It is well known that the biomechanical properties of red blood cell (RBC) membrane are fundamentally important for sustaining cell functions. Changes in these properties are associated with many important physiological and pathological processes. These processes could eventually lead to the manifestation of various blood-related hereditary and non-hereditary diseases such as malaria, hereditary diseases, and sickle-cell disease. In the last few years, human RBCs have attracted significant attention due to their important connection with human health. Numerous researchers have attempted to probe the elastomechanical properties and deformability of the RBC membrane using laboratory experiments and numerical simulations.

The present study investigates the biomechanical properties of healthy and malaria-infected RBC membranes using a newly proposed three-dimensional (3D) multiscale Cauchy-Born model. Here, a microstructure-based, 3D multiscale hyperelastic constitutive model is derived by using the gradient theory based on the Cauchy-Born rule. It is assumed that the RBC membrane undergoes a homogeneous deformation. Following this, the atomistic strain energy density at a junction complex is computed using the coarse-grained Helmholtz free energy function and the average area per junction complex in the reference configuration. Subsequently, the computed atomistic strain energy density function is systematically introduced as the total energy stored in the system for numerical simulation on the continuum scale. The current approach is called a 3D multiscale Cauchy-Born model for the following reasons: (1) the RBC membrane is treated as a closed manifold embedded in a 3D space, (2) the technique is a multiscale method because it runs on the atomistic and continuum level simultaneously, and (3) the Cauchy-Born rule helps to bridge the two simulation scales.

The first stage of this research employed the 2D atomistic-continuum method, based on the higher-order Cauchy-Born rule, to predict the elastic properties and mechanical behavior of the RBC membrane in comparison with previously published works. The results obtained from this study agree well with experimental and numerical results in the open literature. It was observed that the RBC membrane exhibits a strain stiffening mechanism under various loading conditions, which becomes more obvious when the equilibrium spectrin link is straightened due to stretching instead of being convoluted. We suggest that the observed strain-stiffening phenomenon is physiologically relevant and helps prevent membrane damage due to exposure to extreme deformations.

In the next stage of this research, a 3D multiscale Cauchy-Born model in which the actual 3D reference configuration and only the first-order Cauchy-Born rule are employed for numerical simulation is proposed. The advantages of this approach become obvious when the large deformation behavior of the RBC membrane is analyzed using the meshfree method. The computed values of RBC membrane elastic properties and biomechanical responses under various loading condition are in agreement with those obtained from previous studies. By combining the 3D multiscale Cauchy-Born model and the meshfree method, a 3D multiscale Cauchy-Born meshfree method is proposed. The meshfree method is adopted in this study due to its numerous advantages over mesh-based methods. This thesis also presents a state-of-the-art in meshfree method, its application in biomechanics along with perspectives and bibliography.

The concept of pseudo strain energy density was employed in the proposed method to incorporate the precise influence of membrane thickness. With the developed method, the large deformation behavior of the RBC membrane is first examined by numerical simulation of the optical tweezers experiment. It was observed that the proposed method performs well and gives predictions that agree well with experimental results. Numerical studies of the effects of physiological conditions, microstructure parameters, and osmolality on the deformability of RBC membrane were also conducted. The effects of extreme temperature, strains, and loading conditions on the biomechanical properties and deformability of healthy RBC membrane were also investigated. It is concluded that mechanically induced hemolysis may be initiated due to extreme strain and loading, and that increased membrane rigidity due to temperature change may be attributed to the denaturation of membrane protein and to cross-linkage of the underlying spectrin cytoskeleton.

Lastly, the elastomechanical properties and deformability of RBCs parasitized by Plasmodium (P.) falciparum is modeled with the aim of establishing a connection between membrane microstructure details, parasite infection stages, temperature, and deformability of malaria-infected RBC (iRBC) membrane. A multi-fold increase in membrane rigidity is observed as parasitic infection progresses. The stress-strain relationship curves of the iRBC membrane become log-lin semi-logarithmic graph type, and the stresses increase exponentially as strains gradually increase. Furthermore, it is observed that the deformability of the iRBC membrane reduces as parasitic infection progresses, possibly due to the export of parasite proteins to the RBC membrane cytoskeleton. It is concluded that malaria infection significantly alters the RBC membrane microstructure and that the overall rigidity of malaria-infected RBC membrane increases with an increase in temperature and as malaria infection progresses.