Method and apparatus for characterisation of a fluid sample by ultrasonic signals

Abstract

The present disclosure relates to a real-time, non-invasive method and apparatus for determining analytical parameters of a fluidic sample that may be Newtonian or non-Newtonian and liquid, viscous, or semi-solid at room temperature. The method comprises monitoring the temperature of a sample contained in a vessel, generating ultrasonic pulses at a defined pulse-repetition frequency, transmitting the pulses through the sample, and receiving reflected ultrasonic signals after one or multiple traversals. A computer processor determines the acoustic propagation time and, together with temperature data, computes analytical parameters by comparison with a calibration model. Signal filtering, amplification, and advanced processing operations such as Fourier transformation may be employed for impurity quantification using multivariate models. An apparatus implementing the method includes an ultrasonic transducer, an electrical pulse generator, a temperature sensor, and a processor. The system enables quantification of analytes including sugars, organic compounds, and organic or inorganic salts.

Description

D E S C R I P T I O NMETHOD AND APPARATUS FOR CHARACTERISATION OF A FLUID SAMPLE BY ULTRASONIC SIGNALSTECHNICAL FIELD

[0001] The present disclosure relates to the field of analytical measurement technologies. More specifically, it concerns methods for real-time and non-invasive determination of analyte parameters in fluid samples, through analysis of acoustic signals. The disclosure further relates to an apparatus adapted to extract physical or chemical information from acoustically responsive fluid samples without the need for sample removal, or destructive processing.BACKGROUND

[0002] The Process Analytical Technology (PAT) initiative of 2004 was a major breakthrough in the context of pharmaceutical industry. In its Guidance for Industry [1], the Food and Drug Administration (FDA) fostered the development of innovative technologies with the objective of increasing medicine safety and quality, while reducing production time and costs. As pointed out in [2], this framework has been well harnessed in the context of solid dosage forms, while other forms, such as injectables have been lagging behind.

[0003] Previous work, referred in [3] has suggested some avenues for exploring the development of PAT for injectable dosage forms. Among them, the use of acoustic methods was encouraged, due to their non-invasiveness, non-destructiveness, timely results and simplicity. Additionally, as the acoustic waves need a continuous medium to propagate, the technique may be employed not only in solutions or liquid products but also in semi-solid products, such as creams, gels, lotions and ointments. Furthermore, this technology may be applied in other industries, such as, but not limited to cosmetics, food and beverages, and chemical industries. Its application to other finished products is now emphasised as a prerequisite for expanding its range of applications.

[0004] Glucose infusion solution is used in hospital context in a variety of situations including glucose intake in parenteral nutrition, dehydration, and as vehicle for other parenteral drugs. Glucose infusion solution is manufactured in a variety of concentrations usually ranging from 5 % to 50 % of glucose. The pharmacopeial method for the assay of glucose in these products is polarimetry, as stated in the British Pharmacopoeia (BP) [4], This method requires the addition of a small volume of ammonia to a sample of the solution, agitation and a rest period of 30 min before reading. Additionally, for the products other than glucose 5 %, a dilution step is necessary. It is, therefore, a laborious, time-consuming methodinvolving pre-processing steps, which in manufacturing context leads to great holding times, not to mention the laboratory costs for reagents and personnel. Hence, a method that could measure the concentration of glucose in these products in a timely manner, without the necessity of pre-processing steps, easily implementable in the manufacturing line according to PAT principles, that provides results without sampling is in the best interest of the industry, as it reduces production costs and increases the product safety and quality.

[0005] To date, most PAT methods developed for glucose assay are based on Raman spectroscopy [5-8], These are mainly used to monitor the concentration of glucose in bioreactors. However, these methods tend to not return an instantaneous result while the accuracy and precision are usually not satisfactory. As an example, Berry and co-workers [5] developed a method that requires a 10 min spectrum recollection.

[0006] Therefore, the objective of this work is to develop a method for glucose assay in glucose infusion solution that encompasses the commercially available glucose infusion solution products for future in line implementation, with a rapid response and adequate accuracy and precision.

[0007] These facts are disclosed in order to illustrate the technical problem addressed by the present disclosure.GENERAL DESCRIPTION

[0008] The present disclosure relates to real-time, non-invasive analysis of solutions and other fluid products, namely pharmaceutical preparations, while they are being manufactured, using acoustics. More specifically, it concerns methods for real-time and non-invasive determination of analyte parameters in products in the manufacturing line through analysis of acoustic signals. The disclosure further relates to an apparatus adapted to extract physical and chemical information from acoustically responsive products without the need for sample removal or destructive processing.

[0009] The present disclosure relates to a real-time, non-invasive method and apparatus for determining analytical parameters of a fluidic sample that may be Newtonian or non-Newtonian and liquid, viscous, or semi-solid at room temperature. The method includes providing the sample in a container, monitoring its temperature, and generating ultrasonic pulses that propagate through the sample and undergo one or multiple reflections. The reflected signals are acquired by an ultrasonic transducer and converted into electrical signals from which acoustic propagation time is determined. A computer processor processes the propagation time together with the sample temperature and compares the values to a predetermined calibration model to obtain the analytical parameter. The method may further include filtering and amplification of the reflected signal, as well as signal-processing operations such as averaging, peakdetermination, derivative calculations, baseline correction, and Fourier transformation for impurity quantification.

[0010] Analytical parameters measurable by the method include analyte concentration, density, solute concentration in mono- or multi-component solutions, and impurity concentration. Concentration determination may be performed by a polynomial model derived from pre-calibrated samples, while impurity determination and concentration determination in multi-component solutions may employ multivariate quantitative models such as Principal Component Regression or Partial Least Squares, using components that capture the variance of the dataset while preventing overfitting.

[0011] An apparatus for carrying out the method comprises a sample container, an electric signal generator, an ultrasonic transducer configured for emission and reception of ultrasonic signals, a temperature sensor, and a computer processor for storing and processing data. Optional components include an electronic filter and an amplifier. The system is suitable for analyzing sugars, organic compounds, and organic or inorganic salts, among others. The disclosure further encompasses a computer-readable medium containing instructions for performing the processing steps of the method.

[0012] A fluid sample, wherein the fluid may be a Newtonian fluid— exhibiting a constant viscosity independent of shear rate— or a non-Newtonian fluid— exhibiting a viscosity that varies as a function of the applied shear rate or shear stress; the sample being liquid, viscous, or semi-solid at room temperature (20 °C); the method not being limited to biological samples, and further applicable to other pharmaceutical formulations (such as creams, ointments, gels, and syrups) as well as to products from other industries including cosmetics, food, chemical processes, and paints.

[0013] An aspect of the present disclosure relates to real-time non-invasive method for determining / measuring analytic parameter in a fluidic sample comprising:providing the sample in a sample container;monitoring the temperature of the fluidic sample;generating, by an electrical pulse generator, a set of electrical pulses to an ultrasonic transducer coupled to the sample container, each electrical pulse of the set of electrical pulses being generated at a predetermined pulse-repetition frequency;converting, by the ultrasonic transducer, each sent electrical pulse of the set of electrical pulses into an ultrasonic signal for transmitting the ultrasonic signal through the sample,receiving by the ultrasonic transducer, a reflected ultrasonic signal after one or multiple traversal (propagating to) of the sample and converting the reflected ultrasonic signal into a corresponding electrical signal;obtaining, the electrical signal and determining a propagation time of the ultrasonic signal between emission and reception;processing, by a computer processor, the temperature of the sample, and the acoustic signal propagation time to calculate, compare the values with a pre-determined calibration model for each analytical parameter for obtaining the analytical parameter.

[0014] In an embodiment, the method may further comprise, a previous step, of filtering the reflected ultrasonic signal by an electronic filter; and amplifying the reflected ultrasonic signal.

[0015] In an embodiment, the pulse-repetition frequency ranges from 1 Hz to 1 kHz, preferably 1 kHz.

[0016] In an embodiment, the fluidic sample is selected from liquid solution, viscose solution, or semisolid sample.

[0017] In an embodiment, the analytical parameter is selected from: a concentration of an analyte, a density of a fluid, a concentration of a solute in a mono-component solution, a concentration of a solute in a multi-component solution, a concentration of an impurity in a solution, or combinations thereof.

[0018] In an embodiment, obtaining the analyte concentration comprises solving the quadratic polynomial modelA = a0+ b · PT + c · T + d · PT2+ f · T2+ g · PT · T, wherein:A is the analyte concentration;PT is the time of propagation of the acoustic signal;T is the temperature read by the temperature sensor;a0, b, c, d, f, g is are numerical coefficients obtainable by numerical regression from pre-calibrated concentration samples, preferably at least 5 samples.

[0019] In an embodiment, the analyte is sodium chloride in a physiological solution, or glucose in a glucose-based solution, particularly in a glucose-based injectable solution.

[0020] In an embodiment, after reading the electrical signal, obtaining the concentration of an impurity in a solution or from an analyte in a multi-component solution comprises:transforming the read electrical signal from the time domain to the frequency domain by means of a Fourier transform to obtain the frequency spectrum of the electrical signal;processing data obtained from the frequency spectrum of the electrical signal by the computer processor;generating, by the computer processor, a quantitative multivariate model representative of a property of the fluidic sample comprising the temperature of the fluidic sample and the frequency spectrum of the electrical signal to obtain the concentration of the impurity in the solution.

[0021] In an embodiment, the system employs a set of components, defined as orthogonal variables that capture and explain the variance within the dataset. By representing the data through these components,the dimensionality of the dataset is reduced while maintaining the information necessary for reliable model construction and prediction. The number of components is selected based on analytical metrics that indicate the point at which predictive performance is optimized without overfitting.

[0022] In an embodiment, the quantitative multivariate model may comprise a Principal Component Regression model or a Partial Least Squares model.

[0023] In an embodiment, the qualitative multivariate model may comprise a Principal Component Analysis model or a Partial Least Squares Discriminant Analysis model.

[0024] In an embodiment, the impurity comprises 5-hydroxymethylfurfural.

[0025] In an embodiment, electrical pulse comprises a voltage ranging from-40 V to -300 V, preferably -150 V.

[0026] In an embodiment, the processing data step comprises operations selected from a list comprising: calculating an average of the signal read; determining a maximum of the signal read; determining a minimum of the signal read; determining a local maximum of the signal read; determining a local minimum of the signal read; evaluating an acoustic wave of the ultrasonic signal after traversing the fluidic sample; determining a first derivative of the signal read; determining a second derivative of the signal read; smoothing the signal read; performing a Fourier transform of the signal read; correcting a baseline of the signal read; or any combination thereof.

[0027] Another aspect of the present disclosure relates to a real-time non-invasive apparatus for determining / measuring the amount / concentration of analytic parameter in a fluidic sample according to the method of the present disclosure, comprising:a sample container;an electric signal generator for generating electric signals, connected to an ultrasonic transducer; wherein the ultrasonic transducer is configured to convert an electrical signal from the electrical signal generator into ultrasonic signals for transmission through said fluidic sample, and subsequently to receive ultrasonic signals after propagating through the fluidic sample and convert the received ultrasonic signals into electrical signals;a temperature sensor, for measuring the temperature of the fluidic sample;a computer processor configured for processing a data from the electrical signal corresponding to the reflected ultrasonic signal, for storing the data and processed data, and calculate analytic parameters by the relation of the temperature and the acoustic signal propagation time.

[0028] In an embodiment, the apparatus of the present disclosure may further comprising:an electronic filter for removing noise of the reflected ultrasonic signal; andan amplifier, for amplifying the reflected ultrasonic signal.

[0029] In an embodiment, the ultrasonic transducer is a piezoelectric ultrasonic transducer.

[0030] In an embodiment, the electrical signal generator is a pulser-receiver.

[0031] In an embodiment, the ultrasonic transducer is configured to generate ultrasonic signals with a single central frequency.

[0032] In an embodiment, the single central frequency ranges from 1 000 000 Hz to 10 000 000 Hz, preferably 5000000 Hz.

[0033] In an embodiment, the ultrasonic transducer is attached and arranged perpendicularly to the sample container.

[0034] In an embodiment, the temperature sensor is arranged outside the sample container and in contact with the sample container.

[0035] In an embodiment, the temperature sensor is arranged within the sample container.

[0036] In an embodiment, the ultrasonic transducer is connected to the sample container via an ultrasound conduction gel.

[0037] In an embodiment, the sample container is a stainless-steel pipe or an independent vessel.

[0038] In an embodiment, the sample container is an independent vessel having a diameter ranging from 20 to 200 mm, preferably 50 mm, and a wall thickness ranging from 0.1 to 10 mm, preferably 0.5 mm.

[0039] Use of the method / the apparatus of the present disclosure for detection or quantification of for detection or quantification of analytic parameter of a fluidic sample, sugars, organic compounds, and organic or inorganic salts. These analytes represent broader categories encompassing the specific examples such as glucose, 5-HMF, and sodium salts.

[0040] A computer-readable non-transitory medium comprising instructions which, when executed by a computer, cause the computer to carry out the processing step of the method of the present disclosure.BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The following figures provide preferred embodiments for illustrating the disclosure and should not be seen as limiting the scope of invention.

[0042] Figure 1: Schematic representation of an embodiment of an apparatus comprising: a display of an apparatus 1; the apparatus 2 containing all electronic components; a transducer 3; a sample container 4; a temperature sensor 5. Section A is shown in detail in Figure 2.

[0043] Figure 2: Schematic representation of an embodiment of an acoustic signal path in the sample container and sample, wherein the transducer is represented by a reference numeral 6; the sample is represented by a reference numeral 7; the inner opposing wall of the sample container is represented by a reference numeral 8; the acoustic signal before reflection on the opposing inner wall of the sample container is represented by a reference numeral 9a; the acoustic signal after reflection on the opposing inner wall of the sample container is represented by a reference numeral 9b; the sample container wall where the transducer is mounted is represented by a reference numeral 10; the sample container is represented by a reference numeral 11.

[0044] Figure 3: Schematic representation of an embodiment of a typical obtained signal. tfmdenotes the time corresponding to the first maximum of the echo from the inner face of the wall opposing the transducer 8.

[0045] Figure 4: Photography of an embodiment of an ultrasonic A-scan signal with the amplitude plotted against the time of propagation (x-axis). The A- scan signal includes two detected peaks, Peak 1 and Peak 2, and the time difference between them.

[0046] Figure 5: Photography of an embodiment of a first maximum of the acoustic signal of solutions with concentration of NaCI ranging from 0.2 to 1.8 % (w / v) at 20 °C (A) and with temperature ranging from 10 °C to 26 °C, at a concentration of 0.9 % (w / v) (B).

[0047] Figure 6: Schematic representation of embodiments of the model of the acoustic method. On the x-axis is the propagation time of the acoustic signal, in s, on the y-axis, the temperature, in °C, and on the z-axis, the NaCI concentration in % (w / v). The points of three validation days are represented.

[0048] Figure 7: Photography of an embodiment of a graph of obtained concentration of NaCI as a function of a theoretical concentration of NaCI for the acoustic method at 10 °C, 18 °C, and 26 °C. The figures of merit are available in Table 5.

[0049] Figure 8: Photography of an embodiment of a graph of limits of detection (LoD) and limits of quantification (LoQ) computed for each temperature for the acoustic method (Ac).

[0050] Figure 9: Photography of an embodiment of a typical acoustic signal obtained from the reflection of the back wall of the pipe. The point used to build the models is the first maximum, which is located at approximately 6.52 • 10'5s on this example. For visual aid, the considered point is indicated with the dashed line. The first maximum is calculated after a smoothing pre-processing (Savitzky-Golay, 2nd derivative). This allows the reduction of the error due to instrumental noise.

[0051] Figure 10: Photography of an embodiment of a first maximum of solution of glucose with concentrations ranging from 0 to 10 % (w / v). With increasing concentration, the signal is dislocated towards smaller time of propagation.

[0052] Figure 11: Photography of an embodiment of a first maximum of a solution of 5 % (w / v) of glucose collected at temperatures ranging 10 to 25 °C. With increasing temperature, the signal is dislocated towards a smaller time of propagation.

[0053] Figure 12: Schematic representation of an embodiment of the quadratic polynomial model. On the x-axis is the propagation time of the acoustic wave, in s, on the y-axis, the temperature, in °C, and on the z-axis, the glucose concentration, in % (VJ / V). The points of three validation days are represented.

[0054] Figure 13: Photography of an embodiment of a graph of obtained concentration of glucose as function of theoretical concentration of glucose for A: 10 °C, B: 15 °C, C: 20 °C, D: 26 °C, E: superposition of A-D The figures of merit are available in Table 11.

[0055] Figure 14: Photography of an embodiment of a graph of limits of detection (LoD) and limits of quantification (LoQ) of the method computed for each temperature.

[0056] Figure 15: Photography of an embodiment of an acoustic signal (A) in the time domain and respective frequency spectrum (B), after Fourier transform of the former.

[0057] Figure 16: Photography of an embodiment of a frequency spectrum of a glucose solution with concentration of 5 % (w / v), non-degraded and thermally degraded.

[0058] Figure 17: Photography of an embodiment illustrating a comparison of the RMSEC, RMSECV and RMSEP for the model built with the data measured from the solution with glucose 5 % (w / v) (A), with glucose 20 % (w / v) (B) and with all data (C).

[0059] Figure 18: Photography of an embodiment of results of in line determination of glucose 10 % and water. The glucose content considered correct is represented by the horizontal line. The glucose was measured at an average temperature of 17.75 °C and the water for injection at an average temperature of 21.50 °C.

[0060] Figure 19: Photography of an embodiment of a visual representation of the increase of absorbance at 284 nm with the concentration of 5-HMF, for the three independent days.

[0061] Figure 20: Photography of an embodiment of analytical figures of the model with increasing components (A): RMSEC, RMSECV, and RMSEP; (B): R2and Q2.

[0062] Figure 21: Photography of an embodiment of a linear fit of the obtained concentration vs. the theoretical values of the 5-HMF solutions of the calibration set.DETAILED DESCRIPTION

[0063] Figure 1 displays an embodiment of an apparatus 2. The apparatus 2 comprise a pulse-receiver module, an amplifier and a filter, an analogue-to-digital converter unit, a computer I / O interface, asoftware allowing the reception, treatment and calculation with a data and inclusion of a temperature control into a calibration model, and a display 1 for visualisation of the attribute of interest, which may be but is not limited to the value of concentration, density or a warning of out-of-specification product. The apparatus 2 is connected to a transducer 3 and a temperature sensor 5. The pulser-receiver module allows modulation of the pulse repetition frequency, of the input energy of the pulse and of the gain of the received echoes.

[0064] In an embodiment, a short duration electric signal is generated by the pulser-receiver with a predetermined pulse-repetition frequency. Each individual pulse is followed by a lag time (time of "silence") to enable the reception of the echoes. In an embodiment, the frequency of the loop pulse and silence, i.e., the pulse repetition frequency, is 1 kHz. Care should be taken to not increase the pulse repetition frequency to the point where the new signal overlaps with the echoes from the previous loop. The reduction of the pulse repetition frequency leads to increasing analysis time. Alongside the electric signal, a trigger signal is generated.

[0065] In an embodiment, the electric signal is conducted to a transducer 3 that is physically connected to a sample container 4. In an embodiment, the transducer was a piezoelectric transducer with central frequency of 5 MHz. In an embodiment, other central frequencies may be used. However, care should be taken to not choose a too high central frequency, so that the signal is attenuated to the point where it is no longer detectable, nor a too low frequency, so that the peaks are too broad, leading to decreasing accuracy. In an embodiment, the connection between the transducer and the sample container may be done by any common means to do so, such as a permanent connection or using an ultrasound conducting gel. In any case, care should be taken so that the transducer 3 is perpendicular to the sample container 4. In an embodiment, the sample container is a stainless-steel pipe.

[0066] Figure 2 displays a cross-section of the section A of the embodiment of the apparatus shown in Figure 1. The transducer 6 (converts the electric signal to an acoustic signal 9 with the same frequency as the central frequency of the transducer. The acoustic signal propagates through a sample container wall 10, through a sample 7, reflects at an inner face of the opposite wall 8 of the sample holder and returns through the sample 7 and first wall of the sample container 10, reaching the transducer 6. The emitted acoustic signal travels through the sample along a first propagation trajectory 9a, directed toward the inner opposing wall 8 of the sample container. Upon reaching the inner opposing wall 8, the acoustic signal undergoes a first reflection, generating a reflected trajectory 9b that propagates back through the sample toward the transducer wall 10. In some embodiments, the acoustic signal continues beyond the transducer location and undergoes a second reflection on the same or another internal surface of the container, thereby establishing a multi-reflection acoustic trajectory within the sample volume. This configuration enables the system to capture acoustic information derived from at least two successivereflections, thereby enhancing the sensitivity and robustness of the measurement of the sample's physical properties.

[0067] In an embodiment, the transducer receives the acoustic signal 9b and converts it to an electric signal. The electric signal is then interpreted, processed and the time of the first maximum of the echo from the inner face of the wall opposing the transducer is calculated (tfm- Figure 3). The time corresponding to the first maximum is related with the sample attribute of interest, as the time of propagation of the acoustic signal is dependent on the concentration of the analyte or other physicochemical properties of the sample. In an embodiment, the processing of the signal may include averaging a predetermined number of individual consecutive measurements, smoothing of the signal and filtering of frequencies not related with the generated signal.

[0068] In an embodiment, a temperature sensor 5 is placed in contact with the outside of the sample container and close to the transducer. That is, the temperature sensor 5 is positioned in contact with the outside of the sample container as close as possible to the location of the transducer. In an embodiment, the temperature sensor may be insulated so as to not be influenced by the surrounding environmental temperature. Alternatively, in an embodiment, a temperature probe may be inserted in the sample container. In this case, care should be taken so that no sensor component is in the acoustic signal path.

[0069] In an embodiment, the time corresponding to the first maximum and the temperature are integrated and used to calculate the attribute of interest. In an embodiment, this attribute may be a concentration of a given analyte in aqueous solutions or a density of a liquid. Alternatively, having a previous reference of the typical propagation time for a given sample, an out-of-specification warning may be issued, thereby detecting problems in the manufacturing process, such as product dilution.

[0070] The mathematical relation between time of the first maximum of the echo - tfm, the temperature as given by the sensor - T, and the attribute of interest -A - may take the following general form:A = a0+ b ■ tfm+ c ■ T + d ■ tfm2+ f ■ T2+ g ■ tfm■ T (1)being ao,b, c, d, / and g numerical coefficients. In an embodiment, the numerical coefficients are discovered by previous calibration. The calibration is performed with solutions with known concentration, at different and know temperatures. For each solution, the time of propagation of the acoustic signal is measured. The data set that includes the concentration of the solution, the temperature and the time of propagation of the acoustic signal is used to perform a fitting to Eq. 1., calculating the coefficients.

[0071] In an embodiment, the calibration coefficients for the determination of the sodium chloride concentration in physiological solution were found. In an embodiment, the sample was contained in a stainless-steel pipe with 5.08 cm of diameter and 0.318 cm of wall thickness. In an embodiment, the transducer was a piezoelectric transducer with central frequency of 5 MHz. In an embodiment, the pulserepetition frequency was 1 kHz. In these conditions, a₀ = 527.03; b = - 1.39107, c = -0.39; d = 9.07·1010; f = 2.66·10-3and g = 339.9. The adjusted R2of the mathematical model was 0.99995.

[0072] In an embodiment, this model was applied to determine the concentration of sodium chloride solution with 8.96 mg-mL1as determined by an external reference method of potentiometric titration. The average concentration obtained via the acoustic method here described was 8.99 ± 0.03 mg-mL1, which corresponds to a bias of 0.406 %. The obtained precision, as given by the relative standard deviation was 0.362 %.

[0073] In an embodiment, instead of using the direct propagation time, a propagation time of the first and second echoes can be detected (red dots in the Figure 4). By subtracting the two propagation times, it is obtained the time that the ultrasonic wave took only in the liquid (i.e., the time that the wave took in the tube wall is removed). Thus, the method can be developed as a function of velocity. Advantageously, in this way, the methods are transferable to sample containers with different dimensions and different wall thicknesses.

[0074] The following pertains to a PAT development for real-time determination of sodium chloride in physiological saline solution via an acoustic technique.

[0075] In this embodiment, an acoustic technique is based on how the concentration of a solution affects the time of propagation or velocity of the signal that crosses that solution. For the acoustic technique, an electric signal is generated on a signal generator, such as a pulse receiver. If a pulse-receiver is used, as in this case, the same device generates the signal and receives after being propagated. The signal is converted to an acoustic signal by means of a transducer, acoustically coupled to the sample holder. The acoustic signal traverses the sample, is reflected on the back of the wall and returns to the same transducer, that now is on receiving mode. The transducer converts the acoustic signal into an electric signal that is assimilated by the pulse receiver. The signal is then read on an oscilloscope. The first maximum of the reflected signal is used for the determination of the time of propagation of the acoustic signal, i.e, the time required for the acoustic pulse to travel through the sample and back.

[0076] The effect of concentration and temperature on the time of propagation of the signal tend to be studied separately [9], However, this is not an acceptable solution in a development of an in-line sensor. One approach that tried to conjugate both concentration and temperature was the one by Ikeda and coworkers

[0010] , In this work, they measured the speed of sound of solutions with different concentrations of NaCI at temperatures ranging 15 °C to 45 °C. For each temperature, a calibration curve was drawn, and then they extracted 2ndorder polynomial curves of how the slope and / -intercept of the concentration curves varied with temperature. However, as the error of calibration curves is higher at the extremes of the curve, this means that concentrations farther from the central concentration suffer more with the temperature error. The solution herein presented integrates both independent variables (i.e.,temperature and NaCI concentration) into a single three-dimensional model, graphically represented by a surface.

[0077] The development of this method is a step further in the development of a PAT tool that allows in-line quantification of NaCI in solution in a simple manner, without sample processing, in timely manner, without invading or altering the manufacturing line, thus increasing the quality of the product while maintaining its safety and reducing implementation costs.

[0078] In an embodiment, the solutions used for the calibration models and their validations were made by dissolving the appropriate amount of sodium chloride (Merck KGaA, Darmstadt, Germany, with purity > 99.5 %) in purified water (Millipore®, 18 MO cm at 25 °C). Additionally, three bottles of commercial physiological saline solution (NaCI at 0.9 %) supplied by Laboratorios Basi (Mortagua, Portugal) were analysed.

[0079] The following pertains to an acoustic setup of the present disclosure.

[0080] In an embodiment, an analysis was performed in a pulse-echo mode, that is, with the same transducer serving as emitter and receiver of the ultrasonic signal. The signal was generated on a pulser / receiver model 5800 of Panametrics®, with 100 μJ of energy and a pulse repetition frequency of 1 000 Hz. The solutions were analysed inside a 5.08 cm stainless steel pipe with piezoelectric sensor attached outside of the pipe and perpendicular to it. The piezoelectric sensor used was the model V310 SU (Olympus®) with a central frequency of 5 MHz and piezoelectric element of 0.635 cm of diameter. After reception, the ultrasonic signal was analysed by a TDS 1002B 60 MHz oscilloscope of Tektronix®. In an embodiment, the acoustic signal was recorded with an average of 64 accumulations, corresponding to 0.064 s of analysis time. In an embodiment, the solutions were magnetically stirred at ca. 500 rpm and the temperature was controlled with a DT 1 POL 100 digital thermometer (Gesa Termometros, S. L.), with a stated precision of ± 0.07 °C.

[0081] Regarding to collection and processing of the acoustic signal, in an embodiment, a point of the acoustic signal chosen to correspond to the propagation time was the first maximum of the wave that is reflected on the inside of the opposite wall of the pipe.

[0082] In an embodiment, the acoustic signal was smoothed using a Savitzky-Golay, 2ndderivative. In an embodiment, the analysis was performed on the software Origin Pro® 2018 (OriginLab Corporation®).

[0083] In an embodiment, a model that describes the relationship between concentration of NaCI, temperature and time of propagation of the signals consists of a three-dimensional surface. In an embodiment, several model equations that could fit the data were tested for the best fit. For this purpose, the R2and residual sum of squares were evaluated. In an embodiment, the models were developed on the software Origin Pro® 2018 (OriginLab Corporation®).

[0084] In an embodiment, taking in account the best conditions, both methods were validated according to the ICH Q2(R2) guideline

[0011] , as follows.

[0085] In an embodiment, the range of both models covers the concentrations of 0 to 1.8 % (w / v) of sodium chloride, with a total of 8 calibration standards. Each solution was studied in a temperature range of 10.0 to 26.0 °C, with steps of 2 °C.

[0086] In an embodiment, the R2, the adjusted R2, the reduced chi-square (x2) and residual sum of squares were used to determine the suitability of the computed model. The theoretical concentration was plotted against the obtained concentration and relationship between them was evaluated. The equation of the curve was obtained by the least squares method. The R2, slope and y-intercept were obtained.

[0087] In an embodiment, the precision was evaluated by calculation of the RSD of the obtained concentration of five replicates of three quality control solutions on one day (intra-day) and three days (inter-day). In an embodiment, the quality control solutions have nominal concentrations of 0.4, 0.9 and 1.3 % (w / v) of NaCI, corresponding to 44.4 %, 100 % and 144.4 % of the nominal concentration, respectively.

[0088] In an embodiment, accuracy was evaluated by calculating the bias of five replicates of three quality control solutions.

[0089] The bias is given by:Obtained value — True value,.Bias (%) = - ■ - x 100 (2)True value

[0090] In an embodiment, the Limits of detection (LoD) and Limits of quantification (LoQ) are, respectively, calculated using:SDLoD = 3.3 x y (3)andSDLoQ = 10 X — (4)being SD the standard deviation of the response of measurements of the blank (n = 12), and S the slope of the calibration curve.

[0091] For this purpose, in an embodiment, the data obtained at each temperature was used to calculate its respective calibration curve, in an independent way. This allowed the calculation of slope of the calibration curve (S), the SD of the response, and of the LoD and LoQ, as per Equations 3 and 4, respectively. In these calibration curves, the independent variable was the concentration of sodium chloride and the dependent variable was the time of propagation of the acoustic signal.

[0092] In an embodiment, the acoustic signal is generated on the transducer, travels through the sample container, is reflected on the back wall and is detected by the same transducer that generated it. The acoustic signal is attenuated as it travels through the medium. The attenuation increases with the distance travelled and the frequency of the signal. However, with increasing frequency, the signal peaks become sharper, leading to better precision of the determination of the first maximum. Therefore, the acoustic method allowed the use of a transducer with 5 MHz of central frequency. However, this is not significative, because it is not the intensity of the signal that is being measured, but its dislocation along the propagation time axis.

[0093] For the acoustic method, a first set of experiments was conducted in order to determine the change of the propagation time with the concentration of sodium chloride in solution and with temperature, thus proving the concept. This proof of concept is exposed on Figure 5, as a display of the dislocation of the first maximum with changing concentration at constant temperature and with changing temperature at constant concentration, respectively.

[0094] Figure5 provesthat in a solution of sodium chloride, the time of propagation of the acoustic signal decreases with increasing concentration or temperature, while showing that the setup is able to generate and detect acoustic signals with sufficient amplitude and that the differences in the time of propagation are observable and quantifiable. This is in accordance with existing literature

[0010] ,

[0095] In an embodiment, a model integrates the relationship between the independent variables, concentration and temperature of the solution, and the dependent variable, time of propagation of the acoustic signal. To model this relationship, different equations were studied. In an embodiment, the general equations, the R2, adjusted R2and residual sum of squares are compared among models in Table 1 for acoustic method. In an embodiment, only the models that could fit the data were considered.

[0096] Table 1 - Coefficients of determination and residual sum of squares for the tested model equations for the acoustic method.Acoustic methodbModelModel Equation3Residual sum description R2Adjusted R2of squares f l / PT-cA2l / T-dA2Gaussian surface NC = a + bl2^ f ' * 9 ) 0.99994 0.99993 0.0047Rotated( i / PT cos(S)+ T sin(S)- c cos(S)- d sin(S) 'i2i / '-PT sin(S) +T cos(S)+ c sin(S) - d cos(S)']2)Gaussian NC = a + b(2^ f > 9 > ) 0.99994 0.99993 0.0047 surfaceLogarithmic lnCL2InT.2lnPT2inL2L[lc 9 c _ 9_ - - - function NC = a + b 2d2f 2h2-\- b 2d22h2Lorentz function NC = a + - - 577 - r 0.99994 0.99994 0.0047[-m I H¥) lParabolafunctionNC = a + bPT + cT + dPT - - - without2+ fT2interaction termPlane NC = a + bPT + cT 0.96752 0.96721 2.3988 QuadraticNC = a + bPT + cT + dPT2+ f T2+ gPT T 0.99995 0.99994 0.0040 polynomial5thorderpolynomialNC = a + bPT + cPT2+ dPT3+ fPT4+ gPT5+ hT + IT2+ jT3+ kT4+ IT5- - - without £interaction termPower function NC = a + bPTc+ dT? + gPTcTf 0.98614 0.98581 1.0238 Voigt surface NC = a + b 0.99990 0.99989 0.0076 Modified Voigt 4 d g 4ln2 -^^(PT-rp-^rfr-h.)2]NC = a + b c - - - 1- fl — ct - ed9 0.99985 0.99985 0.0109surface n24(PT — f)2+ d24(T — K)2+ g2ndgbeing, a, b, c, d, f, g, h, i, j, k, I, 0, numerical coefficients, NC, the concentration of sodium chloride, in % (w / v), PT the propagation time of the acoustic, in s, and T he temperature, in °C.£Where no values are shown, the data did not converge to create a model.15

[0097] The analysis of Table 1 allows to determine that the model that best represents the data for the acoustic method is the quadratic polynomial, which corresponds to the following equation:NC = a + bPT + cT + dPT2+ fT2+ gPT ■ T (5) being a, b, c, d, f, and g are coefficients, NC, the concentration of NaCI, in % (VJ / V), PT the propagation time of the acoustic signal, in s, and T, the temperature, in °C.

[0098] The values for the coefficients of the models on acoustic method are laid out in Table 2.

[0099] Table 2 - Model coefficients from Equation 5, computed for the acoustic method.Coefficients Acoustic methoda 527.3 ± 16.7b - 1.390-107± 4.9-105c - 0.39 ± 0.07d 9.07·1010± 3.6·109f 2.66·10-3± 7·10-5355.7 ± 1012.3g

[0100] The surface response obtained from the model for the acoustic method is presented on Figure 6.

[0101] The goodness of fit of the model was evaluated with the R2, the adjusted R2, reduced x2and residual sum of squares. The values of these parameters for the acoustic method is seen in Table 3.

[0102] Table 3 - Calibration model parametersMethod R2Adjusted R2Reduced x2Residual Sum of Squares Acoustic 0.99995 0.99994 1.9 · 10-54.0 • 10'3

[0103] As shown in Table 3 and taking into account the information presented in Table 1, it can be concluded that this method is well modelled by Equation 5 with the coefficients presented in Table 2, since both R2and adjusted R2remain above 0.9999 for the acoustic method. Additionally, the residual sum of squares remains very low.

[0104] The obtained vs. theoretical concentration of NaCI at 10 °C, 18 °C and 26 °C are presented on Figure 7 and the respective figures of merit are exhibited in Table 4.

[0105] Table 4 - Figures of merit of the curves computed for obtained vs. theoretical sodium chloride concentrations. Slope and y-intercept are presented with the respective standard errors.Temperature (°C) 10 18 26 Slope 0.997 ± 1.2 • 10'31.001 ± 1 • 10'30.995 ± 1.8 • 10'3y-intercept 0.0044 ± 0.0013 - 6.9 • 10'4± 8.7 • 10'4- 0.0040 ± 0.0019 Acoustic R20.99997 0.99998 0.99993 method Adjusted R20.99998 0.99998 0.99992Residual sum2.8 • 10'41.2 • 10'45.9 • 10'4of squares

[0106] In an embodiment, three synthetic mixtures at the concentrations of 0.4 % (w / v), 0.9 % (w / v), and 1.3 % (w / v) of NaCI, each with five replicates were measured on three separate days. The intra-day precision was evaluated with the results from the first day. The bias was used to evaluate the accuracy and the RSD was used to evaluate the precision. The results from both precision and accuracy can be compared between the two methods in Table 5.

[0107] Table 5 - Intra-day and inter-day precision, and accuracy for the acoustic method. The used concentration levels were 0.4 %(w / v), 0.9 %(w / v), and 1.3 % (w / v) of NaCI. Intra-day results are drawn from the first day of validation.Acoustic method Theoretical concentration0.4 0.9 1.3 (% (w / w) of NaCI)Obtained concentration 1.299 ± 0.398 ± 0.003 0.900 ± 0.003(mean ± SD, %(w / w) of NaCI) 0.003 Precision (RSD, %) 0.766 0.348 0.193 Accuracy (Bias, %) - 0.404 0.003 - 0.079 Obtained concentration 1.300 ± 0.398 ± 0.003 0.900 ± 0.003(mean ± SD, %(w / w) of NaCI) 0.003 Precision (RSD, %) 0.776 0.344 0.222 Accuracy (Bias, %) - 0.474 0.022 0.030Note - RSD: relative standard deviation; SD: standard deviation.

[0108] For the acoustic method, the highest obtained RSD was 0.766 % and 0.776 % for the intra- an inter- day precision, both on the solution of 0.4 % of NaCI. Regarding accuracy, the highest deviation from the true value in the acoustic method was - 0.404 % for the solution of 0.4 % (w / v) of NaCI. It is noteworthy the bias of only 0.022 % and RSD of 0.344 % (w / v) for the concentration of interest (0.9 % of NaCI) for the inter-day with the acoustic method.

[0109] In an embodiment, on each studied temperature, the LoD and LoQ were calculated, by creating a calibration curve between the propagation time of the acoustic signals and the concentration of NaCI. From these calibration curves, the calculation of SD and slope was performed. The LoD and LoQ on each temperature for both methods are represented on Figure 8.

[0110] Figure 8 shows that the LoD of the acoustic method is always lower than 0.013 % (w / v) of NaCI, with increasing tendency with increasing temperature and that the LoQ of the acoustic method fluctuates between 0.02 % and 0.04 % (w / v) of NaCI.

[0111] In an embodiment, the acoustic method was applied to the determination of NaCI in commercial physiological solutions. The results are presented in Table 6.

[0112] Table 6 - Quantification of commercial physiological solution of nominal concentration 0.9 % (w / v) of NaCI.Reference Obtained concentrationNominalconcentration (Mean ± SD, % of NaCI) Accuracy Precision concentration Method(%(w / v) of (bias, %) (RSD, %) (%(w / v) of NaCI) IndividualNaCI) Averagebottle0.897 ±0.0030.899 ± 0.899 ±0.9 0.8955 Acoustic 0.406 0.362 0.003 0.0030.901 ±0.003Note - RSD: relative standard deviation; SD: standard deviation.

[0113] As expected from the accuracy and precision data, in an embodiment, the acoustic method allowed the quantification of sodium chloride on finished product with good accuracy and precision.

[0114] In an embodiment, this work dealt with the development and validation of the acoustic method for determining the assay of NaCI in a physiological solution with the aim of determining whether the acoustic method is suitable for the future development of PAT. This method relies on the change of the time of propagation of the signal with changing concentration of the solution being analysed. In an embodiment, the temperature and concentration were successfully integrated into a single model. In a future embodiment, the development of the method with a sample holder that mimics the pipelines in a manufacturing site will facilitate a future in-line method implementation. This method was validated according to the principles in the guideline ICH Q2(R2).

[0115] In an embodiment, the acoustic method model accomplished an R2larger than 0.9999. The intra-day precision was 0.348 % while the inter-day precision was 0.344 %, both at the 0.9 %(w / v) of NaCIlevel The bias was 0.003 %. The LoD and LoQ of the method vary between 0.006 and 0.0013 % and between 0.02 and 0.04 % (w / v) of NaCI, respectively.

[0116] The following pertains to acoustic PAT for real-time determination of glucose in solution for infusion of the present disclosure.

[0117] In an embodiment, the objective of this work was to develop a method for glucose assay in glucose infusion solution that encompasses the commercially available glucose infusion solution products for future in line implementation, with a rapid response and adequate accuracy and precision. In this context, an acoustic method was developed for the analysis of glucose in glucose infusion solutions.

[0118] Given the variety of glucose in infusion solution products, a single method covering the different concentrations available is considered useful.

[0119] As previously disclosed, in an embodiment, the method herein described is based on the change of time of propagation of an acoustic wave through the sample with varying concentration of glucose. As the concentration increases, the time of propagation decreases, consequently allowing to establish a relationship between time of propagation through the sample in a predetermined distance with glucose concentration. However, the temperature of the solution also has a major influence on the propagation time. As these products are not manufactured at a constant temperature, the impact of temperature needs to be accounted for.

[0120] The change of the time of propagation (or sound velocity) with concentration of solute and temperature is a known phenomenon [9], Nevertheless, the effect of these variables tends to be studied separately, by fixing one variable and varying the other. As far as is known, this approach may be the first that integrates temperature and concentration into the same model, while delving into a very large concentration range.

[0121] In comparison to the previous findings, this disclosure serves a dual purpose: 1) to enlarge the application of acoustic method while PAT tool suitable to other drug injectable product analysis, and 2) to shed light about its discriminatory power, consequently demonstrating their ability as stability-indicating method.

[0122] Surprisingly, the developed method returns results with great accuracy, and precision within a fraction of the time of the pharmacopeial method (i.e., from more than 40 min on the pharmacopoeial method to a fraction of a second), and without any sample preparation or sample withdrawal from the line. In an embodiment, the method may even be applied without any modification of existing manufacturing lines, as long as the materials that constitute them allow sound propagation.

[0123] In an embodiment, the present approach to the integration of temperature and concentration into the same model further allows easiness of implementation in line and greater precision in the results. Furthermore, the issue of the specificity of the acoustic method was resolved. To corroborate the methodtransfer, in an embodiment, the setup was installed at a manufacturing line during the production of a batch of glucose 10 % (w / v). This allowed to test the method in manufacturing conditions.

[0124] In an embodiment, all the solutions were made by dissolving the appropriate amount of glucose monohydrate (Lycadex®, ≥ 97.5 %) in purified water. Three bottles of commercial glucose 5 % (w / v), glucose 10 % (w / v) and glucose 30 % (w / v) were also analysed.

[0125] In an embodiment, the acoustic setup is as previously described in the present application.

[0126] Regarding to collection and processing of the acoustic signal, in an embodiment, the acoustic signal was received and processed as described before.

[0127] In an embodiment, the model that describes the relationship between the concentration of glucose, temperature and time of propagation of the acoustic signals consists of a three-dimensional surface. Several model equations were tested. The model that best described the data was chosen. The model was developed on the Origin Pro® 2018 software (OriginLab Corporation®).

[0128] In an embodiment, the validation of the method was performed as per ICH Q2(R2)

[0011] guideline for analysis of precision, accuracy, limits of quantification and detection, and specificity. The analyses were performed in triplicate on 3 different days.

[0129] In an embodiment, the studied range was from 0 to 60 % (w / v) of glucose, with a total of 25 calibration standards. Each standard was analysed in a temperature range from 10 to 26 °C.

[0130] In an embodiment, the model suitability was verified via the R2, the adjusted R2, the reduced x2 and residual sum of squares. Additionally, the fit of the plot of theoretical concentration with the obtained concentration was evaluated. The equation of the curve was determined using the least squares method. The R2, slope and origin y-intercept were obtained.

[0131] In an embodiment, the precision was evaluated by calculation of the RSD of the obtained concentration of five replicates of six quality control solutions on one day (intra-day) and three days (interday). The quality control solutions have nominal concentrations of 4.5, 6.0, 12.0, 24.0, and 48.0 % (w / v) of glucose.

[0132] In an embodiment, the accuracy was evaluated through the bias of the obtained concentration of five replicates of six quality control solutions from the considered true value.

[0133] In an embodiment, the LoD and the LoQ are, respectively, calculated using Equations 3 and 4. The SD of the response of measurements of the blank had a n of 10.

[0134] In an embodiment, the calculation of the LoD and LoQ was performed for each temperature in an independent way, i.e., for each temperature, a calibration curve was obtained and the SD and slope for that temperature were used.

[0135] In an embodiment, the setup, as previously described, was attached to a transfer line of the manufacturing site. In an embodiment, the line is constituted by stainless steel, with a diameter of 5.08 cm. In an embodiment, data was collected during the manufacturing of a batch of glucose 10 %. Additionally, water for injection was also measured in the same conditions. The signals were treated as in the method development.

[0136] In an embodiment, the developed model was used for the quantification of glucose.

[0137] The typical signal of the ultrasonic wave captured after reflection on the back of the pipe is represented in Figure 9. As the signal seems to dislocate as a whole on the propagation time-axis, one reference point of the signal was chosen. In an embodiment, the chosen reference point was the first maximum, as it corresponds to the wave front.

[0138] In an embodiment, in a first stage, the relation between concentration and time of propagation as well as between temperature and time of propagation were confirmed. For this purpose, in an embodiment, some glucose solutions with concentrations between 0 and 10 % (w / v) at 20 °C were measured for the former and a 5 % (w / v) solution of glucose with varying temperatures between 10 and 26 °C were measured for the latter. The temperature range considered encompasses the typical variation found in the industrial setting. The results of an embodiment are expressed in Figure 10 and Figure 11, respectively.

[0139] In an embodiment, as disposed in Figure 10 and Figure 11, the propagation time of the acoustic signal becomes shorter as concentration of glucose solution and temperature increase. These first experiments allowed to prove the concept and establish that the acoustic signal can be detected with sufficient amplitude and that the differences with changing concentration and temperature are observable.

[0140] In an embodiment, a model is built by plotting the first maximum of the signal with the concentration of the glucose solution and the temperature of the glucose solution. Several models were tested. In an embodiment, a comparison of the models, their R2, adjusted R2and residual sum of squares for the tested models may be found in Table 7.

[0141] Table 7 - Analytical figures of merit of the tested model equationsAdjusted Residual Sum Model description Model Equation3R2IO of Squares f l / PT-cA2l / T-dA2Gaussian surface GC = a + bl2^ f ' * 9 ) 0.97647 0.97618 2885.9 Rotated Gaussian f i / PT cos(S)+ T sin(S)- c cos(S)- d sin(S) '\2i / '-PT sin(S) +T cos(S)+ c sin(S) - d cosCS)^2]0.99935 0.99935 238.5 surface GC = a + b( f > 9 ) )Lorentz function GC — Cl + 2ir 2n 0.99652 0.99650 1280.8]Parabola function0.99678 0.99677 1185.5 without interaction GC = a + bPT + cT + dPT2+ fT2termPlane GC — ci + bPT + cT 0.99656 0.99656 1265.6 Quadratic Polynomial GC = a + bPT + cT + dPT2+ f T2+ gPT T 0.99995 0.99995 17.4 5thorder polynomial0.99726 0.99724 1009.1 without interaction GC = a + bPT + cPT2+ dPT3+ fPT4+ gPT5+ hT + IT2+ jT3+ kT4+ IT5term' ' - GC — ci + b 0.99372 0.99369 2310.4 Voigt surfaceModified VoigtGC = a + 0.99583 0.99581 1535.2+b _[ 7T24(PT-d- _T)2+d24(T-h9- _ + (1 - c^e-^)2+52' ndg{PT-n2^T-hYsurfacebeing, a, b, c, d, f, g, h, i, j, k, l, θ, coefficients, CG, the concentration of glucose, in % (w / v), PT the propagation time, in s, and 7, the temperature, in °C.' ' -

[0142] In an embodiment, the general equation that better describes this relationship is the quadratic polynomial, because of the higher R2and lower residual sum of squares. The model is expressed by the following equation:GC = a + bPT + cT + dPT2+ fT2+ gPT ■ T (8) being a, b, c, d, f, and g are numerical coefficients, GC, the concentration of glucose, in % (VJ / V), PT the propagation time of the acoustic signal, in s, and T, the temperature, in °C.

[0143] In an embodiment, the values for the coefficients on each of the validation day and on the general model are laid out in Table 8.

[0144] Table 8- Model coefficients of the equation 8, computed for the data of each validation day and for the general model, i.e., with all data. The calibration is performed with solutions with known concentration, at different and know temperatures. For each solution, the time of propagation of the acoustic signal is measured. The data set that includes the concentration of the solution, the temperature and the time of propagation of the acoustic signal is used to perform a fitting to Eq. 8, calculating the coefficients.Coefficients Day 1 Day 2 Day 3 Generala 254.7 ± 2.7 254.9 ± 2.9 253.6 ± 2.7 254.4 ± 1.6 b - 2.595·106± 8.7·104- 2.602·106± 9.2·104- 2.565·106± 8.7·104- 2.588·106± 5.1·104c 3.635 ± 0.028 3.635 ± 0.029 3.648 ± 0.028 3.639 ± 0.016 d - 1.585·1010± 7.0·108- 1.578·1010± 7.3·108- 1.608·1010± 7.0·108- 1.590·1010± 4.1·108f 2.76·10-3± 2.6·10-42.79·10-3± 2.8·10-42.71·10-3± 2.6·10-42.75-10'3± 1.6-10’4- 69179.8 ± 404.7 - 69192.1 ± 425.1 - 69366.4 ± 404.3 - 69246.1 ± 237.3g

[0145] The surface response obtained from an embodiment of the general model, i.e., with the points of the three validation days, is presented in Figure 12.

[0146] The goodness of fit of an embodiment of the model was evaluated with the R2, the adjusted R2, reduced x2and residual sum of squares. The values of these parameters for each validation day and for the general model are exposed in Table 9.

[0147] Table 9 - Calibration model parameters.R2Adjusted R2Reduced x2Residual Sum of SquaresDay 1 0.99995 0.99995 0.013 5.57Day 2 0.99995 0.99995 0.015 6.15Day 3 0.99995 0.99995 0.013 5.56General 0.99995 0.99995 0.014 17.41

[0148] As shown in Table 9, in an embodiment, the data is well modelled by Equation 7 with the coefficients presented in Table 8, since both R2and adjusted R2remain above 0.9999 in every validation day and on the general model. Additionally, the residual sum of squares remains below 5.56.

[0149] The obtained vs. theoretical concentration of glucose at 10 °C, 15 °C, 20 °C, and 26 °C of an embodiment are presented in Figure 13 and the respective figures of merit are exhibited in Table 10.

[0150] Table 10 - Figures of merit of the curves computed for obtained vs. theoretical glucose concentrations of an embodiment. Slope and y-intercept are presented with the respective standard errors.Temperature (°C) 10 15 20 26 Slope 1.000 ± 0.001 0.9996 ± 0.0007 1.001 ± 0.001 0.9993 ± 0.0007 y-intercept - 0.0096 ± 0.0271 - 0.0015 ± 0.0191 - 0.0234 ± 0.0268 - 0.0184 ± 0.0190 R20.99993 0.99997 0.99993 0.99997 Adjusted R20.99993 0.99997 0.99993 0.99997 Residual sum1.497 0.741 1.459 0.730of squares

[0151] The precision and accuracy were evaluated for an embodiment with five replicates of five standard solutions at the concentrations of 4.5 %(w / v), 6.0 %(w / v), 12.0 %(w / v) and 24.0 %(w / v), and 48.0 % (w / v) of glucose on three separate days. For the intra-day precision, the results from the first day were considered. The accuracy and precision were evaluated considering the bias and the RSD, respectively. The results are laid out in Table 11.

[0152] Table 11 - Intra-day and inter-day precision, and accuracy for the concentration levels of 4.5 %, 6.0 %, 12.0 %, 24.0 %, and 48.0 % of glucose. Intra-day results are drawn from the first day of validation. For intra-day precision, n = 5, and for inter-day precision, n = 15, considering the same operator.Intra-day Inter-day TheoreticalConcentration Obtained Obtainedconcentration Precision Accuracy concentration Precision Accuracy (%(w / v)ofglucose) (mean ± SD, % of (RSD, %) (Bias, %) (mean ± SD, % of (RSD, %) (Bias, %) glucose(w / v)) glucose (w / v))4.5 4.456 ± 0.051 1.119 1.223 4.558 ± 0.054 1.192 1.291 6.0 6.002 ± 0.040 0.660 - 0.039 6.008 ± 0.043 0.718 0.043 12.0 11.927 ± 0.017 0.140 -0.612 11.921 ± 0.043 0.338 -0.661 24.0 24.008 ± 0.085 0.355 0.031 24.032 ± 0.090 0.373 0.134 48.0 48.087 ± 0.044 0.092 0.182 48.089 ± 0.270 0.562 0.185Note - RSD: relative standard deviation; SD: standard deviation.

[0153] The results of Table 11 indicate that in an embodiment, the method has good precision and accuracy. The maximum RSD on the intra-day precision was 1.119 %, while the maximum RSD for inter-day precision was 1.192 %, both for the concentration level of 4.5 % (w / v) of glucose. Therefore, the method precision is always below 1.2 %. Regarding the accuracy, the maximum bias found was 1.223 % of the nominal concentration and 1.291 %, when all validation days are considered.

[0154] In an embodiment, for each studied temperature, the LoD and LoQ were estimated, according to Equation 3 and Equation 4. Therefore, for each temperature, a calibration curve between the propagation time and concentration of glucose was developed, from which the SD and slope were calculated. The results for each temperature are shown in Figure 14.

[0155] As can be seen in Figure 14, in an embodiment, the LoD of the method varies between 0.02 and 0.05 % (w / v) of glucose and the LoQ varies between 0.06 and 0.13 % (w / v) of glucose. Both LoD and LoQ tend to be higher on higher temperatures.

[0156] After validation, in an embodiment, the method was also applied to commercial solutions of glucose 5 % (w / v), glucose 10 % (w / v) and glucose 30 % (w / v). The obtained results and comparison with the results obtained by a validated method are shown in Table 12.

[0157] Table 12 - Assay of commercial solutions of nominal concentration 5%, 10% and 30% (w / v) of glucose.Reference Obtained concentrationNominal concentration concentration (Mean ± SD, % w / v of glucose) Bias RSD (%, w / v of glucose) (% w / v of (%) (%) glucose) Individual bottle Average4.876 ± 0.0405 4.85 4.871 ± 0.032 4.878 ± 0.037 0.573 0.7494.887 ± 0.0359.858 ± 0.02510 9.89 9.867 ± 0.012 9.865 ± 0.019 - 0.252 0.1879.870 ± 0.01429.905 ± 0.02430 29.88 29.908 ± 0.090 29.913 ± 0.088 0.111 0.29529.927 ± 0.090Note - RSD: relative standard deviation; SD: standard deviation.

[0158] In an embodiment, the method returned results with good accuracy and precision, being the highest bias 0.573 % and the highest RSD 0.749 %, both for glucose 5 % (w / v).

[0159] The following pertains to the method transfer disclosed herein with regard to glucose.

[0160] As a first effort for in-line implementation of the method, in an embodiment, the setup was installed on a manufacturing site during the manufacturing of a batch of glucose 10 % (w / w). The time of propagation of the acoustic signal and temperature were recorded. The validated model was used to obtain the concentration of glucose. The results were compared with the ones obtained through the reference method (polarimetry). Additionally, in an embodiment, the method was also applied to water for injection. The obtained concentrations are displayed in Figure 18.

[0161] Figure 18 emphasises that the method, in an embodiment, delivers results with good precision and accuracy in industrial manufacturing conditions. The mean obtained concentration with the method was 10.028 ± 0.007 % of glucose, with an RSD of 0.073 %, while the considered true value was 9.98 % (w / v) of glucose, corresponding to a bias of 0.484 %. The results of the water were below the LoQ, which means that the manufacturing conditions may lead to a small deviation relative to the model. This is corroborated by the obtained concentration on glucose, always above the considered true concentration. Despite the bias and RSD remaining at an acceptable level, the true impact of the manufacturing conditions should be assessed on further experiments with different concentration levels and temperatures. However, these results anticipate a successful development of this acoustic method as aPAT. It is noteworthy to recall that there is no data on the possibility of detecting degraded solutions on an industrial setting. The present experiment further helps establishing the discriminatory power and stability-indicating nature of the method.

[0162] An aspect of the present disclosure dealt with the development and validation of a method for glucose determination in glucose-based injectable solutions with the objective of developing a PAT tool. In an embodiment, the method is based on the ultrasonic wave propagation time as it relates with the concentration of glucose present on the solution. The method was successfully validated according to international standards (ICH Q2(R2)) demonstrating goodness of fit of the model, with a R2larger than 0.9999 and low residual sum of squares, accuracy with bias inferior to 1.3 % and with RSD inferior to 1.119 % (intra-day) and 1.192 % (inter-day). The LoD and LoQof the method vary between 0.02 and 0.05 % and between 0.06 and 0.13 % (w / v) of glucose, respectively. Furthermore, the method may be specific as the acoustic signal carries information that allow discrimination between solutions with and without glucose impurities. The developed method also possesses a set of characteristics that deem it as potential PAT, particularly, the signal collection time (inferior to 0.1 s) and the non-invasiveness, as all the scanning is done without any equipment being in contact with the samples. These technical characteristics alongside the analytical figures of the method render it as a potential PAT method for real-time determination of glucose in glucose infusion solution as the product is manufactured or even as quality control tool. Comparing the acoustic method with an internally validated polarimetry method, the polarimetry method has similar accuracy (1 % bias) and slightly better precision with a method repeatability of 0.5 % and intermediate precision of 0.3 %.

[0163] To facilitate further method transfer into a manufacturing site, in an embodiment, the method was developed in sample holder which mimic the type of pipes that may be found in an industrial setting. A first set of in line tests in an industrial setting allowed to establish that the method is able to quantify glucose under manufacturing conditions with good accuracy and precision.

[0164] The following pertains to identifying solutions with impurities derived from thermal degradation, namely the 5-HMF, the main glucose impurity of the present disclosure.

[0165] As previously mentioned, the acoustic signal seems to be dislocated as a whole along the propagation time-axis. However, the presence of foreign molecules influences the profile of the signal. In an embodiment, three replicates of the solutions of glucose 5 %(w / v) and glucose 20 %(w / v) were divided into two aliquots.

[0166] In an embodiment, for each solution, one aliquot was thermally degraded (121 °C, 30 min), thus producing minimal amounts of 5-HMF, while the other aliquot was not subjected to heat treatment. The presence of 5-HMF was corroborated with a validated method of UV-Vis spectrophotometry (Perkin Elmer® double beam spectrophotometer, model Lambda 35). In an embodiment, the method has a LoD of 0.02 pg / mL, system precision of 0.1 % and repeatability of 0.6 %.T1

[0167] In an embodiment, all confirmatory measurements were performed in a quartz cuvette with a 1 cm path length. The maximum absorbance of 5-HMF is at 284 nm.

[0168] In an embodiment, for each aliquot, the acoustic signal of the reflection at the back wall of the pipe was collected at 20.0 °C in fifteen separate time intervals. In an embodiment, the signal in the timedomain was transformed with a Fourier transform into a frequency-domain spectrum.

[0169] In an embodiment, the frequency spectrum was used as data to create a PLS-DA model to distinguish between the solutions with and without 5-HMF. A model was built for both studied concentrations and one with all data. Spectra were centred and scaled. In an embodiment, for the model building (calibration set), 75 % of the data were randomly selected for and the remaining 25 % for prediction (test set). In an embodiment, the calibration set was subjected to leave-one-out cross validation. For each model, the root means square error of calibration (RMSEC), of cross validation (RMSECV) and of prediction (RMSEP), the R2and Q2(i.e., the R2of the test set) were computed. Generally, the root mean square error (RMSE) is calculated with the following formula:RMSE =(9)J nwhere n is the number of samples, ẑithe estimated value (in the calibration model, in cross-validation, or on the prediction of samples external to the calibration model, for the RMSEC, RMSECV, and RMSEP, respectively), and zi, the considered true value.

[0170] The specificity of the method may be determined on the basis of a characteristic of the acoustic signal, particularly the frequency spectrum derived from the Fourier transform of said signal. For this, heat-degraded and non-degraded glucose solutions were used to train a PLS-DA model to distinguish the solutions with heat-derived impurities from those without impurities. The main glucose impurity is 5-HMF. On that work, heat was used to degrade the solutions because the mechanism of degradation of glucose into 5-HMF is temperature driven.

[0171] The BP indicates that 5-HMF ought to be tested in glucose infusion solution [4], The stated reference method for control of 5-HMF is UV-Vis spectrophotometry. In operational terms, this means that for the control of this impurity, samples have to be drawn from the manufacturing line, transported to the quality control laboratory, and processed (eventually with dilutive steps). As previously discussed, this quality control paradigm is time-consuming, labour intensive with significative costs in terms of hold times and personnel. Alternatively, the use of PAT allows to better control the product while decreasing manufacturing costs and time [2], In that sense, the acoustic methods were identified as possible PAT for injectable products [3],

[0172] In an embodiment, each prepared solution was divided into two aliquots, being one thermally degraded, resulting in a small amount of 5-HMF, a glucose impurity. In an embodiment, this impurity canbe detected spectrophotometrically by determining the absorbance at 284 nm. The specification for finished product is an absorbance of less than 0.2. The LoD of the method is an absorbance of 0.001. The obtained absorbances are listed in Table 13.

[0173] Table 13 - Absorvances of the studied solutions.Absorbance of the Absorbance of theGlucose concentration Replicatedegraded aliquot non-degraded aliquot1 0.2391 ND5 % 2 0.2556 ND3 0.2306 ND1 0.2078 ND20 % 2 0.2242 ND3 0.2182 NDNote - ND: non-detected.

[0174] In an embodiment, for each aliquot, one non-degraded and other with 5-HMF, the signal reflected from the back wall of the sample container is acquired. The acoustic signal in the time-domain is transformed into a frequency-domain signal, through a Fourier transform. An example of an acoustic signal and corresponding frequency spectrum is presented in Figure 15.

[0175] As expected, in an embodiment, the main peak is located at approximately 5 MHz, as that is the central frequency of the transducer. For comparison, a frequency-domain signal of a glucose 5 % (w / v) solution degraded and non-degraded are superimposed in Figure 16. The signal was truncated at 15 MHz, as above that frequency there was no significative peaks (see Figure 15-B).

[0176] In an embodiment, the differences are not very expressive, being located mainly at ca. 6 MHz, with some minor differences in the 2 MHz and 8 MHz range. In an embodiment, a PLS-DA algorithm, a classification chemometric tool based on PLS, was used to distinguish the degraded from non-degraded solutions. In an embodiment, a model was created for glucose 5 % (VJ / V), another for glucose 20 % (w / v) and another with data from both concentrations. For each model, the signal was truncated at 15 M Hz and 75 % of the data were randomly selected for model building (calibration set) and the remaining 25 % for prediction (test set). The data was centred and scaled. The calibration set was subjected to leave-one-out cross validation.

[0177] For the three models, in an embodiment, the RMSEC, RMSECV, RMSEP, R2, and Q2were plotted against the number of components, being presented in Figure 18.

[0178] The analysis of Figure 17 allows to choose of the number of components for the model. The components are the underlying orthogonal variables that explain the variance in the dataset, allowing the simplification of the dataset while retaining the relevant information. In the case of the model for glucose5 % (w / v) Figure 17-A and -D), the RMSEC and RMSECV are reduced with increasing number of components. However, the RMSEP has a minimum at the third component. Additionally, the Q2maximum is met at the 3rdcomponent, being negative from the 5thcomponent forward. This means that the model overfits the data of the model after the 3rdcomponent. Therefore, 3 components were chosen for the model building. For the model of glucose 20 % (w / v) (Figure 17Error! Reference source not found. -B and -E), the RMSEP meets its first local minimum and the Q2has its first local maximum at the third component being that the chosen number of components. When the two concentrations were used to build a model (Figure 17-C and -F), the RMSEP have the first local minimum with 7 components, while both RMSEC and RMSECV have the first local minimum with 8 components. However, there is no significant difference for the RMSEC and RMSECV from the 7thto the 8thcomponent. The Q2first local maximum is located at the 7thcomponent. Thus, 7 components were chosen. A summary of the analytical metrics for all methods is presented in Table 14.

[0179] Table 14 - Analytical metrics of the models built with the data of solutions with glucose 5 % (w / v), glucose 20 % (w / v) and with all data.Glucose GlucoseModel All data 5 %(w / v) 20 %(w / v)Number of components 3 3 7R20.9380 0.9929 0.9805 Bias 6.8 · 10-173.5 · 10-164.3 · 10-16Slope 0.9380 0.9929 0.9805 CalibrationRMSEC 0.2480 0.0835 0.1395 Cumulative explained variance (%) 93.80 99.29 99.39 Misclassified (%) 0 0 0Cross- RMSECV 0.3042 0.1316 0.3308 Validation Misclassified (%) 1.4 0 1.4Q20.9567 0.9914 0.9333 Prediction RMSEP 0.2051 0.0875 0.2560Misclassified (%) 0 0 0Note - RMSEC: root mean square error of calibration; RMSECV: root mean square error of cross validation; RMSEP: root mean square error of prediction.

[0180] Analysing the data addressed in Figure 17 and Table 14, it can be concluded that the method can be able to distinguish glucose solution with and without the degradation product, even when different glucose concentrations are considered. This characteristic of the analytical method is of great relevance in the context of a PAT application because of the added value to quality control, the condensation of different analysis into a single device, the saved time and the spare of laboratorial resources.

[0181] In an embodiment, this approach can be used to identification of fluid dilution. Furthermore, in an embodiment, using the attenuation of the acoustic wave and the temperature, one can calculate the density of the fluid. For that purpose, one may use the following equation:(6)v21-R1 2

[0182] Where p is the density of sample container,is the velocity of sound in the sample container, v2is the velocity of sound in the sample and / ?1 2is the reflection coefficient between the sample container and the sample. R2is given by the following formula:A2

[0183] where A1, A2, and A3are, respectively, the amplitudes of three echoes from the from the frontier between the sample holder and the sample

[0012] ,

[0184] However, further work is necessary to establish if the temperature and the whole range of glucose concentrations considered affect the distinction between the presence and absence of 5-HMF. Further experiments should be conducted to establish the LoD of 5-HMF.

[0185] The following pertains to quantifying 5-HMF, the main glucose impurity of the present disclosure.

[0186] Previously, an acoustic setting for in-line monitoring of the glucose concentration in glucose infusion solution was used. As part of that work, one shortcoming was identified: the selectivity of the method. In order to reduce that limitation, in an embodiment, a classification multivariate method was used to distinguish degraded from non-degraded glucose infusion samples. In an embodiment, the method can be able to distinguish those solutions accurately, further expanding the capabilities of the method. With such characteristics, one can ask if that methodology can be applied to quantify the impurity itself.

[0187] In an embodiment, the raw acoustic signal is not used because with different temperatures and glucose concentrations, the time-of-flight is altered dislocating the signal in the time-axis (x-axis). In an embodiment, the way to normalise the signal is to apply a Fourier transform to the acoustic signal, obtaining a frequency spectrum which allows comparation between different signals. Then, in an embodiment, the spectrum is used to build a multivariate quantitative model.

[0188] As far as is known, this can be the first attempt to quantify 5-HMF through an acoustic method and a first effort towards a PAT applied to quantification of 5-HMF. Nevertheless, there are other techniques, which could be used as PAT. For starters, the reference UV-Vis spectrophotometry may be installed in line and be used as PAT. However, no examples of this approach could be found in the literature. Other techniques involve PAT-gold standards, such as Raman spectroscopy and NIRS. As examples, Anjos et al.

[0013] developed a Raman spectroscopy method with Fourier transform forcharacterisation of honey. Among the different characteristics analysed, 5-HMF was quantified. The reported R2was 0.990, while the RMSEP was 0.169 mg / kg. No acquisition time was provided.

[0189] The main advantages of the acoustic approach described in the present disclosure over the alternatives reported are the lack of contact of the analyser with the product and the lower time of analysis.

[0190] In an embodiment, this approach may also be used, with or without temperature reading, for the purposes of determination of concentration of solutes in multicomponent solutions or in different fluids, such as the quantification of a preservative in a solution, identification of fluids, such as distinguishing a glucose solution from a sodium chloride solution, identification of solutes in solution, by providing a fingerprint spectrum of a solute, identification of fluid dilution, by determination of the concentration of one or multiple analytes, determination of particle size in a suspension, such as determination of ibuprofen particle size in ibuprofen suspension for oral use, or determination of globule size in emulsion, in products with multiple phases to name a few.

[0191] In an embodiment, the objectives of the present work are: 1) quantify the glucose impurity (5-HMF) through an acoustic method, 2) further expand the capabilities of the acoustic setup described and developed previously in the present disclosure, and 3) develop the base for a PAT methodology that works as an alternative to the established lab-based, labour-intensive reference methods.

[0192] For that, in an embodiment, glucose monohydrate (Lycadex®, > 97.5 %) and 5-HMF (Sigma-Aldrich®, > 99 %) were used to fabricate the solutions used in this work. The solutions were made by dissolving the appropriate amount of substance in purified water (Millipore®, 18 MO cm at 25 °C).

[0193] In an embodiment, a UV-Vis spectrophotometry method was used as reference method of the multivariate model of the acoustic method. A Shimadzu UV 1800 UV-VIS spectrophotometer with double beam was used. The analysis was performed at 284 nm in quartz cells with 10 mm of pathlength. The reference cell was filled with purified water.

[0194] In an embodiment, the acoustic setup employed corresponds to the acoustic setup described throughout the present description. Acoustic signals were collected at 16° C, 20° C, and 24° C.

[0195] In an embodiment, the acoustic signal was subjected to Fourier transform in order to obtain the frequency spectrum. The frequency spectrum was then used for further model building. These computations were performed with " R" v. 4.0.0 and " RStudio" v. 1.3.959 software.

[0196] In an embodiment, the validation for both the reference and the acoustic methods was accomplished in accordance with the ICH Q2(R2) guideline

[0011] , For the acoustic method, the recommendations regarding multivariate methods were considered, namely the validation procedure considers calibration, internal testing and validation, in which the test data is a separate set of data formthe calibration data set, the samples were measured by the new method and the reference method within a reasonable timeframe, the RMSEP was used as a measure of accuracy and precision.

[0197] In an embodiment, the calibration set of the acoustic method had a range from 0.05 to 3.0 μg / mL of 5-HMF in a total of 30 calibration solutions. A model was constructed for three independent days. The calibration set was subjected to leave-one-out cross validation.

[0198] In an embodiment, in order for the UV-Vis spectrophotometry method to encompass the working range of the acoustic method, a larger range of 0.0 - 3.2 μg / mL of 5-HMF was chosen. These working ranges were selected because the BP absorbance limit for the glucose solution is 0.25 for a 1 cm path length at the wavelength of 284 nm, which corresponds to a concentration of 2.0 μg / mL of 5-HMF.

[0199] The following pertains to Chemometric model of the present disclosure.

[0200] In an embodiment, two of the most used multivariate quantitative algorithms, PCR and PLS, were used to model the data. The PCR models were built using the "pls" package

[0014] for R software, while the PLS models were generated using the "mdatools" package

[0015] for R software. R v. 4.0.0 and RStudio v.1.3.959 software were used. The best model was chosen after analysis of the RMSEC, RMSECV, and RMSEP, the R2, and the Q2. The RMSE general formula was already described in Equation 6.

[0201] In an embodiment, some spectrum pre-processing algorithms were tested, namely auto-scaling (mean centring and scaling), truncation, and derivatisation (1stand 2ndorder).

[0202] The conditions which led to better prediction capacity (i.e., lower RMSEP and higher Q2) were chosen for further work.

[0203] In an embodiment, the specificity of both the the acoustic method was assessed by quantification of samples of the matrix and of samples with spiked glucose at 6 % concentration level.

[0204] As stated on the ICH Q2(R2) guideline, for multivariate quantitative methods, in an embodiment, the RMSEP encompasses both precision and accuracy. For this purpose, in an embodiment, a test set constituted by 5 replicates of solutions with 55 %, 75 %, 100 % and 130 % of the test concentration was measured. In order to evaluate the evolution of the accuracy and precision across the studied range, the RMSEP for each level is presented.

[0205] The LoD and LoQ. are, computed with the formulas laid out in the ICH Q2(R2) guideline, already described in Equations 3 and 4, respectively.

[0206] The following pertains to results and discussion of quantification of 5-HMF, the main glucose impurity, of the present disclosure.

[0207] The standard method described in the BP for the assay of 5-HMF is the UV-Vis spectrophotometry [4], In that chapter of the BP, the observed limit is an absorbance of 0.25 for a 1 cm path length at thewavelength of 284 nm. This was experimentally verified. The referred absorbance corresponds to a concentration of 2.0 μg / mL of 5-HMF.

[0208] In an embodiment, the acoustic signal was obtained in the time-domain. However, as the signal dislocates laterally with variable glucose concentration and temperature, the sign moves in the x-axis, which brings difficulty to the analysis. The transformation into a spectrum in the frequency-domain provides a comparable x-axis between the signals. In an embodiment, a Fourier transform was used for this purpose and the resulting spectra were utilised to create quantitative multivariate models (PLS and PCR), (see Figure 15).

[0209] In an embodiment, It is obtained a main peak at ca. 5 MHz, as expected, since that is the central frequency of the transducer.

[0210] In an embodiment, the frequency spectra pre-processing involved mean centring (centring and scaling), derivatives (1stand 2nd) and truncation of the spectrum for the region of 3 MHz to 11 MHz. The truncation was done at these points because that was the region where most of the spectral characteristics occurred.

[0211] Table 15 displays the results of the models generated with different combinations of model algorithm and spectra pre-processing.

[0212] Table 15 - Tested models with different spectra pre-processing and their respective analytical figures.Pre-processing Analytical figuresModelCentred Scaled Truncated 1stderivative 2ndderivative Components R2RMSEC RMSECV Q2RMSEP 4 0.920 0.233 0.248 0.908 0.242 X 7 0.958 0.169 0.197 0.882 0.271X 3 0.941 0.199 0.240 0.869 0.285 X X 6 0.997 0.046 0.225 0.857 0.299X 3 0.850 0.318 0.324 0.900 0.250 X X 5 0.931 0.217 0.230 0.881 0.272X X 3 0.856 0.313 0.326 0.886 0.266 X X X 5 0.946 0.191 0.246 0.860 0.295X 6 0.935 0.210 0.229 0.902 0.246 PLS X X 7 0.949 0.186 0.220 0.899 0.250X X 3 0.945 0.193 0.255 0.880 0.273 X X X 2 0.945 0.193 0.256 0.880 0.273X X 6 0.894 0.266 0.288 0.911 0.236 X X X 7 0.938 0.204 0.230 0.902 0.246X X X 4 0.890 0.273 0.304 0.901 0.248 X X X X 3 0.933 0.213 0.240 0.882 0.270X 8 0.955 0.176 0.228 0.869 0.285 X X 7 0.978 0.124 0.209 0.872 0.282X X 5 0.981 0.114 0.298 0.843 0.312Pre-processing Analytical figures ModelCentred Scaled Truncated 1stderivative 2ndderivative Components R2RMSEC RMSECV Q2RMSEP X X X 6 0.979 0.120 0.295 0.840 0.315X X 6 0.882 0.287 0.331 0.876 0.278 PLS X X X 5 0.909 0.251 0.290 0.868 0.286 (cont.}X X X 6 0.920 0.233 0.300 0.883 0.270 X X X X 4 0.917 0.237 0.279 0.867 0.2885 0.859 0.303 0.309 0.899 0.250 X 5 0.910 0.241 0.247 0.861 0.294X 5 0.911 0.239 0.246 0.873 0.280 X X 5 0.909 0.241 0.248 0.860 0.295X 5 0.841 0.322 0.328 0.901 0.248 X X 5 0.909 0.241 0.248 0.861 0.295X X 3 0.813 0.351 0.356 0.882 0.271 PCR X X X 2 0.887 0.273 0.277 0.836 0.319X 8 0.874 0.276 0.292 0.869 0.295 X X 9 0.901 0.248 0.259 0.848 0.307X X 8 0.883 0.255 0.282 0.848 0.307 X X X 5 0.861 0.282 0.306 0.819 0.336X X 9 0.811 0.338 0.358 0.876 0.277 X X X 9 0.880 0.273 0.285 0.832 0.324X X X 9 0.834 0.322 0.336 0.897 0.253Pre-processing Analytical figuresModelCentred Scaled Truncated 1stderivative 2ndderivative Components R2RMSEC RMSECV Q2RMSEP X X X X 9 0.900 0.249 0.260 0.876 0.278X 10 0.671 0.446 0.472 0.644 0.470 X X 10 0.645 0.458 0.490 0.634 0.789X X 10 0.650 0.442 0.487 0.482 0.567 PCR X X X 10 0.775 0.341 0.390 0.709 0.425 (cont.}X X 20 0.843 0.292 0.326 0.877 0.277 X X X 15 0.834 0.307 0.335 0.790 0.361X X X 15 0.824 0.317 0.344 0.867 0.288 X X X X 11 0.845 0.304 0.324 0.816 0.338Note - PCR: principal component regression; PLS: partial least squares; RMSEC: root mean square error of calibration; RMSECV: root mean square error of cross validation; RMSEP: root mean square error of prediction.

[0213] The data in Table 15 indicates that the best model in terms of prediction power, in an embodiment, was obtained using the PLS algorithm with truncation of the spectra and applying a 1stderivative transformation, since these pre-processing led to better prediction results, namely, a lower RMSEP and a higher Q2, with the use of 6 components.

[0214] Figure 20 showcases the evolution of RMSEC, RMSECV, RMSEP, R2, and Q2with increasing number of components for the chosen model.

[0215] Figure 20 confirms the use of the 6thcomponent because the RMSEP has a minimum (0.236) and the Q2has a maximum (0.910) at that component. After that, the model starts to overfit the data and gets worse predictions, i.e., an increase of R2with decrease of Q2. The RMSEC and RMSECV do not offer much additional information because for the first 10 components, the latter closely follows the former. The obtained RMSEC was 0.275 μg / mL and the RMSECV was 0.292 μg / mL.

[0216] The plot and linear fit between obtained concentration and considered true values of an embodiment may be found in Figure 21. The model fits the data better when the R2and slope are closer to 1 and the y intercept is close to 0. The R2was 0.894. The slope of the obtained curve was 0.971, while the y-intercept was 0.059. Although the R2is not in close agreement with the objectives, it is not too far off, being close to 0.9. These results are in fact quite common in multivariate methods. Nevertheless, this deviation may be due to fact that the spectral features between the different spectra are too similar to allow a better fit of the model, or due to the error introduced by the reference method, i.e., UV-Vis.

[0217] Table 15 shows that the RMSEP of the test set of an embodiment is 0.236. Considering the intraday data, the RMSEP is 0.247 and the Q2is 0.902. The RMSEC and RMSECV are 0.241 and 0.336, respectively, while the R2is 0.914.

[0218] In an embodiment, the SD of the blank measurements was 0.075 μg / mL (n = 12), while the obtained slope of the calibration curve was 0.971. Applying Equation 3 and Equation 4, the LoD and LoQ of the method is 0.256 μg / mL and 0.775 μg / mL, respectively.

[0219] In an embodiment, the specificity of the method was evaluated by quantifying samples of the matrix, samples with excess glucose and samples of 5-HMF in water. For the blank samples, a total of 52 spectra were considered, while the quantification of 5-HMF was made with 9 spectra each. In an embodiment, the spectra were collected in all considered temperatures. The results are laid out in Table 16.

[0220] Table 16- Specificity results of quantification of blank, and 5-HMF samples with modified matrix.Reference Obtained concentration RMSEP Sample concentration (mean ± SD, pg / mL of (pg / mL of (pg / mL of 5-HMF) 5-HMF) 5-HMF) Blank 0.0 -0.163 ± 0.075 0.396 5-HMF in 0 % (w / w)1.594 1.790 ± 0.111 0.225 glucose5-HMF in 6 % (w / w)1.624 1.864 ± 0.083 0.254 glucoseNote - RMSEP: root mean square error of prediction; SD: standard deviation.

[0221] The data of Table 16 shows that, in an embodiment, the matrix has no effect on the performance of the method. On the one hand, the RMSEP of the 5-HMF solutions in altered matrix are similar to the RMSEP obtained by the test set. On the other hand, the mean obtained concentrations are close to the reference concentrations. The RMSEP of the blank solutions is somewhat larger than the RMSEP of the test set. This may be due to two reasons: 1) the model does not include the 0 μg / mL point, and 2) the 0 μg / mL is below the LoD of the method. Therefore, the method is specific to 5-HMF.

[0222] To verify the temperature effect and the robustness of the method, in an embodiment, data for the calibration and test sets were captured with three different temperatures so that the model incorporated that source of variability. To test the effect of temperature, in an embodiment, the data from both the calibration and test sets was reorganised to build new models. Therefore, the temperature segregated sets are organised in the following manner: the new calibration set is composed of spectra of two of the three temperatures and the new test set is composed of the spectra of the remainder temperature. This was done for each of the three tested temperatures. The RMSE, R2and Q2of these models are presented in Table 17.

[0223] Table 17 - Temperature effect. Data from temperatures not included in the model are tested by that model.Test set temperature RMSEC RMSECV RMSEP R2Q216 °C 0.248 0.264 0.285 0.907 0.87820 °C 0.242 0.262 0.204 0.912 0.93424 °C 0.133 0.187 0.269 0.973 0.891Note - RMSEC: root mean square error of calibration; RMSECV: root mean square error of cross validation; RMSEP: root mean square error of prediction.

[0224] By comparing the results in Table 17 with those of the general model, can be seen that the RMSEs, R2and Q2are comparable. Therefore, the prediction power holds when data obtained with newtemperatures are tested. Comparing this work with its counterpart for the quantification of glucose, this method seems to provide temperature-independent results, which figures as a further advantage.

[0225] This work comes in the sequence of the work previously disclosed in the present disclosure, in particular the development of an acoustic method that may serve as PAT applied to injectable drug products. In an embodiment, instead of relying on the time of propagation of an acoustic signal, the method uses the frequency spectrum to build a PLS model, this time for quantification of 5-HMF, the impurity of glucose, in glucose infusion solution. The model was validated according to the ICH Q2(R2) guideline. The model has an R2of 0.894 with RMSEC of 0.266 μg / mL, and RMSECV of 0.288 μg / mL. It allowed prediction with an RMSEP of 0.236 μg / mL and Q2of 0.911. This prediction ability is comparable or even superior to other techniques that are possible to be used as PAT, i.e., Raman spectroscopy and NIRS.

[0226] Comparing the present method with other techniques available, the developed method presents a number of advantages, particularly: 1) no need of adaptation of the manufacturing line, 2) no contact between the analyser and product, which reduces the risk of cross-contamination, 3) reduced costs of implementation, and 4) reduced acquisition time (ca. 0.1 s).

[0227] The work further aimed to broaden the capabilities of the acoustic method, resulting in two complementary approaches implemented with the same setup. When comparing with the propagation time approach, the present approach seems to be temperature independent. This is a great advantage because it simplifies the analysis and method development. Further work needs to be done to confirm and establish the limits of temperature to which a model is valid and to improve the error and range of the method. Some possible improvements may also include the use of other transducers with different dynamic ranges and central frequencies.

[0228] Despite the shortcomings of the method (relatively high LoD and LoQ, and RMSEs), the developed method may be appropriate for additional development into a full use PAT tool in service of increased control over the quality and safety of injectable drug products.

[0229] The terms "determining," "measuring," "evaluating," "assessing," "assaying," and "analyzing" are often used interchangeably herein to refer to forms of measurement. The terms include determining if an element is present or not (for example, detection). These terms can include quantitative, qualitative or quantitative and qualitative determinations. Assessing can be relative or absolute. " Detecting the presence of" can include determining the amount of something present in addition to determining whether it is present or absent depending on the context.

[0230] The term "comprising" whenever used in this document is intended to indicate the presence of stated features, integers, steps, components, but not to preclude the presence or addition of one or more other features, integers, steps, components or groups thereof.

[0231] The disclosure should not be seen in any way restricted to the embodiments described and a person with ordinary skill in the art will foresee many possibilities to modifications thereof. The abovedescribed embodiments are combinable.

[0232] The following dependent claims further set out particular embodiments of the disclosure.

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[0015] Kucheryavskiy, S. (2020). mdatools - R package for chemometrics. Chemometrics and Intelligent Laboratory Systems, 198, 103937. https: / / doi. Org / 10.1016 / j.chemolab.2020.103937

Claims

1. C L A I M S1. A real-time non-invasive method for determining / measuring analytic parameter in a fluidic sample comprising:3.providing the fluidic sample in a sample container;4.monitoring the temperature of the fluidic sample;5.generating, by an electrical pulse generator, a set of electrical pulses to an ultrasonic transducer coupled to the sample container, each electrical pulse of the set of electrical pulses being generated at a predetermined pulse-repetition frequency;6.converting, by the ultrasonic transducer, each sent electrical pulse of the set of electrical pulses into an ultrasonic signal for transmitting the ultrasonic signal through the fluidic sample, receiving by the ultrasonic transducer, a reflected ultrasonic signal after one or multiple traversal of the fluidic sample and converting the reflected ultrasonic signal into a corresponding electrical signal;7.obtaining, the electrical signal and determining a propagation time of the ultrasonic signal between emission and reception;8.processing, by a computer processor, the temperature of the fluidic sample, and the acoustic signal propagation time to calculate, compare the values with a pre-determined calibration model for each analytical parameter for obtaining the analytical parameter.

2. The method according to any of the previous claims, further comprising, a previous step, of filtering the reflected ultrasonic signal by an electronic filter; and amplifying the reflected ultrasonic signal.

3. The method according to any of the previous claims, wherein the pulse-repetition frequency ranges from 1 Hz to 1 kHz, preferably 1 kHz.

4. The method according to any of the previous claims wherein the fluidic sample is selected from liquid solution, viscose solution, or semi-solid sample.

5. The method according to any of the previous claims, wherein the analytical parameter is selected from: a concentration of an analyte, a density of a fluid, a concentration of a solute in a monocomponent solution, a concentration of a solute in a multi-component solution, a concentration of an impurity in a solution, or combinations thereof.

6. The method according to any of the previous claims and claim 5, wherein obtaining the analyte concentration comprises solving the quadratic polynomial model14.A = a0+ b · PT + c · T + d · PT2+ f · T2+ g · PT · T, wherein: A is the analyte concentration;15.PT is the time of propagation or velocity of the acoustic signal;16.T is the temperature read by the temperature sensor;17.a0, b, c, d, f, g is are numerical coefficients obtainable by numerical regression from pre-calibrated concentration fluidic samples, preferably at least 5 fluidic samples.

7. The method according to the previous claim wherein the analyte is sodium chloride in a physiological solution, or glucose in a glucose-based solution, particularly in a glucose-based injectable solution.

8. The method according to any of the previous claims 1-5, 7, wherein, after reading the electrical signal, obtaining the concentration of an impurity in a solution or the concentration of an analyte compound comprises:20.transforming the read electrical signal from the time domain to the frequency domain by means of a Fourier transform to obtain the frequency spectrum of the electrical signal;21.processing data obtained from the frequency spectrum of the electrical signal by the computer processor;22.generating, by the computer processor, a quantitative multivariate model representative of a property of the fluidic sample comprising the temperature of the fluidic sample and the frequency spectrum of the electrical signal to obtain the concentration of the impurity in the solution.

9. The method according to the previous claim, wherein the quantitative multivariate model comprise a Principal Component Regression model or a Partial Least Squares model.

10. The method according to any of claims 8 to 9, wherein the impurity comprises 5- hydroxymethylfurfural.

11. The method according to any of the previous claims, wherein the electrical pulse comprises a voltage ranging from-40 V to -300 V, preferably - 150 V.

12. The method according to any of the previous claims, wherein the processing data step comprises operations selected from a list comprising: calculating an average of the signal read; determining a maximum of the signal read; determining a minimum of the signal read; determining a local maximum of the signal read; determining a local minimum of the signal read; evaluating an acoustic wave of the ultrasonic signal after traversing the fluidic sample; determining a first derivative of the signal read; determining a second derivative of the signal read; smoothing the signal read; performinga Fourier transform of the signal read; correcting a baseline of the signal read; or any combination thereof.

13. A real-time non-invasive apparatus for determining / measuring the amount / concentration of analytic parameter in a fluidic sample according to the method of any of the previous claim, comprising: a sample container;28.an electric signal generator for generating electric signals, connected to an ultrasonic transducer; wherein the ultrasonic transducer is configured to convert an electrical signal from the electrical signal generator into ultrasonic signals for transmission through said fluidic sample, and subsequently to receive ultrasonic signals after propagating through the fluidic sample and convert the received ultrasonic signals into electrical signals;29.a temperature sensor, for measuring the temperature of the fluidic sample;30.a computer processor configured for processing a data from the electrical signal corresponding to the reflected ultrasonic signal, for storing the data and processed data, and calculate analytic parameters by the relation of the temperature and the acoustic signal propagation time.

14. The apparatus according to the previous claim further comprising:32.an electronic filter for removing noise of the reflected ultrasonic signal;33.an amplifier, for amplifying the reflected ultrasonic signal.

15. The apparatus according to any of the previous claims 13 to 14, wherein the ultrasonic transducer is a piezoelectric ultrasonic transducer.

16. The apparatus according to any of the previous claims 13 to 15 wherein the electrical signal generator is a pulser-receiver.

17. The apparatus according to any of the previous claims 13 to 16, wherein the ultrasonic transducer is configured to generate ultrasonic signals with a single central frequency.

18. The system according to any of the previous claims 13 to 17 wherein the single central frequency ranges from 1000000 Hz to 10000000 Hz, preferably 5000000 Hz.

19. The apparatus according to any of the previous claims 13 to 18wherein the ultrasonic transducer is attached and arranged perpendicularly to the sample container.

20. The apparatus according to any of the previous claims 13 to 19, wherein the temperature sensor is arranged outside the sample container and in contact with the sample container.

21. The apparatus according to any of the previous claims 13 to 20, wherein the temperature sensor is arranged within the sample container.

22. The apparatus according to any of the previous claims 13 to 21, wherein the ultrasonic transducer is connected to the sample container via an ultrasound conduction gel.

23. The apparatus according to any of the previous claims 13 to 22, wherein the sample container is a stainless-steel pipe or an independent vessel.

24. The apparatus according to any of the previous claims 13 to 23, wherein the sample container is an independent vessel having a diameter ranging from 20 to 200 mm, preferably 50 mm, and a wall thickness ranging from 0.1 to 10 mm, preferably 0.5 mm.

25. Use of the method according to any of the previous claims 1 to 12, the apparatus according to any of the claims 13 to 24, for detection or quantification of analytic parameter of a fluidic sample, sugars, organic compounds, and organic or inorganic salts.

26. A computer-readable non-transitory medium comprising instructions which, when executed by a computer, cause the computer to carry out the processing step of the method of any of the previous claims.

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