Microchemostat-microbial continuous culture in a polymer-based, instrumented microbioreactor

In a chemostat, microbial cells reach a steady state condition at which cell biomass production, substrates and the product concentrations remain constant. These features make continuous culture a unique and powerful tool for biological and physiological research. We present a polymer-based microbioreactor system integrated with optical density (OD), pH, and dissolved oxygen (DO) real-time measurements for continuous cultivation of microbial cells. Escherichia coli (E. coli) cells are continuously cultured in a 150 microL, membrane-aerated, well-mixed microbioreactor fed by a pressure-driven flow of fresh medium through a microchannel. Chemotaxisial back growth of bacterial cells into the medium feed channel is prevented by local heating. Using poly(ethylene glycol) (PEG)-grafted poly(acrylic acid) (PAA) copolymer films, the inner surfaces of poly(methyl methacrylate) (PMMA) and poly(dimethylsiloxane) (PDMS) of the microbioreactor are modified to generate bio-inert surfaces resistant to non-specific protein adsorption and cell adhesion. The modified surfaces of microbioreactor effectively reduce wall growth of E. coli for a prolonged period of cultivation. Steady state conditions at different dilution rates are demonstrated and characterized by steady OD, pH, and DO levels.     

Production of reactive oxygen species in endothelial cells under different pulsatile shear stresses and glucose concentrations

A hemodynamic Lab-on-a-chip system was developed in this study. This system has two unique features: (1) it consists of a microfluidic network with an array of endothelial cell seeding sites for testing them under multiple conditions, and (2) the flow rate and the frequency of the culture medium in the microchannel are controlled by a pulsation free pump to mimic the flow profile of the blood in the blood vessel under different physiological conditions. The investigated physiological conditions were: (1) the resting condition in a normal shear stress of 15 dyne cm(-2) with a normal heart rate of 70 bpm, (2) an exhaustive exercise condition with a high shear stress of 30 dyne cm(-2) and a fast heart rate of 140 bpm, and (3) a constant high shear stress of 30 dyne cm(-2). Two chemical conditions were investigated (10 mM and 20 mM glucose) to mimic hyperglycemic conditions in diabetes patients. The effects of various shear stresses either alone or in combination with different glucose concentrations on endothelial cells were examined using the developed hemodynamic Lab-on-a-chip system by assessing two parameters. One is the intracellular level of reactive oxygen species (ROS) determined by a fluorescent probe, H(2)DCFDA. Another is the mitochondrial morphology revealed with a fluorescent dye, MitoTracker Green FM. The results showed that ROS level was elevated nearly 4-fold after 60 min of exhaustive exercise. We found that the pulsatile nature of the fluid was the determination factor for causing ROS generation in the cells as almost no increase of ROS was detected in the constant shear stress condition. Similarly, much higher level of ROS was detected when 10 mM glucose was applied to the cells under normal or high pulsatile shear stresses compared with under a static condition. These results suggest that it is necessary to use pulsatile shear stress to represent the physiological conditions of the blood flow, and demonstrate the advantage of utilizing this newly developed hemodynamic Lab-on-a-chip system over the conventional non-pulsatile system in the future shear stress related studies.     

Microfluidic arrays for logarithmically perfused embryonic stem cell culture

We present a microfluidic device for culturing adherent cells over a logarithmic range of flow rates. The device sets flow rates through four separate cell-culture chambers using syringe-driven flow and a network of fluidic resistances. The design is easy to fabricate with no on-chip valves and is scalable both in the number of culture chambers as well as in the range of applied flow rates. Using particle velocimetry, we have characterized the flow-rate range. We have also demonstrated an extension of the design that combines the logarithmic flow-rate functionality with a logarithmic concentration gradient across the array. Using fluorescence measurements we have verified that a logarithmic concentration gradient was established in the extended device. Compared with static cell culture, both devices enable greater control over the soluble microenvironment by controlling the transport of molecules to and away from the cells. This approach is particularly relevant for cell types such as embryonic stem cells (ESCs) which are especially sensitive to the microenvironment. We have demonstrated for the first time culture of murine ESCs (mESCs) in continuous, logarithmically scaled perfusion for 4 days, with flow rates varying >300x across the array. Cells grown in the slowest flow rate did not proliferate, while colonies grown in higher flow rates exhibited healthy round morphology. We have also demonstrated logarithmically scaled continuous perfusion culture of 3T3 fibroblasts for 3 days, with proliferation at all flow rates except the slowest rate.     

Patterning of a random copolymer of poly[lactide-co-glycotide-co-(epsilon-caprolactone)] by UV embossing for tissue engineering

The random copolymer, poly[lactide-co-glycotide-co-(epsilon-caprolactone)] (PLGACL) diacrylate was prepared by ring-opening polymerization of L-lactide, glycolide, and epsilon-caprolactone initiated with tetra(ethylene glycol). The diacrylated polymers were extensively characterized. With a UV embossing method, these copolymers were successfully fabricated into microchannels separated by microwalls with a high aspect (height/width) ratio. The PLGACL network films showed good cytocompatibility. Varieties of microstructures were fabricated, such as 10 x 40 x 60, 10 x 80 x 60, 25 x 40 x 60, or 25 x 80 x 60 microm(3) structures (microwall width x microchannel width x microwall height). The results demonstrated that smooth muscle cells (SMCs) can grow not only on the microchannel surfaces but also on the surfaces of the microwall and sidewall. The SMCs aligned along the 25 microm wide microwall with an elongated morphology and proliferated very slowly in comparison to those on the smooth surface with a longer cell-culture term. Few cells could attach and spread on the surface of the 40 microm wide microchannel, while the cells flourished on the 80 microm, or more than 80 microm, wide microchannel with a spindle morphology. The biophysical mechanism mediated by the micropattern geometry is discussed. Overall, the present micropattern, consisting of biodegradable and cytocompatible PLGACL, provides a promising scaffold for tissue engineering.     

Diffusion dependent cell behavior in microenvironments

Understanding the interaction between soluble factors and cells in the cellular microenvironment is critical to understanding a wide range of diseases. Microchannel culture systems provide a tool for separating diffusion and convection based transport making possible controlled studies of the effects of soluble factors in the cellular microenvironment. In this paper we compare the proliferation kinetics of cells in traditional culture flasks to those in microfluidic channels, and explore the relationship between microchannel geometry and cell proliferation. PDMS (polydimethylsiloxane) microfluidic channels were fabricated using micromolding methods. Fall armyworm ovarian cells (Sf9) were homogeneously seeded in a series of different sized microchannels and cultured under a no flow condition. The proliferation rates of Sf9 cells in all of the microchannels were slower than in the flask culture over the first 24 h of culture. The proliferation rates in the microchannels then continuously decreased reaching 5% of that in the flasks over the next 48 h and maintained this level for 5 days. This growth inhibition was reversible and influenced only by the cell seeding density and the channel height but not the channel length or width. One possible explanation for the observed dimension-dependent cell proliferation is the accumulation of different functional molecules in the diffusion dominant microchannel environment. This study provides insights into the potential effects of the diffusion of soluble factors and related effects on cell behavior in microenvironments relevant to the emerging use of microchannel culture systems.     

微流控芯片中细胞动态胞吞二氧化硅纳米颗粒的研究

研究了用微流控芯片在体外模拟人体血液流动状态下细胞胞吞二氧化硅纳米粒子的方法和特性. 通过调节储液池的液面差, 使细胞从微通道入口流入并在通道内沉积贴壁生长. 将含有贴壁细胞的微流控芯片放入37 ℃/体积分数5%CO₂的培养箱中, 使细胞培养液连续流过贴壁细胞. 培养24 h后, 在流动的培养液中加入作为荧光标记物的500 nm 粒径的掺杂有异硫氰酸荧光素(FITC)的二氧化硅微球(MSN), 继续培养6 h后, 用荧光显微镜测定细胞胞吞二氧化硅纳米粒子后的荧光强度, 考察了不同流速下细胞对二氧化硅微球摄入量的影响. 结果表明, 在动态条件下, 细胞对二氧化硅微球的吞噬量明显下降, 当流速从0.022 mm/s 增加至0.74 mm/s时, 吞噬量从静态测得值的74.7%下降至7.1%.     

A practical guide to microfluidic perfusion culture of adherent mammalian cells

Culturing cells at microscales allows control over microenvironmental cues, such as cell-cell and cell-matrix interactions; the potential to scale experiments; the use of small culture volumes; and the ability to integrate with microsystem technologies for on-chip experimentation. Microfluidic perfusion culture in particular allows controlled delivery and removal of soluble biochemical molecules in the extracellular microenvironment, and controlled application of mechanical forces exerted via fluid flow. There are many challenges to designing and operating a robust microfluidic perfusion culture system for routine culture of adherent mammalian cells. The current literature on microfluidic perfusion culture treats microfluidic design, device fabrication, cell culture, and micro-assays independently. Here we systematically present and discuss important design considerations in the context of the entire microfluidic perfusion culture system. These design considerations include the choice of materials, culture configurations, microfluidic network fabrication and micro-assays. We also present technical issues such as sterilization; seeding cells in both 2D and 3D configurations; and operating the system under optimized mass transport and shear stress conditions, free of air-bubbles. The integrative and systematic treatment of the microfluidic system design and fabrication, cell culture, and micro-assays provides novices with an effective starting point to build and operate a robust microfludic perfusion culture system for various applications.     

Effects of flow and diffusion on chemotaxis studies in a microfabricated gradient generator

An understanding of chemotaxis at the level of cell-molecule interactions is important because of its relevance in cancer, immunology, and microbiology, just to name a few. This study quantifies the effects of flow on cell migration during chemotaxis in a microfluidic device. The chemotaxis gradient within the device was modeled and compared to experimental results. Chemotaxis experiments were performed using the chemokine CXCL8 under different flow rates with human HL60 promyelocytic leukemia cells expressing a transfected CXCR2 chemokine receptor. Cell trajectories were separated into x and y axis components. When the microchannel flow rates were increased, cell trajectories along the x axis were found to be significantly affected (p < 0.05). Total migration distances were not affected. These results should be considered when using similar microfluidic devices for chemotaxis studies so that flow bias can be minimized. It may be possible to use this effect to estimate the total tractile force exerted by a cell during chemotaxis, which would be particularly valuable for cells whose tractile forces are below the level of detection with standard techniques of traction-force microscopy.     

Oxygen consumption of cell suspension in a poly(dimethylsiloxane) (PDMS) microchannel estimated by scanning electrochemical microscopy

A quantitative analysis of the oxygen concentration profile near a poly(dimethylsiloxane) (PDMS) microfluidic device was performed using scanning electrochemical microscopy (SECM). A microchannel filled with sodium sulfite (Na(2)SO(3)) aqueous solution was imaged by SECM, showing that the oxygen diffusion layer of the PDMS microchannel was observed to be hemicylindrical. Based on a theoretical analysis of the hemicylindrical diffusion layer of the microchannel, the total oxygen mass transfer rates of oxygen to the PDMS microchannel filled with the Na(2)SO(3) solution was calculated to be (4.01 +/- 0.30) x 10(-12) mol s(-1). This is the maximum value of the oxygen transfer rate for this PDMS microchannel device. The oxygen consumption rate increased almost linearly with the logarithm of the concentration of E. coli cells (10(6) approximately 10(8) cells). The respiratory activity for a single E. coli cell was estimated to be approximately 4.31 x 10(-20) mol s(-1) cell(-1).     

Development of a microfluidic platform for single-cell secretion analysis using a direct photoactive cell-attaching method

A precise understanding of individual cellular processes is essential to meet the expectations of most advanced cell biology. Therefore single-cell analysis is considered to be one of possible approach to overcome any misleading of cell characteristics by averaging large groups of cells in bulk conditions. In the present work, we modified a newly designed microchip for single-cell analysis and regulated the cell-adhesive area inside a cell-chamber of the microfluidic system. By using surface-modification techniques involving a silanization compound, a photo-labile linker and the 2-methacryloyloxyethyl phosphorylcholine (MPC) polymer were covalently bonded on the surface of a microchannel. The MPC polymer was utilized as a non-biofouling compound for inhibiting non-specific binding of the biological samples inside the microchannel, and was selectively removed by a photochemical reaction that controlled the cell attachment. To achieve the desired single-macrophage patterning and culture in the cell-chamber of the microchannel, the cell density and flow rate of the culture medium were optimized. We found that a cell density of 2.0 × 10(6) cells/ml was the appropriate condition to introduce a single cell in each cell chamber. Furthermore, the macrophage was cultured in a small size of the cell chamber in a safe way for 5 h at a flow rate of 0.2 μl/min under the medium condition. This strategy can be a powerful tool for broadening new possibilities in studies of individual cellular processes in a dynamic microfluidic device.     

A pumpless cell culture chip with the constant medium perfusion-rate maintained by balanced droplet dispensing

This paper presents a pumpless cell culture chip, where a constant-rate medium perfusion is achieved by balanced droplet dispensing. Previous pumpless cell culture chips, where the gravity-driven flow is induced by gradually decreasing the hydraulic-head difference, Δh, between source and drain reservoirs, result in a decreasing perfusion-rate. However, the present pumpless cell culture chip, where autonomous droplet dispensers are integrated on the source reservoirs, results in a constant perfusion-rate using a constant Δh maintained by balanced droplet dispensing between the source-inlet and the drain-outlet. In the experimental study, constant perfusion-rates of 0.1, 0.2, and 0.3 μl min(-1) are obtained by Δh of 38, 76, and 114 mm, respectively. At the constant perfusion-rate (Q=0.2 μl min(-1)), H358 lung cancer cells show the maximum growth-rate of 57.8 ± 21.1% d(-1), which is 1.9 times higher than the 30.2 ± 10.3% d(-1) of the static culture. At a perfusion-rate varying between 0.1-0.3 μl min(-1) (average=0.2 μl min(-1)), however, the H358 cells show a growth-rate of 46.9 ± 8.3% d(-1), which is lower than that of the constant Q of 0.2 μl min(-1). The constant-rate perfusion culture (Q=0.1, 0.2, and 0.3 μl min(-1)) also results in an average cell viability of 89.2%, which is higher than 75.9% of the static culture. This pumpless cell culture chip offers a favorable environment to cells with a high growth-rate and viability, thus having potential for use in cell-based bio-assays.     

Understanding microchannel culture: parameters involved in soluble factor signaling

While the importance of autocrine-paracrine signaling in vivo is clear, the ability to study the effects of secreted endogenous factors in vitro is hampered by canonical culture platforms. In multi-well plates, the large air-liquid interface gives rise to convective flows that continually mix the fluid disrupting the local diffusion-based accumulation. Simple microchannels provide a more controlled microenvironment that can be used to study secreted factor effects. Here, we utilize microchannel culture to examine basic culture parameters and their interactions using normal mammary gland epithelial cells (NMuMG). The following parameters were studied: (1) cell density (80 vs. 240 cells mm(-2)), (2) exogenous growth factors (epidermal growth factor [EGF] vs. fetal bovine serum), (3) medium change frequency (1 h, 4 h, 12 h), and (4) culture platform (microchannels vs. 96-well plates). The cells exhibited increased growth rates in microchannels as compared to 96-well plates. Cell proliferation increased as the frequency of media change decreased. For the microchannel geometries used, important threshold concentrations were reached in a few hours. In aggregate, the results indicate that the function of the four factors and their interactions on NMuMG growth are spatially and temporally related by molecular diffusion in the controlled microchannel space. The convective-free microchannel environment may prove useful for studying soluble factor signaling in vitro, and to test models and predictions of autocrine-paracrine signaling.     

Development of an osteoblast-based 3D continuous-perfusion microfluidic system for drug screening

In this work, we demonstrated that biological cells could be cultured in a continuous-perfusion glass microchip system for drug screening. We used mouse Col1a1GFP MC-3T3 E1 osteoblastic cells, which have a marker gene system expressing green fluorescent protein (GFP) under the control of osteoblast-specific promoters. With our microchip-based cell culture system, we realized automated long-term monitoring of cells and sampling of the culture supernatant system for osteoblast differentiation assay using a small number of cells. The system successfully monitored cells for 10 days. Under the 3D microchannel condition, shear stress (0.07 dyne/cm² at a flow rate of 0.2 μL/min) was applied to the cells and it enhanced the GFP expression and differentiation of the osteoblasts. Analysis of alkaline phosphatase (ALP), which is an enzyme marker of osteoblasts, supported the results of GFP expression. In the case of differentiation medium containing bone morphogenetic protein 2, we found that ALP activity in the culture supernatant was enhanced 10 times in the microchannel compared with the static condition in 48-well dishes. A combined system of a microchip and a cell-based sensor might allow us to monitor osteogenic differentiation easily, precisely, and noninvasively. Our system can be applied in high-throughput drug screening assay for discovering osteogenic compounds.     

Patterning cells and shear flow conditions: convenient observation of endothelial cell remoulding, enhanced production of angiogenesis factors and drug response

We present a method that allows patterning cells and shear flow conditions for endothelial cell based assays. This method is novel in combining (1) cell culture on the surface of a substrate both topographically and chemically patterned; (2) multi-shear flow assays after covering the cell substrate with a microfluidic cover plate containing microchannels of different channel widths, and (3) conventional immunostaining assays after removal of the cover plate. This method has the advantage of performing cell cultures and immunoassays in standard cell biology environments with open access, facilitating the formation of confluent cell layers and the observation of cell responses to shear-flow and drug stimulations. To obtain multi-shear stress conditions, a single channel with stepwise increasing channel widths was patterned on the surfaces of both the substrate and the microfluidic cover plate. As results, we observed excellent viability of endothelial cells in the whole range of applied shear stresses (0-25 dyn cm(-2)) and shear stress dependent cytoskeleton remoulding, activation of von Willebrand factor (vWF), and re-organisation of angiogenesis factors such as tetra peptide acetyl-Ser-Asp-Lys-Pro (AcSDKP) of endothelial cells. To validate this approach for drug analysis, we also studied drug effects under shear stress conditions. Our results indicate that the drug effect of combretastatin A-4, an anti-tumour vascular targeting drug, could be significantly enhanced under shear flow conditions.     

Importance of dynamic culture for evaluating osteoblast activity on dense silicon-substituted hydroxyapatite

This paper reports an investigation on human osteoblast-like cells (SaOs-2) seeded onto pure hydroxyapatite (HA) and silicon-substituted HA (SiHA) tablets under static and dynamic culture conditions. The biological characterizations were conducted in classical static conditions in multi-wells plates, and in a perfusion bioreactor that permits continuous circulation of culture medium at 2 mL/h. The morphology, proliferation and differentiation of osteoblastic cells were examined for the two types of samples in the both culture conditions after 1, 3 and 8 days. Under dynamic conditions, cells cultured on SiHA surfaces showed a faster adhesion process and the formation of longer and thinner focal adhesions than in static conditions. The number of cells grown onto both ceramic surfaces was higher in dynamic conditions when compared with static conditions. Moreover, a higher activity of alkaline phosphatase was found for cells seeded under dynamic conditions. Our findings suggest that the application of perfusion culture system on cells cultured on dense substrates is valuable for predicting in vivo behaviour of cells on biomaterials.     

Cell receptor and surface ligand density effects on dynamic states of adhering circulating tumor cells

Dynamic states of cancer cells moving under shear flow in an antibody-functionalized microchannel are investigated experimentally and theoretically. The cell motion is analyzed with the aid of a simplified physical model featuring a receptor-coated rigid sphere moving above a solid surface with immobilized ligands. The motion of the sphere is described by the Langevin equation accounting for the hydrodynamic loadings, gravitational force, receptor-ligand bindings, and thermal fluctuations; the receptor-ligand bonds are modeled as linear springs. Depending on the applied shear flow rate, three dynamic states of cell motion have been identified: (i) free motion, (ii) rolling adhesion, and (iii) firm adhesion. Of particular interest is the fraction of captured circulating tumor cells, defined as the capture ratio, via specific receptor-ligand bonds. The cell capture ratio decreases with increasing shear flow rate with a characteristic rate. Based on both experimental and theoretical results, the characteristic flow rate increases monotonically with increasing either cell-receptor or surface-ligand density within certain ranges. Utilizing it as a scaling parameter, flow-rate dependent capture ratios for various cell-surface combinations collapse onto a single curve described by an exponential formula.     

Direct measurement of the impact of impaired erythrocyte deformability on microvascular network perfusion in a microfluidic device

The ability of red blood cells (RBCs, erythrocytes) to deform and pass through capillaries is essential for continual flow of blood in the microvasculature, which ensures an adequate supply of oxygen and nutrients, prompt removal of metabolic waste products, transport of drugs and hormones, and traffic of circulating cells to and from all living tissues. This paper presents a novel tool for evaluating the impact of impaired deformability of RBCs on the flow of blood in the microvasculature by directly measuring perfusion of a test microchannel network with dimensions and topology similar to the real microcirculation. The measurement of microchannel network perfusion is compared with RBC filtration -- a conventional assay of RBC deformability. In contrast to RBC filterability, network perfusion depends linearly on RBC deformability modulated by graded exposure to glutaraldehyde, showing a higher sensitivity to small changes of deformability. The direct measurement of microchannel network perfusion represents a new concept for the field of blood rheology and should prove beneficial for basic science and clinical applications.     

Electrically induced colloidal clusters for generating shear mixing and visualizing flow in microchannels

When aqueous suspensions of 1 μm, negatively charged polystyrene particles are subject to a 1 kHz alternating electric field of strength greater than 7 kV(rms) m(-1), dynamic elliptical clusters of particles spontaneously form. With potential applications in microchannel fluidics in mind, we characterize how cluster formation and particle circulation, driven by induced dipole-dipole interactions, is critically dependent on time, field strength, electrolyte concentration, and cell thickness. Logarithmic growth of cluster size is observed, and particle velocity within the clusters is found to be proportional to cluster length. Increasing cell thickness from 10 to 60 μm increases the projected cluster area but decreases cluster aspect ratio as the result of changing particle dispersal rates. Clusters are shown to generate significant fluid shear suitable for microchannel mixing applications. These clusters are observed to distort under transverse fluid flow and, above a critical flow rate, to undergo a transition to form regularly spaced particle streams, which may be suitable for two-dimensional visualization of fluid flow.     

Traction force microscopy on-chip: shear deformation of fibroblast cells

We develop here a microfabrication compatible force measurement technique termed as ultrasoft polydimethylsiloxane-based traction force microscopy (UPTFM). This technique is devised for mapping the cellular traction forces imparted on the adhering substrate, so as to depict the physiological state of the cells surviving in the micro-confinement. We subsequently integrate the technique with a microfluidic platform for evaluating different states of stress in adherent mouse skin fibroblast L929 cells. Utilizing this technique, we monitor the spatio-temporal evolution of cellular traction forces for static incubation periods with no media replenishment as well as for dynamic flow conditions that inherently induce cell deformation and detachment. While the studies conducted on a quiescent fluid medium enable us to obtain an optimal static cell incubation period, those executed under dynamic flow conditions provide us with the minuscule details of the cellular response, deformation and detachment processes. We elucidate the correlation between shear activated cytosolic calcium ion release profile and the local traction forces as an attempt to apply UPTFM in the domain of functional biological purposes. Pertinently, we map the centroidal displacement and the maximum traction stress in characterizing the critical shear rate conditions for the onset of the cell peeling-off process, and demonstrate their contrasting features in comparison to the vesicle lift off processes in a shear flow. Theoretically, these deviations can only be explained by taking physiologically relevant cell adhesion models into consideration, which, while retaining the intrinsic simplicity, are able to reproduce the key experimental outcomes at least with qualitative agreement. We execute further theoretical investigations with variable magnitudes of membrane stiffness, viscosity and adhesion strength, so as to come up with interesting biophysical confluences.     

Chromatographic behaviour of single cells in a microchannel with dynamic geometry

We present the design of a microchannel with dynamic geometry that imparts different flow rates to different cells based on their physical properties. This dynamic microchannel is formed between a textured surface and a flexible membrane. As cells flow through the microchannel, the height of the channel oscillates causing periodic entrapment of the larger cells, and as a result, attenuating their velocity relative to the bulk liquid. The smaller cells are not slowed by the moving microstructure, and move synchronously with the bulk liquid. The ability of the dynamic microchannel to selectively attenuate the flow rate of eukaryotic cells is similar to a size-exclusion chromatography column, but with the opposite behavior. The speed of smaller substances is attenuated relative to the larger substances in traditional size-exclusion chromatography columns, whereas the speed of the larger substances that is attenuated in the dynamic microchannel. We verified this property by tracking the flow of single cells through the dynamic microchannel. L1210 mouse lymphoma cells (MLCs), peripheral blood mononuclear cells (PBMCs), and red blood cells (RBCs) were used as model cells. We showed that the flow rate of MLC is slowed by more than 50% compared to PBMCs and RBCs. We characterized the operation of the microchannel by measuring the velocity of each of the three cell types as a function of the pressures used to oscillate the membrane position, as well as the duty cycle of the oscillation.