Since two quantum states that are local unitary (LU) equivalent have the same amount of entanglement, it is meaningful to find a practical method to determine the LU equivalence of given quantum states. In this paper, we present a valid process to find the unitary tensor product decomposition for an arbitrary unitary matrix. Then, by using this process, the conditions for determining the local unitary equivalence of quantum states are obtained. A numerical verification is carried out, which shows the practicability of our protocol. We also present a property of LU invariants by using the universality of quantum gates which can be used to construct the complete set of LU invariants. Quantum entanglement is one of the most extraordinary features in quantum information science, and quantum entangled states have become the most important physical resource . In partDefinition 1. Let ρ and for some unitary operators At present, there are many results on LU equivalence and LU invariants ,22,23,24In this section, we will present a sufficient and necessary condition for the existence of the unitary tensor decomposition of an arbitrary unitary matrix. We start with the bipartite decomposition.U and V as W. Then, according to the tensor product of matrices, one obtainsSet We have Thus, we setU and V are arbitrary For unitary matrix W be any To summarize, let Theorem 1. If V as klW are the block matrices of W, andTo simplify the expression, we set We can obtain Without loss of generality, one still sets Thus, we haveThen, by using the decomposition scheme in One can then derive the decomposition scheme of We use the rand function in MATLAB to generate a random matrix ,26. ThisExample 1. As an example, let us consider the tensor decomposition of the following unitary matrix:which is generated randomly by andAccording to the previous analysis, W can be decomposed as andExample 2. We consider a andwhich is randomly generated byAfter numerical verification, the unitary tensor decomposition The Matlab code is supplied in the The key to investigating the local unitary equivalence of quantum states lies in the unitary tensor decomposition of the corresponding unitary matrix. In this section, we present a general method to determine the LU equivalence of any pair of non-degenerate quantum states by the unitary tensor decomposition protocol derived in the above section.Let To certify that In the following, we consider bipartite quantum systems as an example. The processes of judging the local unitary equivalence of quantum states are as follows:W can be decomposed into the tensor product of two unitary matrices, such as Example 3. We consider two quantum stateswith spectral decompositions Then, the matrix Therefore, the quantum states ρ and σ are local unitary equivalent.f is an LU invariant, then for any quantum state U and V, it satisfiesG be the set of all “single-qubit” and n qubits can be implemented using a circuit containing G. Then, for any unitary matrices U and V, there exist unitary matrices Let nd so on . Let G bTheorem 2. A function f is an LU invariant if and only if f is invariable under LU operations of the form Proof. U and V can be rewritten as I can be used as a complement. We haveThe “only if” is obvious. For the if part, one has to prove that the following equationIn this paper, we have studied the local unitary equivalence of quantum systems from the perspective of unitary matrix tensor decomposition. We have presented a detailed process to find the unitary matrices in the tensor decomposition of an arbitrary tensor-factorable unitary matrix. We have also derived a property of LU invariants that may be used to find a complete set of LU invariants.It should be noted that our schemes are convenient to discuss the local unitary equivalence when the number and the dimension of the subsystems are small. As quantum systems get more complex, the amount of computations increases exponentially. Therefore, we need to further find more convenient and efficient strategies to judge the local unitary equivalence of multipartite high-dimensional quantum systems.


Bubbles in air are ephemeral because of gravity‐induced drainage and liquid evaporation, which severely limits their applications, especially as intriguing bio/chemical reactors. In this work, a new approach using acoustic levitation combined with controlled liquid compensation to stabilize bubbles is proposed. Due to the suppression of drainage by sound field and prevention of capillary waves by liquid compensation, the bubbles can remain stable and intact permanently. It has been found that the acoustically levitated bubble shows a significantly enhanced particle adsorption ability because of the oscillation of the bubble and the presence of internal acoustic streaming. The results shed light on the development of novel air‐purification techniques without consuming any solid filters. This work reports a new approach to stabilize bubbles that by using acoustic levitation combined with controlled liquid compensation the bubbles can remain intact permanently. The acoustically levitated bubble shows a significantly enhanced particle adsorption ability which shed light on the developing of novel air‐purification techniques without consuming of any solid filters. A single bubble is used to measure trace levels of sulfur dioxide, due to the increased conductance of bubbles when exposed to low concentrations of sulfur dioxide gas. It can also be used to detect methamphetamine in aerosols by electrical analysis of the bubble wall. Because of the excellent adsorption ability of the gas–liquid interface, air bubbles were used for adsorption of aerosol particles, which showed the promising application of bubbles for air purification.Bubble films play important roles in many natural and industrial processes because they provide unique boundaries for the related heat and mass transfer.1 For  which is dependent on the viscosity of the solution, the type of surfactants, and bubble size. To enhance the bubble lifetime, various types of approaches have been utilized to restrain the liquid drainage in the bubble film, such as introducing surfactant, electrolyte, and colloidal particles. However, these approaches inevitably cause “contamination” of the bubble because of the introduced stabilizer. Alternatively, the bubbles or foams can also be stabilized by sound field using acoustic levitation, which provides a contact‐free stabilization mechanism to the bubbles or foams, through suppression of the liquid drainage.Regarding these applications, stable bubbles with retarded bursting are highly desired. However, the lifetime of the conventional “soap” bubbles is usually only a few seconds, because of gravity‐induced liquid drainage,6, 7Until now, bubbles of sufficiently long lifetime and without any chemical stabilizers are still a technical challenge. In the present work, we propose technique to fabricate never‐bursting bubbles via acoustic levitation and controlled liquid compensation. Owing to the elimination of capillary waves on the bubble surface by the liquid compensation, the acoustically levitated bubbles can remain intact permanently. The never‐bursting bubble shows enhanced aerosol particle adsorption and provides a promising platform for air purification.22.1Figure in which the acoustically levitated drop was flattened into a thin film by enhancing sound intensity. The liquid film was dragged by a needle from its center to form a sound cavity  bubble, it can last over tens of minutes, more than one order of magnitude longer than that without sound stabilization  and bottom (l = 0) remained constant during levitation (20 min) , where the sound potential well was located and resulted in the liquid accumulation. The thickness reduction at the equator region is probably due to evaporation, where the evaporation rate is fastest.In this work, the drops and bubbles were levitated and manipulated with a single‐axis acoustic levitator  Figure , indicatPA exerted on the bubble surface were calculated  of the bubble film would be adjusted upon the variation of acoustic power. Moreover, sufficient high sound intensity often results in atomization, which eventually leads to bubble rupture. On the contrary, too low sound intensity generates insufficient acoustic radiation force and the levitation would be easily disturbed. Therefore, in the experiments, the sound intensity was adjusted to an optimized level against both atomization and external disturbance.The acoustic power plays a crucial role in levitation stability. On one hand, the equilibrium shape of the levitated bubble and local curvature of the bubble film are determined by the competition between surface tension and acoustic radiation pressure:2.2 Moreover, the existence of acoustic streaming around the levitated drop may facilitate its evaporation, especially at the drop equatorial region, which is also confirmed by the experimental observation in present work 1/3fc−2/3) around 109 µm. The density ρ and kinematic viscosity υ of SDS solution in the experiment are 994 kg m−3 and 1.157 × 10−6 m2 s−1, respectively, and the surface tension σ is 32.55 mN m−1. Equation pcpc decreases linearly with the thinning of the film  control for the pump motor, G is the current MGV value, and tG is the threshold value (185 in the present work) before the emergence of capillary waves. By utilizing the liquid compensation system, a SDS bubble can remain intact for approximately half an hour, which has experienced three evaporation–compensation cycles. The results hint the acoustically levitated bubble can remain intact permanently as long as the working time of the system.Since the status of the levitated bubble, i.e., the emergence of capillary waves on bubble surface can be detected by the MGV value Figure , we furt2.4 we thus explored to use the liquid film of the acoustically levitated bubble as a collector for aerosol particles. Because of the superstability arising from sound field, the levitated bubble was able to survive from puncturing by a needle yet remain intact  Stage I, the particles reach and contact the bubble surface driven by the acoustic streaming. 2) Stage II, once in contact with the bubble surface, the particles are trapped at the air–liquid interface. For Stage II, the liquid type as well as SDS concentration plays a role because of the varied surface tension, viscosity, etc. However, it should be noted that for the aerosol particles all the liquids can enable sufficient fast trapping and irreversible adsorption.5 Ther plays an essential role to accelerate the contact between particles and bubble surface, which is not sensitive to the bubble size and liquid type. The injected particles circulated with the acoustic streaming, during which the particles impinged onto the bubble at a speed ≈0.01 m s−1. Once the imping particles contact with the air–liquid interface, they can be adsorbed within 0.1 ms. Moreover, the levitated bubble usually rotates around the vertical axis, which further enhance the mass transfer between the bubble surface and the injected aerosol gas.We have found that the acoustic streaming inside the bubble, which was aroused from bubble oscillation,33 plaBased on the facts that acoustically levitated bubble has extraordinary particles adsorption ability and the never‐bursting bubble technique, we proposed a potential air‐purification system by using a levitated bubble as a filter element Figure . Since t3In summary, we have achieved extraordinary stability of bubbles by using acoustic levitation combined with controlled liquid compensation, through which the bubbles can remain unburst permanently. In addition to sound field induced bubble stability, the critical novelty of our technique lies in the suppression of capillary waves on the bubble surface via liquid compensation thus preventing the atomization and bubble rupture. The extraordinary stability and ever‐lasting life of the bubble enable them to be used for aerosol particle adsorption. It has been found that the adsorption in the acoustically levitated bubble is significantly enhanced due to the bubble oscillation and the internal acoustic streaming. Based on these results, we have proposed an air purification system, in which polluted air was injected into the levitated bubble, purified by the bubble films and the clean air was collected in a controlled manner. Our work provides a reference for the fabrication of never‐bursting bubbles and sheds light on the developing of novel air cleaners using bubble film as filters.4 The bubble was trapped at one of the sound pressure nodes in the levitator. The sound field was adjusted to a suitable intensity to enable satisfactory levitation stability in which the levitation position did not show noticeable horizontal or vertical shift.A single‐axis acoustic levitator  comprising a transmitter and reflector . Thus, the position and distribution of the illuminated film were determined by the laser sheet, not the camera. On the other hand, the depth of focus of the cylindrical lens is 28 mm, which is larger than the diameter of the bubble, to ensure the thin laser sheet has uniform thickness at the focus. The image of bubble film profile was captured by a high‐speed camera . The thickness of bubble film was measured using a software called ImageJ, after calibration in the software.To build the relation between the bubble image and the associated physical/chemical processes, it is necessary to obtain the MGV of the images. The images were captured by the high‐speed CCD camera. To ensure the reproducibility of MGV, the photographic process was conducted at a fixed illumination condition by using a stable LED light source. A real‐time processing algorithm running on the control computer was written with OpenCV library to get the bubble contour. The photos were transferred into a 256 gray‐scale image via gray processing, where the gray value is 0 for black pixels and 255 for white pixels. The MGV of the bubble was obtained from the integration of the corresponding pixels in the contour area.GT, a push of the peristaltic pump was triggered and a droplet of ≈5 µL was squeezed out. It is worth noting that in order to avoid possible destabilization caused by the liquid compensation, the introduced droplet was moved slowly to contact the bubble to realize a moderate coalescence. The threshold MGV GT was set below the MGV corresponding to the appearance of capillary waves.Liquid compensation to the acoustically levitated bubble was realized by depositing a droplet using a microsyringe connected with a computer‐controlled peristaltic pump Figure . The com−3) was generated by an aerosol generator  and injected into the acoustically levitated bubble using a microsyringe connected with a computer‐controlled peristaltic pump. The needle was inserted from the top of the bubble, and penetrated the bubble film without rupture because of the superstability arising from sound field. Aerosol particle adsorption was detected by the changes in bubble transparency, which is represented by the MGV of the images. The purified air was collected and analyzed by an aerosol analyzer .The aerosol gas  wasπ2af2A , the reflector was set as a rigid boundary, and the side wall of the levitation zone was set as a radiation boundary.The sound field in the ultrasonic levitator and the sound radiation pressure on the bubble surface were calculated using the commercial finite element software COMSOL Multiphysics 5.6. A 2D axisymmetric model (frequency domain) was used in the calculation, and the physical field control grid was set as the “finer grid” built in the software. The simulation range was determined by the geometry of the levitation space. The boundary conditions of the levitation zone were set separately, i.e., the normal acceleration at the emitter was calculated as 4ρ0 = 1.18 kg m−3, sound velocity c0 = 346.12 m s−1). According to the levitation position and shape of bubbles in the ultrasonic field, the corresponding bubble model was constructed, and its boundary condition was set as a continuous boundary, which is determined by the acoustic impedance mismatch between the two phases separated by the interface. However, for the calculation of the sound field inside the bubble, the impedance of the bubble film (air–water interface) cannot be set according to the impedance mismatch between water and air because of the oscillation or even resonance of bubbles in the sound field. This suggests that the acoustic impedance of the bubble film, which can be estimated from the mean density of the bubble over its whole volume instead of the density of liquid in the film, may be appreciably reduced.In the levitator, the acoustic medium was air  velocity of the medium.The sound pressure and sound pressure level were obtained by solving the Helmholtz equation in the acoustics module of the software. According to King's theory,35 theFA, which is the integral of PA exerted on both the inner and outer surfaces of the bubblem is the mass of the bubble, and g is acceleration of gravity.The weight of the levitated sample is balanced by the acoustic radiation force The authors declare no conflict of interest.Supporting InformationClick here for additional data file.Supplemental Movie 1Click here for additional data file.Supplemental Movie 2Click here for additional data file.Supplemental Movie 3Click here for additional data file.Supplemental Movie 4Click here for additional data file.


The electrical resistivity data obtained was found to be at least two orders of magnitude higher than the limited data available in the literature. Challenges in the resistivity cell’s development and performance are discussed, with a focus on various propellants and their mixtures with ethanol and moisture concentrations. The resistivity of propellant mixtures containing moisture concentrations ranging from 5 to 500 ppm and ethanol concentrations ranging between 1000 and 125,000 ppm was determined. The resistivity was tested across 10-min and 1-h periods and was performed in accordance with the contemporary IEC 60247 standard.Metered-dose inhalers employ propellants to produce pharmaceutical aerosols for treating respiratory conditions like asthma. In the liquid phase, the DC volume resistivity of pharmaceutical propellants, including R134a, R152a, and R227ea, was studied at saturation pressures and room temperature (not vapour phase). These measurements are essential for industries like refrigerants. Aerosols from metered dose inhalers (MDIs) with these propellants become electrically charged, affecting medicament deposition in lung. The resistivity was measured using a novel concentric cylinder-type capacitance cell designed in-house. The resistivity for the propellants  was found to be 3.02 × 10 Such HFCs were developed to overcome environmental issues associated with the use of chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs), as the chlorine in those molecules is responsible for the depletion of the ozone layer. Besides their application in MDIs, they are also used as refrigerants2. It has been recognised that when these inhalers deliver the aerosols, they become electrically charged. Consequently, the medicament deposition in the human lungs is also influenced by the level and polarity of the charge. The resistivity of the propellant, which typically makes up more than 99% of the inhaled dose, is an important aspect for understanding the extent of charging in aerosols delivered by such devices3. Higher resistivity limit charge dissipation in the propellant, causing charge to accumulate4. Suspensions used in MDIs contain micron-sized drug particles suspended in the propellant, while in solution MDIs, the drug is dissolved in the propellant using a cosolvent. The main co-solvent in MDI formulations is ethanol to increase drug or excipient solubility5. A thorough understanding of these mechanisms requires systematically studying the materials and processes involved. Such an understanding may enable one to control the charge-to-mass ratio of the aerosol to achieve site-specific lung deposition of the active pharmaceutical ingredients (API).R134a  in different applications, particularly under the strong impetus of the EU F-gas regulation and the 2016 Kigali Amendment of the Montreal Protocol to phase down the global use of high-GWP HFCs14. Understanding the resistivity of R152a in relation to R134a and R227ea is, therefore, critical to further adopting R152a and determining its potential as an inhaler propellant. Moreover, R152a is a flammable substance; therefore, there is a risk of the propellant catching fire during the actuation of an inhaler if substantial charges develop, making it imperative that the resistivity is accurately determined to prevent such a scenario from occurring. Determining the volume resistivity of the propellants with mixtures of moisture and ethanol would also significantly help further our understanding of the properties of inhaler formulation and potentially improve them due to ethanol and moisture being widely used as cosolvents. The aim of this study is to design a novel resistivity cell capable of measuring high resistivities while ensuring the experimental process minimises contamination of samples to determine propellant resistivities with more precision and accuracy than previous studies. It is also to collect data on the propellants and their mixtures with ethanol and moisture with respect to their resistivity in the liquid phase at room temperature.R152a possesses a global warming potential (GWP) substantially lower than the R134a and R227ea HFCs15. The volume resistivity expressed by Eq. . This constant convert measured resistance to resistivity. The accurate value of this constant is found experimentally using calibration liquids with known resistivity. This is essential because the electrode's geometrical surface area often differs from the electrochemical area where electron transfer occurs in liquid dielectrics17.The factor 18. This is the time interval for the charge carriers to cross the interelectrode gap filled with the propellant. When a DC potential difference, V, is applied between the electrodes separated by a distance, L, the charge carriers will move in a uniform electric field, E, which is given by Eq. (The charge carrier’s mobility can be determined using the time-of-flight (ToF) methodn by Eq. :3\documeThe propellants in liquid form under pressure behave as dielectric liquids. The charge carriers will be randomly distributed in the bulk of the liquid. When an external electric field stresses the liquid, the charge carriers will start moving across the electrode gap and manifest as electric current. This current can be measured using an electrometer connected in series with a liquid-filled gap. A single current peak will be registered if the dielectric liquid contains charge carriers with the same polarity. The magnitude of the drift velocity of the charge carriers, v, within the electrode gap, can be obtained as follows:The drift velocity is also proportional to the field:Suppose the applied electric field is not strong enough to generate new charge carriers through ionisation or dissociation processes in the liquid or by injecting electrons from the cathode into the bulk liquid. In that case, the conduction current is defined by the movement of charge carriers that already exist in the liquid, and the current will demonstrate Ohmic behaviour; the current, I, is proportional to V.19. The outer housing exists primarily to ensure the firm positioning of the cylindrical electrodes. It also serves to improve safety by protecting the user from the electrodes and shielding the signal from stray electric fields external to the cell that may affect the measurement.The resistivity cell consists of concentric cylinders enclosed by an outer stainless-steel housing with custom stainless-steel flanges mounted to both ends see Fig. A and B. 20.The electrodes are constructed from stainless steel 316 (SS316) and subjected to electro-polishing to ensure the metal in contact with the fluid possesses a smooth surface. Moreover, the calculations according to BS EN 13480‑3:2017 suggest the design configuration is able to withstand a theoretical maximum working pressure of 9.08 MPa21.The electric field within the resistivity cell was calculated using a simplified model on the COMSOL Multiphysics  software with the finite element method. The simulation was used to determine the length of the guard electrodes when facing the cathode, at which the measuring volume would possess a homogenous electric field. The minimum length was determined to minimise the volume of fluid required for each test and was found to be around 5 mm at each end of the measuring electrode. The boundary conditions were assigned to the model, with the anode assigned a 500 V electric potential and the other cell components outside the fluid being grounded. The maximum electric field strength determined by the simulation within the cell was around 600 kV/m, much higher than the average field strength of 250 kV/m within the measuring volume. The model was meshed and solved for its electric potential distribution in the geometry. Poisson's equation for electrical potential (φ), denoted in Eq. , was solg to Eq. :8\docume22.The simulation was performed assuming that space charges were absent and the resistivity of the liquid was homogenous. The electric field is homogenous within the measuring volume while being significantly distorted at the bottom region between the electrodes and the EPDM seal and at the top of the anode, as shown in Fig. The 500 ml whitey cylinders were pre-dried in a drying oven set at 102 °C and left overnight to remove any contaminants, including moisture. They were then removed from the oven, set to one side, and allowed to cool. They were then fitted with a blank at one end and a ball valve at the other (so that long syringe needles could be inserted directly into the centre of the cylinder). They were then evacuated, filled with either 152a or 134a to ‘condition’ the metal surface with the existing moisture contained within the propellants, and left overnight in the lab at room temperature.23. A small amount of the activated sieve was added to an amber glass bottle and then filled with absolute ethanol. The bottle was then shaken by hand before being stored in a desiccator overnight in the lab. The moisture content of the ethanol was re-determined by injecting it again into the Karl Fisher apparatus. If the ethanol was not sufficiently dry, then more of the pre-dried molecular sieve was placed into another amber glass bottle, and the dried ethanol was decanted into the bottle and left in a desiccator overnight.A molecular sieve  was placed in a suitable container, connected to a 400 ml/min nitrogen purge, and put into an adapted drying oven. The oven was switched on, and the temperature was ramped up at 60 °C per hour to 300 °C to dry and activate the sieve. The oven was then switched off and allowed to cool. A bottle of absolute fresh ethanol was opened, and water content was pre-determined via colorimetric titration (Karl Fischer titration) by injecting it into a Mitsubishi Chemical Analytech CA-310 moisture metre in accordance with ASTM-D1533The moisture content was then analysed using the Karl Fisher apparatus, and the clear liquid was decanted into a glass sample bottle fitted with a crimp-type septum. It was stored in a desiccator until needed.The sample cylinder was evacuated, and a septum was added to the ball valve beneath a Swagelok nut. The required amount of ethanol was measured in an appropriately sized microlitre syringe, and the weight was recorded before injecting it into the cylinder through the septum and valve into the cylinder. The syringe was re-weighed, and the weight difference injected was recorded. The septum was detached, and the cylinder was plunged into liquid nitrogen for one minute. It was then weighed before attaching a 134a and 152a supply cylinder. The valves were opened, and liquified propellant was transferred into the cylinder. The sample cylinder was detached and re-weighed to determine the amount of 134a transferred. If the weight recorded was below the required amount, the transfer method was repeated until the correct amount of 134a had been deposited into the sample cylinder. The cylinder was put aside for four days to reach room temperature and to condition the metal surface again before analysing the contents for moisture.This preparation was similar to the procedure described above, with the exception that water was delivered into the cylinder via a microliter syringe with the liquefied propellant. If the moisture content was below the levels calculated, the cylinder contents would be emptied, and the procedure would be repeated. The water concentration in this study is expressed as parts per million (ppm), defined with respect to the mass.To calculate the resistivity, a voltage of 100 V DC was applied to the 2-mm gap for 10- and 60-min intervals, leading to an average field strength of about 50 kV/m, with the final current being used after a steady state had been achieved, indicating that the charge carriers have reached dynamic equilibrium.–2 Torr) and then inserting the liquid propellant. The measured values allow one to easily discern whether the propellant is in its gaseous or liquid state, as they differ by orders of magnitude.A voltage of 100 V was applied due to void the dielectric breakdown, safety concerns, and to comply with the IEC standards. Initially, the current was measured for 10-min intervals before increasing the interval to an hour. The HFCs were also investigated at commercial-grade purity, with > 99.9% for R134a, R227ea, and R152a. However, it should be noted that these propellants are hygroscopic, and both commercial and pharmaceutical-grade samples may contain about 10 ppm of moisture. The procedure used involved purging the cell with nitrogen before vacuum pumping the cell with an ultimate vacuum pressure of 6 Pa  was filled to its maximum safe volume (400 ml) with propellant. The transfer cylinder was evacuated with a vacuum pump before filling. Then the cylinder was briefly chilled in liquid nitrogen to cool, using thermal gloves and goggles. The transfer cylinder was then filled from a larger cylinder before weighing it. The cell was then purged with nitrogen gas for 10 min, which helped to remove moisture and oxygen. The cell was then evacuated with a vacuum pump for 30 min using 10A scale was used to determine the volume being filled. The pressure and temperature were measured from the refrigerant gauge, and the cell wall temperature was noted down using a RS pro 206-3722 temperature sensor. The electrometer and voltage source was connected to the cell using crocodile clips, and 100 V was applied from the voltage source. The electrometer was connected to the LabVIEW  program on the laptop, and the current was measured over time. The final current measurement value was used to calculate the resistivity; after the initial peak, the current decayed and reached a steady state where the charge carriers reached dynamic equilibrium. The tests were measured and repeated at least three times at room temperature (21–23 °C) and various humidities in the lab. The propellant was then evacuated into a ventilated fume hood. The device was enclosed in a grounded metallic cage that served as a Faraday cage to prevent electromagnetic fields from affecting the results. It also helped to protect the user from experiencing an electric shock during the experiment in the event of accidentally touching the electrified pipe at the bottom that connects to the anode. The cage was set up so that the power source turns off if it is opened while the voltage is on. The propellant mixtures with ethanol and water were also tested in the same way, with the mixtures tested in order of smallest concentration of ethanol  or water  to highest. Before testing each concentration, the cell was purged with nitrogen, and the vacuum pump was used to empty the cell.The electrical resistivity was determined for three of the most widely used substitutes for CFC and HCFC propellants. After the DC voltage was applied, the recorded current decreased after an initial spike due to polarization effects. Transient charge-carrier drift processes occur due to ions being attracted to or repelled from electrodes based on their polarity. Figure Our tests have shown that stable measurement values could be taken after 10 min and that extended stress does not lead to significant further change. The tests are labelled by the order in which they were performed. It can be seen that the current values measured tend to decrease slightly as the order of the tests increases. This may be because the cell gets flushed with each test with the propellant, and some impurities get removed, leading to measured smaller current values. The measurements were repeated at least five times. Similar diagrams are observed for each of the propellants. The graphs tended to peak with a few hundred nA, with R134a tests peaking at higher currents when the voltage source was switched on at around 2000 nA before stabilising at approximately 50 nA. The 134a tests peaking at higher current values may be because these tests were conducted earlier than the other propellants; therefore, contaminant concentrations may have been slightly higher before being flushed after repeated trials. Initial tests for each propellant tended to peak much higher and settle at slightly higher current values after 10 min. It may be wise to repeat the tests more times until the readings stabilise and discard initial test results due to contaminant fears to attain more reliable results.The ToF, is determined from the time interval between when the voltage is applied first to the moment of the peak current. The value obtained for all three pure propellants is 1 ms, limited by the time resolution of the current measurement. The charge carrier mobility is then calculated as Figure 2H4F2  ∙ 1010 Ωm, and (2.37 ± 0.4) ∙ 109 Ωm, respectively. The uncertainties quoted are the standard deviations from the set of measurements taken.The tests were repeated at least three times due to the limited number of samples available. The resulting values of the resistivity for pure R134a, R227ea, and R152a, defined as the mean of the 10-min interval measurements, are (3.02 ± 0.18) ∙ 10Several small instrumental uncertainties limit the measurement. There is a 0.2% uncertainty in the current measured by the electrometer; the cell constant has an assumed uncertainty of 0.5%; and the applied voltage value has an uncertainty of 1%. Using Gaussian error propagation, the resistivity has a total instrumental uncertainty of about 1.1%. This is smaller than the standard deviations quoted above; the measurement is, therefore not dominated by instrumental uncertainties.9 analysed liquid R134a at varying temperatures. His results indicate that the resistivity of R134a is temperature-independent and in the order of 108 Ωm. However, our measured values are on the order of 1010 Ωm for ambient temperatures and saturation pressures for liquid phase measurements. A similar trend is observed when comparing the results to those obtained by Fellows et al.8. The measurements for R152a, which were performed to serve as a reference, correspond well to existing data. However, the measured value of the DC resistivity for R134a is about a factor of 45 higher.Table As the resistivity is highly dependent on the water content and other impurities of the tested substance and the value of the applied field strength, such deviations are not unusual. The maximum water content present in our propellants, according to the manufacturer’s specifications, is about 10 ppm. As described above, the measurement’s uncertainties are assumed to contribute further to the detected deviations.Maintaining the quality of the test fluid sample is very important because its electrical properties are susceptible to contamination and impurities. This is one of the reasons why it is very hard to compare measurements from various researchers because of differences in the purity level of the test fluid sample. Also, comparing properties between researchers can be difficult because the temperature and pressure are not always given.There are several reasons for these significant discrepancies; one is possible impurities. Water content, for example, strongly influences the resistivity; the resistivity decreases when water is added. This study prepared the samples very carefully to minimise moisture contamination. Also, before the propellants were inserted into the cell, the transfer was handled with additional precautions: a heat gun was used on the transfer cylinder, and its nuts were loosened to evaporate and flush out any residual moisture. Moreover, no plastic pipes were used as all these HFAs are considered highly hygroscopic and can even make plastic parts more likely to introduce water via diffusion phenomena. The maximum water content present in our propellants, according to the manufacturer’s specifications, is at most 10 ppm.The resistivity also tends to be a strong function of the electric field. Lower test voltages can be another reason for higher resistivity measurements compared to previous researchers. But in this measurement, applying voltages above 100 V was impossible due to spacing between anode and cathode (2-mm) to avoid dielectric breakdown.9 used a modified cell arrangement according to IEC 60247 without guard ring. The absence of a guard ring forced him to calibrate the test cell with a well-known liquid in advance.Additionally, there are differences in the experimental setup. FejaTo summarise, several factors make comparisons to other experiments difficult: the purity level of the test fluid sample directly influences electrical properties, but temperature, pressure, and applied voltage values also have an impact. The improved and custom-designed cell used for this measurement is also likely to contribute to a more accurate result than the literature.8 and Feja9 studied the DC resistivity of pure R134a and R152a. However, this study presents further information regarding the resistivity of mixtures of propellants with moisture and ethanol.Fellows et al.+ and hydroxide OH−. The hydrogen ions react with the water molecules at a low rate, forming hydronium ions, H3O+. These charge carriers reduce the resistivity and will then respond with the electrons from the cathode and anode, forming dihydrogen H2 and water H2O and oxygen O2.Figure The values for 134a water concentrations can be seen to decrease exponentially in resistivity with increasing water concentrations before levelling off at 500 ppm of moisture. There is an initial significant decline in resistivity between the pure propellant and the addition of 46 ppm of moisture, resulting in order of magnitude decrease in resistivity. The graph for 152a and moisture shows a similar pattern with similar resistivity values for the different moisture concentrations, where the concentration of 900 ppm of moisture showed a resistivity value that had plateaued relative to the 500 ppm value. This plateau shows that added water concentrations may no longer significantly affect the resistivity of the mixture. This may be due to added water concentrations that cause the resistivity to approach the value for water.As has already been observed in Fig. The HFC molecules cluster around the charged ions, but for 152a the ionic solvated cluster is smaller than that for 134a. This means that drag against the rest of the liquid medium as the ion moves in the cell field will be less, and the ionic velocity will be higher, leading to a higher cell current and lower resistivity for 152a.24:Figure 3CH2OH2+ and CH3CH2O− will lower the energy of the carried charge by virtue of the larger molecule, providing a considerable redistribution of the charge by polarising the bonds within the molecule. Ethanol charge dissipation is more potent than HFC solvation, meaning at low ethanol concentrations (less than 1%), the ions are surrounded by a much smaller HFC solvent cage, which is also more tenuously attached. But when ethanol concentration rises, a ‘hybrid’ solvation is formed, where both HFC and neutral ethanol molecules make up the solvation cage.The two ions CHAs displayed in Fig. An explanation for the plateau and subsequent rise of resistivity for larger ethanol concentrations can be found by assuming that the rate at which negative ethanol ions are created slows down and is no longer proportional to the ethanol concentration.25 is a weak form of coupling between polar molecules; in this case, the partially negatively charged oxygen ion will bond with the partially positively charged hydrogen ion of another ethanol molecule. Hydrogen bonding is enhanced for the negatively charged ethanol ion CH3CH2O− because the oxygen carries an even larger partial negative charge.Instead, hydrogen bonding will occur with an increased presence of ethanol molecules, both for neutral ethanol molecules and for ethanol ions. Hydrogen bondingConsequently, larger clusters of charge carriers and a larger solvent cage are formed, and their ionic mobility and drift velocity drop; hence, this new dynamic state increases the resistivity of the propellant mixture. Further studies with varying temperatures and larger sample sizes should be conducted to more precisely estimate the concentration at which the plateau and turn-around effects occur.The ToF for the mixtures was estimated as previously for the pure propellants by determining the time interval between when the voltage was switched on and when the peak current occurred. The current as a function of time was measured at least three times for each concentration value. However, the result is again limited by the time resolution of the measurement and was therefore again determined as 1 ms, leading to the same drift velocities of In Fig. Knowing precisely how moisture and ethanol content influence resistivity can help improve medical inhaler formulations and increase their effectiveness. The resistivity of the propellant used in MDIs must be controlled and maintained at a fixed value; otherwise, an electrical charge will accumulate, which will prevent the uniform dissipation of the drug aerosol and limit the deposition of the pharmaceutical in the human lungs. More studies are needed to quantify the dependence of the electrical properties of propellants on a variety of conditions, for example, different temperatures and air humidity levels.Furthermore, the studies performed with 152a are crucial to assessing its potential to be used as a propellant in MDIs, replacing 134a and 227ea in the future. The risk of being ignited during charge accumulation must be minimised, and therefore the resistivity properties of the pure substance and in mixture with water and ethanol have been extensively investigated. The sample provided by the sponsoring pharmaceutical company and we have no control over the range for extension. That is the reason the values for the range are different.10 Ωm, 1.31 × 1010 Ωm, and 2.37 × 109 Ωm, respectively. The resistivity values are generally higher than those quoted in the literature, which is attributed to several factors, such as higher purity, custom cell design, and an improved experimental process. The resistivity was also measured for mixtures of propellants 134a and 152a with different water and ethanol concentrations. It was observed that the resistivity dropped with increased moisture content. The dependence of the resistivity on the ethanol concentration was found particularly interesting. The measurements showed that adding ethanol caused a significant reduction in resistivity values for mixtures up to around 4% concentration, after which the resistivity values plateaued and even began to increase. This suggests that a specific concentration range of ethanol can significantly alter the electrical properties of these propellants. The reason for that is the formation of large molecule clusters and solvent cages that limit the mobility of charge carriers and thus increase the electrical resistivity.In conclusion, the resistivity of propellants, including 134a, 152a, and 227ea, and their mixtures with different concentrations of ethanol and water were examined using a novel device developed for this study. The measured resistivity values for pure R134a, R227ea, and R152a were found to be 3.02 × 10The findings of this research can contribute to developing more efficient and effective propellants for various industrial applications, such as metered-dose inhalers. Precise knowledge and control of the resistivity can avoid charge effects, which would be detrimental to consistent lung deposition of drug aerosols. Future studies may investigate the effects of other additives and their concentration ranges on the resistivity of propellants to enhance their properties for specific applications. These measurements are experimentally very challenging. It is crucial to minimise the contamination of the samples with moisture, and the pressure in the cell must remain stable to ensure the propellants stay in liquid form, avoiding vapour formation. Therefore, improvements to the experimental setup should also be the subject of future studies.Supplementary Figure S1.


Patient and Public Involvement (PPI) in research has become a key component recommended by research commissioners, grant award bodies and specified in government policies. Despite the increased call for PPI, few studies have demonstrated how to implement PPI within large‐scale research studies.The aim of the current study was to provide a case example of the implementation of a patient advisory group in a large‐scale mental health research programme (PATHWAY) and to benchmark this against UK standards.A PPI group was incorporated throughout the PATHWAY research programme, from grant development to dissemination. The group attended regular meetings and supported participant recruitment, evaluated patient‐facing documents, supported the piloting of the research intervention and co‐developed the dissemination and impact strategy. The implementation of PPI throughout the project was benchmarked against the UK standards for PPI.The inclusion of PPI in the PATHWAY project provided tangible changes to the research project  but also proved to be a beneficial experience to PPI members through the development of new skills and the opportunity to provide a patient voice in research. We show how PPI was involved across seven study phases and provide examples of implementation of the six UK standards. The study did not include PPI in data analysis but met all the UK standards for PPI. Challenges regarding practical components , increasing diversity and PPI members' knowledge of research were highlighted as areas for further improvement.We provide a case example of how PPI can be implemented throughout a research lifecycle and we note the barriers faced and make suggestions for PPI in future implementation and research.PPI members were involved throughout the lifecycle of the research programme. The PPI lead was a co‐author on the manuscript and contributed to report writing. The programme included two feasibility trials and two randomized controlled trials with integrated qualitative and health economics analyses . The overall aim of the programme was to reduce symptoms of anxiety and/or depression in cardiac rehabilitation (CR) patients by integrating metacognitive therapy MCT20 in CR3PPI was integrated throughout all stages of the research programme. Figure Members of the public were recruited via patient networks, with the following eligibility criteria: experience of one or more of the following was required: 1) heart disease; (2) psychological distress and/or (3) being a carer of someone with one or more of these conditions. A group of 10 advisors was formed following an expression of interest from 16 people. Of the initial 10 advisors, 3 members left. The most common reason for withdrawing was due to illhealth. Demographic characteristics of the 10 PPI advisors and the PPI Lead are included in Table  heart di3.1Consultations with service users at two cardiac service user group meetings  were conducted. Two meetings were held, which focused on (1) the research background and preliminary ideas and (2) discussions related to the research proposal and PPI plans. Further consultations, funded by a Research Design Service (RDS) NW bursary, were conducted with Ticker Club members regarding the acceptability and feasibility of the research. An advisor from the RDS NW and a service user were included as co‐applicants on the grant application and reviewed the lay summary and PPI sections of the grant application.The PPI Lead and the PPI Chair were members of the PATHWAY executive committee, while a PPI member independent of the research team and PPI advisory group was a member of the trial steering committee. As part of the executive and trial steering committee, PPI representatives provided input on study design, conduct, consultation about emerging findings and dissemination and impact planning. Attendance at executive committees allowed the PPI lead and chair to contextualize research findings and review them with the advisory group.3.23.2.1All patient‐facing material was reviewed and approved by the PPI group before its submission to ethics. This included service users ensuring that the information provided in consent forms and participant information sheets was sufficient and written in a lay format. The advisory group also reviewed the order of study documentation in the information packs to ensure that it was engaging and inviting for prospective patients.3.2.2Service users were involved in the development of the home‐based MCT manual, focusing specifically on ensuring that the format and readability of the manual were appropriate for patients.3.2.3PPI members contributed to the layout of the home‐based manual. Four PPI members piloted the home‐based manual. In doing so, members completed each module in the manual along with the telephone support calls, which for the purposes of the pilot were delivered by the research team. This allowed researchers to evaluate the timing and content of the telephone support calls. Following the pilot, PPI members provided feedback on the manual and support calls via feedback meetings. PPI members commented that (1) more emphasis should be placed on the ease of use and flexibility in using the modules to enhance compliance; (2) a question section should be added to give the patient the opportunity to clarify/discuss any issues with the therapist in the subsequent telephone call; (3) an estimation of the amount of time to complete each module should be included; (4) the language at times was too technical, which resulted in minor modifications to the text and (5) overall the modules were easy to follow. All of the suggested changes were implemented in the manual ahead of the feasibility trial.While piloting the home‐based manual benefitted the research team, the advisory group also noted that piloting the self‐help manual supported them in developing further knowledge and understanding of MCT, anxiety and depression. Some advisors felt that piloting the manual changed their beliefs about their own thinking and their personal ways of coping with and understanding anxiety and/or depression symptoms. One PPI member reported that ‘I think it's great that psychological, the emotional side is now being sort of trying to be managed because it's not been there. … I didn′t know until we started getting the paperwork what it was [anxiety and depression] … and now I know why I didn′t want to go out of the house for six months. I never ever suffered with depression before, but I now know why’ (PPI member 3).3.2.4The PPI group also aided in co‐developing a recruitment strategy for approaching participants across all workstreams. This ensured that the language used when approaching and inviting potential participants to take part was appropriate and engaging. In addition, for the health economics workstream, the group provided feedback on potential sources of recruitment.3.2.5To increase the rate of return of follow‐up questionnaires, service users were asked for suggestions on how to enhance follow‐up participation and decrease the drop‐out rate. Suggestions included the creation of a participant newsletter, which highlighted the importance of questionnaire completion and its benefit to patients and NHS services while providing trial updates and maintaining patient engagement. The newsletter was co‐produced between PPI members and the research team and provided a significant benefit in improving the rate of return for follow‐up questionnaires.Service users were not involved in the data analysis, although qualitative and quantitative data were discussed with the PPI group, which aided in ensuring that key messages were presented in a format that was accessible to the public; for example, service users commented on the importance of including the treatment recovery rate, as they felt this was an important outcome for patients.3.2.6A stated preference survey using a discrete choice experiment was designed to estimate preferences for psychological care within the CR pathway.3.2.7A qualitative process evaluation was embedded into the PATHWAY trial. The PPI group was consulted about the design of the qualitative process evaluation and the materials used to collect qualitative data. Initially, the group provided feedback on the longitudinal nature of the qualitative component of the research and confirmed that they felt this would not be burdensome for participants. The group was also consulted about the qualitative interview topic guides, with the aim of ensuring that all areas of relevance were covered during interviews, the correct language was used and topics that could be understood to be potentially sensitive were handled in an appropriate way.3.3Group activities were held with the PPI group to aid the development of the dissemination plan with a focus on (1) identifying key messages, target audiences, format and publication/venues and (2) styles of dissemination. Discussions were conducted to determine results of relevance to the public, explanations of future steps and language use in dissemination work. The group aided in the development of resources with members being involved in creating videos, blogs and presentations of their experiences taking part in PPI, which helped to provide a patient voice. They also played a key role in the development and delivery of a live event disseminating the study results for patients, clinicians and members of the public: helping to inform the format of the event and taking part in the event by discussing why they chose to be involved in the project and the role they played in the research.3.3.1Evaluations of the PPI approach were conducted throughout the project through feedback meetings, telephone calls and a summative questionnaire completion .In the future, the group commented that further assistance was needed for individuals reintegrating into the group when they had been away for personal or health reasons. This could have been facilitated by a one‐to‐one meeting with the PPI lead and PPI member before the meeting to update on any changes to the group and progress made during missed meetings.4.3when we first started most, possibly all of us didn′t understand the nature of the actual treatment. It was quite a long way down the line before we saw the materials … and understood more about how the treatment would work. I think some training earlier on in the process would have put us in a position where we were better informed to contribute. (PPI Member 6)Advisory group members felt well supported; measures were put in place to accommodate those with additional needs or disabilities from the start of the project and were reviewed regularly. In addition, there was a range of learning opportunities offered to the group throughout the project, such as working with the team on presentations. PPI members also communicated that taking part in PPI had increased their trust in research and researchers and made them more likely to discuss research with friends and family. PPI members commented on the increased understanding they gained, ‘I have gained a better understanding of all the difficult decisions that researchers have to make’ (PPI Member 5). There were however a number of ways in which learning opportunities could have been further supported. While the advisory group ultimately felt that sufficient information had been given, at times confusion around some of the processes, protocols and unfamiliarity with the psychological intervention (MCT) had resulted in feelings of being under‐utilized. For example, although the psychological intervention used within the trial (MCT) was explained to the group, this was not done until later in the research programme. One member commented that,The group also felt that, while the research team provided sufficient information on the research process, this was a high volume of information, and providing them with a handbook or online training materials outlining the research processes would have been useful: allowing them to look up aspects of the research and refresh on processes in their own time. Providing such information at the start of the research process could have also aided in setting expectations with the PPI team around what they could and could not change. For example, PPI members wondered if it was possible to change the wording on validated questionnaires, which was outside the scope of what they were able to do. However, the research team did provide an explanation as to why this was not possible, the implications for the project and how questionnaires are developed.Throughout the project, we had PPI representation at both the steering and executive team meetings and the principal investigator met with the PPI lead at these meetings and also at the PPI groups. To support PPI members and to ensure they felt comfortable attending these meetings, the PPI lead would accompany the PPI member to the meetings. PPI members were also provided with a copy of the previous meeting minutes, the meeting slides and the meeting agenda before the meeting. Following the meeting, the PPI lead and the research fellow were available for the PPI member to contact and ask questions if they felt uncomfortable to asking these during the team meeting.4.4The PPI group felt that the varying types of communication  and amount of communication outside of meetings were sufficient. However, the initial frequency of meetings, format and approach of meetings required improvements. While recaps of previous meetings were originally provided at the start of each meeting to reduce the impact of long gaps between meetings, it was viewed by members as wasting time and detracting from project business, as such email communication between meetings was increased to reduce the length of the recap at subsequent meetings. The group felt that they were able to speak without opinions being dismissed and that this also allowed them to say when they did not understand. They felt the research team was responsive and adjusted their language  when speaking with PPI members. However, one member highlighted that expressing a different opinion to the rest of the group can be intimidating and can result in the feeling that they have to agree with the consensus. As such, members were specifically encouraged to express alternative views, and varying formats were offered to provide feedback , which is paramount in ensuring open and honest feedback from members.4.5The advisory group felt that their input was taken on board and the research team was very open to feedback from them. Being involved in the co‐development of the home‐based MCT intervention was felt by the group to be their most significant impact as they could see the adaptions following their suggestions. Advisors felt their input on this also had the most impact on patients as it ensured the accessibility of the home‐based intervention.4.6The structure of governance included a PPI lead and PPI chairman as members of the executive committee and an independent PPI member as a member of the steering committee. This helped to ensure that PPI representation was considered at all project governance levels. Reviews of the PPI approach were conducted throughout the project and adjustments were made where needed. Future considerations were suggestions surrounding funding for PPI activities, as there were some additional opportunities that the group was unable to undertake due to funding not being allocated for them. Therefore, future planning for public involvement should include the allocation of funding for additional PPI opportunities such as attendance at conferences. Further suggestions include clarification of what payments can cover  and ensuring clear procedures around paperwork and timing of payments to ensure clear expectations on how long a payment may take.5PPI can play an important role by providing a patient's perspective that can be utilized throughout all phases of a research study. The current paper illustrated how PPI can be implemented as well as how national PPI standards might be met, and implementation improved upon further.5.1Throughout the research programme, PPI resulted in tangible changes in patient‐facing documents, the layout of the home‐based intervention, the development of newsletters and participation in dissemination events. In doing so, PPI members aided in ensuring the appropriateness of the language being used, the format of interventions and aided in ensuring research findings were presented in an accessible and user‐friendly manner. The implementation of PPI in our PATHWAY programme was consistent with previous studies, which have advocated for PPI throughout all phases of research.5.2To assess if PPI met national guidelines for quality and consistency, we benchmarked our strategy against the UK standards for public involvement.One of the main sources of difficulty that we observed between researchers and advisory group members was the advisory groups' lack of knowledge of the research processes, which is commonly noted as a barrier.In addition, there were practical challenges that were encountered in implementing PPI including frequency of meetings, format and delivery of meetings and language use. At times, there were long gaps between meetings, which created inconsistency and feelings of underutilization. In the future, setting clear expectations at the study's outset can aid in establishing accountability between researchers and the PPI group. According to Ocloo et al.'sWhile a common challenge of PPI surrounds issues of power dynamics,5.3While the PATHWAY programme incorporated PPI throughout the lifecycle of the research project, further assessment of the impact and effectiveness of PPI in PATHWAY is required. Assessment of PPI was conducted using a questionnaire developed by the study team, but this measure has not been validated and items focused largely on assessing the impact of taking part in a PPI group. It would have been useful to include assessments of the barriers and enablers to PPI engagement during sessions and to examine the personal frameworks used by PPI members in assessing and advising on the research process. Similarly, an evaluation was not conducted on the impact that PPI had on the researchers themselves.6The current paper provided an account of how PPI was implemented throughout the lifecycle of PATHWAY. PPI was a component of our clinical trials, stated preference survey and qualitative research. We benchmarked PPI against UK standards, and although we appear to be compliant, we found specific areas for improvement. We provide an overview and examples of our practice in the PATHWAY programme and make specific suggestions that could be useful in guiding future studies.Lora Capobianco and Adrian Wells contributed to conceptualization, investigation, writing – original and subsequent drafts and editing and project administration. Cintia Faija, Bethany Cooper, Lindsey Brown, Rebecca McPhillips and Gemma Shields contributed to the writing – review and editing. Adrian Wells contributed to supervision and funding acquisition.A. W. is the director of the MCT Institute and developer of MCT. A. W. has written books on cognitive behaviour therapy and MCT. The remaining authors declare no conflict of interest.Supporting information.Click here for additional data file.


In this report we present a rare case of pancreatoblastoma in an adult patient. Whilst they are amongst the most common malignant pancreatic tumours in children, presentations in adults are exceedingly rare, with a small number of reported cases. Its presentation is often non-specific in terms of clinical examination, and subsequent imaging can show similar findings to those seen in benign neoplasms. This report highlights the difficulty of achieving a diagnosis and subsequent treatment of such an uncommon disease. Biopsy and resultant histology are essential in diagnosis and surgical resection remains the preferred modality of treatment. However, the use of chemotherapy and its efficacy in adults remains unclear, and the prognosis documented in existing literature for adults is worse when compared to paediatric presentations. This case emphasises the need to consider pancreatoblastoma as a differential diagnosis when suspecting pancreatic or abdominal malignancies to achieve early detection and diagnosis, in order to provide optimal treatment and improve patient outcomes. Pancreatoblastoma is a rare type of malignant pancreatic tumour more commonly found in childhood in comparison to adults ,2. They This case report presents a rare example of a pancreatoblastoma presenting in an adult and demonstrates the difficulty of diagnosing such a malignancy, as well as the challenges of treating this disease. There remains a lack of universal guidance in the management of pancreatoblastoma in adults. Whilst surgical resection remains the primary treatment of choice where possible, the role of adjuvant chemotherapy and which regimens to use still needs to be firmly established.A 75-year-old male with an Eastern Cooperative Oncology Group (ECOG) performance status score of 0 presented to the Emergency Department in September of 2022 with chest pain that was also associated with abdominal pain and nausea, these symptoms began in August of 2022. His observations and routine bloods were unremarkable at the time of this presentation, and his symptoms were thought to be due to the patient’s known history of irritable bowel syndrome. The patient also had a past medical history of hypertension and benign prostatic hyperplasia. These symptoms persisted and he presented once again in November of 2022 with intermittent chest pain and abdominal pain, as well as a reduction in appetite and weight loss. Routine blood tests and observations were once again normal, and subsequent CEA and Ca 19-9 testing were also unremarkable. The patient was then listed for a gastroscopy given his persistent symptoms, which did not show any sign of malignancy. A subsequent Computerized Tomography (CT) scan  imaging confirmed the size and location of the disease, as well as extensive superior mesenteric vein (SMV) and portal vein involvement with solitary liver metastases. Subsequent endoscopic ultrasound (EUS) guided core biopsy confirmed pancreatoblastoma. Since the mass was locally advanced and involved several blood vessels it was deemed inoperable due to the complexity of its location and the concern of liver metastases.The patient was offered a FOLFIRINOX regimen of chemotherapy and managed to complete one cycle before complications arose, and a subsequent admission occurred in March 2023. An interim CT scan during this period showed local disease progression which resulted in a malignant stricture of the common bile duct (CBD), this led to a biliary stent insertion due to CBD obstruction caused by the increased size of the malignancy. The CT scan also showed significant progression in the size of the pancreatic head tumour and the size of the liver metastases despite one cycle of chemotherapy.Following the patient's recovery from his endoscopic retrograde cholangiopancreatography (ERCP) and stent insertion, the second cycle of FOLFIRINOX was attempted and unfortunately suspended as the patient could no longer tolerate the treatment due to side effects such as poor appetite, nausea and vomiting, and excessive weight loss. A decision was then made in conjunction with the patient that he would be for best supportive care. Five months after this decision was made the patient remains stable and currently has palliative care input in the community from his local hospice to manage his symptoms.Pancreatoblastomas are slow-growing tumours that originate from the exocrine cells of the pancreas. They frequently present in a non-specific manner and given their slow growth by the time patients often present, the tumours can grow to a significant size. As a result, symptoms such as abdominal pain or distension can often be the primary presenting complaint . Whilst This report highlights the presence of a pancreatic head tumour, which is the most common site for a pancreatoblastoma. Despite this, it can be found at any point of the pancreas, as case reports have shown findings of tumours both in the body and tail also . Due to Due to the rarity of this disease, much remains unknown about its aetiology with links being made with syndromes such as familial adenomatous polyposis (FAP) or Beckwith-Wiedemann syndrome . AchieviSurgical resection is the main and most effective treatment modality. However, this is dependent on several factors, such as the progression of the disease, its location, and the presence of metastases. Resection can result in a distal pancreatectomy including a splenectomy, depending on whether lesions are present on the body and tail. Prognosis can be positive with a complete resection of the tumour, as surgery has been shown to be associated with a survival time of 15 months in comparison to just five months in patients who had unresected tumours ,11. SurvWhilst chemotherapy has been shown to have a role in both pre- and post-surgery there remains a distinct absence of universal treatment guidelines for adults in this area. Chemotherapy plays a significant role, particularly when the disease is unresectable, involves local blood vessels, or has metastasised, all of which occurred in our case. Although chemotherapy was given and unfortunately not tolerated in this case, at present there remains no clear optimal regimen. Despite this chemotherapy does appear to be of some benefit in palliating metastatic or recurrent disease .Whilst pancreatoblastoma is a rare malignancy especially in adults, given its non-specific presentation both on clinical and imaging examination it can be very difficult to diagnose without a successful biopsy. Therefore, it must be considered as a differential diagnosis when suspecting atypical pancreatic malignancies, in order to achieve as early detection and diagnosis as possible. Early detection is critical, as often patients will present once the tumour has grown to a substantial size and achieved a significant degree of local infiltration. This can pose a challenging scenario for surgeons, as was shown in this case with the malignancy being deemed inoperable.There remains a lack of an optimal standardised treatment regimen in adults due to the rarity of this disease highlighting the need for further research and analysis. This case emphasises the importance of early detection and diagnosis, as they play a key role in maximising the possibility of surgical resection as a treatment option and ultimately improving patient outcomes.


Thorough data of morphometric measurements of arteries forming Circle of Willis (CW) is crucial for radiological and neurosurgical interventions. This systematic review has been conducted with the objective to find an effective range of length and diameter of anterior cerebral artery (ACA) and to observe whether there is any change in the length and diameter of ACA depending on age or sex. Articles based on length and diameter of ACA via any mode of study like cadaveric or radiological were considered in this systematic review. A comprehensive literature search using databases Cochrane Library, PubMed, and Scopus for relevant articles was done. Research papers which answered the focused questions were selected for data analysis. It was observed that the range of length and diameter of ACA were 8.1 mm-21 mm and 0.5 Å-3.4 mm, respectively. In majority of the studies, length and diameter of ACA were more in the younger age group (>40 years); and the length of ACA was more in females whereas the diameter of ACA was more in males. These data will be applicable for better construction and decipherment of angiographic images. This will help in the proper and guided treatment of intracranial pathologies. The supply of nutrients to the brain remains unceased for the brain to be alive. Circle of Willis (CW) is the safest tool for the brain. If there is any unilateral blockage in the arterial supply to the brain, it will be compensated by supply via CW . The knoThe ACA supplies blood to the medial cerebral hemisphere  which is responsible for perception and understanding. Blockage of this artery can lead to disconnection of non-dominant hemisphere from centers concerned with the organization of speech and skilled motor activity in the dominant hemisphere resulting in agraphia and apraxia .Conjunction between the internal carotid and vertebral artery at the base of brain is known as the CW. In front of CW lies ACA which is the terminal branch of internal carotid artery (ICA). The ACA of both sides are connected to each other by anterior communicating artery (ACoA). Posterior cerebral arteries (PCA) lie behind in CW. PCA is the terminal branch of basilar artery. PCA of a side is connected to ICA of the same side by the posterior communicating artery (PCoA) . Most ofThe present study aims to ascertain various studies concerning morphometric measurements of ACA. Study of ACA is crucial during surgeries of the anterior part of CW. ACA is the most common vessel for the development of intracranial aneurysms . The capWe did not find any systematic review on the morphometric evaluation of ACA. This systematic review included research articles that had evaluated the length and/or diameter of ACA via cadaveric or angiographic study like digital subtraction angiography (DSA), computed tomography angiography (CTA), and magnetic resonance angiography (MRA). The data from various studies are pooled based on age and gender. Hence, a systematic review was conducted to find an effective range of length and diameter of ACA in order to help the neurosurgeons while dealing with complexities like aneurysm, arterial dissection, etc. Morphometry of the artery helps in choosing the correct size of catheters for endovascular interventions .MethodsThis systematic review was conducted with the objective to find an effective range of length and diameter of ACA and to observe whether there is any change in the length and diameter of ACA depending on age or sex.Review QuestionIs there any dimorphism related to age and sex in morphometry of the anterior cerebral artery? This systematic review was based on articles in accordance with the above review question. “PRISMA Statement 2020”  guidelines were used for this present study . We follAll the studies included in this systematic review were observational  studies. PRISMA 2020 guidelines were followed for screening and selecting the studies for this systematic review. Articles were selected after a comprehensive database search. The methodological quality of the studies was done (via ROBIS tool)  .Exclusion Criteria-All the studies which were not in the English language were excluded.-Studies involving the measurement of pathological segments of ACA  were not included.Assessment of Quality of StudyThe risk of bias was calculated by the ROBIS tool. Each study was rated “low concern,” “high concern,” or “unclear concern” by ROBIS. “Low concern” relates to the articles with clear specifications of the review question and objectives. “High concern” refers to the studies with a lack of pre-specified objectives for addressing the review question. Studies with insufficient information to make a judgement about the risk of bias lies in the category of “unclear concern” .ResultAll the studies included in this systematic review were cross-sectional studies. The review was conducted in accordance with the “PRISMA Statement 2020”  Figure . AssessmLength of ACAA varying range of length was found in the included studies. After observing the results of the range of length of all the included articles, we found a minimum value of 8.1 mm and a maximum of 21 mm. Among all the included studies, minimum (8.1 mm) and maximum (21 mm) values of length of ACA were recorded in the study of Karatas et al. and Shatri et al. respectively -12. DimeSex-Wise Distribution of ACA LengthOne study was found that observed the gender-wise distribution of length of ACA. Sharma S et al. differed and concluded ACA length to be more in females .Age-Wise Distribution of Length of ACATwo of the included studies considered age as the criteria for observing the length of ACA. Studies of Shatri et al. and Sharma S et al. supported each other’s conclusion of length being more in the younger age group , 19.Diameter of ACAOn analyzing the range of observed diameter among the included studies, it was noticed that the minimum and maximum values were 0.5Å and 3.4 mm respectively. Cadaveric studies of Karatas et al. and Vohra et al. observed both the minimum (0.05 mm) and maximum (3.4 mm) values of diameter ,27. The Sex-Wise Distribution of ACA DiameterFour studies evaluated the diameter of ACA in males and females. Out of these four studies, three were of the opinion of diameter being more in males. The only study of Sharma et al. stated it to be more in females . WhereasAge-Wise Distribution of Diameter of ACAFour of the included studies observed the diameter of ACA in young and old populations (age > 40 years). Studies of Sharma et al., Krabbe-Hartkamp et al., and Maaly et al. opined that the diameter of ACA is more in younger age group , 30-31. Overall as such no significant difference was noticed in the pattern or range of length or diameter of ACA, depending on whether the study was cadaveric or radiological. Results of studies included in our systematic review have been mentioned in Table DiscussionThe length and diameter of ACA are very crucial as they can be used to investigate pathological conditions. There is a considerable individual variation in the pattern and caliber of vessels that make up the circulus arteriosus. Although a complete circular channel almost always exists anatomically, one vessel is usually sufficiently narrowed to reduce its role as a collateral route and the circle is rarely functionally complete in individuals .Arteries of the left side (ACA) appear to be nearly the same as those of the right one, as the increase of perimeter of the arterial polygon is achieved by means of a harmonious increase of all its sides.In our review of 21 articles; we observed that the range of length and diameter of ACA were 8.1 mm-21 mm and 0.5 Å-3.4 mm, respectively. In the majority of the studies the length and diameter of ACA were more in the younger age group (>40 years); and the length of ACA was more in females whereas the diameter of ACA was more in males.Sex-Wise Distribution of Morphometry of ACAMales’ head measures more than females’. Brain weight is more in males . This miAge-Wise Distribution of Morphometry of ACASympathomimetic activity increases with age leading to vasoconstriction; which may be the reason for the decrease of diameter and length with age. This effect may be overpowering the compensative widening of centripetal vessels in elderly people. Age-related differences in ACA had been explained by a compensative widening of the centripetal vessels in elderly people . This ma· Decrease in stroke volume of the heart.· Weakening of the elasticity of arterial walls.· Presence of arteriosclerotic changes.These factors are also responsible for the decrease in the velocity of blood flow in vessels in elderly people .Clinical implicationsThe ACA has a high incidence of hypoplasia or aplasia; and hence is more prone to ischemic complications . HypoplaLimitations of the studyThis study required a great range of evidence from diverse databases with peer-reviewed material and gaining entry in various database was problematic. Moreover, all the articles included were not pertaining to all the factors .After observing the data on morphometry of ACA of all the studies, we conclude that there is a wide range of length and diameter of ACA, so it is difficult to find specific values for length and/or diameter. These data will be applicable for better construction and decipherment of angiographic images. The maximum number (31.8%) of the studies has a length in the range of 13.5 mm to 14.5 mm. As far as the diameter is concerned, the maximum number (27.3%) of the studies observed diameter of ACA to be nearly 2.5 mm. These findings of the basic knowledge of ACA are essential for interventional radiologists and neurosurgeons for planning the management of the patient.