Traditional cell cultures are performed in two-dimensional (2D) systems such as Petri dishes, multiwell plates or flasks. However, they cannot realistically mimic the morphophysiological complexity of the original three-dimensional (3D) in vivo environment from which the cells of specific lines originate. Without opposing animal experimentation but promoting its responsible application, the development of alternative cell culture systems tries to ensure compliance with the 3R principles. Reduction (reduction in the animals used for in vivo tests), Refinement (experimental design optimization to limit stress and affliction to laboratory animals) and Replacement (total or partial replacement of animal testing with alternative valid methods) are increasingly desired and strongly recommended as fundamental ethical aspects in the use of animals in scientific experiments.
Traditional cell cultures are performed in two-dimensional (2D) systems such as Petri dishes, multiwell plates or flasks. However, they cannot realistically mimic the morphophysiological complexity of the original three-dimensional (3D) in vivo environment from which the cells of specific lines originate 
. Without opposing animal experimentation but promoting its responsible application, the development of alternative cell culture systems tries to ensure compliance with the 3R principles. Reduction (reduction in the animals used for in vivo tests), Refinement (experimental design optimization to limit stress and affliction to laboratory animals) and Replacement (total or partial replacement of animal testing with alternative valid methods) are increasingly desired and strongly recommended as fundamental ethical aspects in the use of animals in scientific experiments 
Three-dimensional cell cultures can better mimic in vivo conditions than two-dimensional monolayer cell cultures, since, after isolation, cells generally lose their original morphology, changing the way they perform most of their physiological functions. Growth on an adhesion substrate results in cellular loss of polarity and it understandably influences intracellular trafficking, the functionality of subcellular compartments and some functions such as cell signaling and secretion, limiting the access to the culture media’s nutrients, the gaseous exchanges and the removal of waste substances 
. In 2D cell cultures the complex network of regulatory interactions in the extracellular matrix (ECM), cells and tissue are altered, therefore the use of properly designed 3D culture systems assists researchers in obtaining more reliable results, deepening our understanding of what really happens in vivo [4,5]
. Many studies report data concerning the significant differences in the morphology, protein expression, differentiation, viability, and functionality of cells grown in 2D or 3D systems [1,3,6,7,8,9,10,11]
Three-dimensional cell cultures can be successfully used for many different applications, including cell or drug screenings [12,13,14,15]
and tissue generation (engineering) purposes [16,17,18]
; however, the reproduction of a biomimetic environment is challenging [19,20,21]
. It is very important to replicate as close as possible the original in vivo physiological cell microenvironment. When dealing with 3D cell cultures, one of the big issues is to provide a physiological exchange of substances (gas and molecules) between cells and their related microenvironment, inward for the cell nutrients and outward for the waste products. It is known that unfortunately 2D cell culture usually results in low nutrients and/or hypoxic regions related to cellular aggregation phenomena, biological media and gas consumption rates 
The use of optimized ECM-analog biomaterials with physico-chemical and structural properties, able to guarantee optimized degradation or residence rate and micro/nanoporosity, improves in vitro cell proliferation, differentiation, and interactions [23,24]
Decellularized engineered ECM and bioreactor-based solutions constitute valid alternatives to 2D cell cultures. The application of decellularization protocols in tissue engineering and regenerative medicine limits the possible immune response in the transplanted host by removing all the potential immunogenic biomaterials. The non-immunogenic ECM can be re-cellularized with autologous or stem cells, carrying out a fully personalized medicine approach [25,26]
. In addition, micro-bioreactors can be regarded as a major step toward more complex organ-on-a-chip (OoC) systems , providing manageable 3D cell culture settings usually including suitable fluid flow supply and low amounts of chemicals and cells .
2. Physiological Exchange of Substances
In physiological conditions, the exchange of substances and gases between cells and the environment takes place thanks to blood microcirculation at the level of the capillaries. Blood circulates from the arterioles to capillaries, then to venules and the topology of these vessels changes according to the different tissues that are sprinkled. Some beds are structured as trees, others as arcades or sinuses or portal systems . The capillary density (CD) depends on the varying oxygen and nutrients requirements to keep a stable metabolism. The average CD in human tissue is around 600 per mm3 and it changes according to the different organism’s tissues. The CD is higher in the brain, kidneys, liver and myocardium (around 2500–3000 per mm3), reduced in the phasic units of the skeletal musculature (around 300–400 per mm3) and even lower in the bones, fat, connective tissues and in the tonic units of the skeletal musculature (less than 100 per mm3) .
Considering an average capillary diameter of 8 μm and length of 5 mm , it can be calculated the average distance between adjacent capillaries which is around 30–40 μm (around 1–3 cell width). To reach a particular cell, molecules exit the capillary and cross one or two cells to reach the target one. A capillary vessel can be considered as a tube consisting of a single endothelial cells’ layer less than 1 μm thick . There are three types of capillaries: (i) the continuous type with cells tightly joined together, which are present in muscles, nerves, and connective tissues; (ii) the fenestrated type, with cells so thin that internal vesicles form small pores 100 nm thick and 6 nm in diameter (typically around 1000 pores/μm2); (iii) the discontinuous type with distinct intercellular gaps (around 5 μm in diameter) and a broken basement membrane, commonly found in organs such as the liver, spleen, and bone marrow, the functions of which include the injection or extraction of whole cells, large molecules and extraneous particles in/from the blood stream .
The nutritive and waste substances pass the capillary pores by means of a dynamic equilibrium established between the hydraulic pressure and the osmotic pressure gradients between the blood inside the capillarie
s and the interstitial fluid in the ECM. In particular, the blood’s osmotic pressure (oncotic pressure) is around 25–30 mmHg and it is higher than the one of interstitial fluid which is around 0 mmHg. The osmotic pressure gradient is constant between the blood circuit and the surrounding tissues including the arterial capillaries and the venous capillaries. While the hydraulic pressure in blood decreases, going from the arterial capillaries (where it is around 40 mmHg) to the venous capillaries (which is around 15 mmHg), in the interstitial fluid it is around 2 mmHg. Since, in the arterial capillaries, the hydraulic pressure in the blood is higher than the oncotic pressure, filtration, a flow that goes from capillaries to tissues, occurs. On the contrary, in the venous capillaries, the oncotic pressure is higher than the hydraulic one and liquids are reabsorbed in capillaries due to a flow from tissues to capillaries (Figure 1).
The exchange of molecules between blood microcirculation and cells forming tissues and organs is due to filtration, reabsorption and at the same time diffusion through the capillary membrane of substances at a different concentration on the two sides of the capillary membrane. The presence of capillaries drastically reduces the diffusion length, since they are very close to each other.
Figure 1. The scheme represents an arterial capillary (in red) connected to a venous capillary (in blue) and surrounded by a generic tissue constituted by cells. The arrows show the movement of fluids around the capillary, due to filtration (in the arterial side) and reabsorption (in the venous side).
3. Theory behind the Molecule Transport Mechanisms
Referring to the theory behind the movement of particles across a capillary’s membrane, it can be considered a unidimensional motion, assuming the concentration gradient across the membrane as constant. This approximation is certainly valid in the dynamic environment of the biological systems where, while cells consume nutrients and produce wastes, capillaries provide nutrients and remove wastes, keeping the concentration gradients across capillary’s membrane constant.
The flux of molecules due to diffusion can be calculated as:
- ΔC=(C2−C1) is the concentration gradient of a generic molecule between the external and internal part of the capillary membrane;
- P is the permeability coefficient and can be calculated as:
- Δx is the capillary membrane thickness;
- α is the partition coefficient and can be calculated as:
- N is the number of pores;
- A is the capillary surface;
- R is the pore radius;
- n is the pore density;
- DM is the membrane diffusion coefficient and can be calculated as:
- ϵ2 is a coefficient that depends on the trajectory of the particle inside the pore;
- r is the particle radius (it is an approximation which considers the molecules passing the pore to have a spherical shape);
- D is the diffusion coefficient which can be calculated as:
This last equation is valid if the particle which diffuses has a spherical shape. In this work, the particles will be considered, as first approximation, to have a spherical shape.
While the flux of molecules through the capillaries can be calculated as a function of the pressure and the osmotic gradient across the capillary.
- k is the Boltzman constant;
- T is the temperature;
- η is the blood viscosity;
For instance, considering a pore density of 100 pore/μm2 , a pore diameter of 6 nm, a capillary thickness of 1000 nm, at a body temperature of 37 °C, a glucose molecule, with a relative radius of 4.5 Å and present at a concentration of 80 mg/dl in blood, will diffuse through the capillary at 28.5∙10−2 mg/m2s (roughly 7.6∙1017 molecules/(m2s)). In a capillary with 8 μm of diameter and 1 mm of length, there will be a flux of glucose due to the diffusion of 5.7∙10−28 mg/s (roughly 1.5∙10−9 molecules/s). In the same conditions, considering a pressure gradient of 40 mmHg and an osmotic pressure gradient of 25 mmHg, the flux of glucose due to filtration will be of 3.6∙10−6 mg/m2s (roughly 9.6∙1012 molecules/m2s). In a single capillary, the filtrated glucose will be 7.2∙10−33 mg/s, corresponding to roughly 1.9∙10−14 molecules/s. Thus, in the case of glucose, the dominant phenomenon is diffusion. Considering a total number of capillaries in the human body equal to 4∙109, it can be calculated a movement of glucose equal to different kilograms per day. In general, the exchange of substances between blood and tissues is dominated by diffusion, referring to a very small space (as mentioned before: 2–3 cell width, around 40 μm).
- Δp=(p2−p1) is the hydraulic pressure gradient across the capillary membrane;
- Δπ=(π2−π1) is the osmotic pressure gradient across the capillary membrane;
- Lp is the filtration coefficient and can be calculated as:
4. Cell Microenvironment: Static and 3D Cell Screening
Mimicking the best possible cellular microenvironment does not only mean having control overflows, since many parameters such as shear stress, cell interactions, pH, CO2, temperature, and O2 variations affect its regulation and balance. Although it is well-known that in any kind of cell screening applications, it is very important to control the cell microenvironment, the current in vitro systems are still far from having an appreciable level of control on it . Generally, supports such as Petri dishes, flasks and vials are used to culture cells in a static condition, leading to temperature and chemical gradients that could make it difficult to maintain homeostasis . In addition, the use of standard static cell culture supports requires a lot of manual procedures, such as the addition of fresh culture medium and the removal of the old one, resulting in time-demanding procedures for the operator and stressful conditions for cells.
One of the alternatives to static cell culture procedures is the use of in vivo experiments that are undoubtedly able to reduce the gap between in vitro and in vivo screening procedures. Unfortunately
, in vivo providing manageable 3experimentation in basic and pre-clinical practice involves a considerable waste of resources, both in monetary and ethical terms, considering the number of animals to be sacrificed. Over the years and with the progress in biomedical and technological fields, there has been a tendency to drastically reduce in vivo experiments using the advanced alternatives to animal testing towards the 3Rs (Replacement, Reduction, Refinement) approach. . Although replacing should be the main purpose of the 3Rs, its implementation in the short-term is ambitious, while minimizing the number of animals and refining their welfare should be feasible in the short/middle-term .
A solid alternative to animal tests is cell scaffolds, as 3
D cell culture can setteffectively mimic the cellular and tissue microarchitecture . Both for pharmacolog
ngs usuall and pathologies modelling, 3D scaffolds represent one of the most successful platforms for biomedical applications .
Dattola et al. developed a pol
y(vinyl) alcohol (PVA) 3D scaffold where stem cells grew incland differentiated into cardiac cells (Figure 2) . These scaffolds mimicked the mechanical properties of ECM in which cardiomyocytes proliferated in vivo, demonstrated by the contractile property detected in the cardiomyocytes grown on the proposed scaffold. However, it was fo
din that cells colonized only the outermost part of the scaffold, since they could not survive deep into the bulk volume, because the nutrients were not properly provided in the innermost layers of the 3D scaffolds.
They provided a continuous supply of nutrients and oxy
Figure 2. 3D PVA scaffolds in which stem cells are grown . (a) macroscopic view of the 3D wet scaffold at room temperature; (b) scanning electron microscope cross sectional details of the 3D structure; (c) fluorescence microscopy image of DAPI stained cell homogeneously distributed on a Matrigel coated PVA scaffold.
gen suitable fluid flow suppwhile removing metabolic wastes by creating an artificial network. This enabled the production of large, engineered tissues and the assembly of multiples organoids or spheroids to generate a whole system in vitro. Microfluidic systems also allowed precise culture conditions and better monitoring of cells. Once cells were cultured three-dimensionally in vitro, these considerations should be taken in account to reproduce in vivo conditions. In this contest microfluidic scaffolds effectively tried to solve the main issues related to the establishment of 3D cell cultures. Microfluidic systems, as an amelioration of the 3D scaffold methods, aimed to reduce in vitro cultured cells’ discomfort and death related to inadequate nutrients distribution and catabolites clearance. Microfluidic cell culture solutions allowed non-invasively time-saving sampling and screening, reducing post-seeding inhomogeneity, since their tunable design and networks enable multiple and automated procedures .
luidics assisted 3D cell culture b
y and low amounts mechanically and chemically controlling cellular microenvironment, gas and temperature gradients, shear-stress and most of the relevant physical-chemical properties. Nowadays, these solutions are customized for the main biomedical applications, including cell therapy, drug, and toxicity assays (Table 1).
Table 1. Summary of a selection of the most representative and recent 3D microfluidic cell culture applications.
f chemicals and cells [28 these studies concern drug screening and OoC applications, witnessing the increasing interest in regenerative and personalized medicine. Consulting the papers cited in the table, it is possible to extrapolate how, in general, microfluidics can reduce time and costs, allowing the implementation of high-throughput screening in drug discovery and disease models.
In the work of Shin et al. , a reproducible protocol to induce intestinal morphogenesis in microfluidic platforms using Caco-2 cell line was reported. Authors established a disease model, developing in vitro intestinal epithelial layers suitable to study intestinal physiology and host-microbiome interactions. Regional differentiation markers such as KRT20, villin, CEACAM1 and CYP3A4 were considerably expressed in the villus region, suggesting cytodifferentiation of the 3D epithelial layers.
Bircsak et al.  used an OrganoPlate LiverTox™ platform to co-culture three different cell lines: (i) iPSC-derived hepatocytes (ii) THP-1 monoblast and (iii) endothelial cells, respectively, in the ratio of 5:5:1, reproducing a hepatic model for hepatotoxicity. The liver model was evaluated for albumin, urea, alpha-fetoprotein synthesis, cell viability and CYP3A4 activity over 15 days. A total of 159 hepatotoxic compounds were screened, evaluating liver response to drugs using viability, nuclear size, urea and albumin assays.
In recent years, devices such as “body-on-a-chip” or “human-on-a-chip” have become ever more common and some of the recently proposed systems are already have the ability to reproduce multi-organ interactions. In Maschmeyer et al. , the authors introduced a four-organ-chip system modeling human intestine, liver, skin and kidney. The device, composed by two polycarbonate cover-plates and by a PDMS-glass chip, can accommodate both a blood and an excretory system, each controlled by a dedicated peristaltic micro-pump. This device has been designed to support absorption, distribution, metabolism and excretion (ADME) and profiling of substances
,29 along with repeated toxicity testing of drugs. Authors successfully co-cultured the different cell types for 28 days
,30 reporting a high cell viability and discrete physiological tissue architecture over the entire period. Finally
,31] metabolic and gene analysis confirmed the establishment of a reproducible homeostasis between all four tissues