Developing a machine learning enabled integrated formulation and process design framework for a pharmaceutical dropwise additive manufacturing printer

Abstract

The pharmaceutical manufacturing sector needs to rapidly evolve to absorb the next wave of disruptive industrial innovations – Industry 4.0. This involves incorporating technologies like artificial intelligence, smart factories and 3D printing to automate, miniaturize and personalize the production processes. The goal of this study is to build a formulation and process design (FPD) framework for a pharmaceutical 3D printing technique called drop-on-demand (DoD) printing. FPD can automate the determination of formulation properties and printing conditions (input conditions) for DoD operation that can guarantee production of drug products with desired functional attributes. This study proposes to build the FPD framework in two parts: the first part involves building a machine learning model to simulate the forward problem – predicting DoD operation based on input conditions and the second part seeks to solve and experimentally validate the inverse problem – predicting input conditions that can yield desired DoD operation.

Introduction

Pharmaceutical manufacturing is entering a period of radical transformation. The industry is taking steps to modernize its manufacturing resources by transitioning away from mass production and simultaneously adopting innovations in manufacturing technology like continuous processing, real time quality assurance and digitalization. Recent disruptions to drug supply chains, caused in part by the Covid-19 pandemic, have amplified the urgency to complete this transformation quickly so as to ensure a safe and reliable supply of medications at all times¹.

Conventionally, pharmaceuticals are manufactured in bulk following a globalized production scheme. Manufacturing is fragmented with the product being made in stages in multiple locations using batch production techniques. Although this scheme has allowed the pharmaceutical industry to leverage economy of scale and reduce production costs, it suffers from several limitations in quality assurance, supply reliability and product customization. Fragmented manufacturing makes it difficult to track quality of intermediates at each processing stage and inventory location. This has led to the persistent problem of drug product recalls, which continue in alarming numbers despite advances in manufacturing technology. Reliance on multi-echelon supply chains makes the production process vulnerable to local disruptions. A majority of drug shortages have been attributed to such production disruptions^2,3. Bulk manufacturing of drugs is also not conducive to producing patient personalized medication, which is an important future goal of the healthcare sector⁴.

To overcome these challenges there has been an increased focus in recent times to adopt an Industry 4.0 framework for manufacturing pharmaceutical products. Industry 4.0 is the next major disruption in manufacturing technology that seeks to incorporate advances in artificial intelligence (AI), internet of things (IoT) and smart factories etc. into current production processes⁵. This technology has the capability to address the aforementioned challenges: 1) To mitigate the production of quality deficient products, Industry 4.0 advocates for incorporating quality-by-design (QbD) and real-time monitoring (RTM) into the manufacturing process. These can ensure that quality is built into products during production as opposed inefficiently discarding off-spec product using post-manufacturing quality testing steps^6,7. 2) It also promotes the use of smart factories to carry out the fabrication of products. Smart factories are highly ‘intelligent’ production facilities that are designed with modular operation and continuous processing that can autonomously carry out the manufacturing steps without requiring operator guidance⁸. These facilities can greatly speed-up drug production and thereby increase the responsiveness and robustness of supply chains. 3) Finally, Industry 4.0 advocates for incorporating additive manufacturing (AM) or 3D printing (3DP) technology into the manufacturing process. AM allows for easy customization of product and supports distributed manufacturing; both of which can enable personalization of drug products⁹.

Despite its benefits, incorporation of Industry 4.0 in pharmaceutical manufacturing remains challenging. Reluctance to change conventional production schemes, regulatory challenges and deficiencies in technical know-how have all contributed to much of the pharmaceutical manufacturing sector continuing to operate with outdated Industry 2.0 strategies (bulk mass manufacturing, Figure 1). Furthermore, many of the changes being proposed today – continuous processing, computer aided design and automation are still concerned with bringing the manufacturing sector into an Industry 3.0 framework (computerization and automation)⁵. Modernizing pharmaceutical manufacturing to meet Industry 4.0 standards would therefore require a joint effort from academia, industry and regulatory authorities to bridge the vast knowledge gap. The goal of this study is to aid the advance of Industry 4.0 technology in pharmaceutical manufacturing by address some technical challenges in automating the drug product manufacturing processes.

Figure 1.

Four industrial revolutions in the context of pharmaceutical manufacturing. Disruptive innovations like AI, robotics and automation will create the next industrial revolution – Industry 4.0 (Arden et al., 2021).

Manufacturing of drug products, specifically solid oral dosages, is generally carried out conventionally in three broad steps: synthesis, purification and drug product manufacturing. First, the active pharmaceutical ingredient (API) is synthesized in a series of reaction steps. Next, the API is purified using various separation unit operations, often terminating with a final crystallization step. Finally, the crystallized API is processed into the consumable solid oral dosage form via a series of downstream drug product manufacturing operations (filtration, drying, granulation, tableting etc.)². Typically, these operations are carried out in large-scale batch units for bulk manufacturing. The Industry 4.0 vision of smart factories, on the other hand, requires these processes to be downscaled and operated continuously for smaller production volumes. Multiple studies have aimed at miniaturizing these processes and building small-scale continuous manufacturing units or mini-plants^10–13. Developing these mini-plants further into smart factories with other Industry 4.0 capabilities, however, requires automation in its operations, real-time decision making and transparent communications.

A critical knowledge gap in this direction is building a method that can automate the design of the formulation properties and manufacturing conditions and for drug product production step. Current practice for designing formulations for drug products relies on cumbersome experimental testing for a variety of excipients and conditions– a process that is time and resource intensive and often produces suboptimal designs. Manufacturability and processing efficiency are also not considered in the design stage, as a result the production operation is carried out inefficiently. An integrated formulation and process design (FPD) framework would enable the simultaneous design of optimal formulation and manufacturing conditions for making drug products that can meet specified functional requirements (like rapid/delayed drug release, regulatory limits for drug loading uniformity etc.) – thereby offering significant savings in time and resources^14,15. This is particularly important for manufacturing personalized dosages as different formulation and manufacturing conditions could be required for producing drug products with individualized API amounts and release profiles. Another area of application for FPDs is altering drug product formulations based on excipient availability, developing such a framework can mitigate production halts due to shortages of specific formulation components. Despite its advantages, development of such a framework has received little attention in academia and industry.

The goal of this study is to therefore build an integrated FPD framework for a drop-on-demand (DoD) type of pharmaceutical 3DP platform. DoD is a versatile AM technique that has been demonstrated to be a highly effective drug product manufacturing process. It can continuously produce personalized drug products using a variety of formulations and has been integrated with upstream API synthesis operations^16–18. Building an FPD framework will be an important milestone in developing Industry 4.0 capabilities for the DoD platform. The proposed FPD framework constitutes an instance of the broader product and process design (PPD) strategy where the goal is to determine optimal product properties and optimal process parameters (such as, temperature, pressure, reaction time etc.)¹⁹. This strategy seeks to identify optimal trade-offs, such that the product meets design specifications while also ensuring high efficiency in the associated manufacturing process. PPD has seen a variety of applications including solvent design, molecule design, food product design and also in the design of pharmaceutical solid oral dosages^15,20,21. Both FPD and PPD require the development of models that can predict the product performance (functionalities like content uniformity, drug release profile etc.) given formulation properties and processing conditions. The larger goal however is to ‘invert’ this model and use it to estimate formulation properties and manufacturing conditions that can make products that meet the performance requirements¹⁹.

In this study an FPD framework is built for the DoD printer platform by first developing a process model using a machine learning approach, to simulate the printer’s operation. Next, a solution scheme is proposed for ‘inverting’ this model, the inverted machine learning model is then used for designing the formulation and printing conditions that can produce drug products that will meet required product quality and performance requirements. Formulation and printing condition designs recommended by the inverted model are also experimentally validated by testing the performance of the manufactured product. Two API systems are used for this validation: atorvastatin and lisinopril.

Drop-on-demand (DoD) printing

This study uses dropwise additive manufacturing or drop-on-demand (DoD) printing to manufacture drug products. DoD is a type of inkjet printing in which the printhead releases drops in a controlled manner ‘on demand’ ²². In recent years, it has been used as a 3DP technique for manufacturing personalized pharmaceutical dosages. Similar to other inkjets, it processes liquid inks, which in this case are the API containing formulation²³.

The DoD printer apparatus consists of a high-precision positive displacement pump that precisely draws the ink formulation from a reservoir vessel. This formulation is then pumped through a nozzle where drop ejection is triggered. The generated droplets are discharged onto an inactive substrate (capsule, placebo tablet or edible film) to form the drug product. Drug loading is varied by changing either the number or size of drops printed onto the substrate (Figure 2)^24,25. This offers a flexible route to customize drug loading by avoiding the need to change upstream parameters like formulation concentration etc. Critical process parameters of the DoD operation, such as droplet volume, are captured and logged in real time using in-line sensors^26,27. DoD is a versatile system and can process a variety of formulations, including suspensions, melts and solutions. Operating with suspension formulations enables producing dosages with a wider range of drug loadings²⁸. The experiments reported in this study will operate with suspension formulations, i.e., with API crystals suspended in a carrier fluid. A major constraint on the excipients (carrier fluids) used in these formulations is that they must be nontoxic inactives approved by the United States Food and Drug Administration (FDA) for use in solid oral dosages. Another constraint on the carrier fluids is that it should not dissolve the API. API dissolution is undesirable as it will alter the crystal size distribution achieved in upstream unit operations (such as crystallization), may result in change in polymorphic form and thus will change the dissolution behavior of the drug product. Further details on the operation of DoD and equipment used are available in studies by Hirshfield et al. and Icten et al.^24,25

Figure 2.

Schematic (left) and apparatus (right) of the DoD platform.

Integrated formulation and process design for DoD printer

A recent study by Sundarkumar et al. demonstrates integration of the DoD platform with upstream API synthesis steps and shows how this integrated system can achieve continuous manufacturing of the drug product at small scales¹⁸. This integration places the DoD technology in a favorable position to be incorporated into end-to-end mini plants and smart factories to manufacture personalized dosages. To further enhance this potential, it is necessary to incorporate Industry 4.0 technologies into the DoD platform. This study seeks to make an important advancement in this direction – building an integrated FPD framework for the DoD printer. FPD framework can automate multiple decision-making steps and determine optimal formulation properties and printing conditions for manufacturing individualized drug products with assured quality. This will in turn increase the speed and robustness of the DoD operation and the mini-plant of which it is a part. To build this framework, a two-part design is proposed (Figure 3):

Figure 3.

Conceptual design and solution for the FPD framework. The framework is proposed to be built in two parts: Part 1 is to solve the forward simulation problem by building an ANN model to predict design targets based on given input conditions. Part 2 is to solve the inverse problem using a sample and search approach. The first step here is to compute the constitutive variables based on the design targets and the second step aims to map this solution onto the domain of the original input variables

1. The first part is developing a model to simulate the ‘forward’ process, i.e., given the formulation and process conditions, predict the essential design target of the corresponding drug product. The design target here is the set of performance specifications that the product must satisfy: for drug products this can be regulatory requirements for variables like variance in drug loading or dissolution profile.

2. The second part is to develop a scheme to solve the ‘inverse’ of this forward simulation problem, i.e., given the values for design targets compute the input conditions that can achieve these targets.

Part 1: Machine learning model for the DoD printer

In the context of DoD, this ‘forward’ simulation would need to predict whether drop formation occurs consistently for a given set of input conditions (formulation and printing conditions). Consistency of drop formation is measured in terms the variance in volumes of successive drops printed, including consideration of the number of satellite drops generated. As the drug product is comprised of multiple printed drops, consistency of drop formation directly affects the variance in drug loading in manufactured dosages. There are some theoretical models that have been developed for this forward simulation (Figure 5)^23,29. These models demarcate feasible zones for inkjet printing using dimensionless numbers like Reynolds number (Re), Ohnesorge number (Oh) and Weber number (We). Regions with insufficient printing energy and onset of splashing are also identified.

Figure 5.

Results of experimental datapoints plotted onto theoretical design spaces proposed by Daly et al. and Derby (Daly et al., 2015; Derby, 2011). It is seen that consistent and inconsistent datapoints are highly interspersed with no clear demarcation between the two; thereby rendering the theoretical models unsuitable for classification. There are many correlations reported for estimating the insufficient energy line, therefore despite being slightly under the theoretical stable zone, these datapoints are representative of the poor classification achieved.

Analysis conducted in this study found that these models are not suitable for simulating the operation of DoD due to a variety of factors, including large differences in drop sizes, nonideal rheological properties of suspensions and polymeric carrier inks etc. (discussion reported in the results section). Therefore, an alternate process model is required for the printer platform. Data-driven models have been frequently employed in simulating different operating parameters for inkjets including printability, drop size and satellite drop formation etc.^30–33. Machine learning models, in particular, enable capturing the complex fluid physics involved in drop formation with relative ease. Therefore, this study aims to build a machine learning model for the DoD system.

A variety of machine learning techniques can be applied for this simulation, among them artificial neural networks (ANNs) offer attractive advantages like modelling abstract functional spaces, quick execution and ease of implementation. ANNs are a category of machine learning techniques that are comprised of layers of interconnected nodes that transform and map an input vector signal onto the target domain. ANNs have been used successfully to solve a variety of forward and invers problems. For example Nagy () used ANNs with optimized topology for the dynamic modeling a fermentation bioreactor and the inverted ANN for control. The first part of this study thus aims to build a machine learning model using ANNs for simulating the operation of the DoD printer (Figure 3).

The operation metric most relevant to this case is printing consistency (also called printability). Printing consistency is defined in terms of a binary variable (‘0’ or ‘1’) that indicates whether drops are being printed with ‘sufficient’ consistency (‘1’). It is a function of both inter-drop volume variance and number of satellite drops formed. Low printing consistency (‘0’) would lead to dosages being manufactured with high variation in drug loading. Simulating printing consistency thus allows the ANN model to predict whether the given input conditions would yield on-spec product.

Part 2: Scheme to solve the inverse estimation problem

This ANN model simulates the forward problem by estimating design target values for given inputs. To develop the FPD framework the inverse of this needs to be solved. Eden et al. recommend a two-step approach to formulate this inverse problem (Figure 3)¹⁹:

1. Step 1: Based on the design target specifications compute the constitutive parameters. Constitutive parameters here are those intermediate variables, which when used as input conditions for manufacturing, yield products that satisfy design targets. This step is akin to reversing the simulation problem.

2. Step 2: Solve the reverse property prediction problem. Constitutive parameters may or may not be directly related to the input variables. This step computes the original input variables using constitutive parameters calculated in the previous step.

3. Example: Consider solving the inverse problem for DoD where the goal is to identify inputs that can produce dosages with <5% variability (relative standard deviation) in drug loading (FDA guideline). Step 1 in this scenario would be to identify values for constitutive parameters that can manufacture dosages with the specified design target. Constitutive parameters in this case are viscosity, surface tension, density of formulation and stroke length, stroke frequency of printing etc. Values of these variables that meet the design target would be computed in step 1. Step 2 would then be to identify compositions of the excipient mixture that can provide required values of viscosity, surface tension etc. and estimate settings on equipment that can give required values of stroke length etc. Step 2 thus maps the constitutive parameters onto the original input space that can be directly controlled in the manufacturing operation.

4. Therefore, using this two-step scheme input variables can be determined from design targets and the inverse estimation problem can be solved.

Materials and Methods

To build the ANN model for DoD, a dataset is required for training the model in which printer operation is experimentally determined. To ensure that the model applicability range is broad, this dataset needs to be generated using a diverse set of APIs, carrier fluids and printing conditions. Code for this model is developed in a Python environment and a variety of open-source libraries are used for the same. The chemicals and python libraries used in model building are summarized below.

Chemicals

The APIs used in this study are: acetaminophen (APAP, micronized ‘$\mu$’ and semi fine ‘sf’; Mallinckrodt Pharmaceuticals), mefenamic acid, lisinopril and phenylbutazone (TCI America), celecoxib (ChemShuttle), atorvastatin (Dr. Reddy’s Laboratories). Carrier fluids used are: triglyceride oil – NEOBEE 895 (Stepan company), polyethylene glycol 200 (PEG; TCI America), glycerol (Fisher chemicals), hexamethyldisiloxane (HMDSO; Acros organics). Aerosil R972 was used as a rheological modifier for HMDSO (5wt%, Evonik industries).

Python libraries

Tensorflow: It is an open source package that enables building and training many alternative machine learning models including ANNs³⁴: the DoD model is built primarily using this package. SAlib: Sensitivity analysis library or SAlib is a python package containing commonly used sensitivity analysis methods and sampling tools³⁵. This package is used for performing sensitivity analysis and for sampling points using Latin hypercube. Scikit-learn: This is a python-based data analysis and machine learning tool³⁶, it is used for normalization of the dataset.

Results and Discussion

Dataset generation

To generate the training dataset, the operation of the DoD is experimentally evaluated under a variety of input conditions. To obtain a broad set of formulation properties, different API – carrier fluid mixtures are prepared for printing (Table 1). Each of these pairs are then printed at a variety of printing conditions. Following are the input properties varied in the dataset:

Table 1.

API- carrier fluid pairs used in generating the experimental dataset.

Carrier	API
Coconut oil	μ - APAP
Coconut oil	sf - APAP
PEG – water	celecoxib
PEG	mefenamic acid
Glycerol – water	mefenamic acid
Glycerol – water	phenyl butazone
HMDSO	mefenamic acid

1. Formulation properties. These properties change only if the API – carrier pair is changed and include physical properties of the formulation: viscosity, surface tension, density, particle size distribution (D10, D50, D90) and particle shape (Aspect Ratio) of the API. One formulation property that is varied for each API-carrier pair is particle concentration, it also affects formulation viscosity and this relationship is captured using the Krieger-Dougherty equation¹⁷.

2. Printing conditions. These are the parameter settings available on the DoD printer to tune its operation and include variables (Figure 4): stroke length (‘disp’)- this is the distance traversed by the pump piston per actuation, stroke rate (‘rpm’)- this is the speed at which the stroke length is traversed, actuation per drop (‘vstrokes’): these are the number of actuations set to print one drop, this parameter can be greater than 1 if energy imparted by a single actuation is insufficient for drop formation (thus requiring multiple actuations to affect one drop ejection). An additional variable that can be considered is nozzle size, this however has been assumed to be constant in the present study.

Figure 4.

Printing properties available on the DoD printer. These are the parameter settings available on the equipment to tune its operation.

A total of 557 unique combinations of formulation properties and printing conditions are created for this dataset. DoD operation is evaluated at each point by printing a pre-set number of drops and testing for inter-drop variability and satellite drop formation. A binary value for printing consistency is assigned to each condition using the following metric:

$$printingconsistency=\left\{1ifvar<1anddropscoreϵ\left[0.97,1.03\right],else0\right\}$$ #(1)

Here $var$ is the inter-drop volume variance and $dropscore$ is the number of drops printed relative to the number of drops set to print ($dropscore=\frac{\#dropsprinted}{\#setpoint}$). This parameter can differ from 1 if many satellite drops are being formed or fewer drops are being ejected due to insufficient energy. The resulting dataset thus has 557 datapoints with 11 input and 1 output feature defining each experimental instance, few sample points from the dataset are shown in Table 2.

Table 2.

Experimental dataset sample. Each experimental instance has 11 input features (8 formulation and 3 printing) and 1 output feature.

Printing conditions			Formulation properties								Output
disp	rpm	vstrokes	Viscosity combined	Surface tension	density	D10	D50	D90	Aspect ratio	Particle conc	Printing consistency
mm	rpm	#	mPas	mN/m	kg/m3	μm	μm	μm	-	mg/mL	-
3	800	2	24.86	30	910	11	16	43	1.393	40	0
1.5	600	1	32.26	50	1093	30	154	371	8.567	20	0
2	700	2	41.71	43.5	1124	16	190	424	1.366	10	1
3	800	3	41.71	43.5	1124	16	190	424	1.366	10	0

Comparison with theoretical design spaces

Before describing the results of model training, performance of theoretical inkjet models is assessed on this dataset. Experimental datapoints generated are plotted on theoretical design spaces (Figure 5)^23,29. Yellow points represent consistent printing conditions and blue points show inconsistent printing. The datapoints are seen to be highly interspersed with no clear demarcation between them indicating that theoretical inkjet models are insufficient in simulating DoD operation. This can be attributed to several reasons:

1. The drop sizes used in many theoretical inkjet studies are very small (of the order of 10 picoliters) whereas drop sizes in DoD are around 6 orders of magnitude higher (at around 10 microliters). This large difference in drop volumes may create some additional effects in drop dynamics, viscosity and surface tension that are not captured in the theoretical models. Bigger drops are preferred for DoD operation due to several reasons: the first is that larger drops reduce the time to produce dosages in the size range of typical solid oral drug products. The primary quality concern in solid oral dosages is to ensure high precision in drug loading, thus the high precision in shape gained by printing ultra-small droplets is superfluous. Additionally, in the case of suspension-based formulations, it is desirable to directly employ particle sizes typically produced in crystallization and micronization operations. Thus, for effective drop formation this means using nozzle internal diameters at least 5 times larger than the mean particle size.

2. Formulations printed with DoD contain polymeric carrier fluids and particle suspensions which makes their rheology more complex than the Newtonian fluids used in theoretical studies.

3. 3. Physical parameters available on DoD (stroke length, stroke rate and actuations per drop) have an indirect and non-linear relationship with the dimensionless numbers (Re, Oh and We). Thus, controlling DoD operation to lie within some range of dimensionless numbers is difficult.

Developing a machine leaning model for DoD can mitigate these challenges and provide a tool to predict the operation of DoD.

Machine learning model for DoD

Before training the model, the experimental dataset is preprocessed by scaling all input features into standard normal distributions. To determine structure of the ANN to be used, a hyperparameter tuning is done via superstructure search. Different components of the model structure like number of hidden layers, number of nodes, regularization per layer, activation function and learning rate etc. are varied. A number of 10,000 model architectures are evaluated and accuracy of the model in each instance is logged.

The following model delivers the highest accuracy with fewest trainable parameters (Table 3): 11 input nodes, 2 hidden layers with 3 and 5 nodes respectively and 1 output node (a total of 62 trainable parameters). The model also uses L1 regularization, Adam optimizer for training and the ‘tanh’ activation function ($tanh\left(x\right)=\frac{e^x-e^{-x}}{e^x+e^{-x}}$). The input dataset is randomly sampled and a part of the dataset is used for training (450 points) while the rest is set aside for testing. Model training is carried out using the ‘k’-fold cross validation scheme (k = 5). Results of the trained model are reported in the form of a confusion matrix (Figure 6B) that tracks the true positive, true negative, false positive and false negative classifications.

Table 3.

Models with the highest validation binary accuracy resulting from the hyperparameter tuning. Model 3 gives the highest accuracy with the lowest total number of parameters (62 parameters).

Hyperparameters	Model 1	Model 2	Model 3	Model 4	Model 5
# layers	2	3	2	2	3
Nodes #1	9	6	3	7	8
Nodes #2	6	3	5	8	3
Nodes #3	-	9	-	-	6
Regularization 1	2.98e-3	1.34e-3	9.21e-4	2.69e-3	4.94e-4
Regularization 2	2.88e-3	2.42e-3	4.18e-3	2.76e-3	2.21e-3
Regularization 3	-	7.29e-3	-	-	7.12e-3
Output regularization	1.01e-3	1.76e-3	1.47e-3	2.95e-3	8.21e-3
Activation function	leaky_relu	elu	tanh	relu	Selu
Learning rate	3.80e-3	7.03e-3	7.86e-3	4.64e-3	1.05e-3
Validation binary accuracy	0.88	0.87	0.85	0.85	0.84

Figure 6.

A) DoD model training results; and B) sensitivity analysis. The ANN model gives an accuracy of 86% on the training set and 80% on the test set which is comparable to results reported in literature. Sensitivity analysis results show printing conditions to be the dominant property group followed by carrier fluid properties and particle properties. The parameters ‘rpm’, ‘vstrokes’ and ‘disp’ are stroke rate, actuations per drop and stroke length respectively.

Model accuracy is seen to vary slightly across evaluations, primarily due to the stochastic nature of model training (Adam optimization is based on stochastic gradient descent). The model is seen to give an accuracy of 85% ± 0.2 (to be read as (85 ± 0.2) %, all error in this study is reported as standard error with number of samples = 100) on the training set and 80% ± 0.4 on the test set, averaged over 100 training cycles (with different training & test sets and optimizer descent routes) (Figure 6A). This is comparable with accuracy values reported in literature for inkjet printer models that range from 70% to 90%^30–33.

To identify the importance of individual features in the model, a sensitivity analysis is carried out using Sobol’s method ³⁷. The results, averaged over 100 training cycles (Figure 6B), show that the printing conditions of actuations per drop (vstrokes) and stroke length (disp) have the largest contribution in predicting printability. These parameters affect the trigger frequency for drop formation and volume of formulation in a drop. Poorly tuning them could lead to non-uniform triggering creating unevenly sized drops or oversize drops breaking up into several satellite drops. Formulation properties of viscosity, surface tension and density are the next biggest contributors to printability followed by aspect ratio, stroke rate and size distribution. Viscosity, surface tension and density affect $Oh,ReandWe$ and particle size distribution and aspect ratio primarily affect the break-up of filament preceding drop ejection. Contribution of particle concentration was found to be somewhat low, which could be because a part of its contribution is captured in viscosity via the Krieger-Dougherty relationship¹⁷.

In summary, the first part of the study builds a model for the DoD system that predicts printing consistency for given formulation properties and printing conditions with good accuracy. The next part tackles inversion and subsequent solution of this problem.

Formulation process design framework

To build the FPD framework the inverse estimation problem has to be solved. The two-step approach proposed by Eden et al. 2004 and discussed earlier is applied in this case: Step 1) to compute constitutive variables from the design targets, and Step 2) to compute the original input parameters.

Step 1: Reverse simulation to compute constitutive variables

Solving the reverse problem for ANN models is challenging as they are inherently directional in nature. Knowing values for model outputs does not provide any information about the inputs that generate them. Consider the DoD model, if a design target of ‘1’ for printing consistency is specified, a unique value cannot be obtained for input conditions as there are infinitely many solutions for this problem. One widely-used technique to overcome this is to employ genetic algorithms^21,38 to successively iterate through multiple input conditions and identify local optima. This strategy is useful for large models with longer execution times as optimal solutions can be identified with limited model evaluations. The DoD model by comparison is smaller and thus faster to execute, thereby allowing the evaluation of more input conditions. Thus, instead of employing a genetic algorithm to find optimal input conditions, in this case candidate solutions can be found by sampling and search, i.e., by sampling a large number of input conditions and searching for the optimal (best) solutions among them (Figure 8). The first part of this solution step thus samples a large number of input conditions (2¹⁰ combinations of formulation properties and printing conditions) using a broad sampling scheme (Latin hypercube) to fully cover the input domain. Then the DoD model is evaluated on all points (this is only possible due to fast execution) and points with high printing consistency predictions are screened (printing consistency > 0.75).

Figure 8.

Sample solution for the inverse estimation problem. First the user specifies design targets (drug loading, capsule size and size distribution). Then the sample and search scheme is used to compute the constitutive variables. These are then sent to the human expert who maps the solution onto the original input domain.

Another important consideration at this stage is to reduce the number of false positive classifications propagating through into the solution. False positives are those solutions where the model predicts consistent printing to occur for a given input set but in practice that input set gives inconsistent printing. If the FPD framework recommends a false positive solution then the formulation and process designed according to it would yield off-spec dosages being manufactured. These would have to be discarded, thereby causing losses in material and time.

To overcome this problem, a false positive pruning step is introduced at this stage. This is a smaller ANN with fewer trainable parameters – 11 inputs (formulation and printing parameters), 0 hidden layers and 1 output node (12 parameters in total). This is the smallest ANN model that can be built, other model parameters like activation function learning rate etc. are determined via hyperparameter optimization. Points marked as ‘high printing consistency’ (printing consistency > 0.75) in the previous step, are renormalized (to a standard normal distribution), the pruner is then trained on these points to identify regions rich in true positives by recomputing the printing consistency metric. Points with recomputed printing consistency > 0.5 are then taken to subsequent steps. These points are equivalent in terms of DoD operation as they have lower likelihoods of being false positives and can yield drops with high printing consistency. Results of applying the false positive pruner on high consistency training and test points are shown in figure 7A. Averaging performance over 100 training cycles on the experimental dataset, selecting ‘high printing consistency’ points and applying the false positive pruner enabled discarding around 80.6% (±1.7) false positives in the test set and around 94.9% (±0.4%) false positives in the training set.

Figure 7.

A) Results of applying the false positive pruner on the experimental dataset; B) Role of the human expert in translating model recommendations into executable formulation and printing designs

A series of heuristics are now applied on points flagged as consistent by the pruner to identify the most desirable solution. The first heuristic applied is a test for the robustness of each solution, the goal here is to identify solutions that have many high printing consistency neighbors. This is helpful in cases where the model recommended solution condition cannot be replicated exactly in manufacturing but some neighboring points can be manufactured. For example, in figure 7B the model recommends designing a formulation with viscosity, surface tension and density values of 52 mPas, 59.4 mN/m and 1064.5 kg/m³ respectively. This formulation cannot be constructed given the materials at hand, however a close neighborhood point can be achieved (with 50 mPas viscosity, 65.5 mN/m surface tension and 1195 kg/m³ density). Therefore, points with more robust neighbors are desirable as they offer greater manufacturing flexibility.

To compute robustness, the region around the solution (± 10% hypercube centered at the solution point) is sampled using Latin hypercube (2³ points). The DoD model is evaluated at each point, high consistency points are screened and the false positive pruner is applied. Robustness score is then computed as:

$$robustnessscore=\frac{\#recomputedprintingconsistency>0.5}{Totalsampledpoints}$$ #(3)

100 points with the highest robustness score values are then screened and taken to the next step. The next heuristic seeks to identify points with lowest actuations per drop (vstrokes). This is a discrete parameter that can only take values of either 1, 2 or 3. It has been empirically observed that having higher values for this variable increases the possibility of excessive satellite drop formation. Thus 10 solutions with the lowest actuations per drop are screened. Amongst these points, the final heuristic then identifies the solution with the lowest stroke length (disp). Having larger stroke lengths translates to producing bigger drops thereby increasing the risk of satellite drop formation and inconsistent printing. Note that the parameters- actuations per drop and stroke length are the most sensitive variables for the model (Figure 6B). The solution resulting from this step is the final constitutive variable set recommended by the DoD model for manufacturing dosages (Figure 8).

Although this scheme provides an efficient way to compute candidate input solutions, it does suffer from a few limitations. Using ANNs (a purely data driven, black box, method) obscures the underlying relationships between different parameters. Thus, no information is obtained on the physical significance of the structure and parameter values of the model. Another limitation in the model is variation in the recommended formulation and printing design solutions. In some cases, for the same user input, the design solutions recommended by the model can differ (maximum relative standard error of 6.8% is observed amongst all predicted parameters averaged over 100 prediction cycles). This variation can be attributed to three sources of stochasticity: 1) variation in DoD model training, 2) variation in training the false positive pruner, and 3) variation in the sample and search technique. Although this variation is moderate, it can potentially create problems during manufacturing if formulation uniformity is a critical quality attribute. Incorporating physical methods into this model could address both concerns by transforming the ANN into a grey-box (hybrid) model (that gives some qualitative information about the process) and reducing the variation generated due to training stochasticity. Additionally, redesigning the heuristics used may improve the screening of solutions and further reduce variation in results.

Step 2: Computing original input parameters using constitutive variables calculated above

This step seeks to calculate values for the original input variables that can yield the constitutive variables determined in Step 1 (Figure 7B). The variables to be determined are carrier components, compositions and the resulting blend properties. Solving this problem is challenging as there is a deficiency in the physical property data and models available for pharmaceutical APIs and excipients. A major hindrance here is a lack of solubility prediction models, the primary consideration for API – formulation compatibility is that the formulation must not dissolve the API. Dissolving the API before printing can lead to changes in the crystal size and dissolution behavior. Most of the liquid excipients used with DoD (PEGs, food oils, silicon oils) have poorly understood solubility behavior. Additionally, novel APIs have little to no information available on solubility or degeneration potential in various solvents. Moreover, there is also a lack of general models to predict physical properties such as viscosity and surface tension of polymeric and suspension blends. A further limitation is the difficulty of creating formulations with sharp differences in surface tension and density. Usually hydrophilic solvents have higher densities (>1000 kg/m³) and surface tensions (>30 mN/m) compared to hydrophobic solvents. Thus, it is challenging to design a formulation blend that has low density but high surface tension and vice-versa. In the light of these deficiencies, automating this step of formulation is not possible at this time. This study recommends employing a human expert for this step until physical property models for pharmaceutical excipients become more widely available. Human experts have been used in similar applications when required predictive property models are not available³⁸.

Based on the constitutive variables calculated above, the human expert will identify the excipients to use (that do not dissolve the API), and their compositions. For some model recommendations, it might not be possible to achieve the exact formulation due to a limited availability of excipients. In such cases the human expert can follow the sensitivity chart for guidance on parameter matching priority. An inexact match is more acceptable for variables that have lower sensitivity scores. The formulation designed by the human expert is then used for manufacturing the dosages.

Figure 7B explains the role of the human expert in greater detail. In the constitutive variable set recommended by the model, 5 properties are user specified: particle concentration (calculated based on required drug loading and dosage volume), D10, D50, D90 and aspect ratio (AR). These values are not altered by the expert. The human expert also does not change the model recommended printing conditions: stroke length (disp), stroke rate (rpm) and actuations per drop (vstrokes). These variables can only take discrete integer values (stroke length can take discrete values at an interval of 0.5 mm: 1, 1.5, 2…) which are solely determined by the model. The main role of the expert is to pick the solvents and their compositions for the formulation such that its properties are close to the model recommended designs for viscosity, surface tension and density. For the example shown in figure 7B, the expert has selected two solvents (glycerol and water) that do not dissolve atorvastatin. These were chosen as their combination (75–25 wt% mixture) yield a close match to the model recommendations for formulation design. Two alternatives are available for this choice – silicon oil and triglyceride oil (NEOBEE), which also demonstrate low atorvastatin solubility. However, choosing them would lead to a larger deviation from model recommended formulation properties which can lead to inconsistent printing conditions. The expert’s decision therefore impacts two broad categories: 1) Solvent compatibility with API and 2) Proximity to recommended formulation design. A poor selection of these parameters can lead to alteration of crystal size distribution, dissolution properties and can also lead to formulations deviating a lot from model recommendations with greater risk of inconsistent printing.

Experimental validation

The proposed FPD scheme is experimentally validated for two test APIs, atorvastatin and lisinopril. The common dosage levels used for these APIs are obtained from the FDA’s orange book (atorvastatin: 10mg, 20mg, 40mg, 80mg; lisinopril: 2.5mg, 5mg, 10mg, 20mg). To obtain manufacturing conditions, the user specifies the required dosage amount, capsule size to use and particle size distribution of the API crystals (for systems with integrated crystallizer – DoD the size distribution can be obtained from the crystallizer outlet). Then the scheme discussed in Figure 8 is followed and a condition set is obtained for constitutive variables. The human expert then maps them onto the original input space. For some cases the difference in surface tension and density between model predicted and expert selected formulations is high. This is because for the available excipients only viscosity could be closely matched to model predictions, a closer match for the other two parameters can be obtained by exploring more surfactant and blending excipients. The printing conditions obtained as a result are then validated experimentally using the DoD apparatus. Three replicates are performed for both atorvastatin and lisinopril, in each case inter drop volume variance (‘var’) and drop score are computed based on equations discussed in previous sections. The experimental consistency scores obtained in each case are reported and the results are summarized in Table 4 below. Step 1 column reports the model predicted constitutive variable values and Step 2 column shows the parameters determined by the human expert. Consistency results from printing at the expert’s conditions are reported in the final field. It is seen that consistent printing is observed for all model recommendations. Thus, the FPD framework developed is a useful tool to compute optimal formulation properties and printing conditions that can manufacture dosages meeting required design targets.

Table 4.

Results of experimental validation of the proposed FPD framework for two test APIs- Atorvastatin and Lisinopril.

Atorvastatin
Drug loading	10 mg			20 mg			40 mg			80 mg
	Step1	Step 2		Step1	Step 2		Step1	Step 2		Step1	Step 2
disp (mm)	1.5	1.5		1.5	1.5		2.0	2.0		2.0	2.0
rpm	804.0	804.0		889.0	889.0		863.0	863.0		753.0	753.0
vstrokes (#)	2.0	2.0		2.0	2.0		2.0	2.0		2.0	2.0
carrier	-	glycerol, water		-	glycerol, water		-	glycerol, water		-	glycerol, water
comp (wt %)	-	[0.75, 0.25]		-	[0.75, 0.25]		-	[0.75, 0.25]		-	[0.7,0.3]
visc (mPas)	52.0	52.1		59.0	54.4		55.1	59.5		61.2	57.7
surf_ten (mN/m)	59.4	65.5		36.4	65.5		48.1	65.5		65.0	66.0
density (kg/m3)	1061.5	1195.0		1042.5	1195.0		942.6	1195.0		1040.3	1182.0
conc (mg/mL)	10.0	10.0		20.0	20.0		40.0	40.0		80.0	80.0
D10 (μm)	24.0	24.0		24.0	24.0		24.0	24.0		24.0	24.0
D50 (μm)	221.0	221.0		221.0	221.0		221.0	221.0		221.0	221.0
D90 (μm)	433.0	433.0		433.0	433.0		433.0	433.0		433.0	433.0
AR	1.26	1.26		1.26	1.26		1.26	1.26		1.26	1.26
var	{0.41, 0.16, 0.11}			{0.13, 0.24, 0.68}			{0.12, 0.09, 0.42}			{0.68, 0.19, 0.86}
drop score	{1, 1, 1}			{1, 1, 1}			{1, 1, 1}			{1, 1, 1}
overall consistency	{consistent, consistent, consistent}			{consistent, consistent, consistent}			{consistent,consistent, consistent}			{consistent, consistent,consistent}
Lisinopril
Drug loading	2.5 mg			5 mg			10 mg			20 mg
	Step1		Step 2	Step1		Step 2	Step1		Step 2	Step1	Step 2
disp (mm)	1.5		1.5	1.0		1.0	1.0		1.0	1.0	1.0
rpm	533.0		533.0	865.0		865.0	812.0		812.0	590.0	590.0
vstrokes (#)	1.0		1.0	2.0		2.0	2.0		2.0	1.0	1.0
carrier	-		NEOBEE	-		NEOBEE	-		NEOBEE	-	NEOBEE
comp (wt%)	-		[1]	-		[1]	-		[1]	-	[1]
visc (mPas)	18.1		21.2	19.8		21.4	18.1		21.8	16.7	22.7
surf_ten (mN/m)	35.9		30	32		30	55.954		31.9	21.4	30
density (kg/m3)	942.6		910	814.2		910	882.7		910	823.6	910
conc (mg/mL)	2.5		2.5	5.0		5.0	10.0		10.0	20.0	20.0
D10 (μm)	84.0		84.0	84.0		84.0	84.0		84.0	84.0	84.0
D50 (μm)	1160.0		1160.0	1160.0		1160.0	1160.0		1160.0	1160.0	1160.0
D90 (μm)	2256.0		2256.0	2256.0		2256.0	2256.0		2256.0	2256.0	2256.0
var	{0.002, 0.23, 0.003}			{0.03,0.36, 0.04}			{0.07,0. 02,0.06}			{0.03,0.007, 0.03}
drop score	{1.02, 1, 1}			{1, 1, 1}			{1, 1, 1}			{1, 1, 1}
overall consistency	{consistent, consistent, consistent}			{consistent, consistent, consistent}			{consistent, consistent, consistent}			{consistent, consistent,consistent}

Conclusions

In summary, this study presents a novel integrated formulation and process design framework for a pharmaceutical 3D printing platform. It recommends manufacturing conditions with which to operate order to produce dosages that meet design targets. To build this framework, first a process model is developed to predict printing consistency of DoD using an ANN model. Model execution is fast and accuracy is comparable to other DoD inkjet models. To build the FPD framework the inverse solution of this simulation is desired. It is solved in two steps: Step 1) Constitutive variables are computed using a sample and search scheme. A large number of points are sampled using Latin hypercube, model is evaluated at each instance and high consistency points are screened. Then a false positive pruner and a series of heuristics are applied to all candidate solutions to identify the most desirable point. Step 2) A human expert is used to map the constitutive variable solution onto the original input space. This point is experimentally validated for two test APIs by printing drops at the recommended printing conditions and calculating printing consistency. All the model recommended points are seen to exhibit high printing consistency.

The functionalities of this framework can be readily expanded. Development of more physical property prediction models for pharmaceutical excipients, solutions and suspensions will allow for replacing the human expert with a fully automated design scheme. Incorporating this modification will be the first step towards autonomous operation for the DoD printer. Another avenue for flexibility is to enhance the existing data driven process model with more physics informed models. These hybrid structure would transform the methods developed into ‘grey-box’ models that could offer enhanced accuracy and process understanding. In conclusion, development of this FPD framework marks an important contribution in incorporating Industry 4.0 technologies in pharmaceutical manufacturing and holds great potential in enabling implementation of other allied innovations.

Abbreviations

3DP

3D Printing

API

Active Pharmaceutical Ingredient

AM

Additive Manufacturing

AI

Artificial Intelligence

ANN

Artificial Neural Network

DoD

Drop on Demand

FPD

Formulation and Process Design

HMDSO

Hexamethyldisiloxane

IoT

Internet of Things

Oh

Ohnesorge number

PPD

Product and Process Design

QbD

Quality by Design

RTM

Real Time Monitoring

Re

Reynolds number

FDA

United States Food and Drug Administration

We

Weber number

Statement on data availability

The experimental dataset generated in the study is available as a supplementary to this article.