased latency of garbage collection. These increased latency are mostly caused by the increased number of page migrations in 3D SSDs.According to the above observations, we propose a GC-assisting method called PreGC to relieve the performance cliff. By pre-migrating a part of valid pages ahead of normal GC time, page migration latency can be distributed into other system time and thus can be largely reduced during GC period.We evaluate the proposed PreGC with real-world workloads on the SSDsim simulator. The results show that performance cliff can be significantly relieved by lowering down the tail latency.The contributions of this paper are listed as follows:The rest of this paper is organized as follows. This section first introduces the basic structure of 3D SSDs, in which the large block problem is mentioned. Then, we illustrate the mechanism of garbage collection. At last, layer speed variations are illustrated to show the uneven data hotness problem in 3D charge-trap (CT) SSDs.SSDs are composed of a controller and flash arrays. The controller is responsible for organizing data access on flash arrays and for effectively using a flash. For example, the flash translation layer is used to manage the mapping between physical addresses and logical addresses. The garbage collection mechanism cleans invalid data blocks to overcome the out-of-place nature of flash memory. Moreover, error correction and wear leveling are designed to make data reliable and to even cause wear on flash blocks.The flash arrays in 3D SSDs are composed of 3D flash memory, which greatly increases the capacity of SSDs by vertically stacking multiple layers. Due to the out-of-place update feature of flash memory, a lot of invalid data would be generated after SSD has been used for a while. Garbage collection is used to reuse the space occupied by these invalid data. The granularity to perform GC is a block, but the basic unit of read and write is page. The process of GC is mainly divided into two stages: valid data migration and block erase. After a victim block is selected, valid pages are first migrated into another block. After all valid pages are migrated, block would be erased to be a free block again. Thus, the latency of GC is decided not only by block erase but also by page migrations.This part introduces the charge trap (CT)-based flash memory, a special type of 3D flash memory widely used in 3D SSDs, which utilizes an effective way to construct a vertical flash structure. There are multiple gate stack layers and vertical cylinder channels in 3D CT flash ,21, as sThis paper focuses on optimizing the performance of 3D SSDs in the view of garbage collection. As previous works related to garbage collection schemes have been discussed in By utilizing the logic in programming and reads, several works have been proposed. Wu et al.  proposedBy exploiting the physical feature of layer-to-layer structures, other works have been proposed. Chen et al.  exploiteDifferent from the above method of hiding the necessary latency or a method of improving the long tail latency by reducing the frequency of GC blocking I/O such as GFTL , which pThis section presents our preliminary study on 3D SSD performance based on the two problems of big block size and data unevenness. First, we introduce the experimental setup of this study, including 3D SSD configurations and workloads. Then, three observations from the studied results are explained in details. At last, through analysis and comparison, it is concluded that sharply increased page migrations during GC are the main cause of severe performance cliffs in 3D SSDs.We used SSDsim to simulate 2D SSDs, and some of its components were modified to simulate 3D SSDs by adding layer information for data. The parameter configurations for 2D and 3D SSDs are shown in Six real-world workloads  were choBased on these settings, the SSD performance cliff by GC was first observed by analyzing request response time series. Then, in order to find the reason behind this phenomenon, extra two experimental results including migrated page numbers and latency distribution in the GC period were then shown and analyzed.A main indicator for SSD performance is its response time, which is the latency in processing read and write requests. Request response time during a period of about two milion requests in the workload hm0 was collected and shown in As GC performance in 3D SSDS is affected by the big block problem, which would induce increased page migrations, we collected page migrations numbers of each GC in workload hm0, as shown in As illustrated in As the block erase time for both SSDs is similar because of the technology development of 3D flash memory, the latency of page migrations is the main cause of high GC latency. Therefore, the server performance cliff problem of 3D SSDs uncovered above is mainly caused by the sharply increased number of page migrations. According to this conclusion, this paper proposes a reduction in page migrations for 3D SSDs by pre-migrating valid pages near the time when GC is invoked. Next, the detailed design of our method would be presented.This section introduces our proposed PreGC method from three aspects: overview, workflow, and cooperation with normal GC. First, the architectural overview of PreGC is presented. Then, the workflow of PreGC is illustrated to show when to trigger PreGC, how to perform page migrations in PreGC, and when to stop these migrations. Lastly, how PreGC can assist normal GC for performance cliff reduction is shown.The overview of 3D SSDs with PreGC is shown in As PreGC is a method of performing partial page migrations ahead of normal GC time, it has to work together with existing GC methods. PreGC mainly contains two components to judge when to invoke and stop the pre-migration operations: invoking and stopping. Briefly speaking, the invoking condition depends on the ratio of free blocks, which is similar to that in normal GC. However, in order to make a balance between write amplification and GC page migration reduction, the threshold ratio for invoking PreGC should be deliberately designed. The stopping condition of PreGC depends on how many valid pages exist in the victim block. As there is no need to migrate all valid pages, which may make normal GC ahead of its original, the threshold ratio is set to a value a little below the invoking threshold of normal GC. Details of the workflow to use PreGC within the right module of In order to better describe the specific implementation process of PreGC, a workflow chart is presented in the right part of From the above workflow, we can find that the effectiveness of PreGC largely depends on system idle time as well as the pre-migration numbers. Thus, it would be evaluated comprehensively with multiple workloads having varied system idle time and with multiple parameter settings of PreGC is a novel method to improve the performance of SSD by working together with GC and is actually not a replacement for existing GC methods that we call normal GC in this paper. Thus, PreGC is orthogonal with normal GC methods. This section presents how PreGC assists the normal GC to reduce page migrations. PreGC is often used before the normal GC on the victim block, as shown in This section first describes the experiment platform and parameter configurations to evaluate our proposed PreGC. Then, the experimental results about performance and overhead of PreGC are shown and analyzed under five real-world workloads by comparing with the original GC method.The experiment designed for PreGC evaluation is illustrated from the following four aspects. First, SSD configurations using the SSDsim simulator  are presSSD configurations: The proposed PreGC method was integrated into the controller of 3D SSDs, and all experiments were conducted on a flash simulator named SSDsim , which iReal-world workloads: To evaluate the effectiveness of PreGC on performance cliff and tail latency reduction, five real-world workloads with different features were chosen from Umass , as listParameter settings: There were two thresholds involved in the PreGC flow chart, as illustrated earlier, which are the free block ratio threshold Tblock used to invoke page migrations in PreGC and the valid page ratio threshold Compared methods: Our PreGC method is designed to assist the traditional GC methods, and we are the first to propose such a GC assistance from the aspect of page migrations. Thus, we compare the performance and overhead of SSD systems with and without ProGC together with the original GC method, and the excellent partial GC method GFTL. Moreover, we combined PreGC and GFTL to prove that our approach can work with other methods. The four compared methods are denoted as PreGC, Original, GFTL, and GFTL after PreGC.It is worth mentioning that the comparison of the methods from GFTL and PreGC shows in We first analyze the results of PreGC on normal page migration, which indicates the number of migrated pages when GC happens. As PreGC migrates some valid pages in advance, page migrations when GC happens are reduced, noting that our PreGC method does not reduce the overall migrated pages. We call page migrations in GC normal. Details about the reduction are presented in In order to show the effect PreGC on page migrations, the average number of normally migrated pages is computed as Equation , in whicEquation , in whicThe comparison results without and with PreGC, the numbers of invoked PreGC, and the average pre-migration numbers by PreGC are presented in By analyzing the results of PreGC numbers and average pre-migrated page numbers, it can be found that pre-migrated page numbers are larger than normal page migration reduction and varies among workloads. These results are largely affected by the system idle time in workloads; due to that, page pre-migration can only be performed during the system is idle, the system status should be detected after each page pre-migration operation, and the next page pre-migration operation continues when the detection result of system status is idle. From This section presents the performance results of the original and PreGC in terms of performance cliff and tail latency.Performance cliff: In order to intuitively compare the performance results before and after applying our proposed PreGC method, the performance cliff for workload hm0 is shown in Tail latency: Another quantitative evaluation of tail latency results with the 95th percentile and 99th percentile are presented in As PreGC would migrate valid pages in advance before normal GC is invoked, the migrated pages might be updated during the pre-migration period and the victim block chosen in PreGC may not be the victim block in normal GC. Thus, PreGC would induce an extra write amplification, the results of which are shown in The above results have already verified the effectiveness of our proposed PreGC method under specific parameters. This section presents the performance result for more settings on key parameters in our implementation. However, if the value continues to increase after a suitable value, it will cause the valid pages to be migrated too early, which will lead to a lot of invalid data to be generated and results in more GC; then, the request may be suspended for a longer period of time, which makes the tail latency longer. Second, the 99th tail latency increases as the value of Our PreGC method provides an assistance to existing GC methods and are orthogonal with many GC optimization methods. The pre-migrations would happen between the PreGC invoking time and normal GC invoking time when SSD system is idle. Thus, the effectiveness of PreGC can be largely exploited for workloads that have long system idle time close to the GC invoking time. Although PreGC can relieve performance improvements on tail latency, the problem of write amplification caused by the pre-migration of valid pages, that is, the amount of data actually written in the SSDs, is many times the amount of data that the host requests to write. Although it is inevitable for pre-migrations to cause write amplification, PreGC applies a mechanism to stop it in time to alleviate the problem. Therefore, the write amplification brought about by this method is within the small range. The other overhead is to store two thresholds for triggering and stopping PreGC. As the two parameters only take up a small space, the storage overhead caused by our method can be ignored.In order to satisfy the increased concerns about SSD performance, this paper studied GC performance, which closely relates to system performance, in the view of performance cliff and tail latency. Several observations have been found from our preliminary experiments. The root cause of performance cliff, increased page migrations, has been figured out. A new garbage collection method, PreGC, is proposed to invoke partial page migrations in advance, which can reduce the GC latency effectively. Experimental results have shown the effectiveness of PreGC. As our method is also suitable for optimizing wear leveling schemes, we will study this problem in our future work.


Hence, the presented concepts enable adaptive impedance matching with favorable characteristics for low-energy sensor systems, i.e., minimized footprint, power level and reaction time.Near-field interfaces with miniaturized coil systems and low output power levels, such as applied in biomedical sensor systems, can suffer from severe efficiency degradation due to dynamic impedance mismatches, reducing battery life of the power transmitter unit and requiring to increase the level of electromagnetic emission. Moreover, the stability of weakly-coupled power transfer systems is generally limited by transient changes in coil alignment and load power consumption. Hence, a central research question in the domain of wireless power transfer is how to realize an adaptive impedance matching system under the constraints of a simultaneous power feedback to increase the system’s efficiency and stability, while maintaining circuit characteristics such as small size, low power consumption and fast reaction times. This paper presents a novel approach based on a two-stage control loop implemented in the primary-side reader unit, which uses a digital PI controller to maintain the rectifier output voltage for power feedback and an on-top perturb-and-observe controller configuring the setpoint of the voltage controller to maximize efficiency. The paper mathematically analyzes the AC and DC transfer characteristics of a resonant inductive link to design the reactive AC matching network, the digital voltage controller and ultimately the DC-domain impedance matching algorithm. It was found that static reactive L networks result in suitable efficiency levels for coils with sufficiently high quality factor even without adaptive tuning of operational frequency or reactive components. Furthermore, the regulated output voltage of the rectifier is a direct measure of the DC load impedance when using a regular DC/DC converter to supply the load circuits, so that this quantity can be tuned to maximize efficiency. A prototype implementation demonstrates the algorithms in a 40.68 MHz inductive link with load power levels from 10 to 100 mW and tuning time constants of 300 ms, while allowing for a simplified receiver with a footprint smaller than 200 mm The technology of inductive coupling has been widely adopted to supply low-power embedded sensor systems, as it is a reliable and convenient mechanism of wireless power transfer (WPT). Consequently, especially biomedical sensor systems such as cochlear implants to improve hearing , retinalThe operational principle of inductive coupling is shown in er coils ,5,6,7,8,However, these peak efficiency levels can only be reached for a certain complex load impedance lignment ,9:(3)ZL,It is very likely that this optimal impedance does not correspond to the actual load impedance y supply . This ispower feedback have been established in the literature: Here, the supply voltage To overcome the limited reliability of the link for weak coupling, mechanisms of nt level ,11,12,13maximum efficiency point tracking (MEPT), has been addressed by various approaches:Moreover, changes in coil distance and alignment alter As the first category of adaptive matching in the AC domain, being in line with classical RF circuit design, reconfigurable reactive matching networks with switchable arrays of capacitors and/or inductors have been proposed to transform both real and imaginary parts of the load impedance and input impedance to the corresponding optimal values ,15,16. HDefining the second category of adaptive matching, a voltage conversion in the DC domain is equivalent to a resistance transformation. The concept is classically used in the domain of energy harvesting, i.e., to maximize the power being extracted from solar cells, but has also been applied to the domain of WPT: A DC/DC converter is located at the output of the rectifier stage see  to supplThis implies that a DC/DC converter modifies the DC load resistance In the first circuit and control topologies that applied these principles to the field of WPT, the impedance transformation ratio was determined by the switching duty cycles of individual transistors within the primary- and secondary-side DC/DC converters ,18. EffiAs perturbing the duty cycle of several transistors will result in complex control circuits when simultaneously regulating the load voltage, the concept of post-regulation was established: a regular output-controlled DC/DC converter regulates the output voltage of the link, while a primary-side parameter such as the amplifier’s supply voltage  or the pTo enable a fast transient settling of the efficiency optimization in the range of 300 ms, one requires control mechanisms maintaining a certain relation of primary-side coil current, load current and coupling factor  or a cerposed by , which efunction : here, tAs a result, it is the objective of this work to analyze and realize a maximum efficiency point tracker for the application in miniaturized and weakly coupled systems, which optimizes the DC-to-DC power transfer efficiency, implements a power feedback mechanism and requires only a fraction of the low power levels to be transferred, i.e., a few mW. The dynamic optimization should avoid restricting approximations while still providing fast reaction times.The approach is enabled by the mathematical dimensioning of the reactive matching networks and the generalized efficiency analysis of nonlinear radio-frequency power conditioning circuits in The separation distance of the power transfer coils Intan RHS2164 [The power consumption of the load electronics  RHS2164 ) even duThroughout the paper, we examine the impact of the concepts for an exemplary case scenario of a brain implant, such as applied in the context of brain computer interfaces and neural disease research . These sWith respect to the electromagnetic interface, the exemplary analysis is based on the capacitively segmented planar spiral coils optimized in . These cIn the first part of our analysis, we focus on the efficiency characteristics of the unregulated link including primary-side power amplifier and rectifier such as shown in The optimal load impedance L,opt of  already nsidered , but notThen, the overall impedance resulting from the AC load resistance dance of :(9)ZL,opUsing (9) and solving for the parallel components, we obtain: These generic results automatically specify the optimal values for the particular cases of series resonance With the z-domain transfer function Now, every set of the controller’s parameters  in the first step and then to measure the effect on the target metric (observation). If the latter has changed favorably, the perturbation will be increased into the same direction; otherwise, the direction will be changed. In the presented application, this means that the setpoint of the rectifier’s output voltage A method for modifying the control variable  and hase, e.g., ,18,20). start the next perturbation step when the error of the voltage controller size of the perturbation step has to be adapted to the standard deviation of the efficiency measurement: if the standard deviation is high, there will be a certain probability of detecting the wrong sign of an efficiency change and of stepping into the false search direction. On the one hand, a higher perturbation step allows for a more distinct change in efficiency and enables a faster convergence towards the optimum. On the other hand, the optimum cannot be precisely reached. Hence, speed and precision can be traded upon the needs of the application.There are questions that still remain: When should the next perturbation step start? How large should the perturbation be? A custom approach of the proposed tracking scheme is to The nested mechanisms of power feedback (by voltage regulation) and maximum efficiency point tracking are graphically summarized in the flowchart of Silicon Labs EFR32BG) to execute measurement and control tasks. Moreover, both devices can measure the ingoing or outgoing DC power level at the WPT interface  technology, shown in ion, cf. ) to limiLinear Technology LTC3130 buck-boost converter with a Murata LQH3NPZ 10 µH inductor is complemented by a feedback resistor Lattice iCE40UP) generates the 40.68 MHz RF signal driving the gate of the class E amplifier’s transistor; a logic buffer integrated circuit (Nexperia 74AUP2G16) operates as a gate driver.In particular, the primary side features an adjustable voltage converter to realize the control of the rectifier output voltage: a Linear Technology LTC3130 with a Wuerth WE-PMI 10 µH inductor) with wide input range, configured for a constant output voltage of The secondary side applies a low-power buck-boost converter : here, the total system efficiency Whenever the voltage controller has settled, i.e., the voltage controller’s error term stays below 50 mV in three subsequent sampling steps, the maximum efficiency point tracking algorithm is executed (with the step index ressions  and (40)The parameters of the controllers are chosen as derived above and compiled in In summary, the receiver only executes minimal measurement tasks, which can run in a lightweight task along any main application, while the computations for power feedback and maximum efficiency point tracking are offloaded on to the transmitter side.In the following section, the realized system is to subject to a series of static and dynamic measurements to evaluate the theoretical foundations of voltage control and efficiency optimization. All experiments implement the case scenario specified in Saleae Logic Pro 16 analyzer with the setup shown in In the first step of the practical evaluation, the relation of rectifier output voltage and efficiency, being the essential relation required for the given efficiency point tracking mechanism, is analyzed. In this basic configuration, the power transfer coils are separated by a distance The relation of the given parameters and the rectifier output voltage The measured efficiency levels were also verified with the harmonic balance simulation setup described in The operability and stability of the voltage controller was analyzed for the maximum nominal coil separation distance of 20 mm, as the increased distance leads to a higher time constant Applying a series of steps in the setpoint of the controller across the suitable output voltage range results in the system behavior of icted by  for the An exemplary reaction of the voltage controller to transient changes of the load power consumption is provided in Finally, voltage controller and maximum efficiency point tracker are both enabled as provided in the flowchart of First, the system is operated at the nominal operational distance of 10 mm with a base power consumption level of 25 mW. After 0.3 s of acquisition time, the power consumption is increased to 90 mW, and it is decreased back to 25 mW at 1.2 s. Input and output currents are recorded as described in The system’s reaction with respect to output voltage  Cr1 cf. , which iIn a last experiment on a larger time scale, the coil separation distance changes between 10 mm and 20 mm  versus the custom low-power near-field communication (NFC) system published by the authors of this work in . The cusWhile the efficiency of the wireless power transfer interface is the objective function of the optimization, the self-consumption of the primary- and secondary-side microcontroller systems should not exceed the energy saved due to the optimization. As a result, the power consumption of both devices was measured with respect to four main categories, as summarized in Both the theoretical analysis and the experimental evaluation of the adaptive tuning mechanisms resulted in a series of concepts and findings that enable a small-scale and low-power wireless power transfer interface with favorable stability and efficiency metrics:adaptive output network or adaptive tuning of the operational frequency when operating with coils of high quality factor  do not work for high-frequency systems with strongly nonlinear power electronics. However, the overall efficiency has a particular optimum, so that it can be optimized even by relatively simple approaches such as perturb-and-observe algorithms.While rectifier’s output voltage regulation in z-domain, which was also stable in the experimental evaluation. However, combining the model with the effects of the DC/DC-converter load, for which the load resistance is a function of the output voltage such as given by (Assuming a constant voltage transfer function of these nonlinear devices (with voltage gains of given by , and, nomaximum efficiency point tracking concept perturbing the setpoint of the voltage controller are that:It operates with a simple topology at the secondary side, using a standard output-regulated DC/DC converter at the load and requiring only a measurement of the DC output voltage and current.Its algorithm can easily be incorporated into the primary-side digital control unit.It can act on top of the voltage controller, which assures system stability. This is even improved by triggering the MEPT algorithm only when the error term of the voltage controller The particular advantages of the presented In the practical evaluation, the tracking system successfully reestablished the maximum efficiency point: With achieved efficiency levels of around 50% as well as optimal voltages of 4 V for 25 mW and 8 V for 90 mW, as shown in overall power budget of the adaptive impedance matching solution is important to be evaluated: the power overhead due to adaptive matching includes the positions of adaptive tuning and wireless communication of With respect to the self-consumption of the power-conditioning circuits, the If the efficiency increase outweighs this additional power requirement must be evaluated for the individual application. While a regular system would experience a degraded efficiency However, Equation  assumes time to reestablish the maximum efficiency point of approximately 300 ms identifies which type of transient changes can be compensated: for power changes of longer duration, adaptive matching is possible; for shorter duration of the individual power consumption levels, the optimum will not be reached. For the given case scenario of a neural implant, time constants of physiological changes and periods stimulation are in the range of a few 100 ms to 1 s [The s to 1 s , so thatadditionally required electric components to implement our concepts include a current sense amplifier, a two-channel analog-to-digital converter as well as a wireless communication interface for both primary and secondary side. While typical primary-side reader units are equipped with these components anyhow, hardware components and cost of an adaptive receiver do almost double compared to a simple receiver topology only including matching network, rectifier and voltage regulator. For the case of active biomedical sensor systems already featuring a secondary-side microcontroller and a wireless interface, the concept can be implemented with a minor increase of cost due to the additional current sense amplifier.The maximum efficiency point tracking systems reported in the literature and compared to the concept of this paper in the radar plot of For the practical application of an adaptive WPT impedance matching system, a series of characteristics are of major importance: First, the power levels