## 1 Introduction  
Mechanical properties of single cells have been proven to be clinically useful biomarkers of various pathological changes, such as cardiovascular disease [1], hematologic diseases [2], and cancer [3]. In erythrocytes, membrane is the only structural component that maintains its mechanical stability when delivering oxygen through the systemic circulation and returning to the pulmonary circulation. During their normal lifespan of 120 days, erythrocytes experience a series of metabolic and physical damages as well as mechanical stresses as they age. Cumulative effects from these factors result in membrane failure, such as vesiculation and mechanical degradation, as well as hemoglobin modification, which transforms a normal discocyte to an echinocyte [4]. Many pathological processes, such as malaria [5], sickle cell anemia [6], hypertension [7], diabetes [8], and such medical procedures as blood banking [9], extracorporeal circuit for hemodialysis [10], and cardiopulmonary bypass [4], can lead to accelerated membrane degradation, remodeling, and failure.  
Study of membrane mechanics at the single cell level requires an application of external load to cell membranes and an accurate calibration of the induced stress and strain for individually tracked cells. Many experimental measurement methods, such as micropipette aspiration, atomic force microscopy, microplate stretchers, and optical tweezers, rely on physical contact, the details of which can be found in some review papers [11; 12; 13]. Although the physics underlying these techniques can be scaled up, in many existing settings, these techniques suffer from low throughput and can only measure one single cell at a time. To compensate the heterogeneous nature of biological materials, a high-throughput method of loading and measurement on individual cells is required.  
Electrodeformation of cell membranes is a relatively new technique that has the potential to measure many single cells at once. When the electric field is non-uniform, the net force exerted on the cell membrane will move the cell toward (or against) the direction of the electric field maxima, given the cell is more (or less) polarizable than the surrounding medium, known as dielectrophoresis (DEP), as shown in Figure 1a. DEP has been widely utilized to separate and sort biological cells in microfluidic settings, the details of which can be found in several review papers [14; 15; 16; 17; 18]. Electrodeformation of cell membrane is induced by the electrical forces exerted on the induced charges or by the effective dipole in the cell (Figure 1b). Application of DEP in single cell biomechanics was pioneered by [PERSON] and [PERSON] [19], where an inhomogeneous high frequency electric field was used to induce transient electrodeformation of single cells. Such method has been advanced by virtue of microfabrication techniques, such as an interdigitated electrode array, which allows for quantitative measurements of multiple cells at a time. Applications have been found in a wide range of cell types, such as erythrocytes [20; 21; 22; 23], platelet [24], mammalian cells [25], plant protoplasts [26], and cervical cancer cells [27].  
In this paper, we postulate that the repeated electrical and mechanical stresses can induce membrane changes of single erythrocytes. We bring together the signal modulation technique and DEP to impose cyclic electromechanical loading using mathematical convenience waveforms in a microfluidic setting. This provides an opportunity to test this hypothesis and allows us to explore the progression of membrane failure in circulating erythrocytes, such as mechanical degradation, irreversible membrane damage, and lysis of erythrocytes.