Environmentally Friendly Photothermal Membranes for Halite Recovery from Reverse Osmosis Brine via Solar-Driven Membrane Crystallization.

Modern society and industrial development rely heavily on the availability of freshwater and minerals. Seawater reverse osmosis (SWRO) has been widely adopted for freshwater supply, although many questions have arisen about its environmental sustainability owing to the disposal of hypersaline rejected solutions (brine). This scenario has accelerated significant developments towards the hybridization of SWRO with membrane distillation-crystallization (MD-MCr), which can extract water and minerals from spent brine. Nevertheless, the substantial specific energy consumption associated with MD-MCr remains a significant limitation. In this work, energy harvesting was secured from renewables by hotspots embodied in the membranes, implementing the revolutionary approach of brine mining via photothermal membrane crystallization (PhMCr). This method employs self-heating nanostructured interfaces under solar radiation to enhance water evaporation, creating a carefully controlled supersaturated environment responsible for the extraction of minerals. Photothermal mixed matrix photothermal membranes (MMMs) were developed by incorporating graphene oxide (GO) or carbon black (CB) into polyvinylidene fluoride (PVDF) solubilized in an eco-friendly solvent (i.e., triethyl phosphate (TEP)). MMMs were prepared using non-solvent-induced phase separation (NIPS). The effect of GO or GB on the morphology of MMMs and the photothermal behavior was examined. Light-to-heat conversion was used in PhMCr experiments to facilitate the evaporation of water from the SWRO brine to supersaturation, leading to sodium chloride (NaCl) nucleation and crystallization. Overall, the results indicate exciting perspectives of PhMCr in brine valorization for a sustainable desalination industry.

A workflow for the development of template-assisted membrane crystallization downstream processing for monoclonal antibody purification.

Monoclonal antibodies (mAbs) are commonly used biologic drugs for the treatment of diseases such as rheumatoid arthritis, multiple sclerosis, COVID-19 and various cancers. They are produced in Chinese hamster ovary cell lines and are purified via a number of complex and expensive chromatography-based steps, operated in batch mode, that rely heavily on protein A resin. The major drawback of conventional procedures is the high cost of the adsorption media and the extensive use of chemicals for the regeneration of the chromatographic columns, with an environmental cost. We have shown that conventional protein A chromatography can be replaced with a single crystallization step and gram-scale production can be achieved in continuous flow using the template-assisted membrane crystallization process. The templates are embedded in a membrane (e.g., porous polyvinylidene fluoride with a layer of polymerized polyvinyl alcohol) and serve as nucleants for crystallization. mAbs are flexible proteins that are difficult to crystallize, so it can be challenging to determine the optimal conditions for crystallization. The objective of this protocol is to establish a systematic and flexible approach for the design of a robust, economic and sustainable mAb purification platform to replace at least the protein A affinity stage in traditional chromatography-based purification platforms. The procedure provides details on how to establish the optimal parameters for separation (crystallization conditions, choice of templates, choice of membrane) and advice on analytical and characterization methods.

NiSe and CoSe Topological Nodal-Line Semimetals: A Sustainable Platform for Efficient Thermoplasmonics and Solar-Driven Photothermal Membrane Distillation.

The control of heat at the nanoscale via the excitation of localized surface plasmons in nanoparticles (NPs) irradiated with light holds great potential in several fields (cancer therapy, catalysis, desalination). To date, most thermoplasmonic applications are based on Ag and Au NPs, whose cost of raw materials inevitably limits the scalability for industrial applications requiring large amounts of photothermal NPs, as in the case of desalination plants. On the other hand, alternative nanomaterials proposed so far exhibit severe restrictions associated with the insufficient photothermal efficacy in the visible, the poor chemical stability, and the challenging scalability. Here, it is demonstrated the outstanding potential of NiSe and CoSe topological nodal-line semimetals for thermoplasmonics. The anisotropic dielectric properties of NiSe and CoSe activate additional plasmonic resonances. Specifically, NiSe and CoSe NPs support multiple localized surface plasmons in the optical range, resulting in a broadband matching with sunlight radiation spectrum. Finally, it is validated the proposed NiSe and CoSe-based thermoplasmonic platform by implementing solar-driven membrane distillation by adopting NiSe and CoSe nanofillers embedded in a polymeric membrane for seawater desalination. Remarkably, replacing Ag with NiSe and CoSe for solar membrane distillation increases the transmembrane flux by 330% and 690%, respectively. Correspondingly, costs of raw materials are also reduced by 24 and 11 times, respectively. The results pave the way for the advent of NiSe and CoSe for efficient and sustainable thermoplasmonics and related applications exploiting sunlight within the paradigm of the circular blue economy.

The advent of thermoplasmonic membrane distillation.

Freshwater scarcity is a vital societal challenge related to climate change, population pressure, and agricultural and industrial demands. Therefore, sustainable desalination/purification of salty/contaminated water for human uses is particularly relevant. Membrane distillation is an emerging hybrid thermal-membrane technology with the potential to overcome the drawbacks of conventional desalination by a synergic exploitation of the water-energy nexus. Although membrane distillation is considered a green technology, efficient heat management remains a critical concern affecting the cost of the process and hindering its viability at large scale. A multidisciplinary approach that involves materials chemistry, physical chemistry, chemical engineering, and materials and polymer science is required to solve this problem. The combination of solar energy with membrane distillation is considered a potentially feasible low-cost approach for providing high-quality freshwater with a low carbon footprint. In particular, recent discoveries about efficient light-to-heat conversion in nanomaterials have opened unprecedented perspectives for the implementation of sunlight-based renewable energy in membrane distillation. The integration of nanofillers enabling photothermal effects into membranes has been demonstrated to be able to significantly enhance the energy efficiency without impacting on economic costs. Here, we provide a comprehensive overview on the state of the art, the opportunities, open challenges and pitfalls of the emerging field of solar-driven membrane distillation. We also assess the peculiar physicochemical properties and synthesis scalability of photothermal materials, as well as the strategies for their integration into polymeric nanocomposite membranes enabling efficient light-to-heat conversion and freshwater.

Dimensionally controlled graphene-based surfaces for photothermal membrane crystallization.

Membrane-based photothermal crystallization - a pioneering technology for mining valuable minerals from seawater and brines - exploits self-heating nanostructured interfaces to boost water evaporation, so achieving a controlled supersaturation environment that promotes the nucleation and growth of salts. This work explores, for the first time, the use of two-dimensional graphene thin films (2D-G) and three dimensional vertically orientated graphene sheet arrays (3D-G) as potential photothermal membranes applied to the dehydration of sodium chloride, potassium chloride and magnesium sulfate hypersaline solutions, followed by salt crystallization. A systematic study sheds light on the role of vertical alignment of graphene sheets on the interfacial, light absorption and photothermal characteristics of the membrane, impacting on the water evaporation rate and on the crystal size distribution of the investigated salts. Overall, 3D-G facilitates the crystallization of the salts because of superior light-to-heat conversion leading to a 3-fold improvement of the evaporation rate with respect to 2D-G. The exploitation of sunlight graphene-based interfaces is demonstrated as a potential sustainable solution to aqueous wastes valorization via recovery in solid phase of dissolved salts using renewable solar energy.

Effects of groundwater abstraction and desalination brine deep injection on a coastal aquifer.

As a result of climate change, population increase and improvement of living standards, the water demand is annually growing drawing worldwide attention on seawater desalination to face water crisis. The total global desalination capacity is dominated by Reverse Osmosis (RO) and, often, this desalination process is fed with the brackish water extracted from coastal aquifers. After this process the desalted freshwater is obtained at a recovery factor of ca. 50%, while concentrate byproduct, named brine, is disposed back to coastal aquifers, seas, oceans or evaporative ponds, determining detrimental effects on the surrounding environment. A common approach to clean out the brine is the deep-well injection into coastal aquifers, exacerbating the seawater intrusion. The ultimate result is a reduction of the available water both in terms quantity and quality hampering the benefits of the desalination. The aim of this study is to investigate the effects of brine water injection in the Nile coastal aquifer, one of the largest underground freshwater reservoirs in the world, and to find a way to minimize and manage the environmental impact of the RO process. In order to simulate the effects of the brackish water extraction and the brine deep-injection on the Nile coastal aquifer, a combined seawater intrusion, numerical models for flow and salt transport model in aquifers and the solution-diffusion in RO practices were implemented. Different management scenarios were considered and their consequences on salt mass storage in the Nile coastal aquifer evaluated. According to the numerical results, the salinization of the coastal aquifer can be mitigated by reducing the concentration of the water feeding the reverse osmosis plant, i.e., mixing the extracted brackish water with a lower salinity water. Besides, low feed salinity leads to significant gains by decreasing the specific energy consumption of the desalination process.

Tuning the Electrochemical Properties of Novel Asymmetric Integral Sulfonated Polysulfone Cation Exchange Membranes.

In this study, novel asymmetric integral cation exchange membranes were prepared by the wet phase inversion of sulfonated polysulfone (SPSf) solutions. SPSf with different degrees of sulfonation (DS) was synthesized by variation in the amount of chlorosulfonic acid utilized as a sulfonating agent. The characterization of SPSf samples was performed using FTIR and 1H-NMR techniques. SPSf with a DS of 0.31 (0.67 meq/g corresponding ion exchange capacity) was chosen to prepare the membranes, as polymers with a higher DS resulted in poor mechanical properties and excessive swelling in water. By a systematic study, the opportunity to tune the properties of SPSf membranes by acting on the composition of the polymeric solution was demonstrated. The effect of two different phase inversion parameters, solvent type and co-solvent ratio, were investigated by morphological and electrochemical characterization. The best properties (permselectivity of 0.86 and electrical resistance of 6.3 Ω∙cm2) were obtained for the membrane prepared with 2-propanol (IPA):1-Methyl-2-pyrrolidinone (NMP) in a 20:80 ratio. This membrane was further characterized in different solution concentrations to estimate its performance in a Reverse Electrodialysis (RED) operation. Although the estimated generated power was less than that of the commercial CMX (Neosepta) membrane, used as a benchmark, the tailor-made membrane can be considered as a cost-effective alternative, as one of the main limitations to the commercialization of RED is the high membrane price.

Energy Harvesting from Brines by Reverse Electrodialysis Using Nafion Membranes.

Ion exchange membranes (IEMs) have consolidated applications in energy conversion and storage systems, like fuel cells and battery separators. Moreover, in the perspective to address the global need for non-carbon-based and renewable energies, salinity-gradient power (SGP) harvesting by reverse electrodialysis (RED) is attracting significant interest in recent years. In particular, brine solutions produced in desalination plants can be used as concentrated streams in a SGP-RED stack, providing a smart solution to the problem of brine disposal. Although Nafion is probably the most prominent commercial cation exchange membrane for electrochemical applications, no study has investigated yet its potential in RED. In this work, Nafion 117 and Nafion 115 membranes were tested for NaCl and NaCl + MgCl2 solutions, in order to measure the gross power density extracted under high salinity gradient and to evaluate the effect of Mg2+ (the most abundant divalent cation in natural feeds) on the efficiency in energy conversion. Moreover, performance of commercial CMX (Neosepta) and Fuji-CEM 80050 (Fujifilm) cation exchange membranes, already widely applied for RED applications, were used as a benchmark for Nafion membranes. In addition, complementary characterization (i.e., electrochemical impedance and membrane potential test) was carried out on the membranes with the aim to evaluate the predominance of electrochemical properties in different aqueous solutions. In all tests, Nafion 117 exhibited superior performance when 0.5/4.0 M NaCl fed through 500 µm-thick compartments at a linear velocity 1.5 cm·s-1. However, the gross power density of 1.38 W·m-2 detected in the case of pure NaCl solutions decreased to 1.08 W·m-2 in the presence of magnesium chloride. In particular, the presence of magnesium resulted in a drastic effect on the electrochemical properties of Fuji-CEM-80050, while the impact on other membranes investigated was less severe.

On the Aggregation and Nucleation Mechanism of the Monoclonal Antibody Anti-CD20 Near Liquid-Liquid Phase Separation (LLPS).

The crystallization of Anti-CD20, a full-length monoclonal antibody, has been studied in the PEG400/Na2SO4/Water system near Liquid-Liquid Phase Separation (LLPS) conditions by both sitting-drop vapour diffusion and batch methods. In order to understand the Anti-CD20 crystallization propensity in the solvent system of different compositions, we investigated some measurable parameters, normally used to assess protein conformational and colloidal stability in solution, with the aim to understand the aggregation mechanism of this complex biomacromolecule. We propose that under crystallization conditions a minor population of specifically aggregated protein molecules are present. While this minor species hardly contributes to the measured average solution behaviour, it induces and promotes crystal formation. The existence of this minor species is the result of the LLPS occurring concomitantly under crystallization conditions.

Membrane bioreactor for investigation of neurodegeneration.

To gain a better understanding of neurodegeneration mechanisms and for preclinical evaluation of new therapeutics more accurate models of neuronal tissue are required. Our strategy was based on the implementation of advanced engineered system, like membrane bioreactor, in which neurons were cultured in the extracapillary space of poly(l-lactic acid) (PLLA) microtube array (MTA) membranes within a dynamic device designed to recapitulate specific microenvironment of living neuronal tissue. The high membrane permeability and the optimized fluid dynamic conditions created by PLLA-MTA membrane bioreactor provide a 3D low-shear stress environment fully controlled at molecular level with enhanced diffusion of nutrients and waste removal that successfully develops neuronal-like tissue. This neuronal membrane bioreactor was employed as in vitro model of ß-amyloid -induced toxicity associated to Alzheimer's disease, to test for the first time the potential neuroprotective effect of the isoflavone glycitein. Glycitein protected neurons from the events induced by ß-amyloid aggregation, such as the production of ROS, the activation of apoptotic markers and ensuring the viability and maintenance of cellular metabolic activity. PLLA-MTA membrane bioreactor has great potential as investigational tool in preclinical research, contributing to expand the available in vitro devices for drug screening.

Photothermal Membrane Distillation for Seawater Desalination.

Thermoplasmonic effects notably improve the efficiency of vacuum membrane distillation, an economically sustainable tool for high-quality seawater desalination. Poly(vinylidene fluoride) (PVDF) membranes filled with spherical silver nanoparticles are used, whose size is tuned for the aim. With the addition of plasmonic nanoparticles in the membrane, the transmembrane flux increases by 11 times, and, moreover, the temperature at the membrane interface is higher than bulk temperature.

Bioinspired Synthesis of CaCO3 Superstructures through a Novel Hydrogel Composite Membranes Mineralization Platform: A Comprehensive View.

Hydrogel composite membranes (HCMs) are used as novel mineralization platforms for the bioinspired synthesis of CaCO3 superstructures. A comprehensive statistical analysis of the experimental results reveals quantitative relationships between crystallization conditions and crystal texture and a strong selectivity toward complex morphologies when monomers bearing carboxyl and hydroxyl groups are used together in the hydrogel layer synthesis in HCMs.

Kinetics of oxygen uptake by cells potentially used in a tissue engineered trachea.

Synthetic polymer scaffold seeded with autologous cells have a clinical translational potential. A rational design oriented to clinical applications must ensure an efficient mass transfer of nutrients as a function of specific metabolic rates, especially for precariously vascularized tissues grown in vitro or integrated in vivo. In this work, luminescence lifetime-based sensors were used to provide accurate, extensive and non-invasive measurements of the oxygen uptake rate for human mesenchymal stem cells (hMSCs), tracheal epithelial cells (hTEpiCs) and human chondrocytes (hCCs) within a range of 2-40% O2 partial pressure. Estimated Michaelis-Menten parameters were: V(max) = 0.099 pmol/cell⋅h and K(M) = 2.12 × 10(-7) mol/cm(3) for hMSCs, V(max) = 1.23 pmol/cell⋅h and K(M) = 2.14 × 10(-7) mol/cm(3) for hTEpiCs, V(max) = 0.515 pmol/cell⋅h and K(M) = 1.65 × 10(-7) mol/cm(3) for hCCs. Kinetics data served as an input to a preliminary computational simulation of cell culture on a poly-ethylene terephthalate (PET) tracheal scaffold obtaining an efficient mass transfer at cell density of 10(6) cell/cm(3). Oxygen concentration affected the glucose uptake and lactate production rates of cells that adapted their metabolism according to energy demand in hypoxic and normoxic conditions.

Insights into the polymorphism of glycine: membrane crystallization in an electric field.

In this work we studied glycine crystallization with two main objectives: (i) to get improved control of crystal growth and polymorphic selectivity of organic molecules; (ii) to achieve additional insights into the nucleation mechanisms of glycine polymorphs. To reach these goals, membrane crystallization technology, a tool which allows improved control of supersaturation in solution crystallization, was used under different operating conditions: the variable solvent removal rate, acidic and almost neutral pH, the presence of a pulsed electric field. The traditional explanation for the crystallization of α and γ glycine polymorphs from aqueous solution is based on the general cyclic dimer hypothesis and the self-poisoning mechanism. In contrast with both the conventional theories, experimental results suggest that the relative nucleation rates with respect to the relative growth kinetics of the two forms under the different conditions play a dominant role in determining the polymorphic outcome. Our results instead support a molecular nucleation route where open chain dimers can behave as building units for both γ- and α-glycines in the rate determining structuring step of the two-step nucleation mechanism.

Human lymphocytes cultured in 3-D bioreactors: influence of configuration on metabolite transport and reactions.

Peripheral blood lymphocytes isolated from healthy human donors' buffy coat were cultured in membrane bio-reactors (MBR) designed in two different configurations: a conventional hollow-fiber (HF) bundle of modified polyetheretherketone (PEEK-WC) arranged in parallel, and a cross-assembled PEEK-WC and polyethersulfone (PES) HF membranes having different structural properties. Both bioreactors were experimentally compared in terms of metabolic activity of cultured cells, monitored over 8 days with respect to glucose uptake rate (GUR) and lactate production rate (LPR), and mathematically modelled by Computational Fluid Dynamics (CFD) method in order to investigate the impact of geometrical configuration and transport properties of biomaterials. The almost uniform trend of GUR from day 2 to day 7 (average of 0.0497 ± 0.0076 ng/h cell) and the low LPR (that decreased from an initial value of 2.92 ± 0.0055 pg/h cell to practically zero at day 8) provided evidence for superior performance of crossed-HFMBR in reproducing an optimal in vitro physiological environment with quite uniform concentration distribution of species in the extracellular space of the bioreactor and able to maintain lymphocyte viability and functions. The crossed HFMBR also resulted in an enhanced production of interleukin IL-2 over 8 days (average of 0.995 ± 0.25 pg/h/Mcell) and IL-10 in the first 3 days (average of 6.46 ± 0.28 pg/h/Mcell) which were up to one order of magnitude higher with respect to values measured in the parallel configuration.

Energetics of protein nucleation on rough polymeric surfaces.

Metropolis Monte Carlo (MC) algorithm of the two-dimensional Ising model is used to study the heterogeneous nucleation of protein crystals on rough polymeric surfaces. The theoretical findings are compared to those obtained from classical nucleation theory (CNT), and to experimental data from protein model hen egg white lysozyme (HEWL) crystallized on poly(vinylidene fluoride) or PVDF, poly(dimethylsiloxane) or PDMS and Hyflon homemade membranes. The reduction of the activation energy for the nucleation process on polymeric membranes, predicted to occur at increasing surface roughness, results in a nucleation kinetics that is many orders of magnitude faster than in homogeneous phase. In general, MC stochastic dynamics offers the unique opportunity to investigate the effects of collective molecular aggregation at site level on the nucleation rate and, consequently, allows to identify optimal morphological and structural properties of polymeric membranes for a fine control of the crystallization kinetics.

Oxygen mass transfer in a human tissue-engineered trachea.

On June 2008, the first human tissue-engineered trachea replacement was performed using decellularized (de-antigenised) cadaveric donor trachea, seeded with recipient epithelial cells on the internal surface of the graft and mesenchymal stem-cell-derived chondrocytes on the external. During the follow-up, cytological analysis at 4 postoperative days showed a migration of the stem-cells derived chondrocytes from the outer to the inner surface of the first 2 cm of the graft length. With the aim to rationalize these clinical findings, and under the hypothesis that cellular migration is driven by the oxygen gradients developing from the external part of the construct (exposed to O(2) deficiency) towards the better oxygenated epithelial region, an accurate computational model of oxygen transport in the trachea engineered construct was developed and solved using finite element method (FEM). Results confirm that critical limitation to oxygen transport prevalently occurs from proximal to middle section, within the first 2.8 cm of longitudinal length, in good agreement with experimental observation. In the proximal section, recognized as the most critical part of the engineered construct, the severe O(2) mass transfer limitation causes a drastic reduction of the diffusive flux within a distance of 650 microm. At cell density of 1 x 10(7)cells/cm(3), the 30% c.a of the total section area is under oxygen deficiency (O(2) partial pressure below the critical threshold of 38 mmHg). Along the whole tracheal construct, the Thiele modulus ranges within 2.3 and 3.7 in the external chondrocyte compartment, confirming thus the importance of the mass transfer limitation to oxygen diffusion rate. In general, the efficiency of the O(2) transport reduces considerably in the region close to proximal section.

Antisolvent membrane crystallization of pharmaceutical compounds.

This article describes a modification of the conventional membrane crystallization technique in which a membrane is used to dose the solvent/antisolvent composition to generate supersaturation and induce crystallization in a drug solution. Two operative configurations are proposed: (a) solvent/antisolvent demixing crystallization, where the solvent is removed in at higher flow rate than the antisolvent so that phase inversion promotes supersaturation and (b) antisolvent addition, in which the antisolvent is dosed into the crystallizing drug solution. In both cases, solvent/antisolvent migration occurs in vapor phase and it is controlled by the porous membrane structure, acting on the operative process parameters. This mechanism is different than that observed when forcing the liquid phases through the pores and the more finely controllable supersaturated environment would generate crystals with the desired characteristics. Two organic molecules of relevant industrial implication, like paracetamol and glycine, were used to test the new systems. Experiments demonstrated that, by using antisolvent membrane crystallization in both configurations, accurate control of solution composition at the crystallization point has been achieved with effects on crystals morphology.

Human hepatocyte functions in a crossed hollow fiber membrane bioreactor.

An important challenge in liver tissue engineering is the development of bioartificial systems that are able to favour the liver reconstruction and to modulate liver cell behaviour. A crossed hollow fiber membrane bioreactor was developed to support the long-term maintenance and differentiation of human hepatocytes. The bioreactor consists of two types of hollow fiber (HF) membranes with different molecular weight cut-off (MWCO) and physico-chemical properties cross-assembled in alternating manner: modified polyetheretherketone (PEEK-WC) and polyethersulfone (PES), used for the medium inflow and outflow, respectively. The combination of these two fiber set produces an extracapillary network for the adhesion of cells and a high mass exchange through the cross-flow of culture medium. The transport of liver specific products such as albumin and urea together with the transport of drug such as diazepam was modelled and compared with the experimental metabolic data. The theoretical metabolite concentration differed 7.5% for albumin and 5% for urea with respect to experimental data. The optimised perfusion conditions of the bioreactor allowed the maintenance of liver functions in terms of urea synthesis, albumin secretion and diazepam biotransformation up to 18 days of culture. In particular the good performance of the bioreactor was confirmed by the high rate of urea synthesis (28.7 microg/h 10(6) cells) and diazepam biotransformation. In the bioreactor human hepatocytes expressed at high levels the individual cytochrome P450 isoenzymes involved in the diazepam metabolism. The results demonstrated that crossed HF membrane bioreactor is able to support the maintenance of primary human hepatocytes preserving their liver specific functions for all investigated period. This device may be a potential tool in the liver tissue engineering for drug metabolism/toxicity testing and study of disease pathogenesis alternatively to animal experimentation.

Mass transfer and metabolic reactions in hepatocyte spheroids cultured in rotating wall gas-permeable membrane system.

Isolated hepatocytes in spheroid configuration exhibit a high degree of cell-cell contacts, which are important in the maintenance of viability and liver specific functions. In the absence of a vascular network, the cells in a large spheroid size experience mass transfer limitations of metabolites and oxygen in the core of aggregates. In this paper transport phenomena related to the diffusion and reaction of oxygen, glucose and lactate are mathematically described and experimentally verified for hepatocyte spheroids cultured in a rotating-wall polystyrene system (RWPS) not permeable for gases and in a rotating-wall membrane system (RWMS) with oxygen-permeable membrane. The concentration profiles of glucose, oxygen and lactate in the hepatocyte spheroids were estimated for different diameters of aggregates by solving the mass transfer equations for simultaneous diffusion and reaction, by finite element method. Simulation results evidenced that, for aggregates with size lower than 300 microm cultured in both RWPS and RWMS systems, the concentration profiles of glucose and lactate towards the core of spheroids (effective diffusion coefficients in the order of 10(-11)m(2)/s) are not significantly affected by the metabolic rate (c.a 10(-6)microg/mm(3)/s for glucose and about one order of magnitude less for lactate). On the contrary, the transport of oxygen (diffusion coefficient: 3.4 x 10(-10)m(2)/s, reaction rate: 1.5 x 10(-5)microg/mm(3)/s) is critically affected by the size of the multicellular spheroids and significant gradients in oxygen concentration may develop in spheroids. Aggregates with a size greater than 200 microm suffer severe oxygen limitation in the most part of its size attaining the lowest partial pressure in the centre. The improved viability predicted by the model culturing hepatocyte spheroids in the RWMS, characterized by a higher O(2) permeability with respect to RWPS, was experimentally confirmed. The results demonstrated that the mathematical model used in this study represents a useful support to experimental procedures in order to obtain hepatocyte spheroids with optimal size.