Lately, curious structures have been erected in arid regions: they are large nets able to catch water from fog. Tiny droplets condense on the mesh and are collected on the bottom of it. This innovative technology is crucial to obtain drinkable water in these inhospitable areas. Many studies aim to understand the behavior of droplets trapped on this entanglement of fibers. However, the motion of a droplet sliding on a network of inclined fibers and encountering several crossings when going down remains an open question. Here, we look at the path chosen by such a drop and, especially, we analyze its behavior at the different nodes of the array. We show that droplets may change from one fiber to another one depending on the slope and the diameter of these fibers. We prove that we can force a droplet to follow a specific path simply by carefully designing the fiber mesh. These findings are expected to provide a very convenient way to manipulate small droplets in applications from microfluidics to fog harvesting. Certain cacti can catch water droplets from fog and carry them to their stems2. Spiderwebs have a remarkable ability to collect water in air due to the structure of the silk3. All these processes involve water droplets on fiber-like structures and are widely studied. For example, Hou et al.4, Wang et al.5 and Chen et al.7 look at water harvesting on bio-inspired fibers.In nature, many organisms have or produce particular structures which turn out to be very efficient at collecting water. In arid regions, some mosses are able to collect water thanks to tiny hairs on their leaves8, on porous media9 or on fiber networks10 is of considerable interest. Both the design11 and the surface properties12 of the fiber mesh have been studied to improve the efficiency of the water collection. Bearing in mind these issues, it seems logical to strive for a better understanding of the behavior of droplets on fiber arrays.These examples inspired new technologies like fog harvesting systems. Indeed, the collection of water in desert areas is a major challenge. An innovative way to obtain water is to collect fog droplets thanks to a large mesh net. Therefore, looking at the collection process of water droplets on inclined fibers14 or on the motion of the droplets along an inclined wire17. They aim to understand how droplets deform on the fiber, how they slide, how the tilted angle influences the motion,… Gilet et al.18 study a droplet gliding along a vertical fiber and encountering several horizontal fibers. For this very specific case, they establish a criterion for determining whether the droplet crosses the node or stops. These results are used to create complex droplets on fiber networks19. Sauret et al.21 examine the geometry of silicone oil drops trapped at the meeting of two randomly oriented horizontal fibers from a static point of view. Other studies look after droplets on flexible fibers23. Even though the motion of a droplet on a vertical fiber has been addressed and the fiber inclination has been considered from a static point of view, the dynamics of a droplet on an array of randomly inclined fibers remains an open question.Many researches focus on drops on horizontal fibersIn this paper, we aim to understand how a droplet moves on a network of perpendicular fibers with various orientations. Especially, we look at the behavior of the droplet at the crossing of two wires. When a droplet reaches a node, it faces three different possibilities: this droplet can either be trapped at the node or go through it and if it crosses the node, the droplet can either stay on the initial fiber or change to the other one. We determine the conditions under which the droplet crosses the node and the criteria for choosing one fiber or the other after the crossing. A critical volume is found for the trapping of the droplet and seems to be related to the orientation of the crossing and the fiber diameters. Moreover, for a crossing of identical fibers, we show that the droplet detaches along the most inclined fiber. This means that it can either stay on the initial fiber or change to the other depending on their slope. A more surprising result is obtained for crossings made of two different fibers. Indeed, by changing the fiber diameters, we can force the droplet to choose the largest fiber even though it is not the steepest one. This finding involves that it is possible to force a droplet to follow a determinist path on a fiber array just by choosing the suitable set of fiber diameters. This can be seen from Fig. μl to 10 μ1 on the fibers.We work with a Dow Corning silicone oil with a viscosity μm and 300 μm. For each experiment, two fibers are stretched and attached on a rigid frame at four fixing points that are in the same plane to insure the contact between the fibers. So, the fibers simply touch each other. The fixations guarantee that the fibers cross each other with an angle α to the initially horizontal fiber.We use nylon fibers with diameters of 200 a, the fiber coming from the right has a diameter b as shown in Fig. α as the angle between the right fiber and the horizontal direction. This angle varies from 0° to 90° in steps of 5°. For each angle, a droplet is launched from the right fiber and slides to the crossing where it remains trapped. We choose to deposit and let the droplet slide on the fiber rather than directly placing it on the node in order to mimic as closely as possible the motion of a droplet on a fiber array. Note, the droplet loses some matter while going down due to the fiber coating. However, as we place the droplet close to the node (about 1 cm), the mass loss is negligible. The volume of the initial droplet, V, is gradually increased until it detaches. This transition between the trapping and the releasing of the drop defines a critical volume Vmax.Our purpose is to find out how we can control the motion of a droplet on a fiber mesh. We investigate a case which appears simple at first sight: an oil droplet sliding on an inclined fiber and reaching a crossing. In our experiments, we start with nodes made of two perpendicular fibers to study the phenomenon in that specific geometry before generalizing to other angles. The fiber coming from the left and going down to the right has a diameter a = b). For a specific angle α, small droplets slide along the right fiber and stop at the crossing as it can be seen from Fig. Vmax always cross the fiber a and stay on the initial fiber. This case is represented in Fig. α = 45°, both fibers are exactly equivalent: no fiber is steeper than the other. The droplet randomly chooses one fiber or the other after the crossing.First, we look at symmetric nodes  or on its complementary fiber (with a slope 90° − α), the critical volumes are equal and the final fiber is the same. Moreover, our data indicate that the fiber diameter influences the transition volume: the thicker the fiber, the larger the volume.We determined the maximal volumes, −2 m/s for the steepest fibers and the largest droplets. The capillary number compares viscosity and capillarity and is defined as G, the capillary forces Fa and Fb acting on the contact lines on both fibers and the forces due to the presence of a liquid film along the fibers Ffa and Ffb. Indeed, prior to the detachment, the droplet surrounds both fibers but when it leaves the node, it has to detach from one of the fibers. There is a resistive force due to the detachment of the droplet from the fiber that is acting against the motion of the droplet. This force is larger both when the surface tension is higher and when the film is wider. Therefore, Ffa and Ffb are directly proportional to the surface tension L. These forces can be seen as forces resisting the droplet detachment.Based on our observations, we propose a model to predict the volume at which a droplet crosses the node. The detachment process is a really slow process. The droplet is drastically slowed down at the crossing. The typical speed of the droplets is about 10We consider the balance of all the forces along the detachment direction. We have to distinguish two cases: (i) For et al.13 and the force Ffb as L is the wetting length along fiber b. As we assume a nearly spherical shape, r is the droplet radius and L is the wetting length along the fiber a and The weight can be rewritten as mentclass2pt{minimα. μm and μm. We find that r, our model overestimates the critical volume and Based on Eqs  and 6),,6), we cμm fiber and a 300 μm fiber and we rotate them. We test two different situations: launching the droplet on the thin fiber (named 200 μm–300 μm) or launching it on the thick fiber (named 300 μm-200 μm). We are able to detect the transition as done before. During our experiments on asymmetric nodes, we notice unexpected behaviors. Indeed, unlike the symmetric case where the droplets select the steepest fiber after the crossing, some droplets do not choose the steepest but the thickest fiber. As shown in Fig. μm fiber with a 50° slope, the droplet switches to the 300 μm fiber even though its slope is lower. This means that by choosing the right fiber diameters, we can force the droplet to select the thickest fiber even if it is not the steepest.After the study of symmetric nodes, we focus on asymmetric crossings  as the force due to the film depends on the wetting length along this fiber. Then, we consider the data for droplets crossing a 300 μm fiber (the left branch of the case 300 μm-200 μm and the right branch of the case 200 μm-300 μm). We obtain α different from 45°. It confirms that when the node is made of two different fibers, the transition between droplets changing or staying on the initial fiber is no longer at 45°. There is a range of angles in which the relevant parameter is no more the slope of the fiber but its thickness.We apply the exact same model as the one presented here above. We just specify the suitable fiber diameters After the detailed study of oil droplets sliding on perpendicular fibers, we try to generalize our results for other liquids and other angles between the fibers.μm in diameter. The shape of the graphs is similar and we can apply the model given by Eqs ..μm in diμm in diameter and we cross them with an angle of 60° and 30°. Then, we rotate the node as done for the previous experiments. Our conclusions for α until it reaches a maximum and then decreases. The maximum occurs when both fibers have the same slope. For Vmax, has to be studied over different ranges of α, i.e. from Finally, we change the angle (i) For These equations lead to generalized expressions of the radius μm, 250 μm and 350 μm) and three other fibers go from the top right to the bottom left with increasing diameters . The droplet is placed on the thinnest fiber. As all fibers have the same slope, the droplet always chooses the thickest fiber. Given the way we built the network, the droplet switches from one fiber to the other at each node. As shown in Fig. The results allow us to understand how a droplet progresses on a fiber mesh. For an array made of perpendicular fibers, the droplet detaches along the steepest fiber. This means that if the droplet is initially on the most inclined fiber, it remains on it during its motion, crossing after crossing. If not, at the first crossing, it changes to the steepest fiber and stays on it afterwards. So, by rotating the whole array, we can switch from one way to the other. Another possibility, which may be even more convenient, is to pick the right fiber diameters. Indeed, from an appropriate angle, the droplet always changes from one fiber to a thicker one. In Fig. In this paper, we proposed one of the first studies focusing on the droplet motion on a fiber network. We showed that both the fiber steepness and the fiber diameter are crucial parameters when talking about fiber-based microfluidics. We focused on the crossings of fiber arrays and we determined the critical volume above which droplets go through the nodes. We proposed a model based on the competition between the gravity and the forces due to the film that wets both fibers with a single fitting parameter. This model is able to predict the detachment volume. Moreover, it could be advantageously implemented for situations involving other driving forces. On a network made of perpendicular identical fibers, we revealed that droplets always opt for the steepest fiber at each crossing. When fibers have different diameters, we highlighted that, for certain angles, droplets select the thickest fiber regardless of its slope. We showed that our model still works for other liquids and other angles between the fibers. The only limitation is the use of liquids that totally wet the fibers. Further experiments should be performed to extend our findings to droplets that only partially wet the fibers. In that case, wetting properties of the substrate are crucial  as well as the droplets themselves. The way the droplet is placed on the fiber influences the droplet behavior due to the wetting hysteresis. The contact angle difference between the top and the bottom of the droplet may prevent the droplet to slide. This problem requires a specific attention. However, our results prove that by cleverly designing a fiber network, a droplet can easily be guided through an asymmetric fiber maze.This convenient technique is an opportunity to develop an easy fiber-based microfluidics which does not require pumps, microchannels or expensive equipments. Moreover, this is a chance to optimize the fog harvesting simply by changing the geometry of fog nets which are currently developed.


The tunnelling of electrons through barriers is important in field emission sources and in interconnects within electronic devices. Here we use the analogy between the electromagnetic wave equation and the Schrodinger equation to find potential barriers that, when added before an existing barrier, increase the transmission probability. A single pre-barrier of negative potential behaves as a dielectric “antireflection coating”, as previously reported. However, we obtain an unexpected and much greater enhancement of transmission when the pre-barrier has a positive potential of height smaller than the energy of the incident electron, an unfamiliar optical case, corresponding to media with superluminal phase velocities as in dilute free electron media and anomalous dispersion at X-ray frequencies. We use a finite difference time domain algorithm to evaluate the transmission through a triangular field emission barrier with a pre-barrier that meets the new condition. We show that the transmission is enhanced for an incident wavepacket, producing a larger field emission current than for an uncoated barrier. Examples are given of available materials to enhance transmission in practical applications. The results are significant for showing how to increase electron transmission in field emission and at interconnects between dissimilar materials in all types of electronic devices. Electrons are also transported across barriers between metals and semiconductors in the source and drain contacts of metal-oxide-semiconductor (MOS) devices and from one semiconductor to another in contacts within MOS and many other types of devices. Interconnect–related dissipation is a key constraint in current and future strategies for power reduction in integrated circuits consisting of densely packed components. Current strategies for reducing interconnect dissipation include low resistance materials such as nanotube conductors3. However, the inherent resistance at interfaces between materials created by potential barriers remains a contributing factor. In many cases, the height of the barrier is determined by fundamental material properties such as the work functions of the materials. Therefore, it is important to find ways to increase transmission of matter waves through a given barrier of predetermined height and width by supplementing the given barrier with additional potential distributions that act as reflection suppression layers or, in the language of optics, by using an “antireflection coating”. The idea of an antireflection coating is compatible with the natural analogy4 between matter waves, governed by Schrodinger’s equation and light waves, governed by the electromagnetic wave equation. It is often required in optics to increase light transmission through a given layer by adding layers to the front and or rear of the given layer. In the cases of interest here, adding a “pre-barrier” at the interface is the required option. Strategies for designing appropriate pre-barrier potentials are suggested by the analogy between matter waves and electromagnetic waves, and this has been a productive way of creating designs for increasing the transmission probability through quantum mechanical barriers6. Methods for minimizing reflections at interfaces in optics are well advanced using matrix calculation methods such as that of Abeles8, methods that are widely used for designing wavelength-selective optical coatings9. The coating of an optical element with layers of selected refractive index and thickness can be used to suppress reflections, to induce transmission and to create band pass filters. The design of structures that show enhanced transmission for matter waves is also possible and the fabrication of resonant structures with the properties of a Fabry-Perot interferometer11 consisting of two identical barriers separated by a region of constant potential, has already been implemented in the resonant tunnelling or Esaki diode. The resonant cavity idea is not well suited to antireflection of general barriers, because of its inconvenient reliance on the symmetry of two participating barriers. However, we propose that the optical analogy is worth pursuing further to look for new classes of solutions to the matter wave barrier antireflection problem.The transport of electrons from one medium to another through a potential barrier is of interest in many device applications. For example, electrons are transported across a barrier from a metal to a vacuum in field emission electron sources as implemented in the scanning tunnelling microscopeet al. for the enhancement of transmission of light through a metallic film12. The analogous case where it is desired to increase matter wave transmission through a potential barrier that may be complex to account for the loss or gain of probability has been discussed following the work of Bender and Boettcher in 199813 who studied the quantum mechanics of pseudo-Hermitian Parity-Time  relative to the potential describing the incident medium, in keeping with the analogy between potential in the Schrodinger equation and the refractive index of conventional media well known in optics.The matrix methods of thin film optics have an analogous approach in Schrodinger wave mechanics known as the transfer matrix methodIn the following sections, we first examine the transmission of electrons through a rectangular barrier using the transfer matrix method for incident plane waves. We then apply a finite difference time domain method for solving the time dependent Schrodinger equation for incident wavepackets and apply it to enhancing the transmission through a triangular field emission barrier.11 of Schrodinger waves propagating in one dimension from a region of fixed potential energy V0 (the incident medium) into a region of varying potential energy V can be set up. The region with potential energy V has an equivalent refractive index (complex) given by:m is the effective mass of the electron inside the region of potential energy V, and m0 is the mass of the electron in the incident medium. Note that the incident electron kinetic energy E − V0 is assumed positive. The refractive index in equation  is positive or negative. When V < V0, a potential “well” is formed, (E-V) is positive and the layer is analogous to a dielectric layer with a positive real refractive index greater than one. When V > E, (E-V) is negative  and the layer is analogous to a “perfect metal” with a positive, purely imaginary refractive index. For both of these cases, where the region of potential energy V is analogous to a purely real or purely imaginary refractive index, the analogous dielectric permittivity E > V > V0 is possible for matter waves but is unfamiliar in optics. The condition 0 < η < 1 is usually associated in optics with a strong resonant absorption in an anomalous-dispersive medium where η < 1 with 24 and the latter case occurs in the weakly ionized upper atmosphere. Case 2 is, as we shall show, an important case for matter waves, but its rarity in optics may be the reason it has been previously overlooked as a method of achieving barrier antireflection for matter waves. In optics, the condition 0 < η < 1 leads to phase velocities of waves exceeding speed of light c, although the group velocity is invariably less than c because of dispersion. Case 4 is familiar for light waves in absorbing media but not for matter waves as it only applies in cases where probability is not conserved as a consequence of the addition or removal of particle probability from the system. Case 4 will not be further pursued here.The value of the equivalent refractive index of the region of potential energy mentclass2pt{minim25, Al Shakhs et al. have studied the properties of the simple optical system consisting of a bi-layer immersed in vacuum, where one of the layers has the real part of the dielectric permittivity greater than one (dielectric–like) and the other layer has the real part of the permittivity less than one . To achieve the enhancement of the optical transmission of the metal-like layer, these authors have shown that either the condition d1 of the first layer is related to the thickness d2 of the second layer by the relation:There is a wealth of experience with optical antireflection coatings made up of layers of different refractive index. Selecting just one relevant example from a recent paperk is the free space wave vector where 5, who designed arrays of potential wells with The optical analogy of case 1 of Fig. (E-V) is negative, that is, when there is no classical transmission. This is the analogy of the optical problem of the antireflection coating of an ideal metal layer using a single non-absorbing dielectric layer. The conditions et al. by choosing one layer from case 1 of Fig. We now address the problem of antireflection coating of a potential barrier for which mentclass2pt{minimV2 and width w2, we apply a rectangular pre-barrier of height V1 and width w1. Applying the optical analogy, the height V1 and width w1 need to be chosen so that the effective refractive index et al. discussed in section 2. Guided by the work of Gaylord and Brennan, one achieves the matter wave analogy to these conditions when E is the incident electron energy, so that the pre-barrier is actually a potential well as shown in Fig. We now calculate the transmission probability for two adjacent rectangular barriers, with the aim of achieving antireflection effects for particle probability. In order to achieve antireflection of given rectangular barrier of height et al., by choosing a “pre-barrier”  of height −V1 and width w1. The width w1 is varied to find the dependence of the transmission for an incident electron with To illustrate this case, we use the transfer matrix method to calculate the transmission probability for a given barrier coupled to a pre-barrier, where the pre-barrier is adjustable. Consider a given barrier height w1. The result agrees well with Shakhs et al. who found for the analogous optical problem that a positive derivative of transmission probability at zero thickness of the pre-barrier leads to transmission enhancement. However, as we discussed previously, there is another choice of pre-barrier that corresponds to unfamiliar superluminal optical media and therefore has not previously been considered. We show in Fig. V1 approaches E. Therefore a highly favorable condition for transmission enhancement can be specified as Figure The remaining possibility is a pre-barrier where 26 for solving the time–dependent Schrodinger equation for an incident wavepacket. This approach is suitable for use with barrier potentials of general shape, including the types of barriers encountered in realistic field emission devices that include band bending effects. The use of a wavepacket of finite dimension gives a generality and a flexibility that is not possible in a time independent, plane wave approach. Wave packets enable the description of processes where coherence is important, as for example in solid state devices where excitation arises from short pulses27 or from a confined spatial region of a device.In order to calculate the transmission of a general real-valued potential barrier, we use a finite difference time domain (FDTD) numerical algorithm22 for the transmission probability of a plane wave through an idealized representation of a field emission barrier. The exact solution highlights the departures from the WKB predictions and the need to include quantum effects for electrons above the barrier height.Our FDTD approach has been benchmarked against a recently developed exact solution by Forbes and Deane28. In the following example, we choose the electric field to be F = 8 V/nm.The triangular barrier is the simplest representation of a field emission barrier, when the barrier edge rounding caused by the image charge effect is not included. The height of the barrier is determined by the work function of the metal, and the slope of the top of the barrier is determined by the electric field in the vacuum outside the metal. The barrier shown in Fig. 22 for incident plane waves. A wave-packet width of s = 2 nm in real-space is used for the FDTD calculation. The result shown in the figure is converged for increasing wavepacket width. Figure Figure The result above demonstrates the feasibility of using the FDTD numerical method for finding the transmission probability of triangular barriers for a wide range of incident electron energy both below and above the barrier height, provided that an appropriate choice is made for the wavepacket width. Since there is no available analytic solution for the combination of a rectangular and a triangular barrier we wish to investigate, and because the sloping part of the potential requires inelegant conversion to a stepped potential in the transfer matrix method, we will use FDTD as a tool to calculate the transmission probability in this case.V1 that meets the new condition V2 is the height of the field emission barrier. The effective mass of the electron is assumed to be equal to its rest mass in this example.In this section, we will use the FDTD method to investigate whether transmission enhancement could be achieved for a given triangular field emission barrier using a rectangular pre-barrier of height Consider the configuration shown in the inset of Fig. Figure We show in the Supplementary Figure 32. Two possible configurations are shown in Fig. Our strategy for enhancing field emission from a given material is to coat the material with a thin layer of another material. Enhancement of the transmission for electrons at the Fermi energy of the base material will in general yield the best results, since these electrons have the highest transmission for the uncoated barrier. In practice, a barrier of height just below the energy of an electron at the Fermi energy of the incident medium could be achieved by selection of a material with appropriate work function and electron affinityet al. for the optical case of a dielectric antireflection coating of a metal. Pursuing the case when the pre-barrier is a barrier of slightly smaller height V1 than the electron energy, specified as V2 was found. The optical analogy for this case requires special and unfamiliar superluminal media with refractive index less than unity where either the frequency is well above all bound resonances, or otherwise the medium contains only free electrons. Applying our findings to a triangular field emission barrier, we used the FDTD method for solving the time dependent Schrodinger equation to show an example of a useful enhancement for a factor of at least two that occurs when a pre-barrier of slightly less than the incident electron energy is added as a pre-barrier to the field emission barrier. We show that the pre-barrier confines probability by slowing down the particle, giving a superficial resemblance to the confinement of probability in resonant tunneling barrier structures. We have given some examples of how to realize configurations where a pre-barrier could be useful in realizing enhanced transmission in practice. This work has further significance in that it shows how matter wave ‘optics’ is free from the constraint applying to normal optical media where equivalent refractive indices are greater than unity. The relaxation of this constraint leads to interesting possibilities for the design of barrier systems with optimized transmission and reflection properties.In this paper, we have outlined the analogies between the propagation of matter waves in a region of given potential and the propagation of electromagnetic waves in a medium of given refractive index and identify cases that are well known and a case that is previously unexplored. Following a known case of an optical analogy, we have found some transmission enhancement of a given rectangular barrier by the addition of a pre-barrier in the form of a well, in agreement with the findings of Shakhs m.The time-dependent Schrodinger equation is written in the 1D form:For convenience, we separate the complex wave function x and Δt, so that:Nx and Nt respectively the total number of space steps and time steps. For a given time t, we assign:Space and time step number are respectively denoted as Using the finite difference method in the following form:We obtain numerical expressions for the updated wave functions in terms of the values at the previous time step.V to be expressed in eV.The constants 35The FDTD scheme is stable provided the following condition appliesThe initial condition is set to be a Gaussian wave packet as follows:So the initial probability density function iswith normalization x = 0 and x = L.The width of the Gaussian wavepacket is determined by s. The probability of finding the particle within the range of V(x) defined over the interval of x in . The solution range L is determined so that a given wavepacket can be sufficiently evolved while remaining within the range . For example, a convenient choice is w refers to the range of the non-trivial potential. The initial central position of the wavepacket is set so that it does not touch either the boundary of the solution range or the non-trivial potential. We make the spatial step fine enough to ensure that energy conservation is obeyed. Time step size is determined by equation (−6. In other cases, the evolution time can be adjusted according to the specific question under investigation.The program was implemented in Matlab. The input parameters that specify the potential are To confirm the reliability of the computational algorithm and the suitability of the choice of free parameters, we use the calculation of transmission through a simple barrier as a test case.E0 incident on a rectangular barrier with width w and height For a particle with energy where This result is readily gained by representing the particle as a sum of plane waves in the regions outside the barrier, and as a sum of attenuated waves inside the barrier. The boundary conditions are that the wavefunction and its first derivative are continuous across the boundaries of the potential. A test case of the FDTD method is shown in Fig. As shown in Fig. By solving the time-independent Schrodinger equation with plane wave approximation, we can write down the wave function for each different potential region separately, and then by matching the boundary conditions for wave function itself and the first derivative, we can find the transfer matrix, and thus find the tunnelling probability.ith region with potential Vi, wave function is written asmi is effective mass, E is kinetic energy, ħ is reduced Planck constant.For Mi whereThen we obtain the following form of the generalized 2 by 2 matrix The total transfer matrix is obtained as matrix products of each individual matrix m.Transmission probability is defined as Mathematica.The analytical results based on the transfer matrix method for the transmission probability of the two adjacent rectangular barriers were derived and evaluated using Computer implementation in Matlab and Mathematica can be obtained from the authors if requested. Supplementary Information


Three of the four calibration methods used the  192Ir source. Dwell times were calculated to deliver 1 Gy to the TLDs irradiated either in air or water. Dwell time calculations were confirmed by direct measurement using an ionization chamber. The fourth method of calibration used 6 MV photons from a medical linear accelerator, and an energy correction factor was applied to account for the difference in sensitivity of the TLDs in  192Ir and 6 M V. The results of the four TLD calibration methods are presented in terms of the results of a brachytherapy audit where seven Australian centers irradiated three sets of TLDs in a water phantom. The results were in agreement within estimated uncertainties when the TLDs were calibrated with the  192Ir source. Calibrating TLDs in a phantom similar to that used for the audit proved to be the most practical method and provided the greatest confidence in measured dose. When calibrated using 6 MV photons, the TLD results were consistently higher than the  192Ir−calibrated TLDs, suggesting this method does not fully correct for the response of the TLDs when irradiated in the audit phantom.For the purpose of dose measurement using a high‐dose rate PACS number: 87 Furthermore, there is some debate on the variation of this energy response factor with distance from the source, with Meigooni et al. suggesting this factor may range in value by up to 8.5% over a distance of 1–100 mm in water from the source due to the shift of the photon spectrum to lower energies with increasing depth. In contrast, Karaiskos et al. determined this variation with distance (up to 150 mm) to be less than 3%.Thermoluminescent dosimeters (TLDs) were recently used in an audit of HDR brachytherapy centers in Australia. To determine the absolute dose delivered to the TLDs, it was first necessary to calibrate the TLDs to establish the relationship between TLD reading and absorbed dose. A literature search of high dose rate brachytherapy audits and brachytherapy Ir field.–2 Th 192Ir dosimetry are commonly calibrated with a  60Co or a megavoltage source because these sources can be readily accessed, can precisely deliver a prescribed dose of radiation using well‐established dosimetry  that are becoming increasingly popular for dosimetry audits.The purpose of this project was to investigate a range of methods for calibrating TLDs for use with a high‐dose rate y audits.10Three methods of TLD calibration were investigated using the Nucletron V2 source . For each method we first describe the technique used to calculate the dwell time at the defined point to deliver the prescribed dose. We then describe how we confirmed the calculation through measurement with an ionization chamber before proceeding to irradiate the TLDs. The fourth method describes the irradiation procedure using a 6 MV linac. In all cases, the aim was to deliver 1 Gy to the TLDs, as this was the dose that was prescribed for the Brachytherapy Audit. We present the results in terms of the results of the dosimetry audit. Uncertainty in the audit results are thus examined in relation to the uncertainty in the four alternative TLD calibration processes.6×1×1 mm (square) rods of lithium‐fluoride doped with magnesium and titanium  TLDs . TLD readout was performed using an automated TLD reader with hot nitrogen heating . Sensitivity factors were established for individual TLDs using standard irradiation, and the area under the glow curve for a temperature of 270°C was evaluated after a 10 s pre‐read anneal on 165°C. The TLDs were annealed at 400°C between two irradiations using a dedicated annealing oven . To account for the difference in response for each of the individual TLDs, a sensitivity correction was applied to each TLD as described by Meigooni et al.All measurements were made with ni et al.2 192Ir source (Methods 1–3) used either a PTW 30010 (Methods 1 and 3) or PTW TW 30013 chamber (Method 2) with a PTW UNIDOS E electrometer . Both chambers have an external PMMA wall of thickness 0.335 mm, an internal graphite wall of thickness 0.09 mm, with an active volume defined by a radius and half length 3.1 mm 11.5 mm, respectively. The PTW 30010 air kerma chamber calibration coefficient  for use with Ir‐192 was derived through interpolation of response in a  60Co and a kilovoltage X‐ray beam at the Australian Radiation Protection and Nuclear Safety Agency (ARPANSA) laboratory, as previously described. The air kerma calibration coefficient for the waterproof (PTW 30013) chamber, which has the same dimensions as the 30010 chamber, was derived through direct comparison, by measurement of the air kerma rate (AKR), using the  192Ir source and air‐kerma calibration jig described in Method 1.All absorbed dose measurements made with the escribed.11 The 192Ir source was determined 100 mm from the source using a Nucletron in‐air calibration jig , the PTW 30010 chamber and the air kerma calibration coefficient determined at the National Physical Laboratory  in the UK. Details of this calibration procedure have been previously described;(–) however, in contrast to the ARPANSA factor, the NPL factor takes into account a number of corrections such as scatter and non‐uniformity effects that would normally be applied in addition to the air kerma correction factor when following the recommendations of the International Atomic Energy Agency TecDoc 1274. To determine the AKR of the source, the chamber is placed in the jig assembly  applied, and the result is divided by the irradiation time. For the measurement of absorbed dose in water, however, the corrections included in the NPL calibration coefficient are not required. Hence, we used the ARPANSA‐derived factor  with the appropriate correction factors when the chamber was used to determine the absorbed dose.The AKR of the n the UK.12 Det and is shown in Fig TLDA) divided by the average TLD calibration reading (TLDC).The design of the Brachytherapy Audit phantom is based on that of Roué et al.14 andAttcath, of 1.0017 was included in the calculation of dwell times for the in‐air irradiations.The first method required the TLDs to be irradiated using an air‐jig assembly similar to the Nucletron air‐jig assembly, but with the additional feature of variable source–catheter distance. The TLDs were placed in a PMMA holder replacing the ionization chamber. The central axis of the catheters was placed at 50 mm from the central axis of the TLDs. For each irradiation, a set of three TLDs were irradiated by sending the source down each of the catheters so that it dwelled at a point 50 mm perpendicular to the central TLD to deliver a dose of 0.5 Gy . The catheters in the jig have walls 0.28 mm thick and a correction factor for attenuation, diations.11 Table XI indicates that air attenuation is approximately 0.1% per 100 mm, and so for a distance of 50 mm we have assumed this effect to be negligible. To convert air kerma to absorbed dose to water, we applied the ratio of mass energy absorption coefficients for water and air averaged over the  192Ir spectrum (1.11).The dwell time for each source position was calculated using the previously derived source AKR, applying the inverse square law, a factor to account for air attenuation and a factor to convert air kerma to absorbed dose. The IAEA TecDoc 127413 TabAttHold, was estimated by measuring the TLD response with increasing thicknesses of acrylic (in the form of cylinders mounted on the holder), and extrapolating the responses back to zero thickness. The attenuation was calculated from the ratio of the TLD response in the holder and the extrapolated response at zero thickness. Using this method, the attenuation of the holder was estimated to be 1.3% and the dwell times increased accordingly.The wall thickness of the PMMA TLD holder was 2.7 mm. The attenuation factor for this holder, Mu  as follows:NK,ARP is the ARPANSA derived air kerma chamber factor (4.890×107 Gy/C), (μ¯trρ)aw is the ratio of mass energy absorption coefficients  as described by Butler et al. to determine a kn of 1.0351 for our chambers which have an active volume defined by a radius and half length 3.1 mm and 11.5 mm, respectively. Due to their small cross‐sectional area (1 × 1 mm), the effect of non‐uniformity in fluence across the TLDs was assumed to be negligible for all calibration methods.Prior to irradiating the TLDs, the dwell time calculation was confirmed through measurements made using the ionization chamber and catheter arrangement shown in Fig. 475×645×560 mm) water tank. For each irradiation, a set of three TLDs were irradiated by sending the source down each of the catheters so that it dwelled at a point 50 mm perpendicular to the central TLD to deliver a dose of 0.5 Gy .The second method required the TLDs to be irradiated using the air‐jig assembly as described in Method 1 and similar to that shown in Fig.  and the parameters of Daskalov et al., which at 50 mm perpendicular to the source, states the dose rate is 0.0446 cGh−1U−1, where U is defined as the air kerma strength and U=1 μGy m2h−1.The dwell time for each source position was calculated using the previously derived source AKR, the TG‐43 formalism,9 and  who considered an adaptation of TRS 277 using the high‐energy X‐ray formalism (which they refer to as the Bragg‐Gray method).To confirm the dwell time calculation, measurements made with the ionization chamber were converted to absorbed dose using the methods of Tolli and Johansson,19 wND, the absorbed dose to air factor, was derived from the ARPANSA NK,ARP value, ND=NK(1‐g)kattkm  has been assumed. A value for kattkm for the PTW chamber is not listed in TRS 277 and so we used the value quoted in the PTW handbook (0.972) for the 30010 chamber to obtain an ND value of 4.74×107 Gy/C.The modified Bragg‐Gray formalism, according to Tolli and Johansson, was defined as:Sw,a, used by Tolli and Johansson,(–) was 1.137. For the perturbation due to the chamber wall pwall, Tolli and Johansson quote a value of 1.018 for the A‐150 chamber and 1.001 (at 50 mm) for the graphite wall chamber. Ferreira et al. quotes a value for Awall  of 0.990 for the PTW chamber. We therefore used this value (0.990) in our calculations, though assumed an uncertainty of ±0.5%, as the chamber was placed directly in water and the cap not used.The stopping power ratio, ohansson,–19 w a chamber with an aluminum central electrode over‐responds by approximately 2% at 50 mm from the source in water. Therefore, the proposed factor to account for the central electrode perturbation, pcel, is 0.98.According to Tolli and Johansson,19 a cpd is the correction factor for the displacement of the effective point of measurement. Using the formalism of Tolli and Johansson, the measurement point is at the center of the chamber. The non‐uniformity in fluence across the chamber is accounted for with the non‐uniformity factor pn  with PMMA would have a negligible effect on attenuation. In summary, no correction factors for the nonwater equivalence were included in the calculations.The catheters used for these measurements were the Nucletron 5F ProGuide catheters which have a wall thickness of 0.24 mm and were placed inside a PMMA rod with a wall thickness of 3.9 mm. The distance between the center of the catheter and the center of the central TLD was 50 mm which included 5.4 mm of plastic materials supporting the source and TLDs. Based on our previous work,11 we To confirm the dwell time calculations, measurements made with the ionization chamber were converted to absorbed dose using the formalism and factors described in Method 2.100×100 mm field. Using standard methods, the number of monitor units required to deliver 1 Gy to the TLDs was calculated using the previously determined percentage depth dose at 100 mm. The TLDs were contained within the plane containing the central axis of an NE 2571 ionization chamber and perpendicular to the beam central axis. The formalism of TRS 398 and an absorbed dose to water chamber calibration coefficient  was used to convert the ionization chamber readings to absorbed dose to water in the 6 MV beam. To derive an energy correction factor, the TLDs were irradiated in a range of X‐ray energies and a factor for  192Ir was interpolated using the methodologies of Kron et al. assuming a mean energy of 258 keV for  192Ir at a depth of 50 mm in water. The curve fit is based on the equation:α1 and α2 are two curve fit parameters  that determine the exponential fall‐off at low energies and the inverse cubic fall‐off towards higher energies, respectively. The other two curve fit parameters E1 and E2  allow for an energy shift for the two components. All curve fit parameters were derived from measurements made with kilovoltage,  137Cs, and megavoltage X‐ray sources, and do not include the values derived from the measurements made with the  192Ir source. The interpolated value was found to be 1.03 and we have assumed an uncertainty of 5% (1 SD) based on the recommendations of the AAPM TG‐43U1 report  600c 6 MV linear accelerator was used to irradiate eight TLDs on two separate occasions in solid water. The TLDs were placed at a depth of 100 mm in the solid water with a source‐to‐surface distance of 1000 mm, on et al.1 assuTLDA) readings compared with the readings from the TLD calibration set (TLDC). For Methods 1–3 there are two results: the first is based on the calculated dose , and the second is based on the measured dose . The uncertainty in each Brachytherapy Audit result is therefore a combination (summed in quadrature) of the uncertainty in the TLD readings (TLDA and TLDC) and the uncertainties in either the calculated or measured dose. Each of the uncertainties associated with the calculated and (ionization chamber) measured dose is discussed in the Discussion section, with further details provided in the online supplementary material.The results of the Brachytherapy Audit are stated as the ratio of the Audit site TLD . Similarly for each of the calibration methods described in this paper, a minimum of nine TLDs were irradiated and the standard uncertainty is again 0.7%.At the audit sites, a total of nine TLDs were exposed to a nominal dose of 1 Gy. The standard deviation of the nine TLDs from each site was always within The dose measured with the ionization chamber and the in‐air jig was 2.2% higher than the calculated dose Table . Based oThe measured dose was 1.1% higher than the calculated dose Table . Based oUsing Method 3, the measured dose was 1.5% lower than the calculated dose Table . Based oUsing Method 4, the results of the TLD audit indicate that, on average, centers delivered a dose 6% higher than the prescribed dose Table .TLDA and TLDC, each 0.7%) and the uncertainties in either the calculated or measured dose. Accurate dosimetry for  192Ir is challenging in the absence of a suitable formalism and a dose‐to‐water primary standard, as such, each of the methods of calculation and measurement carry a wide range of uncertainties, many of which have been estimated, which has resulted in an overall uncertainty in the results of the Brachytherapy Audit. The estimated standard uncertainties are summarized in Tables We have described four different methods of TLD calibration for applications involving high dose rate brachytherapy. For Methods 1–3, prior to TLD irradiation we calculated the amount of time the source should rest at its dwell position to deliver the required dose and we confirmed this calculation by direct measurement. The results from the Brachytherapy Audit therefore carry an uncertainty which is the sum in quadrature of the uncertainty in the TLD readings  in the distance of the source to the measurement point of the TLD and chamber.The AKR of the source was determined using the NPL chamber factor  and has been ignored. The polarity correction is also expected to be small and an uncertainty of 0.2% is included in the value of Nk to take this into account.For all ionization chamber measurements made with the  ignored.11 The 192Ir spectrum (1.11 with standard uncertainty 3%) to determine the absorbed dose to water. When TLDs calibrated in this way are used in water, the spectrum incident on the TLD will include more low‐energy photons due to scatter in the water, to which the TLD may overrespond. Based on the energy response data shown in Fig.  192Ir in air relative to 6 MV is 1.01, suggesting a 1% over‐response. As the TLDs were placed in a PMMA holder 2.7 mm thick, we would expect this over‐response to be less than 1%. This could however, potentially explain why the audit results were higher than expected . Furthermore, the TLDs were irradiated in a plane perpendicular to the source, which is in contrast to the geometry for the audit TLDs which were contained in a plane 30 mm above and below the source. Such variations in geometry  will again produce differences in the spectrum leading to variations in the TLD response. Based on the work of Karaiskos et al., we have assumed the angular response of the TLDs to be negligible at less than 1%. A standard uncertainty of 3% has been included in the uncertainty analysis to account for these uncertainties. It is not clear, however, if the value we have used for the ratio of mass energy absorption coefficients for water and air is correct in this setting, and we therefore have the least confidence in this method of calibration due to uncertainties in the factor used to determine the absorbed dose to water from the calculation/measurement of air kerma and the attenuation factor of the TLD holder. In addition there are a number of factors that are common to both the calculation and measurement methods limiting the independence of these methodologies. The method, however, is reasonably simple to use once a suitable calibration jig has been constructed and a chamber calibration coefficient determined. In summary, the total uncertainty budget for Method 1 (including the TLDA and TLDC readings) is 4%  when the dose to the calibration TLDs is based on calculated or measured dose.In both the measurement and calculation of dwell times, we have used the ratio of mass energy absorption coefficients for water and air averaged over the Ir in air13 rel and the previously measured air kerma rate based on the NPL‐derived chamber calibration coefficient. The data from the Daskalov study are based on Monte Carlo calculations and have not been verified experimentally, but are supported by previous calculations and measurements with similar sources. Daskalov and colleagues state that their calculations agree with measurements to within their experimental error of 5% within 70 mm of the source, and we have taken the standard uncertainty to be approximately half this value at 50 mm.Calculation of dwell times for the in‐water measurement relied on the data provided by Daskalov et al.17 and which uses an absorbed dose‐to‐air chamber factor rather than an air kerma‐based factor. To derive a value of ND from NK we assumed a value of g=0.003 based on published values for  60Co. However, it is expected this value will be less for  192Ir, but the uncertainty in this value will be negligible compared with other factors. For the remaining factors, we used a combination of values published by Tolli and Johansson, Ferreira et al., Bielajew, and Butler et al. and assumed their published uncertainty for each of these factors, resulting in an overall uncertainty as shown in Table As there is no standard formalism for measurement of absorbed dose to water using a Farmer type chamber, we used the modified Bragg‐Gray formalism according to Tolli and Johansson19 whi which contain the same data used by the Nucletron brachytherapy planning computers used by most of the centers in the audit. The calculation method, therefore, does carry some degree of interdependence . The close agreement of the measured and calculated results (within 1.1%) confirm our confidence in this method and if we assume an overall uncertainty of 3% (including the 0.7% uncertainty in TLD readings) for this method of calibration, we can say that all sites that participated in the audit irradiated their TLDs to 1 Gy within the expected uncertainty. In summary, the total uncertainty budget for Method 2 (including the TLDA and TLDC readings) is 3%  when the dose to the calibration TLDs is based on calculated or measured dose.This method of TLD calibration was the most difficult of all methods to perform and is least practical for regular TLD calibration as it required careful placement of the delicate in‐air jig into the large water tank. It was, however, possible to minimize the amount of non‐water equivalent material in the irradiation field. The method of calculation used the Daskalov tables17 whiTLDA and TLDC readings) is 3% or 2% , respectively, when the dose to the calibration TLDs is based on calculated or measured dose.The uncertainties described in Method 2 mostly apply to Method 3. There are, however, three major differences .< 1 mm). The major disadvantage of this method, however, is the introduction of the energy correction factor. The energy correction factor for TLD‐100 LiF:Mg,Ti measured by Meigooni et al. was 1.045, with a standard uncertainty of 3%, at a depth of 5.32 cm in polystyrene. This factor varied by up to 8.5% when the depth of overlying phantom material ranged from 10 to 100 mm, and this variation was assumed to be related to changes in the  192Ir spectrum with depth. This variation of TLD response with energy, however, was challenged by Thomason and Higgins who determined the energy response was negligible  and challenged the experimental methods used by Meigooni to explain their difference in results. Over decades, many authors have quoted an energy correction factor for LiF:Mg,Ti interpolated from measurements made with kilovoltage units  and megavoltage therapy linacs,  60Co or  137Cs sources. Each of these investigators have used a variety of narrow beam and heavily or lightly filtered kilovoltage sources and a range of methods to determine mean energy of the irradiating source. Based on our work in deriving the energy factor of 1.03 , the energy correction factors would be 1.02 and 1.04, respectively , which is consistent with the findings of Karaiskos et al. and considerably less than up to 8.5% as suggested by Meigooni et al.Irradiating the TLDs using a clinical linac is relatively quick, the dosimetry has a high level of confidence due to the availability of internationally accepted data, and geometric uncertainties are minimal. Using a high‐energy clinical linac with a relatively flat beam and minimal uncertainties from using water‐equivalent materials provided a high level of confidence in the dose delivered to the TLDs. Uncertainties in measured dose relate only to the correction factors applied to the ionization chamber reading and a small positional uncertainty relating the measurement point of the ionization chamber to the TLDs  is closer to  192Ir and therefore potentially minimizes the uncertainty in interpolation over a shorter energy range. Based on the data shown in Fig.  192Ir relative to  60Co is still approximately 3%. We did not have access to a therapy  60Co unit for this work. A cell irradiator was made available for the data point shown in Fig. An alternative to using a 6 MV linac would be the use of a  and may also partly explain differences in values reported in the literature. Furthermore, whilst we may be comparing TLDs with identical chemical composition, the detectors may vary in doping, shape, and size, leading to variations in response due to volume averaging, detector self‐absorption, and perturbation effects. Unfortunately, deriving the response from interpolation in a range of X‐ray energies may also carry a large degree of uncertainty and this will most likely be the largest source of error in the overall uncertainty in TLD readings. In line with AAPM TG‐43U1 recommendations, we have assumed a standard error of ±5% in our derived energy correction factor for the reasons stated above and because of the limited data in the energy range between our highest kilovoltage source (100 keV) and our reference 6 MV linac. This factor, however, cannot have a value less than 1.00 and so the standard error is more likely to be ‐3% to +5% Based on this method, however, it would appear that all centers delivered a dose higher than expected  and there does not exist a universally accepted dosimetry formalism, we suggest that the source of discrepancy between the  192Ir methods and the 6 MV method may be due to some underlying source of systematic uncertainty in the energy correction factor used with Method 4 when applied to the phantom measurements. It should be noted that if the energy correction factor of 1.03 had not been applied, then the values shown in the final column of Table TLDA and TLDC readings) is 5%  when the dose to the calibration TLDs is based on measured dose. This uncertainty is dominated by the 5% uncertainty in the energy correction factor, and therefore this method may be more suitable for use with detectors with a smaller energy response such as OSLDs.Differences in heating (temperature profiles) and annealing processes may also have an effect on TLD response3 and ed Table . Althoug were defined as ‘optimal’ if within 1.5 SD and ‘within tolerance’ if within 2 SD. The combined standard uncertainty for the European and Brazilian audits was 6.54% (2 SD) and 2.8% , respectively. This translates to optimal levels of ≤5% and ≤3%, and tolerance levels of 5%–7% and 3%–6%, respectively. Based on the TLD methods presented in this paper, optimal and tolerance levels would range from ≤3% and 3%–4%  to ≤7.5% and 7.5%–10% (for Method 4). Using this criterion, we can conclude that all centers participating in the audit were within the optimal level.The results of the Brachytherapy Audit are summarized in Table ,24 w 192Ir applications. Using a clinical linear accelerator is convenient, the dosimetry is well understood, and several TLDs can be irradiated in a short period of time. The major disadvantage of this method is the uncertainty in the energy correction factor, which is dependent on a range of measurement conditions and TLD characteristics. The uncertainty in this method was the highest of all methods investigated (±5%) and all dose measurements using this method were consistently higher than the methods using the  192Ir source. Calibrating TLDs with the  192Ir source requires careful measurement setup due to the high dose gradients surrounding the source. Consensus documents providing rigorous review of the correction factors applied to commonly used ionization chambers for measurement of absorbed dose do not exist, leading to some uncertainty in measurement of dose. In each of the methods using the  192Ir source, it was necessary to use a common source of data; however, all three methods resulted in similar audit results. Method 3 used a phantom very similar in design to the Audit phantom (which was the purpose of this work) and hence a similar geometry in terms of distance between source and TLD. In addition, it used similar amounts of water and phantom material, and it provided minimal uncertainty in source — TLD distance and the overall uncertainty was lowest (2%). Method 3 is, therefore, our chosen method for presentation of the results of the Brachytherapy Audit.We present four methods for calibration of TLDs for use with high‐dose rate The authors would like to acknowledge Dr Ivaldo Ferreira, formerly of the EQUAL‐ESTRO Laboratory, Villejuif, France for his advice in carrying out these measurements. We would also like to thank Dr Jack Venselaar for sharing the details of the European audit. We acknowledge the excellent work of Peter Pinder and his team at the Peter MacCallum Cancer Centre for their expertise in manufacturing the high precision phantoms. We are also most grateful to The Wesley Cancer Care Centre (Premion), The Peter MacCallum Cancer Centre, The University of Newcastle, The Calvary Mater Hospital, Nucletron Australia, Global Medical Solutions, Varian Oncology Systems for their generous support of this project.Supplementary MaterialClick here for additional data file.


The quality of therapeutic proteins such as hormones, subunit and conjugate vaccines, and antibodies is critical to the safety and efficacy of modern medicine. Identifying malformed proteins at the point-of-care can prevent adverse immune reactions in patients; this is of special concern when there is an insecure supply chain resulting in the delivery of degraded, or even counterfeit, drug product. Identification of degraded protein, for example human growth hormone, is demonstrated by applying automated anomaly detection algorithms. Detection of the degraded protein differs from previous applications of machine-learning and classification to spectral analysis: only example spectra of genuine, high-quality drug products are used to construct the classifier. The algorithm is tested on Raman spectra acquired on protein dilutions typical of formulated drug product and at sample volumes of 25 µL, below the typical overfill (waste) volumes present in vials of injectable drug product. The algorithm is demonstrated to correctly classify anomalous recombinant human growth hormone (rhGH) with 92% sensitivity and 98% specificity even when the algorithm has only previously encountered high-quality drug product. Several factors have been correlated to immunogenicity: these include impurities, such as protein aggregates3, differences in glycosylation, deamidation or oxidation5, and protein misfolding6.The use of therapeutic proteins has become common practice in medicine and their success has stimulated significant investment towards the discovery and manufacture of a wide range of biopharmaceuticals. A central challenge of protein therapies is the potential to trigger antibody formation. Triggering such an immune response has consequences for both the efficacy of the therapy and the safety of the patient10. Despite these policies, a study looking for freeze events during distribution found that up to 76% of the vaccine vials tested showed evidence of spoilage due to freezing11. Point-of-care applications are especially challenging as a quality determination must be made rapidly on small sample volumes in clinical settings that may be resource constrained.Rapid quality assessment of therapeutic proteins is essential when there is the possibility of an insecure supply chain – resulting in the shipment of degraded proteins or in the sale of counterfeit products – or when there is a need to closely monitor and control biopharmaceutical manufacturing. Formulated proteins require cold distribution and storage, a major limiting factor for treating populations in rural and developing areas. In India, concerns about spoilage necessitate preventative measures such as discarding vaccine vials that have been distributed to three vaccination clinic events, even if the vials remain unopened, resulting in a vaccine wastage rate of roughly 60%12, and demonstrate a classification technique that is capable of identifying degraded material based on changes in the scattered Raman spectrum.The above immunogenic factors all involve changes in the molecular characteristics of the protein that may be possible to measure at the point of care using Raman spectroscopy. Here we present a Raman instrument capable of measuring proteins in solution at dose relevant concentrations and with a sample volume small enough that it could be taken from the overfill volume used in vial packing of drug products13, is commonly used in the analysis of biological materials14 and has been used for the verification of primary and secondary structure of proteins since 195817. The published examples of protein Raman spectra have typically been reported for solid powders and for solutions with concentrations in excess of 5 mg/mL, higher than many formulated products. Previous work has been limited to high protein concentrations because of the small cross-sections for Raman scattering coupled with the potential for photo-degradation of the protein under high illumination. Traditionally, to detect proteins at lower, dose-relevant, concentrations has required a switch to Surface Enhanced Raman Scattering (SERS).Raman spectroscopy, discovered in 1928 by C.V. Raman and K.S. Krishnan20. The resonance enhancement enables detection down to the single molecule level20. The SERS signal is related to the constituent amino acids and amide backbone of the protein22, but the spectrum differs from the spectra of the protein in solution due to the fact that the SERS technique is sensitive to the orientation of the adsorbed protein23. Therefore, if the orientation of the protein cannot be controlled there will not be a unique spectrum associated with any given protein when using SERS. Additionally, this technique requires a consumable substrate with a limited shelf life25. Fortunately these complications can be avoided as several therapeutic proteins are provided in formulation at concentrations high enough that the signal enhancement from SERS is not needed. Here we show that characterization of these proteins is possible using spontaneous Raman spectroscopy of free-proteins in solution, provided the sample holder and optical system are well designed. Our approach was to employ the double-pass, confocal optical geometry illustrated in Fig. 12.Surface Enhanced Raman Scattering is a technique where the protein is adsorbed to a metallic substrate, resulting in resonance enhancement of the excitation field30, the challenge here is to develop a classifier that can detect a myriad of degraded protein forms that that the algorithm has never encountered before. This is a specific case of the general One Class Classification problem in chemometrics31. In this problem, there is a large set of data in one class, and a limited or non-existent set of data in the ‘other’ class. This problem occurs in a number of domains with examples including anomaly detection in gas turbines32 and classification of documents as relevant to a user33. One class classification has been applied for Raman spectroscopy based identification of unknown bacterial strains34 and the detection of simple mixtures of chlorinated solvents35. This work expands the technique to the Raman spectral analysis of complex molecules with a particular focus on therapeutic proteins.Alongside the Raman instrument reported here, we have developed a classification algorithm that is capable of classifying a protein that has degraded. While automated classification algorithms have been widely used for spectral classificationWe demonstrate two different approaches to training the classification algorithm using only “good” protein spectra. In both cases the goal is to train the classifier so that it ignores systematic variations associated with the instrument such as shot noise, alignment drift, etc. and instead focuses on spectral features that are correlated with the protein analyte. In the first approach the algorithm is trained using only spectra from high-quality recombinant human growth hormone (rhGH) and in the second approach the training uses both the high-quality rhGH and spectra from three unrelated high-quality proteins of various sizes. The addition of the different protein spectra improves the algorithms ability to identify the protein variants and the algorithm is demonstrated to correctly classify degraded recombinant human growth hormone (rhGH) with 92% sensitivity and 98% specificity for the range of degraded and un-degraded samples used for this work.Raman spectra were collected using a purpose built system, shown in Fig. Recognizing that the Raman signal will be collected primarily from the region close to the focus of the microscope objective, the dimensions of the liquid containing well were set at 4 mm wide, 6 mm long, and 0.8 mm deep along the optical path for a total volume of approximately 19 µL. The sample holder did not need to be any larger than this because the increased sample volume would not improve the amount of sample-laser interaction and the walls and mirror in the sample holder were metallic, so they added no background Raman signal. The depth of the sample holder was set to allow the microscope objective to focus light on the back mirror to achieve an increase in excitation and collection as described above, while at the same time moving the excitation spot as far from the fused silica window as possible to reduce the background signal from the window.To use the holder a 20–25 µL drop of material was added to the well, over filling it slightly, and then the well was capped with the mirror. This prevented the formation of an air bubble between the sample and mirror, resulted in a consistent sample volume and geometry with no meniscus, and effectively sealed the sample preventing it from drying during long spectrum acquisitions. The inverted configuration ensured that neither the sample holder nor the microscope objective needed to move during sample loading or cleaning operations. This allowed the system to be used without re-aligning the optics each time a new sample was presented to the system.36 but these have an unavoidable overlap of the excitation laser with the capillary walls resulting in a significant background signal due to the capillary material and an attenuation of the excitation light due to scattering or absorption by the capillary material. The impact of the background signal due to the capillary material can be mitigated by choosing a material with a small Raman cross section such as Teflon, but this approach has not been shown to improve the protein limit of detection37.Sample volumes down to 1 μL are possible with capillary based sample holdersThe excitation laser used with this system was a fiber coupled Ondax laser operating at 830 nm (R0-830-PLR-300-MM-1) delivering approximately 100 mW of laser power to the sample. Light was delivered from the laser to collimating optics via a 105 μm core multimode fiber. The collimated light was passed through a Semrock 830 nm MaxLine Laser clean-up filter to remove any amplified spontaneous emission from the laser and any Raman light generated within the delivery fiber. The filtered light was coupled into the optical path of the microscope objective by a Semrock long pass filter operated as a dichroic mirror. Collected light was passed back through the Semrock filter and then through an additional long pass filter to further attenuate Rayleigh scattered excitation light before being coupled into a fiber bundle for delivery to the spectrometer. A diagram of the system is given in Fig. Spectra were acquired using an Acton SP-300i grating spectrometer. The use of a mirror in this sample holder does significantly increase the amount of Rayleigh scattered light collected by the system. To prevent the scattered excitation light from saturating the detector the grating in the spectrometer was adjusted to position the scattered excitation light off of the sensor. To generate the spectra presented here the following procedure was used. For each sample of protein solution, 100 spectra were collected with an integration time of 10 s per spectrum. Cosmic ray events were identified in the 10 s spectra and removed. After cosmic ray removal, the individual spectra were scaled to match the median value of pixels 200 to 300 across the 100 spectra set to account for variation in the laser power. This region was chosen because it was beyond the filter turn on region and generally contained no strong spectral peaks. The individual 10 s spectra were then smoothed across wavelength using the Savitzky-Golay filter function (Matlab) with a degree of 11. A representative sample spectrum was created by taking the mean value of the 100 filtered and smoothed spectra at each wavelength, and a noise spectrum was created for each measurement by taking the standard deviation at each wavelength across the sample spectra.38. Calibration of the Raman shift was performed using a polystyrene sample with a well-known Raman spectrum.The sample spectrum resulting from this processing contained Raman and fluorescence signal from the protein, sample holder, and the buffer that made up the bulk of the protein solution. A characteristic background spectrum for each protein buffer was created using the process described above but with the appropriate buffer solution rather than a protein sample. The characteristic background spectrum for the rhGH buffer is shown in Fig. The proteins used in this experiment were obtained from several suppliers. Somatropin, recombinantly produced human growth hormone (rhGH), was obtained from Sandoz supplied in 10 mM sodium phosphate buffer at a pH of 7.0 and a concentration of 10.7 mg/ml. This material was frozen and stored at −20 °C for shipping, thawed for aliquoting, and the aliquots stored at −80 °C before being thawed for use. The interferon was obtained from RayBiotech (228-10819-3) as a lyophilized powder from a 1 mg/ml solution containing 2.3 mg Sodium phosphate dibasic and 0.55 mg sodium phosphate monobasic buffer and reconstituted in distilled water at a concentration of 3.5 mg/ml. The interferon was used directly after reconstituting to avoid the potential damage of a freeze-thaw cycle. The Immunoglobulin-G (IgG) was obtained from Bethyl Laboratories (P80-105), purified from serum and at a concentration of 1 mg/mL. The IgG was supplied in phosphate buffered saline containing 0.09% sodium azide. Lyophilized insulin powder was obtained from Sigma (I2643) and reconstituted in a 0.01 N HCl solution at a maximum concentration of 11 mg/ml. The proteins examined here were supplied in, or reconstituted into, variants of Phosphate Buffered Saline (PBS) except for insulin which was reconstituted in 0.01 N HCL. Drug product buffers may contain sugars or similar molecules with unique Raman signatures but here we maintained similar buffers where possible to allow for direct comparison of the limits of detection and to avoid buffer exchange.A series of oxidized human growth hormone samples were prepared from reference material in order to examine the sensitivity of the instrument to changes in proteins due to degradation processes. The oxidized samples were generated by exposing Sandoz Somatropin to 5% hydrogen peroxide (Sigma) and then incubating the material at 37 °C overnight. This resulted in varying levels of oxidation of the Methionine groups M14, M125, and M170. A summary of the oxidation levels of the sample material is given in Table To prepare the reference and oxidized rhGH samples for LC-MS they were first fragmented into peptides and transferred from their original buffers to a buffer suitable for LC-MS. The first step in fragmenting the proteins was to dissolve the samples in 6 M Guanidinium chloride to denature the proteins. The disulfide bonds within the proteins were then broken by a reduction step using 10 mM dithiothreitol (DTT) at 70 °C for 30 minutes followed by an alkylation step using 55 mM iodoacetamide (IAA) at room temperature for one hour in the dark.In preparation for digestion, the proteins were then dialyzed three times in Tris-HCl buffer, pH at 6.8, via 10 kD Amicon membrane centrifugal filters  at 12,000 rpm for 15 minutes. The proteins were then digested with Trypsin at room temperature overnight to fragment the proteins into peptides while minimizing artificial oxidation. The digestion process was terminated with 20 µL 5% formic acid and the peptide solutions were aliquotted to 20 µL samples and stored at −80 °C for further analysis.A Dionex 3000 UPLC system  was used for the liquid chromatographic separation and a Thermo LTQ XL  was used for the mass spectrometry. The liquid chromatographic separation used a self-packed capillary column with an internal diameter of 75 μm and a length of 150 mm packed with Magic C18 . The LC separation method was carried out by a 75 minute gradient elution program, using 0.1% formic acid in water as Phase A and 0.1% formic acid in acetonitrile as Phase B, at a flow rate 200 nL/min. The ratio of Phase B was increased from 2% to 40% over the first 50 minutes, then increased to 95% over the next 5 minutes and kept there for 10 minutes. The ratio of Phase B was then decreased from 95% to 2% in 2 minutes and maintained at 2% to the end of the program.The coupled linear ion trap mass analyzer was operated in the data-dependent CID fragmentation mode and it was adjusted automatically between MS and MS/MS acquisition in nine cycles with a full scan mode at m/z 300-2,000 Da. Thermo Proteome Discover 1.4 was used to analyze the raw data, using a human growth hormone sequence database file and assuming full trypsin specificity. The tolerance for precursor ions was set at 50 ppm and the tolerance for product ions was set at 1.0 Da. Carbamidomethylation of cysteine was selected as a static modification and deamidation on asparagine and oxidation on methionine were selected for dynamic modification search. The final confirmation of the modifications was by manual search.39. A variety of classifiers including Support Vector Machines35, neural networks33, and nearest-neighbors41 have been applied to this problem. The approach used in this paper will be to define an ellipsoid in N dimensions (where N is the size of the spectrum for classification), making the classifier presented a variant of the Minimum Volume Ellipsoid approach developed by Rousseuw44.The goal of this work was to develop a classifier capable of recognizing if a particular sample under test was high-quality rhGH or degraded rhGH. A standard binary classifier could be developed for this problem with an output of either “good material” or “bad material”. The standard classification algorithms for this problem work by defining a boundary between the two classes, based on examples from each class. These algorithms assume that the samples presented to the classifier adequately sample the space of possible spectra generated by each class. However, in this application a complete set of “bad” examples does not exist, the range of degraded products is too large to adequately sample, and instead the classifier must define the boundary with only examples of the “good” class. This problem falls into the general field of one-class classification−1 was chosen because it contains the brightest features associated with protein structure and composition, resulting in a sample spectrum represented by a vector 830 points long. The data is then scaled into the region 0-1, to reduce the impact of small changes in concentration. The next step is to apply Principal Component Analysis (PCA) to further reduce the dimensionality of the data. The PCA algorithm finds a set of vectors in the original space that can be used to represent the data. The vectors are ranked by the amount of variation in the original data each vector captures. By using a set of principal components smaller than the dimension of the original space, the length of the vector representing each data point is reduced. Additionally, if the data set for the PCA algorithm is chosen correctly then the principal components themselves should be directly related to spectral information relevant to classifying the proteins.Given the high dimensionality of the data  and the small number (5) of repeated experiments generated degraded samples overfitting in the classifier is an important concern. Information about protein structure and condition is not uniformly distributed in the spectrum of the protein, so the first step after spectral processing is a dimension reduction to reduce the impact of spectral variation in low information regions on the classification algorithm. After background subtraction and residual polynomial fitting the first step in dimension reduction is to truncate the spectrum to an appropriate spectral region. The region from 800 to 1721 cmTwo methods of performing the initial principal component analysis for dimensionality reduction were investigated. In Method 1 the PCA algorithm was applied to a one set of spectra of the high-quality (un-degraded) rhGH. In Method 2 the spectra for the high-quality rhGH were combined with spectra from the three other high-quality proteins. The high-quality rhGH training set was formed from five data sets collected over the course of the year. As part of this research the impact of the number of data sets included in the training set was investigated. In both Method 1 and Method 2, the N-highest ranked principal components were used to form a reduced dimensional space, and the test data was projected into this space. N was chosen such that the resulting PC space captured at least 60% of the variation in the training set. This reduced dimension data set was used as the input to the classifier.x =  is the representation of the spectrum in the N dimensional space generated after the first round of PCA, σ is the vector representing the ellipse axes lengths, and Θ is a tuning parameter which controls the size of the ellipse. ⊘ is the Hadamard division operator indicating element-wise division of two vectors. The term (Ax − c) uses a projection matrix A and centroid vector c to project the data from the N-dimensional PC-projected space into an N-dimensional space centered on the classification ellipsoid with its coordinate axes aligned with the ellipsoids axes. A second round of PCA is performed using just the rhGH training data to define the matrix A, centroid vector c, and axis length vector σ. In this round the principal components now form the axes of the ellipse and set the projection matrix, A, the eigenvalues are used to set the relative size of the ellipse along each axis, σ, and the centroid of the projected high-quality rhGH spectra, c, is used to shift the projected data into the center of the ellipse. In this way the longest dimension of the ellipse will be aligned with the direction in which the un-degraded rhGH spectra are most spread, and the shortest dimension will be aligned with the direction in which the data are least spread. The performance of this classifier depends on the value of Θ. As a sample independent approach, the value of Θ can be set so that the classification ellipsoid captures 99% of the training examples.The classifier examined here is constructed by defining an ellipsoidal surface that encloses the spectra representing the high-quality rhGH material. The ellipsoid is chosen to follow the shape of the high-quality rhGH material and the resulting classifier can be written from the equation of an ellipsoid in N dimensional space as47. A detailed peak assignment and interpretation is given in the supplementary material. To gauge the repeatability of the system several spectra were taken of rhGH over a long time period at a fixed concentration and of Insulin over a short time period with a variable concentration as indicated in Fig. The characteristic spectrum of four proteins is shown in Fig. Oxidized human growth hormone was prepared and analyzed by mass spectrometry, circular dichroism spectroscopy, and by Raman spectroscopy. A summary of the mass spectrometry analysis is given in Table 48. The changes in the Raman spectra may be due to structural changes in the non-helix regions of the rhGH in addition to changes due to the chemical process of oxidizing the Methionine residues. Currently the changes in the Raman spectra do not result in a quantifiable measurement of protein oxidation, the changes are too large and too variable to be directly tied to protein oxidation. Rather than trying to produce a quantifiable measure of oxidation an alternate approach was pursued, developing a classifier to give a binary measure of the protein as either “good” or “bad”.Figure Two variations of the classification scheme outlined in the methods section were examined: one which uses only spectra from rhGH to define the classification boundary (Method 1) and one which also includes spectra from independent high quality proteins in the first step of dimension reduction (Method 2). In both approaches there are three parameters that can be adjusted to control the performance of the classifier: the number of rhGH spectra included in the first round of PCA, the size of the first PC space, and the relative size of the classification ellipse which is controlled by the tuning parameter Θ. The number of rhGH spectra included in the first round of PCA was kept variable to examine how the performance of the classifier changed as the amount of information about the high-quality rhGH increased while the other two parameters were set as discussed below.The size of the first PC space can be set by making a decision about how much variation in the input data should be captured in the PCA. The eigenvectors associated with each principal component can be used as a proxy for the amount of variation in the original training data captured by each principal component. The higher this parameter is set, the more principal components will be required to represent the data. Aiming to capture ~60% of the variation in the first input set results in a PC space of 9–30 components, representing a significant reduction in dimensionality while maintaining most of the variation in the data. The size of the classification ellipse was set so that the classifier identified 99% of the test data set as “good” material using the assumption that the classifier should at least be able to identify the training set as “good” material.With N set to capture 60% of the training data variation and Θ set so that the classification ellipse encloses 99% of the training set, it is possible to compare the results of the two methods of generating the first principal component space. Figure As expressed in Equation To explore the performance of the classifier as the amount of information available increases the number of training examples to use in the first round of PCA was varied, using one, two, three, four, or all five sets of spectra collected over the course of a year. The bar charts in Fig. The classification system discussed here can provide a binary judgment on the quality of a protein drug product without requiring the operator to interpret the spectrum of the protein. From the point of view of the end user they place a small drop of material into the system and get a “probably good” or “probably bad” indication. This basic approach allows such a system to be deployed in a point of care application since it does not require any expertise on the part of the user to evaluate the data, and only requires the ability to dispense a small sample of drug product. Physically, the current system takes the form of a large bench-top instrument but it is possible to reduce the size to something approaching a shoebox allowing deployment beyond clinical locations. As developed here, the system does have some limitations.Currently the system relies on example spectra from “good” proteins at the correct concentration to form its classification boundary and can separate the “good” from “bad” proteins with reasonable accuracy on the set of good and degraded proteins examined here. Due to the pre-processing scaling of the Raman spectra into the 0–1 range the classifier is insensitive to small changes in protein concentration. However, a change in concentration can signal that the drug product being tested is not the correct formulation or has undergone some degradation process. Monitoring the scale factor or testing using a UV absorption measurement to verify the protein concentration should be done as part of the drug quality check. The algorithm presented builds a model for “good” proteins based on examples of the good protein. This must be done separately for each drug product to be evaluated by the system, and then in use the system must be told what drug it is examining. Finally, the data presented here represent a fairly small set of both high quality and degraded drug product. In terms of oxidation, summarized in Table 12. This approach allows testing of both the batch and single dose of the drug even in cases when the cost of sacrificing even a single dose is prohibitive, and will allow a hospital or clinic to identify drugs that have degraded unexpectedly or to find counterfeit drugs which have slipped into the supply chain. By monitoring every dose, they will be able to catch problems that they would have missed when only checking batches of medicine they suspect are degraded or counterfeit.Characterization of proteins at or below their therapeutic dose concentration within the correct buffer has numerous applications ranging from process analytics during the manufacture of bio-therapeutics to point of care applications where the quality of a protein can be checked before being administered to a patient. The system presented here can make repeatable spectral measurements of proteins at relevant concentrations and the classification algorithm can be used to identify “good” proteins without having to sample the entire space of “bad” proteins. Point-of-care applications benefit from the small sample volumes (25 μL) utilized for these experiments, which is small enough that it could be taken from the “overfill volume” used to ensure that a syringe can withdraw a full dose from a vial11. A system similar to the one presented here could be used to verify the quality of the vaccine material being used during a vaccination event. By catching spoiled material before it’s administered to patients the efficiency of a vaccination program can be improved. A more aggressive application of the system may allow a reduction in vaccine wastage. A large source of wastage in vaccine delivery in India has to do with the incomplete utilization of vaccines packaged in multi-dose vials8. When a vaccination event is held the best practices require that at the end of the event any opened vaccine vial be discarded, and that any unopened vial that has been issued but unused across three vaccination sessions also be discarded8. This is to ensure the safety and efficacy of the vaccines. A system that can determine if the vaccine in an opened vial is still good could allow the re-issuing of opened vaccine vials and unused but previously issued vials, while at the same time catching material that should be in good condition but that may have experienced degradation due to an undocumented problem with storage conditions. In this application there is a direct risk to the patient, since it will allow the use of material that would have previously been discarded, and determining if the system presented here is adequate for this task will require extensive testing on a wide range of high quality and degraded vaccine material. Beyond protein based medicine and vaccines, there is currently need for a counterfeit medicine detection tool. The World Health Organization Global Surveillance and Monitoring Systems report49 estimates that about US$30.5 billion is spent worldwide on substandard and falsified medical products, resulting in significant threats to the health of patients.Stepping beyond therapeutic protein products, the system described here could be used to verify the integrity of vaccines. As stated in the introduction, during one study of the vaccine distribution cold chain in India as much as 76% of the vaccine vials tested showed evidence of spoilage51. Changes in the gylcosylation state of mucin proteins in mucus/sputum could be used for diagnosis of COPD52, levels of serum albumin can be indicative of liver failure53, and relative levels of albumin to IgG, IgA, and IgM can be markers for diseases of the kidneys and liver54. Mucin proteins in mucus55 along with albumin, IgG, IgA and IgM in serum56 all occur at concentrations high enough to be directly visible in the system presented here. In this diagnostic application there can be a wealth of data for the “no-disease” state from the population of healthy patients and a much smaller amount of data from the population with a disease. A variant detection approach could be used to identify that a change has occurred in the patients’ serum or mucus proteome, signaling the need for further investigation.The basic approach presented in this paper, build a classifier based on the normal state of a protein and then try to determine when that protein is degraded, can also be applied to diagnostic applications of Raman spectroscopy. Particularly, this approach can be applied to the analysis of biofluids which is an active area of spectroscopy researchSupplementary Information