Modeling of physical-mechanical and microbiological properties of tablets made of complex fluidized bed granules containing living yeast cells using common mixing rules

1.1. Formulation of tablets containing living microorganisms

Probiotic microorganisms can promote patient health when taken in sufficient quantities (Joint FAO/WHO Working Group, 2002). This requires suitable dosage forms and manufacturing processes that allow for gentle processing (Broeckx et al., 2016). While liquid dosage forms are easy to produce without critical stress on the microorganisms, their storage stability is usually limited. Although cooling can improve their stability, it is complex and expensive (Santivarangkna, 2016). Drying is a more convenient and cost-effective method for conservation compared to freezing (Lievense and van’t Riet, 1993), which typically allows for even greater storage stability than cooling (Meryman, 1974). However, drying can result in a reduction of viability but the surviving cells can be converted into a dry, storable form and subsequently reactivated (Broeckx et al., 2016). Suitable processes and process parameters, as well as formulations that minimize stress to the microorganisms, are the basic prerequisites to ensure that the inactivation is reversible. Various processes are suitable for life-preserving drying, such as classic freeze-drying, spray drying, or fluidized bed spray granulation (Broeckx et al., 2016; Lievense and van’t Riet, 1993).

Although dried powders or granules can be administered directly or packaged in capsules, tableting is usually preferred. Loose granules expose microorganisms to harsh stomach conditions more than other dosage forms. Packaging into capsules is also more expensive than tableting. However, tableting is associated with pressure and shear stresses that can be lethal to microorganisms, leading to irreversible inactivation. This effect increases with higher compression stress (Ayorinde et al., 2011; Blair et al., 1991; Chan and Zhang, 2002; Silva et al., 2013; Fassihi and Parker, 1987; Muller et al., 2014; Nagashima et al., 2013; Plumpton et al., 1986a, Plumpton et al., 1986b; Poulin et al., 2011; Stadler and Viernstein, 2001; Vorländer et al., 2025a, Vorländer et al., 2025b; Vorländer et al., 2024; Vorländer et al., 2023a; Vorländer et al., 2023c; Vorländer et al., 2023d; Vorländer et al., 2023b; Vorländer et al., 2020). Therefore, process and formulation parameters must be carefully selected.

Especially the formulation was addressed in many studies dealing with compaction of viable microorganisms dried by lyophilization, spray-drying or granulation (Ayorinde et al., 2011; Azhar and Munaim, 2021; Blair et al., 1991; Brachkova et al., 2009; Byl et al., 2018; Chan and Zhang, 2002; Silva et al., 2013; Fassihi and Parker, 1987; Hoffmann and Daniels, 2019; Huq et al., 2016; Klayraung et al., 2009; Maggi et al., 2000; Muller et al., 2014; Nagashima et al., 2013; Oktavia et al., 2020; Plumpton et al., 1986a, Plumpton et al., 1986b; Poulin et al., 2011; Sánchez et al., 2018; Shu et al., 2020; Stadler and Viernstein, 2003; Stadler and Viernstein, 2001; Villena et al., 2015; Vorländer et al., 2023a; Vorländer et al., 2023c; Vorländer et al., 2023d; Vorländer et al., 2023b; Vorländer et al., 2020).

Although fluidized bed granulation is a promising method for drying microorganisms (Vorländer et al., 2023a), it has been little used and knowledge on the influence of the formulation on survival during tableting of granules is limited (Ayorinde et al., 2011; Blair et al., 1991; Fassihi and Parker, 1987; Hoffmann et al., 2020; Hoffmann and Daniels, 2019; Plumpton et al., 1986a, Plumpton et al., 1986b; Vorländer et al., 2025a, Vorländer et al., 2025b; Vorländer et al., 2023a; Vorländer et al., 2023c; Vorländer et al., 2023b) (in some of these publications wet granules were oven-dried). In previous studies by the same authors, the survival of microorganisms during tableting of granules prepared by fluidized bed spray granulation was found to depend on the carrier material used (Vorländer et al., 2025b; Vorländer et al., 2023a; Vorländer et al., 2023c; Vorländer et al., 2023b). This dependence was attributed to specific deformation characteristics of the carrier materials, and survival could be correlated with reduction of porosity during compression across formulations (Vorländer et al., 2023c; Vorländer et al., 2023b). However, granulation of carrier materials with microorganisms and protectants was also found to negatively affect properties such as compressibility, compactibility, and tabletability (Vorländer et al., 2025a, Vorländer et al., 2025b; Vorländer et al., 2023b). To what extent the combination of different deforming materials during granulation has positively or negatively reinforcing effects on physical-mechanical and microbiological tablet properties has not yet been investigated. This is addressed in the present study. For this purpose, granules based on binary mixtures and a ternary mixture of three dry binders (dicalcium phosphate (DCP), lactose (LAC) and microcrystalline cellulose (MCC)) are tableted and the physical-mechanical tablet properties as well as the viability of the microorganisms are analyzed.

1.2. Modeling physical-mechanical properties of multi-component tablets

Predicting the properties of tablets made from blends of different components based on the characterization of the tableting properties of the pure components is the subject of numerous studies (Puckhaber et al., 2023). The development of reliable models is crucial for efficient formulation development with minimal experimental effort. To this end, for the prediction of powder blend tableting behavior it is necessary to be able to describe both the compressibility and the compactibility of the pure components precisely using suitable models. These are then combined in a suitable way to predict the compressibility, compactibility and tableting behavior of multi-component tablets.

For the compressibility of binary mixtures of microcrystalline cellulose (MCC) and lactose (LAC), a linear dependence of tablet porosity on the mass fraction of the components has been reported (Busignies et al., 2006). Furthermore, it was postulated that the compression of the components occurs independently of each other (Frenning et al., 2009). Based on this, the compressibility of binary pellet mixtures was fitted using Kawakita’s compressibility model (Kawakita and Lüdde, 1971), and a linear correlation was found between the effective Kawakita parameters obtained and the volume fraction of the components (Frenning et al., 2009). However, these parameters depend on the initial bulk volume and are not intrinsic material properties (Mazel et al., 2011).

Therefore, Mazel et al. took a different approach and used the Kawakita parameters of the individual components to calculate the respective porosities of these and successfully predicted the porosity of the binary mixture during compression by volumetric weighting (Mazel et al., 2011). This approach allowed the prediction of the compressibility of physical powder mixtures of up to five components (Busignies et al., 2012).

One approach to predict the tensile strength of binary mixtures of one well and one poorly compactable component is based on the percolation theory (Kuentz and Leuenberger, 2000). However, this model is only valid for a small compression stress range up to 60 MPa (Kuentz and Leuenberger, 2000). In further studies, the model was extended for the combination of two components with good compactibility (Ramírez et al., 2004). However, the application requires experimental data of the binary mixture and is not suitable for prediction on the basis of single component investigations (Wu et al., 2005). Therefore, Wu et al. used the Ryshkewitch-Duckworth (Duckworth, 1953; Ryshkewitch, 1953) model to describe the compactibility of the individual components and were able to predict the compactibility of binary (Wu et al., 2005) and multi-component tablets (Wu et al., 2006) by taking the volume fraction into account. Reynolds et al. enabled improved prediction accuracy by using a geometric mean rule (Reynolds et al., 2017).

Based on this, the present study investigates the possibility of predicting the physicomechanical properties of granules with living microorganisms using the compaction of the carrier materials and spray-dried microorganisms. In order to also predict the survival of the microorganisms, the application of analogous volume-weighted mixing rules for the microbiological tablet properties is examined.