Fractal approach to the rheology of concentrated cell suspensions

Abstract

Results on the rheological behavior of novel CHO cell suspensions in a large range of concentrations are reported. The concentration-dependent yield stress and elastic plateau modulus are formalized in the context of fractal aggregates under shear, and quite different exponents are found as compared to the case of red blood cell suspensions. This is explained in terms of intrinsic microscopic parameters such as the cell-cell adhesion energy and cell elasticity but also the cell's individual dynamic properties, found to correlate well with viscoelastic data at large concentrations (φ ≥ 0.5).The rheology of complex fluids has been studied extensively over the past decades [1] and has revealed very intriguing behaviors, in particular properties of suspensions, either micronic or colloidal, are still a subject of interest [2,3,4,5]. Classical behaviors of suspensions reveal shear-thinning effects usually, but other unusual ones like shear-thickening [6] (i.e. viscosity increase with shear rate) or yield stress have been observed [2,5]. The yield stress is the critical value of the shear stress needed to induce flow for a given fluid. It is closely related to the internal structure of the fluid therefore its ability to form (or break) particle clusters under flow. In this respect many studies have focused on solid sphere suspensions.On the other hand, there are much less works dedicated to suspensions of deformable particles, such as biological cell suspensions. The main works can be found in the field of blood rheology. Suspensions of Red Blood Cells (RBC) within plasma were first investigated by Chien [7,8] and revealed a shear-thinning behavior, but a more detailed inspection of the viscosity-shear rate diagrams showed that at low shear rates, the stress level is close to a constant σ s (Pa), called the yield stress. The well-known Casson's model [9], √ σ = √ σ s + √ µγ, relating the shear stress σ to the shear rateγ (µ being a constant viscosity) can be used to determine the yield stress. Chien and coauthors obtained σ s for a large range of hematocrit (H), i.e. the RBC volume concentration [10]. They showed a relationship of the type σ s ∼ (H −b)3 (b being a constant hematocrit) as also observed in a recent work [11].It is still not known yet whether this type of behavior is universal, or rather it could depend on cell type, cell shape or other biological effects such as cell adhesion or cell elasticity. In particular, one proposed explanation of the yield stress in RBCs suspensions is based on the existence of "rouleaux" which build due to cell interactions and exhibit large shape aspect ratios [8] and a fractal dimension D. Therefore it is necessary to apply strong enough stresses in order to break such aggregates, in close relation with the yield stress.In this letter we propose to investigate the rheology of a new cell suspension, consisting of CHO cells (Chinese Hamster Ovary cells) in a large range of concentrations. Such cells are commonly used in biology, easy to culture, and can be genetically modified ...

An elasto-visco-plastic model of cell aggregates

“…This assumption applies depending on the value of the yield stress: it has to be small enough so that the condition |B n · I − 3| 1 is always satisfied during the motion. The experiments by Iordan et al [20] give an indication of the order of magnitude of the yield stress. In this regime, for small elastic strain, one can use linear elasticity while for larger stress, the natural configuration evolves, keeping the deformations with respect to the evolving natural configuration small.…”

“…Relationships between yield stress and individual cell properties, such as cell interfacial energy or their elastic moduli, has been provided relating the micro-and macroproperties by Snabre [37,38]. Using this approach, Iordan et al [20] were able to determine typical intrinsic properties for concentrated suspensions of Chinese Hamster Ovary cells (CHO). Other works deal with different types of cell suspensions [10,12,11,13,42], and similar behaviors are observed.…”

“…In the second case, according to the theory of the dynamics of colloidal particles and flocculated suspensions, the yield stress should increase with the second or the third power of the volume ratio [6,38,7]. Iordan et al [20] measured τ (φ) to be proportional to φ 8.4 . They also find the dependence of the shear elastic modulus to vary like φ 11.6 , not very far from other recent results for weakly aggregated suspensions [32].…”

“…The internal stress then relaxes until an asymptotic value is reached. This phenomenon could be explained using relaxation combined with a yield stress, as observed with other types of yield stress fluids of rheological interest [20,32]. Therefore, models of viscoelastic behaviors coupled with a yield stress, although not yet much investigated, could be helpful in such cases [2,35,36].…”

“…The model is illustrated in Sections 2 and 3 and it is then applied to cell aggregates and compared to different experiments in Section 4. Steady shear is considered in Section 4.1 where the results are compared with relevant data [20], stress relaxation and oscillatory shear tests are discussed in Sections 4.2 and 4.3, elastic recovery after shear is illustrated in Section 4.4. In the last section, compression experiments taken from the literature [10,12,13,42] are re-considered in the framework of this new model.…”