Full Monte Carlo (FMC) calculation of dose distribution has been recognized to have superior accuracy, compared with the pencil beam algorithm (PBA). However, since the FMC methods require long calculation time, it is difficult to apply them to routine treatment planning at present. In order to improve the situation, a simplified Monte Carlo (SMC) method has been introduced to the dose kernel calculation applicable to dose optimization procedure for the proton pencil beam scanning. We have evaluated accuracy of the SMC calculation by comparing a result of the dose kernel calculation using the SMC method with that using the FMC method in an inhomogeneous phantom. The dose distribution obtained by the SMC method was in good agreement with that obtained by the FMC method. To assess the usefulness of SMC calculation in clinical situations, we have compared results of the dose calculation using the SMC with those using the PBA method for three clinical cases of tumor treatment. The dose distributions calculated with the PBA dose kernels appear to be homogeneous in the planning target volumes (PTVs). In practice, the dose distributions calculated with the SMC dose kernels with the spot weights optimized with the PBA method show largely inhomogeneous dose distributions in the PTVs, while those with the spot weights optimized with the SMC method have moderately homogeneous distributions in the PTVs. Calculation using the SMC method is faster than that using the GEANT4 by three orders of magnitude. In addition, the graphic processing unit (GPU) boosts the calculation speed by 13 times for the treatment planning using the SMC method. Thence, the SMC method will be applicable to routine clinical treatment planning for reproduction of the complex dose distribution more accurately than the PBA method in a reasonably short time by use of the GPU‐based calculation engine.PACS number(s): 87.55.Gh Proton therapy has an advantage of dose localization that enables better dose conformation to a tumor and spares critical organs and normal tissues surrounding the tumor.field and applicability to moving organs, the number of facilities adopting the pencil beam scanning (PBS) technique is increasing rapidly due to the inherent better dose conformity, the lack of need of manufacturing patient‐specific devices, and the lower ambient neutron dose.A simplified Monte Carlo (SMC) methodWe evaluated accuracy of the SMC calculation by comparing a dose distribution in an inhomogeneous phantom obtained by using the SMC method with dose distribution obtained by using the FMC method. In order to assess the usefulness of SMC calculation in clinical environment, we compared dose calculation results using the SMC method with those using the PBA method for three cases when the PBS would be used as a beam delivery method. Since it takes a reasonably short time for the SMC to complete dose calculation, it will have a possibility of being used for routine treatment planning.A multipurpose nozzle has been installed in the NCCHE. A PBS mode, as well as a beam‐wobbling mode, can be selected in this nozzle. Primary proton beam energy can be selected from one of 206 MeV, 192 MeV, and 176 MeV in the PBS mode at present. In the near future, more number of therapeutic beam energies will be available. In the present calculation study of clinical cases, we used 150 MeV as the primary proton energy using the passive beam delivery system, since 176 MeV proton beam has too long a range for clinical cases of head and neck. In the PBS mode, this nozzle uses a binary range shifter (RS) made from PMMA for the range shifting. The thickness of the range shifter can be controlled from 0 to 127 mm, with a resolution of 1 mm. The water‐equivalent thickness ratio of the PMMA is 1.16. σeff,x and σeff,y in σeff,θx and σeff,θy in Leff,x and Leff,y in , residual range in water. It is assumed that the trajectory of each proton is determined only by the multiple Coulomb scattering with a scattering angles expressed as a normal random number with a standard deviation following the Highland's formula.The SMC method calculates a dose distribution by tracking individual proton paths. It starts calculation at the entrance of patient body with initial beam parameters provided by the effective source model.300×300×400 mm3  and the other consists from a lung tissue‐simulated material (ρ=0.217 g cm−3). The materials are defined in the PTSIM toolkit. The entrance faces of the two blocks are placed at a depth of 150 mm in water. The interface between the two blocks is placed on the beam central axis around which an initial pencil beam is generated. Such a selection of beam arrangement is considered to be the most challenging situation for pencil beam dose calculation algorithms. Dose distributions in the inhomogeneous phantom were calculated by the SMC and the FMC methods with 106 generated protons using the same input data of the proton beam. The resulting laterally integrated depth‐dose curves and isodose curves have been compared. In this case, we used a laterally integrated depth‐dose curve in water calculated by the FMC method as the depth‐dose curve used in the SMC method. We take the voxel size of 1 mm in all directions.To verify the accuracy of the SMC method, we compared a dose distribution for 206 MeV in water and that in a numerical inhomogeneous phantom obtained by the SMC method with those by the FMC method. As a FMC calculation, we used the PTSIM×400 mm3 . The inhFor simulation, we have selected three clinical cases that have been treated at NCCHE using the proton beam with the passive beam delivery system. Two head and neck cases are labeled case A and B, and a lung and bronchus case is labeled case C in this article. All the cases use two‐beam port irradiation. To assess the usefulness of SMC calculations in the clinical environment, we compared the dose calculation results obtained by using the SMC method with those using the PBA method if the PBS would be used as a beam delivery method for the target. The software for dose calculation using the PBA method has been developed in‐house for the study based on the algorithm shown in Hong.12 mm×12 mm grids in lateral directions considering the large beam size and by 5 mm water‐equivalent depth. For the CT input data, we take the in‐plane pixel sizes of either 1.17 or 1.88 mm depending on the case and slice separations of either 3 or 4 mm. The size of dose calculation grid is taken as the same as the CT voxel.Spot geometry for each field is arranged so that spots are regularly spaced on Before proceeding to comparison of dose distributions in inhomogeneous phantom between the SMC and FMC methods, we compared dose distribution in water obtained by the SMC method with that by the FMC method to investigate the effect of different physics model employed in each method on the dose distribution. (z=234.5 mm) in the FMC method as 100%. We found good agreement of overall dose in water‐equivalent distributions between the SMC and FMC methods, although we noticed overestimation of calculated dose in a number of places with the SMC method. The shallowest Bragg peak is dominated by proton tracks penetrating through the bone, while protons penetrating through the lung slab produce the deepest Bragg peak (z=296.5 mm), and the protons escaping both slabs produce the middle peak (z=257.5 mm). We also notice small dose difference of about 0.6% in the region behind the bone slab and before the first peak. It may come from more reduction of primary protons in the bone slab due to the more nuclear reaction rate in the bone slab than in water in the FMC method, while the SMC method cannot reproduce the effect due to the adoption of the water‐equivalent model. And the rms relative dose in water‐equivalent difference in In order to evaluate accuracy of the SMC method for practical cases, dose distributions obtained by the SMC and FMC methods have been calculated for the inhomogeneous numerical phantom consisting of a bone material and a lung material in water. Laterally integrated depth‐dose in water‐equivalent distributions in the phantom are shown in (σ∼10 mm) due to the scattering in the binary RS, disregarding density heterogeneities across a pencil beam can lead to considerable errors in the dose estimation. (D95=93.8%), as shown as the red line in the D95 of the PTV reduces to 68.9%, as shown in D95 increases to 88.5% of prescription dose in the PTV by using SMC TP, as shown in By showing comparisons of dose distributions between the PBA method and the SMC method for three clinical cases, we find that the treatment plan obtained by the PBA method will have a risk of radiation hazard and/or local recurrence for the target and a risk of possible complications for OARs for complex clinical cases.6 primary protons per a dose kernel in the case A . Calculation time required for obtaining both the dose optimization and full dose calculation with the optimized spot weights is approximately 232 s on the CPU in this case. Thus, calculation time required for obtaining dose kernels accounts for about 90% of the total calculation time. The time required for calculating all dose kernels by the SMC method is approximately 16.2 times longer than that by the PBA with an original spot decomposed into 121 subspots. Thus the SMC method is estimated to be faster than the VMCpro by a factor of 1.9 to 4.6. The dose calculation time depends on the size of PTV. If the dose calculation using the SMC method applies to the larger PTV volume of about 1000 ml , the calculation time is estimated to be approximately 12,273 s. On the other hand, Kohno et al.We implemented the SMC method in the dose calculation by parallel computation on a 3.7 GHz Quad‐Core Intel Xeon Processor E5 . We used the Intel C++ compiler . We parallelized the part of dose calculation by OpenMP. The calculation time required for obtaining dose kernels by the SMC method was approximately 2116 s on the central processing unit (CPU) for 106 primary protons were generated per a dose kernel. Thus, the GPU‐based SMC calculation speed for dose kernels calculation is about 16 times faster than the CPU‐based one. Calculation time required for both dose optimization and full dose calculation with the optimized spot weights was 44 s on the GPU in this case. Thus, calculation time required for obtaining the dose kernels accounts for about 75% of the total calculation time on the GPU. Therefore, we expect the total calculation time of approximately 12.8 min on the GPU‐based calculation engine for the target volume of 1000 ml. The time can be considered reasonably short for routine clinical uses.2880 CUDA cores. The calculation time required for obtaining the dose kernels was 133 s on the GPU‐based calculation engine when 10We have developed a dose kernel calculation algorithm using the SMC method applicable to the spot scanning system recently installed in the NCCHE in Japan. Calculation using the SMC method is faster than that using the general‐purpose FMC code by three orders of magnitude. In addition, the SMC method was found to be faster than the existing fast Monte Carlo method. Another advantage of the SMC method is easy implementation since it can use the same input data for the PBA calculation. We evaluated accuracy of the SMC method by comparison with the FMC method. We clarified the effect of model difference of the SMC and FMC methods on the dose calculation. Overall, the dose distribution obtained by the SMC method was in good agreement with that obtained by the FMC method in the inhomogeneous phantom. To assess the usefulness of SMC calculations in the clinical environment, we compared a treatment planning result using the SMC method with that using the PBA method for three cases when the PBS would be used as a beam delivery method. The results show that the SMC method can reproduce the complex dose distribution more accurately in a reasonably short time than the PBA method. Since the treatment plan using dose kernels obtained by the PBA method provides inaccurate dose distribution for clinical cases with heavily heterogeneous structure, it will increase clinical risks. Therefore, we should replace it by a treatment plan using the SMC dose kernels as soon as possible.We appreciate SHI Accelerator Service Ltd. and Health Labor Sciences Research Grant (No. 26270701) for their support with this study.Creative Commons Attribution 4.0 International License.This work is licensed under a


The World Health Organization refers to stroke, the second most frequent cause of death in the world, in terms of pandemic. Present treatments are only effective within precise time windows. Only 10% of thrombolysis patients are eligible. Late assessment of the patient resulting from admission and lack of knowledge of the symptoms is the main explanation of lack of eligibility.The aim is the measurement of the time of access to treatment facilities for stroke victims, using ambulances (firemen ambulances or EMS ambulances) and private car. The method proposed analyses the potential geographic accessibility of stroke care infrastructure in different scenarios. The study allows better considering of the issues inherent to an area: difficult weather conditions, traffic congestion and failure to respect the distance limits of emergency transport.Depending on the scenario, access times vary considerably within the same commune. For example, between the first and the second scenario for cities in the north of Rhône county, there is a 10 min difference to the nearest Primary Stroke Center (PSC). For the first scenario, 90% of the population is 20 min away of the PSC and 96% for the second scenario. Likewise, depending on the modal vector , overall accessibility from the emergency call to admission to a Comprehensive Stroke Center (CSC) can vary by as much as 15 min.The setting up of the various scenarios and modal comparison based on the calculation of overall accessibility makes this a new method for calculating potential access to care facilities. It is important to take into account the specific pathological features and the availability of care facilities for modelling. This method is innovative and recommendable for measuring accessibility in the field of health care. This study makes possible to highlight the patients’ extension of care delays. Thus, this can impact the improvement of patient care and rethink the healthcare organization. Stroke is addressed here but it is applicable to other pathologies. Stroke is the main cause of non-traumatic disability and the second major cause of death in the world. WHO  refers to stroke in terms of pandemic. Indeed, stroke caused 6.7 million deaths in 2012 .Stroke is a pathology bound to the notion of time. The effectiveness of treatment today is limited to precise temporal windows. For eligible patients, thrombolysis must be performed within 4 h 30 min of the appearance of the symptoms and thrombectomy within 6 h. Only 10% of patients are eligible for thrombolysis. This small proportion would seem to be the result of the late presentation of the patient and poor knowledge of the symptoms [Assessment of geographic accessibility is essential in many kinds of pathology. With the development and perfecting of Geographic Information Systems (GIS) in recent years, attempts have been made in a number of studies to model this accessibility as the use of a GIS to assess access times has been validated , 6. Two In the case of travel impedance to nearest provider , 12 a fiA review of the literature on the accessibility of stroke care facilities shows that no study of this kind had been performed in France. It was therefore essential to perform such analysis to learn more about territorial accessibility in the Rhône area. Furthermore, the limits of previous studies were taken into account—factors that are not inherently geographic such as traffic difficulties and the modelling of different types of transport and transporter. This consideration also made it possible to use different accessibility scenarios to adapt the study to territorial issues.The aim of this study was to develop a measure method of accessibility according to the localization of patients and the different means of care.2 with a population of 1,798,511 in 2014 , i.e. 543 persons per square kilometre. Persons over 65, known to have a greater risk of stroke [Our study area is the Rhône administrative county in France Fig. . The couf stroke , form 15f stroke  as thesef stroke . The driRoute500 road database of the Institut national de l’information géographique et forestière (IGN). This database shows the main 500,000 kilometres of French roads: motorways, national main roads and departmental roads but passes over many residential and urban sections. Therefore, we have chosen to use the IGN BDCarto database, with more than a million kilometres of roads—the entire French road network—to get a more complete picture of the territory.The choice of road network is primordial for modelling transport operations. Description of accessibility using Euclidian distances  is a firUnité Mobile Hospitalière, UMH  before entry to a hospital. The mobile unit assesses the seriousness of the case, makes a diagnosis, performs the necessary emergency and therapeutic support and then transfers the patient to a suitable hospital with facilities available—which is not necessarily the nearest one.The ability of a care system to handle acute complications of medical or traumatic pathologies depends on many geographic and spatial criteria, making it a key public health issue. The times needed for access to treatment are a major factor in the care system. Two main types of vital emergency care system coexist in developed countries. The ‘Anglo-Saxon’ system relies on management of prehospital emergency by paramedics in order to transfer the patient to the nearest hospital. In this context, the goal is the fastest transport to medical facility. This system is mostly that of United States, Canada and United Kingdom where most of intensive care is performed at the hospital. The other system relies on emergency physicians involved at the scene of injury. This Emergency Medical Service (EMS) system is effective in France, Greece, Germany, Canada or Austria for example . The ‘FrStructures Mobile d’Urgence et de Réanimation, SMUR (Mobile Intensive Care Unit) that are located at public hospitals. Each SMUR is in charge of operational coverage of a defined population area. The segmentation of SMUR sectors depends on administrative boundaries without considering care access times for the population.In France, the UMHs are part of Service d’Aide Médicale Urgente or SAMU  is in charge of the reception and the triage of calls for each SMUR area. It is responsible for all prehospital medical or traumatic emergencies 24 h a day and 7 days a week, using the 15 call. Each centre is equipped with advanced telephone equipment and numerous information systems . The SAMU centres are manned by medical staff, triage emergency doctors, general practitioners and non-medical staff .The Decide and implement the most suitable response to the call as rapidly as possible,Check the availability of the public or private hospitalisation facilities appropriate for the condition of the patient, and ensure that arrangements were made for the arrival of the latter,If necessary, organise transport to a public or private hospital, using a public service (the fire brigade) or a private ambulance company,Oversee the admission of the patient, involving coordination of on-site care by the SMUR team and the hospital admission service,Provide support in the search for a specialised technical facility for non-academic hospitals.The work of SAMU units is specified by decree and can be summarised in five broad categories:The EMS system in France is not only based on UMH care. In fact, UMHs are the second level of EMS system. The first level is composed of basic life support (BLS) fire department ambulances, based at fire stations .In Rhône county, it is not possible for patient to go directly to the Comprehensive Stroke Center (CSC), with private car. The patients are constantly transported by ambulances (SAMU or firemen ambulance). For stroke care there is a dedicated procedure from the call to EMS to the admission in CSC who not includes transport by private car. In most cases, stroke patients are transported to hospital by firemen because they don’t need medical transport.10.4.1 [Code de la Route (Highway Code). As the BDCarto database does not include this information, the collaborative database OpenStreetMap [All the cartographic analyses shown in this work were produced using the program ArcMap 10.4.1 . MeasuretreetMap  was usedtreetMap , a EuropNetwork Analyst extension of ArcMap 10.4.1 was used for these scenarios [Various kinds of modelling were conducted with the varying of speed limits to take into account all the territorial issues involved in the Rhône county. The cenarios , 8, 19. The first scenario is the case of patient transportation by private car, the driver respects the speed limitations. The postulate is the movement of patients by their own means (their own vehicle or with help of a friend or relation) to the closest treatment facility. If the driver of private car decides not to respect the speed limitations, the other scenarios can be applied.Scenario 2 is for driving in an emergency situation. The following hypothesis is used when modelling tends to show access to stroke care facilities from all points in the network: for private car, a third part transports the patient and takes the decision not to respect the speed limits. Petzäll et al.  measuredScenario 2’ is a complementary scenario which models the accessibility depending on the kind of area. In fact, on the basis of variation times between urban and rural areas , 31–33, In Scenario 3, with lower speeds due to severe weather conditions, we consider that the driver takes the decision to reduce his speed by 20 kph (12 mph) and thus respect the R413-2 article of French Highway Code recommendations if weather conditions are difficult .The fourth scenario is an adaptation of scenario 2 and analysis of SAMU interventions during traffic jam hours.A series of polygons was calculated for the zones covered (isochrones) representing the distance that can be attained from each stroke treatment facility in a particular length of time. The first stage thus consists of listing and geolocalising each stroke treatment infrastructure. Thus, public hospital emergency departments, Primary Stroke Center (PSC) and Comprehensive Stroke Center (CSC)  in the RPreliminary measurement of accessibility to facilities from all points in the network with 10, 20, 30, 45 and 60-min access time was thus calculated. These time steps were chosen after bibliographic analysis , 36, 37.Although it is pertinent to characterise the area according to the time required for travel from any point in the network to the treatment facility, it is even more interesting to model overall admission time. Treatment of stroke requires the best possible upstream taking in hand of the patient , 38. ThiIlots Regroupés pour l’Information Statistique, small zones grouped for statistical information), the smallest administrative division of Insee  and that respect demographic (populations of 2000) and geographic criteria [This overall approach was represented on the basis of IRIS area units , the entire territory is less than 30 min from the closest emergency department. Similarly, for PSC, with the exception of a very small part of the area (the northern and western extremes), communes in the Rhône county have access in less than 30 min. However, the north-western third of the Rhone area is more than 30 min from the nearest CSC Fig. . There aThe third scenario consists of travelling 20 kph (12 mph) slower than the speed limits because of difficult weather conditions . Access time is naturally longer in this case. The northern part of the Rhône—the Beaujolais area in particular—is harder hit once again. This section is more than 30 min from the nearest emergency department. The western and northern parts of the county are thus more than 30 min from a facility and even more than 45 min from a facility when potential access times to the closest PSC units are measured. Few CSC facilities are available in the Rhône and neighbouring counties and potential access time is very varied. Indeed, some areas are distinctly underprivileged. Access to thrombectomy for the populations of the communes concerned is thus affected. Here again, the north-western part of the county has markedly fewer facilities and access times exceed 60 min , 98% have 20-min access time to the nearest emergency department Fig. . Thus, vHowever, access to facilities from all points in the network is evaluated here. For a real assessment of access to facilities, it seems more interesting to perform an examination of the full admission of patients from emergency call to arrival in an CSC facility.Analysing accessibility at all points in the network of each stroke patient admission facility is an approach that has already been studied , 19, 24,It is reminded that fire brigade access capability is greater than that of the SMUR medical teams. This greater density explains why potential access to patients by firemen and the admission of the formers to care facilities is greater than that of the SAMU, whatever the scenario. Thus the median access time by fire brigades is the best, as it is the average time. When speed limits are respected, median time for the firemen is 40.9 min and average time is 45.7 min from access to admission to the closest CSC facility, in comparison with a median of 45.9 min and an average of 55.9 min for the SAMU.As regards the territory, the towns at the northern extremity of the county display the most marked deficit in case of transport by the SMUR rather than the fire brigade, should every fire station be available. Thus stroke victims in the town of Monsols are between 1 h 45 min and 2 h 10 min from the CSC when transported by the SAMU and between 1 h 10 min and 1 h 30 min with the fire brigade—a gain of between 15 min and 1 h when speed limits are respected Fig. . AdmissiThe pattern is the same when speed limits are raised Fig.  or lowerIncreasing the limits by 20 kph (12 mph) highlights the influence of the Lyons metropolis on the territory. The density of facilities—fire stations, SMUR units and CSC—here accounts for the marked influence of the Lyons urban area. Here, whatever the type of transport, patients are less than 45 min from admission to an CSC facility. In addition, in most of the territory increasing the speed limits by 20 kph can result in the patient gaining 15 min in CSC admission.Finally, the main observation about reducing speed limits by 20 kph concerns the question of the eligibility of the patient for treatment. Travelling time in the northern most part of the Rhône county is 2 h with the firemen and possibly more with the SMUR. Without allowing for inter-hospital time but only times between the onset of symptoms and the 15 (emergency) call at between 15 min and 5 h , most ofThe prime interest of the study is to model various scenarios based on different transport speeds. These multiple speeds are based on a review of the literature and on SAMU interventions.This study has some practical implications. The different kind of transport are described and modelled. This modelling relies on transport times based on measured times that allows the comparison, for equivalent care conditions, between three kinds of transportation: private car and ambulances (firemen ambulance or SAMU ambulance) triggered by SAMU.Classically, the accessibility is measured from patient’s care place to the nearest facility. This problematic has been analysed in this study, but the model has been more developed. Like it is observed in real case of care, the patient cannot go to the facility with his own mean. In a real context, the patient depends on modal transport and the access times linked to his care are from the trigger of transport care to his admission in a facility. The model presented gives a response to these care conditions.Another practical implication is the emergence of territorial disparities. The measurement of access times to stroke patients allows to bring to light areas where we observe an extension of access delays to treatment.As the method has been set out clearly, the finesses of modelling should now be improved. For example, ‘travel impactors’  were notRoute500, the Institut Géographique National database commonly used in France for the various studies of this kind makes possible to use the Odomatrix program [BDCarto database for its considerable exhaustiveness as it covers more than 1 million kilometres of road network. Although the use of this database is essential for the best possible analysis of the territory and to be as close to reality as possible, no speed limits are attributed to the sections. It was therefore necessary to use a participative facility—Open Street Map in this case—to model access times. This type of information can be one of the limits of the study. It is therefore planned to acquire a professional database such as Garmin® or TomTom® to gain accuracy in modelling.Another limit but that is also a strong point of the study is the method used to know the maximum permitted speed in each section.  program  to calcuThe various modelling takes into account the accessibility of the territory at all points in the road network. The improvement of modelling would require integration of the time taken by emergency teams from the road network to the patient’s door. The question of accessibility is raised in particular for large housing block areas and residential zones where access to the patient’s door from the road network may require time in the light of the complex configuration of buildings and in particular blocks with no lifts.Another note is about the required average time at the time regulation for decision-making and intervention average time. In the study, we use the set times by Adeoye et al. , from thThe modes of transport, firemen vs EMS, were compared is this study. This comparison was done to validate the method. In fact, in most cases, stroke patients are transported to hospital by firemen because they don’t need medical transport. Given the proportion of interventions, this comparison doesn’t have a high interest. Furthermore, the fire stations representation, which reflects the faster response of firemen, must be put into perspective. In fact, the future models should highlight the fire stations capacity to intervene. Apart from the highly-urbanized areas like Lyon and his urban agglomeration, firemen in rural fire stations are mostly volunteers. For this reason, if the nearest fire station doesn’t have the sufficient number of firemen, they can’t intervene and manage stroke patient which would extend access delays. The modelling of fire station ability to intervene will be feasible by representing their capacity according to the moment of the day, day/night in particular.This study is innovative and allows a characterization of the territory in term of potential accessibility by network and localization of every mode of transport, in term of patient location. In this case, the comparison between EMS (SMUR) and firemen transport will be improved, yet the study shows the capacities of GIS. Only access delays for a patient to healthcare structure are evaluated, the medical aspect linked to the patient psychological state at the moment of his management is not studied.These different models are a method of decision making for healthcare organization. The use of our method and models as a complementary tool for regulation could be the subject of future studies.Furthermore, this study is also innovative because the transport care is estimated as a whole, from 15 call to admission in CSC. With this kind of model, it’s easier to estimate the patient eligibility to thrombolysis and thrombectomy, with assumption of quickly recognizing of signs by the patient or people in his environment.


Photoacoustic tomography relies on a dense coverage of the surface surrounding the imaged object with ultrasound sensors in order to enable an accurate reconstruction. A curved arrangement of integrating line sensors is proposed that is able to acquire data for a linear projection image of the absorbed energy density distribution in the object. Upon rotation of the object relative to the array, three-dimensional (3D) images can be obtained.The proposed design is based on the cost-effective piezoelectric polymer film technology with 64 line shaped sensors arranged on a half-cylindrical surface. It is combined with an optical parametric oscillator for the near infrared as a source for laser pulses. Image reconstruction from recorded signals consists of two-dimensional (2D) back projection followed by an inverse Radon transform.The tomograph exhibits a spatial resolution on the order of 200 to 250 μm. In a phantom experiment, the steps from acquisition of a single, 2D projection image to a full 3D image are demonstrated. Finally, in vivo projection images of a human finger are shown, revealing the near real-time imaging capability of the device in 2D. The combination of these favorable properties arises from the thermoelastic generation of sound waves by deeply penetrating, diffuse light from pulsed laser sources. In three-dimensional (3D) photoacoustic tomography (PAT), sensors are distributed around the volume of interest to detect the sound waves. PAT devices are composed of optical and ultrasound components and may become quite complex. Although still much less expensive than magnetic resonance tomography devices, the costs of commercial photoacoustic tomographs for small animal imaging are rather high and it has become an attractive alternative to design and manufacture PAT devices in the own lab. This is facilitated by the availability of multichannel analog to digital converters with the desired bandwidth. Also, pulsed laser sources that are suitable for photoacoustic excitation, primarily optical parametric oscillators (OPOs), are offered with specifications ideal for this purpose.3 at a low level of complexity that allows the devices to be home-made, it is possible to use a relatively small array of sensors arranged on a curve or line that is moved relative to the object. In PAT, images of the absorbed energy density are reconstructed by applying appropriate tomographic algorithms to the acquired time-resolved signals. For an accurate reconstruction, a dense coverage of a preferably closed detection surface with sensor elements is crucial. This can require several hundred to tens of thousands detector positions. To achieve this high number of detectors, several approaches have been proposed. Very flexible is the scanning of a single sensor across an area surrounding the object or a plane close to the object Line detectors have special features that distinguish them from point-like detectors. The first one is the reduction of the imaging problem to two dimensions, leading to the projection imaging capability described above. Another, favorable property is the geometrical attenuation. While point like detectors receiving signals from a small source will show a drop of signal amplitude proportional to the reciprocal distance, line detectors only exhibit an attenuation proportional to the inverse of the square root of the distance. Furthermore, if detectors with a finite size are treated as point detectors in image reconstruction, this leads to a limitation in image resolution In this work, we present a photoacoustic tomograph manufactured of relatively low-cost components such as standard electronics and a piezoelectric polymer film, combined with an OPO for the near infrared. The tomograph has 64 line sensors in an arrangement as shown in 22.1a that is not touching the sensor line, as outlined in The tomograph was designed following the requirements for an array of line shaped sensor elements with infinite length. This ensured the applicability of image reconstruction methods that are based on strict two-dimensional wave propagation R = 50 mm. Assuming an imaging area with radius a = 20 mm centered on the axis of the cylinder led to a length of L = 150 mm. The array consisted of 64 sensor elements with a width of 1.5 mm, distributed on the cylindrical surface with an angular increment of 2.8°. For this number of elements we used a 32-channel data acquisition device with 2:1 multiplexing for each input.The line sensors in the array were arranged on a semi-cylindrical surface with a radius of 2.2Pulses from a Q-switched Nd:YAG laser at a wavelength of 532 nm pumped an optical parametric oscillator (OPO) (Innolas SpitLight OPO 600) at a repetition rate of 20 Hz. Two glass fibers with 1 mm core diameter guided the laser pulses to the tomograph, where they illuminated the sample from two opposite sides, parallel to the line detector orientation. Lenses imaged the fiber tips onto the sample, giving circular areas with adjustable size. Samples were held on a motorized rotation stage and submerged in water, which was filled into the half-cylindrical opening of the tomograph. A separate device provided the control signals for the multiplexer in the tomograph and the step motor in the rotation stage. In a Labview code that controlled the whole imaging procedure, the number of laser pulses over which the signals were averaged at each rotational position of the sample could be selected. Usually, the number of angular positions for a complete rotation of the sample was 400, with an increment of 0.9°. Since 2:1 multiplexing required two laser pulses at each position, the total number of laser pulses was 800 for acquiring data from a full rotation without signal averaging, taking 40 s.2.3A calibration measurement was made in order to determine the relative sensitivities of the line sensors and their exact positions. These data were used for improving the accuracy of the image reconstruction. Although the tolerances in the manufacturing process were kept as low as possible, the radial distances of individual sensor elements relative to the cylinder axis varied slightly, due to small variations in the thickness of the adhesive layers between PVC substrate, circuit board and PVDF film. These were in the range of <100 μm, having an effect on the image resolution, which was expected to be on the same order of magnitude. For the calibration experiment, a small droplet of black oil paint with about 150 μm radius was embedded in a block of agar and was fixed near the axis of the cylindrical array. Due to the symmetric arrangement of illumination and sample, it could be expected that the amplitude of the spherical wave should be identical at all sensors. Variations occurring in the individual, detected amplitudes could therefore be attributed to the different sensitivities. To determine the exact radial positions of the sensor elements, the time of flight and travel distance of the spherical wave to each sensor element were extracted from the measured signals. Under the assumption that the deviations from the ideal cylindrical shape were small, a curve assuming constant radial position for all detectors was fitted to the experimental distances, yielding the exact source position and a value of the mean array radius. Adding the differences between the experimental and fitted distance values to the mean radius yielded the exact radial positions of the sensor elements.2.4u,v-plane gave a disk like source, for which we calculated the spectrum and multiplied it with the simulated transfer function of the layer system The result was then compared with the spectrum of the experimental signal. Since the electrical response was almost flat in the region of interest, it was not taken into account in this simulation.The frequency response of the line sensors was simulated by calculating the response of the PVDF film to a plane wave at normal incidence. For this simulation we adapted a method used by Cox et al., who used it to calculate the frequency-dependent directivity of a planar polymer film used as Fabry-Perot interferometric ultrasound sensor 2.5ϕ of the sample are used to reconstruct 2D images. Due to the integrating property of the line detectors, these images are projections of the initial pressure distribution in the sample into a plane spanned by coordinates u and v perpendicular to the line direction. This distribution is directly proportional to the absorbed energy density. To reconstruct a projection, an algorithm based on two-dimensional acoustic wave propagation is employed, where the recorded pressure signals are back projected onto cylinders with the line detector in the center. It can be derived from the universal back projection algorithm, which was initially established for three-dimensional photoacoustic tomography with point like detectors The image reconstruction procedure for line detectors has been described in detail earlier v-direction, projections of the initial pressure distribution are recorded for ϕ-values covering at least 180°. For a complete 3D reconstruction, the final step is to apply the inverse Radon transform to projection data in planes with constant v, perpendicular to the rotation axis. This final step of the reconstruction requires the exact localization of the axis of the rotary stage relative to the reconstructed volume. Any slight movement of this axis relative to the detector array, for instance during mounting of the sample, could deteriorate the quality of the resulting image. Therefore, we implemented a method to determine the exact u-coordinate of the rotation axis from the recorded projection images. A small, photoacoustic source generates a sinusoidal structure in the input signals for the inverse Radon transform. These input signals are the line projections of the initial pressure distribution as a function of distance u and of the angle ϕ. They are the classical “sinograms” as they are found, for instance, in X-ray computed tomography with parallel beams. From such a sinusoidal curve generated by a point source the position of the rotation axis is found by determining its symmetry line. The steps of the reconstruction are illustrated in the next section, By rotating the sample relative to the tomograph about an axis parallel to the 33.1−1. A pulse energy per fiber of about 6 mJ was used, giving a radiant exposure of ∼ 3 mJ/cm2 from each side. u-v-frame of the tomograph using the back projection algorithm  solution (0.5 g/l) and was formed to a knot. Data were acquired at an OPO wavelength of 750 nm, where the absorption coefficient of the ICG solution was 140 cmlgorithm b. After 3.23.2.13.2.2To estimate the spatial resolution of the device, we built a phantom containing several black polystyrene microspheres with 100 μm diameter, embedded in scattering agar. 3.2.32 at 800 nm wavelength were used. From Monte Carlo simulations using the optical constants of the phantom, we obtained the energy density deposited in the absorbing liquid (aμ = 8 cm−1) within the tubes. For the scattering coefficient of the agar, we used values of SMOFlipid  reported by Held et al. We made a measurement of the sensitivity of the line detectors using a phantom similar to the one shown above in Section 3.2.43.3v-axis) near the center of the cylindrical array and illuminated from one side along the direction of the cylinder axis with a radiant exposure of 16 mJ/cm2. In this experiment, free beam illumination was used instead of optical fibers, allowing a higher pulse energy at the target. With five times averaging and multiplexing, a single projection was captured in 0.5 s. In vivo images of the fingertip of one of the authors were taken at a wavelength of 750 nm. The finger was fixed vertically (parallel to the 4In this work, we report on the design and manufacturing of a photoacoustic array tomograph capable of generating almost real-time 2D projections and 3D tomographic images of the absorbed energy distribution in biological objects. Projection images are generated because of the integrating effect of the extended line detectors in the array. They can be useful for the observation of objects in an extended volume. In the case of the line detector tomograph presented here, this volume is given by the length of the line sensors times the cross sectional area of the illuminating laser beam. An object located anywhere within this volume will be visible in the projection image. An important step in the manufacturing of a PVDF array is the production and contacting of the sensor elements. PVDF film can be purchased in large sheets with metal electrode layers deposited on both sides. Separate elements can be created by patterning the electrodes, e.g. by etching. Especially for the long and thin line elements used in our study, there is always a risk that a thin scratch on the nanometer thin metal film disrupts the electrode, leading to the loss of entire elements. Therefore, we chose to use a method that had been proposed earlier for generating small, point like detectors. It uses metal electrodes on a circuit board adjacent to the piezoelectric film to determine the shape and extension of the sensor elements The design of the array was guided by several requirements. For instance, the array dimensions were chosen for a typical sample size of four centimeters. This determined the length of the lines (according to Eq. 5The presented line detector array is capable of generating 2D photoacoustic projection images of extended volumes with a small number of sensor elements in almost real-time. Three-dimensional imaging is possible by rotating of the object relative to the array. In combination with the very flexible piezoelectric polymer film technology, a photoacoustic tomography device can be manufactured that exhibits a relatively low level of complexity, making it a cost-effective alternative to commercial devices.The authors declare that there are no conflicts of interest.


The common practice in the Israel defense Forces is that exertional heat related injury patients undergo a heat tolerance test 6–8 weeks post event as part of the “return to duty” process. In the case of a positive heat tolerance test the individual is classified as heat intolerant, in some cases however, the thermoregulatory recovery may be longer , and therefore a second heat tolerancetest is scheduled 6-8 weeks later. The presented case reports emphasize the possibility of different recovery periods of the thermoregulatory center and the distinction between congenital and acquired physiological heat intolerance.Two young healthy males (A and B) were diagnosed with exertional heat related injury during a pre-recruitment sorting process. Both underwent a heat tolerance test, and were found heat intolerant. During the next months they repeated the test several times. Patient A was finally diagnosed as heat tolerant and patient B was diagnosed as heat intolerant.Susceptibility to heat is a significant determinant for active young people such as athletes and soldiers. Both cases emphasize the importance of the heat tolerance test (and repeated test when needed) as a criteria for an exertional heat related injury patient to return to duty/play and to perform intense physical activities. These cases also emphasize the effectiveness and sensitivity of the test in identifying a temporary and a permanent state of heat intolerance. Due to the fact that the last test results were borderline and since the subject insisted to be tested again, another HTT was scheduled 3 months later (8 months after the EHI occurrence).Three months after the first HTT the patient underwent a second test. The test was summarized as positive, mainly because of the endpoint HR Fig. , that wa °C Fig. . To noteThis 3rd HTT was summarized as negative according to the HTT’s criteria Figs. , 2; accorec upon collapse was 40 °C and he was diagnosed as EHS. The patient was immediately cooled by spraying copious amount of tap water. When Trec of 37 °C was measured he was evacuated to a near hospital. An investigation of the case revealed sleep deprivation and apparently mild hypohydration.A young , apparently healthy, averagely fit male (he trained frequently during the year prior to the event and lost 20 kg of his body weight). He collapsed during a vigorous exercise as part of a military pre-recruitment sorting process. His T2)]. His military medical profile was adjusted to accommodate this condition, which prevented him from intense physically activities during military service.Six weeks after the event, an HTT was performed. The results indicated HI Figs. , 4 and drec and HR) that define one’s tolerance to perform exercise under heat load conditions. Presently, the IDF’s HTT protocol provides the only validated scientific tool to diagnose HI. This test has been adopted along the years by other institutes around the world and is being used as a clinically diagnostic tool for back to duty decisions [The underlying reasons for HI are yet not fully understood. The decision to allow the individual to return to training and engage in intense physical activities should be determined, under predetermined conditions, by valid physiological criteria . This period may allow sufficient time for physiological recovery.rec value in subject B compared to subject A, at the time of collapse) is associated with longer recovery time of the thermoregulatory mechanism.When comparing subject A first and last HTT , it can be concluded that HI was probably not congenital but associated with the heat injury. On the other hand, in the case of subject B, heat intolerance was observed in subsequent HTTs even 11 months after the EHI. What seems like permanent heat intolerance could have been either a sequel of the EHS or a congenital deficiency in the thermoregulatory mechanisms. The latter can explain the EHS during the exposure to exercise under heat load conditions. Moreover, it might be speculated that the severity of the EHI (higher TThe two cases presented in this manuscript demonstrate that the HTT is an effective and sensitive screening tool for identifying both temporary and permanent states of HI and emphasize the importance and relevance of performing a HTT (and repeated tests when needed) after EHI, in order to determine the state of tolerance to heat before returning to duty/play.Nevertheless, the ability neither to predict recovery time after EHS nor to understand the mechanisms that cause HI is still unattainable. At this point, encouraging performing an HTT after heat injuries and in case of positive results to repeat the test every 3 months for at least 1 year is the recommended policy.Due to the unfamiliarity of this complex phenomenon among physicians, both military and civilian, and due to the increasing number of participants (and heat injuries) in extreme sport events in the general population, we suggest that this issue will be further discussed and considered by clinicians when they are required to have a decision. We also point to the necessity to find biological/molecular biomarkers that will assist in evaluating the recovery after EHS. These markers may also further contribute to a better understanding of HI mechanism and physiological recovery process following heat injuries.Written informed consent was obtained from the patient for publication of this case report and any accompanying images. A copy of the written consent is available for review by the Editor-in-Chief of this journal.


Evidence supporting the practice of skin‐to‐skin contact and breastfeeding soon after birth points to physiologic, social, and psychological benefits for both mother and baby. The 2009 revision of Step 4 of the WHO/UNICEF “Ten Steps to Successful Breastfeeding” elaborated on the practice of skin‐to‐skin contact between the mother and her newly born baby indicating that the practice should be “immediate” and “without separation” unless documented medically justifiable reasons for delayed contact or interruption exist. While in immediate, continuous, uninterrupted skin‐to‐skin contact with mother in the first hour after birth, babies progress through 9 instinctive, complex, distinct, and observable stages including self‐attachment and suckling. However, the most recent Cochrane review of early skin‐to‐skin contact cites inconsistencies in the practice; the authors found “inadequate evidence with respect to details … such as timing of initiation and dose.” This paper introduces a novel algorithm to analyse the practice of skin to skin in the first hour using two data sets and suggests opportunities for practice improvement. The algorithm considers the mother's Robson criteria, skin‐to‐skin experience, and Widström's 9 Stages. Using data from vaginal births in Japan and caesarean births in Australia, the algorithm utilizes data in a new way to highlight challenges to best practice. The use of a tool to analyse the implementation of skin‐to‐skin care in the first hour after birth illuminates the successes, barriers, and opportunities for improvement to achieving the standard of care for babies. Future application should involve more diverse facilities and Robson's classifications. They would then be categorized as “No: Emergent Care for Mother or Infant.” If the separation results in a delay of less than 5 min, the pair is categorized as yellow—a caution for the hospital to review—but the dyad continues on the blue best practice path.The next element of the model considers continuous SSC during the full first hour or so. If the newborn is removed from SSC either for emergent or routine care any time within the first hour or so after birth, it is recorded.The algorithm considers the standard of uninterrupted or undisturbed SSC next. Dyads are recategorized if staff interfere with the newborn during the first hour or if the mother or family interferes with the newborn's innate behaviours. Staff “helping” the newborn to latch would be considered interrupting, because the SSC standard includes newborn crawling, familiarizing, and self‐attaching.Best practice is ultimately measured through the achievement of Widström's 9 Stages during the first hour or so after birth. Immediate, continuous, and uninterrupted practice optimizes the infant's ability to achieve this goal.If a dyad experienced immediate, continuous, uninterrupted SSC for the first hour or so after birth and progressed through Widström's Stages and suckled, they have achieved the standard of best practice.33.1Analysis of the Japanese dyads is presented in Figure All 14 babies were immediately placed in SSC with their mother. None were removed due to hospital policy or emergent care. Thirteen of the 14 babies received continuous SSC with their mother. One baby was removed at 50 min. Seven of the 13 remaining newborns were interrupted by staff who “helped” the newborn to breastfeed during the first hour. Six newborns were uninterrupted. One of the newborns who had immediate, continuous, uninterrupted SSC progressed through Widstrom's 9 Stages and achieved the standard of self‐attachment and suckling. The other five newborns did not progress past the Activity Stage (Stage 4).3.2Analysis of the Australian study is presented in Figure One baby was immediately placed in SSC with mother. Seven were placed in SSC with mother within 5 min of birth. Twelve received SSC later than 5 min after the birth (between 5.01 and 65.05 min), and one did not receive any SSC within the first 2 hr after birth. Seven of the mothers who received immediate SSC, or SSC within 5 min of birth, did not experience continuous SSC because they received less than 45 min of initial SSC with mother. The newborns were removed from the mother for routine care. One baby was not removed for routine care. One mother requested the baby to be removed, and it was recorded as “interrupted” on the algorithm. None of the babies met the standard for SSC—immediate, continuous, uninterrupted SSC for at least an hour, progressing through Widström's 9 Stages, self‐attaching to the breast and suckling.44.1The algorithm allows us to examine SSC during the first hour after birth in relation to the international standard of immediate, continuous, uninterrupted SSC with the goal of progressing to self‐attached suckling followed by sleep. By using the HCP‐S2S‐IA, the hospital can review practice in order to better understand their barriers to achieving the standard of care and more clearly identify where to direct interventions aimed at improvement.A review of the algorithm Figure  represenHospital practices were also successful at supporting the continuous aspect of SSC. Only one infant was removed and that was for routine care at 50 min. Hospital practices could be reviewed to determine whether staffing issues or staff education would help to ensure continuous SSC for at least 60 min, or until the newborn falls asleep (around 90 min after birth), for all mothers.More than half of the mothers in the Japanese data set were subject to interruption by staff during the first hour after birth. Two of the newborns were moved by the staff. The other five were moved and then latched by the staff to the mother's nipple. We speculate that this may be a result of the historic understanding Step 4 of the BFHI, “Help mothers initiate breastfeeding within a half‐hour of birth.” This could easily be interpreted as assisting a mother to latch her baby within 30 min of the birth. In 2009, WHO clarified this step, emphasizing SSC during the first hour or so after birth, although the wording of the step itself was unchanged .Examination of uninterrupted SSC in the Australian data set indicates that the single mother who did not have her newborn removed for routine care by the staff asked for the newborn to be removed due to nausea. According to analysis, 20 of the 21 Australian newborns were unable to complete at least 60 min of SSC due to hospital policies or routine care. The tool provides feedback to the hospital regarding the current barriers in implementing immediate, continuous, uninterrupted SSC after elective caesarean birth.4.34.3.1The algorithm allows review and deeper understanding of the barriers to best practice of immediate, continuous SSC during the first hour after birth. The first question concerns immediate SSC between the mother and baby. Was the newborn placed immediately (within 5 min) on the mother's chest? What could be preventing this implementation of best practice? This could be the case if the hospital has a protocol, for example, that includes babies born by caesarean in the classification of those who should not be eligible for immediate SSC. This was the case for a number of mothers in the Australian study. Other challenges could be a policy about births that occur in the Emergency Department or if certain anaesthesia was used. Perhaps the hospital has no policy about SSC as best practice, and implementation is based on staff preference or mother request. Does the facility not allow for staffing the required number of nurses to enable SSC? Perhaps swaddling or washing or routinely assessing every baby while on a warming table was required by protocol, or conducted by staff choice, before SSC could be started. These would be included as No: Hospital Policy or Protocol on the algorithm. This categorization could highlight for the hospital the barriers to best practice.None of the separation in our two example cases revealed prevention of immediate SSC due to emergent care for the mother or infant. This would have been the categorization if newborn did not have an initial birth cry or had a low 1‐min Apgar requiring transfer to the NICU team, rather than to the mother's chest, or, the mother has haemorrhaged, requiring the newborn to be placed elsewhere. It is vital for a hospital to recognize if the lack of immediate SSC contact is due to hospital policy or a need for emergent care. Each reflects opportunities for more in depth review or quality improvement projects.The next element of the model considers continuous SSC during the full first hour or so. Continuous SSC is vital for the warmth, respirations, and colonization of the newborn. Because the newborn will need to begin again the progression through Widström's 9 Stages after separation from the mother, any separation can be problematic because the newborn has limited time before falling asleep after birth. It is important to understand why the separation is occurring. Are there concerns about the infant's respirations? Are there concerns about the mother haemorrhaging? These would be examples of Emergent Care. None of the infants in these two examples were removed during the first hour for emergent care. If they had been, it would highlight a concern about the status of the mother and/or infant immediately after birth. Were the newborns removed for routine care? This occurred both in the Japanese data set and the Australian data set. Routine care during the first hour after birth can and should be conducted while mother and infant remain in SSC. This pathway of the algorithm highlights an opportunity for staff education.The algorithm considers the standard of uninterrupted or undisturbed SSC next. Dyads are recategorized if staff interfere with the newborn during the first hour or if the mother or family interferes with the newborn's innate behaviours. This could be subtle or significant. It is possible for staff to shift a newborn, to take vital signs, for mother to eat and shift position all without disturbing the newborn through the progression of the nine stages. It is possible to move the mother from an operating table to the stretcher without separating or interfering with newborn behaviour. On the other hand, it is possible to disrupt a newborn when checking vitals or helping a mother to shift position. Staff gently helping to reposition a newborn's head to maintain a clear airway could be done in a way that does not interrupt the newborn. Flipping a baby over and rearranging the newborn's body could be very disruptive. Staff “helping” the newborn to latch would be considered interrupting, because the SSC standard includes newborn crawling, familiarizing, and self‐attaching. It is this “help” that is highlighted in the Japanese data, presenting an opportunity for staff education on the latest understanding of best practice.The ultimate goal of immediate, continuous, uninterrupted SSC during the first hour after birth is manifested through the instinctive behaviour of the newborn during this time. If needed, this can be observed closely as Widström's 9 Stages. However, even when unobserved, this is the neurological pattern of behaviour that infants progress through during the first hour. Video allows us to examine this closely, but a secure knowledge of the instinctive behaviour allows us to understand when a newborn has, or has not, achieved all of the stages. Each stage is clear, even without close observation. Did the newborn open their eyes? Did the newborn move their arms and shift their body? Did the newborn progress to the breast? Did the newborn lick the nipple? Mothers, partners, and health care providers can know and understand whether the newborn progressed through the stages and achieved suckling and sleeping, without needing to stand over the dyad for the full hour. If a newborn has not achieved these stages—why would they not open their eyes? Why would they not crawl? Why would they not lick? Why would they not suckle?—needs to lead to further examination of these newborns, perhaps by examining their exposure to labour medications  combines Robson's criteria for obstetric classification, parameters for best practice of SSC  along with Widström's 9 Stages in order to evaluate the experience of mothers and babies in the first hour after birth. Although the exemplar sample sizes were small, differences could be discerned, and opportunities for practice improvement can be elucidated. Larger samples with more varied Robson classifications are likely to assist hospital staff further in understanding the barriers within more discrete populations of mothers. Because every birthing facility has unique strengths and challenges, use of the algorithm periodically will allow new barriers to be documented and progress celebrated. This simple algorithm for hospitals to follow could have far‐reaching impact on making practice visible, auditing, and reporting practices enabling the achievement of best practice, as well as providing a consistent measure for future research.The authors declare that they have no conflicts of interest.KB and KC substantially contributed to the creation of the algorithm. JS substantially contributed to the data and analysis, with KB and KC, of the Australian caesarean data into the algorithm. YT substantially contributed to the data and analysis, with KB and KC, of the Japanese vaginal birth data into the algorithm. All authors contributed to the writing of the paper. All authors contributed to the interpretation of the data, drafting and revising the article, and final approval of the version to be published.


Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be expected to acquire its simplest form. However, the lack of a core structure for vortex filaments appears to result in a helicity that does not retain its key attribute as a quadratic invariant. By defining a spanwise vector to the vortex through the use of a Seifert framing, we are able to introduce twist and henceforth recover the key properties of helicity. We present several examples for calculating internal twist to illustrate why the centreline helicity alone will lead to ambiguous results if a twist contribution is not introduced. Our choice of the spanwise vector can be expressed in terms of the tangential component of velocity along the filament. Since the tangential velocity does not alter the configuration of the vortex at later times, we are able to recover a similar equation for the internal twist angle to that of classical vortex tubes. Our results allow us to explain how a quasi-classical limit of helicity emerges from helicity considerations for individual superfluid vortex filaments. Ideal classical fluids possess a number of conserved quantities such as energy, momentum, angular momentum and kinetic helicity. Of these, only energy and kinetic helicity correspond to quadratic invariants in the system. First identified as an invariant for ideal classical fluids by Moffatt234567894He are different, similar knotted vortex excitations would be expected to arise. However, their experimental verification would be more of a challenge since it is only recently that direct visualization of quantized vortices in 4He has become possible using small tracer particlesIf vorticity is concentrated within vortex tubes, the helicity is in part determined by the self-knotting and linking of the vortices within a tangle. In recent years, it has become possible to realize particular cases of knotted vortex tubes produced in water and to study them under controlled conditions in the laboratoryIn contrast to classical fluids, in superfluids, the vorticity is concentrated along line filaments and the circulation is quantized in units of Planck’s constant. Moreover, superfluid vortices are not subject to diffusive processes that are present in classical fluids. Yet, although superfluid vortices appear to resemble vortices of ideal classical fluids, their topology is not frozen into the flow because quantum effects can act to allow vortices to undergo reconnections. In other words, superfluid vortices are not constrained by the Helmholtz laws of vortex motion. Given these observations, it appears that helicity would acquire its simplest form in a superfluid. At the same time, reconnections delineate the boundaries of sharply defined intervals involving constant vortex topologies. This makes superfluids an ideal setting in which to understand properties of helicity and how it relates to the topology of the superfluid vortex filaments.4He. In this case, the vortex core size is of the order of 1 Å. Moreover, since superfluid helium is a liquid, it is much more reasonable to assume that it behaves as an incompressible fluid. The vortex filament model has served as an excellent description to study the dynamics of vortices in this system.Numerical studies of knotted vortex structures have previously been performed using both a hydrodynamic description based on a vortex filament modelSince a vortex filament has no internal structure associated with the vorticity field, there is no notion of the twisting of the vortex lines within the core of a vortex as is the case for vortex tubes with a cross-sectional area characterising the finite extent of the vorticity field. Such a scenario leads to a number of complications when evaluating helicity for a vortex filament. In particular, it would appear that helicity conservation can not be satisfied, even in between reconnection events.In this work, we will show that without introducing the notion of an internal twist, helicity conservation can not be satisfied within the vortex filament model. To introduce internal twist, a spanwise vector must be defined along the length of the filament. We will show that a natural choice is to set the spanwise vector to coincide with a direction of constant velocity potential upon which we are able to recover the key properties of helicity. In superfluids the quantum mechanical phase of the order parameter plays the role of the velocity potential. We note that similar choices have been suggested also by other authors16171820We will begin by recalling some key results concerning helicity in classical fluids. Helicity in fluid dynamics is defined asv = v is the velocity field, and κ. This flux can be identified with the circulation which for quantized vortices is given by κ = h/m. Here, h is Planck’s constant and m is the atomic mass (e.g. of the 4He atom). Following Moffatt and RiccaLij is the Gauss linking number), the writhe where the integration is over the whole space where the flow is defined, ξ so that the position vector of a vortex filament is given by s = s. It is then natural to introduce the Frenet-Serret basis given by c, and torsion τ of each vortex filament:To provide more explicit expressions for these terms, we parameterize a vortex in terms of its arclength i with position vector s by Ci, we can then identify a unit span-wise vector N that determines the twisting of the vortex lines within the vortex tube such thatwhere This vector can be attributed to a ribbon like structure that is oriented with respect to the unit normal and and binormal vectors. With these definitions, the different helicity components can be written as2223The use of the Frenet-Serret equations results in a twist contribution to the helicity that is given byTtors can be evaluated using the local torsion τ(ξ). The last term in Ttw. We note that, since N is defined in terms of the normal and binormal unit-vectors, a constant value of N only implies that the total twist is zero. The internal twist can still be nonzero if torsion is also nonzero.Here the torsion part of the twist N. However, the internal twist depends on the choice for NN is prescribed, the self-linking number for vortex i, which equals Wi + Ti, also becomes a topological invariant. It follows that by redefining N we may designate different values to the helicity.For closed vortex tubes, both the Gauss linking number and the internal twist can only take integer values. The writhe, the Gauss linking number, and the torsion part of the twist do not depend on the way one prescribes the spanwise vector W and total twist T = Ttors + Ttw vary continuously. However, if at some time t = tc a curve passes through an inflectional configuration, i.e., its curvature c(ξ) vanishes at some point ξ = ξc, then the torsion part of the helicity Ttors develops a jump of ±1. At the instant when the curve has a point with zero curvature, the local torsion, τ, diverges around ξ = ξc, but this divergence is integrable. The resulting jump is compensated by a jump in the internal twist of Theoretically it has been shown that under continuous deformation of the vortex tube, writhe φ can be identified with the phase of the order parameter such that When the superfluid is described by a complex wavefunction (order parameter Ψ) then vorticity can arise only in the form of line-like topological defects. For pure line vortices (i.e. neglecting other excitations in the superfluid), the corresponding velocity potential If we ignore compressibility effects and focus on the incompressible motion given by the vortices that correspond to pure line defects, the superfluid velocity can be calculated using the standard Biot-Savart lawr ≠ s (i.e. not lying on a vortex). At a point r = s, the divergent integrand implies that the normal and binormal components of the velocity are not well defined at the vortex line. In contrast, the tangential component of vBS remains well-behaved. This difficulty can be circumvented by regularizing the integral in the vicinity of the point on a vortex as described in the Methods section.where the integration is carried out along all the vortex lines. This equation can be directly applied at any point If the Biot-Savart integral is inserted into the φ in what follows, we will assume this represents only this component of the phase. The direction of the constant phase  of the complex wavefunction has also been proposed by others as a possible direction that can be used to define N for superfluid vortices1617N turns out to be equivalent to using the so-called Seifert framing. .Although a vortex filament has no internal core structure, on physical grounds a vortex is endowed with a scalar field, the velocity potential that permits us to identify a spanwise vector along a direction of constant phase. We note that in order to maintain full consistency throughout our formulation, it is important to work with the incompressible component of the phase (i.e. its divergence free projection). Therefore, whenever we refer to N as defined, it is now possible to recover a torsion and internal twist contribution to helicity. To see how this arises, we note that in the Seifert framing we haveThis particular framing is special because the total helicity is always zero when evaluated in this frame20r* = s + εN represents a point located near a point s lying on the vortex. Here C* given by r = r* the phase is constant so that we can write φ(r*(ξ*)) = φ0, where φ0 is an arbitrary constant. This implies thatwhere C*. In the limit ε → 0, C* and C coincide and the tangent vector C. However, the above cannot be used to deduce that the tangential Biot-Savart velocity along the vortex is zero. This is because, even if the azimuthal component (component around the vortex centreline) of where N given by After inserting the definition for dξ/dξ*.where r = r* are given byWe would expect that the leading order terms for the Biot-Savart velocity at ε → 0, we obtain thatNow substituting θ after calculating the tangential component of the Biot-Savart velocity and the local torsion.This implies that we may obtain the internal twist angle T, defined in To clarify the relation between classical and quantum vortices, in order to establish how a quasiclassical limit can arise from the quantum case, let us consider the scenario of a classical vortex tube with a finite but small cross-sectional area. As shown by Moffatt and RiccaIn the case when the characteristic length scale along the vortex tube is much larger than the vortex core, it may be convenient to use the filament representation and study the dynamics of how the centreline vorticity evolves. However, this filament description of a vortex tube follows from a scale separation assumption rather than being an intrinsic representation of the actual vorticity field. A key difference with a superfluid vortex is that the internal vorticity structure now gives rise to a component of velocity along the centreline of the vortex tube. The total velocity for a vortex filament used to model a thin vortex tube is therefore given byThe additional tangential twist velocity arising from the twisting of the vortex flux lines is given byτ(ξ) is the local torsion at ξ and N describes the rotation of the vorticity fluxlines inside the vortex core, as illustrated in vtwist velocity would need to be constant on each vortex. The helicity conservation would then fix the time dependence of vtwist.Here N is determined by the structure of the vorticity field within the core of a classical vortex and, as such, the helicity is not necessarily the same as for a superfluid vortex.We can now see that if the total tangential velocity is zero everywhere on the vortex, we recover i is obtained using the following equation:By assuming that the helicity would remain zero also for the classical case, and that the twist velocity remains constant along the filament as required by incompressibility, the internal twist angle for vortex i. If we want that the helicity is simply given by linking, one should only replace vBS in i alone, i.e., set Lij = 0.Here T. The difference appears only in the local value of the internal twist angle, i.e., the frame in the classical case is generally different from the Seifert case since it is associated with the structure of the vorticity within the core.Both A, i.e.:Initially, we will focus on idealised vortex configurations to elucidate the different properties of helicity in order to facilitate our understanding of how helicity behaves in more realistic situations. A straight vortex with only an azimuthal velocity field around its core has zero helicity. We will, therefore, consider perturbations on an otherwise straight vortex in the form of a helical Kelvin wave with amplitude z to the arc-length ξ. The unit tangent The last equation relates λ = 2π/k) areIn this case, the local torsion is constant and equal to The value for the writhe implies that the tangential component of the Biot-Savart velocity is constant and given byUsing Ttw = −1 (per period). We note that the formulation given by θ0 = π, the spanwise vector becomesConsequently, for helicity to be zero, the internal part of the twist becomes N does not rotate around the z-axis, as shown in panes a) and c) of Therefore, for small amplitudes m, where the configuration is given byNext, we consider a superfluid vortex ring with one Kelvin mode, ϕ is the azimuthal angle of a cylindrical coordinate system, R is the ring radius, and A is the amplitude of the Kelvin wave. As the amplitude of the Kelvin wave is increased from zero, the standard Biot-Savart velocity vBS produces a nonzero component along the vortex tangent. On the other hand, if there are no other vortices threading the vortex ring, the helicity should remain zero for any Kelvin wave amplitude.Here Ttw as defined must be equal to zero in order for the helicity to remain zero. However, at a critical amplitude of Ac = R/(m2 + 1), m separate inflection points appear where the curvature vanishes and the torsion part of the twist jumps by m due to divergences in the local torsion. [Note that in the article by Moffatt and RiccaAc = R/m2 which seems to be valid only for large m]. This behaviour is illustrated in A > Ac, the internal twist must give rise to a compensating contribution of Ttw = −m to conserve helicity. These observations are also consistent with the predictions of Moffat and RiccaHowever, if we evaluate the local torsion and the writhe we notice that at small amplitudes they exactly cancel each other. This implies that the internal twist N, we can either use θ when using the Seifert frame, m = 3 at various Kelvin wave amplitudes. At the critical amplitude, Ac, the angle θ has a jump of π at the azimuthal locations i = 1, …, m. This jump compensates the jump of −π in the normal N vector varies smoothly as we move along the length of the vortex. The behaviour of the unit vectors N is illustrated in m = 3. We note that in this case, the normal and binormal vectors make three complete rotations around the tangent only for amplitudes above Ac.To determine the internal twist angle (up to a constant), and, therefore, also the spanwise vector, Ttors is not effected and subsequently no changes occur in Ttw. If mutual friction is added into the equations of motion (see Methods), the amplitudes of the Kelvin waves decay with time. This is also accompanied by a decay of internal twist that can be clearly seen in our simulations. An example of a simulation where mutual friction is included for an initial helical vortex ring is presented in the inset of We will now focus on how the different contributions to helicity vary in time under a dynamical evolution of a vortex filament. In particular, we will be interested in an example where the vortex passes through an inflection point as it evolves. One example where inflection points appear is a breather solutionx, y, and z in mm’s), parametrized by t ∈ [0, 2π), is given byWe have also modelled the dynamics of a trefoil knot at zero temperature. The main panel of As for the vortex ring, we observe integer jumps in the torsion even though we are at zero temperature due to the creation of inflection points as can be seen in N in the Seifert frame and the normal vector The behaviour of the spanwise vector The conservation of helicity during vortex reconnections is an interesting topic of its own because in superfluids reconnections of vortex filaments can arise from quantum mechanical effects that are absent in classical fluids. In a microscopic model, such as that given by the Gross-Pitaevskii equation, they are made possible by the “quantum-pressure” term which acts to couple the incompressible and compressible modes of the system. Using the Gross-Pitaevskii model, the effect of reconnections on helicity has recently been analyzed in several papers16171819a0 = 0.0025 mm, which is of the order of the numerical resolution given by the inter-point separation which varies between 0.005 mm and 0.010 mm. A reconnection is then performed when the vortex separation is smaller than 0.004 mm, provided that the total length decreases. Additionally, we have included a rather large mutual friction, α = 1, in order to smooth out the small scale structures.In the vortex filament model, reconnections must be modelled phenomenologically by using a “cut-and-paste” -method. Nevertheless, it is instructive to see what happens when we follow the dynamics through a single reconnection. When reconnections are modelled in this way, the calculation of the local torsion, which requires third order derivates of the vortex positions, becomes numerically very challenging and typically the torsion part of the twist cannot be properly determined. The reason is that in a microscopic model, reconnections lead to strong radiation of sound that dissipates energy of high frequency Kelvin waves resulting in well-behaved dynamics. This physical process is absent in a vortex filament model. In order to reduce the noise when calculating the torsion, we have increased the vortex core size in this simulation to Helicity for vortex filaments we note that a classical vortex tube is well approximated by a bundle of vortex filaments that are aligned to the local vorticity field within the core of a classical vortex. In fact, such a quasiclassical limit of vorticity in superfluids has already been invoked to explain the measured Kolmogorov spectrum in superfluid turbulenceThe above results reveal the consequences of working in the Seifert framing. However, a central question that remains is how would a quasiclassical limit of helicity emerge if we accept that helicity is trivially zero for a single superfluid vortex filament. From our considerations presented in Section Helicity for vortex filaments that for a classical vortex tube, the twist is determined by the vorticity within the core and is unrelated to the Seifert frame. This implies that aside from the microscopic attributes of helicity for a single vortex filament, the quasiclassical limit should give rise to an emergent helicity conservation when the bundle evolves in the absence of reconnections.The bundles (or polarized discrete vortices) are created by stirring the superfluid. Remarkably, once formed, these polarized vortex bundles behave as coherent structures and can persist as has been illustrated from numerical simulations in ref. Methods section. Upon integrating this configuration with the vortex filament model, we evaluated how the centreline writhe and the twist varied with time as shown in Methods section, our results provide direct evidence of the emergence of a nontrivial quasiclassical helicity as an invariant of coherent vortex bundles.To illustrate this behaviour, we have performed a numerical simulation of a bundle consisting of seven vortex rings perturbed with Kelvin waves and twisted 3 times around the bundle centreline, as shown in When decomposing helicity into its constituent contributions, linking number, writhe, torsion, and internal twist, we find that the first three are completely prescribed by the instantaneous configuration of a vortex filament, whereas internal twist requires a spanwise vector to be defined. The sum of the first three contributions is an integer value and varies only when inflection points appear. In that regard, the torsion contribution to the helicity should always be retained when evaluating the helicity of a superfluid vortex which would otherwise never remain conserved under deformations of the vortex (even those that do not form inflection points). This is consistent with the results found in ref. Ttors and the other giving a change of −1. In other words the internal twist remains constant during the LIA dynamics. Inclusion of the internal twist restores helicity conservation even when inflection points are formed. Defining the twist using the direction of the phase precludes the possibility of having an isolated twisted vortex ring. The phase of a twisted circular superfluid vortex would have a singularity at the centre. This is in contrast to the conventional definition of the twist. A circular vortex tube may be twisted, as illustrated by our bundle calculations where the tube was modeled by using seven vortices. The twisting of vorticity lines inside the tube induces a velocity along the vortex, but does not change the velocity potential outside the vortex tube.At zero temperature, the LIA , where only the local term of N that remains well-defined throughout the dynamics and in doing so it restores many of the characteristics of helicity that are known to hold for vortices in classical fluids. Secondly, it ensures helicity is conserved throughout the dynamics for superfluids even during reconnection events even though the different contributions would change to reflect the changing topology of the vortex lines. A consequence of the Seifert framing is that this choice connects the linking with the internal twist. For example, two vortex rings which separately have zero twist, become twisted if linked (e.g. a Hopf link). Thirdly and most significantly, we have shown how a nontrivial quasiclassical limit of helicity can emerge that is independent of the Seifert framing.Whether the Seifert framing for superfluid vortices could be justified from first principles is left as an open question in this work. However, it appears to be a reasonable choice from at least three physical points. Firstly, it provides an unambiguous means to define the spanwise vector The dynamics of quantized vortices is typically modelled with the filament modelvn corresponds to the normal fluid velocity while vs corresponds to the superfluid velocity which is given by vs = vBS + vEx where vEx corresponds to some externally imposed irrotational superflow which we set equal to zero. Both the normal (vn) and superfluid (vs) velocities are evaluated at the vortex (centreline), s, whereas derivatives are evaluated with respect to the arc-length, such that α and α′ represent mutual friction coefficients that depend on temperature and pressure. The effect of the corresponding terms is to damp out excitations such as Kelvin waves on the vortices. For calculations at finite temperature we also ignore the coupling from superfluid vortices on the normal component and take vn = 0. This approximation is especially suitable in superfluid 3He where the viscosity of the normal component is high.Here vBS. This is accomplished by introducing a finite core size cut-off. This way the singularity in the azimuthal component of the velocity  can be avoided and the Biot-Savart velocity at a vortex point becomesSince we need to evaluate the superfluid velocity along the vortex centreline, we must introduce a cutoff to avoid the singularities in the superfluid velocity field arising from the divergent terms appearing in ξ, and the integral omits the short segments l± around the point s. The first term is called the local term and it produces a velocity along the binormal with amplitude proportional to local curvature c = |s″|. The coefficient a0 is the vortex core size and the β-parameter is related to the core structure, being 1/4 for a solid rotating core model (Rankine vortex) and 1/2 for a hollow core vortex. It is tuned such that the local term gives the same velocity for a vortex ring  as that of a classical vortex ring with a similar core structure. The approximation made for the local term is valid when Here the derivates are again with respect to arc-length R = 1 mm, and A = 0.1 mm. The twist of the bundle was achieved by twisting the 6 outermost vortices by 3 times (corresponding to an angle of 6π) with respect to the untwisted bundle, which can be obtained by setting the 6 outermost vortices at directions determined by the constant phase directions of 0, 2π/6, …, 10π/6, of the centre vortex . The twisting angle with respect to this untwisted configuration was chosen to depend linearly on the arc-length along the centreline. The distance of the outermost vortices from the centre vortex was 0.1 mm. Around 7000 points where used to discretise the vortices. These parameters were chosen primarily due to constraints set by the numerics.For the initial configuration we used a bundle of seven vortices where the centremost vortex, which initially is also the centreline, had a shape of the ring with a Kelvin-wave, θ, appearing in During the time evolution of the vortex bundle the centreline was determined by averaging over the azimuthal locations of the seven different vortices. When deformations from a circle are not too large, this approximation is suitable. When evaluating the internal twist for the bundle, the direction of the different vortices with respect to the Serret-Frenet basis of the centreline was determined. In other words, the angle, As long as the bundle remains coherent, the twist of the different vortices remains the same. The only exception was the centremost vortex, which initially determined the centreline. Because the centremost vortex may be very close to the centreline, the twist was determined using only the initially six outermost vortices.How to cite this article: Hänninen, R. et al. Helicity within the vortex filament model. Sci. Rep.6, 37571; doi: 10.1038/srep37571 (2016).Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.