id
stringlengths 24
24
| idx
int64 0
402
| paragraph
stringlengths 106
17.2k
|
|---|---|---|
65b7c7fb9138d23161faff06 | 43 | Fabrication of cell-laden constructs from GelMA-CBP bioinks. The suitability of GelMA-CBP bioinks containing 3T3 fibroblasts for 3D cell culture applications was evaluated by crosslinking the inks and encapsulating the cells within puck-like constructs (Figure ). The bioinks were formulated by creating a pre-ink that, upon mixing with a suspension of cells in cell culture media, resulted in 1 or 5% GelMA, 0.5% CBP, 0.5% LAP, and a final cell density of 0.5 x 10 6 (for 1 and 5% GelMA) or 5 x 10 6 cells/mL (for 5% GelMA only). After mixing the pre-ink and the cell suspension at a 4:1 (w/v) ratio, the bioinks obtained were gel-like and the cells were well dispersed within them. The bioinks were cast within puck molds and crosslinked using 405 nm light at 15% intensity. Cell viability in the center planes of the crosslinked hydrogels, as assessed using a fluorescent Live/Dead assay and confocal microscopy, was > 90% over 14 days for all the bioink formulations, showing that the introduction of CBP in the GelMA crosslinked network does not have a negative impact on cell survival (Figure ). |
65b7c7fb9138d23161faff06 | 44 | The fibroblasts inside the constructs displayed a rounded morphology even after 14 days. It is known that cells display a different morphology when grown as monolayers on 2D substrates than in 3D environments, even when cultured on top of a 3D material. When fibroblasts are seeded onto a 2D surface, they tend to spread and elongate, while in a 3D environment this does not necessarily occur. The porosity of the material seems to play a key role in the cell's morphology, with larger pore sizes required to yield elongated fibroblasts. In addition, when cells are encapsulated in bulk hydrogels, lack of pore interconnectivity and small pore size can limit cell elongation and migration, which we postulate is the main reason for the 3T3 fibroblasts remaining in a rounded morphology within our bulk material. It was also observed that the pucks contracted over time, with ca. 25% and 10% contraction for the 1% and 5% GelMA bioinks, respectively (Figure ). There were no significant differences in contraction between the pucks with and without cells, indicating that this behaviour is intrinsic to the materials and not due to remodelling or stress being exerted by the cells. We speculate that this phenomenon is related to the interaction of the CBP, which is rich in carboxylate groups, with ions in the cell culture media. |
65b7c7fb9138d23161faff06 | 45 | Overall, the bulk GelMA-CBP hydrogels showed compatibility with 3T3 fibroblasts, which presented high viability over time. Next, mesh-like constructs were fabricated through extrusion 3D bioprinting at 37 ºC and crosslinking using 405 nm light from 5%GelMA-0.5%CBP-0.5%LAP bioinks with cells incorporated at two densities: 0.5 x 10 6 and 5 x 10 6 cells/mL (Figure ). All the bioprinted constructs showed cell viability within the hydrogels > 90% over the 14 days of culture (Figure ). Cell morphology within the hydrogels depended on the cell density used in the bioink (Figure ). The lower density (0.5 x 10 6 cells/mL) resulted in cells with rounded morphology, while the higher density (5 x 10 6 cells/mL) led to fibroblasts that changed over time from a rounded to an elongated morphology. This finding highlights the key role that bulk cell density plays in the cellular morphology within 3D microenvironments. These findings are consistent with previous reports, where low cell densities have been shown to negatively impact the elongation of fibroblasts bioprinted within GelMA-based bioinks. Although the fibroblasts showed an elongated morphology that more closely resembled that observed for cells on 2D surfaces, cellcell interactions were limited, suggesting hindrance due to a small pore size within the bulk hydrogel. It is worth noting that a different morphology progression was observed between the bioprinted and those in the cast pucks when the same bioink composition and cell density were used. We attribute the differences in cell morphology outcome to the size of the bioprinted constructs, where the width of the meshes are in the sub-millimeter range, while the bulk puck hydrogels are millimeter in diameter and thickness. These differences could impact the transport of nutrients within the 3D microenvironments as well as change the proximity of the cells to an external "surface" that could lead to elongation of cells. This is supported by literature reports that show that 3T3 fibroblasts display more elongated morphologies within micropatterned GelMA constructs than within a bulk hydrogel. These results reveal a clear advantage of using thin 3D bioprinted scaffolds with sub-millimetre features over mold cast materials for 3D cell culture experiments and biomimetic models. CBP surfaces was expected given the presence of RGD motifs in GelMA. To quantitatively evaluate the different morphologies within and on top of the GelMA-CBP materials, we measured the cell area over time (Figure ). In agreement with our qualitative observations, when cells were bioprinted at a density of 0.5 x 10 6 cells/mL, they remained rounded without significant changes in the area. Conversely, when the cell density was increased to 5 x 10 6 cells/mL, we observed a statistically larger area. This trend was more marked at days 7 and 14, in agreement with our qualitative observation of fibroblast elongation at higher cell density in the bioink. |
65b7c7fb9138d23161faff06 | 46 | Finally, the cells seeded on top the constructs presented statistically significant higher area compared to the cells within the hydrogels at all timepoints. 3D printed GelMA-Carbopol structures for dynamic tissue modeling. Many organs in the human body, like the heart or lungs, are constantly subjected to cyclic mechanical stress, making 3D printing bioinks that result in stretchable hydrogel structures attractive for dynamic tissue modeling. GelMA-CBP show tunable mechanical properties and excellent stretchability, opening the door to building dynamic tissue biomimetic constructs. To assess GelMA-CBP constructs as mimetics that can undergo cyclic mechanical stress and result in relevant biological cell readouts, we 3D printed dog-bone meshes using 5%GelMA-0.5%CBP-0.5%LAP inks and cultured 3T3 fibroblasts on top of them. A cell and tissue (CaT) stretcher 6 was used to subject the cells to uniaxial stretching for 24 h with cycles between 0 and 20% strain at a frequency of 0.33 Hz (Figure ). |
65b7c7fb9138d23161faff06 | 47 | The expression of alpha-smooth muscle actin (αSMA), an indicator of fibroblast-to-myofibroblast transition, and filamentous actin (F-actin) were quantified by fluorescence staining and confocal imaging of samples stretched for 24 h and compared to static controls. Intensity values were extracted from the images through background subtraction and thresholding (details on the image processing steps are presented in Supplementary Information, Figure ). The 3T3 fibroblasts showed a statistically significant increase in αSMA expression (~2.8-fold) after 24 h of stretching compared to the static control (Figures ). These results indicate that the 3D printed GelMA-CBP constructs subjected to cyclic mechanical stress can effectively induce a fibroblast-tomyofibroblast transition, a hallmark of fibrosis in organs like the liver or the lung. Contrary to αSMA, we observed a statistically significant decrease in the expression of F-actin after 24 h of stretching (Figure ,C,E), in agreement with previous reported data. For example, the work from Zhang and coworkers reported a time dependent reduction of F-actin induced by uniaxial cyclic stretching (10%, 1Hz) in rat bone marrow mesenchymal stem cells. The F-actin cytoskeleton plays a relevant role in various cellular processes, and there is significant literature reporting that stretching can lead to either reinforcement or fluidization of the cell body. Reinforcement results from enhanced actin polymerization and a concomitant increase in cytoskeletal stiffness. On the other hand, fluidization is a cellular response intended to relieve stress and is characterized by a decrease of F-actin expression and the corresponding softening of the cell body. Under our experimental conditions, the cyclic stretching of 3T3 fibroblasts for cycles from 0 to 20% strain at 0.33 Hz. (A) Schematic representation of the seeding, stretching, and imaging process. (B) Fluorescence labelling of the nucleus (DAPI -cyan), αSMA (primary antibody -green), F-actin (phalloidin -magenta), and merged image of all channels for 3T3 fibroblasts cultured under static and cyclic stretch conditions. (C) Zoomed in merged image of static and stretched conditions. Quantification of (D) αSMA expression and (E) F-actin for 3T3 fibroblasts cultured under static and cyclic stretch conditions. ** indicates a statistically significant difference with p < 0.01. A two-tailed t-test was done for comparisons between two groups. Data is presented as the mean and standard deviation for n ≥ 3 independently prepared samples. |
65b7c7fb9138d23161faff06 | 48 | Development of a 3D printed dynamic lung tissue model. Given the promising results obtained for 3T3 fibroblasts subjected to cyclic stretch, we focused on developing a dynamic lung tissue model. To this end, dog-bone shape constructs were 3D printed using 3%GelMA-0.5%CBP-0.5%LAP inks. The crosslinked structures made from the 3% GelMA ink had mechanical properties that recapitulated the storage and compression moduli (G' and E) of porcine lung tissue, making it the best candidate to mimic the lung tissue (Figures ). Primary human lung fibroblasts (hLFs) were seeded on top of the dog-bone structures and cultured for five days under static conditions before starting the cyclic stretching. The stretching amplitude and frequency were chosen to mimic the normal human breathing process. hLFs grown under static or stretching conditions showed the expected spread out and narrow elongated morphologies typical of lung fibroblasts (Figures ). Additionally, the cyclic stretching induced a statistically significant increase in αSMA expression, indicating a fibroblast-to-myofibroblast transition, which is seen during the genesis of lung fibrosis (Figure ). |
65b7c7fb9138d23161faff06 | 49 | On the other hand, contrary to our observations from 3T3 fibroblasts, the F-actin expression of hLFs was not changed by exposure to cyclic stretching (Figure ). It has been reported that the pre-stress experienced by the cells, defined as the cytoskeletal tension under static conditions (proportional to the material stiffness), can affect the stability of actin fibers upon stretching. High cellular pre-stress is associated with the depolymerization of actin fibers upon cyclic stretching, while low pre-stress induces reinforcement. Following this logic, the stiffness of the hydrogels used for the 3T3 and hLF experiments could influence the F-actin expression within the cells, with a more pronounced reduction in the F-actin expression for the cells stretched on the stiffer material (5% GelMA). The 3T3 fibroblasts stretched on the stiffer hydrogels (5% GelMA) |
65b7c7fb9138d23161faff06 | 50 | showed a more pronounced decrease in F-actin expression relative to the static control than the hLFs grown on top of the softer hydrogels (3% GelMA), which was the expected trend. However, it is worth noting that the response to the substrate stiffness could be different for the 3T3 fibroblasts and the hLFs and the stretching parameters used were not identical, meaning that the stiffness of the hydrogel was not the only experimental variable. Overall, these results show that the 3D printed GelMA-CBP models could mimic the lung dynamic environment and produce relevant biological readouts, but that additional research is needed to pinpoint the differences Quantification of (C) αSMA and (D) F-actin expression from HLFs cultured under static and cyclic stretch conditions. Statistically significant differences are indicated with * for p < 0.05. A twotailed t-test was employed for comparisons between two groups. Data is presented as the mean and standard deviation for n ≥ 3 independently prepared samples. |
65b7c7fb9138d23161faff06 | 51 | The differences observed in the αSMA expression, the high printability, and tunable mechanical properties of the GelMA-CBP bioinks are promising for the development of dynamic tissue models. However, further research is needed to fabricate complex models that more accurately reflect the microenvironment in the tissue. Follow up research studying the impact of the time, frequency, strain, stretching pattern, and uniaxial vs volumetric stretching is paramount to understand how cells respond to constant mechanical stimulus on top of these 3D printed materials and select the conditions that replicate in vivo biology. Other important factors to consider for future studies are how the dimensionality of the microenvironment (2D -on top vs. 3D -within the material) and the presence of soluble biochemical cues (e.g., cytokines and growth factors such as TGF-β1) impact cells. Including lung epithelial cells on top of the material and hLF within it and exposing the co-culture to immune cells and biomolecules of interest could dramatically improve the accuracy of the biomimetic lung model. Refining the mechanical properties of the constructs is also essential, since a limitation of the current model is that the viscous component of tissue is not fully recapitulated by the inks presented. Using more viscoelastic (e.g., double network) instead of mostly elastic hydrogels (i.e., covalently crosslinked) may be key to mimic the mechanical properties of the extracellular matrix in humans. This additional work is crucial for developing fully functional dynamic tissue models that can be used in lieu of animal models. We anticipate that the GelMA bioinks can be refined to overcome all these limitations and help answer critical questions related to ageing and disease tissue states. |
65b7c7fb9138d23161faff06 | 52 | GelMA-CBP inks were formulated, showing adequate rheological properties for extrusion 3D bioprinting at low concentrations of both components at a physiologically relevant temperature of 37 ºC. The inks presented both shear thinning and thixotropic behavior with near instant and complete recovery, two properties that are fundamental to facilitating extrusion 3D bioprinting and high cell viability. The ink rheological properties were determined by the concentration of both GelMA and CBP, with the latter having a greater impact on ink rheology. CBP not only acts as a rheological modifier but also improves the mechanical properties of the crosslinked material, which was reflected in an increase in the G' values compared to GelMA without CBP. The concentration of both GelMA and CBP affected the printability. Small variations in CBP content (from 0.1% to 0.5%) resulted large improvements in printability, with 0.5% being the optimal concentration for the concentration of LAP used. It was possible to print complex constructs with high shape fidelity at low concentrations of GelMA (1%-7%) and CBP (0.5%) at 37 ºC. 3T3 fibroblast-laden cast constructs were obtained with a cell viability above 90%. The developed material was 3D bioprinted with good cell viability at days 3, 7, and 14 and adequate morphology. |
65b7c7fb9138d23161faff06 | 53 | The inks allowed dynamic tissue modelling. Specifically, fibroblast-to-myofibroblast transition was demonstrated in a lung tissue model after 24 h of stretching of hLFs. The addition of epithelial and immune cells and interrogating the impact of the type of stretching (uniaxial vs volumetric) are necessary further optimization steps to model the lung more accurately. In closing, our work solves the three key issues of GelMA-based bioinks for extrusion 3D bioprinting, by allowing the printing of complex constructs using: i) low concentrations of GelMA, ii) low concentrations of additive, and iii) physiological temperatures. Our work lays the foundation for using GelMA materials in tissue engineering, regenerative medicine, and implantable medical device applications. Then, the backgrounds were subtracted. Next, the previously generated ROI was used to identify the cells on both channels. Finally, the mean intensity per cell was calculated for F-actin and αSMA. |
65ae52639138d2316179adbc | 0 | Microfluidics is a multidisciplinary field based on the manipulation of fluids within channels with dimensions on the order of tens to hundreds of micrometers. In such microchannels, the behavior of a liquid is significantly different than at the macroscale due to the dominance of surface tension and viscosity, which allows precise prediction of the fluid flow . In these constrained environments, reactions are highly dependent on mass transport, and the control of mass transport in microfluidic devices through membranes has grown considerably over the last decade . On the one hand, microfluidics allows the miniaturization of a process as well as the acceleration of reactions, reduction of reagents, waste and cost, and optimization of energy and space . On the other hand, membranes are among the best technologies available in industrial waste management applications and filtration processes (e.g., biomedical , pharmaceutical , food , and metallurgy processes), allowing for modular and compact systems. Therefore, the combination of microfluidics and membrane technology can magnify their respective advantages providing more valuable solutions not only for industrial processes but also for reproducing biological processes. |
65ae52639138d2316179adbc | 1 | Microfluidics facilitates the recreation of biological processes by mimicking in vivo microenvironments into in vitro models as the organs-on-chip (OOC); but it can also facilitate tasks such as cell sorting , DNA amplification , and point-of-care diagnostics and detection . In microfluidic devices for biomedical applications, membranes can play diverse roles including cell and particle separation, selective transport of biomolecules, and contribution to precise fluid control within the system. Furthermore, membranes can simulate physiological barriers, such as the intestinal, alveolar, or blood-brain barriers to study drug transport, disease mechanisms, and tissue interactions (Figure ). |
65ae52639138d2316179adbc | 2 | The choice of membrane materials is pivotal to the success of microfluidic devices. Materials like polydimethylsiloxane (PDMS), polyethylene glycol (PEG), and polycarbonate are commonly employed due to their biocompatibility, flexibility, and ease of fabrication . These materials offer a range of physical properties suitable for different applications, allowing researchers to tailor membranes to specific experimental needs. In summary, membranes in microfluidics play a crucial role in replicating physiological barriers, facilitating cell interactions, and controlling molecular transport. Selecting appropriate membrane materials and properties is key to achieving the desired functionalities and advancing biomedical research applications. This review aims to highlight the importance of the synergy between membrane technology and microfluidics to create more sophisticated and biologically relevant microfluidic platforms. In this paper, the laws governing mass transport across membranes are introduced; then the current state and future perspectives of membrane technologies on organs-on-chip and microfluidic artificial organs are discussed. This work summarizes the roles of membranes in these devices, the required properties, the most suitable materials, and the current limitations to guide researchers in designing more effective membrane-based microfluidic devices. |
65ae52639138d2316179adbc | 3 | A membrane is a selective barrier between two phases that allows mass transfer under the action of a driving force (e.g., gradients in pressure, temperature, concentration, or electrical potential) . The stream that passes the membrane is called 'permeate', whereas the remainder is defined as 'retentate'. The transport mechanisms across a membrane depend on the membrane's morphology, and two typical morphologies can be distinguished: porous and dense. In dense membranes, the interactions between permeate and membrane material dictate the transport rate and selectivity. Transport in such systems is described by the solution/diffusion model in which the combination of Fick's law (diffusion) and Henry's law (solubility) leads to the equation: |
65ae52639138d2316179adbc | 4 | 𝑆 𝑖 * 𝐷 𝑖 * ∆𝑝 𝛿𝑚 (1) where J is the flux of diffusing species normalized for the membrane surface area (mol/s m 2 ), Si is the solubility of the permeant i (mol/m 3 Pa), Di is the diffusion coefficient of the permeant in the material (m 2 /s), ∆p is the pressure difference between the high and low-pressure side, and δm is the membrane thickness. |
65ae52639138d2316179adbc | 5 | Permeability of a membrane to a specific permeant is an intrinsic property of the membrane's material because both the solubility and diffusivity of component i depend on the chemical and physical interactions with the membrane's material. For example, in the case of gas separation through dense polymer membranes, D always decreases with the increasing size of the gas molecule. The extent of this decrease is generally dependent on the flexibility of the polymer backbone. On the other hand, the solubility of gases generally increases with molecular size, because the intermolecular forces between gas and polymer increase. These are some general rules which can be useful for a first understanding, while a comprehensive review of the relationships between material structure and transport properties can be found in the work of Matteucci et al. and Wang et al. In porous membranes, transport occurs through the empty spaces in the membrane, as a consequence transport is governed in the first place by membrane morphology. Morphology includes surface and volume porosity, pore size distribution, and tortuosity. Depending on the pore size, different mechanisms will dominate molecular transport. These mechanisms include, broadly: Knudsen diffusion, surface diffusion, capillary condensation, and molecular sieving . For an exhaustive review of the permeation mechanisms in porous membranes, we like to refer to the work of Oyama et al. and Stratis et al. The properties used to estimate the separation performance of a porous membrane are permeance, retention, and molecular weight cut-off (MWCO). The permeance is defined as the net transport of constituents through the membrane 2 . Since transport is not an intrinsic membrane material property, permeance is not normalized for the membrane thickness. |
65ae52639138d2316179adbc | 6 | It is important to clearly distinguish the terms membrane permeance and permeability. The permeance represents the mass transfer performance of a porous membrane, while on the other hand, the permeability is an intrinsic characteristic of the dense material that composes the membrane. Thus, two PC membranes with different pore densities will have the same permeability for component i, but different permeances. The selectivity of porous membranes is quantified by the Retention (R), a parameter related to the concentration of component i in the feed and permeate as given by eqn. ( ): |
65ae52639138d2316179adbc | 7 | In summary, the performance of dense membranes is strictly material-dependent, and it is evaluated by the membrane's permeability and selectivity. On the other hand, the performance of porous membranes is morphology and material-dependent and it is evaluated by parameters such as permeance, retention, and the MWCO. Membranes can be operated in two modes: in the so-called 'dead-end' mode, where a feed stream is completely transported through the membrane, or in continuous mode, in which the feed flows along the membrane. Similar to heat exchange, continuous operations can be performed in co-current, counter-current, and crossflow . Overall, the optimum performance in a membrane-based process comes from the optimization of the membrane module material and morphology as well as the optimization of process conditions. |
65ae52639138d2316179adbc | 8 | Organs-on-chip (OOC) are microfluidic platforms that integrate human microtissues in a controlled microphysiological environment. OOC systems narrow the gap between in vitro and in vivo testing by recapitulating key aspects of human (patho)physiology as continuous perfusion of nutrients and mechanical stress, providing a promising tool for drug development and personalized medicine . Although each type of OOC is different, many of the OOC platforms developed so far consist of an 'organ 'containing cells of the organ of interest and a perfusion compartment that can include blood vessel endothelial cells and/or immune cells. Generally, a porous polymeric membrane is applied between the two compartments to provide structural support for cell layers and to ensure a separation of transport processes by confining convective fluid flow to the perfused channels while allowing for diffusive transport of nutrients, secreted factors, and metabolites between the compartments. Flexible membranes also enable the mechanical actuation and stretching of cells and have been used for emulating peristalsislike motions in gut-on-chip or breathing in lung-on-chip. Similarly, non-porous membranes deflected by gas pressure have been employed to compress or stretch cells in cartilage , heart , and bone-on-chip 34 models. It is known that cells react to environmental cues, thus all the physical properties of the membrane such as roughness , surface microstructure , mechanical strength , hydrophilicity , and porosity have a significant effect on cellular adhesion and membrane biocompatibility. Despite their importance, these aspects are often neglected in OOC in which membranes are typically obtained from commercial Transwell inserts or filter membranes . |
65ae52639138d2316179adbc | 9 | In this chapter, we will discuss how membranes' physical properties affect cells, and we will describe the most employed membrane materials in organs on chip. We will then review the literature on the gut-on-chip as an example of membrane-based OOC. We believe that the gut-on-chip model presents the richest landscape for research due to its primary role in drug metabolism and microbiota-host cross-talk and its relevance in various infectious diseases. For the sake of brevity, in this paper, we will not consider the other OOC models. For a detailed review of all membranebased OOC, we would like to refer to the work of Rahimnejad et al. |
65ae52639138d2316179adbc | 10 | The surface roughness of the membrane can significantly influence cell behavior . Dowling et al. altered polystyrene surface to determine the effect of surface roughness and plasma treatment on the adhesion and spreading of MG63 osteosarcoma cells. They observed an enhanced cell adhesion on substrates with higher surface roughness while, contrarily, roughness negatively affected the spreading of MG63, as spreading decreased as surface roughness increased. Similarly, Majhy et al. , who studied the cellular behavior of cervical (HeLa) and breast (MDA MB 231) cancer cell lines on PDMS with a roughness ratio in the range of 1.05-3 (roughness:5-150 nm), explain that an intermediate roughness ratio (≈ 2) is optimal for the formation of focal adhesion points resulting in maximum cell-substrate interaction, stable adhesion, and therefore, the highest cell growth and proliferation. Above a critical roughness ratio, the cell membrane's elasticity precludes the cells' penetration into deep surface grooves, leading to only point-contact that reduces cell-substrate interaction and causes a notable drop in cell proliferation. demonstrated that the critical roughness level and thus the response to surface roughness stimulus is cell-type specific. They developed surface roughness gradients ranging from the nano to the micrometer scale on magnesium substrates to study the response of endothelial cells (ECs) and smooth muscle cells (SMCs) to improve the biocompatibility of vascular implants. Both cell types respond evidently to varying roughness on the Mg-based material, but high surface roughness (1.0-2.0 μm) with a network of ridge/valley structures provided a most favorable microenvironment to ECs proliferation while disfavoured that of SMCs. |
65ae52639138d2316179adbc | 11 | Surface wettability is a measure of surface energy. Surface energy can be altered or tuned by the addition of hydrophobic or hydrophilic groups. Plasma treatment, for example, is a well-known procedure for increasing the hydrophilicity of many hydrophobic surfaces including PDMS, PET, PLGA, and COC. The hydrophilicity of a material is a strong determinant of protein adsorption and thus cell adhesion . In 2D cell culture, hydrophilic substrates promote cell adhesion and proliferation , with moderate hydrophilicity yielding often the best cell response . Conversely, in 3D cell culture, specifically for spheroid formation, high hydrophobic substrates induce the formation of spheroid-like cell aggregates at a higher degree of sphericity, as shown by Ferrari et al. and Lee et al. among others . Zan et al. investigated the behaviors of three chondrogenic cell lines on PDMS substrates with different grades of hydrophilicity (WCA: 38.5°-120.4) and different stiffness (elastic modulus: 3.6-214.9 MPa). The response of different cell lines to an identical substrate was different, however, among the two factors influencing cell behaviors, the substrate wettability dominated cell proliferation while the substrate stiffness played a major role in the cell migration and spread and the expression of cell adhesive molecule and chondrogenic gene. This result confirms the suggestion of Wala et al. that initial cell adhesion and proliferation are regulated by surface properties such as hydrophilicity and roughness, while material properties such as stiffness influence later stages of cell growth. |
65ae52639138d2316179adbc | 12 | Cells are not only sensitive to dynamic mechanical stimuli such as strain or fluidic shear stress but are also sensitive to the mechanical properties of the substrate such as the stiffness. The range of ECM stiffness in the body is massive. Many orders of magnitude separate the softest tissue -the brain, with an elastic modulus of tenths of kPa-to the hardest -calcified bones with a modulus of the hundreds of MPa -and each specific cell type is tuned to the mechanical environment in which it resides. In particular, the stiffness of the cell microenvironment has a crucial role in many physiological and pathological processes of blood vessels as well as in the differentiation fate of stem cells . Bosworth et al. demonstrated that substrate stiffness influences the barrier function of the Blood-Brain barrier model. More specifically, iPSC-derived brain microvascular endotheliallike cells exhibit differences in passive but not in active barrier function in response to substrate stiffness. Recently, Zhou et al. observed significant vascular cell differences while remaining in a physiological range of substrate stiffness (18 vs 86 kPa). Compared with the 18 kPa substrate, on the 86 kPa substrate, the size of VECs increased, the production of NO decreased, the proliferation rate increased, and cells showed 560 differentially expressed genes, indicating that even a small increase in stiffness within the physiological range have a higher impact on vascular cell behaviors. Engler et al. looked at the relationship between substrate stiffness and mesenchymal stem cells (MSCs) differentiation, showing a dependency of the lineage of differentiation on the stiffness of the substrate. Indeed, soft PAA substrates with a stiffness of 0.1-1 kPa corresponding to brain tissue and 8-17 kPa corresponding to muscles led to neurogenic and myogenic differentiation respectively, while stiff substrates of 25-40 kPa induced osteogenic differentiation. |
65ae52639138d2316179adbc | 13 | Many studies demonstrated the ability of cells to adapt their cytoskeleton and, if needed, the nucleus morphology as a response to the surface microtopographies . This ability is often exploited to align and guide the growth of nerve and muscle cells through substrate microstructures like wells or grooves. For instance, Peng et al. proposed a micro/nanostructured PLGA conduit for nerve regeneration, which enhanced the migration rate and the cell guidance ability of immortalized neuron progenitors compared to flat PLGA membranes. Similar to microfibers or grooves, microchannels represent also a major category of microstructures and their geometry affects cellular behavior, as demonstrated by Esch et al. . Esch and colleagues grew HUVECs on square and semi-circular microfluidic channels in static conditions and under flow, finding that the expression of VE-cadherin that regulates cell-cell interactions were similar in the two geometries. However, vinculin, responsible for focal adhesions, was less present in square channels than in semicircular ones, suggesting that the latter promotes better cellsurface communication. |
65ae52639138d2316179adbc | 14 | Porous membranes commonly used in tissue barrier and co-culture models allow the exchange of soluble factors between cell populations and in some cases even cellcell physical contact . These membranes also provide mechanical support for the cells and establish a partition to define apical and basal compartments. Casillo et al. grew endothelial cells on non-porous and porous SiO2 membranes with different pore sizes and pore spacings. On porous membranes, cells showed fewer focal adhesions and less fibronectin fibrillogenesis than on nons with smaller pores compared to membranes with a bigger -porous substrate, and this effect was accentuated on membrane porosity. However, cell-cell interactions in the form of tight junctions measured by ZO-1 activity showed an opposite trend. They concluded that porosity, especially with small pore spacing, could limit cell adhesion, but weaker cell-substrate interaction might lead to stronger cell-cell interaction. Nonetheless, Wen et al. found no influence of the porosity on the differentiation of ASCs on PAA hydrogels, suggesting that the effect of porosity on cells may depend on multiple factors. Overall, chemical, and physical modifications of substrates and their effect on cell behavior are well studied and documented for cell culture on non-porous substrates, while yet limited research has been done on membrane-based models. |
65ae52639138d2316179adbc | 15 | Although a wide variety of natural and synthetic polymers is employed in the fabrication of scaffolds for tissue engineering, most OOC porous membranes are fabricated by only a few polymers, namely: PDMS, PC, poly(ethylene terephthalate) (PET), poly(1-caprolactone) (PCL) and Polylactic acid (PLA). Moreover, the choice of the membrane material is generally driven by practical reasons rather than the properties of the polymer related to the application. The current repertoire of commercially available flat porous membranes is limited; mainly led by PC, and PET track-etched membranes produced for Transwell inserts or filter membranes. Their fabrication is based on irradiating the material to create tracks that are then etched to produce through pores with sizes ranging from 400 nm to 8 µm. The porosity of these membranes remains low to reduce the incidence of merged tracks or double pores, and the pores density is intrinsically nonuniform due to the random nature of the irradiation. Furthermore, these membranes are too thick and rigid to represent the native basal membrane. PC track-etched membranes are extensively used in OoCs since reference data from PC transwell cell culture are widely available, thus employing PC in OoCs seemed to be a natural way of transferring knowledge from the standard cell culture system. PC is a highly hydrophobic, inert, transparent, and non-biodegradable thermoplastic. It is very stiff, with Young's modulus of approximately 2-2.4 GPa which is not comparable to any body's tissues . PET is another popular polymer for commercial membranes and inserts that is used in OoCs . PET shares many properties with PC; it is also a hydrophobic, inert, transparent thermoplastic with high stiffness (Young's modulus of 2-3 GPa) . Thus, like PC, PET is unsuitable for OoCs which apply stretch stimuli to the cells by deformation of the support membrane. Among self-produced membranes, PDMS porous membranes are to date the most employed in OoCs since they join the advantages of PDMS to those of the fabrication methods. PDMS is a low-cost elastomeric polymer characterized by physiological indifference, biocompatibility, excellent resistance to biodegradation, chemical stability, excellent gas permeability, optical transparency, and a tunable Young modulus in the physiological range (360 kPa -2 MPa) . With its flexible nature and low elastic modulus, this polymer is the most suited for applying cyclic stretch to cells. Moreover, PDMS membranes are fabricated by commonly used microfabrication techniques such as spin coating and soft lithography, which allow control over pore size and pore-topore distance in the micrometer scale . Nevertheless, this polymer also features several drawbacks that are fueling the demand for new alternative materials. PDMS is highly hydrophobic and requires surface modification approaches, as oxygen plasma, to improve its cell affinity . Besides, PDMSbased membranes absorb hydrophobic molecules such as drugs and markers commonly used in cell culture in vitro assays 130 , compromising the study results. In addition, the fabrication techniques used for PDMS-based membranes and devices have limited scalability, thus hampering production at an industrially relevant scale . As an alternative to the before-mentioned biostable materials, biodegradable polymers like aliphatic polyesters such as PLA and PCL are used to fabricate porous membranes for OoCs. PLA is one of the stiffest biocompatible polymers with Young's modulus of 3-4 GPa, making it unsuitable for membranes that should be exposed to mechanical stretch. It is, however, less hydrophobic compared to the polymers being investigated for OoCs (water contact angle of 61°) . Contrarily, PCL is characterized by a lower Young modulus of 400 MPa and a glass transition temperature of -60°C 122, resulting in a flexible polymer with a rubber-like consistency at room temperature. PCL is also one of the most hydrophobic polymers treated with a water contact angle of 140° 143 . The biodegradable nature of both polymers holds the potential for functioning as a temporary membrane, to be later replaced by the ECM of the cells creating an entirely natural cell layer. Tough, it must be considered that the pores' size might change over time due to the degradation and that the acid degradation products could affect cells. To overcome the limitations of synthetic polymer membranes, natural polymers have recently been adopted to produce membranes that better mimic the composition and function of the epithelial barrier. Arik et al. described a viable new approach to construct vitrified membranes from collagen type I hydrogel, demonstrating improved biocompatibility and are subjected to biochemical degradation by collagenase II. developed two types of collagen/elastin membranes: vitrified and non-vitrified, with stiffnesses ranging from several hundred of kPa down to 1 kPa. used a free-standing extracellular matrix gel to engineer a lymphatic vessel model. Furthermore, non-autologous proteins, such as spider silk proteins, have already been applied to form thick (3-9 μm) nonporous membranes to model the retinal pigment epithelium. Recently, Tasiopoulos et al. synthesized 470 ± 110 nm thin, mechanically robust, and fibrillar nanomembranes of recombinant spider silk proteins, where they grew endothelial and smooth muscle cells in the attempt to model the vessel wall. |
65ae52639138d2316179adbc | 16 | The human intestine is a dynamic organ where intricate interactions between the host and microbes regulate intestinal balance. While various in vitro models of human intestinal diseases exist, many models struggle to reliably mimic human intestinal responses to biological changes and medical treatments (Figure ). Human colorectal adenocarcinoma lines such as the Caco-2 or HT-29 have been used as a source of human intestinal epithelial cells and they are often cultured in Transwell plates. These cell culture systems involve growing cells on a semi-permeable membrane that separates them into apical and basolateral compartments, providing the ability to measure cell barrier permeability and assess interactions between different cell types 148 . Despite the versatile benefits of cell and tissue cultures, the static cultures of intestinal epithelial cells in the Transwell format are limited in replicating the in vivo-like 3D villous morphology. The absence of a 3D microenvironment is often a symptom of inadequate cytodifferentiation which may result in inaccurate outcomes of these models 149 . Intestinal organoid models show promising cytodifferentiation and regeneration, but their inability to incorporate luminal flow and physical bowel movements hinders the accurate replication of complex host-microbe crosstalk 148 . Gut-on-chips, functioning as minimal tissue units, can replicate certain aspects of human physiology in both health and disease, providing insights into the underlying biology of diseases and tissue regeneration. Utilizing micro-scaled OOC, researchers can follow dynamic changes in cell and tissue functions via real-time monitoring through imaging techniques and sensors. OOCs also enable researchers to isolate and study the effects of single-cell type, cell-cell interactions, and tissue-tissue interactions, contributing to a deeper understanding of native organ function and the impacts of various treatments 150-152 (Figure ). Different membranes' materials, coating, and functions employed in gut-on-chip devices are reported in Table . Its purpose is to give the reader a general idea of the occurrence of each membrane material and the respective choice of coating, as well as to summarise the different components of each Gut-on-Chip and the resulting main findings. Moreover, Table reveals a notable emphasis on replicating physiological conditions in organ-on-chip technologies, particularly in terms of biological components and mechanical stimuli, but highlights slower progress in developing biomimetic porous membranes. Current limitations toward more physiologically relevant membrane models include excessive thickness, smooth surfaces with artificial pores that poorly replicate the native basement membrane structure, and challenges in tuning membrane stiffness. |
65ae52639138d2316179adbc | 17 | Biomembranes should be more extensively investigated as an intelligent biomimetic system to provide important stimuli to cells as well as enhance specific intercellular interactions within the OCC system. Finally, a key technological issue needs to be faced. The large-scale fabrication of microfluidic devices is challenging, and the integration of membranes is still laborious and time-consuming. Therefore, novel processing techniques of membranes in microfluidics are crucial for membrane-based microfluidics to reach its full potential. |
65ae52639138d2316179adbc | 18 | Although AO technology has improved significantly in the past few decades, the quality of life of patients with organ failure is still poor and the technology must be improved further. This chapter will summarize the state of the art of membrane technology for microfluidic membrane-based AO devices, with a focus on artificial lungs, along with the current challenges in this field. |
65ae52639138d2316179adbc | 19 | Long-term respiratory support is carried out through the extracorporeal membrane oxygenation (ECMO) system. This treatment is reserved for cases where mechanical ventilation cannot supply the necessary oxygen demand, i.e., in severe lung failure due to aging, chronic lung diseases, or acute virus infections (e.g. COVID-19, MERS) . The main purpose of the ECMO system is to provide support until the body naturally recovers (bridge-to-recovery) , or in rarer cases until the patient receives an organ transplant (bridge-to-transplantation) . ECMO is also used as a standard of care for premature neonates whose lungs are immature and cannot provide sufficient oxygenation to satisfy their physiological needs 158 . |
65ae52639138d2316179adbc | 20 | ECMO, however, has inherent complications such as bleeding due to erythrocyte and platelet damage, thrombosis due to contact activation of the coagulation cascade 159 , arrhythmias, inflammation, and possible infections. It requires multiple transfusions to compensate for blood damage or to avoid hemodilution, especially for premature newborns. As a result, most devices have clinical lifetimes measured in days and a systemic inflammatory response syndrome (SIRS) occurs in 60% of ECMO survivors 160 . Additional limitations include ECMO therapy being non-ambulatory, labor-intensive, time-limited, and costly. |
65ae52639138d2316179adbc | 21 | 1) Surface areas and priming volumes that are a fraction of current technologies thereby decreasing device size. The introduction of the dual-lumen cannula allowing for single-site cannulation coupled with more compact oxygenators could permit the awaking and early mobilization of ECMO patients, which has been shown to improve therapy outcomes and shorten hospitalization . |
65ae52639138d2316179adbc | 22 | In blood oxygenators, membranes are responsible for physically separating the blood side from the gas side while still allowing gas exchange. The requirements to be respected by membranes for ECMO systems are, firstly, to meet the desired gas permeability as well as a suitable selectivity for O2/CO2, and to maintain them over time. The ideal membrane should allow oxygen exchange rates comparable to the human lung, thus between 210-3200 ml/min 166 . Secondly, mechanical, and chemical characteristics of the membrane should be stable and minimize or ideally avoid plasma leakage. Last but foremost, membrane materials should be hemocompatible, hence prevent protein adsorption, platelets activation, and inflammation. Hemocompatibility is so far the biggest challenge faced by membrane technology in AO. |
65ae52639138d2316179adbc | 23 | To date, the main parameter characterizing ECMO membrane's performance is the oxygen and carbon dioxide transfer rate, 𝑁 (mol/s), within the oxygenator. 𝑁 is directly proportional to the mass transfer coefficient, 𝐾 (mol/m 2 s Pa), to the gas exchange surface area 𝐴 (m 2 ), and to the driving force of gas exchange i.e., the difference in gas partial pressures: |
65ae52639138d2316179adbc | 24 | N is also, by definition, inversely proportional to the total resistance to gas mass transport, Rtotal. As the membrane module can be described with a resistances-in-series model, Rtotal is related to the sum of the partial resistance in the gas, the membrane and the liquid phase, respectively 𝑅 𝑡𝑜𝑡𝑎𝑙 = 𝑅 𝐺 + 𝑅 𝑀 + 𝑅 𝐵 (8) |
65ae52639138d2316179adbc | 25 | Reducing each phase resistance will hence improve the overall gas transfer rate of the oxygenator. However, the magnitude of each resistance is not the same. For instance, the gas phase resistance is negligible 167 , while the blood phase boundary layer resistance is the highest and can be 100 times larger than the membrane resistance This phenomenon is particularly important in gas/liquid transfers in the laminar flow regimes. The absence of turbulences in the blood flow creates a boundary layer at the blood/membrane interface with increasing concentrations of gases that are not removed by convection (Figure ). This saturated layer at the membrane surface acts like a diffusional barrier to the gas transfer reducing the transfer rate and keeping the gas transfer efficiency below the technical possibilities of the membrane. This was confirmed also by the work of Vacanti's group 169 who tested the gas transfer in a microfluidic oxygenator across three different membranes: dense poly(dimethyl siloxane) (PDMS) membranes (63 µm and 12 µm thick) and porous polycarbonate (PC) with pore size of 1 µm. The gas transfer for all three membranes was in the same range, confirming that the bottleneck in the blood oxygenation performance is the mass transfer rate in the blood phase rather than the permeance of the membrane. This highlights the importance of an optimized and efficient blood module design. |
65ae52639138d2316179adbc | 26 | In proposed for the first time microporous materials as candidates for membrane oxygenators in CPB. They tested membranes made of polyethylene, sintered nickel, and cellulose acetate-based polymers with a pore diameter of 1-10 μm. Although through pores increased the efficiency of gas exchange by providing direct contact of blood with air, significant plasma leakage and a high risk of air embolism were noted. |
65ae52639138d2316179adbc | 27 | The first generation of blood oxygenators based on porous membranes was developed only after the appearance in the 1980s of hydrophobic polypropylene (PP) membranes with submicron pores for ultrafiltration. These membranes have excellent gas permeance, a porosity of up to 55% with a pore diameter of up to 0.03 μm 171 , and a hydrophobic surface energy that prevents the penetration of plasma into the pores. However, porous PP membranes have a short lifetime of only several hours after which the gas permeance is reduced by membrane wetting (Figure ). Indeed, the adsorption of plasma proteins onto the pore's surface increases the surface energy of the material, eventually allowing the plasma to break through 154 . |
65ae52639138d2316179adbc | 28 | Compared to porous PP membranes, where gas molecules can freely permeate through, PMP membranes possess an asymmetric sponge-like structure with a dense hydrophobic outer skin. The high porosity and uniform pore distribution in the membrane's inner wall ensure high permeability of oxygen and carbon dioxide, while the thin non-porous outer skin avoids direct contact of liquids and gas. Thanks to PMP's high intrinsic gas permeability, reduced plasma leakages, and the possibility of operating for several weeks , PMP became the most widely used membrane material for long-term ECMO. |
65ae52639138d2316179adbc | 29 | The discovery of the excellent gas transfer capacity of silicone rubber by Kammermeyer in 1957 lead the way toward a new type of non-porous membrane for gas exchange processes In microfluidic blood oxygenators, PDMS is the material of choice to fabricate flat nonporous membranes due to its excellent permeability to oxygen and carbon dioxide (PO2: 800 Barrer, PCO2: 3800 Barrer at 35°C 179 ) and its ease of microfabrication by spin coating or casting. Even though the gas permeability is an intrinsic property of the material, in the case of PDMS membranes the fabrication method, as well as surface treatments, can influence the arrangement of polymer chains, increasing or reducing the free volumes that allow gas diffusion inside the network, thus impacting the final gas permeability of the membrane. |
65ae52639138d2316179adbc | 30 | Lamberti et al. investigated the effect of PDMS composition, i.e., the ratio between PDMS oligomers and curing agent, on its permeation properties to air. They focused on three membrane compositions: 5:1, 10:1, and 20:1 weight ratio of polymer base to curing agent and observed that increasing the polymer/curing agent ratio, the permeability of the membrane increases. This is due to a lower amount of cross-linked PDMS oligomers which allows an easier and faster diffusion of gases across the membrane. However, a PDMS membrane with a lower curing agent ratio is also more elastic, sticky, and harder to handle and integrate into a microfluidic device. |
65ae52639138d2316179adbc | 31 | Surface treatments and storage conditions of PDMS membranes also influence their gas permeability. A common treatment to convert PDMS surface from a hydrophobic to a hydrophilic state is the exposure to oxygen or air plasma. As part of such a transformation, surface methyl groups are removed and replaced with hydroxyl groups (SiO2). Studies from Markov et al. and revealed that the SiO2 layer created by plasma treatment on the exposed surface significantly impedes the diffusion of oxygen through PDMS. Moreover, Markov and colleagues also investigated the effect of storage conditions after treatment. They found that the PDMS completely recovered its original permeability after a 3-day storage in air, while the gas diffusion barrier remained significant for up to 3 weeks if PDMS was maintained in contact with water. |
65ae52639138d2316179adbc | 32 | The latest studies identified and tested new classes of polymers such as polyester, polycellulose, and fluoropolymer as new candidate materials for a new generation of ECMO membranes. Fluoropolymers such as PTFE and PVDF (or PVDF-co-HFP) demonstrated to be highly promising due to their hydrophobic, oleophobic, and low surface energy properties which inhibit undesirable protein adsorption and prevent the cascade reaction of immune response and blood coagulation . In work, the PVDF-co-HFP membrane coated with Hyflon AD60X (a fluoropolymer with extremely low surface energy) showed competitive performance in terms of blood oxygenation, low protein adsorption, and absence of hemolysis, compared to commercial polyolefin membranes (PMP). However, processing PTFE polymer into a thin, hollow fiber shape is still technically challenging due to its high melt viscosity. |
65ae52639138d2316179adbc | 33 | To date, various small-scale microfluidic artificial lung designs have been constructed and tested at lab scales . Microfluidic artificial lungs are commonly formed by a single blood layer and a single gas layer separated by a gas diffusion membrane. One of the first examples was the flat-plate membrane oxygenator developed by in 1977. Despite Hung's pioneering work, the important hydraulic resistance of the small-diameter blood channels and the advent of hollow fiber membrane technology delayed the research in microfluidic artificial lungs. |
65ae52639138d2316179adbc | 34 | In 2008, introduced theoretical models to study the suitability of different designs for microfluidic blood oxygenators with various heights and geometries 209 . They implemented two small-scale prototypes; one of the designs featured an array of 15 μm-tall, rectangular blood channels, and a 130 μm-thick PDMS gas exchange membrane and was successfully tested on porcine blood. They predicted that a scaleup version able to oxygenate a blood flow of 4 L min-1 could have a priming volume as small as 13 ml and a total volume of 252 cm 3 not including manifolds 204 . |
65ae52639138d2316179adbc | 35 | In the following years, many research groups developed and tested new micro-oxygenators. Particularly of note is the work of who created a microfluidic lung assist device with a 9 μm-thick silicon membrane and a 100 μm-tall, blood channels network with physiological blood flow. They applied the natural branching and scaling as described by Murray's law 211 , coupled with iterative computational fluid dynamic analysis to create a vascular network with uniform flow at bifurcations, biomimetic vessel length, and shear stress in the arterial range. However, the limitation to a single channel height throughout the entire network imposed by photolithography limited the gas exchange efficiency of the microchannels. |
65ae52639138d2316179adbc | 36 | In the attempt to improve the overall gas transfer efficiency of the microfluidic artificial lungs, in 2009, stacked two blood and four gas channel layers fabricating for the first time a microfluidic oxygenator with double-sided diffusion of oxygen into the blood channels. Successively, among others adopted this promising approach. In 2018, Dabaghi's group developed a microfluidic membrane oxygenator with double-sided gas transfer microchannels with the capability of being operated in a pumpless manner . Oxygen uptake in the double-sided device was increased by up to 343% compared to the single-sided device with the same design. They then assembled 4 devices to build a lung assist device (LAD) for preterm neonates with respiratory distress syndrome. The LAD could provide adequate oxygenation up to a blood flow rate of 60 ml/min using pure oxygen with a pressure drop low enough (10-51 mmHg) to enable a pumpless operation (Figure ). Recently, the same research group further ameliorated this approach by introducing for the first time a micro-oxygenator with four-sided oxygen diffusion 201 . Their novel design included embedded hollow air chambers between blood microchannels to involve also the side walls in gas exchange, increasing the gas exchange surface area without affecting blood flow characteristics or the channel's geometry. Compared with its equivalent double-sided gas exchange design, the new design's performance is enhanced by up to 223%. Although proof of concept has been demonstrated for this new configuration, a more reliable fabrication approach needs to be developed, and the robustness of the device must be further evaluated (Figure ). |
65ae52639138d2316179adbc | 37 | A different technique was adopted by Femmer et al. to enhance oxygen uptake in the blood channels. They used passive micromixers and chaotic advection principles to mix the fluid as it travels through a channel and increase oxygen mass transfer in the blood phase. Staggered herringbone micromixer structures with 50 µm depth and 125 µm width were patterned on channels in groups of six. Although this design demonstrated the reduction of oxygen diffusion resistance in blood, the advection phenomena may produce zones of high shear stress as well as stagnation zones along the microchannel which can lead to clot formation. |
65ae52639138d2316179adbc | 38 | Toward the direction of truly portable artificial lungs, the work of must be cited. designed the microfluidic oxygenator units in which the gas side of the membrane was directly exposed to air, thus eliminating the need for a ventilating gas supply. subsequently arranged in parallel 10 oxygenator units and tested the resulting LAD in vitro and in vivo in two newborn piglets. The heart pressure was sufficient to drive the blood flow and the oxygen exchange was 30 ml/min m 2 at a blood flow rate of up to 1.6 L/min m 2 . Although the results of Rochow's group support the feasibility of a pumpless microfluidic artificial lung efficient with ambient air, the hemocompatibility of the device and its lifetime in in vivo testing must be further assessed. |
65ae52639138d2316179adbc | 39 | A summary of microfluidic artificial lungs in the literature is given in Table . Four parameters describe the design: blood channel height (H), membrane material, membrane thickness (δm), and gas exchange surface area. While three parameters describe the oxygenator performances: blood flow rate, oxygen transfer, and pressure drop (ΔP). Data on gas exchange represent the maximum values reported. To conclude, it is important to reiterate that the key bottleneck is not the permselectivity of the membrane (although better performance is still desired), but the hemocompatibility of the membrane material to increase the device lifetime. The development of a compliant, resistant, hemocompatible, and superamphiphobic membrane will be an important breakthrough . In addition, especially for microfluidic artificial lungs, particular effort should be devoted to creating a biomimetic blood module design that improves the mass transfer coefficient of gasses. |
65ae52639138d2316179adbc | 40 | Membrane technology is the central component in many fields of life science as artificial organs, tissue engineering, medical equipment, and in vitro blood diagnosis. Microfluidics has developed into a promising research direction for miniaturization and improvement of analytical chemistry and bioscience processes. Combining membrane technologies with microfluidics can promote better developments in both fields. This manuscript reviews applications of membrane-based microfluidics in life science, focusing on organs-on-chip and microfluidic artificial organs. |
65ae52639138d2316179adbc | 41 | The tables clearly show the different efforts put into the recapitulation of the physiological conditions in terms of biological components and mechanical stimuli, compared to the recreation of a relevant model of the native basement membrane. Indeed, despite the great advancement in OOC technologies with new materials, better actuators and sensors, and a rapidly expanding library of different organs on a chip, the advance in the development of biomimetic porous membranes is very slow. The main limitations that need to be addressed for the creation of more physiologically relevant membrane models are: |
65ae52639138d2316179adbc | 42 | • Membrane stiffness. The polymers presented in this chapter (with PDMS being an exception) possess a high elastic modulus in the GPa range which is significantly stiffer than the native BM. On the other hand, the use of natural biodegradable polymers and hydrogels with low elastic modulus raises the issue of insufficient mechanical stability of the free-standing membranes over time. |
65ae52639138d2316179adbc | 43 | Along with the stated considerations, the manufacturing, handling, and integration of a free-standing ultrathin membrane with low stiffness into microfluidic devices is still challenging. Researchers must keep in mind that for OoC to reach their goal of drug testing devices, it is required to improve the accuracy and consistency of these microfluidic models, while enabling serial production. Indeed, the manufacture of thousands of devices per day will be necessary to meet a possible future demand of pharmaceutical industries. Instead, to date, the manufacturing process of organs-on-chip can be considered as artisanal, where each device is made by hand, at a maximum production throughput of several devices per day. For this to happen novel cost-effective materials and novel fabrication techniques should be adopted . |
65ae52639138d2316179adbc | 44 | Through microfabrication techniques, it is possible to create artificial blood networks with feature sizes that are comparable to those in the natural lungs. This substantially increases the efficiency of gas exchange and decreases the blood prime volume of microfluidic artificial lungs in comparison with commercial oxygenators. However, despite their efficiency, two main hurdles still need to be addressed for microfluidic artificial lungs to become a clinical reality: long-term hemocompatibility and scalability. |
65ae52639138d2316179adbc | 45 | • Hemocompatibility. ECMO clinical applications require artificial lung lifetimes of up to several months (i.e. lung failure or chronic lung disease) and up to now, microfluidic artificial lungs have not demonstrated this level of hemocompatibility. Though they can better mimic the vascular physiology, the impact on blood compatibility has not yet been quantified. The development of microfluidic artificial lungs for long-term application should include: |
65ae52639138d2316179adbc | 46 | 2) An optimized vascular network coupled with effective surface modifications and coatings to minimize the foreign body response of the device 227 . The functions of the heart and arteries are mechanical rather than chemical, thus an effort to recreate in the systems the forces and stresses produced by the blood flow on the walls of the cardiovascular vessels is mandatory. The blood flow path should reproduce the circular vascular channels geometry, follow natural scaling and branching laws, and exhibit velocities and shear stress in a physiological range. |
65ae52639138d2316179adbc | 47 | To meet the high throughput required at the clinical level, the challenge for microfluidic oxygenators is to enhance their gas exchange performance at higher blood flow rates (up to 4-7 L/min). To do so, the combination of two approaches is necessary: 1) fabricating devices with larger gas exchange surface area (i.e., not only one or two-sided gas exchange) to improve the oxygenation capacity of a single device and 2) parallelization of several devices to increase the overall throughput. Although the work of Santos et al. 215 demonstrated a single device capable of achieving a reasonable oxygen transfer at a blood flow rate of 30 ml/min, further improvements must still be made toward the goal of treating adult blood flow rates with physiological shear rates and pressure drops. |
65ae52639138d2316179adbc | 48 | Moreover, the applicability of microfluidic blood oxygenators at a clinical scale is closely tied to the available manufacturing technologies and materials. Current microfabrication techniques are labourintensive, limiting the production rates, and based on fabrication methods that limit channel depth to a single level. In addition, all the microfluidic devices proposed up to now are produced by lithography methods, which impair the creation of circular channels, and are made of PDMS which makes them not compatible with the actual massproduction techniques. A promising solution may be high-resolution 3D printing or precision computer numerical control (CNC) machining since they are capable of fabrication at the microscale level with great degree of freedom in size and 3D designs. other authors suggested some unconventional techniques, for instance, using lubricant-infused mould, combining PDMS membrane with SU-8 and quartz or developing materials or hybrid microfluidic structures with better performances than PDMS for biomedical applications 228 . |
62ab0dfb20a4ed576140df87 | 0 | oxidation states (Fig. , right). This particular chemical behavior leads to the facile generation of alkylradical fragments through single-electron-transfer (SET) oxidative addition from precursors such as redoxactive esters (RAE) or Katritzky salts (KS). The recent years have witnessed significant efforts towards mimicking the redox behavior of transition metals by main-group elements. For instance, pnictogens can take part in SN2-type polar oxidative additions resulting in two-electron maneuvering throughout (n)/(n+2) redox catalytic cycles, emulating those of late transition metals (Fig. , left). However, the radicalactivation of redox-active electrophiles is often restricted to first-row transition metals, and examples by a well-defined main group-element complex are rare. |
62ab0dfb20a4ed576140df87 | 1 | Very recently, bismuth redox catalysis has been established as an emerging platform for organic synthesis. In this context, our group has shown how polar Bi(III/V) or Bi(I/III) catalytic cycles can lead to the development of C-F, C-O, or C-H bond-forming reactions, among others. Nevertheless, even though persistent and stable radicals of heavier main-group elements are known, the studies for bismuth are much more limited, and bismuth radical catalysis has been significantly underexplored. Bi(II/III) catalytic cycles have been postulated for the living radical polymerization of alkenes, or the cycloisomerization of 4iodoalkenes. This, together with further reports probing the existence of bismuth(II)-centered radicals, prompted us to explore the behavior of the Bi(I/II) pair in SET-based oxidative additions of redox-active alkyl electrophiles. Here, we disclose how a well-defined bismuthinidene (1) reacts with alkyl phthalimide esters and alkyl Katritzky salts to give alkyl-bismuth(III) adducts, which were found to behave as Bi-C radical-equilibrium complexes (Fig. , bottom). Additionally, we discovered that α-amino alkyl-radical fragments resulting from this process can be easily oxidized by Bi(II), giving rise to iminium ions that can be trapped by N-nucleophiles. This observation led to the development of a Bi-catalyzed radical C-N cross-coupling reaction with a wide scope of both coupling partners (Fig. , top). In spite of the vast number of alkyl-radical couplings developed during the past decade, seldom examples of C(sp 3 )-N bond formation from redox-active radical precursors have been reported, mainly relying on photoredox setups, electrochemical synthesis, or the use of an excess of chemical oxidant. In this report, we demonstrate that catalytic amounts of a Bi(I) complex can promote this type of transformation in an autonomous manner, without the need of a photoredox system, a chemical oxidant, an external base, or an electrochemical setup. |
62ab0dfb20a4ed576140df87 | 2 | As a result of the high nucleophilicity of the 6p 2 lone pair on the Bi(I) center, bismuthinidene 1 has recently been shown to engage in polar SN2-type reactions with alkyl halides and triflates. Similarly, 1 reacted quantitatively with a range of benzyl (pseudo)halides (Cl, Br, I, OMs) to give benzyl bismuth(III) complexes 5-8 (Fig. ). Cyclic voltammetry analysis of 1 (E1/2 = -0.85 vs Fc 0/+ ) evidences that such C-X cleavages should proceed through a classical SN2 pathway (Ep/2 < -2.0 V vs Fc 0/+ ). On the other hand, the electrochemical behavior observed suggested that 1 could potentially engage in SET oxidative addition processes with alkyl redox-active electrophiles (Fig. ). Accordingly, reaction of 1 with 1 equivalent of tetrachlorophthalimide ester 2 (Ep/2 = -1.1 V vs Fc 0/+ ) cleanly afforded benzyl bismuth(III) complex 9, after SET and fragmentation upon release of CO2, followed by radical recombination. The resulting alkyl bismuth(III) adduct could be fully characterized by NMR, HRMS and single-crystal X-ray diffraction. |
62ab0dfb20a4ed576140df87 | 3 | Furthermore, Katritzky salt 4 (Ep/2 = -1.2 V vs Fc 0/+ ) also underwent radical oxidative addition with 1 to give 10. As expected, non-chlorinated phthalimide ester 3 (Ep/2 = -2.0 V vs Fc 0/+ ) remained unreacted when mixed with 1. Besides benzyl groups, the same process occurs with primary (11), or secondary (13) RAEs, leading to stable alkyl-bismuth(III) complexes. Interestingly, the process is orthogonal to classical polar transition-metal oxidative additions, as it could be performed in the presence of an aryl bromide, giving 12 as the sole product in 93% yield (Fig ). This reactivity is a rare example where bismuth, besides emulating the redox behavior of first-row transition metals during oxidative addition, allows the isolation and characterization of the corresponding alkyl-metal species resulting from radical recombination. Furthermore, when 13 was analyzed by EPR spectroscopy a weak but steady signal of the carbon-centered radical could be observed (see Supplementary Materials), which points to 13 being a radical-equilibrium complex. Based on this, the reaction of bismuthinidene 1 with cyclopropylmethyl iodide was monitored by NMR at low temperature in the dark (Fig. ). Complete conversion to cyclopropylmethyl adduct 14 was observed within one hour at -20 °C. When the mixture was warmed to 50 °C, a slow but steady conversion to ring-opening compound 16 was observed (35% after 12 h). This indicates that homolysis of the Bi-C bond in 14 takes place, and the complex is in equilibrium with its corresponding in-cage radical pair (18). ); potential in V vs Fc 0/+ converted from V vs SCE (-2.13 V). c Yields and conversions determined by H NMR, unless noted otherwise. TCPhth = tetrachlorophthalimide. |
62ab0dfb20a4ed576140df87 | 4 | Conversely, when cyclopropylmethyl redox-active ester 15 was reacted with bismuthinidene 1, a complex analogous to 14 was not observed. Instead, radical ring-opening product 17 was immediately obtained, even in the dark. This is consistent with the two distinct mechanistic scenarios for the oxidative addition. On one hand, polar SN2-type reaction of cyclopropylmethyl iodide with 1 initially leads to 14, which eventually ring-opens via radical equilibrium. On the other hand, SET and fragmentation of RAE 15 leads to an incage bismuth(II)/alkyl radical pair (18), for which cyclopropane ring-opening is faster than radical recombination, resulting in the formation of 17 (Fig. ). The radical-equilibrium hypothesis is consistent with the reactivity displayed by these complexes: the secondary alkyl radical derived from 13 reacts with Michael acceptors such as phenylvinylsulfone giving Giese addition product 21, either in the dark (57%) or under blue-light irradiation (85%) (Fig. ). The alkyl-radical fragment of several complexes was successfully trapped with TEMPO leading to C(sp 3 )-OTEMP adducts. Moreover, we observed that catalytic amounts of 1 can promote Giese-type reactions, among others, upon blue light irradiation (for these catalytic examples, and for TEMPO trapping experiments, see Supplementary Information). Interestingly, when attempting the isolation of α-amino alkyl-bismuth(III) adduct 23 derived from proline, we observed the exclusive formation of the product of decarboxylative amination 24, with recovery of bismuthinidene 1 (Fig. , right). It was speculated that product 24 would arise from the oxidation of the corresponding α-amino alkyl radical by a highly reactive bismuth(II) species. This would lead to the formation of an electrophilic iminium ion, which ultimately reacts with the tetrachlorophthalimide (TCNPhth) anion to forge the C-N bond (for details, see Fig. and Supplementary Information). At this point, it was envisaged that this reactivity could be exploited to engage the corresponding iminium with external N-nucleophiles, leading to a formal C-N cross-coupling reaction. After optimization of the conditions, we found that the reaction of RAE 22 with 3 equivalents of benzimidazole (25) in the presence of 10 mol% of 1 in DMA at 25 °C afforded the product of C-N cross coupling (26) in 88% yield within 2 h (Fig. ). Under these conditions, the only observed side products were 24 (nucleophilic competition by TCPhth) and the expected amide bond-formation product 27, which could be minimized by controlling the stoichiometry and selecting the appropriate solvent (Fig. , entry 1 vs 3), respectively (see Supplementary Information for optimization details). Control experiments without Bi catalyst led exclusively to acyltransfer product (entry 2). The high efficiency of the optimized reaction relies on the faster kinetics of the Bi-radical process compared to the background amide formation. For example, the reaction could be carried out at -30 °C in DMF (entry 4), or at room temperature in DMA in only 10 min (entry 5), giving the desired product in 56% and 85% yield, respectively. To exclude completely the requirement of photoexcitation for any of the steps of the transformation to proceed, the reaction was carried out under exclusion of ambient light, giving comparative results (entry 6). Finally, we found that addition of TEMPO completely inhibits the reaction, presumably due to the inertness of the formed bismuth-TEMPO adduct (entry 7). The scope of the transformation is presented in Fig. . RAEs of readily available natural and non-natural α-amino acids were interrogated (either fully protected, or with free N-H bonds) as electrophilic partners. |
62ab0dfb20a4ed576140df87 | 5 | C-N coupling products derived from proline (26), phenylalanine (28), valine (29) or pipecolic acid (30, 32) were successfully obtained in good to excellent yields. In order to compete favorably with TCPhth, synthetically relevant N-heterocycles bearing free N-H bonds were evaluated. Using proline-derived RAE 22, the corresponding C-N coupling products with a variety of benzimidazoles (26, 40), imidazoles (33, 39, 41), and pyrazoles (31, 32, 35-38) were obtained. Non-symmetrical heterocycles such as benzotriazole (34) could also be accommodated, providing the product in a 5:1 N1/N2 ratio of regioisomers. A range of functional groups with different electronic properties were also tolerated (38, 41, 45). Since the radical process is orthogonal to classical transition metal-catalyzed cross-coupling reactions, different heteroaryl halides (35-37) and heteroaryl boronic esters (31, 32) could be well tolerated. The strategy was successfully applied in the modification of bioactive molecules, such as theophylline (42, 57%, single regioisomer). The successful coupling using thiabendazole (43, 61%) provides another illustrative example of the orthogonal reactivity to transition metals, as the Lewis-basic sites on both starting material and product could inhibit catalysis by binding to a metal center. In the absence of external nucleophiles, the product of decarboxylative amination via formal CO2 extrusion was obtained. For this process, both α-amino RAEs and α-oxo RAEs reacted, giving hemiaminal-type structures such as 44 and 45 in good yields. Overall, this strategy is complementary to the photochemical protocol reported by Fu and co-workers, allowing the use of α-heteroatom RAEs, instead of unbiased alkyl substrates. To shed light into the mechanism, we monitored the catalytic reaction of α-amino RAE 22 by NMR with 10 mol% of bismuthinidene 1 at -40 °C using DMF-d7 as solvent. In this scenario, the pair of rotamers of α-amino alkyl-bismuth(III) intermediate 23 accumulated upon consumption of the RAE, coexisting with bismuthinidene 1. It is important to mention that complex 23 was characterized by reaction of 1 with 22 in a separate stoichiometric experiment (see Supplementary Information for details). The accumulated 23 decays into 1 after 1 h at -20 °C (Fig. , slow Bi(I/II/III) pathway). However, we observed that the consumption of RAE 22 to give decarboxylative-amination product 24 occurs at a faster rate than the former process (for details on kinetic analysis, see Supplementary Information). Thus, an alternative pathway should be considered in which in-cage radical pair 23' reacts through SET, leading to iminium cation 46 upon regeneration of Bi(I) (Fig. , fast Bi(I/II) pathway). Competing radical recombination of 23' leads to some accumulation of 23, which eventually collapses into the reaction product (24) and 1. Overall, the radical oxidative addition appears to be the rate-limiting step of the dominant pathway, as suggested by the continuous presence of 1 throughout the entire course of the reaction. |
62ab0dfb20a4ed576140df87 | 6 | In summary, we have developed a radical oxidative addition of redox-active carbon electrophiles to lowvalent bismuth, based on the SET from a well-defined Bi(I) complex to alkyl RAEs and KS. This process led to a family of alkyl-bismuth(III) complexes, which were found to be in equilibrium with the corresponding in-cage radical pair formed by bismuth(II) and a free alkyl radical. Unbiased alkylbismuth(III) complexes are stable and can be characterized both in solution and in solid state. On the other hand, α-amino alkyl-bismuth(III) intermediates collapse back to bismuth(I) upon releasing iminium cations, which can be trapped by external N-nucleophiles. This led to the development of a bismuth-catalyzed C-N cross-coupling reaction, using complex N-heterocyclic compounds. This new type of radical catalysis is promoted by bismuth in an autonomous manner, through a radical Bi(I/II) or Bi(I/II/III) redox cycle, without the need of a photoredox system, a chemical oxidant, an external base, or an electrochemical set-up. Overall, these findings open up a field of radical couplings by a main-group element and pave the way for the rational design of synthetically relevant transformations based on Bi radical catalysis. |
630f3a8858843b843ca424ff | 0 | First-principles quantum mechanical calculations have been widely successful in describing chemical processes at a fundamental level. However, the interpretability of these calculations is still an ongoing subject of debate . How does one move between the electrons and nuclei of first-principles calculations to the more intuitive building blocks of chemistry, such as atoms, bonds, lone-pairs etc.? Significant progress has been made in the forward direction by considering the topography and topology of quantum-mechanical objects, in a field that has become known as quantum-chemical topology (QCT) . Early examples, such as Bader's partitioning of atoms-in-molecules (AIM) via the basins of attraction of the electron density ρ, demonstrated that it was possible to recover the concepts of atoms and bonds . Later, such methods were generalized and applied to properties such as the electron localization function (ELF) and the Laplacian of the density, ∇ 2 ρ , which elucidate the role and locations of lone pairs and core and valence regions in chemical reactions. The Laplacian can also be used to delimit regions of strong and weak correlation and is crucial to the construction of kinetic energy functionals . The relationship between topology and the description of the overall system as a set of open quantum sub-systems, as initially demonstrated by Bader , has also been generalized . |
630f3a8858843b843ca424ff | 1 | The use of topology to derive chemically-intuitive quantities from first-principles calculations is an important part of strengthening the link between quantum mechanics and chemistry. However, it is also important to be able to move in the other direction -to be able to incorporate chemical ideas into first-principles calculations. Ideally, one would be able to set up a feedback loop whereby chemically-intuitive quantities can be calculated from first-principles and fed back into the calculation to improve the results. This work investigates one route to achieving this for density functional theory (DFT) calculations, by providing a method to calculate topological properties of functions defined on a real-space integration grid. This is achieved by the construction of a neighbourhood graph over the DFT gridpoints and it is demonstrated that intrinsic properties of the graph, such as maximal spanning trees and strongly-connected subgraphs, correspond to chemically-relevant properties. Having such topological information available on a pergridpoint basis allows for its direct incorporation into DFT calculations. |
630f3a8858843b843ca424ff | 2 | A brief primer on notation and relevant mathematical concepts is provided in appendix. A. It is important to clarify that in what follows, and in the field of QCT more broadly, the term "topology" is used in a looser sense (with some exceptions -see ) than in the branch of mathematics bearing the same name. We use the term in it's broader sense as pertaining to properties of a geometric object (in our case, a quantum-mechanical function) that are preserved under continuous deformations (in our case, small deformations of a molecule). In this work, the topological properties of interest will be properties of the topography of the quantum-mechanical function of interest. For example, maxima, minima and saddle points are topographical features, but their existence and connectivity are topological properties. These topological properties are insensitive to the level of theory used to describe a molecule (e.g Hartree-Fock or DFT). However, in contrast to stricter definitions of conservation in mathematics, topological properties in QCT are typically not conserved through chemical processes, such as bond breaking or formation -a fact which underpins their usefulness in identifying and classifying such phenomena. |
630f3a8858843b843ca424ff | 3 | assuming the spacing s is small enough to resolve variations in f accurately. Despite the simplicity of a uniform grid, it is common to generate G in a less trivial fashion to reduce the storage requirements and the computational cost of operations on F . For example, in order to make routine DFT calculations feasible, typical grids used to perform real space integration become less dense further from atomic nuclei, where the electron density is lower and quantummechanical functions vary more slowly . Topological analysis on such non-uniform grids has been carried out previously in the context of Bader's quantum theory of atoms in molecules (QTAIM ) . However, such methods rely on the ability to freely evaluate f and it's gradient ∇f . In the present work, a method to perform topological analysis without supplementing the function evaluations given in Eq. 1 is developed. This method is therefore a strict post-processing of F and can be easily applied to an arbitrary function (or set of datapoints with the form of Eq. 1). This also permits it's packaging as a generally-applicable software tool . |
630f3a8858843b843ca424ff | 4 | Determining the neighbours of a given grid point, as was done in Eq. 3 for a uniform grid, is a necessary prerequisite to performing a topographical analysis. Even simple topographical objects, such as local maxima and minima, are defined with reference to the behaviour of the function when moving to "nearby" points. It is possible to encode the necessary information about the neighbours of a given grid point in the edges of a neighbourhood graph N with nodes given by the points in G, and edges connecting each node x ∈ G to a set of neighbours N (x) ⊂ G \ x. In this section, the construction of such graphs is investigated. |
630f3a8858843b843ca424ff | 5 | There are many ways to construct a neighbourhood graph N for an arbitrary set of points G (a few are shown in Fig. ). In practice, G will be limited to a finite region of R N and we will not be primarily concerned with the boundary of points forming the convex hull H(G), but only the bulk B(G) = G\H(G). The goal when choosing a construction is to most closely preserve the topography of f (and topology thereof) when moving from its representation in R N to its representation on G. This leads to enforcing the following requirements for N : |
630f3a8858843b843ca424ff | 6 | Which would not have a unique solution (M would be singular) if {y -x : y ∈ N (x)} did not form a basis. Condition 3 is necessary, but not sufficient, for condition 4, which ensures that the gradient can be followed as well as approximated on the graph. These conditions serve to narrow down the choice of graph construction. For example, given the goal of defining a neighbourhood, it might be tempting to use the set of n nearest neighbours of each point N (n) (x) to define the n-nearest-neighbour graph: |
630f3a8858843b843ca424ff | 7 | where the reverse condition x ∈ N (n) (y) has been included to ensure that the graph is undirected. Examples of nearest neighbour graphs N 2 and N 3 are shown in Fig. for a 2D grid, where we can see they suffer from several shortcomings. In particular, they are not necessarily connected or move-preserving which leads to the introduction of fictitious local maxima and local minima as can be seen in Fig. . |
630f3a8858843b843ca424ff | 8 | A sensible choice of graph to overcome the issues with nearest-neighbour graphs is a triangulation. A triangulation of a grid G is a set of simplices (N -dimensional analogues of triangles) that tile the convex hull H(G) (see, for example, N D in Fig. ). Any triangulation immediately satisfies the requirements given in section II C 1 and possesses high-quality numerical gradients, even for the pathological case of a random grid, as can be seen in Fig. . |
630f3a8858843b843ca424ff | 9 | The specific case of a Delaunay triangulation (DT) satisfies many additional desirable criteria , several of which also serve as independent definitions of the DT . Of particular relevance here, for a grid of points G and function evaluations F , the DT minimizes the area (volume for d > 2) of the polyhedral surface representing F -an illustration of this condition is shown in Fig. (left). The DT also minimizes the size of the largest open ball (b(x; d) = {y ∈ R N : |y -x| < d}) which bounds a simplex and thus avoids large simplices corresponding to large neighbourhoods -this is also shown in Fig. (lower right). |
630f3a8858843b843ca424ff | 10 | Given a grid point y ∈ G, the region {x ∈ R N : x → G = y} where f N N (x) = f (y) is known as the Voronoi cell of y. The neighbourhood graph obtained via a Delaunay triangulation is equivalent to connecting points with corresponding Voronoi cells that are adjacent in R N . Such connectivity of Voronoi cells of grid points is also known to be useful when approximating the flux of gradient paths between cells . We employ the QHull implementation of Delaunay triangulation , using the python interface provided by SciPy . Constructing the Delaunay triangulation in N -dimensions is equivalent to constructing the convex hull of the points lifted into an N + 1 dimensional paraboloid -QHull constructs the Delaunay triangulation by constructing this convex hull using the QuickHull algorithm . |
630f3a8858843b843ca424ff | 11 | Along with a suitable definition for neighbourhoods, it is important to be able to identify regions of interest in G. In particular, given a function f : R N → R, it is essential to be able to identify connected subsets of R N for which f is locally maximal. These include pointlike maxima of f (e.g the point x = 0 for f = -|x|), but also spatially-extended maxima (e.g the shell at |x| = 1 of f (x) = -(|x| -1) 2 ). Such a subset (and it's analogue on G) will be refereed to as a maxima family M and the set of maxima families of f as M(f ). Then, for a given family |
630f3a8858843b843ca424ff | 12 | The concept of a steepest ascent path generalizes straightforwardly to a graph and so one might also expect basins of attraction to generalize straightforwardly. However, in general, the maxima of f will not lie exactly on the grid G. This means that the set of points on the graph that are best suited to represent a particular maxima family will not all have exactly the same function values and maxima families can only be approximately defined. In the present work, the definition is based upon an expansion around the local maxima of the graph |
630f3a8858843b843ca424ff | 13 | which are typically the closest points on G to maxima families of f . In order to construct the basins of attraction, two objects must be constructed; A : G → M L (G) which maps a point to the local maximum whose basin of attraction it resides in (in analogy to the point of attraction A(x) ∈ R N ) and the families of local maxima M(f, G) (in analogy to the maxima families M(f ) on R N ). The basins of attraction for the maxima families are then |
630f3a8858843b843ca424ff | 14 | The algorithm to determine A is based on that of Henkelman et. al. , but applied to a graph rather than to a uniform grid. A schematic is shown in Fig. and the steps are detailed below: As noted in , step 6 of this algorithm allows rediscovery of previous steepest ascent paths and significantly improves runtime performance. Once we have constructed the map A : G → M L (G) associating points to local maxima, we turn our attention to the algorithm to cluster local maxima into families FIG. . Regions with a deviation d(xi, x) of less than t = 0.25 for two maxima x1 and x2 of a function f (x). Note that the region for the smaller maxima is smaller, thanks to the scaleindependence of the deviation measure (Eq. 16). |
630f3a8858843b843ca424ff | 15 | This is essentially the fractional change in the function value due to moving from x to y, and therefore d(x, y) ∈ [0, 1] independently of the scale of the function. Once d(x, y) has been defined, a tolerance t can be chosen such that d(x, y) < t defines a stationary region around each maxima (see Fig. ) and apply the following algorithm to cluster local maxima into families. The algorithm begins by constructing a flood fill around each local maxima according to the tolerance and ends by merging overlapping flood fills into connected families (see Fig. ): |
630f3a8858843b843ca424ff | 16 | E. Basins of attraction: Example applications 1. Calculation parameters Unless stated otherwise, example applications presented in the rest of this work were carried out using quantities from a Hartree-Fock calculation with a cc-pVDZ basis set. For topology analysis, the quantity of interest is then evaluated on a DFT grid generated using an Lindh-Malmqvist-Gagliardi (LMG) radial grid (with a threshold of 10 -10 ), a Lebedev angular grid (with degree between 15 and 25 depending on the radius) and by pruning points with a weight of less than 10 -12 . This results in a relatively coarse DFT grid (∼ 10 4 points per atom), with the hope of replicating the worstcase scenario that would be encountered in real-world applications. Hartree-Fock was used rather than DFT so that the dependence of the topology analysis on the grid could be investigated independently of the quality of Fock-matrix integration (for which the DFT grid is used). |
630f3a8858843b843ca424ff | 17 | An object of central importance in quantum chemistry is the electron density ρ(r) : R 3 → R + . Bader demonstrated a correspondence between the basins of attraction of the electron charge density and atoms in molecules . Specifically, each basin of attraction contains exactly one atom in a molecular system, allowing one to uniquely assign the electronic charge present on each atom as the integral of the charge density over its basin of attraction. This leads to the bader charges, here defined in R 3 as |
630f3a8858843b843ca424ff | 18 | where w(x) are grid integration weights (typically generated along with the grid itself , but which could be taken as the volume of the Voronoi cell of x). The basins of attraction for the electron density of a benzene molecule are shown in Fig. . Near to the z = 0 plane (Fig. , top) the basins of attraction are delimited into six wedges, each containing a single H basin and a single C basin, according to the sixfold rotational symmetry of benzene. However, further from the nuclei some points are assigned to basins of attraction outside of their wedge (Fig. , bottom, white circle). For the coarse grids specified in Sec. II E 1, this misassignment affects approximately 1% of the points. However, as these points are in regions of low electron density, the error in Bader charges resulting from this misassignment is of the order of 1/1000 th of an electron. The convergence of Bader charges as a function of grid size is investigated in detail in Sec. II H 1. |
630f3a8858843b843ca424ff | 19 | Bader charge analysis as carried out in section II E 2 is insensitive to the treatment of maxima families. This is because, for molecular systems, the electron density ρ has no extended maxima, only distinct point-like maxima near to each nucleus. However, this is not true for the Laplacian of the electron density ∇ 2 ρ. Indeed, the electronic shell structure of atoms leads to ∇ 2 ρ exhibiting alternating regions of charge concentration (∇ 2 ρ < 0) and charge depletion (∇ 2 ρ > 0) as one moves radially away from the nucleus . This naturally leads to spatiallyextended maximal shells of ∇ 2 ρ and derived quantities, as can be seen for a Neon atom in Fig. . The changes in the shell structure of the Laplacian upon bond formation will be discussed in Sec. II G 2. |
630f3a8858843b843ca424ff | 20 | Given a target function value f iso , an isosurface of f can be defined as {x ∈ R N : f (x) = f iso }. Due to the delocalized nature of electrons in molecules, isosurfaces are commonly used in molecular visualization. The ability to identify families of maxima allows the topological analysis of such isosurfaces by defining an auxiliary function f I (x) = exp(-|f (x) -f iso |) which will be maximal where f (x) = f iso . The maxima family (or families) where f I (x) ≈ 0 then serve as a suitable definition of isosurfaces. An example of this can be seen in Fig. , where non-covalent bonding in H 2 under a strong magnetic field (as explored in ) can be identified as the separation of the half-maximum-value isosurface of the electron density (where ρ(x) = max(ρ)/2) into two distinct maxima families. |
630f3a8858843b843ca424ff | 21 | A critical path is defined as a path linking two local maxima on N that maximizes the minimum value of f encountered (the critical value of that path). The equivalent of this path in R N necessarily passes through a firstorder saddle point of f known as a critical point and, in analogy, the point of minimum f on a critical path in N is labelled as a critical point (see Fig. ). Given a neighbourhood graph N , edge weights are assigned as the average of the function values at the endpoints of the edge. It is then possible to find critical paths rapidly by noting that they are paths on the maximum spanning tree (MST) of N (see appendix A), which is denoted as M (N ) (the critical-path problem essentially becomes the widest path problem from graph theory). In fact, the critical path between two local maxima on N is the only path linking the maxima on M (N ), thanks to the fact that M (N ) is acyclic. The union of all critical paths is called the critical tree, which can be found rapidly and in it's entirety by repeatedly pruning the maximum spanning tree according to the following algorithm (shown in Fig. ): |
630f3a8858843b843ca424ff | 22 | 1. Maximum spanning tree: Let M be the maximum spanning tree of N , evaluated with edge weights given by the average of function values on the endpoints of each edge. . Bottom: Non-covalent bonding of the 1σ β g 1σ β g component of the triplet state (which, under this magnetic field, is the ground state ). The axes are in bohr. |
630f3a8858843b843ca424ff | 23 | The critical tree is inherently acyclic (as it is a subgraph of the maximum spanning tree) -a direct consequence of the definition of a critical path. However, it is possible that there are multiple paths with very similar critical values between a given pair of local maxima. For example, the electronic charge density of a benzene molecule exhibits local maxima at the nuclei which can be linked together by traversing the aromatic ring either clockwise, or anticlockwise (see Fig. ). Both of these routes have very similar critical values, but only one (that which has the slightly larger critical value within a finite precision computation) will be included in the critical tree. For the benzene system this means that whichever bond happens to have the lowest electron density will be excluded from the maximum spanning tree, and hence also from the critical tree. However, such bonds can be re-introduced by considering neighbouring basins of attraction, using the following gap-filling algorithm (this produces a critical network according to the definition of Bader ): |
630f3a8858843b843ca424ff | 24 | 2. Iterate: Iterate over pairs of maxima x, y ∈ M L (G). Step 8 identifies a non-critical path between neighbouring regions by noting that the critical point is pushed right to the edge of the shared border of the regions (see path P BC in Fig. ). In order for two regions to be critically linked, the critical point must instead constitute a saddle point in the bulk of the shared boundary (as is the case for paths P AC and P AB in Fig. ). |
630f3a8858843b843ca424ff | 25 | Cluster the paths into a flat set P flat = {P ∈ P : D(P ) < t flat } where the function value changes by a small amount (according to some tolerance t flat ) along the path. Consider the rest of the paths to be non-flat P non-flat = P \ P flat . |
630f3a8858843b843ca424ff | 26 | In an alternative scheme, one might use the subgraphs of the cleaved critical tree to define the maxima families when identifying basins of attraction. However, the flood fill technique introduced in section II D is more robust in practice (as the flood fills are more densely connected over surface-like maxima than a tree). |
630f3a8858843b843ca424ff | 27 | FIG. . The critical network of the electron density of a benzene molecule, evaluated by post-processing the maximum spanning tree on a Delaunay triangulation according to the algorithms given in section II F. The bond that was filled in by the gap-filling algorithm is shown in red; the remaining black lines are the pruned maximum spanning tree. To improve the smoothness of the bonds, the DFT grid used for this plot contains around twice the number of gridpoints as the coarser grids used in the rest of this work. The axes are in bohr. |
630f3a8858843b843ca424ff | 28 | In Bader analysis, paths on the critical network are called bond paths, and provide a unique (although not necessarily optimal ) definition of molecular bonds . The bond paths for benzene, evaluated using the algorithm given in section II F, are shown in Fig. . All bonds are recovered (one of which via the gap filling algorithm given in section II F), leading to the familiar hexagonal benzene bonding network. In Bader analysis, the critical points are known as bond critial points -the values of the electron density at these points are given in Tab. I alongside values calculated using existing methods that require ρ(r) at arbitrary r. |
630f3a8858843b843ca424ff | 29 | Charge concentration (∇ 2 ρ < 0), or depletion (∇ 2 ρ > 0), is most relevant to chemistry when it occurs in the valence region of an atom in a molecule. In particular, it has been noted that the maxima of valence charge concentration (depletion) correlate with the active regions for electrophilic (nucleophilic) attack . Critical networks spanning these maxima form the valence shell charge concentration/depletion (VSCC/D) graphs . Such graphs can be easily examined by constructing the . Values of the charge density (in e/bohr 3 ) for each bond critical point identified in benzene for named grid sizes in QUEST. The values can be clearly seen to be split into groups of 4 and 2 as a result of the DFT grid breaking sixfold symmetry. The level of theory is as specified in Sec. II E 1 and results using QChem v5.0 and the Multiwfn package v3.8 are also given. critical network of -∇ 2 ρ (charge concentration) or ∇ 2 ρ (charge depletion). An example for the VSCC graph of a water molecule is shown in Fig. .f Fig. of ). This VSCC graph can clearly be seen to connect the lone pairs either side of the oxygen atom. This behaviour is reflected in the critical network of the 90% ELF isosurface (Fig. , middle), where the lone pairs can be very clearly seen as lobes aligned along the perpendicular direction to the bonds. Such charge concentration arises from distortions in the valence shell of the oxygen atom due to the hydrogen atoms, which can be seen by looking at the maxima families of |∇ 2 ρ(r)| (Fig. , bottom, valence shells are shown in blue, c.f the shells of Ne in Fig. ) -note that core shells (pink, for example) retain their spherical nature. |
630f3a8858843b843ca424ff | 30 | Applying a magnetic field to a molecule induces a current density vector field J(x) : R 3 → R 3 . The stagnation graph of J is the subset of R 3 where |J(x)| = 0 and in general consists of isolated stagnation points and extended stagnation lines . These stagnation graphs form a compact representation of the topology of the vector field and have significance in ring-current models and NMR spectra . The stagnation graph can be obtained as the critical network of -|J|, as can be seen for a C 2 H 2 molecule in Fig. . This stagnation graph exhibits the same features as a more detailed analysis at signifi- cantly reduced cost . The graph is known to contain a stagnation line that bisects the molecule -this can be seen in Fig. , but is quite ragged due to the decreasing density of DFT grid points as we move further from the nuclei. In combination with this, the single-valued (|J| = 0) and line-like (and therefore weakly-connected) nature of stagnation graphs make for a challenging test case for topological analysis. In any case, the approximate stagnation points determined via the present analysis on DFT grids can be used as a starting point for the derivative based optimization and refinement of the stagnation graph presented in Ref. . Utilising the starting points from the algorithms in the present work can significantly reduce the cost of determining detailed stagnation graphs using the derivative based approaches. |
630f3a8858843b843ca424ff | 31 | Thanks to the favorable properties of the Delaunay triangulation (see Sec. II C 1), topological properties, such as the number of maxima and saddle points etc., converge almost instantly. Topographical properties (such as Bader charges) also converge quickly, as can be seen in Figs. DFT grids well before 1 million grid points. Results using the uniform-grid Multiwfn package, v3.8 with charge densities calculated using QChem, v5.0 are also shown (the same numbers are obtained if Psi4 v1.6.1 is used in place of QChem). Such uniform-grid methods routinely use tens of millions of grid points -we quote results obtained using Multiwfn's "Lunatic quality grid" (of order 10 million points) and using an even larger custom grid (of order 100 million points, obtained by specifying a custom spacing), which we denote as extralunatic, which was necessary to achieve convergence in all cases. |
630f3a8858843b843ca424ff | 32 | DFT grids converge particularly quickly as they are designed for rapid convergence of integral quantities, but even the uniform grids shown in Fig. perform well thanks to their connectivity with a triangulation, rather than a simple grid (see also Fig. ). Performance on such uniform grids is particularly important in calculations involving a plane-wave basis set, where real-space properties are most naturally evaluated on a uniform grid via a fast Fourier transformation. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.