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This section mainly covers the basic mechanics of RBCs. It starts with a brief overview of the structure and functions of RBCs, followed by a discussion on the impact of deformability of RBCs and how measurements of deformability relate to specific blood borne diseases.

3.2.1 Function and structure

Red blood cell (RBC), also named erythrocyte, is the largest population of cells in most vertebrates. There are roughly 20 to 30 trillion RBCs in an adult human at any time 37. RBCs are derived from hemopoietic stem cells in the bone marrow. The mature RBC in the circulatory system is in an oval biconcave-disk shape. It contains no nucleus or organelles, only the haemoglobin meshwork with a lipid bilayer membrane as the sack 38_{. Therefore, the main structure of RBCs}

includes three components: the fluid cytoplasm (haemoglobin), the lipid membrane, and the membrane skeleton. Haemoglobin is an iron-containing metalloprotein in charge of carrying oxygen, of which the heme prosthetic group presents the red colour. The lipid membrane of RBCs consists of phospholipid bilayer and intramembrane proteins. The membrane skeleton is formed by a

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spectrin–actin protein network, which is attached to the transmembrane proteins and adjacent to the lipid membrane. The loosely packed cytoplasm, without nucleus or organelles, allows RBCs to go through the narrowest capillary with high flexibility of distortion. They are circulated within the blood vessels of different diameters (about 3 µm to 25 mm) under different wall shear stress (1-60 dyne/cm2). Gas exchange is the primary function of RBCs circulating through the whole body, during which the oxygen diffuses from the oxygenated RBCs to surrounding cells and carbon dioxide produced by cellular respiration diffuses from the interstitial fluid into the RBCs.

3.2.2 Deformability of red blood cells

The ability to greatly deform is one of the most important properties of RBCs, that not only allows RBCs to pass through capillaries but also aids them maintain unscathed when experiencing significant stress during circulation 39. Hence, the decrease in deformability can cause detrimental repercussion immediately. Deformability of RBCs is typically described in terms of viscosity, shear modulus, and bending modulus, which comes from two contributions. The first part is the rheological properties of the intracellular fluid of RBCs, which is ruled by hemoglobin concentration and physicochemical properties of it. The second contributor is the rheological properties of RBC membrane and membrane skeleton. Any disturbance in the internal and external environment can trigger the RBCs deformability changes, particularly in many pathological conditions 40. For example, the variations in osmotic conditions 41, the increase in intracellular calcium ion 42, temperature variation (hypothermia) and the alteration in membrane composition 43 will all affect the deformability of RBCs 44.

RBC abnormalities in hematological disorders and diseases are often accompanied by altered RBC deformability. For example, sickle cell anemia 45 is caused by the genetic defect of molecular structure of hemoglobin S (HbS) 46 which undergoes gelation and fiber formation during deoxygenated process, which changes intracellular fluid to a viscoelastic material and decreases the deformability 47_{. Another example of decreased deformability is malaria infection} 48_{. Malaria parasites which enter RBCs cytoplasm not only change the internal}

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expressing the intramembrane proteins. Both alterations reduce the deformability of the RBCs dramatically during the parasite life cycle. The detailed pathology is discussed in chapter 6.1.

3.2.3 Measuring deformability of red blood cells

The mechanical properties of RBCs have been widely studied since last century 35, 39, 49. One important aim of these RBCs biomechanics studies is to provide further insights to fill in gaps of current pathophysiology knowledge and lead to new methods of early diagnosis and effective treatment. Initial biomechanical approaches to studying RBCs rheology mainly includes biochemical methods, simple shear flow approaches (cone-plate viscometer and counter-rotating rheoscope), MA and optical tweezers 50-51_{. During the exploration,}

chemical stiffening methods 52 _{have been established for manipulating the RBCs}

deformation. For example, diamide 53, a sulfhydryl reagent which oxidizes sulfhydryl groups to the disulfide form, primarily affects the membrane stiffness of RBCs and affects no strain rate of cytoplasm. Glutaraldehyde 54-55, as another frequently used chemical, causes cross-linking of membrane proteins as well as haemoglobin, which increases the effective viscosity of both lipid membrane and cytoplasm, and in turn reduces the deformability of entire RBCs. These chemical approaches helped in establishing the knowledge of comprehensive RBCs rheology and developing the practical models 56-58 for simulation studies.

In 1971, Miller et al. 59-60 studied malarial parasites infected mammalian RBCs by viscometer and cell-filtration methods, which was the first study indicating that the deformability of RBCs could be impaired by infection of malarial parasites. A comprehensive investigation of mechanical properties of healthy and malarial parasite infected RBCs at different stages was conducted using optical tweezers in 2004 by Mills et al. 61. Around the same time, a microfluidic device was first used to investigate the blockage of infected RBCs passing through the different sizes of narrow elastomeric channels 62. Similar to malaria studies, the mainstream of sickle RBCs mechanical study used optical tweezers 63 _{and MA} 64 _{in the past. With the development of nanostructure and}

microstructure fabrication, microfluidics technique has been increasingly applied in sickle RBCs mechanics investigation. It provides the platform for manipulating

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a large population of RBCs and the opportunity of observing individual rheological behaviours.