Normalization of Blood Viscosity According to the Hematocrit and the Shear Rate

C. Trejo-Soto, A. Hernandez-Machado

View Publication

More ▾

In this article, we describe the general features of red blood cell membranes and their effect on blood flow and blood rheology. We first present a basic description of membranes and move forward to red blood cell membranes’ characteristics and modeling. We later review the specific properties of red blood cells, presenting recent numerical and experimental microfluidics studies that elucidate the effect of the elastic properties of the red blood cell membrane on blood flow and hemorheology. Finally, we describe specific hemorheological pathologies directly related to the mechanical properties of red blood cells and their effect on microcirculation, reviewing microfluidic applications for the diagnosis and treatment of these diseases.

Microfluidics approach to the mechanical properties of red blood cell membrane and their effect on blood rheology

C.Trejo-Soto, G.R. Lazaro, I. Pagonabarraga, A. Hernandez-Machado

View Publication

More ▾

In this article, we describe the general features of red blood cell membranes and their effect on blood flow and blood rheology. We first present a basic description of membranes and move forward to red blood cell membranes’ characteristics and modeling. We later review the specific properties of red blood cells, presenting recent numerical and experimental microfluidics studies that elucidate the effect of the elastic properties of the red blood cell membrane on blood flow and hemorheology. Finally, we describe specific hemorheological pathologies directly related to the mechanical properties of red blood cells and their effect on microcirculation, reviewing microfluidic applications for the diagnosis and treatment of these diseases.

Membrane rigidity regulates E. coli proliferation rates

S. Salinas-Almaguer, M. Mell, V.G. Almenro-Vedia, M. Calero, K.V. M. Robledo-Sanchez, J.C. Ruiz-Suarez, T. Alarcon, R. A. Barrio, A. Hernández-Machado, F. Monroy

View Publication

More ▾

Combining single cell experiments, population dynamics and theoretical methods of membrane mechanics, we put forward that the rate of cell proliferation in E. coli colonies can be regulated by modifiers of the mechanical properties of the bacterial membrane. Bacterial proliferation was modelled as mediated by cell division through a membrane constriction divisome based on FtsZ, a mechanically competent protein at elastic interaction against membrane rigidity. Using membrane fluctuation spectroscopy in the single cells, we revealed either membrane stiffening when considering hydrophobic long chain fatty substances, or membrane softening if short-chained hydrophilic molecules are used. Membrane stiffeners caused hindered growth under normal division in the microbial cultures, as expected for membrane rigidification. Membrane softeners, however, altered regular cell division causing persistent microbes that abnormally grow as long filamentous cells proliferating apparently faster. We invoke the concept of effective growth rate under the assumption of a heterogeneous population structure composed by distinguishable individuals with different FtsZ-content leading the possible forms of cell proliferation, from regular division in two normal daughters to continuous growing filamentation and budding. The results settle altogether into a master plot that captures a universal scaling between membrane rigidity and the divisional instability mediated by FtsZ at the onset of membrane constriction.

Blood rheological characterization of β-thalassemia trait and iron deficiency using front microrheometry

L.Mendez-Mora, M.Cabello-Fusares, J.Ferre-Torres, C.Riera-Llobet, E. Krishnevskaya, C.Trejo-Soto, S.Payan-Pernia, I.Hernandez Rodríguez, C.Morales Indiano, T. Alarcon, J.-Ll. Vives-Corrons, A.Hernandez-Machado

View Publication

More ▾

The purpose of this work is to develop a hematocrit-independent method for the detection of beta-thalassemia trait (β-TT) and iron deficiency anemia (IDA), through the rheological characterization of whole blood samples from different donors. The results obtained herein are the basis for the development of a front microrheometry point-of-care device for the diagnosis and clinical follow-up of β-TT patients suffering hematological diseases and alterations in the morphology of the red blood cell (RBC). The viscosity is calculated as a function of the mean front velocity by detecting the sample fluid-air interface advancing through a microfluidic channel. Different viscosity curves are obtained for healthy donors, β-TT and IDA samples. A mathematical model is introduced to compare samples of distinct hematocrit, classifying the viscosity curve patterns with respect to the health condition of blood. The viscosity of the fluid at certain shear rate values varies depending on several RBC factors such as shape and size, hemoglobin (Hb) content, membrane rigidity and hematocrit concentration. Blood and plasma from healthy donors are used as reference. To validate their potential clinical value as a diagnostic tool, the viscosity results are compared to those obtained by the gold-standard method for RBC deformability evaluation, the Laser-Optical Rotational Red Cell Analyzer (LoRRCA).

Pitting of malaria parasites in microfluidic devices mimicking spleen interendothelial slits

A. Elizalde-Torrent, C. Trejo-Soto, L. Mendez-Mora, , M. Nicolau, O. Ezama, M. Gualdron-Lopez , C. Fernandez-Becerra, T. Alarcon, A. Hernandez-Machado, H.A. del Portillo

View Publication

More ▾

The spleen is a hematopoietic organ that participates in cellular and humoral immunity. It also serves as a quality control mechanism for removing senescent and/or poorly deformable red blood cells (RBCs) from circulation. Pitting is a specialized process by which the spleen extracts particles, including malaria parasites, from within circulating RBCs during their passage through the interendothelial slits (IES) in the splenic cords. To study this physiological function in vitro, we have developed two microfluidic devices modeling the IES, according to the hypothesis that at a certain range of mechanical stress on the RBC, regulated through both slit size and blood flow, would force it undergo the pitting process without affecting the cell integrity. To prove its functionality in replicating pitting of malaria parasites, we have performed a characterization of P. falciparum-infected RBCs (P.f.-RBCs) after their passage through the devices, determining hemolysis and the proportion of once-infected RBCs (O-iRBCs), defined by the presence of a parasite antigen and absence of DAPI staining of parasite DNA using a flow cytometry-based approach. The passage of P.f.-RBCs through the devices at the physiological flow rate did not affect cell integrity and resulted in an increase of the frequency of O-iRBCs. Both microfluidic device models were capable to replicate the pitting of P.f.-RBCs ex vivo by means of mechanical constraints without cellular involvement, shedding new insights on the role of the spleen in the pathophysiology of malaria.

Red blood cell in low Reynolds number flow: a vorticity-based characterization of shapes in two dimensions

A.F. Gallen,M. Castro, A. Hernandez-Machado

View Publication

More ▾

Studies on the mechanical properties of red blood cells improve the diagnosis of some blood-related diseases. Some existing numerical methods have successfully simulated the coupling between a fluid and red blood cells. This paper introduces an alternative phase-field model formulation of two-dimensional cells that solves the vorticity and stream function that simplifies the numerical implementation. We integrate red blood cell dynamics immersed in a Poiseuille flow and reproduce previously reported morphologies (slippers or parachutes). In the case of flow in a very wide channel, we discover a new metastable shape referred to as ‘anti-parachute’ that evolves into a horizontal slipper centered on the channel. This sort of metastable morphology may contribute to the dynamical response of the blood.

Microrheometer for Biofluidic Analysis: Electronic Detection of the Fluid-Front Advancement

Lourdes Méndez Mora, Maria Cabello Fusarés, Josep Ferré Torres, Carla Riera Llobet, Samantha López, Claudia Trejo Soto, Tomas Alarcón & Aurora Hernández-Machado

View Publication

More ▾

The motivation for this study was to develop a microdevice for the precise rheological characterization of biofluids, especially blood. The method presented was based on the principles of rheometry and fluid mechanics at the microscale. Traditional rheometers require a considerable amount of space, are expensive, and require a large volume of sample. A mathematical model was developed that, combined with a proper experimental model, allowed us to characterize the viscosity of Newtonian and non?Newtonian fluids at different shear rates. The technology presented here is the basis of a point?of?care device capable of describing the nonlinear rheology of biofluids by the fluid/air interface front velocity characterization through a microchannel. The proposed microrheometer uses a small amount of sample to deliver fast and accurate results, without needing a large laboratory space. Blood samples from healthy donors at distinct hematocrit percentages were the non?Newtonian fluid selected for the study. Water and plasma were employed as testing Newtonian fluids for validation of the system. The viscosity results obtained for the Newtonian and non?Newtonian fluids were consistent with pertinent studies cited in this paper. In addition, the results achieved using the proposed method allowed distinguishing between blood samples with different characteristics.

Dipole–dipole interactions control the interfacial rheological response of cyclodextrin/ surfactant solutions

J. Roberto Romero-Arias, Alberto S. Luviano, Miguel Costas, Aurora Hernández-Machado & Rafael A. Barrio

View Publication

More ▾

Recent surface rheological study has shown that aqueous solutions of a-cyclodextrin (aCD) with anionic surfactants (S) display a remarkable viscoelasticity at the liquid/air interface, which has not been observed in similar systems. The dilatational modulus is various orders of magnitude larger than those for the binary mixtures aCD + water and S + water. The rheological response has been qualitatively related to the bulk distribution of species, the 2 : 1 inclusion complexes (aCD2 : S) playing a fundamental role. In this work, we have developed a model that considers dipole–dipole interactions between 2 : 1 inclusion complexes ordered on the liquid/air interface. When the model is applied to the specific experimental conditions, the dependencies on concentration and temperature of the dilatational modulus and the surface tension were found to be in excellent agreement with the data, indicating clearly that dipole–dipole interactions determine and control the rheological behavior of the interface.

On Gaussian curvature and membrane fission

Mara Denisse Rueda-Contreras, Andreu F. Gallen, J. Roberto Romero-Arias, Aurora Hernandez-Machado & Rafael A. Barrio

View Publication

More ▾

We propose a three-dimensional mathematical model to describe dynamical processes of membrane fission. The model is based on a phase field equation that includes the Gaussian curvature contribution to the bending energy. With the addition of the Gaussian curvature energy term numerical simulations agree with the predictions that tubular shapes can break down into multiple vesicles. A dispersion relation obtained with linear analysis predicts the wavelength of the instability and the number of formed vesicles. Finally, a membrane shape diagram is obtained for the different Gaussian and bending modulus, showing different shape regimes.

An integrated detection method for flow viscosity measurements in microdevices

Angeles Ivon Rodriguez-Villarreal, Laura Ortega Taña, Joan Cid, Aurora Hernández-Machado, Tomas Alarcon, Pere Miribel-Catala, Jordi Colomer-Farrarons

View Publication

More ▾

Point-of-care devices can analyze or characterize a sample in a short time. New technologies in medical science seek integrations of different measurement techniques for a complete analysis. This study describes the fabrication method, tests, and results of microtechnology as an approach for an integrated rheometer. The portable device measured the average flow velocity to calculate its viscosity. The whole system encompasses a microdevice integrated to a data acquisition system powered by USB and controlled by full custom software. As a result, we obtained an easy-to-handle and fabricate hand-held microrheometer. The device was tested using Newtonian fluids such as Mili-Q water, an aqueous solution of Ethyleneglycol at 40% and 25% and Non-Newtonian blood samples. The whole device can provide the non-linear viscosity of a 0.08 ml blood sample in less than 30 seconds, in a wide range of shear rate with an accuracy of 93%. More importantly, due to its detection method and simplicity, it can be enclosed within almost any fluidic microsystem, including biomedical applications.

The dynamics of shapes of vesicles membranes with time dependent spontaneous curvature

R.A. Barrio, T. Alarcon, A. Hernández-Machado

View Publication

More ▾

We study the time evolution of the shape of a vesicle membrane under time-dependent spontaneous curvature by means of phase-field model. We introduce the variation in time of the spontaneous curvature via a second field which represents the concentration of a substance that anchors with the lipid bilayer thus changing the local curvature and producing constriction. This constriction is mediated by the action on the membrane of an structure resembling the role of a Z ring. Our phase-field model is able to reproduce a number of different shapes that have been experimentally observed. Different shapes are associated with different constraints imposed upon the model regarding conservation of membrane area. In particular, we show that if area is conserved our model reproduces the so-called L-form shape. By contrast, if the area of the membrane is allowed to grow, our model reproduces the formation of a septum in the vicinity of the constriction. Furthermore, we propose a new term in the free energy which allows the membrane to evolve towards eventual pinching.

Coaxial flow focusing microfluidic devices: Experiments and theory

R. Rodriguez-Trujillo, Y-H. Kim-Im, A. Hernández-Machado

View Publication

More ▾

A coaxial flow focusing PDMS (polydimethylsiloxane) microfluidic device has been designed and manufactured by soft lithography in order to experimentally study a miscible inner flow. We studied a coaxially focused inner flow (formed by an aqueous fluorescein solution) which was fully isolated from all microchannel surfaces by an additional water outer flow. Different flow rates were used to produce a variety of flow ratios and a 3D reconstruction of the cross-section was performed using confocal microscope images. The results showed an elliptical section of the coaxially focused inner flow that changes in shape depending on the flow rate ratio applied. We have also developed a mathematical model that allows us to predict and control the geometry of the coaxially focused inner flow.

Enhanced imbibitions from cooperation between wetting and inertia via pulsatile forcing

J. Flores Gerónimo , A. Hernández-Machado E. Corvera Poire

View Publication

More ▾

We study the dynamics of microfluidic interfaces driven by pulsatile pressures in the presence of neutral and hydrophilic walls. For this, we propose a new phase field model that takes inertia into account. For neutral wetting, the interface dynamics is characterized by a response function that depends on a non-dimensional frequency, which involves the time scale associated with inertia. We have found a regime, for large values of this non-dimensional frequency, in which inertia is relevant, and our model is necessary for a correct description of the dynamics. For hydrophilic walls, the dynamics of the contact line with pulsatile forcing is basically undistinguishable to the dynamics of imbibition solely due to wetting. However, we observe that the presence of inertia causes the interface to advance faster than in the absence of pulsatile forcing. This is because pulsatile forcing induces inertia at the bulk to cooperate with wetting creating an enhancement of the imbibition process. We characterize this complex dynamics with transitory exponents that, at early times, are larger than the Washburn ones, and tend to the Washburn exponent at long times, when the interface feels less and less the driving force applied at the entrance of the microchannel, and the dynamics is dominated solely by wetting.

Collective behavior of red blood cells in confined channels

G.R. Lazaro, A. Hernández-Machado, I. Pagonabarraga

View Publication

More ▾

We study the flow properties of red blood cells in confined channels, when the channel width is comparable to the cell size. We focus on the case of intermediate concentrations when hydrodynamic interactions between cells play a dominant role. This regime is different to the case of low concentration in which the cells behave as hydrodynamically isolated. In this last case, the dynamic behavior is entirely controlled by the interplay between the interaction with the wall and the elastic response of the cell membrane. Our results highlight the different fluid properties when collective flow is present. The cells acquire a characteristic slipper shape, and parachute shapes are only observed at very large capillary numbers. We have characterized the spatial ordering and the layering by means of a pairwise correlation function. Focusing effects are observed at the core of the channel instead of at the lateral position typical of the single-train case. These results indicate that at these intermediate concentrations we observed at the microscale the first steps of the well-known macroscopic Fahraeus-Lindqvist effect. The rheological properties of the suspension are studied by means of the effective viscosity, with an expected shear-thinning behavior. Two main differences are obtained with respect to the single-train case. First, a large magnitude of the viscosity is obtained indicating a high resistance to flow. Secondly, the shear-thinning behavior is obtained at larger values of the capillary number respect to the single-train case. These results suggest that the phenomena of ordering in space and orientation occur at higher values of the capillary number.

Front Microrheology of Biological Fluids

C. Trejo-Soto, E. Costa-Miracle, I. Rodríguez-Villarreal, J. Cid, M. Castro, T. Alarcón, A. Hernández-Machado

View Publication

More ▾

We present a study of front microrheology through the development of a microfluidic device and method that describes accurately the non-linear rheology of blood, by means of a simple optical detection method based on tracking the fluid-air interface moving inside a microchannel. We study the behavior of Newtonian fluids of different viscosities and densities, as well, we performed measures for blood at different red blood cells concentration and at different days from its extraction. We have developed a scaling method which allows us to determine a relation between the red blood cell properties at different days from its extraction, according to the agreggation properties of red blood cell. Our results have been compared with theoretical and bibliographical results, which shows realiable results with an error around 6%. In general, our device and method is usefull as a viscometer and rheometer, as well as, it enables to establish a relation between blood viscosity and its red blood cells characteristics.

Front microrheology of the non-Newtonian behaviour of blood: scaling theory of erythrocyte aggregation by aging

C. Trejo-Soto, E. Costa-Miracle, I. Rodriguez-Villarreal, J. Cid, M. Castro, T. Alarcón, A. Hernández-Machado

View Publication

More ▾

We introduce a new framework to study the non-Newtonian behaviour of fluids at the microscale based on the analysis of front advancement. We apply this methodology to study the non-linear rheology of blood in microchannels. We carry out experiments in which the non-linear viscosity of blood samples is quantified at different haematocrits and ages. Under these conditions, blood exhibits a power-law dependence on the shear rate. In order to analyse our experimental data, we put forward a scaling theory which allows us to define an adhesion scaling number. This theory yields a scaling behaviour of the viscosity expressed as a function of the adhesion capillary number. By applying this scaling theory to samples of different ages, we are able to quantify how the characteristic adhesion energy varies as time progresses. This connection between microscopic and mesoscopic properties allows us to estimate quantitatively the change in the cell–cell adhesion energies as the sample ages.

Elastic and dynamic properties of membrane phase-field models

Guillermo R. Lázaro, I. Pagonabarraga, A. Hernández-Machado

View Publication

More ▾

Phase-field models have been extensively used to study interfacial phenomena, from solidification to vesicle dynamics. In this article, we analyze a phase-field model that captures the relevant physical features that characterize biological membranes. We show that the Helfrich theory of elasticity of membranes can be applied to phase-field models, allowing to derive the expressions of the stress tensor, lateral stress profile and elastic moduli. We discuss the relevance and interpretations of these magnitudes from a phase-field perspective. Taking the sharp-interface limit we show that the membrane macroscopic equilibrium equation can be derived from the equilibrium condition of the phase-field interface. We also study two dynamic models that describe the behaviour of a membrane. From the study of the relaxational behaviour of the membrane we characterize the relevant dynamics of each model, and discuss their applications.

Capillary Filling at the Microscale: Control of Fluid Front Using Geometry

C. Trejo-Soto, E. Costa-Miracle, I. Rodríguez-Villarreal, J. Cid, T. Alarcón, A. Hernández-Machado

View Publication

More ▾

We propose an experimental and theoretical framework for the study of capillary filling at the micro-scale. Our methodology enables us to control the fluid flow regime so that we can characterise properties of Newtonian fluids such as their viscosity. In particular, we study a viscous, non-inertial, non-Washburn regime in which the position of the fluid front increases linearly with time for the whole duration of the experiment. The operating shear-rate range of our apparatus extends over nearly two orders of magnitude. Further, we analyse the advancement of a fluid front within a microcapillary in a system of two immiscible Newtonian liquids. We observe a non-Washburn regime in which the front can accelerate or decelerate depending on the viscosity contrast between the two liquids. We then propose a theoretical model which enables us to study and explain both non-Washburn regimes. Furthermore, our theoretical model allows us to put forward ways to control the emergence of these regimes by means of geometrical parameters of the experimental set-up. Our methodology allows us to design and calibrate a micro-viscosimetre which works at constant pressure.

Phase-field modelling of the dynamics of Z-ring formation in liposomes: Onset of constriction and coarsening

C. B. Picallo, R. A. Barrio, C. Varea, T. Alarcón, A. Hernández-Machado

View Publication

More ▾

We propose a model for the dynamics of the formation of rings of FtsZ on tubular liposomes which produce constriction on the corresponding membrane. Our phase-field model is based on a simple bending energy that captures the dynamics of the interplay between the protein and the membrane. The short-time regime is analyzed by a linear dispersion relation, with which we are able to predict the number of rings per unit length on a tubular liposome. We study numerically the long-time dynamics of the system in the non-linear regime where we observe coarsening of Z-rings on tubular liposomes. In particular, our numerical results show that, during the coarsening process, the number of Z-rings decreases as the radius of tubular liposome increases. This is consistent with the experimental observation that the separation between rings is proportional to the radius of the liposome. Our model predicts that the mechanism for the increased rate of coarsening in liposomes of larger radius is a consequence of the increased interface energy.

Superconfinement tailors fluid flow at micro-scales

Siti Aminah Setu, Roel P. A. Dullens, Aurora Hernández-Machado, Ignacio Pagonabarraga, Dirk G. A. L. Aarts, Rodrigo Ledesma-Aguilar

View Publication

More ▾

Understanding fluid dynamics under extreme confinement, where device and intrinsic fluid length scales become comparable, is essential to successfully develop the coming generations of fluidic devices. Here we report measurements of advancing fluid fronts in such a regime, which we dub superconfinement. We find that the strong coupling between contact-line friction and geometric confinement gives rise to a new stability regime where the maximum speed for a stable moving front exhibits a distinctive response to changes in the bounding geometry. Unstable fronts develop into drop-emitting jets controlled by thermal fluctuations. Numerical simulations reveal that the dynamics in superconfined systems is dominated by interfacial forces. Henceforth, we present a theory that quantifies our experiments in terms of the relevant interfacial length-scale, which in our system is the intrinsic contact-line slip length. Our findings show that length-scale overlap can be used as a new fluid-control mechanism in strongly confined systems.