Sarah Barns Thesis
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NUMERICAL MODELLING OF RED BLOOD CELL MORPHOLOGY AND DEFORMABILITY SARAH BARNS BEng(Mech)(Hons), GradCert(TerEd), GradDip(Math) Submitted in fulfilment for the requirements of the degree DOCTOR OF PHILOSOPHY School of Chemistry, Physics and Mechanical Engineering, Science and Engineering Faculty, Queensland University of Technology in collaboration with The Australian Red Cross Blood Service, Brisbane, Queensland, Australia 2018 Statement of Originality The work contained in this thesis has not been previously submitted to meet requirements for an award at this or any other higher education institution. To the best of my knowledge and belief, the thesis contains no material previously published or written by another person except where due reference is made. Signature: QUT Verified Signature Date: July 28, 2018 Numerical Modelling of Red Blood Cell Morphology and Deformability Page i Keywords . Red blood cell . Numerical modelling . Course-grained particle method . Morphology . Shape . Deformability . Discocyte . Echinocyte . AFM indentation . Optical tweezer stretching . Membrane . Mechanics . Hertz contact . Mechanical deformation Page ii Numerical Modelling of Red Blood Cell Morphology and Deformability Abstract The primary function of the red blood cell (RBC) is to distribute oxygen throughout the body. This requires RBCs to squeeze through narrow blood vessels which can be just half their own diameter, making cellular deformability critical for performance. RBC deformability is predominately controlled by the properties of the cell membrane, which consists of an outer lipid bilayer with embedded proteins and cholesterol, and a spectrin-based cytoskeleton tethered beneath. The strength of the bilayer’s resistance to bending and surface area changes, as well as the strength of the cytoskeleton’s resistance to stretch and shear dictate the cell’s ability to deform under external loading. Changes within the RBC membrane’s physical structure can reduce deformability, making the cells less efficient at moving through the body. This occurs naturally as RBCs age, but is accelerated during the storage of RBCs prior to transfusion, and also during the progression of diseases such as malaria. Although changes within the RBC membrane are well-accepted as the basis of deformability loss, the specifics of the underlying mechanisms remain unclear. Furthermore, given deformability differences can be detected experimentally, measuring RBC deformability in various experimental setups has been proposed as a potential tool for quantifying the quality of RBC units prior to transfusion and for the diagnosis of disease. Underlying structural changes of the RBC membrane can be explored with numerical models, which allow investigation of the mechanical aspects that define RBC behaviour at a much smaller scale than is possible with experimentation, which becomes challenging and costly. Deeper insight into how the mechanical state of the membrane contributes to physical changes in RBCs will aid in developing new strategies for improving RBC storage, potentially leading to higher quality RBCs for transfusion and longer maximum storage durations. It may also contribute to understanding the mechanical basis of RBC conditions. Therefore, the impact of mechanical changes within the RBC membrane on deformability was investigated using the coarse-grained particle method (CGPM). Secondly, deformability measurements in indentation and stretching setups were explored to understand their potential for detecting differences in mechanical properties of the membrane. Numerical Modelling of Red Blood Cell Morphology and Deformability Page iii As a first step of this study, the typical RBC discocyte resting shape was predicted in both 2D and 3D and validated against experimental observations from the literature. The models were then adapted to investigate the behaviour of RBCs when placed under a local compressive force to simulate indentation with atomic force microscopy (AFM), as well as when a global tensile force was applied to the cell, modelling stretching within an optical tweezer setup. Indentation investigations revealed that changes to the membrane’s bending stiffness had the most dominant impact on deformability in this loading scenario. As bending stiffness is mainly provided by the bilayer, AFM indentation would be well- suited to detecting physical changes within this part of the RBC membrane. Force- deformation curves from RBC indentation have been historically analysed using Hertzian contact theory to extract Young’s modulus for the membrane. However numerical investigations showed that this method of analysis was extremely limited in its application to RBC indentation problems due to difficulties justifying underlying assumptions of solid contact and negligible substrate influence. Furthermore, Young’s modulus predictions were highly sensitive to the region of the cell indented and the degree of adhesion, meaning that the deformability of both the cell and substrate were being measured rather than the membrane in isolation. Therefore an alternative method of analysis is required to reconcile the comparison of measurements between different AFM setups to further mature this technique. The stretching investigations showed that changes to the membrane’s linear stiffness had the most dominant impact on deformability in this loading scenario. Given that linear stiffness of the membrane is mainly associated with the spectrin- based cytoskeleton, the optical tweezer setup would be well-suited to detecting changes to cytoskeletal mechanical properties. To inform experimental design, it was found that optical bead size had little impact on deformability measurements, while the degree of adhesion did have a significant impact. As a final step in this study, the capacity to predict the discocyte-echinocyte resting shape sequence was explored. This found that impacting the spontaneous curvature for local regions gave rise to the development of echinocyte morphologies. This established a baseline direction for testing echinocyte morphologies in deformability scenarios in the future when experimental data becomes available. The CGPM models developed in this project have been shown effective in predicting the physical behaviour of RBCs under local compressive and global Page iv Numerical Modelling of Red Blood Cell Morphology and Deformability tensile loading. They may then form the basis of future work informing the design of devices and data analysis techniques for quantifying the deformability of RBC units prior to transfusion or for the diagnosis of disease. However, as the current methodology relies on the stiffness coefficients being tailored to the specific application, improved optimisation for the stiffness coefficients and greater sophistication in the energy equations should be considered. Resolving the lack of universality of the model should enable improved performance and predictive power going forward. Numerical Modelling of Red Blood Cell Morphology and Deformability Page v Acknowledgements I would like to thank my partner Laurie for supporting me through this PhD, including the sacrifices associated with commuting between Brisbane and Melbourne for the first two years. I would also like to thank my family and friends for their ongoing support. Furthermore, special thanks to the friends who have been on the research pathway alongside me, particularly Ted Pickering, Marie Anne Balanant, Ari Bo and Chris From. I would like to thank my supervisory team of YuanTong Gu, Emilie Sauret and Robert Flower. I appreciate YuanTong allowing me the time and space to pursue my teaching ambitions, Emilie for being an ever-reliable source of advice and direction, and Robert for welcoming me into the Blood Service community. I would also like to extend thanks to the wider Blood Service Research & Development Team, and in particular Helen Faddy who was instrumental in providing feedback through the last few months in preparing this document. I would like to thank the undergraduate students who have worked on this project across both final year projects and the vacation research experience scheme. Finally, I would also like to acknowledge the top-up scholarship I received from the Alexander Steele Young Lions Memorial Foundation which eased the financial pressures of pursuing a PhD over the last three years. Page vi Numerical Modelling of Red Blood Cell Morphology and Deformability List of Publications Peer-Reviewed Journal Articles: . S. Barns, M. A. Balanant, E. Sauret, R. Flower, S. Saha, and Y. Gu, "Investigation of red blood cell mechanical properties using AFM indentation and coarse-grained particle method," BioMedical Engineering OnLine, vol. 16, pp. 1-21, 2017. Available from: http://doi.org/10.1186/s12938-017-0429-5 . S. Barns, E. Sauret, S. Saha, R. Flower, and Y. Gu, "Two-Layer Red Blood Cell Membrane Model using the Discrete Element Method," Applied Mechanics and Materials, vol. 846, pp. 270-275, 2016. Available from: http://doi.org/10.4028/www.scientific.net/AMM.846.270 Extended Conference Abstract: . M. A. Balanant, S. Barns, E. Sauret, and Y. T. Gu, "Investigation of Red Blood Cell Membrane Elasticity using AFM Indentation and the Coarse- Grained Particle Method," in 10th Australasian Biomechanics Conference, Melbourne, Australia, 2016. Poster Presentation: . S. Barns, E. Sauret, R. Flower, and Y.T. Gu, “Numerical Investigation of Red Blood Cell Membrane Mechanical Properties on Deformability during Indentation,” in 27th Regional Congress of