The aim was to test whether the null hypothesis of error‐free therapy was met. The patient is treated repeatedly if the P‐value in all the fluence maps sets is higher than the level of 0.01. The best compatibility between treatment fractions was obtained for the stereotactic technique. The technique with breath‐holding gave the lowest percentage of compliance of the analyzed fluence pairs. The results indicate that the repeatability of the treatment is associated with the radiotherapy technique. Treated volume location is also an essential factor found in the evaluation of treatment accuracy. The EPID device is a useful tool in assessing the repeatability of radiotherapy. The proposed method of fluence maps comparison also allows us to assess in which therapeutic session the patient was treated differently from the other fractions.The accuracy of radiotherapy is the subject of continuous discussion, and dosimetry methods, particularly in dynamic techniques, are being developed. At the same time, many oncology centers develop quality procedures, including pretreatment and online dose verification and proper patient tracking methods. This work aims to present the possibility of using portal dosimetry in the assessment of radiotherapy repeatability. The analysis was conducted on 74 cases treated with dynamic techniques. Transit dosimetry was made for each collision‐free radiation beam. It allowed the comparison of summary fluence maps, obtained for fractions with the corresponding summary maps from all other treatment fractions. For evaluation of the compatibility in the fluence map pairs (6798), the gamma coefficient was calculated. The results were considered in four groups, depending on the used radiotherapy technique: stereotactic fractionated radiotherapy, breath‐hold, free‐breathing, and conventionally fractionated other cases. The  However, several criteria must be met. One of them is the precision of the radiation dose delivery.One of the principles in medicine is "first, do no harm." This dictum applied in radiotherapy means to protect the critical organs as much as possible. Dynamic intensity‐modulated radiotherapy (IMRT) or volumetric modulated arc therapy (VMAT) techniques allow to achieve a dose distribution that meets the physician's expectations and indications of radiotherapeutic protocols. Therapeutic doses in the treated volumes are achieved while doses in critical organs located in the immediate vicinity are acceptable. Unfortunately, any change in the geometry of the irradiated volume, or an inaccurate positioning of the patient, result in a significant change in the dose distributions. Figure Figure In radiotherapy, orthogonal x‐ray imaging or cone‐beam tomography (CBCT) is performed before the therapeutic session to minimize the differences between the planned and actual patient position. The acquired two‐ or three‐dimensional images are compared with reference images sent from the treatment planning system. Nevertheless, one should remember that on C‐arm linear accelerators, the image verifications are mostly performed before switching to radiation exposure. If there are differences between the planned and the actual patient position, the action is required. Patient position is adjusted to the planned one. However, during the therapeutic session, the patient may intentionally or passively change the position. In such case, the actual dose distribution in the patient body is unknown. Hence, it seems so important to control these changes occurring during the therapeutic session.Modern C‐arm accelerators are equipped with real‐time dose‐monitoring systems, that is, portal matrices . Therefore, in addition to the old‐fashioned use of matrices to control the patient treatment position and regular use for pretreatment dosimetry, EPID matrices allow to register a signal that can later be reconstructed, as a dose distribution during the therapeutic session with the patient.For physics and computer science, the VMAT technique with an acting EPID is a type of megavolt cone‐beam computed tomography. From that, as in CT, the needful information is given to reconstruct the patient anatomy and dose distribution. There are many published articles on how to calculate the dose distribution based on the real‐time EPID image.Since useful tools to compare the measured fluence map with that calculated during treatment planning are available, one can focus solely on treatment repeatability. Fluence maps measured during the therapeutic session can be compared with each other. It can be assumed that the patient is repeatably treated if these do not differ from each other. A patient who is treated repeatably is highly likely to be treated as planned. Measurement of a dose or fluence map, taking into account the patient's body, is called transit dosimetry.The aforementioned common use of portal matrices allows to check the dose distribution by measuring fluence maps before the therapeutic session without the patient.The process of pretreatment verification with patient absence is performed to check whether the movement of the collimator leaves and the gantry can be carried out, in other words, if the treatment is possible from the strictly technical point of view. The calculated dose distribution in a patient is converted into a fluence map for the patient geometry conditions. The compatibility of both types of fluence maps gives certainty that the radiation registered by EPID is generated correctly without a patient being present. Dose verification is more complicated. It is assumed that if there is an agreement between the calculated and measured fluence maps, there is an agreement between the calculated and realized dose distribution. It can be assumed that if the additional condition of correct positioning of the patient and maintaining this position during the entire irradiation is met.The parameter adopted for comparing two data sets, including dose distributions or fluence maps, is the gamma coefficient.Figure The study aims to present the possibilities of EPID dosimetry use in assessing the repeatability of radiotherapy.1.AComposite Image function was used in the Portal Dosimetry module of the ARIA v 15.1 software . Summary fluence maps obtained for a single fraction were compared with the corresponding summary maps from all other treatment fractions. All pairs of fluence maps were used for the analysis. The similarity in fluence maps pairs was assessed based on the gamma coefficient calculated in the analyzed field. The field bounded by the multileaf collimator (MLC) enlarged by 1cm was taken for evaluation.During radiotherapeutic sessions, transit dosimetry was made for each collision‐free radiation beam. It means that the EPID matrix measured the fluence maps while the beams passed through the patient body. All measurements were performed on a‐Si 1200 imagers installed on TrueBeam and Edge accelerators . The arrays have an active area of 40 cm x 40 cm with a pixel number of 1190 x 1190 and a pixel resolution of 0.34 mm at isocenter.Portal Dosimetry module was also used to compare fluence maps and gamma calculations.Acceptable dose difference values of 2% and dose shift value by 2 mm were assumed. Pairs of fluence maps were agreed if this criteria , are met in 98% of analyzed field points. The adopted gamma criteria: . The 0) assumes that treatment is repeatable when all pairs of fluence maps match, making all comparisons meet the gamma criteria. The alternative H1 hypothesis is: the treatment is not reproducible due to the lack of agreement between the compared fluence maps. The assumption is that the patient is treated in an unrepeatable way if the p‐value between the compared sets is lower than 0.01. There is no base to reject the null hypothesis. The 2chi or Fisher's exact test was made depending on the analyzed set size.Mann–Whitney U‐test was used to compare the treatment repeatability of different irradiation techniques. All tests were two‐tailed with type I error rate fixed at 0.01. Statistical analyzes were performed with Statistica v 12 software . In Table The null hypothesis , and 39 meet (A = 39), the 2chi test shows value of P = 0.0059. Consequently, one can reject the null hypothesis and accept an alternative: the patient is not being treated in a repeated way.If we consider ten fractions of radiation therapy and EPID measurement is performed each day, we obtain a set of 45 comparisons of fluence maps. Assuming that radiation therapy is performed in a repeatable way, then C = 45 and D = 0. If 44 comparisons meet the gamma criteria (A = 44), and one comparison does not (B = 1), then the This way of comparing fluence maps also allows us to assess in which therapeutic session the patient was treated differently from the other fractions.2P‐value higher than 0.01) estimated in 2chi or Fisher's exact test shows the compliance with measured fluence maps for given gamma criteria of .The performed analysis indicates that the highest percentage of repeatable treatment is obtained in stereotactic radiotherapy and the lowest in the BH technique Table . It meanP‐values presented in Table The results of the analysis performed for the DC group in the mediastinum, abdominal cavity, and pelvis with conventional fractionation demonstrate that for an average of 75% of the fluence maps pairs, the gamma coefficient is less than or equal to one. The statistical analysis shows that the patients in this group are not irradiated in a repeatable way. Since it is a rectal treatment, significant changes in anatomic shape and volume of patient's organs are likely to affect the result achieved. Additionally, there is one patient in this group, who is irradiated in two fractions that differ considerably from other fractions. The analysis presented in Fig. p‐value is less than 0.01.In the FB techniques for 58% of pairs, the gamma criteria are met Table . A statiP‐value is less than 0.01. In the chest wall area, the 2 mm shifts are unavoidable. The radiation dose is related to the energy deposited in the matter. Therefore, the lung volume changes due to respiratory movements affect the dose distribution and the measured fluence map.The analysis of the fluence maps pairs in BH cases showed that the average compatibility of the analyzed fluence pairs is 20%  is much lower than 2% and 2mm. It can be assumed that the differences between measurements higher than these values are related to the mobility of the patient.Previous experiments indicate that such a high degree of maps similarity for  gamma criteria are not always obtained and are challenging to achieve.P = 0.0147 means that there are no differences between the theoretical and analyzed groups. The patients were treated in the repeatable way.It can be concluded that only these patients, who are treated with the fractionated stereotactic technique, are irradiated repeatably. The presented results indicate that the repeatability of the treatment is associated with the radiotherapy technique. It is not surprising that the stereotactic technique is performed with high precision and repeatability. All stereotactic patients included in the analysis were treated in this way. It is definitely due to the number of fractions and the excellent immobilization of the patient. Locations of the tumors in stereotactic treatment are crucial too. In the brain region, changes in the position of the anatomical structures are minimal. In extracranial cases, anatomy changes are observed more frequently. This was confirmed based on the results from two cases — when the lymph nodes located in the abdominal cavity were irradiated. The question is what difference in the dose and its shift have to be assumed in the gamma coefficient calculations, to proof the lack of treatment repeatability, using real‐time fluence map measurements? There is no doubt that they should be associated with the location of the tumor. For brain and craniofacial tumors, a tolerance of 2% and 2 mm is optimal. The analysis shows that all patients in this group were treated reproducibly. In the mediastinum and pelvis tumor location (DC group), the analysis shows that no patient was irradiated repeatably for the  conditions. Shifts in anatomical organs position in the abdominal cavity are undoubtedly higher than 2 mm, so the values of 3% and 3 mm were adopted, and the analysis was performed again. The reanalysis in DC group shows that approximately 88% of the analyzed pairs of fluence maps meet the gamma condition of . The value of P = 0.018), except two patients, whose results differed considerably from the rest. Therefore, it can be assumed that patients treated with this technique are irradiated repeatedly within the dose range of 3% and 5mm shift.In the FB and BH groups, very little compatibility between pairs of fluence maps was obtained. Therefore the analysis was redone for 3% and 5 mm conditions, which allowed to achieve 98% of the analyzed surface. In irradiation of chest wall after mastectomy at FB, assuming new gamma criteria, 94% of patients were treated repeatedly  condition. Only 75% of the analyzed pairs of fluence maps meet this criterion, and the Resource data confirm that the use of EPID in radiotherapy verification reduces errors, which undoubtedly improves treatment results.4The system which measures the fluence maps during the therapeutic session makes it possible to assess the treatment repeatability.Analysis of fluence maps performed based on EPID, during the therapeutic session, shows significant differences in the dose deposited in patient body, depending on the applied radiotherapy technique and tumor location. The highest repeatability was achieved with the stereotactic techniques, whereas the lowest during breast radiation therapy.The calculations show that various radiation techniques and various tumor locations require different criteria, in order to optimize the treatment repeatability assessment.All additional actions aimed at improving the radiotherapy results and/or patient's safety is extremely important. Fluence maps assessment is an example of such action, especially given the fact that it does not extend the treatment duration, and does not expose patient to additional dose.Further research is required in order to define the optimum repeatability criteria for various techniques and tumor locations.Krzysztof Ślosarek conceived and designed the analysis, contributed data or analysis tools, and wrote the paper.Dominika Plaza, Aleksandra Nas, and Marta Reudelsdorf collected the data.Jacek Wendykier and Barbara Bekman performed the analysis and other contribution: language corrections.Aleksandra Grządziel performed the analysis, wrote the paper, and other contribution: language corrections.


Using adaptive optics optical coherence tomography, human photoreceptors and retinal pigment epithelium (RPE) cells are typically visualized on a small field of view of ∼1° to 2°. In addition, volume averaging is required for visualizing the RPE cell mosaic. To increase the imaging area, we introduce a lens based spectral domain AO-OCT system that shows low aberrations within an extended imaging area of 4°×4° while maintaining a high  transverse resolution (at >7 mm pupil diameter) in the order of 2 µm. A new concept for wavefront sensing is introduced that uses light mainly originating from the RPE layer and yields images of the RPE cell mosaic in a single volume acquisition. The capability of the instrument for in vivo imaging is demonstrated by visualizing various cell structures within the posterior retinal layers over an extended field of view. The angle where the aberrations can be assumed as constant is known as isoplanatic angle and varies between individuals . For larVisualization of RPE and ganglion cells is of high clinical interest. Speckles that are inherently present in OCT imaging degrade the visibility of these cell types in single OCT scans. It has been shown that averaging of several OCT volumes reduces the appearance of speckles because of cell motility and allows for a clear visualization of these cell types ,16,23. HOne key aspect for adaptive optics imaging is an accurate wavefront sensing. In AO-OCT this can be done with the implementation of a separate laser beacon  or by usIn this paper we introduce a spectral domain AO-OCT instrument that is capable to record high resolution images over an extended FoV. Aberrations introduced by the system over the scanning angle of 4°×4° are reduced by the implementation of lens based telescopes and careful system alignment. Wavefront sensing is performed using only the cross polarized component of the light that is backscattered from the retina that mainly originates from the RPE because of its depolarizing character. To stabilize wavefront sensing over the large field of view, the sensor exposure is synchronized with the slow scanner of the OCT system. Finally, we introduce a new post processing method for compensating B-scan rotation and retinal curvature that facilitates posterior retinal layer segmentation. With this instrument the cone and RPE cell mosaics are visualized over an extended FoV and with a single volume acquisition. Through image stitching of 7 volumes, a horizontal field of view of ∼22° is achieved. Imaging results are presented from healthy volunteers and the RPE cell density is quantified in six healthy subjects.2.The system evolved from our previously presented adaptive optics scanning laser ophthalmoscope (AO-SLO) setup . HoweverThe light passes through a second and a third telescope that image the plane of the DM onto the horizontal and vertical galvanometer scanners , respectively. Then the light passes through a fourth telescope that incorporates a flat mirror. In our previous setup a second deformable mirror was placed at this location for additional field correction in AO-SLO . HoweverLight in an orthogonal polarization state is reflected by the polarizing beam splitter and traverses another Glan Thompson polarizer oriented orthogonal to the first one. The light is then directed to the custom developed Shack-Hartmann wavefront sensor  for measIn the reference arm the light exiting the fiber is collimated and traverses a similar Glan-Thompson polarizer as in the sample arm for dispersion compensation and for matching the polarization state of the light in the sample arm. Additional glass components are placed in the reference arm to compensate for dispersion in the sample arm that is introduced by the lenses and the aqueous humor of the eye. The hardware dispersion compensation  was optimized in order to achieve an axial resolution in the model eye that is close to the theoretically expected one . The light is then back-reflected by a mirror that is mounted on a translation stage for adjusting the reference arm length.The light is back coupled into the single mode fiber from both arms and is directed to a customized spectrometer that records the modulated spectrum caused by interference of the light returning from sample and reference arm, respectively. The spectrometer consists of a collimator, a diffraction grating, a focusing lens, and a line scan camera . In order to increase the acquisition speed, the spectrometer is designed such that the full spectrum of the light is captured by using only the central 800 pixels of the camera. As a result, an imaging speed of 250 kHz A-scan rate is achieved. The measured imaging depth range of the system is 2.36 mm.2.1For wavefront sensing only light returning from the retina that is in an orthogonal polarization state compared to the incident polarization state is used. This configuration greatly attenuates reflexes originating from the lens surfaces or from the cornea of the imaged subject. In addition, mainly light backscattered from the retinal pigment epithelium will be measured as this layer is known to depolarize the light –32. As a2.2All measurements were performed according to the tenets of the Declaration of Helsinki and after approval of the study by the local ethics committee. Informed consent was obtained from each subject prior to the measurement after explaining the nature and form of the measurements. Healthy volunteers were recruited with the selection criteria of negligible media opacities and the ability to fixate stable. In total, 6 subjects participated in the study with a mean age of 32.8 (age range between 26 and 51 years). No drugs were administered for dilating the pupil as in most subjects the diameter of the pupil under the low light conditions in the lab was larger than 5 mm. Subjects were asked to fixate on an internal fixation target that was optically set to infinity. As accommodation of subjects has not been prevented, some data sets showed varying focus settings (associated with varying visibility of cone photoreceptors) and were discarded.The instrument supports an imaging beam diameter of 7 mm and the scanning is performed over a FoV of 4°×4°. In the alignment and AO convergence mode, the beam is scanned over the entire FoV with a sparse sampling of 50 B-scans in the y-direction. This enables wavefront measurement and correction with a loop frequency in the order of 2-3 Hz. The AO algorithm automatically adapted to the observed pupil size. After subject alignment the AO-loop was closed and convergence of the loop below the Marechal criterion for diffraction limit (root mean square (RMS) error of the residual aberrations below λ/14 = 60 nm) is typically achieved within few seconds. After convergence, a volume acquisition is started (during this time the AO correction is not updated). For data recording we tested several sampling densities with the aim of good visualization of the cone mosaic pattern while minimizing motion artifacts. We found that a configuration of 750×750 pixels  provided the best imaging results. The recording time of a single volume was ∼2.5 seconds with a B-scan rate of ∼300 frames per second.2.3The recorded spectral data has been processed in a similar way as in standard OCT processing. The laterally averaged spectra are subtracted from each A-line spectrum before re-scaling of the spectral data into k-space. For dispersion compensation (dispersion mismatch of the measured eye to the model eye), a second order phase term, depending on the k-number was added. In order to compensate for rotation of the B-scan image  and curvature of the retina we introduce a new concept. For rotation compensation, a linear phase term was added to the spectral data depending on the A-scan position. Lateral subject motion  during data recording will result in a change of rotation. However, we did not observe noticeable changes in the rotation within a volume scan unless the scan contained severe motion artefacts and had to be discarded anyway. Axial motion may induce a rotation of the B-scan as well, but this influence was minimized by the short recording time of each B-scan. Finally, the residual curvature of the retinal image (that was noticeable in the 4°×4° FoV) was compensated by adding a linear phase term to each A-scan that depended quadratically on the A-scan location. This procedure has the advantage of a sub-pixel correction of the shape and rotation.The determination of the corresponding phase terms was done manually on the first B-scan (by observing the corresponding rotation and deformation of the image) and after setting of these parameters the entire data set was evaluated by means of the Fast Fourier transform (FFT) with the same settings. As the correction for the retinal shape is done prior to FFT, the data has been zero padded only once in order to double the number of pixels within an A-scan. Axial displacement between B-scans was determined after the data processing procedure mentioned above, by averaging of all A-scans laterally and by peak detection of the first strong signal along the A-scan starting from the choroid to the anterior layers that corresponds to the RPE. With this information axial motion between B-scans was compensated. In a final step lateral motion is corrected by using cross correlation between successive B-scans. The motion corrected data is then stored as 3D stack and image planes corresponding to various retinal layers are retrieved for display.3.A total of six subjects were recruited for imaging. Visualization 1 shows a fly-through movie of all recorded B-scans. In order to visualize anterior layers in this movie , the contrast is set in such a way that the photoreceptor band appears slightly saturated.Posterior to the RPE layer but anterior to the choriocapillaris, another layer can be identified similar to reports from other groups ,33, thatVisualization 2 shows an en-face fly-trough  of the posterior retinal layers (IS/OS to choriocapillaris). After motion correction the obtained FoV is 3.8° (x) × 4° (y). In the periphery of Corresponding en-face AO-OCT images that have been extracted at four different layers are displayed in Visualization 2). Similarly, at the level of the choriocapillaris, vessel like structures can be seen in the central part of the image while these structures are less visible in the periphery. In between the photoreceptor bands, within the outer segments, bright reflection spots are clearly visible  that probably originate from defects in the packing density of the cone outer segment discs [At the foveal center the visibility of the cone mosaic is less pronounced, specifically at the IS/OS layer as individual cones can only partially be resolved. At the level of the RPE, a regular cell mosaic can be seen  µm (range: 13.3 µm- 14.3 µm). These results are in good agreement with values known from histology and from previous reports . The lowVisualization 3 that shows an en-face fly through movie of the 3D data set). As can be observed at the posterior retinal layers, the spacing between the cones at this eccentricity is much larger than in the fovea. In addition, the axial position of the cones appears to be more irregular specifically at the COST layer.In a next step we recorded volumes at some eccentricity from the fovea. The averaged B-scan displayed on a logarithmic scale  shows thVisualization 3 as en-face fly through movie on a logarithmic scale. In the large FoV images, the observation of details is difficult as the total number of pixels of each image has to be reduced for display in this paper. Thus, we provide enlarged regions of interest (that are indicated by the white boxes in this figure) that can be viewed in In total we acquired retinal images of the same healthy volunteer at seven different locations spanning a horizontal FoV of ∼22°. The averaged B-scans were stitched together (using the Image J plugin “Mosaic J”) and can be viewed in In order to demonstrate the capability of the instrument for large FoV imaging, we present a stitched en-face view of the COST and RPE layers that were retrieved from the recorded volume data in 4.We presented imaging results with an AO-OCT instrument that is capable of recording images on a larger FoV while maintaining imaging with a large pupil size. Various cellular structures such as cone photoreceptors and RPE cell mosaics could be visualized with a single volume acquisition. The visibility of individual cells can be improved by applying a filter (using Fiji image processing software and applying a mean filter with radius of 1 pixel). The result is shown in The RPE cell mosaic visualization capability of the instrument in a single volume acquisition is demonstrated by the visibility of Yellott’s ring in the FFT of the corresponding images cf.  and 4. TThe importance of high lateral resolution for visualizing the RPE mosaic manifests itself by the lower visibility of the mosaic in those subjects whose pupil size was below 6.5 mm . Here we want to point out that for visualizing cone photoreceptors (at some eccentricity from the fovea) minimizing of aberrations is not as critical as for the RPE, as cones show a high directionality of the backscattered light. This can be seen for example in Another aspect is a high axial resolution that is needed for separating the thin RPE layer showing the mosaic from other layers as pointed out in previous work . We achiOne current problem of our technique specifically for visualizing foveal cones is the rather low sampling density that is close to or even below the Nyquist criterion in the fovea centralis. In this work we used a compromise between high sampling density and short measurement times and found the used scanning pattern as best suited for visualizing structures outside the fovea. As subject motion remains an issue specifically for imaging patients with poorer fixation capabilities, recording of several volumes can be employed to increase the likeliness of obtaining a single volume with minimal motion artefacts.Another issue in the fovea region are motion artifacts that are more pronounced as the imaging beam is visible to the subject and distracts from the fixation target. Both factors influence the en-face image quality in this region and thus the ability to clearly resolve foveal cones. However, the fovea is only a small part of the retina, and these cells could potentially be visualized on a smaller FoV by changing the scanning pattern. In addition, higher imaging speeds could be introduced that enable a higher sampling density and thus a better visualization of these small structures . This can be achieved by implementation of faster cameras, multiple cameras and corresponding switching schemes  or high Although the instrument had been designed to minimize aberrations introduced by the system itself, one remaining problem are aberrations introduced by the eye that vary across the FoV. This leads to a poorer image quality in some parts of the images . Thus, without triggering, the wavefront sensor would be exposed at varying locations along the slow scanning axis. Varying exposure locations usually cause fluctuations in the measured wavefronts and subsequently result in a degradation of AO correction. The possibility of generating B-scans that are of comparable size as obtained with commercial devices allows for a direct comparison to state of the art imaging devices and enables better interpretation of these images as the knowledge on the cellular composition of each layer as provided by AO-OCT is available. On the long term this may add highly relevant information for the clinical routine by simplifying the interpretation of images in a number of retinal diseases known to affect the RPE and photoreceptors such as age-related macular degeneration, central serous chorioretinopathy or inherited retinal dystrophies.5.We presented an adaptive optics assisted spectral domain optical coherence tomography instrument that supports data acquisition on an extended FoV (4° × 4°). Various cell types such as cone photoreceptors, rods, RPE cells can be visualized in a single volume acquisition. The FoV can be further increased by stitching of several volumes, approaching the FoV of standard OCT imaging.


It may be challenging to select the optimal scan duration for single‐photon emission computed tomography (SPECT) protocols because the activity distribution characteristics can differ in every scan. Using simulations and experiments, we investigated whether the scan duration can be optimized for every scan separately by evaluating the activity distribution during scanning. We refer to this as adaptive scanning.99mTc‐labeled macroaggregated albumin (99mTc‐MAA) is injected into the liver. We simulated fast 1‐min detector rotations and updated the reconstruction with the newly collected counts after every rotation. The scan was terminated when one of the two criteria was met: (a) when the mask difference of the detected extrahepatic deposition between two consecutive rotations was lower than 5%; or (b) when the reconstructed extrahepatic activity was negligible with respect to the total reconstructed activity (<0.075%). The performance of adaptive scanning was evaluated using a digital phantom with various activity distributions, a physical phantom experiment, and simulations based on 129 patient activity distributions.The feasibility of adaptive scanning was evaluated for the detection of extrahepatic depositions in the pretreatment procedure of radioembolization, in which The digital phantom data showed that the scan termination times substantially depended on the activity distribution characteristics. The experimental phantom data showed the feasibility of adaptive scanning with physical scanner measurements and illustrated that fast detector motion was not limiting the adaptive scanning performance. The patient data showed a large spread in the scan terminations times. By adaptive scanning, the mean scan duration of the patient distributions was shortened from 20 min  to 4.8 ± 0.2 min. The detection accuracy of extrahepatic depositions was unaffected and the mean difference in the extrahepatic deposition masks (compared with the 20‐min scan) was only 7.0 ± 1.0%.Our study suggests that the SPECT scan duration can be personalized by assessing the activity distribution characteristics during scanning for the detection of extrahepatic depositions in the pretreatment procedure of radioembolization. The adaptive scanning approach might also be of benefit for other SPECT protocols, as long as a measure of interest is available for optimization.  To ensure that the reconstruction answers the imaging question in all cases , scanning is performed with a fixed acquisition time that may be longer than required for most distributions. The scanning efficiency and workflow can be improved if the scan duration is optimized for every activity distribution separately, that is, by scanning shorter for simple activity distributions and longer for complicated ones. We refer to this as adaptive scanning.We aim to evaluate an adaptive scanning technique by performing multiple fast detector rotations  so that the reconstruction can be updated with the extra obtained counts after every rotation. Central to this approach is the existence of a metric of image quality for the task at hand that can be automatically measured. The change in this metric is tracked over the rotations and when its relative change falls below a certain threshold value, the scan is considered to be converged (with respect to the imaging task) and can be terminated. This approach ensures that all activity distributions satisfy the imaging requirement but also that the scan duration is not longer than necessary.99mTc‐labeled macroaggregated albumin (99mTc‐MAA) is injected into the liver to estimate the activity distribution of the 90Y microspheres.This study evaluates the possibility for such an adaptive scan duration for the pretreatment procedure of hepatic radioembolization, in which Previously, it was demonstrated that the lung shunt fraction (LSF) can be accurately determined within minutes of scanning This study will investigate the influence of the activity distribution characteristics on the scan termination times with a simulation study and the performance in clinically encountered distributions with a retrospective patient study. The fast scanning protocol requires continuous detector motion over the multiple rotations in order to reduce the overhead time when compared with regular step‐and‐shoot motion. Since the detector orbit can fluctuate over the rotations and the detector distance and detector rotation angle can fluctuate within one projection, image artifacts or degrading effects may occur. The magnitude of these effects will be evaluated in a phantom study.22.1To distinguish an extrahepatic deposition from a noisy background, a more or less arbitrary elevation of the reconstruction voxel activity and shape is normally assessed by the physician. Our proposed method is an automatic detection approach which we base on work originating from our institute with the same acquisition and reconstruction parameters as in this study.The process of detecting potential extrahepatic depositions is illustrated in Fig. 2.2The total reconstructed activity in the background mask is lower than 0.075% of the total reconstructed activity.The adaptive scan protocol is performed by performing fast detector rotations of 1 min each. The reconstruction is updated with the newly collected counts after every rotation. The following two criteria are evaluated for every intermediate reconstruction and the scan is terminated when one of them is met:The relative difference in the mask of a detected extrahepatic deposition between two subsequent rotations  and divided by the total number of voxels in the most recent mask) is lower than 5%.The rationale behind the first criterion is that there cannot be an extrahepatic deposition if the activity in the background is negligible with respect to the total activity. The threshold of 0.075% was chosen because this is a defined summed extrahepatic activity threshold (0.1%) minus a margin to account for noise fluctuations.The rationale behind the second criterion is that the reconstruction will change substantially in the first few rotations because noise has a major impact. As the rotations progress, however, the reconstruction will become increasingly stable and hence the difference between two rotations will become increasingly smaller. The rate of this convergence is expected to depend on the activity distribution characteristics and will differ in every scan. We believe that, in clinical practice, it is most important to be confident in the shape and location of an extrahepatic deposition so that its origin can be accurately determined. Hence, we will track the mask of the detected extrahepatic deposition over time to serve as a surrogate measure for these properties. The threshold of this extrahepatic mask change is a trade‐off between accuracy and termination speed; we used 5% because with this setting all extrahepatic depositions were accurately detected in the patient study.2.399mTc . Only one parameter was changed at a time (see Table The phantom was configured on a 128 × 128 × 128 grid with a 3.9 mm isotropic voxel size. The nuclear projections were simulated with the Utrecht Monte Carlo System (UMCS),Rotations of 1 min each were simulated by the addition of Poisson noise  and background noise (obtained from a scan with no activity present) to the projections. For every phantom configuration, 20 rotations were evaluated by consecutively adding new counts to the projections.k = 0.5), and a post‐reconstruction Gaussian filter of 5 mm full width at half maximum (FWHM). Attenuation correction was performed with the μ‐map obtained from the low‐dose CT. These reconstruction parameters are the current clinical protocol in our institute.The reconstructions were made with UMCS using the OSEM reconstruction algorithm with six iterations and eight subsets, dual‐energy window scatter correction  was altered by the inclusion of three extrahepatic depositions see Fig. . A hot sScanning was performed on a Siemens Symbia T16 system by performing 20 rotations of 1 min each in continuous motion. The acquisition and reconstruction parameters were (except for the fast continuous detector motion) the same as in the simulation study. The scan duration algorithm was used to determine the optimal scan termination times and the extrahepatic mask and activity differences with the 20‐min scan were measured.Some resolution degradation is expected when scanning with fast continuous detector motion because the detector orbit can fluctuate over the rotations and the detector‐patient distance and the detector rotation angle can fluctuate within one bin. To evaluate the magnitude of the detector orbit fluctuations, the detector distance was measured over the 20 rotations and its standard deviation was calculated. To evaluate the influence of the continuous motion, the phantom was also scanned with a single‐rotation step‐and‐shoot 20‐min scan. The reconstruction of this scan was visually and quantitatively compared to the reconstruction of 20 one‐min rotations.2.599mTc‐MAA  in accordance with the radioembolization guidelines.The potential for adaptive scanning was then evaluated for clinical patient activity distributions. In total, 129 patient projections with corresponding attenuation maps and body, lung, and liver delineations were used. All patients received an injection of approximately 150 MBq Since the patient scans were performed with a single 20‐min rotation, 20 one‐min rotations were created by subsampling uniform random subsets from the 20‐min projection: all counts of the 20‐min projection were considered individual events and their positions  were put in an event list‐mode. This list‐mode was shuffled randomly and the first  5% of this new list‐mode was used to create the 20 one‐min acquisitions. The sampling process was repeated ten times to study the stability of the reconstructions to different noise distributions.The scan duration algorithm was used to determine the optimal scan termination time for every activity distribution. The extrahepatic deposition mask and activity differences with the 20‐min scan were measured. For every detected extrahepatic deposition, the contrast‐to‐noise ratio was calculated by dividing the contrast between the extrahepatic deposition mask and background mask by the standard deviation of the background mask. The background mask was available from the automatic extrahepatic deposition detection methodology and consisted of the body contour from which the liver, lung, and all detected extrahepatic deposition masks were subtracted. The analyses were performed for the ten noise realizations separately.For comparison, the scan duration was also shortened without separate optimization for every patient activity distribution . The scan duration was gradually decreased and it was determined until which the scan duration of all extrahepatic depositions was accurately detected. An extrahepatic deposition was considered to be accurately detected when the automatic detection algorithm retrieved the same number of extrahepatic depositions as in the 20‐min scan and for those masks, the difference in their center of mass was lower than 5 pixels.33.1Examples of the reconstructions obtained from the XCAT phantom with an extrahepatic deposition activity concentration of 0.50 MBq/ml are shown in Fig. The relative change in the mask of the extrahepatic deposition is shown in Fig. The same evaluation as described above was performed on the phantom with 0.05 MBq/ml (instead of 0.50 MBq/ml as above). Slices from the obtained reconstructions are shown in Fig. The scan termination times and corresponding differences in the masks (compared with the 20‐min scan) are shown in Table 3.2The mean detector orbit of the 20 rotations in the phantom study is shown together with the corresponding standard deviation in Fig. Slices from the reconstructions of the phantom experiment with varying scan durations are shown in Fig. This behavior is also found in the graphs on the relative change in the extrahepatic deposition mask in Fig. The reconstruction of the single‐rotation 20‐min scan is shown in Fig. 3.3An example of a patient activity distribution with a high‐concentration extrahepatic deposition is shown in Fig. An example of a patient activity distribution with a low‐concentration of extrahepatic deposition is shown in Fig. The collection of scan termination times for all patient scans  is shown in Fig. For the 129 activity distributions, 28 extrahepatic depositions were detected in 25 patients for the 20‐min scans. Adaptive scanning accurately detected all depositions in all noise realizations (using the 20‐min scans as the ground truth). The CNRs of the detected extrahepatic depositions at the scan termination times are shown  in Fig. The mean scan durations and the mask and activity differences of the extrahepatic depositions at the scan termination times with the 20‐min scan are shown in Table The minimum scan durations (with a single‐rotation) required for the accurate detection of all extrahepatic depositions (using the same detection criteria as with adaptive scanning) are also shown in Table In conclusion, the switch from a single‐rotation scan to an adaptive scanning protocol allows the mean scan duration (for the studied patient distributions) to be reduced from 18.8 ± 1.1 min to 4.8 ± 0.2 min, without compromising the detectability of extrahepatic depositions.4We investigated the potential for an adaptive scan duration protocol in SPECT for the radioembolization pretreatment procedure and showed the feasibility of terminating scans at an earlier point in time without affecting the detectability of extrahepatic depositions.We believe that our approach is not limited to the detection of extrahepatic depositions. As long as a measure of interest is available, adaptive scanning can be performed to shorten the scan duration. For instance, we envision that it could be used in cardiac SPECT since quantitative measures are often evaluated in this protocol. However, we acknowledge that some protocols do not have clearly defined objectives and adaptive scanning would not be possible for these cases.We also acknowledge that the scan duration range that can be achieved in clinical practice is limited. The workup of a patient  requires several minutes and would become the limiting factor for very fast (1‐min) scans. Moreover, patients can only lie still for a certain amount of time  and will start moving for longer scans. It may be beneficial to set a minimum and maximum scan duration to ensure that such practical considerations do not interfere with the scanning workflow.Changes would need to be made to the patient and technician scheduling if adaptive scanning is employed in clinical practice since the scan start and finish times are no longer known in advance. Rather than scanning a patient on a specific scanner at a specific time, the patient would be scanned in a certain timeslot on whichever scanner is first available. This form of scheduling becomes increasingly practical when more scanners are available since scan duration extremities would have less impact on the total workflow.99mTc‐MAA injection in the pretreatment procedure of radioembolization so that the response to every injection is individually monitored. For this purpose, adaptive scanning would be beneficial in minimizing the total time spent in the intervention room.A specific case that does not require scheduling changes would be the use of adaptive scanning in interventional SPECT. Our group is developing a mobile, compact SPECT scanner that can be used in the intervention room.99mTc‐MAA scan is used to assess the perfusion of target lesions  and the activity to the parenchyma. Furthermore, the potential for the 99mTc‐MAA scan to be used for dosimetry planning is being investigated within trials.The method in this work has been developed only for the detection of extrahepatic depositions since this is the most common objective for the pretreatment procedure of radioembolization. There are, however, also institutes where the A pre‐requisite for adaptive scanning to function is that the reconstructions are performed in a fast manner. The current clinical reconstruction software takes approximately a minute to finish, which is likely sufficient for use in clinical practice. Further speed‐up may, for instance, be achieved by employing GPU‐based softwareA further requirement for adaptive scanning to be used in the pretreatment procedure of radioembolization is that the liver and lung delineations need to be present in advance. The lung delineations can be normally be created quickly via thresholding of the Hounsfield units of the low‐dose CT. For liver delineation, atlas‐based methods are often employed. Since the liver and lung delineations are dilated by the relatively large margin of 2 cm to cope with partial volume effects and respiratory motion, small dilatation errors are not expected to substantially alter the results.It was shown that fast scanner rotation resulted in a slightly decreased reconstruction resolution. In clinical practice, however, patient motion is expected to be the major limiting factor for resolution and it is hence not expected that severe problems would arise from the fast detector rotation. If it does prove that the fast detector rotation is undesired, the rotation speed could simply be lowered somewhat .The threshold value for the relative change in the mask to consider the scan converged is linked to the objective that one wants to achieve. A lower threshold provides reconstructions with a higher confidence on the imaging task, a higher threshold allows for faster scans. We chose the 5% threshold in this work because with this value all extrahepatic depositions in the patient scans were accurately detected. Eventually, it depends on the preference of the physician which extrahepatic depositions  need to be detectable and which ones can be safely ignored.Other methods for adaptive scanning have been previously developed (primarily in positron‐emission tomography).The relationships between the extrahepatic deposition characteristics  and resulting optimal scan duration were only studied in the simulation study since the sample size of the patient distributions was too low to obtain statistically significant results. It is interesting to revisit the relationships when more patient data becomes available.et al.The optimal scan durations obtained in the patient study showed that for a substantial fraction of the distributions, the scans could have been terminated after 1 min without affecting the extrahepatic detection accuracy. The study of Van der Velden In our institute, only one SPECT scan is made per radioembolization procedure since the field of view of the detectors is sufficiently large to cover all potential extrahepatic deposition origins. If one, however, wants to visualize multiple body regions , more acquisitions can be made. These scans can be performed with the same methodology as described in this work and should be separately analyzed.The approach in this work investigated a scanner with a rotating detector because such scanners are most used in current clinical practice. SPECT scanners with static detectors are, however, becoming increasingly available . Such devices could similarly benefit from adaptive scanning by evaluating the list‐mode acquisition, for example, every minute and are furthermore not constrained by the scanner mechanics.5The feasibility of an adaptive SPECT scan duration (by assessing the activity distribution characteristics during scanning) was demonstrated for the detection of extrahepatic depositions in the pretreatment procedure of radioembolization. We believe that our approach could also benefit other forms of SPECT scanning, as long as a measure of interest is available for optimization.This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No 646734. No other potential conflicts of interest relevant to this article exist.


In-situ temperature measurement of a workpiece may be made impossible due to it moving through an enclosed, automated induction facility that lacks built-in sensors. This paper uses transition patterns in the microstructure of the hardened region to reconstruct isothermal contour lines of the temperature field during austenitisation. It does so based on a continuous cooling transformation phase diagram and a time-temperature-austenitisation diagram of the considered steel. The presented method serves as a practical approach to validate simulations of the inductive austenitising process and supports simulations of the heat treatment of the work piece. Once these simulations have been iterated upon and validated thoroughly, they may then yield a reconstruction of the entire temperature field during the heat treatment process.Process control in surface hardening depends greatly on the repeatability of the results. Induction heating facilities stand out in this aspect but challenges arise when it comes to the verification of the expected temperatures.  The repeatability inherent in electronically controlled induction circuits further lends itself to a high degree of automation within a production chain. Process design for induction hardening, however, is non-trivial as the short heating times allow for little diffusion, giving the microstructure of the base material some influence on the properties of the hardened surface2. More difficulties are encountered when defining a new geometry, or introducing a workpiece with varying electromagnetic (EM) properties.Induction heating techniques have proven a boon to surface hardening, based on their short process times, precise energy input and resulting low energy usage5. In general, several simplifications and assumptions are always made when simulating a problem  and any simulation needs to be verified in order to produce meaningful data7.In the past, extensive trial and error used up valuable machine time to find new process parameters. Nowadays simulation techniques such as the Finite Element Method (FEM) take on much of the burden by predicting the distribution of heat generation during the heat treatment and inform design decisions before the first test run is scheduled9. Temperature data in particular is relatively easy to obtain10 – as opposed to the magnetic field distribution within steel parts – and is not contingent on further material models, as the phase or stress distributions are. The concrete difficulty of obtaining the temperature data for a given process can vary wildly from one facility to another. Many modern industrial heat treatment facilities are sealed off from any outside interference, simultaneously increasing the controllability of the process and decreasing the risk of injury due to interaction with moving, conducting, and/or hot parts11. These safety and control features come at the expense of accessibility, hindering measurements if no instrumentation has been included during the construction of the facility or the design of the process control software.The most direct way to verify process simulations is to compare the resulting temperature field with data obtained from experimentsIdeally, the heat treatment process is monitored, so that temperature at a certain heating stage or the time dependent temperature of each workpiece is logged, stored, and transferable for quality control and simulations. Often however, this is not the case. On top of that, if the heat treatment process also involves moving workpieces or induction coils, they may obscure line of sight for ad hoc pyrometer measurements and make instrumentation of samples impossible.The method described in this article deals with such a case, where there was virtually no temperature data available. This was due to the induction facility being highly automated (and therefore enclosed), but not instrumented. While material data could be gained from treated and untreated workpieces, there was no information available on the heat treatment curve the bearing underwent during the process, and recording one was infeasible. The only data point was an estimate of 1050 °C, attained through glimpsing into the induction oven from the intake conveyor and seeing a bright yellow shine through the rotating heating assembly. Needless to say that one temperature value of such questionable origin could hardly be used to verify the rather complex multiphysics simulation that would have to be implemented further in the future.in-situ, the temperature history of the hardened workpiece still left its traces in its microstructure. This paper aims at describing a method of combining metallurgical data from phase diagrams usually available to the heat treatment facility with a micrograph analysis of a surface hardened sample in order to deduce several depths of different transition temperatures within the material. Consequently, a general numerical temperature distribution fitted to these temperature-depth pairs can be used to verify the estimated surface temperature.While there was no way of measuring the temperature −1, noting a distinct split of Ac1 into a starting temperature Ac1b and an end temperature Ac1e. All of these temperatures increase with heating rate, so that the heat treatment in practice, with a heating rate of 81.67 Ks−1, experiences Ac1b at 790 °C, Ac1e at 840 °C and Ac3 at 895 °C. Differing cooling rates were examined at this heating rate up to an austenitisation temperature of 1000 °C, with 10 seconds of holding time to allow for appropriate austenitisation of the samples. The material exhibits a distinct bainite nose between λ0.02 and λ0.1. Figure The steel in this study was a modified C38 tempering steel forged into shape and subsequently inductively surface hardened. Its chemical composition is specified by the manufacturer to be according to the ranges listed in Table λ0.012 line in Fig. The heat-treated part consists of a bearing journal surface surrounded by flanges. The shaft was cut through the bearing's axis and one journal surface was trimmed to fit into the bedding. The sample was ground and polished with a 1 μm diamond suspension as the finishing step, and subsequently etched using a 3% nitric acid solution, with the prepared sample shown in Fig. 1b temperature determined through micrograph analysis.A line of Vickers hardness measurements was taken along the same centreline as the micrographs, using a Qness Q10A+ Vickers hardness tester. A measuring load of 1 kgf (HV1) was set to allow for close placement of indentations. Figure 3, Ac1e and Ac1b are determined at the depths of 2500 μm, 4400 μm and 5000 μm, respectively. The performed hardness measurement corroborates these depths fairly well with average hardness of 650HV1 at the surface coinciding with the predicted 628HV10 of the quenched martensite described in Fig. 12. The subsequent hardness drop can be attributed to the incomplete dissolution of ferrite, which has not completely transformed into the austenitic phase during the heating process, as seen in Figs. 1b and thus starting the pearlite to austenite transformation but not completing it.The silhouette of the thermal gradient that the material experienced during heat treatment can be guessed from the overview in Fig. The precise depths can be incorporated into the overview image to show an approximation of the transformation zones present during the heat treatment, as depicted in Fig. 13 but ignore the cooling of the surface.The temperature at the surface may still be of interest, since it is the control parameter of choice in most automated induction facilities. Analytical solutions describing the temperature distribution of induction heated cylindrical parts existA simplified, axisymmetric cylindrical model of the bearing was calculated by FEM simulation with load parameters approximating those of the industrial heat treatment, with detailed parameters given in Table rod = 25 mm and length of lrod = 150 mm. A complex claw-shaped inductor of proprietary geometry encompassed ≈150° of the bearing, which rotated constantly at a distance of 0.5 mm during the hardening process. Since the simplified model was only an axisymmetric slice of the whole circumference, the inductor was represented as a coil of rectangular cross section  with two turns dcoil = 5.4 mm apart, distanced 0.5 mm from the bearing surface. The model air space had a radius of rair = 250 mm. Homogeneous Dirichlet boundary conditions were defined at all surfaces; these confined the magnetic field to the simulated geometry by acting as magnetic insulation. This was well suited, since the field was assumed to be axisymmetric and to not extend past the dimensions of the defined cylinder of air. The mesh within the rod was generated from hexagons with a set width of e0rod = 2.5 mm. The skin depth was 349 μm and divided into 15 elements geometrically scaled from e0skin = 2 μm at the surface to e1skin = 83 μm. The air mesh was generated procedurally to scale from 1.5 mm at the coil surface to e∞air = 15 mm at the model boundary, while the coils were modelled one element thick with a wall thickness of 1 mm. The load was a sine wave current with an amplitude of I = 1850 A and a frequency of f = 10.5 kHz. This amperage was based on a measurement on the induction coil, but increased slightly to result in a solution close to the assumed maximum surface temperature of 1050 °C. The heat transfer model used only the mesh of the rod, and applied a convective film boundary condition of hair = 20 Wm−2K and ambient radiation condition assuming the surface emissivity to be ε = 0.7. The initial temperature distribution was set to be a uniform room temperature 25 °C and the rod was heated for theat = 12 s.The 5° slice of rod had a radius of rThe resulting distribution shows the temperature envelope, i.e. the maximum reached throughout the process, along the path shown in Fig. in-situ measurement possible or available. The thorough investigation of the microstructure in the surface hardened region supplies rather precise ranges of the transition from one microstructural region to another. It is important to note that the transitions are not sharp but rather transitional areas due to local differences in chemistry because of production related segregations and possible variations in the temperature distribution imposed by the inductive heat generation. However, the evaluated transition depths in combination with a TTA-recording for the process conditions supply the transition temperatures for the considered heat treatment quite precisely on a macro scale. The actual transition temperatures in the bearing journal may be somewhat higher, since the TTA-information is drawn from tiny samples with diameter 4 mm that experience homogeneous heating in the dilatometer compared to the 50 mm diameter of the bearing, where a certain degree of overheating is necessary since its core acts as a heat sink during the heating process.As stated in the introduction, the presented method represents an approach for obtaining temperature data of a surface hardening heat treatment process where there is no While the transition lines shown in Fig. The FEM simulation used to extrapolate the surface temperature serves as an example for the verification process: it is a preliminary study using a simplified geometry with estimated process parameters and a linear electromagnetic material model. While the surface temperature fitted in Fig. The temperature history at given points on or slightly below the surface of a surface hardened part can be reconstructed based on microstructural features found by a post-mortem microscopy study provided that a time-temperature austenitisation diagram of the material, which has been recorded for process relevant cooling rates, is available.FEM simulations of the thermal problem can be validated by comparing the calculated temperature field with those reconstructed temperatures. Unknown simulation parameters such as surface to air heat transfer coefficients can inversely be determined by an iterative approach.The following conclusions can be drawn from this work:


Microbial transition state theory (MTS) offers a theoretically explicit mathematical model for substrate limited microbial growth. By considering a first order approximation of the MTS equation one recovers the well-known Monod’s expression for growth, which was regarded as a purely empirical function. The harvest volume of a cell as defined in MTS theory can then be related to the affinity concept, giving a new physical interpretation to it, and a new way to determine its value. Consequences of such a relationship are discussed. All of these expressions rely on empirical rules, differently to enzymology for which analogues of Monod and Haldane expressions have been mathematically derived5). Microbial transition state theory6 recently introduced a new expression for microbial growth based on the statistics of molecules distribution in a medium inspired from chemical transition state theory. In this communication we explore the physical meaning of the affinity concept through the lens of MTS theory and particularly show how it may provide a novel interpretation of Monod’s growth function.Since the success of Monod’s expression Equation  to model8 show the differences in reported literature values for the affinity constant for the same species: these differences are explained by culture history, quality of the experimental data, and posterior data analysis. However little to no consensus can be found in the literature on its interpretation. Furthermore in a review of theoretical derivations of the Monod growth function9 the author concludes that no clear interpretation may be given to the affinity constant. A revision of the affinity concept in Microbiology was made by Button10, where fourteen different expressions for affinity are documented. The concept is largely influenced by the Michaelis-Menten model for enzyme kinetics interpretation of affinity from receptor and ligand binding sites, since Monod’s expression for growth is mathematically equivalent to the Michaelis-Menten expression. As stated by Monod himself, Monod’s growth function is purely empirical, while Michaelis-Menten expression has a rigorous theoretical justification5, thus one might wonder if the concept of affinity for representing cell growth has a solid conceptual ground.Equation 11. The formulation and complexity of both catabolism and anabolism vary greatly depending on the objective the modeller has in mind. On the one hand, when describing the metabolic pathways within a specific microbial species, the formulation takes into account ATP formation and intra cellular intermediates and quickly becomes a very complex web, e.g.12. On the other hand if one is interested in observing the general metabolism of a culture at a macroscopic level then the situation simplifies to just a couple of reactions11. We will focus on the latter.MTS theory relates the growth rate to the amount of energy available to perform cellular work. The central idea of bioenergetics is that the energy consuming anabolism can only be thermodynamically feasible if it is coupled with an energy yielding catabolism. The overall reaction resulting from the coupling is known as metabolismλ times the catabolism the energy requirements of the global metabolic reaction are fulfilled13 .P stand for electron donor, electron acceptor, and products, respectively. 14. Let us consider a first reaction representing catabolism Eq. , a seconyx/s) in microbiology as shown in the Eq. The reader should notice that et al.11 allow computing 6. More precisely, if we denote by MTS theory demonstrates on a theoretically explicit ground a growth rate expression If one considers a first order approximation of the exponential function near zero  then one recovers Monod’s expression of growth:Escherichia coli15 different empirical substrate limiting expressions- all of them with a Monod-like shape- were compared and no difference was found in the identifiability of their parameters.The approximation holds true for high substrate concentrations. More precisely, it can be shown that the two curves differ by less than 10% for E. Coli ML 30. In the cases where no yield was reported the energy dissipation method11 can be used as illustrated in Table Note also that in Eq. mentclass2pt{minimmentclass2pt{minimOn a more conceptual ground, the MTS approach proposes a way to revisit our current perception of the “affinity-concept” of a microbial culture for a given substrate. It offers an alternative view of the microbial affinity notion than its enzymatic analogue related to Michaelis-Menten theory. It unravels a contribution that is related to the yield (mole of biomass formed per mole of substrate consumed) from another that represents the capacity of the microbial culture to explore a fraction of its surroundings in order to harvest substrate (9. The physical interpretation of the affinity concept raises new opportunities to analyse and experimentally challenge the meaning of the This analysis thus plants a seed towards a more physically grounded view of affinity than earlier proposals made from attempts to theoretically derive Monod’s equationSupplementary Material.Dataset 1.


We estimate the amount of phonons caused by this transition applying precise quantum computing key tools, and resulting in a maximum value of 1.23 ± 0.02. Further applications of our microcantilever sensor were assessed using unambiguous mapping of the surface stress induced by the  With this phrase, Feynman exemplifies the implications of reaching a deep understanding of the physical and chemical ice crystal properties. These properties are related to its molecular morphology that depends on the order of the hydrogen–bonds configuration2. Hence, the ice presents stable configurations like cubic  of ice with photolysis and the formation of ionic radicals in comets and other astrophysical media; making it relevant in the understanding of the origins of the earlier solar system and life on Earth8. This underscores the need to understand the crystallization and SPT’s to unravel the still hidden secrets of the ice–related phenomena.14. Notably, the reactivity of water towards a metal oxide surface can be a fundamental tool in the understanding of these interactions16. Among the oxides, magnesium oxide (MgO) has been the subject of many studies due to its high ionic character and simple crystal structure17. Its abilities on catalysis, adsorption–desorption process, and its use as a lattice template for selective growth of thin films have been studied for different purposes21. MgO surface is an ideal platform for water interaction studies due to the formation of free OH group  for the 1.1 mK/s and 0.55 mK/s heating rates were employed. These experimental conditions contribute to maintaining constant the coverage factor and an amount of about two water monolayers on the MgO surface between the experiments.To understand the dynamics of the interstellar ice over which an Structural Phase Transition (SPT) can temporarily progress, we architecturally grew water monolayers on top of the (100)–oriented MgO substrates. We investigated the time evolution of the SPT by monitoring the intensity of the diffraction spots from the Low–Energy Electron Diffraction (LEED) patterns along with full control and discretization of an external perturbation energy. All of our intensity measurements were performed on the spot (10) of the LEED diffraction pattern. Figure entclass1pt{minimac caused by impurities in the MgO crystal lattice as a consequence of the SPT local perturbation within the lattice that is directly mapped on our sensor. Importantly, we show for the first time that the SPT in interstellar ice could be monitored by means of (100)–oriented MgO crystal lattices. To our knowledge, this versatile platform detecting mechanical changes via electron diffraction has not been explicitly examined before.We now turn to the characteristic shape of our findings in Fig. 29, we approximate the dynamics of the phonon in the MgO crystal by means of the following unperturbed Hamiltonian: h) divided by 2c. This model approximate the isotropic lattice strain in the MgO lattice, which is then used to estimate the lattice stress by analizing the coherent elastic scattering of electron diffraction. We explore isotropic stress generated by the water monolayer dynamics, which acts until a depth of about , D denotes the volume–weighted crystallite size, E is the isotropic Young’s modulus and The W–H analysis is a quantitative approach, which differentiates between size induced and strain induce peak broadening by considering the peak width as a function of the Bragg diffraction angle  of interstellar ice at 185 K. Here, we show for the first time that the use of a very precisely experimentally controlled disturbance is highly desirable for the characterization of SPTs in interstellar ice. By monitoring the intensity of the diffraction spot of the Low–Energy Electron Diffraction (LEED) pattern, we obtain the first experimental evidence of the existence of the SPT between the 35 and it was maintained at pressures of 35. The impurities had been monitored by an Ametek LC-Series quadrupole mass spectrometer coupled to our vacuum system that shows a low level of atmospheric impurities consisting of molecular nitrogen and oxygen, as well as the water characteristic ions in the ultra-hight vacuum system. Figure 35. Next, a cooling process of 4 hours was carried out to promote the formation of a predominantly ice with c(Our experimental setup is based on the apparatus used for previous workmentclass2pt{minimc(p(c(p(To induce the gradual ice mentclass2pt{minim


The World Health Organization declared the outbreak of coronavirus disease 2019 (COVID-19) on March 11, 2020, highlighting the importance of preventive actions to limit the spread of infections . On FebrPrime Minister Shinzo Abe declared a state of emergency in 7 of the 47 prefectures on the evening of April 7  and natiOn March 5, 2020, in response to the spread of COVID-19, Kanagawa Prefecture  launched a personalized support program through LINE’s chatbot  .We received data from Kanagawa and analyzed the initial response data of 431,106 individuals aged over 15 years until April 16, 2020 to assess the extent to which preventive actions are being taken and how they have changed over a month, including the date of the declaration of a state of emergency in Kanagawa (April 7). Figure The results show that handwashing and cough etiquette are quite widespread preventive actions, as about 90% of all age groups were practicing them Fig. . On the Figure individual efforts, many of them have already been successfully implemented. However, preventive actions such as teleworking that require more social and political efforts are much more difficult to implement on an individual basis. Therefore, social and political support to promote flexible working practices is an urgent issue that is expected to play a crucial role in curbing the spread of COVID-19 in Japan.It should be noted that this data was collected from LINE users in Kanagawa who voluntarily responded in the early stages of the program and may not be representative of the population of Japan as a whole, or of Kanagawa Prefecture. It is also necessary to note that this analysis did adjust for confunding variables that may change over time or geographically . These findings might indicate that for preventive actions that can be implemented with ESM 1Geographical scope of the location of Kanagawa Prefecture. (PDF 965 kb)ESM 2Daily cumulative number of respondents considered in the analysis. It should be noted that the nationwide LINE surveys led by the Japanese Ministry of Health, Labor and Welfare (MHLW) were conducted on March 31–April 1, April 5–6, April 12–13, and May 1–2 (which are different from the prefecture’s LINE service we used in this study) . For the


Compartmental models have provided a framework for understanding disease transmission dynamics for over 100 years. The predictions from these models are often policy relevant and need to be robust to model assumptions, parameter values and model structure. A selection of compartmental models with the same parameter values but different model structures (ranging from simple structures to complex ones) were compared in the absence and presence of several policy interventions to assess sensitivity to model structure. Models were fitted to data to assess if this might reduce this sensitivity. The compartmental models produced wide-ranging estimates of outcome measures but when fitted to data, the estimates obtained were robust to model structure. This finding suggests that there may be an argument for selecting simple models over complex ones, but the complexity of the model should be determined by the purpose of the model and the use to which it will be put. Advances in computational power have lead to mathematical modelling being used increasingly to solve real-world problems in all fields and levels of decision making. In epidemiology, mathematical models and in particular compartmental models, have been used to explore (among other things) the emergence and spread of disease, and the impact and efficacy of interventions such as drug treatment, vaccine introduction and parasite control . There it is time, S is the susceptible population (at risk of infection), I is the infectious population (capable of transmitting infection) and R is the recovered population (removed and playing no further role in the epidemic). β is the number of contacts per unit time and 1/α is the rate of recovery.The first known contribution of mathematical modelling in epidemiology is Daniel Bernoulli’s work on the inoculation against smallpox in 1760 al, 2008.N (S+I+R) where members of the population mix homogeneously (interact with one another to the same degree). There is no entry into or departure from the population as the dynamics of the disease are much faster than the time scale of birth and death processes; and hence the impact of these processes on the population can be ignored. Any inherent age, demographic and spatial structure is also ignored. There is no initial immunity as all ‘members’ of the susceptible population are equally likely to get infected. The model infers permanent immunity; once recovered, a second infection is impossible. The incubation period of the infectious agent is instantaneous and the duration of infectivity is the same as the duration of the disease (one is infectious as long as one has the disease). Discrete individuals do not exist in the model and it is assumed that individuals who reside in the compartments are identical and as such variation among individuals is unimportant. Thus compartmental models are described as population-level models. It is fractions of the population that flow between compartments and these movements are continuous. The rate of recovery 1/α is constant for each ‘member’ of the population and hence the average duration of infectiousness (and in this case disease) is α.This model results in a fixed population There are several extensions of the SIR model, including the Susceptible-Infectious (SI) model where immunity is ignored (by excluding the Recovered compartment), the Susceptible-Exposed-Infectious-Recovered (SEIR) model that allows for a period of latency/exposure before becoming infectious, the Susceptible-Infectious-Recovered-Susceptible (SIRS) model that allows for temporary immunity and other similar models . As diseIn using several different structures to model the same disease, it is of interest to assess if there are large differences in model predictions because of model structure alone. This paper compares a selection of model structures and the predicted impact of policy interventions. This paper also explores whether fitting the models to data to determine parameter values empirically, reduces sensitivity to model structure.L), a period where clinical symptoms have manifested but the host is not yet infectious (B), and an infectious period (I) that does not grant immunity that is, a person may be re-infected once susceptible (S) again. These models are compared in the absence and presence of drug therapy. Once infected and clinically ill, a patient has the potential to receive drug therapy and those who do not receive drug therapy recover naturally that is, they do not die from the disease but recover through the body’s natural defences at a period longer than the drug recovery period. Patients may seek drug therapy when symptoms have manifested (they feel ill) as well as at the infectious stage. The natural recovery period is assumed to be longer than the drug recovery period and the time to infectiousness, hence natural recovery is only possible once the disease is at the infectious stage and not any earlier. Birth and death, super-infection and the development of immunity through repeated infections are ignored. Such a disease with a latent period and no immunity would need to be modelled using variants of an SEIS general model structure.Different model structures are compared for a disease that has a latent period  and five models are compared in the presence of drug therapy  . These mL is used to characterise the latent phase of the disease. In Model 1 (SLI), the latent (L) and symptomatic (B) stages of the disease have been combined; hence the rate of flow between Latent compartment and the Infectious compartment is 1/(⏃1+σ2). When incorporating drug therapy into the models, one has to consider at what stage of the disease the population has access to drug therapy. As the disease has a latent stage, it is only in the infectious compartment that the population may seek drug therapy and this occurs at the rate p/(q+τ) (incorporating the treatment probability (p), the time to seek treatment (τ) and the drug recovery period). This rate naturally comprises two steps: treatment seeking and recovery through drug therapy. As there is no treated compartment in this model to explicitly allow for this, the total time to move from being infectious to becoming susceptible again is q+τ and hence the population who receive drug therapy (with probability p) do so at a rate of p×1/(q+τ). The population that is infectious but remains untreated recover naturally at the natural recovery rate ((1–p)/δ).The model parameters driving these models and their assumed values are in B) and infectious (I) stages of the disease, where the subscripts u and t in Model 4 represent untreated and treated infections respectively. These models account for the latent period by including a time delay in the force of infection (λ) of size σ1. As symptoms have manifested (population feels ill) in the symptomatic compartment (B), the population may receive drug therapy from both this and the infectious compartments. At the symptomatic stage, p% of the population will seek and receive drug therapy (Model 2) or seek treatment (Model 4) while (1–p)% of the population will remain untreated and become infectious. In Model 2, the time to seek treatment is incorporated in the same manner as for Model 1. In Model 4, owing to the inclusion of Symptomatic and Infectious compartments for the treated population, the time to seek treatment is incorporated explicitly. The latent and symptomatic stages of the disease are captured separately in Models 3 (SLBI) and 5 (Stratified SLBI) and treatment is incorporated in the same way as Models 2 and 4 respectively. Model 6 stratifies the population into the ‘never treated’ and those ‘destined to be treated’ by multiplying the force of infection λ by the treatment probability (p). Treatment can take place at both the symptomatic and infectious compartments and occurs at the rate 1/(q+τ) (incorporating the time to seek treatment and time to drug recovery) while the untreated recover naturally at the natural recovery rate (1/δ). The equations underlying all these models are displayed in the Models 2 (SBI) and 4 (Stratified SBI) do not have a latent compartment, only compartments reflecting the symptomatic  at each time step and treatment coverage is estimated by cumulative treated cases as a proportion of cumulative cases.Models are compared using steady state measures of incidence, prevalence and treatment coverage. Incidence is measured as the number of new cases at each time step, prevalence is measured as the population infected with the disease (Models were fitted to data using least squares approach . Model rp) is 0, model 4 collapses to model 2 and models 5 and 6 collapse to model 3. Under the condition of no treatment, prevalence in the three models is equivalent while incidence differs slightly among model structures  is sometimes the best source of data available to mathematical modellers to use to estimate the treatment probability (the chance of receiving drug therapy) in their models. As shown in the results, depending on the structure of the compartmental model, these two values (treatment coverage and the treatment probability) will not always be equal. Treatment probability π), consider a simple SIS model (S+I = 1) for a cohort of infected individuals governed by the equation: β is the number of contacts per unit time, p is the probability of treatment, 1/q is the drug recovery rate and 1/δ is natural recovery rate. For ease of computation let a = p/q+(1–p)/δ and assume initial conditions of S(0) = 0 and I(0) = 1.In order to assess the relationship between treatment probability (p) and treatment coverage  = 1, this integrates to Using the initial condition π) is a function of the cumulative treated cases (pl/q) and the cumulative cases (βIS).The treatment coverage π=la (the average recovery rate) and β (the transmission coefficient). To establish this relation, one can look at the dynamics of the disease when the SIS model has reached a steady state. At equilibrium, the sum of the inflows to a compartment is equal to the sum of its outflows. Thus for the infectious compartment (I) in an SIS model, a = p/q+(1−p)/δ and S = 1−I into Substituting This simplifies to The trivial (infection-free) equilibriumThe non-trivial equilibrium where infection is presentThis system has two equilibria: β and a. If β<a, the trivial equilibrium is stable but if β > a then the non-trivial equilibrium, the equilibrium where infection is present is non-negative and stable.Both equilibria exist depending on the relationship between β > a and multiplying through by eβt−/eβt− leads to Including p), but rather a function of the p, δ and q.Thus for an SIS model, treatment coverage (π) is not equal to the treatment probability (This result holds for Model 1 but will change for models with different structures (Models 2–5). The results in the section ‘With treatment’ showed that treatment coverage in Model 6 correctly represented the 10% treatment probability. This is because at equilibrium in Model 6, Therefore, π) at equilibrium is treated cases ((B+I)/(q+τ)) as a proportion of incidence (λS) and hence for Model 6, π=p. Thus while treatment coverage data is often used by modellers as the best estimate of treatment probability, depending on the model structure, the treatment coverage predicted by the model may be very different from the treatment probability.Treatment coverage . All other parameter values are held constant at their assumed values in p, the probability of being treated, being in the range of 0.0063–0.0097. At these values of p, the six models make identical predictions for prevalence, treated cases and treatment coverage with only small differences observed in the prediction of incidence, thereby showing the decrease in sensitivity to model structure that can be achieved by fitting models to data.Showing that for different model structures, treatment coverage is not always equal to treatment probability, demonstrates that even for routine anti-disease interventions like drug therapy, model structure has a large impact on model results. This section explores if fitting models to data reduces this sensitivity to model structure that is, if models are fitted to data, does model structure matter less or at all? Model 6 is used to simulate the number of treated cases for data fitting purposes as this was the only one of the six models where Compartment and other models of disease transmission may be used to assess the impact of policy interventions on transmission. Two interventions are applied to the six models to assess sensitivity because of model structure; mass drug administration and VC. These interventions are then scaled up, aimed at eliminating the disease.p. Mass drug administration is implemented over 8 weeks at 75% probability in all models. The graphs on the left in Mass drug administration involves administering drug therapy to the population at risk regardless of disease status . An examβ; the number of contacts with vectors. The coverage of the control as well as the efficacy of process are taken into account in decreasing β where VCβ = (1–cover-age*efficacy)*β. In these models an example of VC is introduced into the models with 50% coverage and 50% efficacy. In some diseases like malaria and dengue, vectors are an active part of disease transmission. VC as an intervention, requires acting on the vector population in a way that interrupts transmission. This may for example be achieved through larviciding, the use of insecticide treated bednets and household spraying with pesticides . In mode−6. The impact of these interventions is estimated as the time to elimination (in weeks) from the start of the interventions. These interventions are tested on the six models that have not been fitted to data and on the models once they have been fitted to data.When interventions are used to eliminate a disease rather than attempt to control it, mathematical models will aim to produce estimates of the length of time to eliminate the disease, the intensity of each of intervention as well as the combinations of interventions that may be used to eliminate a disease. Elimination of infection is defined as the reduction to 0 of locally acquired incidence in a geographical area as the result of deliberate efforts . Two verp, the probability of treatment, is the estimated parameter from the data-fitting process. Thus when uniformly increasing the p to 0.9 at the start of the intervention, the previously fitted value falls away and hence the time to elimination estimates are the same regardless of whether the models are fitted or not. These estimates range widely from 50 weeks (<1 year) to 399 weeks (<8 years) depending on the model structure. These estimates are not robust and clearly sensitive to model structure.As mathematical modelling is increasingly used to aid decision making in the public health sector models need to be rigorously tested for sensitivity to parameter values and model assumptions so that model predictions are robust . IncorpoFitting the five models to data simulated from model 6 , shows that the sensitivity because of model structure can be reduced. As countries become better at collecting routine data and performing clinical trials, opportunities exist for modellers to validate their models with real data. Data quality issues aside, modellers may still be able to use their models to reproduce the data, as well as validate model predictions with a testing dataset. As models are extended to incorporate specific disease dynamics such as immunity , whereas in models 2 and 3, the population has two chances to receive drug therapy (Symptomatic and Infectious compartments) and hence it is harder to eliminate the disease in model 1 than in models 2 and 3. The longest time to elimination estimate is from model 6 . In this model, a segment of the population has no chance to receive drug therapy in the course of the infection and will have to wait until the next round of infections to stand a chance of receiving drug therapy. In this case, it is much harder to eliminate the disease. Modellers should be aware of the treatmentseeking behaviour of the populations they model, but where this information is not available, there is an argument for modelling different treatment-seeking behaviours so that this heterogeneity may be better understood and prudent and conservative estimates may be produced. if they are fitted to the same set of data. Does the argument exist for choosing simple models over complex ones? The answer is yes, but the converse is also true. On one extreme one could have a model that is too simple to be biologically plausible and on the other extreme, the most biologically plausible model may be too complex to be of any practical use. There needs to be a balance between model simplicity and biological plausibility for models to be of practical relevance. Some of the models in this paper have a simple structure while others have more complex structures. The results have shown that models seeking to measure the same phenomenon (e.g. estimating the impact of drug therapy) that differ in structure only, can produce very similar results same class also. Several aspects have been ignored such as immunity, super infection, chemoprophylaxis, drug resistance, heterogeneity of the population and vector population dynamics. Stochasticity was also ignored. It was not in the scope of the paper to include all aspects of disease, but rather to show that even in the most basic disease context, differences still exist because of model structure. These are all areas where further work can be undertaken. Ultimately, model structure (and its complexity) needs to be chosen carefully depending on the focus of the model and the use to which it will be put.This paper sought to compare results between deterministic compartmental models only and did not extend to include other model structures such as agent-based models and time series models. While this is a limitation of the paper, it also serves to show that differences in results because of model structure arise not only among different classes of models but among models in the Compartmental model structures are based on the underlying epidemiological and demographic interactions of a particular disease. Given that there are many choices for these interactions, the number of possible combinations are large . This maAppendices


We read the review by Arabi et al. with great interest which tried to examine the effects of vitamin D supplementation on hemoglobin concentration. It seems that the article suffers from fundamental methodological issues and the conclusions are likely to be erroneous. In this regard, we would like to ask the authors to address the mentioned limitations and to update the analysis in order to provide robust and trustful results. We are concerned that such meta-analyses may lead to the biased findings and conclusions. Dear Editor,We carefully read the article by Arabi et al.  publisheThe authors did not follow the PRISMA guidelines, which focuses on the accuracy and reliability of the reporting of the systematic reviews and meta-analyses. The authors did not sufficiently follow the PICO format . The authors did not clearly address two of the main components of inclusion criteria (participants and comparison). Conducting a systematic review with vague inclusion criteria may lead to problems concerning the validity and applicability of the systematic review . In addiinclusion criteria, point number 1), however, they declared further that the studies carried out in subjects with mean age of ≥17.5 years old were included . Also, it is stated that studies which used oral vitamin D supplementation were included , nevertheless, we noticed that they included studies which have used parenteral or enteral vitamin D supplementation. For instance, they included the study done by Sooragonda et al. [Additionally, we noticed that there are some contradictions in the inclusion criteria. The authors stated that they did not limit their search strategy based on gender, age, etc. (a et al.  which adBased on the Cochrane handbook, including multiple comparisons from one study with a shared intervention group to the meta-analysis is not correct . This apLastly, we noticed that the authors combined the effect sizes of co-intervention studies with vitamin D intervention studies, which is not methodologically correct. The authors included a study which assessed the combination effects of food products fortified with vitamin D and calcium in young adults . In addiTherefore, we conclude that the current review has the potential for producing incorrect and misleading results. Hence, the results of the current review should be interpreted with caution because of the mentioned errors. The correction of the stated faults may result in substantial differences in the conclusions that can be drawn from the present meta-analysis.