LRsetup=LRinitial,SIsetup=SIinitial+/2,APsetup=APfinal. The 3D error is then the magnitude of the vector from the initial (reference) position to the setup position. The calculation was done for every exhale phase in the data for which there was another one at least 30, 60 or 90 seconds later, at an amplitude within 0.5 mm from the first. A correlation between the time interval and the 3D error was also sought. The mean 3D error is found to be roughly equivalent for time intervals  of 30, 60 and 90 seconds between the orthogonal simulated images . The 3D error is less than 1, 2 and 3 mm for 77%, 89% and 98% of the data points, respectively. The actual time between simulated images turned out to be very close to tinterval, with 90% of the second simulated image acquisitions being completed within 38, 68 and 95 seconds of the first simulated image for tinterval of 30, 60 and 90 seconds, respectively. No correlation was found between the length of the time interval and the 3D error. When acquiring respiratory‐gated radiographs for patient setup, only small errors should be expected if those images are not taken simultaneously.Image‐guided patient setup for respiratory‐gated radiotherapy often relies on a pair of respiratory‐gated orthogonal radiographs, acquired one after the other. This study quantifies the error due to changes in the internal/external correlation which may affect asynchronous (non‐simultaneous) imaging. The dataset from eight patients includes internal and external coordinates acquired at 30Hz during multi‐fraction SBRT treatments using the Mitsubishi RTRT system coupled with an external surrogate gating device. We performed a computational simulation of the position of an implanted fiducial marker in an asynchronous orthogonal image set. A comparison is made to the reference position, the actual 3D fiducial location at the initial time point, as would be obtainable by simultaneous orthogonal setup imaging at that time point. The time interval between the two simulated radiographic acquisitions was set to a minimum of 30, 60 or 90 seconds, based on our clinical experience. The setup position is derived from a combination of both the initial (AP) and the final (LR) simulated 2D images in the following way: PACS number: 87.55.ne For a respiratory‐gated treatment, gated imaging should be used for patient setup.,Simultaneous, stereoscopic imaging for patient setup has been achieved on several radiotherapy platforms. The CyberKnife system  uses simultaneous kV imaging from fixed, oblique orientations to localize targets before and during robotic radiosurgery.,Most modern radiotherapy platforms for routine care are equipped with monoscopic kV imaging mounted on the linac gantry, orthogonal to the MV treatment beam.As many clinics would prefer to use a pair of orthogonal kV radiographs for patient setup, it is important to quantify the possible errors that could occur due to the asynchrony (non‐simultaneity) of the acquisitions. There may be localization errors if the orthogonal images are separated in time. Intra‐fractional instability of the internal/external correlation has been noted in a previous study.Note that the 3D setup error that we are investigating has nothing to do with the relationship of the patient position relative to the simulated (planned) position. The calculation that we are reporting on is a separate issue, accounting only for the error due to the temporal separation of the two orthogonal respiratory‐gated radiographs. All other errors must be assessed independently.(gantry=0°), shifts in the superior‐inferior (SI) and medial‐lateral (LR) directions would be visible. Then the second respiratory‐gated radiograph, from either the left or right lateral direction (90° or 270°) would give the coordinates for SI and AP shifts. From our clinical experience, we estimate that the time between the two respiratory‐gated radiographs is no less than 30 seconds and perhaps as long as 90–100 seconds. Therefore, the analysis described below was performed for minimum time intervals of 30, 60 and 90 seconds between the simulated initial and final orthogonal radiographs.For this study, we used the abdominal surface as the surrogate of respiratory motion and assumed an automatically respiratory‐gated image acquisition. This is compatible with the RPM respiratory monitoring system combined with the Trilogy iX treatment platform . The scenario which is being simulated is one in which a respiratory‐gated 2D projection image is then followed by another one from an orthogonal perspective. Assuming that the first 2D image is an anterior‐posterior (AP) view ,The internal and external motion of patients has been derived from the datasets of eight patients undergoing multi‐fraction SBRT treatments.P→ref=. This is the point which would have been reconstructed in 3D by simultaneous radiographs . This is also the position of the internal marker when the first of the two orthogonal 2D radiographs would be acquired. As such, this point also defines P→initial=(=P→ref). The second internal position, P→final, simulating a second simulated setup image from an orthogonal gantry angle, was found by identifying the time point at which the external marker is within the same amplitude gate (±0.5 mm) as for the first simulated acquisition, at least tinterval seconds after the initial time point. The time interval  is set to a minimum of 30, 60 or 90 seconds, respectively; that is, the second acquisition is simulated at the next appropriate end‐of‐exhale after tinterval has passed The simulated setup position is then based on these two simulated images. A diagram illustrating the image acquisition time line of the procedure is shown in Fig. To simulate respiratory‐gated setup imaging, we used the RTRT data to find the 3D location of the internal marker when the external marker was at end‐of‐exhale, and set this as our true reference position, LRinital and SIinital. The second simulated image is then acquired from a lateral view, giving the AP and SI positions of the target, APfinal and SIfinal. The position to which the “patient” is eventually setup is P→setup. Since the SI direction is a shared dimension between the two simulated orthogonal asynchronous images, the SI setup position is taken to be halfway between the values found in the initial and final simulated acquisitions.If the initial image acquisition is simulated with the kV source at 0°, only the LR and SI projection of the position is seen, LRsetup=LRinitial and APsetup=APfinalThe LR and AP positions are found uniquely in the first and second simulated images, respectively: Error→=P→setup−P→ref . Here, P→initial is the 3D location of the fiducial when the initial simulated 2D radiograph is acquired; but also P→initial=P→ref, the 3D location of the fiducial as determined by a simulated simultaneous orthogonal radiograph acquisition. Therefore, the error in each direction is defined as follows:The 3D setup error is defined to be ErrorLR equals zero if the initial kV radiograph is taken from the AP direction (kV source=0°). Therefore, the assumption of the simulated imaging order (AP then LR) will bias our results somewhat. However, from our experience with this dataset, there is little expectation of significant deviation in the lateral direction. Therefore, by maximizing the error from changes in the AP motion, we have essentially made this a worst‐case scenario assessment.Note that the  position to the setup position:The 3D error is the magnitude of the vector from the reference tinterval seconds later at an amplitude within 0.5 mm of the first. To avoid obviously aberrant end‐of‐exhale locations, an additional restriction to consider only those exhale data points within 2 mm of the mean exhale position is used for the simulation. These would most likely be excluded by the user during an actual image acquisition. In addition, a correlation was sought between the time interval  and the 3D error calculation – the hypothesis being that the larger the interval, the larger the error would be.The calculation was done for every exhale phase for which there was another one at least . Patient 4 has the smallest deviations with a mean 3D setup error of 0.3 mm and a 5–95% range of 0.0–0.6 mm .The patient‐specific setup error calculations are shown in Figs. tinterva1, with 90% of the second simulated image acquisitions being completed within 38, 68 and 95 seconds of the first simulated image for tinterval of 30, 60 and 90 seconds, respectively. No correlation was found between the length of the time interval and the 3D error (R<0.3).Pooling all of the patient data together Fig. , the meaErrorAP and ErrorSI). These results are shown in Fig. . This becomes more apparent when the patients are combined  direction first and then from the AP (0o) direction. As always, though, one must account for the other localization errors. Care should be taken to avoid acquiring respiratory‐gated radiographic images during periods of irregular breathing. A method of audio or visual breath coaching may help with this.(–)For the scenario described above, the setup errors associated with asynchronous orthogonal respiratory‐gated kV imaging should not be significant. The majority of the error was found to be in the AP direction. This is most likely due to the fact that the SI error is determined using both radiographic images, essentially halving the error that one would have if only the SI coordinate from the first radiograph was used for the setup. Additional reasons for setup errors in either direction include the size of the setup gating window (1 mm), the relative extent of motion in each direction, and the correlation between the external surrogate and the internal motion in each direction. Details of these last two phenomena were examined in an earlier study.ith this.–13Previous studies have shown that there is a hardware delay between the external trigger and the resumption of the treatment beam during respiratory gating. This gating delay has been measured to be roughly 0.17 seconds.The formulation of the setup error assumes that common landmarks will be visible in both the initial and final images. Although this may not always be the case in clinical practice, it is unclear how to include this possibility in the analysis that has been presented. No published studies have detailed the frequency of common landmarks in respiratory‐gated images. Therefore, the results of this study do not apply to these cases, as the setup error due to respiratory‐gated imaging, as calculated here, may be an over‐ or underestimation, depending on whether the landmarks are visible in only the first or second image. and future studies will examine how they may affect the precision and accuracy of respiratory‐gated radiotherapy. Those analyses have been excluded as they are beyond the scope of the work presented here. By focusing on the effect of internal/external correlation variability on asynchronous planar setup imaging only, the results of this work have isolated one part of the respiratory‐gated treatment process and show that no large errors should be expected relative to simultaneous orthogonal respiratory‐gated setup imaging. The intention of this study has been to give confidence to those practitioners of respiratory‐gated radiotherapy who may have been wary of asynchronous setup imaging. The results of this study indicate that it is an acceptable procedure and should not result in additional localization errors to the respiratory‐gated radiotherapy treatment procedure.The current study focused only on the errors which may be associated with a lengthy respiratory‐gating setup procedure without any consideration of the additional errors which may occur during the treatment delivery. Changes in internal/external correlation or baseline drifts during respiratory‐gated radiotherapy may lead to larger than expected errors in targeted treatment. These phenomena have been reported elsewhere,,–18In a study of the errors associated with asynchronous respiratory‐gated setup imaging, it was found that significant errors should not be expected. Other setup and target localization errors were not investigated in this study and should be properly accounted for in the safety margin construction.This project was funded, in part, by a grant from Varian Medical Systems, Inc.


Development of novel membranes with optimal performance, selectivity, and stability is a key research area in membrane technology. In the present work aromatic polyamidoimideurea (PAIU) is synthesized and tested as promising membrane material for separation of water and alcohol mixtures. The PAIU membrane structure, density, and transport properties are studied. Mass transfer of water and isopropanol through the membrane is estimated by sorption and pervaporation tests to determine equilibrium sorption degree, diffusion coefficients, flux through the membrane, and separation factor. Two techniques of sorption study from liquid and from vapor phases are used as novel approach to experimental study of mass transfer. The vapor sorption calorimetry permits to analyze the behavior of the polymer material in sorption process. In pervaporation of water–isopropanol mixture, almost pure water mainly permeates through PAIU membrane. To improve the performance, a double layer membrane containing a thin PAIU layer on the surface of porous poly(phenylene oxide) support is developed. The double layer membrane is extremely effective in dehydration of isopropanol. Pervaporation is a membrane process that allows separating the components of the liquid mixture by transfer through the membrane by permeation and vaporization3. The membrane acts as a selective barrier between the two phases - the liquid phase of feed and the vapor phase of permeate. The mass transfer through the membrane occurs by the mechanism of “solution-diffusion”4 with the following stages: adsorption of a penetrating component on the membrane surface, dissolution of a component in the membrane material, diffusion of the component through the membrane and desorption from the back side of the membrane. Transport of small molecules through the polymer membrane can be described by the equation: P = D · S, where P is the permeability coefficient, D is the diffusion coefficient, and S is the solubility coefficient. In pervaporation the limiting stage that determines the intensity of the transfer is sorption and dissolution of the components in the membrane material; solubility is a thermodynamic constituent of the mass transfer process5.Membrane technologies have found its application in industrial and ecological processes due to their operational simplicity, low power consumption, modular and compact equipment as compared to physical and chemical analogues6. Separation of water–isopropanol mixture is one of the known applications of pervaporation9. The isopropanol is widely used as a cleaning agent in modern chemical, semiconductor, and electronic industries. Dehydration of wasted isopropanol is essential from environmental and economical points of view. The existence of water–isopropanol (12.2: 87.8 wt%) azeotropic mixture causes difficulties in isopropanol recovery by conventional distillation. Pervaporation does not require any chemicals addition to effective separation of water–alcohol mixture; it is considered as a prospective approach to outperform conventional separation technologies.Pervaporation process is widely used in separation of various liquid mixtures such as solutions with similar boiling points, thermally sensitive compounds, including organic‒organic and water‒organic mixtures with azeotropic point10. Efficiency of polymer membrane materials depends on numerous factors: the chemical nature of macromolecules, physicochemical properties and structure of membrane, properties of separating mixture, etc.Modern industrial tasks stimulate the development of the advanced membranes with improved transport properties. Polymers are the most versatile and feasible materials among diverse choices of membrane materials13. Membranes based on polyimides, polyamidoimides, and polyetherimides have been effective in separating of water–alcohol mixtures by pervaporation20. Polybenzimidazoles have been applied for the dehydration of organic solvents21.Extensive research has been done in finding the optimal polymer membrane that has maximal performance such as selectivity, flux, and stability. Polymers of heteroaromatic structure are known to exhibit specific physical and chemical properties such as increased structural order and glass transition temperature, fixed free volume, and thermodynamic parametersN-methylpyrrolidone, etc) used in their synthesis and in the following membrane preparation. The macromolecule–solvent complexes are so stable that they do not destruct during transition to the solid state. This fact prevents the total removal of the solvent from the samples by long drying at 80 °C in vacuum. The presence of residual solvent greatly influences the transport parameters of the membranes26.Many characteristics including transport properties of these polymers depend on the prehistory of the membrane preparation. The macromolecules of heteroaromatic structure exhibit tendency to the formation of the donor-acceptor bonds with amide solvents  mixture at 70 °С occurred with the significant flux and more than 99 wt% water concentration in permeate.Polymers of heteroaromatic structures exhibit relatively low permeability in diffusion processes. High permeability can be achieved by formation of the composite membrane containing selective polymer in the form of thin top layer arranged on the surface of a porous support that ensures mechanical strength of the membranei) to synthesize PAIU  to study transport properties of the membranes in the pervaporation of a water–isopropanol. The mass transfer in pervaporation depends mainly on the thermodynamic factors responsible for the sorption of penetrant by membrane at equilibrium. Therefore, much attention was paid to the sorption tests of dense films in the medium of water and isopropanol as components of separating mixture.The object of the present work is a polymer of heteroaromatic structure containing imide and amide groups in combination with urea groups in the backbone, so called polyamidoimideurea (PAIU). It can be expected an influence on sorption activity of functional groups in the structure of the monomer unit. The aims of the work are AIU Fig.  and to p3 that is typical for polymers of heteroaromatic structure.Physical properties of PAIU film were determined. The value of water contact angle equal to 78.6° ± 0.1° shows that the surface of the PAIU film is wetted. The PAIU film exhibits the density equal to 1.359 ± 0.006 g/cmg of PAIU is equal to 243 ± 2 °C.Thermal stability and glass transition temperature of PAIU film were characterized by TGA and DSC Fig. . The polTransport properties of PAIU films were estimated for the mass transfer of water and isopropanol mixture. Sorption degrees of water and isopropanol and diffusion coefficients of the penetrants were determined in sorption tests, whereas the PAIU membrane performance and separation factor were determined in pervaporation.The series of sorption and desorption tests were made to estimate sorption and diffusion parameters of water and isopropanol in PAIU film. Sorption tests were performed by immersing the samples into individual pure liquids. Desorption tests were carried out at isothermal and isobaric conditions. It was found that the PAIU film exhibits better sorption of water as compared to isopropanol. Presence of amide and urea functional groups in the PAIU backbone facilitates sorption of water molecules by hydrogen-bonding. Figure Mt is the amount of desorbed substance per time t. The linear part on the desorption curve corresponds to the system obeying the second Fick’s law and enables to calculate the effective diffusion coefficients of liquids. The last parameter characterizes the penetration rate of the liquid molecules and influences on the separation efficiency of the membrane in the pervaporation.The diffusion coefficient of water in the film was estimated based on the Fick’s second law. The kinetic curves of the desorption Fig.  was emplThe kinetic of sorption and desorption processes of PAIU membrane and the linear part on the curve for diffusion coefficient calculation are demonstrated on Fig. Calculated sorption and diffusion parameters are presented in Table y-axis and at higher activity the isotherm has the opposite trend. The partial molar Gibbs energy The interaction between the polymer and water was studied in details by vapor sorption calorimetry at 25 °C. The water sorption isotherm of PAIU is presented on Fig. The results of sorption calorimetric experiments  are presented on Fig. 33.At low water contents, the partial enthalpy of mixing of water with the sample is about −12 ± 0.1 kJ per mole of water (exothermic effect). This shows that at low water contents the film is in the glassy state. The exothermic heat effect arises from the loss of mobility of water during transport from liquid water to the solid glassy matrix of the polymer, where water molecules lose some degrees of freedom. This behavior was observed before in various systems that are able to form a glassy amorphous stateAt higher water contents, the hydration enthalpy became endothermic. It is known that the values of enthalpy of mixing indicate the character of the polymer–penetrant interaction related to the structural features of polymer. The polymer chains become more flexible due to the fact that water acts as a plasticizer and at gradual transition to the elastic state occurs. For the PAIU film the isothermal glass transition is observed at water content of about 4 wt% at 25 °C.αwater/IPA especially in the range of small water concentration in the feed. The fact that sorption and diffusion properties of water are greater than that of isopropanol provides high selectivity of PAIU in separation of water–isopropanol mixture.The performance of PAIU membrane in the separation of a water–isopropanol mixture was studied in a wide range of feed compositions. Figure Data of pervaporation performance  of PAIU membrane and concentration profile of water at the membrane surface as preferably permeate component of feed mixture are shown on Fig. The total flux through PAIU membrane increases with the rise of water concentration in feed. The value of total flux is corresponding to a moderate value of fluxes for polymers of heteroaromatic structure.The sorption isotherm of water Fig.  was usedentclass1pt{minimaDi based on Equation (J is the flux per unit area (g/m2 min), Di is the diffusion coefficient (m2/min), i on the feed side (g/m3), l is membrane thickness, m. Value of i on the surfaces on the permeate side is zero. The results are presented in Table To understand the mechanism of molecular transport in pervaporation over time, Fick’s first law was employed. The diffusion ability of the preferably permeating component (water) was estimated by the calculation of the diffusion coefficients Equation :1\documeentclass1pt{minima36.To improve the performance of isopropanol dehydration in pervaporation, double layer membranes composed of PAIU thin selective layer on a surface of porous PPO film was developed. A porous PPO film was chosen as a support because it has been successfully used for the production of composite membranes with a selective layer that consists of polymers with heteroaromatic structureThe morphology of the PAIU/PPO membrane was investigated by SEM. Figure Characterization of double layer PAIU/PPO membrane: structure characterization by SEM and the effectiveness of PAIU/PPO in pervaporation separation are presented on Fig. PAIU membrane has a dense homogeneous cross-section with small elements of supramolecular structure. The micrograph of the PAIU/PPO demonstrates the uniform structure of the dense PAIU top layer (on the right) and a part of the porous PPO support exhibited a spongy structure. Figure The performance of PAIU/PPO membrane was studied in pervaporation of a water–isopropanol mixture in a wide range of the feed composition including the azeotropic point. Figure Figure 41. The value of the separation factor of the PAIU membrane exceeds that of many previously published reports.The transport properties of PAIU membrane developed in this work were compared with literature data for the case of pervaporation separation of the isopropanol‒ water mixture in composition closed to azeotropic point. Table Physicochemical and transport properties of poly-4,4′-dicarboxydiphenylmethane in the form of PAIU membranes were studied. Combination of imide, amide, and urea groups in the backbone influences PAIU physicochemical and transport properties. The measured value of water contact angle indicates the hydrophilic nature of the surface of PAIU membrane. Mass transfer of water and isopropanol through PAIU membrane was studied by sorption and pervaporation tests to determine main transport parameters: sorption degree, diffusion coefficients, flux through the membrane and separation factor.In pervaporation of water–isopropanol mixture, the PAIU membrane is mainly permeated by water and possesses high separation factor towards water in a wide range of feed composition.Novel approach was proposed for mass transfer study which consists in using two techniques of sorption: from liquid and from vapor phases. The additional technique of vapor sorption calorimetry permits to analyze the behavior of the polymer material in sorption process. Sorption isotherms were obtained and used to model the water concentration profile through the membrane. The developed algorithm based on Fick’s first law can be regarded as alternative method for calculating diffusion coefficients in the membrane.−11 m2/min).The PAIU membrane has higher sorption affinity and diffusion ability of water in comparison with isopropanol. Thus the transport properties of membrane mainly determine the water permeability through the membrane. At low water concentration in the feed the water concentration at the membrane surface is even lower and increases with the increase of water concentration in separating mixture Fig. . The samThe double layer composite membrane consisting of PAIU selective top layer on porous PPO film support also exhibits high selectivity in pervaporation of water–isopropanol mixture. The flux through the PAIU/PPO membrane is a few times greater as compared to the PAIU membrane in the process of the dehydration of an aqueous solution of isopropanol for all feed compositions.N-methylpyrrolidone (NMP), propylene oxide, methanol, and isopropanol of chemically pure (CP) grade were purchased from Vekton (Russia) and were used without further purification. 4,4′-diaminodiphenylurea was were synthesized as described in42. N,N′-diphenylmethane-bis- (trimellitimido)acid was synthesized as described in ref. /-diaminodiphenylcarbamide)-4,4/-N,N′-diphenylmethane-bis-(trimellitimido) carboxylate  was synthesized by low temperature polycondensation  and NMP (8 mL) were placed in a three-neck round bottom flask with a stirrer and a thermometer. After dissolution the flask was cooled to −15 °С and then dichloroanhydride of N,N′-diphenylmethane-bis(trimellitimido) acid (0.001 mol) was added. The stirring was continued for 1 h, after that the cooling bath was removed. Then 1–2 drops of propylene oxide were added and the stirring was continued at room temperature for 5 h. The obtained transparent polymer solution was filtered and used for membrane preparation.Poly  were prepared by casting of PAIU solution in NMP on glass plate followed by evaporation of solvent at 80 °С in air and drying to a constant weight at 80 °С in vacuum. Then dense nonporous PAIU films were subjected to a special treatment by immersing in methanol for 24 h followed by drying at 50 °С in vacuum to constant weight.PAIU/PPO double layer membranes were prepared by casting PAIU solution in NMP on the surface of porous poly (PPO) support that was obtained as described in refs Thermogravimetric analysis (TGA) was conducted using samples of ~10–14 mg. They were contained in a platinum crucible with a heating speed of 10 deg/min in a nitrogen atmosphere. The TG 209 F3 Iris thermo-microbalance (Netzsch) was used for the analysis.Tg) was determined using differential scanning calorimeter DSC 204 F1 . The analysis was conducted under inert atmosphere with samples of approximately 4–5 mg at a scan rate of 10 °C/min from −20 to 300 °C.The glass transition temperature (Membrane morphology was studied by scanning electron microscope SEM Zeiss SUPRA 55VP. Before the test the gold layer was coated on the sample surface by cathode sputtering using the Quorum 150 (Great Britain) installation.The wettability of the films by water was estimated by measuring the contact angle of water on the film surfaces by sessile drop method on the Drop Shape Analyzer DSA 10  under atmospheric pressure and temperature 20 °C. Water was used as test liquid (the surface tension is 72.4 mN/m).46. The mixture of toluene and carbon tetrachloride was used to equilibrate the specimens at 20 °C.The membrane density was estimated by the flotation method with a laboratory made measurement unitSorption of water or isopropanol from liquid phase was tested in the following way. Samples of PAIU film were completely immersed in a bottle containing the solvent under study. The bottle was placed inside a thermostat at a constant temperature of 20 °C. After defined time intervals, the samples were blotted using filter papers to electronic balance (Shinko HTR-220CE) with an accuracy ±0.0001 g. Then the samples were placed back in the same solvent. The experiment was continued until the maximum value of sorption (equilibrium sorption) was reached.After completion of sorption experiments, the solvent desorption was carried out by exposing the samples in the air atmosphere of the desiccator containing zeolites. The weight changes as a function of time were measured. Finally, a sorption curve that shows an uptake of a solvent versus square root of time was plotted and analyzed to determine the diffusion parameters of the PAIU film.S) was calculated by equationms is the weight of a film sample in sorption equilibrium state and md is the weight of a dry sample.The equilibrium sorption degree  were plotted, where Mt is the amount of sorbed/desorbed substance per time t, M∞ is the equilibrium amount of substance that was determined as a difference between the weight of the swollen film and the weight of the film dried to constant weight, and l is the film thickness49.Accordingly the kinetic curves of desorption D was calculated by the equationМt/М∝ < 0.4.The effective diffusion coefficient 51. Sorption calorimetric experiments were conducted at 25 °C in a 28 mm two-chamber sorption calorimetric cell inserted in a double-twin microcalorimeter. The samples under study were previously dried in vacuum at room temperature. After that, they were placed in the upper chamber, and pure water was injected into the lower chamber. In a sorption experiment, water evaporates from the lower chamber, diffuses through the tube that connects the two chambers, and is sorbed by the sample in the upper chamber. It was selected a narrow tube and a relatively high sample mass. This combination provided a slow diffusion of vapor resulting in a hydration process close to equilibrium conditions.The water vapor sorption was studied by sorption calorimetry methodaw in the sorption experiments was calculated from the thermal power of vaporization of water in the lower chamber51. The partial molar enthalpy of mixing of water Pvap and Psorp are the thermal powers registered in the vaporization and sorption chambers, respectively, and The thermal powers released in the two chambers were monitored simultaneously. The activity of water aw is the water activity, R is the gas constant, T is the absolute temperature.The partial molar Gibbs energy of mixing of water The partial molar entropy of mixing of water  with thermal conductivity detector and refractometer IFR–454B2M.Pervaporation experiments were performed using the same equipment as reported previouslyα) in pervaporation of water and isopropanol (IPA) mixture was defined with absolute error of ±1–5 as followThe separation factor (J) was determined as the amount of substance penetrated through the membrane area per time unit. To compare membranes with different thicknesses (l) varying from 20 to 35 µm, the value of normalized flux (Jn) was used. Jn is the flux through membrane with 20 µm thickness calculated asThe total flux through membrane (−2h−1 for PAIU membrane and ±0.05–0.1 g · m−2h−1 for PAIU/PPO membrane.The flux was measured with absolute error of ±0.03–0.05 g · mPSI) that was calculated by equation:Membrane efficiency was estimated through the pervaporation separation index (54. Thus it is important to estimate the diffusion (Di) of the penetrating molecules in PV to understand the mechanism of molecular transport.Mass transport of a binary liquid mixture through a non-porous polymeric membrane is generally described by the solution–diffusion mechanism, which occurs in three steps: sorption, diffusion, and evaporation. Thus, the selectivity and flux are governed by the solubility and diffusivity of each component of the feed mixture to be separated. In pervaporation process, because of establishing the fast equilibrium distribution between the bulk feed and the upstream surface of a membrane, diffusion becomes the limiting step that controls the migration of penetrantsFick’s first law:Ji is the diffusion flux, Di is the diffusion coefficient, μi is the chemical potential, ai is the thermodynamic activity, x is the position, R is the universal gas constant and T is the absolute temperature55.The transport of penetrants inside the membrane can be described with the dai/dx) is separated from other effects within the membrane .In the case of one–dimensional diffusion and assumption that the concentration profile along the diffusion length is linear, the diffusion coefficient of component 56Ji is a flux of gas component i, and pi0 and pil are the partial pressures of component i on both sides of the membrane (0 stands for the surface on the feed side and l stands for the surface on the permeate side).The diffusion coefficient in equation  is simil


Recovering the position of a source from the fluxes of diffusing particles through small receptors allows a biological cell to determine its relative position, spatial localization and guide it to a final target. However, how a source can be recovered from point fluxes remains unclear. Using the Narrow Escape approach for an open domain, we compute the diffusion fluxes of Brownian particles generated by a steady-state gradient from a single source through small holes distributed on a surface in two dimensions. We find that the location of a source can be recovered when there are at least 3 receptors and the source is positioned no further than 10 cell radii away, but this condition is not necessary in a narrow strip. The present approach provides a computational basis for the first step of direction sensing of a gradient at a single cell level. During axonal growth and guidance, the growth cone (the tip of a neuron) uses the concentration of morphogens3 to decide whether or not to continue moving, stop, turn right or left. Bacteria and spermatozoa in particular are able to orient themselves in a chemotaxis gradient10. However, how a cell senses an external gradient concentration depends on its ability to estimate the fluxes of cues. These fluxes have been computed assuming that cues are fully or partially absorbed uniformly at the surface of a detecting ball11. These computations are used to estimate the sensitivity of the local concentration. This, however, is insufficient to establish the orientation of the source of the gradient. Our aim is to clarify how a cell, which is only a few microns in size, can detect the direction of a source. In particular, our main focus is on the directional sensing of cues in neuronal growth cones, although the presented techniques should also be applicable to a wider range of cells.Sensing a molecular gradient made of cue concentration is the first step to transform cell positional information into a genetic specialization and a differentiation signal5. We are exploring here the first possibility, that corresponds to a diffusion-limited regime where any cue hitting a receptor will immediately lead to receptor activation. Examples are chemoattractants that bind with high affinity to the receptor guanylyl cyclase in sperm in order to monitor the rate of binding events rather than the receptor occupancy. Other examples are odorants and endocrine disrupting chemicals that activate channels with fast activation. In neurons TRPV1 channel integrates various stimuli. In addition, we do not consider here a possible time integration of the external cues signal, as described for sperms, which is based on the rate of changes in calcium concentration directly modulated by an external gradient12. We are mainly concerned with growth cone navigation in the developing brain, for which there is no obvious time integration, because the motion of a growth cone is much slower than the binding time of cues13 .The first step of differentiating left from right certainly has to involve the spatial difference in the binding flux of external cues. A receptor can use two mode of decoding: it can respond to the rate or to the binding time17, but this theory cannot be applied directly to open and unbounded domains, because the mean passage time for particles to hit any small target is infinite. To avoid this difficulty, we neglect the receptor binding time of diffusing molecules and consider that cell sensing is possible via direct measurement of the diffusion flux. However, we do not account for any further cellular transduction cascade that translates receptor local activation into an internal signal. A receptor-local memory mechanism is necessary in order to prevent loss of directional information on the gradient due to homogenization of the downstream transduced signal (concentration of a second messenger or surface molecules) inside the cell. Therefore, asymmetric fluxes at the receptor level should lead to an asymmetrical transduction inside the cell. Hence, we do not replace receptors by a homogenized boundary condition that would render measurements of spatial flux differences impossible.Our model for cell direction detection uses a reflecting disk covered with small receptors. The receptors are perfect absorbers for Brownian particles (cues), emanating from a point source. Computing the fluxes of Brownian particles to small targets is part of the Narrow Escape TheoryN = 2 and 3) located on the surface of a detecting disk. We evaluate the effect of different receptor arrangements and also study the influence of an infinitely long, confining narrow strip. Secondly, we estimate the maximum distance from a source at which a given concentration can be detected with a pre-defined accuracy. Finally, we study how the location of a source can be recovered from the difference of fluxes. We demonstrate that the source position of a gradient can be reconstructed or triangulated with three receptors, while sensing of the concentration level can be achieved with two only.In this letter, we first compute the fluxes of diffusing molecules to small targets  for a Brownian particle generated at location x0 that can be absorbed on the boundary of a detecting two-dimensional disk or radius R, Ω = D(R), by windows The probability density function P0(x) is computed by solving the mixed boundary value problem for the Laplace equation17The reflecting boundary condition at P0(x) is non-normalizable in two dimensions, we are only interested in the splitting probability between windows, i.e. the normalized steady-state flux at window k,Although the density Due to the recurrent property of the Brownian motion in two dimensions, the probability to hit a window before going to infinity is one, thusN = 2 windows can be computed using the Green’s function G of the domain using matched asymptotic expansion19 and involves a Green’s function Matrix in general. However, using identity Eq. (D(R) of radius R, for The fluxes for tity Eq. , it is sP2 changes with the distance of the source x0 and the relative position of the windows, we compare Brownian simulations with the analytical expression (6) for a disk  according to the exit point distribution of a process from an internal disk20. Interestingly, already at a distance of L = 10R, the absolute difference between the fluxes ΔP = |P1 − P2| is within 5%, making it impossible to determine source direction or concentration differences in a noisy environment (as long as the amplitude is below the threshold of 5%). This result is independent of the window positions and ΔP → 0 as L increases, see Fig. To evaluate how the probability isk Fig. . For theP depending on the strip width a, even for large source distances L ≥ 100R  + P2 = 1). The domain of sensitivity for a threshold Th is the interior of the two-dimensional regionTo further investigate how the window positions could influence the recovery of the source location, we estimated the maximum distance between the source and the disk containing two absorbing windows located at position DS for two absorbing windows symmetrically positioned  is possible outside DS. Interestingly, with a 1% precision, the domain is around 20× the size of the detecting disk. Beyond this distance, no detection is possible. The detection sensitivity for a given source location x0 and optimal window placement is defined byWe plotted the boundary of the region ned Fig.  and whenπ/2 Fig.  for Th =x2 = −x1, |x1| = |x2| = R givesR is the radius of the disk. Hence, the detection sensitivity decreases as the reciprocal of the distance to the source L = |x0|. With three windows, detection is possible if at least one of the difference between the splitting probability is higher than the threshold Th. We thus define the new sensitivity ratio usingP1, P2 and P3 defined above depending on x1, x2, x3 and x0. This definition accounts for the symmetric positioning of absorbing windows located on the boundary of the disk. The region where the source is detected surrounds the detecting disk Ω. Numerical simulations show the region DS defined in Eq.  are known. With two windows located on a detecting disk and using the expression of the Green’s function (7), we obtain a one dimensional curve , the direction of the source can be recovered. This mechanism requires a comparison between the fluxes of at least three boundary receptors. In addition, the Green’s function method allows us to estimate the boundary of the region of sensitivity characterized by a difference of fluxes between receptors being larger than a predefined sensitivity threshold. The sensitivity decays with the reciprocal of the distance to the source according to Eq. (16, as long as one detecting window is facing away from the source.The ability of a cell to sense a gradient concentration is mediated by the binding of Brownian molecules to receptorsg to Eq. . Further25. We propose that narrow extracellular tubes formed by neurons and glial cells probably allow the genesis of shallow gradients detected by receptors located on the growth cone, although it is not known precisely how these receptors are organized. The dynamics of the growth cone including moving protrusions is certainly an additional mechanism worthy of further investigation in context of direction sensing, but should dominate for short-range distances only. Finally, we suggest here that growth-cone gradient assays in restricted environments could reveal how narrow passages, generated between neurons modulate the search for a final destination. These passages could explain the amplification of the gradient sensing much further than the 10 cell radii, as predicted by the diffusion hypothesis that we have explored here.The present results have several applications, such as growth-cone navigation inside the developing brain. Neurons have to travel millimeters to centimeters to find the correct cortical regions and to form synaptic connections17. The model we used here was developed in the fast binding limit without rebinding4. It remains a challenge to apply the present theory to understand how sperm5 or neurite growth25 localize the source of their cues. We limited the present approach to the initial level of source detection, however the asymmetry of receptor detection needs to persist in the downstream transduction, which certainly is another key question to investigate. Future works should also include the time scales of binding and unbinding events to receptors and explore the consequence of dimension 3, that require generalizing the Narrow escape approach17.Although we focussed on two and three windows only, the results would be similar for two or three receptor clustersSupplementary Information


This article presents an investigation of the dynamical contact between two atomically flat surfaces separated by an ultrathin lubricant film. Using a thermodynamic approach we describe the second-order phase transition between two structural states of the lubricant which leads to the stick–slip mode of boundary friction. An analytical description and numerical simulation with radial distributions of the order parameter, stress and strain were performed to investigate the spatial inhomogeneity. It is shown that in the case when the driving device is connected to the upper part of the friction block through an elastic spring, the frequency of the melting/solidification phase transitions increases with time. The boundary friction mode occurs in tribological systems when the thickness of the lubricant layer separating two contacting surfaces is significantly smaller than the typical size of the surface roughness. At such a system configuration, the lateral motion of the friction surface is followed by a contact interaction between the asperities. A specific case of boundary friction is friction between two atomically flat surfaces separated by a layer of lubricant with thickness of a few atomic diameters –2, or ev2The boundary friction mode can be described within the framework of several theoretical models –12 whereIn our previous work  we studiWe consider a simplified case where the properties of the lubricant are independent of pressure and its behavior can be described within a thermodynamic approach . AssuminT is the temperature of the lubricant; Tc is the critical temperature; εel is the shear component of the elastic stress; α, a and b are positive constants. The order parameter φ is a periodic component of the microscopic density of the material: in a solid-like state of the lubricant φ > 0, while in a liquid-like state φ = 0.where f / ∂εel [Using f / ∂εel ,22 shear0 can be estimated from the condition ∂f / ∂φ = 0 in the following form:where we have introduced the shear modulus of the lubricant μ, that takes nonzero values only in solid-like states. The stationary values of the order parameter φ0 decreases with the growth of both temperature T and elastic strain εel. When the strain exceeds a critical valueAccording to 0 and shear modulus μ0  represents random processes in the heat fluctuation of a small amplitude which cannot significantly affect the system behavior. Nevertheless, it is necessary to take them into account due to the peculiarities of the further numerical calculations [where γ is the kinetic parameter that defines the inertial properties of the system, ξ and order parameter φ(r) we can obtain the distribution of the stress in the lubricant according to Knowing the distribution of strain ε( in r) to an equivalent one-dimensional (coordinate x) with a possible reverse transition.The distribution of the displacements r) as:Within the MDR technique, a one-dimensional distribution of the force density can be defined from the known distribution τ(q(x), the one-dimensional distribution of the displacements  can be calculated as:From the obtained  can be obtained from the equation:and the distribution The elastic component of the friction force in the system can be defined in two ways : and . After that, the procedure described in r) a related value of the order parameter is calculated from The aim of the present work is to take into account the elastic properties of the contacting materials in simulation of the kinetics of the boundary friction in the system shown in X can be estimated from the numerical solution of Fx calculated from X values of the distribution  are also incremented by the same magnitude. Thus, at the beginning of motion, . However,  is set to zero when the lubricant melts  < 0.01 [The displacement of upper stamp ) < 0.01 ).x and r were divided into N segments. All calculated distributions depending on radius r (or coordinate x), were computed at the points ri = ia0 / N (xi = ia0 / N), where . In our simulation we set the time step to be Δt = 10−8 s and number of segments N = 2000.In numerical calculations integrals of V0 at constant system parameters.An analogous dependence was described in , where tX = V0t − X and the elastic force Fu = K(V0t − X). The shear velocity of the upper stamp  also increases according to el exceeds the critical value, is reduced.The dependence shown in Fx(t), <φ>(t) and <εel>(t) show the transition mode where monotonic growth of the friction force Fx and mean value of elastic strain <εel> as well as <φ> are significantly slower. The corresponding time interval from the beginning of motion to the first melting is the largest due to the presence of the spring between the stamp and driving device [V from the very beginning of motion.As it is follows from g device . Such a g device  as the st) obtained for different values of the radial coordinate r is shown in Additional time dependence of the order parameter φa / b ≤ 0 (not shown in the figure) and is followed by a sliding mode with zero friction force Fx = 0 (only the elastic component of the friction force is considered within the proposed model).The temperature of the lubricant can vary during the natural heat exchange with the environment (friction surfaces are considered as a thermostat) . As it fV exceeds some critical value. After the lubricant is melted, the elastic friction force becomes equal to zero, i.e. Fx = 0.Let us note that all presented dependencies relate to the particular situation where elastic stress increases according to V. Moreover, in the case of quasi-static contact, the viscous friction force is not considered, while in the standard dynamic model, it plays significant role [V causes the increase in the frequency of phase transitions, and a critical value of V related to the complete melting of the lubricant is not observed. However, it is worth mentioning that the developed approach allows us to investigate the physical processes directly in the contact area, which is not possible within standard models.In the proposed model, we consider a quasi-static case where the elastic strain is defined by the displacement of the friction surfaces see  instead ant role . Note hoant role . Thus, iFx on the coordinate of the upper friction block X as shown in The dependence of the friction force Fx(X) is periodical . The presented dependencies have a regular form in contrast to the data in V0 , exceed a critical value, εel,c  we have studied the stick–slip friction mode that occurs in the tribological system under shear deformation. The MDR approach allowed us to describe the situation in which elastic stress, strain and order parameter are spatially distributed within contact area. The established stick–slip mode is characterized by continuous phase transitions between solid-like and liquid-like states of the lubricant, which were described as the second-order phase transitions between kinetic states of friction. Within the performed numerical simulation it is shown that an increase of the lubricant temperature leads to smaller amplitudes of the friction force, elastic stress and order parameter, while the frequency of phase transitions increases due to the presence of the spring. It is worth mentioning that the spatial distribution of elastic stress considered in the presented study will always occur in tribological systems with analogous geometrical shape of the contact area; thus, the developed approach can be an additional tool in various experimental investigations for contact problems of this type.


Uca terpsichores that courts under elevated predation risk and that mates and breeds underground in the safety of males' burrows. Sexually receptive females leave their own burrows and are thereby exposed to avian predators as they sequentially approach several courting males before they choose one. Males court by waving their single greatly enlarge claw and sometimes by building a sand hood next to their burrow entrance. Hoods are attractive because they elicit a risk‐reducing orientation behavior in females, and it has been suggested that claw waving may also serve primarily to orient the female to the male. If the wave communicates male quality, then females should discriminate mates on the basis of variation in elements of the wave, as has been shown for other fiddler crabs. Alternatively, variation in elements of the claw waving display may have little effect on the display's utility as a beacon of the location of the male and his burrow. We filmed courting males and females under natural conditions as females responded to claw waving and chose mates. Analysis of the fine‐scale courtship elements between the males that females rejected and those they chose revealed no differences. When predation risk during courtship is high, males' courtship displays may serve primarily to guide females to safe mating and breeding sites and not as indicators of male quality apart from their roles as beacons.The interplay between a receiver's sensory system and a sender's courtship signals is fundamental to the operation of sexual selection. Male courtship signals that match a female receiver's preexisting perceptual biases can be favored yet the message they communicate is not always clear. Do they simply beacon the male's location or also indicate his quality? We explored this question in a species of fiddler crab  U. terpsichores lives in mixed sex, high‐density populations on sand flats and bars in Central American bays and estuaries and are extensively predated by great‐tailed grackles, Quiscalus mexicanus , and then we filmed her using a JVC GZ‐EX355BAA video camera as she approached the next male. We used a close frame that included the female and the small set of males in her vicinity . The camera was supported on a tripod 50 cm high, so the camera‐to‐male angle did not differ by more than 2° between videos. After filming, we placed a vertical and horizontal scale in the frame and filmed it, allowing us to adjust for the angle between the camera and crab. This facilitated measurements of the crab size and the wave features. The definition and clarity were sufficient to allow for very accurate measurements from the videos. We excluded all videos in which the crabs were startled by predators, the males fought each other, the female failed to make a choice, or any of the crabs showed a scare response (run to and enter their burrows or freeze). We made complete recordings of 28 unique female visits (no crab appeared in more than one of the videos).2.3We digitalized the videos using a frame‐by‐frame analysis at 30 frames per second using the software digilite created in MATLAB  by Jan Hemmi and Robert Parker of The Australian National University. The software enables pinpointing of “landmarks” on the males with enlarged claw and body.We used the scale in each video sequence to measure (1) the claw length of the visited male and (2) the claw length of the nearest male to the visited male . Each mate choice sequence was split into two periods: (1) the period during which the female stopped moving and watched the courting males  and (2) the period during which the female moved toward the selected male . We considered that the female made her choice once she reached the selected male's burrow, and he ceased waving or drumming . We counted the number of waves and/or drums given by the selected and nonselected male during the two mate choice periods. For every wave and drum of both males during both periods, we measured the distance the claw tip moved in the upswing and the downswing of the wave/drum . We also measured the duration of each of these movements (“up duration” and “down duration”). For each wave, we measured the maximum height that the claw tip reached . We noted whether the male had a sand hood at his burrow entrance. Finally, we examined wave timing between the selected and nonselected males by first identifying which of their waves overlapped and then noting which of the males produced the leading wave (the first wave to start in an overlapping wave pair).2.4We compared the selected and nonselected males using a mixed model but found that the residuals were not normally distributed. Data transformations did not normalize the residuals, so we used nonparametric tests throughout. We used Wilcoxon tests to compare the (1) number of waves or (2) drums given by the selected and nonselected males and (3) the claw lengths of the selected and nonselected males. We tested whether selected or nonselected males differed in their likelihood of having a sand hood at their burrow entrance using a Fisher's exact test. We compared the number of leading waves produced by selected and nonselected males running a Wilcoxon test.To accommodate the high number of “wave/drum structure” variables measured, we ran a principal component analysis (separately on the waves and drums). We used the mean value for each wave/drum variable  for each male. We then used the PC scores to compare the selected and nonselected males  using Wilcoxon tests.r = Z/√n).Statistics were conducted in SPSS 20 and we set α = .05. We calculated the effect size of the Wilcoxon tests (3x¯(SD) = 1.49 (0.15) cm, n = 28; nonselected male claw length x¯(SD) = 1.52 (0.20) cm, n = 28; Wilcoxon test Z = −0.48, p = .63). They also did not differ in the number of drums they produced, either before or during the process of choice  also did not differ between the selected and nonselected males. The weighting of each measured wave/drum variable on the principle component score is given in Table p = .25).Selected and nonselected males did not differ in whether or not they had sand hoods next to their burrows . When considering all the overlapping waves, the nonselected males were more likely to produce the leading wave .Less than half of the males produced waves that overlapped with those of their neighbors (11/26). There was a total of 42 waves that overlapped between the selected and nonselected males. In those cases where waves overlapped, 10/11 of the nonselected males produced the leading wave . For the study species here, however, the great‐tailed grackle, Quiscalus mexicanus, is a common and persistent avian predator . This behavior is puzzling as we found no preferences on male size or signals. We know that the presence of a hood makes a male more attractive and that the hood itself partially explains this (Christy et al., 4.1We found two differences between the selected and nonselected males. The selected and nonselected males produced the same number of waves before the female started moving toward them, but the selected male produced fewer waves than the nonselected male once the female was making her approach. This is due to a change in the behavior of the selected male as the female nears him: He runs back to his burrow entrance, leading the female and often darting back‐and‐forth to guide the female. This prevents him from waving at the same rate as the nonselected male. In addition, at this stage, females had already made a choice of which male to approach and the candidate displays would be no longer under evaluation.U. terpsichores do not wave synchronously. Less than half of the males produced waves that overlapped with those of their neighbor. Of the overlapping waves, however, the majority were produced by the nonselected males. This may be a statistical anomaly, but it certainly requires further investigation.The other significant difference we found was in wave leadership: Nonselected males were more likely to produce leading waves. In many of the synchronous waving fiddler crab species, synchrony occurs because adjacent males compete with each other to produce leading waves (Backwell et al., 5The variety of wave patterns found among fiddler crab species is still puzzling. Could sexual selection be a strong influence in the evolution of wave display diversity? This study revealed that under high predation risks, female preference for sexual signals are likely due to their role as beacons rather than indicators of male quality. This raises doubt about the power of sexual selection to shape such diversity. However, this study points to a possible origin of the sexual display in stimuli that play to sensory biases selected by predation and studies on other species exposed to a range of predation risk during courtship may reveal how selection shapes the evolution of species‐specific wave displays.None declared.


Purpose Radiotherapy treatment planning of extended volume typically necessitates the utilization of multiple field isocenters and abutting dosimetrically matched fields in order to enable coverage beyond the field size limits. A common example includes total lymphoid irradiation (TLI) treatments, which are conventionally planned using dosimetric matching of the mantle, para-aortic/spleen, and pelvic fields. Due to the large irradiated volume and system limitations, such as field size and couch extension, a combination of couch shifts and sliding of patients are necessary to be correctly executed for accurate delivery of the plan. However, shifting of patients presents a substantial safety issue and has been shown to be prone to errors ranging from minor deviations to geometrical misses warranting a medical event. To address this complex setup and mitigate the safety issues relating to delivery, a practical technique for couch indexing of TLI treatments has been developed and evaluated through a retrospective analysis of couch position.MethodsTM  was utilized. Two groups of patients were treated: 20 patients with table indexing and 10 patients without. The standard deviations (SDs) of the couch positions in longitudinal, lateral, and vertical directions through the entire treatment cycle for each patient were calculated and differences in both groups were analyzed with Student's t-test.The indexing technique is based on the modification of the commonly available slide board to enable indexing of the patient position. Modifications include notching to enable coupling with indexing bars, and the addition of a headrest used to fixate the head of the patient relative to the slide board. For the clinical setup, a Varian Exact CouchResultsThe longitudinal direction showed the largest improvement. In the non-indexed group, the positioning SD ranged from 2.0 to 7.9 cm. With the indexing device, the positioning SD was reduced to a range of 0.4 to 1.3 cm (p < 0.05 with 95% confidence level). The lateral positioning was slightly improved (p < 0.05 with 95% confidence level), while no improvement was observed in the vertical direction.ConclusionsThe conventional matched field TLI treatment is error-prone to geometrical setup error. The feasibility of full indexing TLI treatments was validated and shown to result in a significant reduction of positioning and shifting errors. The ability to obtain a reproducible patient setup and accurate positioning within the treatment coordinate system is of critical importance for the safe and accurate delivery of radiotherapy. This aspect is emphasized in dosimetrically matched fields requiring exact shifts of abutting fields with different isocenters -3. With The non-indexed delivery of treatments incorporating multiple isocenters and dosimetrically matched fields is associated with a number procedural difficulties and safety issues. First, without indexing, it is not discernable how the anatomical sites were set up and treated based on non-indexed couch positions recorded in the record and verify system. Second, couch shifts solely based on values calculated by therapists prior to beam-on allow for the introduction of human error and are a common cause geometrical misses. Third, for tall patients (if the shift from the first isocenter to the third isocenter is more than 51 cm), the couch can reach its longitudinal shift limit, leaving it to the therapy team to slide the patient superiorly to align the pelvis field to the correct isocenter location; since the patient anatomy may be stretched in this scenario, even if the shift is correct, the patient’s geometry is no longer the same so the dosimetric match is no longer achievable. Fourth, without indexing the treatment, the physicists are not able to assign a couch position tolerance limit to detect deviations in the patient setup and to prevent the possibility of mistreatments [An illustration of the TLI field arrangement is presented in Figure TM . It is made of polyethylene construction with six slotted hand grips. Two holes were drilled in the superior area for the patient’s headrest. The position of the headrest was selected so the indexing bar is not interfering with the first (mantle) field. The distance and the size of the two holes were matched to the two pins of the Exact Lok-Bar , which is used to index the slide board to the couch top. For treatment, the Exact Lok-Bar was put to the predetermined notch (H3) to avoid the first (mantle) field going through the metal bar. The Timo Headrest  was attached to the slide board with Velcro so the therapist can use a different size of Timo Headrest based on the patient anatomy. The position of the Timo Headrest was outlined beforehand  field, if the patient’s height requires an unattainable longitudinal shift (beyond the table travel limit of 160 cm), therapists can unlock the Exact Lok-Bar and shift the slide board to the superior notch (H4) Figure . Since tThe dosimetric effect of the indexed device is evaluated based on the recommendations of the American Association of Physicists in Medicine Task Group 176 . Attenuaelectrometer reading taken with the slide board and y is the electrometer reading taken without the slide board. where x is the The skin dose was evaluated with the Optically Stimulated Luminescence Detectors (OSLD)  for 15 MV (n = 3). The experimental setup was 100 cm source skin distance (SSD) and 10 x 10 cm field size with OSLDs placed on the couch or on the slide board with 5 cm backscatter solid water to mimic the treatment setup. A computed tomography (CT) scan of solid water with the slide board was acquired and imported into treatment planning system (TPS) with the analytical anisotropic algorithm to estimate the attenuation and the skin dose with the plan parameters corresponding to the measurement conditions. Two slide boards were constructed: one for simulation and the other for treatment. The patient was simulated at CT with the modified slide board and the Exact bar was placed at H3. The patient’s head was positioned on the Timo Headrest. The midline of the patient was aligned with the sagittal laser to ensure the patient was straight. Prior to the treatment, the therapist took verification images at every isocenter  to ensure the accuracy of the patient setup, with the couch positions acquired and recorded in the system. Tattoos were placed on the patient: one set of tattoos were placed at the second isocenter (spleen), and two midline tattoos were placed at the first and the third isocenters in order to straighten the patient, as well as to serve as reference positions for daily treatments. For tall patients, when the required shift for the pelvis isocenter reached the couch extension limit, the board was slid superiorly from H3 to H4 (a fixed distance of 14 cm) and the remaining couch shift was calculated by Eq. 1. A summary of steps for the procedure is shown in Figure Twenty patients were treated with this immobilization device and 10 patients were treated with the conventional setup. For tall patients, defined as patients for which the shift from the first isocenter to the third isocenter is greater than the couch extension limit, patient sliding is necessitated; within the indexed group, two patients were tall and needed to slide from H3 to H4 to treat the pelvic field Figure , and wit-22, 10-9, and 0.16, respectively). With the conventional setup (non-indexed), the SD of 10 fractions ranged from 2.0 to 7.9 cm and 0.6 to 3.4 cm in longitudinal and lateral directions, respectively  for tall and regular height patients are shown in Figure The observed SD range of the longitudinal table position (2 - 7.9 cm) is representative of the variation of the daily non-indexed couch position through the entire treatment, not the target variation. The large variation of the couch position for patients in the non-indexed group was because (1) therapists laid the patient on a different location on the couch every day because there was no indexed device to guide them otherwise, and (2) for patients requiring an additional sliding in order to treat the pelvic field, larger variations were observed because the shift would be therapist-dependent, differing in the amount from day to day. With properly indexed devices, therapists can predictably set the patient up, such that a tolerance limit can be developed, thus minimizing shifting errors. Couch indexing minimizes errors in radiotherapy, especially for dosimetrically matched treatment fields, which can result in overdose or underdose around the field junction region due to incorrect shift or improper setup. If the shift from the first isocenter to the third isocenter is more than 51 cm, it is possible to reach the longitudinal shift limit, depending on the field setup and the patient’s anatomy. The longitudinal couch position for H3 is 98 cm and the limitation for longitudinal is 160 cm. The first treatment field cannot go through the metal bar so the superior border of the mantle field has to be below H3. If a conservative assumption is made about the length of the mantle field (22 cm), this would result in the mantle isocenter being located relative to the couch at ~109 cm (98 cm + 11 cm). Due to the couch extension limitation of 160 cm, the distance between mantle isocenter and the pelvis isocenter needs to be less than 51 cm (Figure Since the slide board is available in most clinics, with the proposed solution, the slide board not only can be used to transfer patients but also can be used to index TLI treatment without extra cost and storage space. Since the holes are very small compared to the entire board, the rigidity of the board is not expected to be changed. Indexed dosimetrically matched treatments can thus be made safer for the patient due to the predictability of the couch position before the treatment and availability of tolerance table. Moreover, physicists can identify mistreatments and perform dose reconstruction during the treatment cycle via a weekly chart check using the record and verify system -11. The Extended volume treatments require the dosimetric matching of multiple fields with different isocenters, which are prone to shifting errors and positioning errors. An indexed device has been developed and demonstrated to significantly reduce the variation of the couch positions in the longitudinal and lateral directions as compared to the non-indexed treatment. This method is easily adaptable and affordable as it comprises the modification of readily available equipment in most clinics. With this approach, physicists can easily evaluate the setup variation based on the couch position recorded in the system via weekly chart QA during the course. Therapists can calculate the couch position as the second verification before beam on. Furthermore, the safety and the reproducibility of the TLI treatment can be significantly improved with a tight couch position tolerance limit, which also works for tall patients. This study shows the proof of the concept that, with the slide board indexing, the indexed TLI treatment is feasible without large capital expenses.


Superfluidity and superconductivity have been widely studied since the last century in many different contexts ranging from nuclear matter to atomic quantum gases. The rigidity of these systems with respect to external perturbations results in frictionless motion for superfluids and resistance-free electric current flow in superconductors. This peculiar behaviour is lost when external perturbations overcome a critical threshold, i.e. above a critical magnetic field or a critical current for superconductors. In superfluids, such as liquid helium or ultracold gases, the corresponding quantities are a critical rotation rate and a critical velocity respectively. Enhancing the critical values is of great fundamental and practical value. Here we demonstrate that superfluidity can be completely restored for specific, arbitrarily large flow velocities above the critical velocity through quantum interference-induced resonances providing a nonlinear counterpart of the Ramsauer-Townsend effect occurring in ordinary quantum mechanics. We illustrate the robustness of this phenomenon through a thorough analysis in one dimension and prove its generality by showing the persistence of the effect in non-trivial 2d systems. This has far reaching consequences for the fundamental understanding of superfluidity and superconductivity and opens up new application possibilities in quantum metrology, e.g. in rotation sensing. When the flow velocity of a superfluid exceeds a critical velocity vc the creation of excitations becomes energetically favourable. This destroys the frictionless motion, as shown in classic experiments with superfluid helium4 and in more recent experiments with ultracold bosons5 and fermions6.The breakdown of superfluidityThe occurrence of a critical velocity is conventionally understood in terms of a maximum velocity below which there is no or at most a bounded production of excitations. While almost no excitations are present for subcritical velocities, a fast onset of growing excitations occurs for supercritical velocities. The production rate of excitations gradually decreases for further increased velocity as the kinetic energy of the fluid becomes so high that it dominates all other energy scales including those related to defects in the flow channel or in the trapping potential.7. Here we demonstrate this in a case study of the flow of one-dimensional (1d) Bose gases in the presence of a rectangular defect. To illustrate the generality of the effect in terms of dimensionality we then consider 2d defect potentials, showing that the wavepacket dynamics displays the same qualitative results persisting even in the presence of a non-separable potential.This conventional scenario is qualitatively illustrated in Fig. vc. In the case of a superfluid moving through a confining channel, for example, the microscopic interactions with the walls provide the source of possible breakdown of superfluidity. In the present paper we treat the case of a superfluid moving with velocity v in presence of a single defect at a fixed position that is gradually ramped on.In general, the rate of excitation growth depends on the microscopic details of the superfluid and on how it is coupled to the environment. The details of this coupling determine the dissipation mechanism causing the creation of excitations and, ultimately, vc and give a qualitative explanation of the breakdown of superfluidity is provided by the Landau criterion8. The Landau criterion is a cornerstone of our understanding of the dynamical behaviour of superfluids, stating that superfluid flow is sustained against external perturbations or defects up to a critical value of the velocity8. Its elegance, power and usefulness rely both on simplicity and generality. There is no need to know the specific nature of the perturbation or the characteristics of the defects, no need to know all the microscopic details of the superfluid, and no need to compute the excitation spectrum of the moving system; only the knowledge of the low-energy excitation spectrum ε(p) of the system at rest is required. In Landau’s treatment the microscopic description of the dissipation sources is not considered, since the former relies on the determination of the conditions under which the creation of elementary excitations becomes energetically favourable, in contrast to microscopic computations in which the interactions of the superfluid with its environment are explicitly taken into account. By applying a Galilean transformation to the co-moving frame it can be shown that for v < vL (where 8) the production of elementary excitations is energetically unfavourable. From the Landau criterion it follows that for Bose gases with a weak, short-range interaction, the Landau critical velocity is equal to the sound velocity c, so that here “supercritical” means “supersonic”. The detailed analysis of different superfluid systems, including helium and ultracold gases, shows that the Landau criterion often quantitatively overestimates the value of vc, especially in the 2d and 3d cases . This, together with the occurrence of a non-vanishing superfluid fraction also above the Landau critical velocity10 implies that the Landau criterion is neither necessary nor sufficient. However, despite the fact that in general vL ≠ vc, the identification of a critical velocity above which the production of excitations destroys the superfluid motion is a criterion of paramount clarity and relevance.A simple and ingenious way to estimate v > vc superfluidity is destroyed in the sense that a non-vanishing normal fluid component develops and even at zero temperature the superfluid fraction ρS is smaller than the total density ρ, e.g. resulting, for the case of superconductivity, in a non-vanishing resistance. Superfluidity is completely destroyed once ρS = 0 is reached. The conventional picture implies that the latter happens for any velocity larger than some finite velocity, which we denote as vc  or periodic potentialsρs = ρ at zero temperature) for a series of specific, but arbitrarily large incident velocities. Therefore, the notion of the existence of a finite critical velocity above which no superfluid flow exists can no longer be maintained universally.The point we address in this paper at a non-perturbative level is the surprising possibility of stable superfluid propagation with bounded emission of excitations  is the condensate wavefunction, g is the one-dimensional nonlinear coefficient16, and V is an applied external potential.To illustrate the existence of perfect supercritical flow and the associated phenomena arising from it, we choose defects of rectangular shape in the 1d flow of a superfluid, whose behaviour is governed by the Gross-Pitaevskii equationv in an initially flat potential, in which a rectangular defect is then introduced to study the dynamical response. The potential is therefore chosen to be  = ψ0eikx is a plane wave with momentum k and velocity v = ħk/m corresponding to atom density n ≡ |ψ0|2. Since for t = 0 the defect is absent, ψ is a solution with momentum k of the time-independent Gross-Pitaevskii equation. The purpose of ramping on the defect is to adiabatically lead the system towards possible supercritical superfluid solutions for specific values of the momentum k.We consider a homogeneous system with stationary flow at velocity see Fig. :2\docume18, while our simulations consider a time span of less than 100 ms for typical experimental parameters . We therefore expect that the time scale at which superfluidity above the critical velocity is destroyed by dissipation is long compared to the time scales we numerically investigated.Our treatment is based on the use of Gross-Pitaevskii equation and we do not include dissipation explicitly. In current experiments with ultracold atoms superfluidity is preserved for long times of up to a few seconds with velocities of ~μm/ms and rings with radius ≳20 μmg ≠ 0). The reason is that the usual definitions used for linear matter waves20 do not apply to this case. In fact the superposition principle of an incoming and a reflected wave is no longer valid, and furthermore, bound states in the defect can be present due to the interaction term21. For a weakly interacting Bose gas one can quantify the transmitted part of an incident wavepacket by the study of the dynamics in presence of defects29. A different approach, alternative to defining transmission and reflection coefficients, is to characterise the breakdown of superfluidity by studying the drag exerted by a matter wave on an obstacle30 or the stationary wave patterns of a δ-like potential moving at supersonic velocity31. A special case is represented by rectangular defects in 1d. Even though the difficulty of defining the transmission coefficient for a finite g ≠ 0 persists, one can write solutions of the time-independent Gross-Pitaevskii equation in terms of Jacobian functions33. Using such wavefunctions the current-phase relation has been determined for subsonic motion35. Neglecting the mean-field interaction outside the potential well gives raise to a major formal simplification, since it makes possible to analytically calculate the transport properties of the system in terms of incoming and outgoing waves and resonances and bound states are obtained in closed form36.From a theoretical perspective, a challenging point is to define the transmission and reflection coefficients in presence of a nonlinearity  and only evaluate our disturbance estimator for times before any features emerging in the dynamics have reached the system boundaries. Up to that point no difference is found with respect to the homogeneous system for identical finite size systems with the same defect and a different choice of boundary conditions. We ensure that our results are never plotted for times beyond that limit. In fact our L is so large, up to L = 700 times the size of the defect, that we find a very long plateau, for example in the value of For the numerical solution we use the projected fourth-order Runge-Kutta method in the interaction picturesee Fig. , with sti) A supercritical solution of the dynamical equations exists for specific values of the superfluid’s momentum and system parameters (i.e. interaction strength and geometric properties of the defect) and the flow of such a solution is stable under small perturbations. (ii) The perturbations of the propagating flow created by the defect are bounded in time  and no new excitations are produced when the barrier is completely ramped on. (iii) The superfluid flow is physically inducible and accessible.Given the explicit arguments of the Landau criterion it is important to clarify what is meant by completely restored superfluid flow above the critical velocity: 7.It is well known that in the non-interacting regime the transmission coefficient across a square potential, as found by solving the time-independent g = 0) and in the nonlinear (g ≠ 0) case. In the linear case the behaviour of the rate of change of R, as shown in Fig. R is exactly zero there as obtained from a computation with the time-independent Schrödinger equation (and the barrier permanently on)7, while After the barrier has been ramped on, Therefore we are led to take vc ≈ vL = c). In 1d, the Landau criterion allows obtaining quantitatively the critical velocity and, as expected, excitations are produced for v > vc. Additionally, as time progresses v > vc, for which the production of excitations is inhibited. As shown in the inset of Fig. tbarrier. Away from the minima, phonons are emitted . The analysis of the numerical results shows that v < vc in agreement with the Landau criterion.As shown in Fig. t > tbarrier, where g = 0 and for a finite value of g. In both cases the disturbance is evaluated for on- and off-resonance initial momentum. The asymptotic slopes α, and it is seen that in all the cases–including the instantaneous ramp-on with α = 0–the behaviour of α is increased. One can have a qualitative understanding of this by observing that–at the resonances–the disturbance α) approaches a value on the order of unity. A barrier ramped too fast while being crossed by the particles produces a larger disturbance α, comparable to the crossing time through the barrier, explaining the non-monotonous behavior displayed in Fig. α ~ 1 in the units of the figure.The creation of excitations can be well characterised by the slope of the disturbancefor α both for vanishing and finite g, the resonances found in the linear case g = 0 must reproduce the momenta of the Ramsauer-Townsend effect, obtained by a time-independent computation in quantum mechanics textbooks20. This result is confirmed in Fig. g = 0 the resonant momenta obtained by means of this dynamical method coincide with the results obtained by solving the time-independent linear Schrödinger equation. Since it is useful in the following, we note that the incident momenta kres that result in Ramsauer-Townsend resonances, of unity transmission in the linear case (g = 0), are given byn = 1, 2, ….Since we find that gn/V0, we obtain the behaviour of the resonant velocities vres as a function of g. The results are plotted in the left part of Fig. V0) with gn/V0 varying between −0.5 and 7.5. In this figure the dimensionless parameters kresd and gn/V0 are used, meaning that distances are measured in units of d and energies in units of V0. The presented results do not depend on the particular choice of d or V0 as long as those dimensionless parameters are used. Furthermore, by considering the slope k for different values of α, we verified that within the achieved numerical precision, the value of the resonant momenta does not depend on α.In the central right inset of Fig. g = 0 the shift of the resonant momenta is positive for repulsive (g > 0) interactions, while it is negative for attractive (g < 0) interactions. Similar results hold for a potential well (V0 < 0), but with a negative shift for repulsive interactions and a positive one when the interactions are attractive. Our results are plotted in Fig. g, predicting values of kbarrier (defined below) corresponding to a total transmission across the barrier38. These resonant momenta are given by kbarrierd = nπ + δ, where v = ħk/m and k incident momentum). When there is no interaction (g = 0), then δ has to be zero and the linear resonant momenta (4) are recovered. In accordance with ref. a = 2mgn/v2. Note that our result  could be attributed to the fact that our numerical procedure is based on the use of the full time-dependent Gross-Pitaevskii while the analytical computation is based on a perturbative treatment of the time-independent problem. However, as shown in Fig. α, and also bringing this time to zero, the slope g = 0) for which the slope has a clear minimum at the momenta given by the exact time-independent quantum mechanics computation20. Given the fact that the same happens at finite g  ≡ Vd1 + Vd1 where Vd1 is given by Eq. ε = 2 fully transmitted incident velocities occur similarly to what happens in 1d, due to the separability of the problem. For ε ≠ 2 the potential 6 is not separable: nevertheless, both in the linear and in the nonlinear case we find a structure of peaks analogous to the 1d case with the disturbance pertinently defined asVd2  for d ≈ 3 μm.An experimental setup to test the results presented in this paper can be implemented with ultracold Bose gases trapped on an atom chip. A 1d quasi condensate can fill a several hundred microns long potential tubev in the defect-free case and then ramping on the defect. For velocities smaller than a critical velocity vc there is no production of excitations . For a set of arbitrarily large supercritical velocities v > vc the growth of excitations is fully suppressed, contrary to the generic expectation based on the Landau criterion. For these velocities, we find the production of excitations to be bounded in time and to stop entirely when the defect is completely turned on. Such excitation-free supercritical velocities are present both for wells and barriers, and for repulsive and  attractive interactions. We observe that even though in the nonlinear case bound states and bifurcation effects are expected, our protocol of ramping on the defect allows us to access the excitation-free points in a clean way, not depending on the ramping time.We have studied the propagation of matter waves across defects of rectangular shape in 1d and 2d starting from a stationary flow solution with velocity π/k) and the length scale of the defect. The shift from the resonance is positive (negative) for repulsive (attractive) interaction in the case of barrier defects, and vice versa for well defects. We expect that such excitation-free supercritical velocities exist for a wide range of barrier shapes characterised by a well defined length scale, e.g. for trapezoidal defects or two delta-peaked potentials. The steeper the defect is at its edges, the more robust will the inhibition of excitations be in the vicinity of a set of supercritical velocities. We verified that our results are not a specific features of one-dimensionality by showing that similar findings are obtained in a 2d geometry. We also expect that the phenomenon may occur in a fermionic superfluid, but of course further studied in this directions are needed.The obtained excitation-free supercritical velocities are the nonlinear counterpart of the velocities having total transmission in the linear Schrödinger case (Ramsauer-Townsend resonances) and are due to the resonance between the length scale associated with the matter wave momentum , can occur for v > vc for specific shapes of defects. Moreover (perfect) superfluidity persists for a series of specific, arbitrarily large values of the incident velocity. These findings are independent of whether or not the Landau critical velocity coincides with vc or Previous studiesδ potentials separated by a distance d. When this length resonates with the incident wavelength, perfect transmission and complete superfluidity are restored, the key mechanism being the resonance between the non-linear wave propagation of the superfluid and the defect. A general potential not characterized by a single length scale will typically not exhibit  the resonances discussed in the present paper and, in particular, even when only two length scales are involved, transmission resonances will only be present if the lengths are commensurate.We expect that our results are also obtained for other shapes of the defects also characterized by a single length scale, as is the case with two We note that in our treatment we did not explicitly include dissipation. In general the time scale at which superfluidity is destroyed due to dissipation may depend on the incident velocity. However, for typical experimental parameters, dissipation only plays a significant role at time scales longer than our simulation times and therefore our results should hold even in the presence of dissipation. Nonetheless, in future work it would be interesting to include sources of dissipation in the presence of defects characterised by a single length scale.45, to fundamental studies such as the study of analogue gravity models and acoustic Hawking radiation in Bose-Einstein condensates46.Understanding matter-wave propagation in the presence of tailored defect potentials is important in a variety of applications, ranging from quantum technology applications, in particular quantum sensors based on matterwave interferometryMotivated by our work, it will be interesting to study general criteria for the existence and stability of supercritical solutions of the nonlinear Schrödinger equation in the presence of defects with a well-defined length scale. Finding exact solutions would ultimately remove the residual numerical uncertainty in excitation growth at the supercritical velocities with total transmission. Moreover, intriguing possibilities arise for utilising supercritical points in measurement devices based on superfluids and superconductors. Tuning a barrier to a supercritical flow resonance would facilitate precise determination of unknown external parameters affecting the flow velocity, such as rotation, and performing selective measurements at supercritical velocities.