The response to levodopa (LR) is important for managing Parkinson’s Disease and is measured with clinical scales prior to (OFF) and after (ON) levodopa. The aim of this study was to ascertain whether an ambulatory wearable device could predict the LR from the response to the first morning dose. The ON and OFF scores were sorted into six categories of severity so that separating Parkinson’s Kinetigraph (PKG) features corresponding to the ON and OFF scores became a multi-class classification problem according to whether they fell below or above the threshold for each class. Candidate features were extracted from the PKG data and matched to the class labels. Several linear and non-linear candidate statistical models were examined and compared to classify the six categories of severity. The resulting model predicted a clinically significant LR with an area under the receiver operator curve of 0.92. This study shows that ambulatory data could be used to identify a clinically significant response to levodopa. This study has also identified practical steps that would enhance the reliability of this test in future studies. Parkinson’s Disease (PD) is a progressive neurodegenerative disorder that affects the frontal lobe, the brainstem and the autonomic nervous system. Impaired dopamine transmission is a defining feature of PD and can be treated by pharmacological therapies such as levodopa. Evidence of responsiveness to levodopa provides support for the clinical diagnosis of PD and for assessing the suitability for device assisted therapies such as deep brain stimulation (DBS) and delivery of apomorphine or levodopa by pump.Responsiveness to levodopa is often assessed with the levodopa challenge test (LDCT) , followiAlthough LDCT has been used for both research and clinical purposes for more than 30 years . DespiteUPDRS) could be predicted from the change in motor function measured by the PKG following the first levodopa dose in the morning (LRPKG).The recent development of objective measures of the motor features of PD raises the possibility of assessing LR in the home were reviewed by Maetzler et al. ,8 and EsThere are challenges to using this standard PKG to assess the LR. In a standard 6-day PKG, the first dose of levodopa is usually not supramaximal and D2 agonists may be taken. Furthermore, some PwP choose to continue to rest for some time after their first dose to allow it to take effect and this immobility may obscure the presence of bradykinesia. On the other hand, 6 days of data are available, and this may address some of the natural variation in response to levodopa that will be overlooked by a single dose administration.ON and UPDRSIIIOFF) during an LDCT and features from the PKG data were used to build a model of motor function severity levels (MFSL) using Logistic Regression. This model was then used to predict abs∆ and %∆ from the LDCT calculated using the PKG data.In this paper, we describe how data from the UPDRS III in the “OFF” and “ON” state (UPDRSIIIThe data used in this study was collected from 199 people with PD (PwP) who attended one of the three clinics  for an LDCT as part of routine clinical care. In the case of St George’s and Leiden/The Hague, the data was collected and collated as part of other studies approved by institutional ethics with approval to use the deidentified data in related studies. In Kansas, the data was collected and collated as part of routine clinical care with institutional approval to use the deidentified data. As well, data from 191 people without PD and aged >60 was used under approval provided by St Vincent’s Hospital Melbourne Human Research & Ethics Committee. PKGs were also available from 24 subjects who underwent deep brain stimulation (DBS). PKGs were performed prior to DBS and months after DBS. This study was carried out in accordance with the guidelines issued by the National Health and Medical Research Council of Australia for Ethical Conduct in Human Research . Clinical characteristics of participating subjects and inclusion criteria into the analyses are discussed below.Data from the 199 PwP who underwent a LDCT as part of routine clinical care at these 3 clinics were reviewed. Subjects were excluded if; (a) a PKG logger had not been worn at or near the time of the LDCT (median 6 days and 75th percentile 22 days); (b) it was documented that PD medications were consumed prior to the first PKG medication reminder; (c) PD medications were used at the time of the first dose whose pharmacological profile would mask or confound the usual response to levodopa  but not D2 agonists or entacapone); (d) there was no reminder set on the PKG at or around the time of awakening; (e) the first dose occurred before 5:00 am. Of the original 199, 48 were excluded for one or more of the above reasons. The clinical features of the remaining 151 PwP are shown in Controls were 191 subjects aged 60 years and over, without a known neurological disorder and who had worn a PKG logger. Subjects whose bradykinesia scores (as measured by the PKG) were >90th percentile for controls were removed. Thus, there were 174 control subjects. The reason control subjects were included was to provide a large cohort of people who would not be bradykinetic in the early morning and whose bradykinesia score would not change after a nominal “dose time” (DT). DT was 07:00 for building the model: this was chosen to ensure that levels of sleep and inactivity would be similar to the first dose in the morning of PwP. For estimating the delta of the LDCT, DT was 10:00 and chosen explicitly to avoid sleep and inactivity. The UPDRS III was deemed to be “0” at DT.The PKG system consists of a wrist-worn data logger (the PKG logger), a series of algorithms that produce data points every two minutes and a series of graphs and scores that synthesize this data into a clinically useful format known as the PKG. The PKG system  was the http://www.globalkineticscorporation.com.au/ for details). It weighs 35 g and contains a rechargeable battery and a 3-axis accelerometer set to record 11-bit digital measurement of acceleration with a range of ± 4 g and a sampling rate of 50 samples per second using a digital micro-controller and data storage on flash memory. The device is water resistant. The logger has been designed and approved for easy cleaning and reuse and after 6 days of recording, data are uploaded to the cloud for application of the algorithms. The algorithms were built using an expert system approach to model neurologists’ recognition of bradykinesia and dyskinesia on accelerometry data. Inputs to the expert system included Mean Spectral Power (MSP) within bands of acceleration between 0.2 and 4 Hz, peak acceleration, and the amount of time within these epochs that there was no movement. These inputs were weighted to model neurologists’ rating of bradykinesia and dyskinesia and to produce a bradykinesia score (BKS) and dyskinesia score (DKS) every 2 min.The logger is a smart watch that is worn on the most affected wrist  and to other publications [The PKG is the graphical representation of the output of the algorithms from data collected every 2 min over an extended period, typically 6 days. The PKG plotted the BKS and DKS against the time of day. The time that medications were due and consumed were also shown, making it possible to assess whether there were dose related variations in BKS or DKS and how the median value at any time of day compared with a normal subject. Other scores are also provided, including compliance with the reminders, tremor scores , and timications ,18,19,20•Bradykinesia Score (BKS). The score for bradykinesia produced by the PKG algorithm for a 2 min epoch. These inputs were weighted to model neurologists’ rating of bradykinesia. BKS are produced every 2 min while the logger is being worn.•Epoch. In this paper, “epoch” will refer to a 2-min period in which PKG scores are calculated.•Tremor Amplitude (PA): This is the 75th percentile of the magnitude of the tremulous peak identified from the spectrogram from each epoch. Epochs without tremor are scored zero.•OFF Wrist: The logger has a capacitive sensor to detect whether it was being worn. An epoch marked as “OFF wrist” was unavailable for analysis.•Dose reminder: The logger can be programmed to vibrate for 10 s at the time when levodopa should be taken as a reminder to the wearer to take medications.Dose acknowledgement. Following a reminder, the smart screen on the logger can be “swiped” by moving the finger slowly across the screen to indicate when the medication was consumed.OFF and the response to this first dose would be similar to the UPDRSIIION.There are some terms that specifically apply to the first dose of the day  and rela•Dose Time (DT). This is the 5 epochs (10 min), centered on the acknowledgement to the first reminder of the day and shown as a red diamond in •Effect Time (ET): This is the time when levodopa had its peak effect. It is calculated for the PKG as the peak of Smoothed Weekly BKS Time series from 46 min to 90 min after the acknowledgement of the dose reminder.•Active epochs: Epochs whose linearly weighted moving median of BKS ≤ 0.•Inactive epochs: Epochs whose linearly weighted moving median of BKS > 40 were attributed to inactivity or sleep and excluded .•Reminder Time: The PKG logger is programmed to vibrate at specific times to remind subjects to take their medications. Subjects can acknowledge when they actually consume the medications by “swiping” the smart screen on the watch. The first acknowledgement of the reminder is shown as a red diamond in •Weekly Aggregate Mean: Epochs from each Dose time (or Effect time) are aggregated: 5 from each dose and potentially, 6 dose times from the 6 days (week) of recording. Thus potentially, 30 epochs in total are aggregated and these are averaged to produce the weekly aggregate mean.•Weekly Aggregate Standard Deviation: Epochs from each Dose time (or Effect time) are aggregated: 5 from each dose and potential 6 dose times from the 6 days (week) of recording. Thus potentially, 30 epochs in total are aggregated and the standard deviation of the aggregate is calculated to produce the weekly aggregate standard deviation.•Thirty-minute window moving percentiles of BKS. The 10th, 25th, 50th, 75th and 90th percentile of the BKS value of the 15 epochs in the window around the first epoch within the DT (or ET) was estimated. The window was then slid for the five epochs within the DT (or ET) to calculate the 30-min moving percentiles of BKS. The 30-min moving percentiles approximate the shape of the distribution of a window of 30 min around each epoch. They will be referred to as, for instance, BKS_M75P for the 30 min window moving 75th percentile of BKS.•Thirty-minute window weighted moving percentiles of BKS. Similarly, a 30-min weighted moving percentile of the BKS were also calculated. The weighting was linear, being maximal at the center of the window and declining linearly and symmetrically on each side to zero and provides some indication of the influence of shorter window sizes. They will be referred to as, for instance, BKS_WM75P for the 30 min window weighted moving 75th percentile of BKS.•Thirty-minute window moving 50th percentile of Tremor Amplitude. This is calculated in a similar manner to the 30-min moving percentiles of BKS and will be referred to as TA_M50P.•Thirty-minute window weighted moving 50th percentile of Tremor Amplitude. This was calculated in a similar manner to the 30-min window weighted moving percentiles of BKS and will be referred to as TA_WM55P.•Logarithm of 1 + 30 min window weighted moving 50th percentile of Tremor Amplitude: While the BKS is linearly correlated with UPDRS III  and scalThe 5 epochs (10 min) centered on DT and ET were used to calculate further features of motor function from the PKG  for various severities of motor function. The score of each of the items is summed to give a total score. There are two versions of the UPDRS III: the older is known simply as the UPDRS III and the newer version, which is owned by The Movement Disorder Society is termed the MDS-UPDRS III. Six items were added to the scale in the MDS-UPDRS III, so that the maximum possible total score increased from 108 to 132 points. Unfortunately, both versions are frequently used in practice. Formulae for allowing the older and newer total scores to be used have been proposed  but we hIn this study, no subjects had missing values in the UPDRS III. Two clinics used the older UPDRS III scale and one used the MDS-UPDRS III scale. As only the total scores were used, the older scales were adjusted by the addition of 7 points and UDPRS III is used from here to refer to the adjusted score. It is important to note that in the UPDRS III, scores for tremor and bradykinesia contribute ~30% and ~40% (respectively) whereas the BKS of the PKG only relates to bradykinesia with a separate score for tremor.As described earlier, the LDCT is performed by administering a dose of levodopa in the “OFF” state which is then compared with the “ON” state using the UPDRS III. As already noted, there is considerable variation in the performance of this test, which was also apparent in the procedures used by the three clinics participating in this study.•OFF state assessment. All clinics assessed the “OFF” state at least 12 h after the PwP’s last PD medication. No clinic ceased D2 agonist for more than 12 h.•Loading dose. One clinic gave a supramaximal dose of 50% more than their usual first dose of levodopa. One clinic gave 20% more than the usual morning dose in dispersible form. The third reviewed the “ON” state on their usual dose•ON state assessment. Two clinics assessed the “ON” state following the levodopa dose: one from 45 min on and the other at about 50–60 min. The third clinic made the assessment on another day to when the “OFF” state was assessed.OFF. Similarly, the response to this first dose should be similar to the UPDRSIIION. As “ON” and “OFF” have specific clinical meanings, in this study the terminology of motor function at DT (or ET) is used to signify motor function measured by the PKG  and only 25% of PwP took 200 mg or more at the first morning dose .•D2 agonists were taken by 68% of PwP, in which case it constituted a median of 15% (8%–30% Inter-quartile range) of the total levodopa equivalent dose. The size of the levodopa response measured using the UPDRS III, was not smaller in those on D2 agonists  or OFF wrist were excluded, and •ON.Similar exclusions occurred on examination of the ET, and •In some subjects, especially those with impaired gastric emptying, there may be variability in the time to peak effect and in the amplitude of the peak effect. Thus, a single day captured by the LDCT may not represent the summary of the 6 days from the PKG.The PKG records the first dose on six consecutive mornings and the presumption in this study was that the level of motor function at the time of this first dose would be similar to the UPDRSIII PKG see . In modeThese factors are all addressed further in either the model or the analyses of the LDCT in the results.UPDRS). This was to allow severity of motor function to be categorically classified instead of requiring regressions. This allows a more robust employment of the dataset with the non-identically distributed noise and variations in UPDRS III scoring, which introduces complexity for regression models. MFSLUPDRS “0” was set as a UPDRS III score <10 and levels above that were separated by increments of 12.5 UPDRS III units, with all scores ≥60 in level 5  in each MFSLUPDRS. The various PKG features  test was performed to assess the relevance of these features to the target classes. This approach is neutral with respect to models and identifies any statistical relationship, linear or nonlinear, between the features and the class labels . Table 4Based on the above discussion, the feature set was refined to BKS_M10P, BKS_M25P, BKS_M50P, BKS_WM75P, BKS_M90P and TA_WM50P_Log. Although these scores each have considerable relevance, some carry redundant information with respect to one or a combination of the others. Joint Mutual Information Maximization (JMIM)  was usedSeveral discriminative statistical models were examined for the purpose of designing the five binary classifications algorithms. Although the selected features are monotonically and linearly correlated with the UPDRS III, linear and nonlinear models were considered: namely Logistic Regression , SupportWhen comparing the performance of the learning models described above, it was noted that Logistic Regression assumes that the observations in the dataset are independent and that multicollinearity is not present. We previously noted the structural collinearity between BKS_M10P and BKS_M25P. To investigate the effect of the violation of this assumption on Logistic Regression, we introduce a fourth model, where unsupervised reduction of the dimension of these two features into one is achieved using the first component of Principal Component Analyses (PCA) of BKS_M10P and BKS_M25P together with TA_WM50P_Log, followed by a Logistic Regression classifier. Furthermore, as the employed features are moving statistics, neighboring epochs (observations of the same subject) are not independent when 5 epochs in a row are sampled. Two strategies were used to address assumptions regarding independence of observations: (i) using other candidate models whose requirements around this assumption are relaxed (SVM and Gradient Boosting Trees), (ii) assessing the performance of the models both in terms of model selection and out of sample predictions on Weekly Aggregate predictions, where two observations from one subject (weekly aggregate of dose time and effect time) are spaced more than 30 min apart and are thus reasonably independent. Therefore, the use of Logistic Regression as one of the candidate classifiers is possible and the performance comparisons would be meaningful.A train set and a test set were defined for each of the classification problems  area under curve of Receiver Operating Characteristics (ROC AUC) which provides an average Sensitivity at different Specificities; (ii) area under curve of Precision  vs. Recall (=Sensitivity) (PR AUC) which provides an average Precision at different Recalls averaged over the two classes. The performance metric (ii) is reported to account for the class imbalance that varies over the five Classifiers.To tune the critical hyperparameters of each model, and assess their generalisability, a 10-fold hold-out cross validation (CV) on Train set was performed . First iThe Logistic Regression model performs as well, if not better than the other models and is simpler in that it enhances the likelihood of generalizability and interpretability of the algorithm. Thus, the Logistic Regression model was further analyzed for validation and bias-variance assessment using the five classifier models and Logistic Regression was used in the following sections of this study.The generalizability of the classifier models was examined by applying them to an unseen test set. Train and test sets for each classifier model were selected according to the description in the previous section. We decomposed this multi-class classification into 5 binary classification problems, where samples were separated according to whether they fell below or above the threshold for each class. UPDRS) is calculated as the change in the UPDRS III scores (abs∆UPDRS) from the OFF state to the ON state, which was 22 (±11 SD) UPDRS III units for the whole cohort , or the percent improvement, which was 47 (±18 SD) for the whole cohort (see UPDRS and %∆UPDRS. We compare the model with the abs∆UPDRS first and then with %∆UPDRS and the justification for considering the abs∆ is fully reviewed in the Discussion.The aim of this study was to use the model described above to compare the response to levodopa (LR) measured during the LDCT with the change in motor function following the first morning dose measured by the PKG over 6 days. To remind the reader, the LR in the LDCT (LRDT), and similarly at ET(MFSLET). These were used to produce the model’s estimate of the LR: abs∆PKG (MFSLDT-MFSLET) and %∆PKG (abs∆PKG/MFSLDT × 100).For the PKG, the Logistic Regression model designed in Controls were used to augment the number of cases whose LR could be considered insignificant (Support Class 0 for ROC) and ensure class balance. For controls, DT was set at 10:00 a.m. and ET was at the peak of BKS smoothed weekly summary from 45 min to 90 min. UPDRS III was set at “0”. The PwP and Controls included in the assessment of the response to the first morning dose of levodopa in the PKG as a model of the LDCT are shown in PKG as a prediction of abs∆UPDRS was estimated in terms of the two metrics of Receiver Operator Characteristic and Precision-Recall Curve  and one which was not clinically meaningful (Support Class 0).That an uncertain region lay between abs∆•DT did not reflect the subjects’ worse motor function ;That the MFSL•DT and MFSLET, and in latency to peak response, especially from clinical variation in enteric delivery of the drug to absorption sites.Day to day variability in the amplitude MFSLThe performance of the abs∆urve See . When alurve See  in each Means for identifying each of these possibilities were developed and then excluded from the comparison to assess their effect on the ROC statistics . In the UPDRS are clearly positive or clearly negative are included, and cases whose labelling is ambiguous or uncertain are removed. It was noted that (i) the boundary between Level 0 and Level 1 was 10 UPDRS III points (UPDRS were defined as being 11 ≤ abs∆UPDRS ≤ 14 [UPDRS > 14 (Class 1) and an insignificant improvement as abs∆UPDRS ≤ 10 (Class 0). PKG that was intermediate between cases in Class 0 and 1. When uncertain abs∆UPDRS were removed, the ROC AUC and PR AUC improved respectively, to 0.83 and was 0.81.The performance of the model will be enhanced if only subjects whose abs∆I points ; (ii) MFI points . Thus, aDRS ≤ 14 . That isDT was not the most severe level of motor function present in a subjects PKG, it suggests that they may be “already ON”: that is, they may have already received treatment. This is relevant because the aim clinically, when performing an LDCT, is for motor function at the time of the dose during the LDCT to represent the PwP’s worst motor function (highest score) and to this end, anti-PD medications are not taken after the prior evening. Motor function is usually assessed several hours after awakening so any “so-called” sleep benefit has dispersed [If MFSLispersed ,33.DT was in the treated range were found: That is MFSLDT was less than MFSL 3  will be affected by variability in gut motility and gastric emptying causing erratic delivery of levodopa to transport sites in the gut, which would result in day to day variability even if measured by UPDRS III. There is also variation in the UPDRS III itself with variation in assessment by an individual performer and between performers. Excess variability in amplitude of response was assessed by measuring the standard deviation in the MFSLDT and MFSLEF of all epochs in DT and ET of all available days. If both were greater than 1 MFSL  and this compares to 51 min (±25 SD) reported elsewhere . This alPKG to be larger when the 1st dose LED was 150 mg or less compared >200 mg. There was a very similar pattern to the median of the abs∆UPDRS and the size of the 1st dose of the morning.The size of the first dose used on the PKG ranged widely with a median of 150 mg (interquartile range ±50 mg). The minimum was 50 mg and the 10th percentile was 100 mg and 90th 250 mg. These doses are less than those used by most clinics including the three that provided participants for this study. However, there was a non-significant trend for the median abs∆UPDRS decreases following DBS due to improved motor function in the “off” state [PKG will reduce following DBS. PKGs performed before and 6 months after DBS were available for estimation of their abs∆PKG  [The aim of this study was to establish whether data from the PKG could be used to assess LR with a similar classification performance to the LDCT. We designed a Machine Learning model to define 6 levels of motor function severity using UPDRS III scores from before and after a dose of levodopa. The models are designed and validated against unseen data to ensure their generalizability. Employing these models, we could use the PKG data to predict the abs∆s (abs∆) ,37 or ass (abs∆) ,39. Thers (abs∆) ,41 althos (abs∆) , 25% [43s (abs∆)  and 25–5s (abs∆)  are cites (abs∆) ,39, typis (abs∆) ,47, whers (abs∆) ,41,48 ras (abs∆) ,50,51.UPDRS range, those who were “already ON” with deterioration observed later in the day and those with excess variability in response. The issue of an “uncertain zone” in the classification of the abs∆UPDRS is addressed in While the ROC AUC of all subjects was acceptable (0.80), substantial improvement (ROC AUC = 0.92) could be obtained by excluding those in the uncertain abs∆When an LDCT is performed, there is an expectation that “OFF” motor function represents the PwP’s worst motor function. To achieve this, anti-PD medications are not taken after the prior evening and the test is usually performed several hours after awakening so any “so-called” sleep benefit ,33 has dWhatever the mechanism, subjects whose bradykinesia has been partially alleviated at the time of the first PKG reminder could be revealed as having adequately treated bradykinesia at the time of the first dose but having worse levels of motor function later in the day. The statistical method used in this study identified subjects whose level of motor function was already in the treated range and also experienced higher levels of bradykinesia (as identified by the PKG) later in the day. These subjects were flagged as “already ON” at DT: 19% of PwP met this criterion and excluding these PwP improved the ROC AUC and PR AUC (to 0.87 and 0.85 respectively).The main purpose of introducing this flag was to indicate that early morning alleviation of bradykinesia through whatever mechanism  reduced the performance of detecting a levodopa response with the PKG. In applying the PKG as a test of levodopa responsiveness in the future, this would be addressed by specifically requesting PwP to refrain from medications and to be “up and active” for some time prior to the first reminder. The latter point would not only address the potential contribution of sleep benefit but would also reduce the number of epochs removed because of inactivity or sleep see .. This pWhile the effect of variability in gut motility on response to levodopa is well recognized , it is nUPDRS of 30% [OFF was 48 (±13 SD) and less than 10% had UPDRSOFF < 30. The abs∆UPDRS increases with duration of disease, most likely due to increasing severity of UPDRSOFF [UPDRS correlated better with the UPDRSOFF  and the %∆UPDRS cutoff for clinically meaningful results is around 33% [p = 0.015) to have scores that were not clinically significant in absolute terms and this would argue that a different model is required for early disease.The justification for including an “uncertain zone” was both empirical in that it improved the ROC statistics, but also because there is clinical uncertainty about what constitutes a positive response to levodopa. Clinical convention usually recognizes a significant LR as %∆S of 30% ,41 but rS of 30% ,43,44,45UPDRSOFF ,37. PietUPDRSOFF  and withUPDR ≤ 14 being used. The model would be strengthened if a future study included a greater number of cases with parkinsonism of whom clinicians are confident that the LR is not clinical meaningful: these cases might include multi-systems atrophy, progressive supranuclear palsy or vascular parkinsonism.The justification for the size of the zone (4 UPDRS III units) and its location on the UPDRS III scale (11–14) was empirical, drawing on the observations described in The current model suits the clinical question as to whether the LR is suitable for deploying advanced therapies such as deep brain stimulation. In these subjects, fluctuations are well developed and LR is usually large. However, evidence of LR is sometimes sought in early PD for both clinical and research reasons and would argue for a separate model to deal with small amplitude changes in early disease.The median size of the first dose used on the PKG was less than those used by most clinics including the 3 that provided participants for this study. However as noted above, there appears to be little uniformity in the size of the dose: The use of the smaller dose may not affect the interpretation of a LDCT  and doesThere is also no clarity around handling of D2 agonists for a LDCT ,48,49, lPKG and “OFF” and “ON” PKG levels. An indicator of the reliability of the measure based on the presence of excessive inactivity and sleep or the probability that earlier dose has been taken despite advice to the contrary might also be possible. Such a reporting mechanism is subject to further.While this study was intended to test the feasibility of measuring LR using the PKG system, it is relevant to speculate on how it may be incorporated into routine clinical care. If future studies confirm that the prediction of an individual PwP’s LR was accurate providing the PwP is awake and active from 30 or more minutes prior to consuming the first dose since retiring the previous evening, until the dose is effective (~2 h later), then the LR could be considered as part of routine monitoring. Under these circumstances, it might be possible to report the abs∆•PwP are awake and active for 30 or more minutes prior to consuming the first dose.•No PD medications are taken between retiring and the first dose.A Machine Learning model using features from the PKG can be used to predict the LR obtained from a LDCT. The performance of the test for individual PwP is likely to be very high if two practical steps were taken:These suggestions should be confirmed in future studies which also include a greater proportion of people with parkinsonian features that do not respond to levodopa. It does not appear that that a first dose of under 200 mg levodopa substantially alters the modelling, but future studies may be needed to establish a more certain method for ensuring the first dose is adequate for eliciting an LR. This model was built with the assumption that a clinically useful LR was greater than 14 UPDRS III points. The LR in early PD and some other conditions is smaller and a suitable model could be built in the future to address this need.In summary, used appropriately this approach seems likely to be effective in establishing levodopa responsiveness in most cases providing the PKG is performed appropriately.


TPCL) and evaluate the curvature at the TPCL by free energy analysis and inspect the effect of different parameters on the interface shape. A new parameter—which is the deviation of equilibrium curvature at the TPCL from the spherical shape (SR)—is introduced and inspected and it was found that at a Bond number of 13 the maximum deviation, approximately 0.8 of spherical curvature, takes place while for large enough Bond numbers the curvature at the three-phase contact line is near the spherical shape (0.95 < SR < 1). A potential application of this approach is to measure the capillary rise at the TPCL to find the surface tension in high Bond number systems such as those with low surface/interfacial tensions.In the presence of gravity or other external fields, liquid surface curvature deviates from a spherical shape and the surface configuration can be found by numerical integration of the Young–Laplace equation and the typical initial point for integration is the apex of the interface. The meniscus shape in large Bond number systems, which have the central portion of the interface flattened, cannot be determined with the apex as the initial point for integration. Here we find the depth of capillary menisci by considering an initial point for integration to be at the three-phase-contact-line ( The fluid surface tension and the contact angle that the fluid makes with a solid are two important surface parameters that directly relate to the fluid interface shapes. Sessile drops, pendent drops, bubbles, foams and capillary menisci are some of the important fluid interfaces that we are involved with ubiquitously. The Young–Laplace equation is the most famous relation that governs the equilibrium shape of fluid interfaces. It connects a capillary pressure (the inner and outer phase pressure difference across the curved interface) to the interfacial tension between the two fluid phases and the geometric property of the interface—its mean curvature. When two fluid phases meet a solid phase, the competition between their surface energies leads to the formation of a capillary meniscus.Finding the equilibrium shape of fluid interfaces has been frequently studied due to its importance in surface sciencea) determination of surface/interfacial tensions and contact angles, and (b) determination of capillary forces.The calculation of equilibrium shapes of capillary menisci has been done for two main reasons: . He summarized the integration starting point for these interfaces, and for sessile and pendent drops and emergent and captive bubbles the apex of the interface is chosen to be the initial point for integration. Rothenberg et al.5 minimized an objective function—the difference between the experimental and theoretical shapes of the sessile and pendent drops—and as a result of this optimization obtained the surface tensions and contact angles of fluid interfaces. Grzybowski et al.10 considered several floating objects of approximately millimeter size and different hydrophobicities at the interface of water and perfluorodecalin. They calculated the interface shape of menisci by two methods: analytic solution of the Young–Laplace equation and use of the finite element method in the case of no analytical solution with the former method. They found the energy profile and capillary forces of the system from the calculated interface shape.The first calculation of fluid interface shape is attributed to Bashforth and Adams19 computed the shapes of fluid menisci used to infer line tensions from capillary rise in a conical tube and showed that considering the effect of gravity on the liquid–vapor interface shape changed the inferred solid–liquid–vapor line tension values by up to 50%. Danov et al.2 investigated the capillary meniscus around an electrically charged particle deforming a fluid interface and found that the meniscus deformation for small enough particles is the sum of deformations due to gravity and electric forces individually. Kuchin et al.11 carefully examined the shape of the capillary meniscus in the transition zone—where the meniscus meets a thin liquid film at the wall so that both the disjoining/conjoining pressure and the capillary pressure play important roles in deforming the meniscus shape. They mentioned that disjoining/conjoining pressure is the dominant surface force in the case of thin liquid films and capillary pressure is the prevailing force in the spherical part of the meniscus. Rayleigh20 investigated the capillary rise method in order to measure surface tension and proposed two approximate relations: one for systems with Bond numbers smaller than 0.04 and one for systems with Bond numbers larger than 0.04.Asekomhe and Elliott21 investigated two coupled menisci in a capillary and by fitting the upper meniscus curvature to the experimental data predicted the shape of the bottom meniscus. Ratcliffe et al.17 explored the shape of a drop trapped in a constriction. They solved the Young–Laplace equation for the fluid–fluid interface with the constriction imposing its shape on the solid–liquid interface. Lubarda and Talke12 assumed ellipsoidal shapes for sessile drops in the presence of gravity and did the minimization of free energy to get the equilibrium height and droplet spreading. They compared their ellipsoidal results with the numerical solution and found that the ellipsoidal shape assumption is accurate for droplets with contact angles smaller than 120° and for droplets with sizes on the order of the capillary length.Chatterjee22. They considered the vertical axis of the deforming body and the horizontal axis along the horizontal part of the meniscus to be the z and x axes of their system. In order to be able to solve the problem they simplified the problem by considering dz/dx ≪1 and found the solution to be a Bessel function. They further did the integration by starting the integration from arbitrarily small φ and tabulated their results. In order to use their calculation approach a parameter must be fitted to experimental measurement of the system of interest.Hartland and Hartley calculated the external meniscus shape of fluid which has a horizontal part far from the deforming body24. Due to the symmetry of liquid droplets they act like lenses, and today they attract attention as adaptive lenses especially in miniaturized systems where surface forces are dominant. Electrowetting and dielectrophoretic operations are two manipulations that can change meniscus curvature and consequently the focal length of these lenses. Ren et al.3 did several experiments for small droplets and found that even for vertical lenses, the gravity will affect the symmetry of droplets negligibly. As a result, any two immiscible liquids regardless of their density mismatch can be used as an optical lens.Calculation of meniscus shape and specifically the shape of a liquid droplet is also of great interest in optical science24. However, in case of a cylindrical retainer there are some difficulties due to image distortion. Cheong et al. showed that knowing the shape of the meniscus (radius and height) is enough to measure the contact angle. However, they assumed a spherical shape for the meniscus and verified their calculated contact angles with measured ones.Contact angle measurement in biochemical systems—where only a small volume of matter is available—is of great importance. In order to prevent contact line pinning due to evaporation and also to avoid contamination of the biochemical material, instead of using the sessile drop method, microscopic imaging of the capillary meniscus in a retainer such as a test tube, is suggestedSR).Generally speaking, meniscus shape calculation has been done by various methods and for numerous applications. In small capillaries  a capillary meniscus forms part of a sphere and the depth of the meniscus scales with the capillary radius. As the Bond number increases, part of the meniscus becomes flattened due to gravitational effects. In order to find the capillary depth in menisci that are flattened in the center, the initial point for numerical integration cannot be the meniscus apex. As a result, we choose the initial point to be at the three-phase contact line and we inspect the curvature at this point by introducing a parameter which shows the deviation of equilibrium curvature at the three-phase contact line from the spherical shape . At equilibrium the system has constant temperature (TL = TV) and the Young–Laplace equation governs the pressure difference across the fluid interface:PV and PL are the vapor and liquid pressures, z is the elevation with respect to the three-phase contact line, R1 and R2 are the meridional and azimuthal principal radii of curvature of the interface with an axis of rotational symmetry, Rm is the mean radius of surface curvature and subscript I indicates that a property is referred to the interface. The following equation is the third equilibrium condition which relates the chemical potential to the elevation:μi is the chemical potential of component i, Mi is the molar mass of component i and subscript ref indicates the reference point. In order to use these equilibrium conditions for our system we have to use the equations of state. If we assume the liquid phase to be an incompressible liquid and the gas phase to be an ideal gas, then we will have:Ru is the universal gas constant.The system of interest is shown in Fig. Substituting Equation  in 3) r r3) resuentclass1pt{minimaEquation  leads toz − zref) and at small x, exp(x) ≈ 1 + x, we can simplify Equation mentclasspt{minimazref = 0) and that x, z, Rm0 with respect to the capillary radius i.e. B is the Bond number. When in a system both the capillary force and the gravitational force are appreciable, there is a competition between them. This competition can be evaluated by a non-dimensional number—the Bond number—and it is defined as follows:L is a characteristic length scale of the system which in capillaries is usually assumed to be the capillary radius. Most of the previous calculations24 use the curvature at the meniscus apex as an iterated boundary condition to solve the differential equations. However, this approach cannot be used to predict the shape of a meniscus with a flat portion at its center which is the case for systems with large Bond numbers. The challenge in numerically solving this problem upon moving the initial point for integration is to devise an integration procedure using an iterated  boundary condition and stopping conditions that yields a unique solution.We assume the reference point to be at the three-phase contact line (Equation  \documenquations  and 14)zref = 0)z = 0). As a result, the equilibrium meniscus shape will be found by numerically integrating the differential Equations z = 0). A29. It is worth mentioning that considering curvature length (s) as an integrating variable a similar result will be obtained. In this case the following relations exist between the x, z, φ and s:We try to find it by assuming an initial value for x′ = 0 at φ = 0.This set of differential equations should be solved from In order to choose an appropriate LV, SL and SV interfaces. There are two meniscus profiles in this figure which we will name states A and B. We are going to analyze the free energy difference of FB − FA near equilibrium where both cases of A and B have the same volume of water with two different values of xh and zh are the values of x and z at the point closest to the capillary wall at which the turning angle φ = 0. In the case of a meniscus without a flat portion this point would be at the capillary center, but for a meniscus with a flat portion this point is not at the center but rather at the furthest extent of the flat portion. The reference case A is chosen in a way that it has the lowest zh. Since both states A and B have the same volume of water with two different Y is the displacement of the origin of the coordinate system of meniscus B with respect to the origin of the coordinate system of meniscus A due to the liquid volume being the same for A and B:Figure B is shown in its coordinate system where B. By non-dimensionalizing of length scales and by knowing that Y′ would be equal to:In Fig. F) plus potential energy (E)30 governs the system:f) is given by the following and n is the number of moles per unit volume of bulk phases. Using Equations  the intensive Helmholtz energy is given by:n is the adsorbed number of moles per unit area and since we neglect any adsorption effects in the system, for all the three interfaces e) for the bulk phases is:For the interfaces 27) we wiFsurf a portion due to differences in bulk liquid and vapor phase free energies, ΔFbulk, and a portion due to differences in potential energies, ΔFpot. The surface energy difference is the main part of the total energy difference and is based on the combination of interface energies. By using Equations , 33\documef j do not depend on z so we can take them out of the integral. Since VL and total volumes are constant for all the menisci we can simplify the bulk energy as follows:The bulk energy difference relates to Helmholtz free energy of the bulk phases. Based on Equations  and 32)32) the fBy making use of Equations  and 4),,4), the The potential energy difference is obtained by:By calculating the total free energy and plotting it for different values of r and a contact angle of θ. The physical properties of the system corresponding to T = 25 °C are31: P∞ = 3170 Pa, φ = 0 with the starting point for integration of z′ and x′ which has to be fixed before doing the integration. We use free energy analysis to find the appropriate Here we found the meniscus shape for liquid water in a capillary with capillary radius quations  and 17)r and a cAs is shown in Fig. s” as the integrating variable. Figure r = 0.1 m and zero contact angle for the liquid water – water vapour system. In Fig. φ is the integrating variable and the meniscus profile is plotted for a series of s is the integrating variable. In the former case In order to verify this generalization, we redid the calculation by considering “Rm0) is reduced by In Fig. z′ versus x′ for a capillary with radius of 1 cm for four different contact angles of 0°, 25°, 50° and 75°. It illustrates that at constant capillary size, the higher the contact angle, the smaller the reduced meniscus depth. Figure z′ versus x′ for a zero contact angle meniscus at five different capillary radii of 0.1 mm, 1 mm, 5 mm, 10 mm and 100 mm. It can be seen that for small capillaries the meniscus forms part of a sphere and has the largest reduced meniscus depth while for large capillaries the inner majority of the meniscus is flat and the reduced meniscus depth is insignificant compared to capillary radius.After finding the appropriate φ = 0, Figure SR. If the whole meniscus were part of sphere, as was explained in Fig. In order to find the extent of deviation of the meniscus curvature from the spherical shape, we define a parameter However, if only a part of the meniscus around the three-phase contact line forms part of a sphere then the maximum depth of the capillary is: Figure SR is equal to 1 for small capillary sizes. By increasing the size of the capillary the three phase contact line curvature deviates more and more from the spherical shape and the SR becomes smaller than one. At some specific capillary size the three-phase contact line curvature has the maximum deviation from spherical and after that the deviation decreases more and more until the SR again approaches approximately to one. For large capillaries, although there is a large flat portion of the interface around the center of the meniscus, there exists approximately spherical curvature at the three phase contact line. Figure As was shown previously in Fig. 32. For small capillaries, as we expect the depth of the meniscus is equal to the capillary radius for zero contact angle and in general it is equivalent to Equation  or from the meniscus apex . The latter is usually measured due to the use of the Bashforth and Adams table which tabulated the meniscus curvature at the apex. Although working with the former capillary rise is not usual, it can be used in measuring the surface tension in small capillaries and even in larger capillaries in which the meniscus has a flattened center where hrise,b = 0, which will be the case for low surface tension values. These two capillary rises are related by following equation:As shown in Fig. hrise,b = 0) but there is still a capillary rise at the three-phase contact line . Our approach provides a means to measure the surface tension even in cases that there is a big container, or a low surface tension. Figure r/a for different contact angles. Figure b) while in Fig. Rmo with cosθ.In fact, in the case of a flat interface we do not have any capillary rise at the apex  is the integrating variable instead of turning angle (φ) as the integrating variable. The deviation of curvature at the three-phase contact line from that of a spherical shape is examined and it was found that the highest deviation which is about SR = 0.83 happens at a Bond number of approximately 13 for both systems studied. As a result, if the curvature at the three phase contact line is unknown—which is the pre-requirement to solve the Young–Laplace equation—it can be estimated with spherical shape with the deviation reported here. Finally, using the numerical methods presented here to calculate the shapes of capillary menisci in the two systems for various values of capillary radius and contact angle, insight is gained into the dependence of meniscus depths on the various variables. One of the potential applications of this approach is to measure the capillary rise at the three-phase contact line to find the surface tension in high Bond number system such as systems with large capillaries or low surface/interfacial tensions.In this study the capillary meniscus depth is evaluated for various capillary radii and different contact angles for two systems with different properties: the water liquid – water vapor system and the water – soybean oil system. In order to integrate the Young–Laplace equation numerically, we have changed the typical starting point for the integration from the apex of the interface as is used in typical interface shape calculations to be instead at the three-phase contact line, since the apex point cannot be used as the starting point for integration to predict the meniscus shape for systems with larger Bond numbers where the meniscus has some central portion flattened. The curvature at this new integration starting point—at the three-phase contact line—is evaluated by free energy calculation. It was found that the curvature at the three-phase contact line would be the highest acceptable curvature and this value correspond to the smallest system free energy. The same result is obtained if the curvature length (


The unprecedented high-resolution data from the Magnetospheric Multi-Scale (MMS) satellites is revealing the physics of dipolarization fronts created in the aftermath of magnetic reconnection in extraordinary detail. The data shows that the fronts contain structures on small spatial scales beyond the scope of fluid framework. A new kinetic analysis, applied to MMS data here, predicts that global plasma compression produces a unique particle distribution in a narrow boundary layer with separation of electron and ion scale physics. Layer widths on the order of an ion gyro-diameter lead to an ambipolar potential across the magnetic field resulting in strongly sheared flows. Gradients along the magnetic field lines create a potential difference, which can accelerate ions and electrons into beams. These small-scale kinetic effects determine the plasma dynamics in dipolarization fronts, including the origin of the distinctive broadband emissions. The high-resolution data from the Magnetospheric Multi-Scale (MMS) mission2 is revealing the plasma dynamics in DFs in extraordinary detail in the ion and electron gyro scales, which is beyond the scope of traditional fluid and magnetohydrodynamic (MHD) formalisms. DFs are characterized by a pressure gradient over a narrow plasma layer that is dragged with magnetic field lines. They are active regions emitting waves with broadband spectral signatures that are clearly visible to satellites and are diagnostics for the local physics in the DFs. The DFs introduce and distribute mass, momentum, and energy, transported from the heliosphere by the solar wind into the plasmasheet. They are associated with particle acceleration and energy redistribution throughout the near-Earth space environment, which makes them an important contributing factor to the near-Earth space weather. Hence, knowledge of their detailed properties is necessary for developing a predictive capability in this region. However, the physics of the DF dynamics remains obscure because fluid/MHD frameworks generally applied to address them4 ignore the important small-scale kinetic features of the narrow layers and they are not adequately resolved in the global kinetic simulations8 of the magnetotail. These narrow layers maintain strong spatial gradients in critical plasma parameters in both electron and ion gyro scales that determine the kinetic physics. Hence, the objective of this report is to discuss a Vlasov equilibrium solution that captures the vital small-scale spatial variabilities and their kinetic effects in order to quantify their measurable signatures. This equilibrium, which we match to observations, is a rigorous Vlasov solution that can be used as an initial condition to study the stability and nonlinear evolution of DFs.Dipolarization fronts (DF), sometimes called bursty bulk flowset al.9. Important to this physics is the existence of a strongly localized ambipolar electric field transverse to the magnetic field13, which is accompanied by broadband waves14 and energy dissipation. While some of the properties of such boundary layers transverse to the magnetic field have been studied in the context of the plasmasheet-lobe interface15, the consequences of the equilibrium parallel to the magnetic field have not. For example, the origin of the parallel beams in the lobe-plasmasheet boundary19 and those seen in dipolarization fronts21 are not fully understood, although they are thought to be a consequence of the reconnection process. Since the beams are observed even long after reconnection, their physical origin and how they may relate to the overall boundary layer and their causal connection to the global conditions remain nebulous. The Vlasov formulation as discussed below clarifies this and motivates future missions with more precise measurements.The core physics of DFs is similar to that of the lobe-plasmasheet interface discussed by Romero We first consider a pressure gradient across the magnetic field and assuming the particle orbits are not chaotic we construct a distribution function using the fact that any function of the constants of motion is a solution to the Vlasov equation. The relevant constants of motion are the guiding center position, α represents the species, The magnetic field is in the z (north-south) direction and the pressure gradient is normal to the magnetic field in the x (earthward) direction. The subscript 22. The values of the parameters Rα, Sα, Xg1α, and Xg2α are model inputs determined from observations.erf is the error function, 0 determined the distribution function is fully specified and higher moments can be obtained. This distribution function and the self-consistent electrostatic potential satisfy the Vlasov-Poission system and is similar to the the BGK23 class of solutions.The density structure within the boundary layer is obtained in terms of the electrostatic potential as the zeroth moment of the distribution function, Eq. ,3\documes, along the magnetic field. Hence 24, which simplifies the analysis considerably by allowing the assumption of weak coupling between the physics perpendicular to the magnetic field and other orthogonal directions. Hence, to leading order Φ0 may be calculated locally at a given position along the field but non-locally across it.In a dipolar geometry the local values of the magnetic field as well as other plasma parameters vary with position, 2 to find a case of weak compression with low βe cases will be considered in the future. The dipolarization front studied here was observed by MMS on 16 May 2017, near 13:56:59 UTC. Figure We examined data from the MMS missionmentclass2pt{minim25 at 128 samples/s. The bold black line shows the magnetic field magnitude. Figure Bz component in more detail to demonstrate the magnetic dipolarization that defines this event. Figure 26 was not on during this event. The increase in spacecraft potential indicates a drop in plasma density associated with the dipolarization. A density drop lowers the electron thermal current to the spacecraft surface, driving the spacecraft more positive to reach current balance with the ambient plasma27. Figure ne) and proton (ni) densities. Data from the Fast Plasma Investigation (FPI)28 only are used to determine ne, while ni is determined by combining density moments from FPI (up to ∼28 keV) and the Energetic Ion Spectrometer (EIS)29 (>30 keV). The combination techniques used here necessitate a time resolution of 1 spin (∼20 seconds). This combination is required for protons as the plasma sheet proton energy flux distribution peaks between the FPI and EIS energy ranges (near 30 keV). The electron energy distribution function is almost entirely within the FPI energy range  using 32 sample/s FIELDS data30, smoothed using a 1/4 spin boxcar window. Figure Figure nge Fig. , so combBz, collocated with a decrease in plasma density, and an Earthward flow velocity enhancement31, as well as the sudden onset of broadband wave activity32. This dipolarization front is located approximately -14.5 Earth radii down-tail, offset by approximately 9.3 Earth radii in the -y GSE direction and close to the equatorial plane and has a density drop of about 25% across the front.The black dashed lines in all panels of Fig. The data are measured as a function of time in the spacecraft frame. Using the four MMS spacecraft a minimum variance analysis was used to determine the normal vector of the front. Then based on timing between the four satellites we estimated the velocity of the front to be 225 ± 8 km/s, we then used a Galilean transformation (assuming a stationary spacecraft) to convert time to distance. Because the proton flux distribution is cut off on the FPI instrument an accurate proton temperature measurement cannot be made. However, we consider the FPI proton temperature moment to be a lower bound and thus take a proton temperature of 4.7 KeV for model calculations. We estimate a mean electron temperature of 0.7 keV. Furthermore, we used a smaller window of 5 seconds before the front passed to estimate a magnetic field of Figure 33. The electron flow is essentially the E(x) × B flow modified by the inhomogeneity. The origin of the electric field is ambipolar due to the difference in the electron and ion gyro-radii in balance with the Lorentz force and saturates as the pressure gradient scale size reduces below ρi. The ions remain magnetized and execute E(x) × B drift albeit with different magnitude and character than the electrons34 as elaborated in Sec. IV. This is unlike the electron magnetohydrodynamic (eMHD) treatment in which the ions are treated differently and the electric field is inversely proportional to the pressure gradient scale size.Figure Figure E × B velocity gradient and the gyro-frequency  × B drift. If 36. The dependence on the spatial gradient of the flow through the parameter η and its asymmetric appearance in the distribution function is noteworthy. It explains why the temperature in the y direction is preferentially affected by the localized electric field across the magnetic field in the x direction. It also explains the asymmetry in the vx and vy integrations, which breaks the gyrotropy and introduces an effective anisotropy in the temperature in the x and y directions.The physics becomes more transparent if we consider the weak gradient limit defined by 22. PIC simulations38 and laboratory experiment39 show that these instabilities can cumulatively constitute a broadband spectral signature.The stability of this equilibrium was analyzed and found to support a hierarchy of instabilities in the frequency range starting from below the ion gyro-frequency to above the electron gyro-frequency depending on the electric field gradient, which is also defined as the shear frequency E|| peaks in the electron layer and varies in x. Non-thermal plasma particles subjected to E|| will be accelerated along the magnetic field to form inhomogeneous beams or flows. The generation of the beam along the field line by this process provides the physical basis for a non-reconnection origin of the observed beams and its causal connection to the global compression.As we move along the magnetic field the x and z coordinates rotate by an angle 48. Cumulatively the gradient in the parallel and perpendicular flows, which arises naturally as a consequence of the global compression, constitute a rich source for waves in a broad frequency and wave vector band and their emission is necessary to relax the stress, i.e. gradients, that builds up in the layer during the dipolarization process. In particular, the generation of both electrostatic and electromagnetic waves around the lower hybrid frequency by velocity gradient has been extensively studied53. Simulations38 indicate that these waves produce anomalous viscosity and relax the gradients to reach a steady state. Due to the strong spatial gradient in the dipolarization fronts across the magnetic field the plane wave or WKB approximations will break down. Hence, these waves must be treated as an eigenvalue problem in the stationary dipolarization front frame.The stability of inhomogeneous parallel flows has also been analyzed both theoretically and through laboratory experiments. Like its transverse counterpart the spatial gradient in the parallel flow can also support a hierarchy of oscillationsE|| indicates that the off-diagonal terms of the pressure tensor, Existence of 35. Combining them we get The complex attributes of the boundary layer equilibrium are caused by the highly localized ambipolar electric field that develops across it in response to the global compression and are essentially kinetic. Our analysis of the physics in this highly inhomogeneous environment is based on moments of particle distributions that develop self-consistently with the boundary layer variations and quasi-neutrality where the individual particle dynamics is averaged through velocity integration over the distribution. However, for further insight it is instructive to consider individual particle orbits in such an environment. For a weak electric field gradient, i.e., O(ε2) in the equations but they become critical for strong gradients. For strong gradient 34 studied the strong gradient limit. He showed that for strong gradient multiple guiding centers can arise and the particles do not accelerate indefinitely unless the electric field is linear, which is a pathological case. Higher order derivatives prevent indefinite linear acceleration, which results in modified orbits that are no longer the ideal gyro-motion. The particle acquires an effectively larger gyro-radius around a new guiding center.In the weak gradient limit, the higher-order derivatives of the electric field are not important and are lumped into E(x) × B drift thereby reducing the velocity gradient such that η becomes positive. Consequently, the average ion E(x) × B flow for the ion distribution is small and results in average ion η always positive.The strong gradient condition is met around E × B drift, the Lorentz force can balance the transverse electric field and the existence of a pressure gradient is not a necessary condition. Large localized transverse electric fields can be maintained in quasi-neutral plasma with little density gradient as found in the auroral region54 and shown theoretically in the weak gradient limit35. Because the electrons experience a weak gradient condition the electron η remains positive and their orbits are not much affected. But the ions near 3 may have to be revised.When particles execute In the preceding analysis we showed that dipolarization fronts are narrow boundary layers consisting of electron and ion layers with strong spatial variations in velocity as well as temperature and pressure anisotropy. These are generated by the self-consistent ambipolar electric field resulting from global compression. Dipolarization fronts are dynamic regions characterized by plasma distributions that are far from thermodynamic equilibrium in which the stress  generated by global compression constantly adjusts to seek a lower energy state through relaxation. In a collisionless environment the relaxation is achieved through the emission of waves that allows a steady state to be reached. For this purpose the waves must be generated through dissipation of the free energy source of the dipolarization front itself and not imported from outside. The global compression is also responsible for an electric field component along the magnetic field direction, which can produce parallel beams and flows that are unrelated to the reconnection process.8 of the magnetic reconnection process is not practical. Global scale simulations are still limited by artificially small mass ratios and insufficient particles per cell to accurately resolve ion and electron gyro scale variations for ambipolar effects, which our kinetic analysis shows to be significant. More importantly, a global scale kinetic simulation must start from realistic initial condition and be subject to realistic boundary conditions. Because of the sparse nature of observing satellites both of these conditions are poorly defined leading to simulations that may not reflect the actual global response of the system. Hence, we address the small (dissipation) scale dynamics of a DF by using local kinetic analysis in the DF frame, which is anchored in reality by requiring that the distribution function reproduce the observed density and magnetic field profiles reasonably well.Capturing the small-scale details of a DF in global kinetic simulationsβe in order to ignore the correction of the magnetic flux pile up on the equilibrium. Higher βe will be subsequently considered. Perhaps more importantly, this equilibrium model does not include the feedback effects of the waves, which relax the initial gradients in PIC simulations of the plasmasheet-lobe interface38. Since satellites generally observe a steady (saturated) state the observed parameters are relaxed from their initial values. Thus, for more accurate comparison with the data the stability of the equilibrium discussed here will be examined and will be discussed in a future article.Our goal has been to keep the analysis simple in order to develop an insight into the physical underpinnings of the kinetic equilibrium of a dipolarization front. We restricted the analysis to the neighborhood where the pressure gradient across the magnetic field remains approximately constant along the magnetic field. However, on larger scale the pressure gradient will decrease along the magnetic field gradually, which will diminish the electrostatic potential until it becomes negligible. This effect is not included in the model. We also restricted the analysis to low


Use of the video digital format in the classroom is a common way to present clinical cases to stimulate discussion and increase learning. A simulated live performance with actors, also in the classroom, could be an alternative way to present cases that may be more attractive to arouse students’ interest and attention. The aim of the present study was to compare the learning process between a group of students who saw a clinical case as a simulated live scene in the classroom and others seeing the same clinical case projected by video.n = 68), while the other saw the same case projected on video . Before and after attending the seminar, students answered a questionnaire [four questions on theoretical knowledge of delirium (score 0–7) and two on subjective learning perception  (score 0–20)]. At the end, a further question was included on the usefulness of the scene or a video in the learning process .One hundred and thirty-one students (69 from physiotherapy and 62 from medicine) attended an interactive seminar on delirium in older people. Each group was subdivided into two groups: one saw the clinical case as a theatrical performance in the classroom  with a large Effect Size (ES > 0.80). Students of the scene group obtained higher scores on theoretical delirium knowledge [6.41 ± 0.73 vs 5.93 ± 1.31 (p = 0.05)], subjective learning perception questions (what they thought they knew about delirium) (16.28 ± 3.51 versus 15.92 ± 2.47 (p = 0.072)], and the overall questionnaire (22.45 ± 4.15 versus 21.48 ± 2.94 (p = 0.027)] than the video group. Students of the scene group opined that live scene was very useful for learning with a mean score of 9.04 ± 1.16 (range 0–10), and opinion in the student’s video group scored 8.21 ± 1.22 (p = 0.001).Students in both groups (live scene and video) significantly improved in all questionnaire scores after the seminar (All students improved significantly their knowledge but those who saw the theatrical performance obtained slightly better results, which suggest that this form of clinical case presentation in the classroom may be an alternative at least as effective as traditional video projections. The use of images recorded in video format is widespread in the field of training and teaching in health science . Modern Some authors have suggested that students can also learn by watching the simulation without participating actively in it −the concept of learning by observing− which has become popular in the international literature under the term “vicarious learning” or “learning by seeing others” , 5. ThisThe aim of the present study was to ascertain whether differences existed in learning between the group of students who saw a simulated clinical scene with actors in the classroom  and the other who saw the same case in a video projection.A teaching seminar was conducted at the Parc Salut Mar, a university hospital in Barcelona (Spain). Sixty-nine students from physiotherapy and sixty-two from medicine, from two universities (Universidad Autónoma de Barcelona and Universidad Pompeu Fabra) attended the seminar. This seminar was based on the approach to a clinical problem in the form of a simulated live scene with actors in the classroom or projected by video; this was followed by an interactive presentation in the same classroom, which was the same for both options. The students of each program attended the seminar separately in different days; the students of each program were divided into reduced groups chosen at random (the students from both programs were they kept separate).n = 68), and two with the projection of the case recorded on video which had been filmed previously (the same case and the same actors)  . Students from the video group watched the pre-recorded scene all together in the classroom in order to preserve the same conditions as in the other group of students who saw the live performance. At the beginning of the seminar, students were informed of what was happen. They were provided with a written summary of the case to be simulated and answered a questionnaire with four theoretical questions related to delirium in the elderly, and two questions on students’ subjective learning perception with regard to what they thought they knew about delirium   and their opinions on teaching activity were collected from the questionnaires in the form of numerical scores. These were treated as quantitative variables  and their results are expressed as mean and standard deviation. Student’s t-test or Mann-Whitney U test were used to compare scores on the questionnaires (mean comparison of different groups), depending on whether the variables followed a normal distribution. In the case of comparison of means in the same group (before and after), Student’s t-test was used for paired data and also Wilcoxon’s t-test depending on the type of variable distribution. Standard categorisation of effect size (ES) was applied to ascertain the magnitude of change scores on the questionnaires before and after the seminar, according to the formula of Cohen in which ES is equal to the difference between mean scores on a question at the beginning and end of the seminar, divided by the standard deviation of the mean of scores obtained at baseline. This calculation converts the change score into a standard unit of measurement which evaluates whether the difference between the mean score of a question before and after the seminar is small or large depending on the number of standard deviations separating them. The guidelines define an ES of 0.20 as small, 0.50 as moderate and 0.80 as large , 8. Finap = 0.001).The mean scores obtained by students on the questionnaires on understanding of delirium before and after the seminars in both groups  are shown in Table The present study shows that all students both the scene group and the video group significantly improved their knowledge of the main topic. This change was significant from a practical point of view (large ES > 0.80). Thus, we can affirm that the seminar was effective in both groups of students.Similarly, in this study, a tendency towards slightly better results was observed in students who saw the live scene in the classroom than in those who saw the case by video projection. The format of the seminar and the questions discussed on the clinical case (debriefing) and the information provided by the powerpoint were the same in both groups (scene and video); this suggests that the small difference observed could be attributed to the different format in which the clinical case was presented. These results could be in line with those of other authors who published positive teaching experiences utilising actors to represent a clinical scene in the classroom as if it were a theatre , 10. ÜnaEven though the pre-recorded simulation case is also more dependent on technology and bandwidth strength needed for transmission of good quality visual and sound, after having the technology problems resolved, it can be an excellent tool to minimize the risk of something going wrong in the live scene, it allows watching the scene as many times as one wants, pause rewind, etc. Finally, in making decisions for which method to use other factors can be taken into account such as cost, feasibility and teacher preference among other things.The present study had the limitations that the students were not randomised individually for their group assignment. The groups were distributed following the common university method , which may account for both groups not being similar in basal conditions. Before the seminar, students in the clinical scene group had better scores on the theoretical questionnaire than the video group. Although this difference was slight, it could have influenced the higher score obtained by this group at the end of the seminar.On the other hand, we believe the results in learning of the clinical scene group would have been better if the live performance had been interactive, allowing the students to be involved at some point of the live performance by interacting with the actors, as in the experiences of other authors .Finally, from our experience, lectures supported by clinical case presentation as a theatrical performance in a classroom appears to be an attractive alternative to the traditional format and as effective as a video projection. We advocated carrying out further similar experiences in the future to widen this learning practice for it to be better evaluated.All students both the scene group and the video group significantly improved their knowledge of the main topic, but the fact that the results of the clinical scene group were slightly better at the end of seminar suggest that the simulated “live performance” could facilitate better learning providing an element of greater authenticity, ensuring that learning takes place in a more attractive context than the video format and enabling the students to retain the knowledge more effectively. Lectures supported by clinical case presentation as a theatrical performance in a classroom appears to be an attractive alternative to the traditional format and as effective as a video projection.