*Article* **Interaction between Macrophages and Nanoparticles: In Vitro 3D Cultures for the Realistic Assessment of Inflammatory Activation and Modulation of Innate Memory**

**Benjamin J. Swartzwelter 1,†, Alessandro Verde 1, Laura Rehak 2, Mariusz Madej 1,‡, Victor. F. Puntes 3, Anna Chiara De Luca 1, Diana Boraschi 1,4,\* and Paola Italiani 1,4,\***

**Abstract:** Understanding the modes of interaction between human monocytes/macrophages and engineered nanoparticles is the basis for assessing particle safety, in terms of activation of innate/inflammatory reactions, and their possible exploitation for medical applications. In vitro assessment of nanoparticle-macrophage interaction allows for examining the response of primary human cells, but the conventional 2D cultures do not reproduce the three-dimensional spacing of a tissue and the interaction of macrophages with the extracellular tissue matrix, conditions that shape macrophage recognition capacity and reactivity. Here, we have compared traditional 2D cultures with cultures on a 3D collagen matrix for evaluating the capacity gold nanoparticles to induce monocyte activation and subsequent innate memory in human blood monocytes in comparison to bacterial LPS. Results show that monocytes react to stimuli almost in the same way in 2D and 3D cultures in terms of production of TNFα and IL-6, but that notable differences are found when IL-8 and IL-1Ra are examined, in particular in the recall/memory response of primed cells to a second stimulation, with the 3D cultures showing cell activation and memory effects of nanoparticles better. In addition, the response variations in monocytes/macrophages from different donors point towards a personalized assessment of the nanoparticle effects on macrophage activation.

**Keywords:** monocytes; macrophages; gold nanoparticles; in vitro models; innate immunity; inflammation; innate memory; 2D cultures; 3D cultures

#### **1. Introduction**

The interaction of engineered nanoparticles (NPs) with the immune system is a key element both in the assessment of nanotoxicity and in the development of nanomedicines and nanomedical devices [1,2]. Possible changes in immune functions upon interaction with NPs may affect the defensive capability of exposed organisms, thereby increasing their susceptibility to infections and diseases. The immune mechanisms that are principally involved in the interaction with NPs are those of innate immunity, the ancient highly conserved defensive system shared by all organisms, from plants to humans [3]. In humans, innate immunity is mainly based on the surveillance action of a number of cell types, in particular the mononuclear phagocytes (monocytes and macrophages) that populate every tissue in the body with the task of recognizing and eliminating possible threats [4].

**Citation:** Swartzwelter, B.J.; Verde, A.; Rehak, L.; Madej, M.; Puntes, V.F.; De Luca, A.C.; Boraschi, D.; Italiani, P. Interaction between Macrophages and Nanoparticles: In Vitro 3D Cultures for the Realistic Assessment of Inflammatory Activation and Modulation of Innate Memory. *Nanomaterials* **2021**, *11*, 207. https://doi.org/10.3390/nano 11010207

Received: 22 December 2020 Accepted: 13 January 2021 Published: 15 January 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Macrophages are resident in tissues and are deputed to phagocytosis and efferocytosis, being a little reactive to stimulation (e.g., with bacteria) to avoid mounting a potentially destructive inflammatory reaction [5,6]. On the other hand, when a potential danger is identified, macrophages and other tissue cells produce chemotactic factors that attract effector cells from the blood. Monocytes are among these cells, and participate in the effector phase of inflammation/innate defence by efficiently reacting to foreign agents to produce a number of inflammation-related factors, including both inflammatory cytokines such as TNFα and anti-inflammatory agents able to turn off the reaction when the danger is eliminated [6,7]. Many studies have addressed the possible inflammatory/toxic effects of engineered NPs by examining their interaction with monocytes and macrophages. These studies yielded variable results, and their relevance in predicting effects in human beings is unclear. Many studies have been performed with NPs that were not tested for the presence of endotoxin, a ubiquitous bacterial contaminant that cannot be eliminated by sterilization and that is among the most effective activators of monocytes/macrophages [8], a fact that may lead to misinterpretation of the NP inflammatory effect results. In vivo studies are generally performed in the mouse, an animal that, like human beings, possesses both innate and adaptive immunity but that presents a number of important immunerelated differences from humans [9,10]. In vitro studies are largely based on transformed macrophage-like cell lines, which ensure repeatability of results but do not reproduce the behaviour of normal non-tumour cells. Studies with human primary monocytes and monocyte-derived macrophages can mimic several of the conditions of real life, although in many cases they miss the important interaction of these cells with their tissue microenvironment. We have previously established a complex kinetic in vitro model that reproduces the entire course of an inflammatory reaction, as it is experienced by human monocytes that enter an inflamed tissue [11]. With this model, we have described the lack of toxicity/direct inflammatory effect of a number of engineered NPs (Au, Ag, FexOy), used at realistic concentrations, tested for the lack of endotoxin contamination and coated with a biocorona of human serum, as it would happen to NPs entering a human tissue [12,13]. The fact that NPs do not have a direct effect on monocytes/macrophages in inducing inflammation does not exclude that they could have other much subtler effects in modulating their functions. It is known that innate immune cells can develop memory, i.e., reprogram their responses to challenges based on their previous exposure experience [14–17]. Innate memory aims at making monocytes/macrophages better able to cope with subsequent challenges after an initial exposure and is the most important immune defensive mechanism in plants and invertebrates [18–20]. In some cases, however, innate memory can lead to a pathological exacerbation of secondary reactions [21–23]. While our understanding of innate memory is still largely incomplete, it is tempting to speculate that engineered NPs might be used for a targeted reprogramming of innate immunity for preventive and therapeutic scopes, such as in vaccination and immunotherapy [24–27]. Few recent studies show that indeed NPs may prime human monocytes and vertebrate/invertebrate macrophages and induce a modification of their response to a subsequent inflammatory challenge [28–32]. In this study, we have examined the memory-inducing capacity of AuNPs on human primary monocytes to define the most suitable conditions for a realistic evaluation. The choice of AuNPs is based on the fact that they are considered inert and harmless and are therefore largely used in many different clinical applications, raising our interest in examining the possibility that they may nevertheless display immunomodulatory effects. Thus, we have assessed the individual response of cells from six individual donors, to assess the impact of the "immunobiography", i.e., the previous history of exposure, on monocyte reactivity and memory [33]. We have measured the production of four different types of inflammationrelated factors to better understand their mutual balance in the overall response; these are two inflammatory factors (TNFα and IL-6), an alarmin (the chemokine IL-8) and an anti-inflammatory cytokine (IL-1Ra). Lastly, we have compared the cell functions (primary activation, induction of memory, memory response) of monocytes/macrophages cultured in conventional 2D plates with those of cells seeded in a 3D collagen matrix

that represents the architecture of a tissue (skin in this case) and its components. The results show that the production of inflammatory factors is not substantially different in cells cultured in 2D vs. 3D, whereas there is a more abundant production of the alarmin and the anti-inflammatory factor in 3D cultures. The results also show the capacity of AuNPs to induce innate memory was evident in 3D cultures, with the effects being strongly donor-dependent.

#### **2. Materials and Methods**

#### *2.1. Synthesis and Characterization of AuNP*

#### 2.1.1. AuNP Synthesis and Purification

Synthesis of AuNPs was conducted using wet chemistry methods as previously described [34]. Briefly, 1 mL of 25 mM HAuCl4 was rapidly added to 150 mL of a boiling aqueous solution of sodium citrate 2.2 mM. The formation of AuNPs (~10 nm) occurred in a few minutes, and was followed by growth-inducing steps, consisting of the addition of HAuCl4 until reaching the desired NP size. Au NPs of 12 nm diameter were used in this study. Sodium citrate tribasic dihydrate (≥99% purity), gold (III) chloride trihydrate HAuCl4·3H2O (99.9% purity) were from Sigma-Aldrich, Inc. (St. Louis, MO, USA). All reagents were used as received without further purification, and all glass material was sterilized and dehydrogenated in an oven prior to use. Pyrogen-free milli-Q water was used in the preparation of all solutions. AuNPs were purified by centrifugation to discard byproducts and contaminants, then NPs were resuspended in a solution of 2.2 mM sodium citrate (final pH = 6.4) and stored at 4 ◦C in the dark.

#### 2.1.2. Nanoparticle Characterization

NP characterisation was performed as previously described [34]. Briefly, STEM (scanning transmission electron microscopy) images were acquired with an FEI Magellan XHR scanning electron microscope (SEM) (FEI, Hillsboro, OR, USA), operated in transmission mode at 20 kV. UV-Vis spectra of AuNPs in sodium citrate were acquired at room temperature using a Shimadzu UV-2400 spectrophotometer (SSI; Kyoto, Japan), reading a spectral range from 300 to 750 nm. The NP hydrodynamic diameter and Z-potential were acquired by dynamic light scattering and laser doppler velocimetry, using a Malvern Zetasizer Nano ZS instrument (Malvern Panalytical Ltd., Malvern, UK) equipped with a light source wavelength of 632.8 nm and a fixed scattering angle of 173◦.

#### *2.2. LAL Assay*

The endotoxin contamination of the NPs was assessed using the chromogenic Pyrochrome LAL assay (Associates of Cape Cod, Inc.; East Falmouth, MA, USA), according to an optimized protocol that included a number of interference controls [35]. The endotoxin contamination in the AuNPs used in this study was 9.0 EU/mg, which excluded the possibility that endotoxin could activate monocytes in the culture at the NP concentration used (1 μg/mL, corresponding to an endotoxin contamination of 0.009 EU/mL, and 10 μg/mL, corresponding to an endotoxin contamination of 0.09 EU/mL, with monocyte activation detectable above 0.1 EU/mL) [36].

#### *2.3. Human Monocyte Isolation and Culture*

Blood was obtained from healthy donors, upon informed consent and in agreement with the Declaration of Helsinki. The protocol was approved by the Regional Ethics Committee for Clinical Experimentation of the Tuscany Region (Ethics Committee Register n. 14,914 of 16 May 2019). Donors were between 25 and 35 years of age, healthy, non-obese, no smokers, not taking medications. Donors 5 and 6 were female, donors 1 and 3 were of Indo-Aryan ethnicity, and donors 2 and 4–6 were of Caucasian ethnicity. Monocytes were isolated by CD14 positive selection with magnetic microbeads (Miltenyi Biotec, Bergisch Gladbach, Germany) from peripheral blood mononuclear cells (PBMC), obtained by Ficoll-Paque gradient density separation (GE Healthcare, Bio-Sciences AB, Uppsala, Sweden). Monocyte preparations used in the experiments were >95% viable and >95% pure (assessed by trypan blue exclusion and cytosmears).

Monocytes were cultured in culture medium (RPMI 1640 + Glutamax-I; GIBCO by Life Technologies, Paisley, UK) supplemented with 50 μg/mL gentamicin sulfate (GIBCO) and 5% heat-inactivated human AB serum (Sigma-Aldrich, Inc.). Cells (5 × 105) were seeded in a final volume of 0.5 mL in control wells of 24-well flat-bottom plates (well internal diameter 15.6 mm; Corning® Costar®; Corning Inc. Life Sciences, Oneonta, NY, USA), or in wells that contained a round clipping of a 3D collagen matrix (diameter 15.4 mm; stabilized collagen type I from decellularized bovine skin, pore size around 100 μm, thickness 2 mm; clinically used for dermal regeneration; Nevelia®, Symathese Biomateriaux, Chaponost, France), obtained with a puncheon tool. Characterisation of monocytes in 3D cultures showed that they can undergo differentiation into macrophages (both spontaneous and CSF-1 mediated) as expected, and express all the phenotypic and functional markers of resting, M1 and M2 macrophages, depending on the applied stimuli (data not shown).

#### *2.4. Cell Activation and Induction of Innate Memory*

After overnight resting, monocytes were exposed for 24 h to AuNPs (1 μg/mL) or LPS (1 ng/mL; from *E. coli* O55:B5; Sigma-Aldrich, Inc.) or left untreated (control). AuNPs were pre-incubated in 50% human AB serum for 60 min at 37 ◦C, before addition to monocyte cultures. This procedure allowed for the formation of a physiologically relevant biocorona that prevented particle aggregation in the culture medium [37]. Ion release and reduction of NP size were not detectable after 24 h in culture medium without monocytes, thereby excluding particle dissolution (data not shown) [38]. After supernatant collection, cells were washed and cultured with fresh culture medium for an additional 6 days (one medium change) to allow the extinction of the activation induced by the previous stimulation. After the resting phase, the supernatant was collected, and cells were challenged for an additional 24 h with fresh medium alone or containing a ten-fold higher concentration of LPS (10 ng/mL). All supernatants (after the first stimulation, after the resting phase and after the challenge phase) were frozen at −20 ◦C for subsequent cytokine analysis. By visual inspection, cell viability and cell number did not substantially change in response to the different treatments.

#### *2.5. Cytokine Analysis*

The levels of the inflammatory cytokines TNFα and IL-6, of the chemokine IL-8 and of the anti-inflammatory factor IL-1Ra were assessed by ELISA (R&D Systems, Minneapolis, MN, USA). The absorbance of the assay wavelength was measured at 450 nm (subtracting background present at 550 nm) using a Cytation 3 imaging reader (BioTek, Winooski, VT, USA).

#### *2.6. Statistical Analysis*

Data from cytokine measurements have been analysed using the GraphPad Prism9 software (GraphPad Inc., La Jolla, CA, USA), and are presented in terms of ng/106 plated monocytes. Results are reported as mean ± SD of values from 2–8 replicates from the same donor or as median ± quartiles of values from different donors. The statistical significance of differences is indicated by *p* values, calculated using a paired one-tailed non-parametric Wilcoxon signed-rank test.

#### **3. Results**

#### *3.1. Gold Nanoparticle Characterisation*

Gold nanoparticles (AuNPs) used in this study were synthesized in endotoxin-free conditions and characterized as described in Materials and Methods. The master batch contained 6 × 1012 monodispersed particles/mL of sodium citrate 2.2 mM (in endotoxinfree water) at pH 6.4, corresponding to 0.5 mM Au (0.1 mg/mL) and to a total surface area of 2.6 × 1015 nm2/mL. AuNPs showed a diameter of 11.8 ± 0.8 nm by STEM, a

hydrodynamic diameter of 15.1 ± 3.7 nm by DSL, an absorption peak at 516 nm by UV-VIS, a conductivity of 0.793 mS/cm and a Z-potential of −47.0 ± 5.0 mV. The main NP characteristics are shown in Figure 1.

**Figure 1.** Main characteristics of AuNPs. (**Left**): size distribution by STEM; (**Centre**): STEM image; (**Right**): absorbance peak via UV-VIS.

Evaluation of the endotoxin contamination of AuNPs showed limited contamination (9.0 EU/mg). Since endotoxin could directly activate human monocytes in vitro at concentrations above 0.1 EU/mL [36,39], we used AuNP concentrations with endotoxin contamination below such threshold. After preliminary experiments, we selected 1 μg/mL AuNPs as priming concentration (containing 0.009 EU/mL endotoxin) and the 10-fold higher concentration of 10 μg/mL as challenge (containing 0.09 EU/mL endotoxin). Particles were pre-incubated for 60 min in 50% heat-inactivated human AB serum at 37 ◦C before being added to cells in culture to allow for the formation of a coating reproducing the naturally occurring biocorona when NPs come in contact with biological fluids. This procedure did not cause particle agglomeration, but instead it promoted monodispersity when added to the culture medium [37,40].

#### *3.2. In Vitro Development of Macrophage Innate Memory in 2D vs. 3D Cultures*

Purified human blood monocytes were placed in culture either in regular 2D plates or on top of a 3D collagen matrix, as described in Materials and Methods. Cells were either left untreated or exposed for 24 h to LPS or AuNPs. The primary cell activation was measured in terms of production, in the 24 h supernatant, of the inflammatory cytokines TNFα and IL-6, of the chemokine IL-8, and of the anti-inflammatory cytokine IL-1Ra. After supernatant removal and elimination of stimuli, cells were incubated in fresh medium for 6 days, to allow for return to baseline conditions. The 6-day supernatant was removed, and cells were exposed to either fresh medium (control) or LPS for an additional 24 h to assess memory responses, again in terms of cytokine production.

Cells from six donors were individually tested in parallel in 2D and 3D cultures for their primary and memory responses. SEM images in Figure 2 show the morphology of cells in 3D cultures after 24 h-stimulation with LPS (strong activation; upper right) as compared to cells exposed to medium or AuNPs (upper left) and to unprimed and LPS-primed cells after 6 days of culture (return to quiescent-like morphology; lower panels).

**Figure 2.** SEM images of monocytes in 3D culture. Upper panels: monocytes exposed for 24 h to culture medium alone or containing AuNPs (showing identical morphology; (**left**)) or LPS (**right**). Lower panels: monocytes primed with either culture medium alone or containing AuNPs (**left**) or LPS (**right**) observed after 6 days of resting in the absence of stimuli.

#### *3.3. Differences in the Primary Monocyte Reactivity in 2D vs. 3D Cultures*

When assessing the capacity of fresh monocytes to react to LPS and AuNPs in terms of cytokine production, no meaningful differences were in general observed between cells in 2D vs. 3D cultures, with some variability observed from donor to donor. Data in Figure 3 show that LPS significantly activates the production of the inflammatory cytokines TNFα and IL-6 and of the chemokine IL-8, while the levels of the anti-inflammatory factor IL-1Ra are already high in unstimulated cells and not substantially changed by LPS stimulation. AuNPs do not show direct activating capacity, in agreement with previous observations [12,28,39]. The individual donors' data are reported in Table S1.

#### *3.4. Extinction of Inflammatory Activation in Macrophages Six Days after Priming*

After the primary stimulation, monocytes were washed to eliminate the residual stimuli and cultured for an additional six days in fresh medium to allow for the extinction of their activation state and return to a quiescent condition. During this period, cells differentiate to macrophages. Their activation state at the end of the resting period was assessed by measuring the spontaneous production of cytokines. As shown in Table S2, the production of the inflammatory cytokines TNFα and IL-6 is essentially zero both in 2D and 3D cultures, independently of the previous priming of cells (with medium, LPS or AuNPs), suggesting that these cells are not any longer in an inflammatory activation state. The production of the chemokine IL-8 is, however, detectable in 3D (but not in 2D cultures) in unprimed/AuNP-primed cells from 4/6 donors and in LPS-primed cells of all donors. LPS-primed cells displayed a generally higher spontaneous IL-8 production as compared to unprimed cells, while AuNP priming did not have substantial effects. Regarding the

anti-inflammatory cytokine IL-1Ra, this was detectable at low levels in 2D cultures, while it was easily detectable in all 3D samples. IL-1Ra production was measurable in the unprimed macrophages from all donors at significant levels. Priming with either LPS or AuNPs variably but not substantially modulated the spontaneous production of the anti-inflammatory factor in each donor.

**Figure 3.** Primary cytokine production by monocytes in 2D vs. 3D culture. Production of the inflammatory cytokines TNFα and IL-6 (**upper panels**), of the chemokine IL-8 (**lower left panel**) and of the anti-inflammatory cytokine IL-1Ra (**lower right panel**) by monocytes of six individual donors stimulated for 24 h with culture medium alone (medium) or containing 1 ng/mL LPS (LPS) or 1 μg/mL AuNPs (AuNP). Parallel 2D (blue) and 3D (purple) cultures were established. Results are expressed in ng/10<sup>6</sup> cells. The violin plots represent the distribution of the individual donors' values in each experimental condition. The red line indicates the median value, and the yellow lines the first and third quartiles. Individual donors are represented with different symbols: donor 1; donor 2; Δ donor 3; donor 4; donor 5; • donor 6. Statistical significance was assessed with the paired one-tailed non-parametric Wilcoxon signed-rank test. LPS stimulation induced a significant increase (*p* < 0.05) of TNFα, IL-6 and IL-8 vs. medium controls. All other differences, including the 2D vs. 3D comparisons, were not significant.

#### *3.5. Secondary Response of Unprimed Macrophages*

The memory response of macrophages that were previously exposed to culture medium alone (unprimed control), LPS or AuNP was examined, after six days of resting, upon a challenge with LPS. Challenge with AuNP was initially assessed as well (data not shown), but it turned out to be ineffective (no activation induced by AuNPs, as al-

ready observed in the primary response and in previous studies) [12,28,39], and therefore it was not further pursued. LPS challenge in unprimed control macrophages induced significant production of TNFα, IL-6, and IL-8, which was generally more pronounced in the 3D cultures (Figure 4). Again, the production of IL-1Ra was very low in 2D, while well measurable in 3D cultures. It is notable that, as in the primary response, LPS stimulation had relatively little effect on IL-1Ra production (Figure 4); however, with some donor-dependent variability (compare Tables S2 and S3 for individual data).

**Figure 4.** Secondary cytokine production by primed monocytes challenged with LPS in 2D vs. 3D culture. Production of the inflammatory cytokines TNFα and IL-6, the chemokine IL-8 and of the anti-inflammatory cytokine IL-1Ra by monocytes of six donors previously primed in vitro with culture medium alone (unprimed), LPS (LPS-primed) or AuNPs (AuNP-primed). After 24 h priming, cells were rested in culture for 6 days and then challenged with 10 ng/mL LPS for 24 h. Results obtained in 2D cultures are reported in the upper panels, while data from 3D cultures are reported in the lower panels. The violin plots represent the distribution of the individual donors' values in each experimental condition. The red line indicates the median value, and the yellow lines the first and third quartiles. Individual donors are represented with different symbols: donor 1; donor 2; Δ donor 3; donor 4; donor 5; • donor 6. Statistical significance was assessed with the paired one-tailed non-parametric Wilcoxon signed-rank test, and show significant differences (*p* < 0.05) between unprimed and LPS-primed production of TNFα (2D and 3D), IL-6 (2D) and IL-1Ra (2D), while the differences between 2D and 3D were significant for IL-8 and IL-1Ra.

It should be noted that the response of macrophages to LPS, in terms of inflammatory cytokine production, is substantially less abundant compared to monocytes, whereas the quantitative response in terms of IL-8 and IL-1Ra was quite similar between macrophages and monocytes (Figure 4, Tables S1 and S3).

#### *3.6. Memory Response of LPS-Primed Macrophages*

Compared to unprimed cells, in LPS-primed macrophages, the production of TNFα in response to LPS was significantly decreased both in 2D and 3D cultures, in line with the expected tolerance effect of LPS priming (Figure 4). When looking at the individual data (Table S3), for IL-6 production, tolerance was detectable in 3/6 donors in 3D and in all six in 2D cultures, the overall difference being statistically significant only in the latter case (Figure 4). In the case of the chemokine IL-8, LPS priming did not induce a significant overall effect either in 2D or in 3D (Figure 4), although the individual reactivity varied between donors (Table S3). In 2D cultures, a partial decrease was observed in 2 donors and an increase was detectable in one, while in 3D samples LPS priming had no effect in 5/6 donors and increased the response to challenge in one (donor 6, the same as in 2D cultures) (Table S3). The memory response in terms of the production of the anti-inflammatory cytokine IL-1Ra could be better assessed in 3D cultures (as the IL-1Ra production in 2D cultures was very low) and was donor-dependent, with a partial potentiation in 2 donors, and a decrease in other two. Overall, LPS priming did not induce a significant change in IL-1Ra production (Figure 4). A notable difference between 2D and 3D cultures is in the quantitative production of IL-8 and IL-1Ra, substantially more abundant in 3D cultures, while the production of the inflammatory cytokines TNFα and IL-6 was only slightly higher in 3D cultures.

#### *3.7. Memory Response of AuNP-Primed Macrophages*

In AuNP-primed macrophages (Figure 4, Table S3), the challenge-induced TNFα production is modulated in a donor-specific fashion, with a difference between 2D and 3D cultures. Thus, while in 2D it seems that AuNP priming does not substantially influence the response to challenge, in 3D cultures a partial decrease of response is evident in 3 donors. A very similar picture can be observed for the production of the other inflammatory cytokine, IL-6, with a general lack of effect in 2D samples, whereas in 3D cultures two donors show partial potentiation and one partial tolerance. In the case of the chemokine IL-8, the results in 2D and 3D cultures were superimposable, with no substantial effect due to AuNP priming except for one donor (donor 6), in which priming induced a clear potentiation of the memory response. For the anti-inflammatory factor IL-1Ra, better detectable in 3D, AuNP priming could induce a partial tolerance response in one donor, a potentiated response in another one, and no significant changes in the others. Again, the memory effect seems to strongly depend on the donor.

#### **4. Discussion**

This study aimed at assessing whether human monocyte/macrophage reactivity in vitro can differ depending on the culture conditions. In particular, we compared conventional 2D cultures on flat plastic surfaces to 3D cultures in a biological matrix of collagen, derived from decellularized bovine skin and providing a mesh of collagen fibrils with pores around 100 μm. This matrix is used in clinical settings as dermal/epidermal substitute for repairing ulcers and was reportedly able to promote M2/healing macrophage phenotype, i.e., the default phenotype of resident macrophages in homeostatic conditions [40]. Cells seeded in the 3D matrix survived and differentiated as expected, and their sensitivity to activation stimuli was evident also from the morphological point of view (Figure 2). We used the two culture systems in comparison to assess the reactivity of human monocytes/macrophages to AuNPs, using the bacterial LPS as an activation benchmark and examining two important innate immune functions, i.e., the immediate inflammationrelated response to the stimulation of fresh monocytes and the secondary reaction of monocyte-derived macrophages after previous priming (innate memory response). The results show that the primary response is not significantly different between 2D and 3D cultures (Figure 3) and that, in agreement with previous results [12,28,39], AuNPs do not induce a significant cell activation, opposite to the substantial induction of TNFα, IL-6 and IL-8 production in response to LPS. On the other hand, the production of the antiinflammatory factor IL-1Ra is detectable at measurable levels in unstimulated cells and is not significantly varied in cells exposed to LPS or AuNPs. It is known that LPS can induce IL-1Ra production at later times as a feedback mechanism to shut down inflammation. Our data show a slight tendency towards increased IL-1Ra production to LPS, and also to AuNPs in 3D cultures, which, however, did not reach statistical significance due to the substantial donor-to-donor variability. Indeed, monocytes from some donors showed a clear increase while others did not, implying different response kinetics depending on the individual conditions.

While it is now clear that many NPs do not have the capacity for activating human monocytes if they are endotoxin-free [12,13,35,36,39], some data point to the possibility that they can prime monocytes and induce innate memory, which then changes the secondary reaction of cells to a subsequent stimulation [28–32]. We have examined the capacity of AuNPs to induce innate memory in monocytes from six different donors in 2D and 3D cultures. Innate memory is an important phenomenon of immune reprogramming that allows innate cells to react is a more efficient way to a challenge if previously exposed to foreign/dangerous agents [14–20]. The results show that AuNPs do not have a significant capacity to induce memory in 2D cultures, with unprimed vs. AuNP-primed cells from all donors showing a comparable response to LPS (Figure 4, Table S3). In 3D cultures, although the global response is never different between unprimed and AuNP-primed cells, when examining the response of individual donors, it is possible to see memory effects, as for instance for Donor 3 that shows an AuNP priming-dependent decrease in TNFα, IL-6, and IL-1Ra production, which is not evident in 2D cultures, or for Donor 6 that shows an AuNP priming-dependent increase in IL-8 and IL-1Ra that was undetectable in 2D cultures.

Two important notions should be underlined here. First, the unstimulated production of IL-8 and IL-1Ra is detectable at higher levels in unprimed/primed macrophages in 3D cultures compared to the 2D cultures, whereas the production of the inflammatory cytokines TNFα and IL-6 is essentially undetectable in both conditions (Table S2). This implies that the 3D cultures provide a more physiological microenvironment, which promotes the homeostatic tissue-like functions of macrophages, characterised by lack of production of inflammatory factors and abundant production of anti-inflammatory factors [7,8,41]. The significant production of IL-8 goes in the same direction, as this chemokine is involved in ensuring the appropriate homeostatic trafficking of neutrophils and other cells in non-inflammatory conditions [42–44]. Thus, in 3D cultures monocytes developed in the direction of M2/healing macrophages by adopting a classical tissue resident-like antiinflammatory and homeostatic functional phenotype. Notably, IL-1Ra is detectable at significantly lower levels in macrophage 2D cultures, a finding that supports the suitability of 3D cultures for a more realistic assessment of macrophage reactivity. However, it should be noted that we could not find significant qualitative differences in the innate memory activities between cells cultured in 2D vs. 3D conditions. On the other hand, as already mentioned, there is no substantial qualitative and quantitative difference in the reactivity of fresh monocytes in 2D vs. 3D cultures, suggesting that 2D cultures are fully suitable for evaluating acute innate responses.

The second important finding is that the memory response to AuNPs is strongly dependent on donors. While memory responses induced by priming with LPS (a very strong stimulus) are clearer, with exposure to AuNPs (a stimulus that does not induce a detectable primary response) it becomes evident that the priming capacity substantially depends on the donor. Thus, as an example, the 3D memory response in terms of IL-6 is increased production in two donors, a decrease in another two, and no change in the last two donors. This is fully in line with previous preliminary observations [28,30] and underlines the importance of 'immunobiography", i.e., the history of exposure and challenges experienced by the immune system, which is unique for each of us and that can significantly bias our capacity to react appropriately to new challenges [33]. Although the number of donors in this study is limited (six donors), they are quite homogeneous in terms of age and health status (young, healthy, no medications, non-smokers). They encompass

individual of both sexes and of two different ethnic groups, but neither parameter is associated with a defined type of response, further suggesting that the individual history of exposure may be at the basis of response variability.

These findings suggest some important issues in directing future research: the need for adopting suitable models for our in vitro studies of human innate memory, and the importance of performing individual assessments (precision medicine, precision diagnosis, precision toxicology), since it is not possible to generalize findings of efficacy or toxicity to a population that is widely different also in terms of immune history.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/2079-499 1/11/1/207/s1, Table S1: Primary cytokine production by monocytes in 2D vs. 3D cultures; Table S2: Baseline cytokine production by unprimed and primed monocytes after 6-day resting in 2D vs. 3D cultures; Table S3: Secondary cytokine production by unprimed and primed monocytes challenged with LPS after 6-day resting in 2D vs. 3D cultures.

**Author Contributions:** B.J.S. designed and performed the experiments; A.V. analysed the data and performed the statistical analysis; L.R. provided information of the collagen matrix and contributed to data analysis and discussion; M.M. participated to experimental work and data analysis; V.F.P. synthesized and characterized the AuNPs; A.C.D.L. analysed and discussed the results; D.B. analysed and discussed the data and wrote the manuscript; P.I. analysed and discussed the data, prepared the figures and wrote the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the European Commission FP7 project HUMUNITY (GA 316383), the Horizon 2020 projects PANDORA (GA 671881) and ENDONANO (GA 812661), the Italian MIUR Flagship InterOmics project MEMORAT and the PRIN project 20173ZECCM.

**Institutional Review Board Statement:** The study was conducted according to the guidelines of the Declaration of Helsinki, and the protocol was approved by the Regional Ethics Committee for Clinical Experimentation of the Tuscany Region (Ethics Committee Register n. 14,914 of 16 May 2019).

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The data presented in this study are available in this article and its supplementary material.

**Acknowledgments:** The authors wish to thank Paola Migliorini (University of Pisa, Italy) for her help in the coordination and ethical monitoring of the study, and the Morpho-Functional Analysis and Bioimaging Unit of the Stazione Zoologica Anton Dohrn for providing technical assistance for SEM images.

**Conflicts of Interest:** The authors declare no conflict of interest.

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*Article* **Classification of** *Prunus* **Genus by Botanical Origin and Harvest Year Based on Carbohydrates Profile**

**Marius Gheorghe Miricioiu 1, Roxana Elena Ionete 1, Diana Costinel 1 and Oana Romina Botoran 1,2,\***

**Abstract:** The 1H-NMR carbohydrates profiling was used to discriminate fruits from *Rosaceae* family in terms of botanical origin and harvest year. The classification was possible by application of multivariate data analysis, such as principal component analysis (PCA), linear discriminant analysis (LDA) and Pearson analysis. Prior, a heat map was created based on 1H-NMR signals which offered an overview of the content of individual carbohydrates in plum, apricot, cherry and sour cherry, highlighting the similarities. Although, the PCA results were almost satisfactory, based only on carbohydrates signals, the LDA reached 94.39% and 100% classification of fruits according to their botanical origin and growing season, respectively. Additionally, a potential association with the relevant climatic data was explored by applying the Pearson analysis. These findings are intended to create an efficient NMR-based solution capable of differentiating fruit juices based on their basic sugar profile.

**Keywords:** 1H-NMR; carbohydrates; fruits; PCA; LDA

**1. Introduction**

Nowadays, people pay particular attention to a balanced and controlled diet. Thus, there is a high demand for fresh fruits and derived juices which are considered, along with vegetables, the healthiest foods. People have also begun to recognize their beneficial contribution to health by protecting the human body against different type of illnesses through their vitamins which usually result in an immunity increase [1]. Unfortunately, this high demand for quality fruit juices has also attracted some frauds as shown in several studies on this topic [2–5]. Traceability, establishing chemical profile, appropriate physical attributes, adequate textural properties, controlled toxins and microbial contamination, as well as processing and storing method all represent characteristics of high quality, particularly for agricultural products. For example, a common fraudulent act is represented by the adulteration of juices by addition of other types of cheaper juices obtained from less expensive or more common fruits in the respective area [6]. Among others, dilution with water, sugar syrup and colorants, production method (conventional, organic, traditional techniques) as well as non-declared processing technologies (freezing, irradiation) can be mentioned [7]. Fruit juices have a high added value, and they are also more vulnerable to being subjected to different adulteration techniques because of their acknowledged attributes. Accordingly, authorities must be able to determine the compliance of a suspect product based on the product description, identify fraudulent processing practices, prevent adulteration, and control any other practices that may deceive the consumer. As is well known, it is not only consumers who benefit from food authenticity assessment but also the food industry parties which rely on the ability to ensure their commodities' label conformity and brand protection. In order to verify the authenticity of food items and guide and assist law enforcement, official bodies are periodically requesting an updated list of analytical procedures. In this scope, many analytical techniques such as molecular techniques

**Citation:** Miricioiu, M.G.; Ionete, R.E.; Costinel, D.; Botoran, O.R. Classification of *Prunus* Genus by Botanical Origin and Harvest Year Based on Carbohydrates Profile. *Foods* **2022**, *11*, 2838. https:// doi.org/10.3390/foods11182838

Academic Editors: Mourad Kharbach and Samuli Urpelainen

Received: 10 August 2022 Accepted: 9 September 2022 Published: 14 September 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

(DNA-based approaches) [8], isotopic approaches [9], ultraviolet-visible spectrophotometry (UV-VIS), high performance liquid chromatography (HPLC), gas chromatography (GC), inductively coupled plasma mass spectrometry (ICP-MS), atomic absorption spectroscopy (AAS), and infrared spectroscopy (IR) are used to control and to detect the food products' adulteration [2,6]. A single analyte or approach may rarely be associated with overall quality compliance because of the fruit juice matrices' complexity. As a result, their quality is derived from a unique combination of characteristics. To acquire the defined quality markers and control the critical production parameters, it is often essential to use multivariate data analysis. It is easier to discriminate between fruit samples and establish their authenticity when multivariate analysis is used in conjunction with different spectroscopic or chromatographic based methods. Data fusion may offer more precise information about a sample and better interpretation than a single approach, but usually the use of several techniques is not economically profitable, doesn't respect green chemistry principles, and is time consuming. In this respect, nuclear magnetic resonance (NMR) is a non-destructive technique providing high analytical precision, enabling simultaneously compounds identification, exposing complex frauds, and, in conjunction with chemometric analysis, revealing possible markers of fruits authenticity based on their composition profile [10]. Moreover, through NMR, spectra fruits can be classified according to their varietal and geographical origin [11–14], this being possible by application of some dedicated instruments, such as unsupervised machine learning techniques (principal component analysis—PCA) and pattern-recognition tools (discriminant analysis—DA).

The 1H-NMR spectra in combination with PCA and DA have been applied to evaluate changes in the composition and metabolic profile of juices during thermal concentration process [15] for the correlation of different varieties of fruits [16,17] to reveal the juices' adulteration [18], and to evaluate the plant growth regulator in strawberries [19]. Also, the metabolomic analysis of 1H NMR results obtained from fruit juices investigation give an overview about the relationships between the major metabolites and the sensory characteristics of the fruits. Among these metabolites, the carbohydrate content is the most relevant for the maturity level of fruits and for the consumer perception, and its domain is represented by three predominant components: glucose, fructose and sucrose [20,21]. Generally, the glucose and fructose are presented in lower quantities than sucrose and their relation affects the taste of the fruits [22]. Thus, the sweetness of the fruits is directly influenced by the fructose quantity which is 2.3 and 1.7 times sweeter than glucose and sucrose, respectively [20]. Beside this, fructose is highly appreciated for its therapeutic effect on the gastrointestinal tract [22,23]. Also, sucrose is appreciated as sweetener, energy source, and antioxidant [22], but its excessive consumption is closely related to the risk of caries, obesity, and diabetes [24].

In this study, the NMR method coupled with multivariate statistical analysis was used to obtain information about the variation of carbohydrate content in different fruits (plum, cherry, sour cherry, and apricot) from the *Rosaceae* family, *Prunus* genus, harvested in three different years. Furthermore, discrimination models based on DA were developed for samples classification. Another approach was the evaluation of different climatic conditions' (temperature and precipitation) influence over the three investigated years on the fructose, sucrose, glucose, and total carbohydrates content. These data will represent a contribution to regional horticultural varieties' characterization as well as provide useful information for industries which use fruit-derived nutrients in food production.

#### **2. Materials and Methods**

#### *2.1. Chemicals*

All analytical standards and reactants used for samples preparation and data interpretation were purchased from Sigma-Aldrich (St. Louis, MO, USA) and are hereafter listed: HCl (5N), NaOH (5N), D2O, and TMSP.

#### *2.2. Sample Collection and Pre-Treatment*

The fruits analyzed in this study were chosen from the *Rosaceae* family, *Prunus* genus, namely plum, cherry, sour cherry, and apricot. In particular, 76 samples were analyzed from Romania. The fruits were provided by Vâlcea Fruit Growing Research and Development Station, Romania, harvested in a state of consumption maturity, and the collected fruit samples were cooled and transported to the laboratory, assuring the maintenance of the cold chain. Then, the fruits (approximately 5 kg per variety) were washed with water, kept frozen, and stored at −20 ◦C in a freezer until sample preparation.

The juice was obtained by squeezing the whole fruit using a juicer (Moulinex, Jinan, China), and then approximately 100 g of sample was centrifuged with 10,000 rotations/min (Hettich ROTINA 420, Tuttlingen, Germany) for 10 min and filtered through a filter with 45 μm porosity, leading to about 20 mL being obtained. Further, the samples were pH adjusted to 2.65 by using 5 N HCl and 5 N NaOH. For NMR analysis, 700 μL of each sample was combined with 70 μL of deuterium oxide (D2O), 99.9% D containing, and 0.05 wt. % of 3-(trimethylsilyl) propionic-2,2,3, 3-d 4 acid sodium salt as an internal standard (TMSP). The mixtures were transferred to 5 mm NMR tubes.

#### *2.3. NMR Analysis and Data Processing*

All 1H-NMR spectra were recorded at 300 K temperature on a 400 MHz Bruker Avance spectrometer (Bruker France SAS, Wissembourg, France), operating at 9.4 T, equipped with a 5 mm BBO probe and ATM (Automatic Tuning Matching). In addition, the instrument was fitted with an autosampler from Bruker controlled by Icon NMR software which allows a loading of 60 samples. To complete the temperature equilibration, a time delay of 5 min between sample injection and preacquisition calibrations was set. The suppression of H2O signals was assured through Bruker standard pulses sequence, noesygppr-1d, by applying continuous waves during the relaxation delay (10 s) with a mixing time of 10 ms. Each spectrum is the result of 8 scans and 32768 (33 k) data points. The spectral width was adjusted to 6402 Hz with an acquisition time of 2.559 s per scan. Spectra were Fourier transformed, manually phased, baseline corrected, and referenced to TMSP signal at 0 ppm using TopSpin 3.2 software (Bruker Biospin, Rheinstetten, Germany). Principal component analysis (PCA) and discriminant analysis (DA) were performed with LSTAT Addinsoft 2014.5.03 software version (Addinsoft, New York, NY, USA) in order to evaluate some potential variables and their influence on fruit juices' discrimination. Also, to reveal the possible relationships between sugars and climatic conditions, the Pearson correlations coefficient at *p* ≤ 0.05 was used.

#### **3. Results and Discussion**


*2.3.3 Supercritical fluid technology*

Materials that have pressure and temperature greater than their critical state (Pc and Tc) are supercritical fluids. The leading objective of supercritical fluid technology is to regulate cloud seeding and crystal development courses. The most conspicuous supercritical fluid used in the pharmaceutical arena is carbon dioxide, with critical temperature and pressure of 31.0°C and 7.39 atm, respectively, because of its nontoxicity, non-flammability, and low-cost properties [22, 33]. Numerous approaches of employing the supercritical fluid carbon dioxide to produce co-crystals are as

follows: (1) where CO2 is used as an anti-solvent known as gas anti-solvent crystallization (GAS). As an example, the SAS (supercritical anti-solvent crystallization) and AAS (atomization and anti-solvent crystallization) methods of supercritical fluid technology were successfully used in the formation of the indomethacin:saccharin co-crystal, (2) where the carbon dioxide is used as a liquid and molecular movement enhancer called co-crystallization with the supercritical solvent (CSS), (3) where CO2 is utilized as a solvent and molecular movement enhancer called supercritical anti-solvent crystallization (SAS), (4) where CO2 is used as corsage enhancer or anti-solvent called atomization and anti-solvent crystallization (AAS), (5) where CO2 is used as corsage enhancer or anti-solvent called supercritical fluid improved atomization (SEA), and (6) where CO2 is used as a solvent known as rapid expansion of supercritical solutions (RESS) [34].


**1. Introduction**

In the field of fracture mechanics especially linear elastics, the vicinity of notch tip is often symbolized by singular stress entities. Their resistance is measured through stress intensity factor (SIF). The SIF is mainly depended on the distance r from the tip of notch. In this field, parameter T is introduced to enrich the parameter K (SIF) to make the model better in the elastic stress field; this is the K-T approach [1].

In fracture mechanics body of knowledge, it is established that the same Stress Intensity Factor (SIF) is required for two cracks to propagate in the same way. Experiment [2] have shown that two plates with the same SIF and different crack length a1 > a2 show different the propagation of the cracks. The results have shown that the propagation speed of a2 is higher than that of a1. The study concluded that the first term of asymptotic development is not sufficient to predict crack behavior. Therefore, it is necessary to increase the order. The first term asymptotic development is the SIF that determines the initiation and propagation of the crack. In addition, the second term is constant and controls the stability of the propagation direction. It is the transverse component symbolized by T.

Moustabchir, H.; Elkhalfi, A.; Pruncu, C.I.; Arbaoui, J.; Farooq, M.U. An Extended Finite Element Method (XFEM) Study on the Elastic T-Stress Evaluations for a Notch in a Pipe Steel Exposed to Internal Pressure. *Mathematics* **2021**, *9*, 507. https:// doi.org/10.3390/math9050507

**Citation:** Yakoubi, K.; Montassir, S.;

Academic Editor: Krzysztof Kamil Zur ˙

Received: 23 January 2021 Accepted: 22 February 2021 Published: 2 March 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Several studies have shown the significance of the T-Stress, and its influence on different parameters of mechanics. Jayadevan [3] highlighted that plastic zone is manipulated by the variation of T-stress. It means, the plastic area escalates with the increase in absolute value of T-stress and changes its form. Sobotka et al. [4] demonstrated the alteration in the plastic wake with many T-stresses which depends on plastic wakes height (HPW).

T-Stress has been an essential contributing factor in the stability of the direction of the crack propagation. For instance, T negative gives a stable direction, and for T positive it is unstable [5]. Fayed et al. [6] explored the impact of T-stress on propagating crack direction by Maximum Tangential Stress (MTS). The principle of MTS is that the crack propagates in the trend of maximum tangential stress. They obtained that the directions of the overall crack no coincide with the initial direction of the crack. Many studies have concluded the behavior by the fact that the tangential stress is affected by the T-Stress. MTS becomes generalized maximum tangential stress (GMTS), which considers the constraint T in the expression of stress. In the same context Shahani [1] studied the result on the initiating angle of propagating crack of the stress T. The study has shown a negative T value declines the angle of crack initiation, and a positive T value enhances it. Nejati et al. [7] gauged the relationship between T-stress and material properties. Chen et al. [8] has shown that Graded Poisson's ratio affects the T-stress. Additionally, Toshio et al. [9] concluded that the Poison's ratio influences the T-stress on a three-dimensional edge-cracked plate.

Other important research that has shown the influences of the T-stress includes: Zhang et al. [10], which used numerical manifold method (NMM) is employed to calculate the T-stress for two-dimensional functionally graded material (FGM) having numerous cracks. Noritaka et al. [11] has resulted the T-stress might open micro-branches in the mist region. For the bending and tension load, Hancock [12] determined that T decreases with escalating crack length. Matvienko [13] explored the influence of T-stress in problems of the elastic and the elastic-plastic fracture mechanics.

Conventionally, the T-stress is often calculated at the crack tip, which is certainly not the case in this research. The research evaluates the T-stress at the tip of notch through extended finite element method (X-FEM).

The finite element method FE method is limited by the simple cases, as well as the presence of a singularity greatly degrades the convergence of the FEM. Belytschko and Blacken in 1999 added discontinuously enriching function in finite element approximation by respecting boundary conditions. Later, Moës et al. [14] developed the technique and called it as extended finite element method which is abbreviated as X-FEM. The efficiency of the X-FEM is well endorsed in the literature. To simulate the propagation of cracks in porous media, Wang et al. [15] integrated embedded discrete fracture method (EDFM) with X-FEM simulating fracture associated fluid and solid mechanics. Shu et al. [16] investigated the fatigue growth of 3-D multiple cracks by X-FEM. The implementation of X-FEM for composites resulted successfully [17–19]. X-FEM is also used for the calculation and analysis of failure mechanics parameters. Fakkoussi et al. [20] calculated stress intensity factor for mode one by X-FEM. Llavori et al. [21] studied the problems of contact fatigue by X-FEM.

The research study presents the use of X-FEM to calculate T-stress in the notch tip for an arc of the pipe of steel P264GH. Further, it demonstrates the benefits of using the X-FEM approach to compute K-T at the notch point in an arc under pression and revealing the possibility of detecting the crack initiation.

The remaining article is organized as, Section 2 talks about the K-T approach, X-FEM, and the geometry used. Section 3 deals with the numerical result obtained, compared against FEM conclusions, along with the discussion. Finally, the conclusion is in the other section.

#### **2. Materials and Methods**

#### *2.1. K-T Approach*

Stress Intensity Factor has been an essential parameter in the field of linear fracture mechanics, widely used for crack evaluation. SIF measures the strength of the singularity, and integrates various parameters such as load, geometry, and shape of crack. M. Hadj Meliani [22] suggested that a thin structure such as a thin pipe with a longitudinal crack, it is very difficult to characterize the stress field by a single parameter. For linear elasticity, the enrichment of the SIF with the T-stress is required to model the notch tip. In literature, studies show that T explains how geometry influences tenacity (KIC) [22]. T-stress helps in approximating the level of stress at a crack or tip of the notch. The possibility of constructing the K(T) curve numerically has given the opportunity to predict the loading of a crack initiation [23,24]. Including T-stress in calculations, it improves the prediction of propagating crack under the control of mixed loading. The K-T was additionally calculated for through-wall-cracked pipes under various pressure conditions by three dimension-3D FE [25]. The importance of the T-Stress is established in many works.

• T-stress enhances the possibility of crack opening stresses in the context of small crack [26];

$$\sigma\_{\text{xx}}(\mathbf{r}, \theta) = \frac{\mathbf{K}\_1}{\sqrt{2\pi \mathbf{r}}} \mathbf{f}\_{\text{xx}}(\theta) + \mathbf{T} \tag{1}$$

Taking σxx(r, θ) = σcr, for the crack propagation, the first term tends to √K1 2πr fxx(θ) to a because K1 = Syy√πa, and if a tends to zero; the first term becomes negligible intheface to T at the crack point.

$$\lim\_{\mathbf{a}\to\mathbf{0}}\sigma\_{\mathbf{x}\mathbf{x}}(\mathbf{r},\mathbf{\theta})=\sigma\_{\mathbf{cr}}=\mathbf{T} \tag{2}$$

In this case, the T-stress cannot be ignored, T play the role of crack opening, and therefore the importance of T varies with the size of the cracks.

T-Stress could be computed through numerous techniques. Weight Function Method has shown its efficiency in several problems cracking-related such as edge-cracked rectangular plate, circular disk [27]. Kfouri [28] developed a technique for evaluating the T-stress. The method uses the attributes of the path-independent J-integral and is called the Esheby–Integral method.

The stress different method (SDM) has been proposed by Yang [29]. The idea of this method is the errors of the numerical values of σ11 and σ22 near a crack point progress with r in the same way, and the variation must effectively eliminate errors.

$$\mathbf{T} = \sigma\_{\mathbf{yy}} - \sigma\_{\mathbf{xx}} \tag{3}$$

Biaxiality is a parameter that relates the SIF and T-stress:

$$
\beta = \frac{\text{T}\sqrt{\pi \text{a}}}{\text{K}} \tag{4}
$$

#### *2.2. Extended Finite Elements*

One of the uses of the FE method is the study of crack propagation but is limited for simple cases. If the mesh size does not conform to the crack, the FE method does not treat the propagation, and the presence of a singularity degrades the convergence of the FE method.

The solution is to add enrichment function to the FE approximation (see Figure 1); this is the extended finite element method.

$$\mathbf{U} = \sum\_{1}^{N} \mathbf{N}\_{\mathrm{i}} \mathbf{u}\_{\mathrm{i}} + \sum\_{\mathrm{i}}^{N\_{\mathrm{out}}} \mathbf{N}\_{\mathrm{i}} \mathbf{H}(\mathbf{x}) \mathbf{a}\_{\mathrm{i}} + \sum\_{\mathrm{i}}^{N\_{\mathrm{sing}}} \sum\_{\mathrm{j}}^{N\_{\mathrm{sing}}} \mathbf{N}(\mathbf{x})\_{\mathrm{i}} \mathbf{F}(\mathbf{x})\_{\mathrm{j}} \mathbf{b}\_{\mathrm{i}}^{\mathrm{j}} \tag{5}$$

where:

**Figure 1.** Step of enrichment methods.

The X-FEM requires operation to confirm the enrichment status of a knot according to its position in reference to the crack and to evaluate the functions H(x) and F(x). The position (r, θ) in relation to the notch point is calculated herein to know if x is above or below the crack. These operations are carried out using the level sets method. The technique for describing crack is known as level set method. In the X-FEM, it determines the location of the crack and the crack point, and the position to apply discontinuous enrichment and enrichment to the crack point Figure 1. Most importantly, the level set provides an instant result that helps track crack propagation, i.e., as the crack propagates, enrichment at the crack front becomes discontinuous enrichment, and nodes (not enriched) become enriched. There are two-level functions, and the first describes the crack surface (ϕ), second gives the crack front (ψ) [30].

The X-FEM method was applied in several studies. Yousheng Xie et al. [31] have implemented the X-FEM method in the study of propagating crack in mixed mode, and evaluated the crack initiation angle. Reference [32] has shown the performance of the method. The study applied X-FEM to calculate SIF for 3D crack propagation problems for a Compact Tension C-T specimen. X-FEM was also implemented in the analysis of bi-material interfaces, calculating service life and fatigue resistance [33]. An integration between the X-FEM and embedded discrete fracture method (EDFM) is established for simulation of the process of fluid fracture propagation in porous media [15]. Savenkov et al. [34] employed the X-FEM to represent the central surface of the crack. The application of X-FEM for composite models is also carried out supporting current investigation [35,36].

X-FEM was used to predict components failure from a different form of notch [37]. Patria et al. [38] adopted X-FEM to study the mechanical attributes and fracture behavior of (Reinforced Polymeric Composites) RPC materials with single edge notch three-point bending.

#### *2.3. Geometry*

An arc of pipe containing a notch under pression was numerically analyzed using X-FEM in ABAQUS software. The material used is a steel P264GH. The arc characterized by an inner radius Ri = 219.55 mm and thickness t = 6.1 mm. More details on geometry, the shape of the notch, and boundary requirements used are illustrated in Figure 2 and Table 1.

**Figure 2.** Details of the geometry and notch study, with boundary conditions.

**Table 1.** Geometry properties and load.

The mechanical attributes of the material used are presented in Table 2, and the chemical composition of the material are included in Table 3.

**Table 2.** Mechanical characteristics of P264GH.

**Table 3.** Chemical composition of P264GH.

#### **3. Results**

This section presented the results of SIF and T-stress given by X-FEM via an user element UEL subroutine, the calculation was executed by ABAQUS software, we used

**Figure 3.** The mesh of 3D arc, C3D10 with 0.5 mm of size.

elements is 246117. The number of nodes is 363256.

The T-stress is calculated through stress different method, and normalization is done for effect of the T-stress relative to the stress intensity factor by a parameter dimensionless termed biaxiality.

quadratic element C3D20 in the mesh Figure 3, with a size of 0.5 mm. The number of

$$\mathfrak{g} = \frac{\mathbb{T}\sqrt{\pi \mathbf{a}}}{\mathbb{K}}$$

K is the value of stress intensity factor, and a is the notch length.

Figure 4 illustrates the difference of the SIF in mode 1 as a function of r, for a/t = 0.2, by extended finite element.

**Figure 4.** Distribution stress intensity factor SIF at the notch tip–SIF and r for a/t = 0.2.

The elastic SIF distribution at the notch tip decreases with distance from the tip of notch, for a/t = 0.2 the maximum value of SIF is 21 MPa√m at notch tip, i.e., *r* = 0 (see Figure 4). Near the notch tip SIF decreases rapidly to 6 MPa√m at r = 0.3 mm, then its variation becomes slower.

Figure 5 shows the variation of stress σxx,σyy and T. T-stress increases with increasing r up to r = 0.43, and after that it starts to stabilize. The numerical calculation of the stress σxx,σyy by X-FEM is executed by ABAQUS software. Figure 6 gives the Von Mises stress obtained by the Abaqus software.

12

**Figure 5.** T-stress by stress different method.

**Figure 6.** Distributions of Von Mises stress near the notch.

The result obtained of biaxiality are compared with H. Moustabchir [39], who calculated the biaxiality through the finite element method, for the same geometry which is used in this study. Figure 7 gives the variation of biaxiality as a function of a/t, by X-FEM and FEM.

**Figure 7.** Variation of the biaxiality with a/t at the notch.

The biaxiality levels up with the increase a/t, The results are identical with the H. Moustabchir [39] recommendations. Kim and Paulino [40] has also got the same variation. By X-FEM the biaxiality varies from −0.21 to 0.76 for a/t = 0.2 and 0.8, respectively, and it goes from a positive to a negative value at a/t = 0.3. The difference between the results given by X-FEM and FEM is 0.013.

#### **4. Discussion**

SIF measures the strength of the singularity, which explains the rapid variation of the SIF obtained for r = [0, 0.3]. The more approach is made towards the notch tip, the more the stress concentration increases, and therefore, SIF increases. Moustabchir et al. [39] used the volumetric approach to calculate SIF, in the same condition that this research studied. Moustabchir et al. obtained for mode I at tip notch K1 = 21.6 MPa√m, which differs from our result by 0.5. The T-stress can be analyzed by the SDM. The biaxiality increases with the rise in a/t, and the notch depth affects the value of T-stress. The same variation was obtained in other investigations on various materials. Bouchard et al. [41] have shown that T increases with increasing depth for a mono silicon. In [42], Sherry et al. obtained an increase in T in absolute value with the variation of the crack size over the width of a plate. In addition, Ayatollahi et al. [43] obtained for mode I, an increase in T-stress as a function of the depth of the crack for a single edge notched.

If

$$\mathbb{3} = 1$$

√πa K

and

So

K = T √πa i.e., T = σ

β = T

Which is not the case for this study βmax = 0.78, so T = σ, which implies that T has no influence on the notch in our case and our condition.

Many studies have resulted that the influence of the T-stress is remarkable and significant when T is negative [1,3,6], however, in this study for r < 0.43, negative T-stress causes an increase in the plastic zone [27]. This will cause a crack to initiate. In the presence of a crack, negative T can change the direction of propagating crack and decreases the crack growth initiation angle [31].

The K-T approach is an integration between the SIF and the T-stress to improve modelling the elastic stress at the point of the crack. The importance of T-stress has been highlighted, and it takes the place of short crack opening stress. Besides, the importance of the cooperation of SIF and T-stress, such as the K(T) curve was elaborated which gives a prediction of the stress of crack initiation [44]. Neggaz et al. [44] studied the influences of the reinforcements in the structure of composites, with the aim of reducing constraints at notch-tip. Moreover, authors evaluated the effective stress intensity factors in the regard of propagating crack in thin and thick panels. Therefore, an Extended Finite Element Method (XFEM) is novel and improved technique on the elastic T-stress evaluations for a notch in a pipe steel exposed to internal pressure.

#### **5. Conclusions**

Three-dimensional Extended Finite Element (X-FEM) analysis is applied to evaluate the stress intensity factor and the T-stress for an arc of pipe with external notch under internal pressure. The results are presented below:

For more precision, the future objective is to calculate the parameters of fracture mechanics by iso-geometrical analysis.

**Author Contributions:** Data curation, K.Y. and J.A., formal analysis, S.M. and A.E., investigation, H.M. and C.I.P., writing and review of original draft, M.U.F., H.M., and C.I.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data that support the findings of this study are available on request from the corresponding author.

**Acknowledgments:** Authors are thankful to Aqib Mashood Khan for his constructive feedback.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**4. Summary of other important CFD advances**

Here we will discuss some technical innovations that have allowed CFD to become a widely available tool for researchers.

#### **4.1 Coupling of velocity–pressure equations**

Regardless of whether a simulation is steady or unsteady, an iterative process must be undertaken wherein solutions are fed back into the coupled equations and then the solutions are updated to improve accuracy. The pressure and velocity fields are coupled via the governing equations and it is challenging to calculate them simultaneously. A series of approaches was developed that began with the so-called SIMPLE algorithm (Semi-Implicit Method for Pressure Linked Equations) [4, 5]. These references provide extensive detail on the algorithm, which has been joined by a modified SIMPLER version, the SIMPLEC method, and the PISO method. All of these methods continue to be used in today's algorithms. Use of these approaches greatly improves the stability of the pressure–velocity coupling.

#### **4.2 Multigrid calculations**

Another major innovation has been the utilization of multigrid simulations to increase the speed of solution. With a multi-grid method, the governing equations are first solved on a coarse mesh. This solution is then sent to a new mesh that contains smaller elements and iterations with the new mesh are performed. The solution is again passed to a further refined mesh and the process continues until the mesh is identical with the cells that the user has defined (for example in **Figure 5**). Following a converged *Introductory Chapter: A Brief History of and Introduction to Computational Fluid Dynamics DOI: http://dx.doi.org/10.5772/intechopen.97235*

solution on the smallest cells, the process is reversed, information is passed to increasingly coarse meshes until the algorithm arrives back at the initial, coarse mesh.

Through this process, solution information is transferred from the boundary conditions to the interior of the solution domain much faster than if the solution were obtained only on the finest computational mesh. It should be recognized that information is able to travel the distance of a cell size in a single iteration. If the solution domain is composed entirely of small elements, it means many iterations must be processed simply to transfer boundary information to the interior of the domain. The multi-grid approach largely solves this problem.

#### **4.3 Parallel computing**

Parallel computing refers to the simultaneous use of multiple processors during the iterative procedure. The software separates the computational mesh and parses different parts of the mesh to individual CPUs. Each CPU performs iterations on its batch of cells. The results are then collected, information is sent between the batches of cells, and the process is repeated.

To provide an example, a simulation that requires 10,000,000 elements that is solved with 10 processors would involve an allocation of approximately 1,000,000 elements to each processor. Clearly solving for 1,000,000 elements is far faster than the entire solution, and thus a time savings is achieved. On the other hand, there is a loss of efficiency in the partitioning (separating the elements into individual batches for each processor and passing information between the processors).

Parallel processing speed is measured as follows:

$$\text{Speed Up Time} = \frac{\text{Time Required for Simple Process}}{\text{Time Required for Multiple Process}} \tag{1}$$

**Figure 6.** *Example of elements that follow curved boundaries.*

Even with standard personal computers which typically have 4–8 CPU cores, a significant speed up time can be achieved. However, parallel computing is not advised for problems with a small number of elements. As a rule of thumb, each processor core should have approximately 100,000 computational elements assigned to it in order for there to be a time savings. For problems with 100,000 elements, a single processor is typically more efficient. For problems with more than approximately 200,000 elements, two processors are recommended, and so forth.

#### **4.4 Complex element shapes**

The last technical innovation that will be discussed is the advancement in element shapes. Initially, computational elements were made with simple shapes (squares and rectangles). While rectangular elements are suitable for rectangular solution domains, they are not necessarily appropriate for more complex shapes. For example, at curved boundaries, the elements would follow the boundary using a stair-step deployment. Modern day simulation algorithms generally no longer require rectangular elements. The governing equations can be solved with arbitrarily shaped elements. As a representative example, we provide a mesh that was recently used to simulate water flow past an oceanography instrument called the eXpendable BathyThermograph (XBT) As evident from the figure, a mesh has been deployed that is able to exactly follow the curved surface of the device and accurately depict the flow region (**Figure 6**).