Virtual Thermocouple: A Non-Invasive Multipoint Product Temperature Measurement for Lyophilization

12 Monitoring product temperature during lyophilization is of critical importance, especially during the process development stage, as the final product may be jeopardized if its process temperature exceeds a threshold value. While conventional thermocouples can track product temperature, they are invasive and can significantly alter the freezing and drying behavior. In this work, a new methodology for non-invasive product temperature monitoring and drying behavior during the entire lyophilization process is proposed and experimentally validated. The method is based on a new flexible wireless multi-point temperature sensing probe that is attached to the outside of the vial. Combining the wirelessly-collected data with advanced multi-physics simulations allows the accurate extraction of the product temperature non-invasively. 13

the freezing stage, the solution is completely frozen. In the primary drying step, the chamber pressure is lowered and heat 23 from the shelf is supplied to the material for the water to sublime. During this stage, most of the water content is sublimated. 24 The secondary drying step aims to remove the bound water. In this phase, the shelf temperature is raised higher than in the 25 primary drying phase to break any physicochemical interactions that have formed between the water molecules and the frozen 26 material. To preserve product quality, it is necessary for the product temperature to not exceed a threshold value throughout the 27 process and, in particular, during the primary drying stage. This threshold value is a characteristic of the specific product being 28 freeze-dried. For amorphous products, it is often related to the glass transition temperature of the dried product. If the threshold 29 temperature is exceeded, the final dried product may collapse, which could also result in higher moisture content, a longer 30 reconstitution time, and an unacceptable appearance. 31 Accurate process condition monitoring is not only related to the threshold temperature, but is also needed to alleviate 32 machine-to-machine and run-to-run process variations. For instance, a vial's heat transfer coefficient and resulting temperature 33 profile are sensitive to variations across different freeze dryers as well as the spatial distribution of vials inside a given freeze 34 dryer. Although such differences may be tolerable in laboratory-scale experiments, they can cause considerable complications 35 in production-level machines. 36 Inserting miniature fine-gauge thermocouples (TCs) inside the solution to be freeze-dried is the common industry practice 37 today 2 . However, this technique has several issues. First, TCs inserted into the vial may affect the product during drying. This 38 is due to the fact that the thermal distribution inside the product is altered by the relatively high thermal conductivity of the TCs' cause non-trivial temperature measurement uncertainties 5 . Despite these problems, conventional TCs are commonly used to 47 estimate parameters of interest that cannot be measured directly, such as position and temperature of the moving front 6, 7 .

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More advanced approaches have been proposed to monitor product temperature of individual vials during the freeze drying 49 process. A non-invasive temperature monitoring method with thin-film thermocouples (TFTCs) was proposed by Oddone et 50 al. 8 . The proposed method measures vial temperature with TFTCs printed on the outside of the vials. However, this approach 51 does not address two crucial problems. First, the measured temperature is only recorded on the outside vial wall. Hence, 52 it does not represent the actual temperature of the product. Second, TFTCs still require metallic wires to operate, which 53 could cause unintentional heating that may alter the drying process. In our previous work 9 we proposed a wireless solution 54 based on low-power sensing electronics to measure product temperature. This approach resolves the TC-induced heating 55 concern while still allowing for direct product measurement. However, the sensing is invasive and may interfere with the 56 freeze-drying behavior. Ravnik et al. proposed a numerical model to simulate the lyophilization process in a vial 10 . The 57 model demonstrated a reasonably good agreement with experimental results. However, such modeling is highly dependent 58 on pre-calibration/tuning of parameters (e.g., the heat transfer coefficient(k v )) that can vary significantly from vial-to-vial, 59 run-to-run, and machine-to-machine. Consequently, although such a modeling-only approach may be helpful in lab-scale-sized 60 experiments, it is not suitable for large-scale experiments with hundreds of thousands of vials.

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In this article we present a new technology called "Virtual Thermocouple" that allows for a non-invasive and fully wireless 62 measurement approach that overcomes the main above-mentioned limitations. This technology comprises three main parts: 63 a) the flexible non-invasive multi-point sensing probes that are externally attached to the vials, b) the low-power wireless 64 electronics that read and transmit data wirelessly, and c) the numerical model that translates the temperature profile measured 65 from the vial wall to the actual product temperature. In this study, we demonstrate that the proposed method can effectively be 66 used for non-invasive real-time monitoring of the drying dynamics and product temperature during the freeze-drying process.

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The non-invasive wireless process tracking system has been designed to monitor a freeze-drying process across the entire batch 69 with near-zero interaction with the actual product. This is achieved by monitoring temperature at various locations and tracking 70 the sublimation front of the lyophilization process. This method relies on a) attaching flexible temperature sensing probes to the 71 outside of the vial and b) using multiphysics simulation to extract the temperature of the product inside the vial.    copper Kapton laminate Pyralux AP8555R by DuPont. The substrate thickness is 0.127 mm and the copper thickness is 0.018 86 mm. The copper is patterned using a photosensitive lithography microfabrication processes. Specifically, we used negative 87 dry film photoresist TentMaster TM200i by DuPont hot rolled on the flexible substrate and exposed to 14 mW/cm2 of UV 88 light through a photomask using the MA6 Karl Suss aligner. We also used the Copper etchant CE-100 by Transene to form the 89 desired copper traces at the end of the manufacturing step shown in Figure 2   This thermistor is constructed of metal oxides, which when passed through a sintering process, give a negative electrical 94 resistance (R) dependence versus temperature (T ). Due to having a large negative slope, a small temperature change will 95 causes a substantial change in electrical resistance at lower temperature. The disadvantage of such a thermistor is its nonlinear 96 characteristic. Consequently, each thermistor has to be calibrated to ensure measurement accuracy. The Steinhart-Hart(S-H) 97 equation is the most commonly used model to describe the nonlinear characteristic of the thermistor as shown below.
The symbols are as follows: T is the temperature in degrees Kelvin, Ln(R) is the natural logarithm of the measured 99 resistance of the thermistor, and A, B, and C are constants.  The Stefan condition is applied to get interface velocity: where Q S is the normal heat flux jump at the interface. This is evaluated using the Lagrange multiplier with enabled weak wirelessly powering the sensors. Also, to prevent leaks and protect the coaxial cable from the vacuum during freeze drying, a 140 custom vacuum feed-through SMA connector is used to pass the RF coaxial cable inside the chamber to power the antenna.

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The data-collecting computer is also equipped with a 2.4-GHz ANT-connectivity USB stick for enabling the needed sensor 142 connectivity.

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With this setup, three sets of freeze drying experiments are performed to evaluate the flexible temperature sensor performance.

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Each set focuses on exploring a different scenario as described in the next paragraphs. In addition, experiments in each set are 145 repeated at least three times to provide reliable data. Predefined freeze drying recipes (Table 1) are used in all three runs in 146 6R SCHOTT ® pharmaceutical vials with 4 ml filled with 5% D-mannitol solution (Sigma Chemical Company, Germany).

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Type T conventional thermocouples from Omega were used to measure the shelf temperature, air temperature, and product 148 temperatures for all three experiments.

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The first set of experiments (Figure 7(a)) focuses on establishing proper sensor performance on two vial types. Specifically, 150 we test the sensors on two different types of vials made of glass (6R SCHOTT ® vials) and plastic (SiO 2 vials). In each vial 151 type we also insert conventional thermocouples (TCs) at the bottom-center location to measure the product temperature. A

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Thermal IR camera (FLIR Lepton ® 3.5) is used to monitor the freezing behavior of the product.  The second set of experiments (Figure 7  In both vials, thermal image #1 shows the moment right before nucleation occurs. As can be seen in Figure 8a and 8b,    The performance of virtual thermocouple was validated using data from the performed freeze-drying experiments as mentioned 208 in previous sections. To obtain the product temperature inside the vial, the numerical model was tuned to match the sensing 209 element data during the primary drying stage demonstrated in Figure 9. As a result, the numerical thermocouple reading should 210 be close to the product temperature measured by conventional thermocouple in the experiment which would mean the good 211 performance of virtual thermocouple. To simplify the tuning process, input parameters were divided into three groups: the first 212 group is the fixed simulation parameters (Table 2). These are parameters that are not subject to change from run to run for the 213 same product (such as glass vial properties, material properties (i.e. dried product properties), and ice/vapor characteristics).

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The second group are the process simulation parameters (Table 3). These parameters are the real process data including shelf/air The solid lines in Figure 10 show the temperature profiles measured by sensing elements. The simulation is performed for   stops. As shown in Figure 13b, the numerical thermocouple temperature data shows a great agreement with the conventional 237 thermocouple reading. The same tuning process was done to vial #7. Figure 12b shows the conventional thermocouple vs. shown to measure the actual product temperature accurately and non-invasively.
where The cake resistance from the current simulation is calculated according to 26 : where A p is a product area , P sub and P ch are sublimation front and chamber pressures,ṁ ice is an ice sublimation rate. The R p is 246 a measure of vapor flow impedance resulting from the dried layer structure. It is worth noting that in the current multiphysics 247 simulation, the product permeability is the parameter analogous to R p .

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The development of optimal lyophilization procedures for different formulations in vials includes a combination of experimental 265 tests and computational approaches for measuring product temperature. Tight temperature control is essential in both the 266 freezing and primary drying steps because the structure of the dried product (cake) is determined by the freezing and primary 267 drying protocols. To obtain the uniformly dried product across the batch, one needs to accurately control the temperature 268 during these stages. Particularly, the nucleation of ice during the freezing stage should occur in a tight temperature interval.

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Most importantly, the product temperature during the primary drying stage must be kept safely below the collapse temperature.

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Due to the presence of bound water in the product after the primary drying stage, the collapse temperature can be relatively 271 low. Moreover, in order to optimize the process and reduce the primary stage duration, the critical process parameters should 272 be controlled accordingly. Along with the chamber pressure, shelf temperature is one of such parameters which defines the 273 design space for the primary drying stage of the freeze-drying process. Traditionally, the shelf temperature depends on the 274 temperature of heat transfer fluid (i.e. silicon oil, methylene chloride, etc. ) inside the shelves which is tracked by the control 275 system and is set to follow the pre-set profile. However, the heat transfer control obtained by the control and manipulation of 276 the shelf temperature is quite slow, partly because of the thermal inertia of the system, due to which shelf heating and cooling 277 may induce a huge lag in the response of the product temperature. Alternatively, the chamber pressure of the dryer can be 278 controlled and manipulated. This is a very responsive way to control the drying process because the heat flux from shelf to 279 product strongly depends on chamber pressure. However, this approach can be quite risky, because the product temperature 280 practically follows the pressure variations, therefore changes of few pascals could easily jeopardize the product quality.

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Since the critical part of any lyophilization procedure is the primary drying phase, special attention has to be paid to critical freeze-drying process.