# On the Use of Temperature Measurements as a Process Analytical Technology (PAT) for the Monitoring of a Pharmaceutical Freeze-Drying Process

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^{2}

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## Abstract

**:**

## 1. Introduction

_{g}′ but below the collapse temperature. A non-ideal cake appearance is often rejected by quality protocols, even if it has been shown that it does not always impact product quality [12]. Actually, the majority of the investigations have found little or no decrease in product quality for formulations freeze-dried above the collapse temperature, while in a few studies some decrease in long-term stability was observed [13]; this is very interesting because the slight but controlled increase in process temperature that might be allowed would lead to a significant increase in productivity. For crystalline substances, the limit is generally the eutectic temperature; when trespassing it, some liquid forms, causing boiling for the low pressure and a final foamy appearance.

- to monitor product temperature, as it must remain below the threshold value to preserve final product quality. Usually, both product temperature at the bottom of the vial (T
_{B}) and that at the interface of sublimation (T_{i}) should be known. - to identify the occurrence of the ending point of the primary drying stage, corresponding to the time instant when no more ice is present or the thickness of the frozen layer (L
_{froze}_{n}) approaches zero, if a flat and planar interface is assumed. - to estimate the value of the parameters of a mathematical model of the process. The heat transfer coefficient (K
_{v}) and the resistance to mass transfer (R_{p}), which allow us to describe, respectively, the heat transfer to the product and the mass transfer from the product to the drying chamber, are generally selected. They can be used to predict the effect of the operating conditions and thus to optimize the process, minimizing the duration of the drying stage [14,15].

_{v}parameter must be known [27].

## 2. Procedure for Process Monitoring Using Temperature Measurement

#### 2.1. Determination of the End of Primary Drying

#### 2.2. Identification of Process Parameters

_{v}and R

_{p}. Velardi and Barresi [47] have analyzed the effect of the various hypotheses and simplifications adopted, discussing the accuracy versus the complexity of various models as a function of the application. The model proposed used only two parameters to be identified, assuming negligible radial gradient of temperature and composition and, thus, a planar interface separating the dried and the frozen product. This was considered a suitable compromise for monitoring purposes; in fact, it was used extensively in the past both for off-line optimization, to calculate the design space of the primary drying stage [48,49], and for in-line optimization, e.g., in the LyoDriver algorithm [50].

- (a)
- The value of the coefficient K
_{v}can be calculated in a preliminary experiment using the measurement of product temperature. In fact, from the integral energy balance for the frozen product, where K_{v}can be obtained as the ratio of the total energy supplied to the sample and then used to sublimate the initial mass m of ice:$${K}_{v}=\frac{m\mathsf{\Delta}{H}_{s}}{{A}_{v}{{\displaystyle \int}}_{0}^{{t}_{drying}}\left({T}_{shelf}-{T}_{B}\right)dt}$$

_{shelf}might be measured directly using additional thermocouples, taking care to have a good thermal contact; alternatively, it is possible to use the measured value of the technical fluid, and in this case, K

_{v}also includes the resistance of the shelf. The use of Equation (1a) requires estimating the primary drying time (t

_{drying}) with an acceptable accuracy.

_{v}can be obtained using the gravimetric test [15]: at the time t

_{1}(before the ending of the ice sublimation) when the product is removed from the drying chamber, the vial with residual ice is weighed, and the mass of sublimated ice is calculated via difference. This allows us to calculate K

_{v}without any uncertainty on the duration of the sublimation stage, using Equation (1b):

_{1}, but it is necessary to weigh the vials before and at the end of the drying period.

- (b)
- The cake resistance R
_{p}and its variation with L_{dried}can be calculated using the K_{v}value calculated in the previous step. The proposed algorithm is the following:- The heat flux J
_{q}to the product is calculated with Equation (2),$${J}_{q}={K}_{v}\left({T}_{shelf}-{T}_{B}\right)$$_{v}and the measured values of T_{shelf}and of the temperature of the product at the bottom of the vial (T_{B}), whose difference represents the driving force. - The sublimation flux J
_{w}is then calculated using Equation (3),$${J}_{q}=\mathsf{\Delta}{H}_{s}{J}_{w}$$_{s}. - The cake resistance can be calculated from the sublimation flux, which, similarly to the heat flux, can be described as the product of a mass transfer coefficient (1/R
_{p}) times a driving force (the difference between water vapor partial pressure at different locations: the interface and the chamber average):$${J}_{w}=\frac{1}{{R}_{p}}\left({p}_{w,i}-{p}_{w,c}\right)$$During primary drying, it can be assumed that p_{w,c}is equal to chamber pressure (the fraction of air or inert gas is generally negligible), while the water partial pressure at the interface, p_{w,i}, can be calculated: the interface temperature is not known, but T_{B}is measured, and T_{i}can be estimated by iteratively repeating steps (iii) to (v), neglecting the temperature gradient in the vial as a first attempt, or taking a value (1÷2) °C lower than T_{B}on the basis of the experience. - The sublimation flux in the time interval considered also allows us to estimate the evolution of L
_{frozen}(and thus, as difference to total thickness, of L_{dried}) using a mass balance to the frozen layer:$${v}_{i}=\frac{d{L}_{frozen}}{dt}=-\frac{1}{{\rho}_{frozen}-{\rho}_{dried}}{J}_{w}$$_{p}to L_{dried}for each time interval. Integrating Equation (5), it is also possible to monitor the progress of the drying process in-line. - The temperature at the interface can be estimated precisely from the product temperature at the bottom of the container, which is the variable usually measured with thermocouples inserted in vials, considering the heat balance for the frozen product and previous relationships:$${T}_{B}={T}_{shelf}-\frac{1}{{K}_{v}}{\left(\frac{1}{{K}_{v}}+\frac{{L}_{frozen}}{{k}_{frozen}}\right)}^{-1}\left({T}_{shelf}-{T}_{i}\right)$$This, once L
_{frozen}has been calculated from (iv), allows us to calculate p_{w}_{,i}with greater accuracy, and then to calculate R_{p}using Equation (4). - The values of R
_{p}depend on the type of product (and freezing history), but also on the thickness of the dried product, as shown before. To model this dependence, an equation like the following one is usually adopted:$${R}_{p}={R}_{p,0}+\frac{{A}_{{R}_{p}}{L}_{dried}}{1+{B}_{{R}_{p}}{L}_{dried}}$$

_{p,}

_{0}, ${A}_{{R}_{p}}$, and ${B}_{{R}_{p}}$ are fitting parameters that can be easily calculated once the curve R

_{p}vs. L

_{dried}has been obtained in step (iv).

## 3. Experimental Set-Up

#### 3.1. Experimental Apparatus

^{2}) in a 0.2 m

^{3}drying chamber, a vacuum pump, and an external condenser was used for the experimental runs. The service fluid temperature (silicon oil) was monitored using a RTD (Pt100) embedded in the control system of the apparatus. Chamber pressure was monitored with a capacitance gauge (Baratron type 626A, MKS Instruments, Andover, USA) and maintained at the desired value using nitrogen and a controlled leakage system.

#### 3.2. Case Study

_{p}commonly encountered in pharmaceutical applications.

_{B}, while T

_{shelf}was determined using the RTD inserted in the technical fluid.

## 4. Results and Discussions

#### 4.1. Evaluation of PAT Based on Thermocouples

#### 4.1.1. End of Primary Drying

_{v}measurements.

_{drying}is a quantity that must be known in Equation (1a), and it has been assessed (for the sucrose solution) with regards to analyzing the curves of Figure 3A, but for the reasons already discussed, when using the temperature measurement for its definition, an uncertainty exists that will therefore affects the values of K

_{v}and, thus, of R

_{p}. It can be seen that the ice sublimation is completed about 18 h after the onset of the primary drying stage; this value can also be confirmed by the pressure ratio shown in Figure 3B, as this curve reaches the lower asymptote at the same moment. As discussed in the Section 3, this technique also allows us to identify the end of primary drying with uncertainty, but the corresponding value at the offset of the curve should correspond to the end of drying, even in the last vials of the batch.

_{B}is recorded during the full drying process, but when the ice sublimation is approaching the end, i.e., after the time instant when the “sudden” temperature change occurs, the temperature is no longer meaningful; anyway, it is possible to assume that, in case the temperature of the heating shelf and the pressure in the drying chamber are not modified, then the slope of the temperature curve does not change till the end of the primary drying. The missing part of the temperature measures can thus just be hypothesized, and in this work it has been assumed constant until the end of the drying, the slope being very small.

#### 4.1.2. K_{v} Estimation and Uncertainty

_{v}obtained with Equation (1a) for three different values of assumed drying time (minimum, maximum and mean value, uniform time distribution) are shown in Table 1; the results obtained using the four temperature measurements available from the test run are compared. The table also reports the maximum deviation of K

_{v}with respect to the mean value, both for the drying time and for the monitored vials. It appears that K

_{v}is mainly affected by the drying time (±5.4%) and that the dispersion of the results obtained among the four vials is about ±1.8%, which is a small but not negligible value.

_{v}can now be obtained by propagating the main uncertainty contributions that appear in Equation (1a) using the procedure described in the “Guide to the Expression of Uncertainty in Measurement” [54,55]. Drying time and temperature uncertainties are considered here, whereas the uncertainties related to the vial area A

_{v}and water mass m can be neglected. Effects related to temperature differences recorded in different vials are considered a reproducibility contribution and treated in a statistical way. Other aspects, such as the thermocouple wires that perturb the vial sublimation process and the product temperature, which can only be hypothesized towards the end of the drying, have not been considered here, since their role looks negligible after a preliminary investigation.

^{B}(t

_{drying})= 1/√3 h, where the suffix B refers to a type-B method employed here.

_{v}with respect to the drying time can be assessed from Table 1 or numerically with Equation (1a) as ΔK

_{v}/Δt

_{drying}, thus obtaining ${S}_{{t}_{drying}}^{{K}_{v}}$= 1.0 Wm

^{−2}K

^{−1}/h, regardless of the considered vial.

_{v}computation were obtained using two different thermometers.

_{B}was measured in different vials using thermocouple sensors. A maximum error of ± 1 °C was considered, and thus, the standard uncertainty could be obtained using a type-B method considering a uniform distribution, obtaining u

^{B}(T

_{B})=1/√3 °C.

_{shelf}is the fluid temperature measured and controlled by the freeze-dryer. A maximum deviation of ±1 °C from the set-point T

_{shelf}= −20 °C has been considered in this uncertainty evaluation. As for T

_{B}, the standard uncertainty of T

_{shelf}is u

^{B}(T

_{shelf})=1/√3 °C.

_{B}can be considered fully uncorrelated with respect to the measurement T

_{shelf}, these two quantities being obtained or controlled using different thermometers.

_{v}with respect to T

_{shelf}and T

_{B}has been obtained numerically, introducing a small temperature perturbation during the computation of Equation (1a). The two sensitivities are very similar, and they do not depend significantly on the considered vial. The obtained result is ${S}_{{T}_{B}}^{{K}_{v}}$ ≅ ${S}_{{T}_{shelf}}^{{K}_{v}}$ ≅ 1.2 W·m

^{−2}·K

^{−1}/K.

_{v}values when the drying time is 18 h, thus obtaining a standard uncertainty of the average u

^{A}(vial) = 0.16W·m

^{−2}·K

^{−1}.

_{v}is the mean of the four values obtained at time 18 h, and it is K

_{v}=18.7 W·m

^{−2}·K

^{−1}, with an expanded uncertainty (coverage factor 2, confidence level 95%) U=2.4W·m

^{−2}·K

^{−1}, which is about 13% when expressed in relative form.

_{v}, assuming different values of the drying time. In this case, the dispersion on the estimated value of K

_{v}related to the assumption about the drying time is slightly higher than in the case of the sucrose solution (±7.8% max vs. 5.4% max).

_{v}uncertainty can be estimated with the same procedure described for the test with sucrose solution. The sensitivity coefficients are almost the same, but the standard uncertainties of the drying time and reproducibility are slightly larger (from data in Table 2: u

^{B}(t

_{dying})= 1.5/√3 h and u

^{A}(vial) = 0.30W·m

^{−2}·K

^{−1}).

_{v}, computed as the mean value of the K

_{v}values obtained with the four vials at the mean drying time of 18.5 h, is K

_{v}=17.4 W·m

^{−2}·K

^{−1}, with an expanded uncertainty (coverage factor 2, confidence level 95%) U=2.4 W·m

^{−2}·K

^{−1}, that is, about 16% in relative form. The K

_{v}measurements with sucrose and with PVP are thus in agreement.

- The drying time t
_{1}is defined by the user, and its uncertainty is negligible. - A set of about 100 vials was identified as representative of the full batch. The vials were weighed before and after the test, thus obtaining a set of Δm measurements and, with Equation (1b), a set of K
_{v}coefficients. The mean value is 18.7 W·m^{−2}·K^{−1}and the dispersion can be treated using a Type-A method, thus obtaining a standard deviation of about 2 W·m^{−2}·K^{−1}and a standard uncertainty, that is, the standard deviation of the mean value, of about u^{A}(vial) = 0.2 W·m^{−2}·K^{−1}.

_{B}measurements and fully uncorrelated with T

_{Shelf}; the sensitivity coefficients were numerically computed from Equation (1b), thus obtaining results very similar to the ones obtained in the previous tests. Moreover, the gravimetric test was performed using the same thermometers, and thus, the temperature uncertainties are also the same, that is, u

^{B}(T

_{Shelf}) = u

^{B}(T

_{B}) = 1/√3 °C. The overall uncertainty is:

_{v}measured with the gravimetric test is thus K

_{v}= 18.7 W·m

^{−2}·K

^{−1}with an expanded uncertainty (coverage factor 2, confidence level 95%) U = 2 W·m

^{−2}·K

^{−1}, about 11% in relative form.

_{v}measures obtained from recording the full drying of sucrose and PVP, as well as the measurement result from the gravimetric test. The results are in good agreement, with a small difference in the measured values. One should note that the proposed method has a larger uncertainty but also the advantage of saving time, and it can be carried out during the manufacturing run.

#### 4.1.3. Rp Estimation and Monitoring of Primary Drying Progress

_{v}has been estimated, the curve of R

_{p}vs. L

_{dried}can be obtained, and then the three values of the parameters R

_{p}

_{,0}, ${A}_{{R}_{p}}$, and ${B}_{{R}_{p}}$ can be calculated. According to the algorithm previously described, the measurement of product temperature is required to obtain the curve of R

_{p}vs. L

_{dried}, and thus, as various temperature measurements are usually available, different curves of R

_{p}vs. L

_{dried}are obtained, i.e., different sets of values of R

_{p}

_{,0}, ${A}_{{R}_{p}}$, and ${B}_{{R}_{p}}$ (see Figure 5). The approach used in this study is the following:

- estimate the values of R
_{p}_{,0}, ${B}_{{R}_{p}}$, and ${A}_{{R}_{p}}$ from the curve of R_{p}vs. L_{dried}obtained from the first temperature measurement; - use the previously obtained values of R
_{p}_{,0}and ${B}_{{R}_{p}}$ to calculate the value of ${A}_{{R}_{p}}$ in such a way that the data of R_{p}vs. L_{dried}obtained from the other temperature measurements can be best-fitted; - calculate the mean value of ${A}_{{R}_{p}}$ and its standard deviation.

_{p}vs. L

_{dried}curves it is possible to obtain (mean value ± standard deviation): R

_{p,}

_{0}= 10

^{4}m·s

^{−1}, ${A}_{{R}_{p}}$= 2.84·10

^{8}s

^{−1}± 7.6%, and ${B}_{{R}_{p}}$ = 2.16·10

^{3}m

^{−1}. Similarly, for the second product, it is possible to obtain R

_{p,}

_{0}= 5·10

^{4}m·s

^{−1}, ${A}_{{R}_{p}}$ = 8.43·10

^{7}s

^{−1}± 9.61%, and ${B}_{{R}_{p}}$= 0 m

^{−1}. The standard deviation on ${A}_{{R}_{p}}$ is in agreement with that reported in the literature when other methods were used to estimate it [48]. With respect to the estimated R

_{p}values, it is impossible to compare them with a value measured using a different technique, as it was performed for the coefficient K

_{v}. Nevertheless, it is possible to evaluate whether these estimates are correct by running a simulation using the mathematical model of the process with the estimated values of model parameters, then comparing calculated and measured values of product temperature and process duration. Results are shown in Figure 6 for both products, evidencing the accuracy of both the temperature values calculated and the drying time (i.e., the time when L

_{frozen}becomes equal to zero). Graphs B and D of Figure 6 also evidence that even if the direct measurement of the interface position is not possible in normal process conditions, using the proposed PAT and Equation (5), by means of an inferential approach, it may be possible to also monitor this variable, and thus the progress of the primary drying.

#### 4.2. Strengths and Weaknesses of Thermocuples for Pharmaceutical Applications in Comparison with a Contactless Device (IR Camera)

_{v}but also in R

_{p}, because the different freezing conditions may lead to differences in the ice structure and then in the cake porosity, which will be reflected in differences in product temperature and the residual amount of water from vial to vial. Placement of thermocouples in certain zones of a large apparatus may be limited by accessibility, but the use of a system with wireless signal transmission (two different solutions have been presented, for example, in [38,39]) may help solve the problem; at the moment, anyway, contact devices are the only ones that may allow a complete mapping, and the use of wireless modules allows us to increase, with virtually no limitations, the number of probes utilizable without any modifications of the apparatus.

_{p}), as the size of the pores corresponds to that of the ice crystals (in case collapse does not occur) [58]. Recent work by Harguindeguy et al. [59] has also shown how the infrared camera may be effective in investigating the freezing phenomena when controlled nucleation is used (e.g., vacuum-induced surface freezing) and when non-conventional vial loading is used.

_{v}and R

_{p}may be estimated at the end of the primary drying [43] and used to calculate the design space of the primary drying step [62], as well as in-line, taking advantage of the detection of the moving sublimation interface (where the temperature of the product is lower) and, thus, of the thickness of the frozen layer [45,62]. Furthermore, the temperature detected may be used to identify the ending point of the primary drying step, together with the estimated thickness of the frozen layer [45], even if the measurement may be quite noisy.

## 5. Conclusions

_{B}, which is the measured variable, is the highest and thus the most relevant temperature, but the interface temperature may also be estimated, which is useful for a more accurate evaluation of mass transfer in the cake. Modifications will be necessary to adapt the system to be employed if the heat flow from the chamber walls and the upper shelf is significant, because the temperature profiles in the product will be affected.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Symbols

${A}_{{R}_{p}}$ | fitting parameter for cake resistance relationship in Equation (7) |

A_{v} | cross-section area of the vial |

${B}_{{R}_{p}}$ | fitting parameter for cake resistance relationship in Equation (7) |

∆H_{s} | heat of ice sublimation |

J_{q} | heat flux to the product |

J_{w} | sublimation flux |

k_{frozen} | thermal conductivity of the frozen layer |

K_{v} | heat transfer coefficient |

L | thickness of the product |

L_{dried} | thickness of the dried product |

L_{froze}_{n} | thickness of the frozen layer |

m | mass of ice in the vial |

∆m | variation of ice by sublimation in the test |

p_{w,i} | water vapor partial pressure at the interface of sublimation |

p_{w,c} | water vapor partial pressure in the drying chamber |

R_{p} | resistance to mass transfer |

R_{p,}_{0} | fitting parameter for cake resistance relationship (7) |

${S}_{x}^{y}$ | sensitivity coefficient of the output quantity y with respect to the input quantity x evaluated at the measurement values |

T_{B} | product temperature at the bottom of the vial |

T_{i} | product temperature at the interface of sublimation |

T_{shelf} | shelf (or fluid) temperature |

t | time |

t_{drying} | time required to complete the ice sublimation |

U | expanded uncertainty |

u^{A}(x) | standard uncertainty of the quantity x evaluated with type-A method |

u^{B}(x) | standard uncertainty of the quantity x evaluated with type-B method |

u_{c}(x) | combined uncertainty of the quantity x |

v_{i} | interface retreating velocity |

ρ_{dried} | density of the dried product |

ρ_{frozen} | density of the frozen product |

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**Figure 1.**Sketch of the one-dimensional freeze-drying model for primary drying. On the right is an example of the axial temperature profile, evidencing T

_{B}, T

_{i}, and the position of the interface (for completeness, the temperature in the dried part is also shown with a dashed line).

**Figure 2.**

**Upper left**: Example of set up for monitoring the process in a small pilot-scale apparatus, using thin-wire thermocouples.

**Upper right**: Detail of the monitored vial, with the thermocouple inserted through the stopper (TC positioners might also be used). Lower graphs, SEM images of the core of freeze-dried samples: (

**left**) 5% sucrose solution (metallized sample, bar = 200 μm); (

**right**) 5% PVP solution (metallized sample, bar = 100 μm).

**Figure 3.**Product temperature measured by thermocouples inserted in 4 different vials (

**A**,

**C**) and ratio between the signals of the Pirani and Baratron pressure gauges (

**B**,

**D**) during the freeze-drying of the 5% by weight sucrose solution (

**A**,

**B**) and of the 5% by weight PVP solution (

**C**,

**D**).

**Figure 4.**Values of K

_{v}obtained from the measurements in the run with the sucrose solution, in the run with the PVP solution, and in the run where a gravimetric test was carried out. The intervals represent the expanded uncertainty with coverage factor 2. The contributions considered here are the drying time and the temperature measurements, as well as the dispersion among vials.

**Figure 5.**R

_{p}vs. L

_{dried}calculated using the various temperature measurements (lines) and the calculated mean values (symbols) of the parameters expressing the dependence of R

_{p}on L

_{dried}for the sucrose solution (graph

**A**) and the PVP solution (graph

**B**).

**Figure 6.**Comparison between measured (lines) and calculated (symbols) values of product temperature (

**A**,

**C**) and calculated evolution of the thickness of the frozen product (

**B**,

**D**) for the freeze-drying of the 5% by weight sucrose solution (

**A**,

**B**) and of the 5% by weight PVP solution (

**C**,

**D**). Dashed lines identify the ending point of the primary drying stage.

**Table 1.**Values of K

_{v}(W m

^{−2}K

^{−1}) for sucrose solution estimated from different drying times and considering the temperature measured in the 4 vials.

t_{drying} (h) | Sucrose—Vial | $\mathbf{\Delta}{\mathit{K}}_{\mathit{v}}$ $(\mathbf{\Delta}{\mathit{K}}_{\mathit{v}}/\overline{{\mathit{K}}_{\mathit{v}}})$ | |||
---|---|---|---|---|---|

#1 | #2 | #3 | #4 | ||

17 | 20.07 | 19.65 | 20.17 | 19.45 | ±0.36 (±1.8%) |

18 | 18.95 | 18.56 | 19.04 | 18.35 | ±0.35 (±1.9%) |

19 | 18.04 | 17.66 | 18.13 | 17.82 | ±0.34 (±1.9%) |

$\Delta {K}_{v}$ ($\Delta {K}_{v}/\overline{{K}_{v}}$) | ±1.0 (±5.4%) | ±1.0 (±5.4%) | ±1.0 (±5.3%) | ±1.0 (±5.4%) |

**Table 2.**Values of K

_{v}(W·m

^{−2}·K

^{−1}) for PVP solution estimated from different drying times and considering the temperature measured in the 4 vials.

t_{drying} (h) | PVP—Vial | $\mathbf{\Delta}{\mathit{K}}_{\mathit{v}}$ $(\mathbf{\Delta}{\mathit{K}}_{\mathit{v}}/\overline{{\mathit{K}}_{\mathit{v}}})$ | |||
---|---|---|---|---|---|

#1 | #2 | #3 | #4 | ||

17 | 19.34 | 18.69 | 17.93 | 19.13 | ±0.71 (±3.8%) |

18.5 | 17.91 | 17.26 | 16.57 | 17.71 | ±0.67 (±3.9%) |

20 | 16.64 | 15.98 | 15.36 | 16.44 | ±0.64 (±4.0%) |

$\Delta {K}_{v}$ ($\Delta {K}_{v}/\overline{{K}_{v}}$) | ±1.4 (±7.5%) | ±1.4 (±7.8%) | ±1.3 (±7.8%) | ±1.3 (±7.6%) |

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## Share and Cite

**MDPI and ACS Style**

Vallan, A.; Fissore, D.; Pisano, R.; Barresi, A.A.
On the Use of Temperature Measurements as a Process Analytical Technology (PAT) for the Monitoring of a Pharmaceutical Freeze-Drying Process. *Pharmaceutics* **2023**, *15*, 861.
https://doi.org/10.3390/pharmaceutics15030861

**AMA Style**

Vallan A, Fissore D, Pisano R, Barresi AA.
On the Use of Temperature Measurements as a Process Analytical Technology (PAT) for the Monitoring of a Pharmaceutical Freeze-Drying Process. *Pharmaceutics*. 2023; 15(3):861.
https://doi.org/10.3390/pharmaceutics15030861

**Chicago/Turabian Style**

Vallan, Alberto, Davide Fissore, Roberto Pisano, and Antonello A. Barresi.
2023. "On the Use of Temperature Measurements as a Process Analytical Technology (PAT) for the Monitoring of a Pharmaceutical Freeze-Drying Process" *Pharmaceutics* 15, no. 3: 861.
https://doi.org/10.3390/pharmaceutics15030861