By Milton O Assuncao
New developments in the space industry, fueled by public-private partnerships, are increasingly enabling a range of activities to be carried out in low-Earth orbit. The industry is booming; a report by the World Economic Forum projects that the global space economy is set to grow from $630 billion in 2023 to $1.8 trillion by 2035[1]. Beyond commercial opportunities, in-space activities can help government agencies, academia, and private companies carry out research and develop solutions to address many of the world’s pressing challenges in innovative ways.
One such research area is extra-terrestrial pharmaceutical manufacturing, which aims to exploit the effects of microgravity to produce new or enhanced life-saving pharmaceuticals that may only be manufacturable in space. More specifically, it is hypothesized that gravity can influence the crystalline structure attained by a solid substance during manufacturing. A solid substance’s ability to exist in more than one crystalline form is known as polymorphism. Having a particular polymorphic form can alter key properties of a drug, such as bioavailability, solubility, and stability[2,3]. In this context, mathematical modelling can improve our understanding of the mechanisms behind polymorphic crystallization and help predict how crystals grow in low-Earth orbit.
In a recent work conducted at the Mathematics Applications Consortium for Science and Industry (MACSI) at the University of Limerick in collaboration with Varda Space Industries, a novel mathematical framework[4] was developed to investigate gravity-driven polymorphic crystallization. This framework was applied to the crystallization of L-histidine (C₆H₉N₃O₂), an essential amino acid of interest to the pharmaceutical industry[5], which is known to crystallize in two forms: a stable polymorph A and a metastable polymorph B (
).
Figure 1: Render of Varda W-1 capsule docked to Satellite bus. (Source: varda.com)
Varda Space Industries are already collecting experimental data at earth gravity and hypergravity (attained using a centrifuge)[6] which may be used to test the model accuracy, while crystallization experiments on satellites to collect data in microgravity in low-Earth orbit are in advanced stages of planning, after an initial mission which successfully tested a prototype crystallization apparatus.
Using a population-balance approach, our model accounts for many mechanisms, including supersaturation and nucleation, to predict the number density of crystals (ni) as a function of crystal size (L) and time (t). Mathematically, the model consists of two first-order nonlinear hyperbolic partial differential equations for the number densities of the two polymorphs, coupled with an ordinary differential equation for the solute concentration in the solvent. The system of equations and boundary conditions is then analyzed using asymptotic methods to verify the accuracy of the numerical solutions.
Applying the model to study the crystallization of L-histidine, it was possible to obtain the evolution of crystals of both forms over time under microgravity (0.01gEarth), Earth gravity (gEarth) and hypergravity (5gEarth). In Figure 2, we observe that a stronger gravitational field results in fewer but larger crystals of form A, while crystals of form B become fewer and smaller. For illustrative purposes, these population densities are sketched in Fig. 3, with crystals positioned at randomly assigned locations within a crystallization vial.
| Figure 2: Number density of crystals of polymorph i, ni, after 2 hours as a function of the crystal length, L . |
Figure 3: Crystals of each polymorph were randomly allocated inside a vial for varying gravity scenarios, with number and area (L2) proportional to the data in Fig. 2.
The framework outlined above can be built on in future work and is, in principle, equally applicable to the crystallization of other compounds in which polymorphism is known to occur.
This publication has emanated from research supported in part by a grant from Research Ireland co-funded under the European Regional Development Fund under Grant No. 12/RC/2275 P2, and Varda Space Industries. The research was carried out by M. Assunção, K. M. Moroney, D. O’Kiely and M. Vynnycky, members of Mathematics Applications Consortium for Science and Industry (MACSI) and SSPC Research Ireland Centre for Pharmaceuticals.
References
[1] World Economic Forum, Space: The $1.8 Trillion Opportunity for Global Economic Growth, in collaboration with McKinsey & Company, April 2024.
[2] D. J. W. Grant, Polymorphism in Pharmaceutical Solids. New York, NY, USA: Marcel Dekker, 1999.
[3] R. Hilfiker and M. von Raumer, Polymorphism in the Pharmaceutical Industry: Solid Form and Drug Development. Hoboken, NJ, USA: John Wiley & Sons, Ltd, 2019.
[4] M. Assunção, K. M. Moroney, D. O’Kiely and M. Vynnycky, Analysis of a model for polymorphism in gravity-driven, antisolvent crystallization, SIAM Journal on Applied Mathematics, Accepted for publication (2025).
[5] F. Shibata, M. Yokota, and N. Doki, Thermodynamic characteristics of L-histidine polymorphs and effect of ethanol on the crystallization, J. Cryst. Growth, vol. 564, 2021. Article no. 126086 (8 pages)
[6] K. Pal and A. Radocea, Gravity as a knob for tuning particle size distributions of small molecules, Cryst. Growth Des., 24 (2024), pp. 2370–2383.