*3.4.1 Role of oxaliplatin*

*Colorectal Cancer*

are not standard practice.

at 8 years [16].

than 3000 patients without any adverse features depending whether they received chemotherapy within 3 months after surgery or not. Interestingly, 27% of patients received adjuvant therapy in this group without much evidence to support it [12]. They reported a 5-year survival of 75% for those who did not receive chemotherapy versus 78% in those who received therapy. High grade, younger age, low comorbidities and white race were more likely to receive chemotherapy. After adjusting for known variables there was no difference in survival (HR 0.91, 95% CI 0.77–1.09). A number of trials have tried to address the role of adjuvant therapy in stage II colon cancer with conflicting results. QUASAR (Quick and Simple and Reliable), a large UK study investigated the role of adjuvant 5FU in this randomized controlled trial [13]. This study enrolled more than 3000 patients with (91%) stage II cancers (node-negative) which also included 30% rectal cancer. After a median follow up of 5.5 years, there was about 20% reduction in the relative risk of death (any cause mortality HR 0.82; 95% CI 0.70–0.95; p < 0.008) in those treated with chemotherapy compared to placebo controlled arm which translated into small but significant absolute survival benefit of 3.6% (95% CI 1.0–6.0). Despite significant results, number of pitfalls in this trial has raised questions with regard to the benefit seen. The median number of lymph nodes removed in this study was 6 (in more than 60% of patients <12 lymph nodes were removed) which is well below current standards. In addition, there was a group of patients who received radiation therapy (14%) and another proportion received portal vein infusion therapy (6%), which

There were a number of meta-analyses which support the use of adjuvant

International Multicenter Pooled Analysis of Colon Cancer Trial (IMPACT) was a pooled analysis of randomized trials, showed a 2% improvement in 5-year overall survival. In another analysis of more than 150,000 patients with stage II colon cancer from National Cancer Database reported survival advantage of adjuvant therapy (HR 0.76; p < 0.001) [14]. Gill et al. analyzed pooled individual patient data of 3302 patients with stage II and stage III colon cancers. Although there was a statistically significant improvement in disease free survival (by 4%), overall survival difference (absolute benefit of 5%) was not significant [15]. The Adjuvant Colon Cancer End Points (ACCENT) collaboration analyzed individual patient data with regard to long term outcome after adjuvant therapy. Among 6900 patients with stage II cancers, there was 5% improvement survival

Given the conflicting data, adjuvant therapy in stage II colon cancer remains controversial. Several clinicopathological features and molecular markers are associated with poor prognosis in stage II colon cancers. These include T4 primary, bowel obstruction of peroration, poorly differentiated phenotype (including signet ring cells and mucinous) high pre-operative carcinoembryonic antigen (CEA), inadequate lymph node sampling (<13 nodes), lymphovascular space invasion and perineural invasion [17, 18]. Although most expert groups consider these factors as high risk features in stage II colon cancer, some discrepancy exist among their definition for high risk stage colon cancer [19–21]. While most expert groups recommend to consider these adverse factors when considering adjuvant therapy, there is limited evidence to suggest that the presence of one or risk factors are more likely to benefit from adjuvant therapy. In the landmark MOSAIQ trial, 434 patients were considered high risk stage II colon cancer. Although there was trend towards better disease-free survival in the FOLFOX arm compared to 5FU arm, overall survival was essentially similar [22]. The decision regarding adjuvant therapy in this setting will need to be individualized and take into account the patient's preferences

therapy in stage II colon cancer including NSABP, NCCTG and IMPACT.

**166**

regarding therapy.

Two large phase III trials explored the role of oxaliplatin in stage II colon cancer; MOSAIC and NSABP C-07 which have virtually shown the lack of benefit of oxaliplatin in stage II colon cancer [22, 23]. Forty percent and 27% of patients were stage II in MOSAIC and NSABP C07 trials, respectively. An updated 10-year follow up report of MOSAIC confirmed the lack of benefit from oxaliplatin in stage II colon cancer. In fact there was a trend towards adverse outcome in low-risk stage II in MOSAIC, while there is a non-significant trend of improvement in disease free survival (7%) and overall survival (2%) [22]. No disease-free survival or overall survival benefit was seen in NSABP C-07 trial in patients with stage II colon cancer [23]. Therefore oxaliplatin is unlikely to benefit most patients with stage II colon cancer; however, it may be appropriate to discuss oxaliplatin in those with extremely high risk features, given the findings from MOSAIC.


**Progress in Carnot and Chambadal Modeling of Thermomechanical Engine by Considering Entropy Production and Heat Transfer Entropy**

**Michel Feidt 1 and Monica Costea 2,\***

Received: 11 November 2019; Accepted: 13 December 2019; Published: 16 December 2019

**Abstract:** Nowadays the importance of thermomechanical engines is recognized worldwide. Since the industrial revolution, physicists and engineers have sought to maximize the efficiency of these machines, but also the mechanical energy or the power output of the engine, as we have recently found. The optimization procedure applied in many works in the literature focuses on considering new objective functions including economic and environmental criteria (i.e., ECOP ecological coefficient of performance). The debate here is oriented more towards fundamental aspects. It is known that the maximum of the power output is not obtained under the same conditions as the maximum of efficiency. This is shown, among other things, by the so-called nice radical that accounts for efficiency at maximum power, most often for the endoreversible configuration. We propose here to enrich the model and the debate by emphasizing the fundamental role of the heat transfer entropy together with the production of entropy, accounting for the external or internal irreversibilities of the converter. This original modeling to our knowledge, leads to new and more general results that are reported here. The main consequences of the approach are emphasized, and new limits of the efficiency at maximum energy or power output are obtained.

**Keywords:** Carnot engine; optimization; heat transfer entropy; entropy production; new efficiency limits

#### **1. Introduction**

The origin of the industrial era in the 19th century is strongly connected to thermomechanical engines whose importance in our society is well-known. Their rapid development and evolution have contributed to the foundation of thermodynamics as a new branch of science, mainly concerned with fundamental aspects, as well as numerous applications.

The famous reference case is relative to the Carnot engine [1], but it refers only to an Equilibrium Thermodynamics modelling of a totally reversible engine. Additionally, the work done by Carnot generalizes the concept of efficiency according to the First Law of Thermodynamics starting from a purely mechanical approach [2], and the concept of the Carnot cycle. The interactions between the working fluid and the surroundings during a cycle consist of a mechanical energy exchange, *W*, and a calorific energy exchange, *Q*, which are of infinite time duration for reversible conditions. This leads to a quasi-static cycle, whose mean power output of the engine, . *W*, is zero.

Since (approximately) the 80s, a new approach has been developed including the existence of unavoidable heat transfer irreversibilities (endo-reversible machine [3]), and afterward, internal irreversibilities of the converter were also considered, but less frequently. To take account of these irreversibilities, two main forms are reported in the literature:

In the more general case, the entropic ratio could be a function that needs to be specified. This will be considered in this paper.

The main objective encountered in the literature relative to the Non-Equilibrium Thermodynamics approach remains the power output optimization of the engine and the associated conditions (vector of state), as well as the efficiency associated with maximum power.

Numerous studies are concerned with the influence of:

The present paper proposes a new modelling of an irreversible cycle focused on a necessary condition of the cycle existence, namely the heat transfer entropy. As the most important one for the cycle is the entering heat transfer entropy associated with the heat input in the converter (engine), it will be called hereafter, reference entropy, Δ*S*. According to the modeling assumptions that consider all cycle processes in the converter as irreversible, the total entropy production over a cycle, Δ*SI* is added to this reference heat transfer entropy. The coupling consequence of these two entropies in the analytical analysis of an irreversible cycle leads to new results that are reported here.

This new modelling is developed for the exo-reversible and endo-irreversible Carnot engine configuration, as the first possible extension of the primitive Carnot cycle approach.

Then, the remodeled Chambadal [29] engine configuration is described by adding the influence of the converter internal irreversibility. The optimization approach considers two ways to introduce the converter internal irreversibility, namely the entropic ratio model and the entropic production one, each of them being developed for different dependence functions of the system parameters. The consequences of this addition on the optimized power output are reported, and the limit cases—the endo-reversible Carnot engine and endo-irreversible model—are shown to be recovered.

A discussion of the overall results and an attempt to generalize the present study provide new and important upperbounds for the engine performance.

An ongoing next step will be the application of the same methodology to Curzon-Ahlborn [30] modelling of the Carnot engine by including internal irreversibilities of the converter and considering the importance of the heat transfer entropy.

#### **2. The Endo-Irreversible Carnot Engine**

#### *2.1. Cycle Representation in T-S Diagram*

The thermomechanical engine is considered as a system composed of a hot bath (heat source), converter (engine) and cold bath (heat sink), as shown in Figure 1. The coupling of the three subsystems is made by the heat transferred from the source to the working fluid in the engine at its hot side, and the heat rejected by the working fluid to the sink at the cold side, respectively.

In the Carnot engine modeling, the source and sink are two infinite bath (thermostats) at temperatures *THS* and *TCS* respectively. The Carnot engine operates upon an irreversible cycle with perfect thermal contact (no temperature difference) with the two bathes. Thus, one can call it an exo-reversible and endo-irreversible engine.

**Figure 1.** Schematic representation of the thermo-mechanical engine.

The irreversible cycle is identified in Figure 2 from state 1 (beginning of the high temperature isotherm), 2 (exit of the high temperature isotherm and beginning of the adiabatic expansion), 3 (end of the adiabatic expansion and beginning of the low temperature isotherm), and 4 (exit of the low temperature isotherm and beginning of the adiabatic compression, up to state 1). The reversible cycle (marked in red) is also represented in Figure 2 as a starting graphical cycle helping to emphasize the effect of each internal irreversibility considered in the modeling.

**Figure 2.** Representation of the Carnot engine cycle with internal irreversibility and the corresponding reversible one (in red) in T-S diagram.

Both adiabatic and isothermal transformations of the cycle are considered irreversible. Thus, the irreversibility on the isothermal processes is represented on the horizontal lines 12 and 34 by the corresponding production of entropy. As the irreversibility on the adiabatic processes in the cycle is also emphasized by entropy production, the graphical representation is associated to a polytropic processes represented in the T-S diagram by a corresponding dependence *T* = *f(S)*. For simplicity, a linear dependence *T* = *f(S)* between states 2 and 3, and 4 and 1, respectively, replaced the real one in the analytical and graphical analysis of the cycle.

Consequently, the production of entropy on a cycle Δ*SI* representing the total amount of entropy produced in the universe per cycle (= engine + environment) is expressed as:

$$
\Delta S\_I = \Delta S\_{IH} + \Delta S\_{IEx} + \Delta S\_{ICo} + \Delta S\_{IC} \tag{1}
$$

with Δ*SIH,* production of entropy on the hot isotherm;

Δ*SIEx,* production of entropy during the adiabatic expansion; Δ*SICo,* production of entropy during the adiabatic compression; and Δ*SIC,* production of entropy on the cold isotherm, as shown in Figure 2.

Furthermore, for the hot temperature isotherm, the entropy production Δ*SIH* corresponds to:

$$
\Delta S\_H = \Delta S + \Delta S\_{IH\_1} \tag{2}
$$

where the reference heat transfer entropy is expressed as:

$$
\Delta S = \frac{Q\_H}{T\_{HS}}\text{\,\,\,}\tag{3}
$$

and it equals the entropy change in the hot bath (in module).

Similarly, for the cold temperature isotherm, the entropy production Δ*SIC* corresponds to:

$$
\Delta S\_{\overline{C}} = \Delta S\_{\overline{S}} - \Delta S\_{\overline{IC}\prime} \tag{4}
$$

as all production of entropy terms are positive (see Figure 2).

The two entropy productions Δ*SIH* and Δ*SIC* correspond to the graphical representation in Figure 3. One outlines here that the entropy balance over the irreversible cycle is expressed as:

$$
\Delta S + \Delta S\_I = \Delta S\_S = \frac{Q\_C}{T\_{CS}},
\tag{5}
$$

where Δ*SS* represents the heat transfer entropy corresponding to the heat transferred to the sink.

Note that the commutations between isothermal and adiabatic processes are assumed to be instantaneous. Moreover, one observes that while the two real isothermal processes are well identified on the diagram, it is not the same for the irreversible adiabatic processes linking state 2 to 3, and then 4 to 1. All the curves inscribed in the rectangle (2-3'-3-2'-2) satisfying the criterion of increasing entropy on the adiabatic expansion process are possible.

Plotting a linear transformation in the *T-S* diagram between state 2 and 3 is not the only physical acceptable solution, because in the frame of Non-Equilibrium Thermodynamics, one only has access to points 2 and 3 representing the adiabatic case.

The same discourse can be renewed for the adiabatic compression between 4 and 1. In short, all the curves inscribed in the rectangle (4-4'-1-1'-4) satisfying the criterion of increasing entropy on the adiabatic process are possible. The linear transformation in the *T-S* diagram between state 4 and 1 is again a possible intermediate solution.

This irreversibility approach is similar to the one of a recent publication [31].

The graphical analysis of the cycle with linearized processes between 23 and 41 illustrated in Figure 2 shows the area representing the corresponding linearized work per cycle *WL* as:

$$
\mathcal{W}\_L = \left(\frac{\Delta S\_H + \Delta S\_C}{2}\right) (T\_{HS} - T\_{CS}).\tag{6}
$$

This 'geometric' work (6) is different from the 'thermodynamic' (or mechanical) work that will be expressed in Section 2.2 by (10) since (6) depends on the linear assumption regarding the representation of the irreversible adiabatic processes between 23 and 41 as done in many references [31]. Nevertheless, it does not reflect the exact physical behavior of the endo-irreversible Carnot heat engine that could be different to the linear one. Thus, only (10), which is based on energy and entropy balances, will provide the correct expression of the mechanical work.

#### *2.2. Analytical Model*

Considering the adiabaticity (no thermal loss) and exo-reversibility assumptions for the cycle in this model, the heat transfer at the source and sink are respectively:

$$Q\_{HS} = Q\_H > 0 \; ; \; Q\_{CS} = Q\_{\overline{C}} < 0. \tag{7}$$

The exo-reversibility of the heat transfer relative to the two thermostats imposes:

$$T\_{HS} = T\_H \; ; \; T\_{CS} = T\_C \; . \tag{8}$$

Thus, the entropy balance on the system can be written as:

$$\frac{Q\_{HS}}{T\_{HS}} + \Delta S\_I = \frac{|Q\_{CS}|}{T\_{CS}},\tag{9}$$

where from the expression of the mechanical work per cycle from the First Law when the entropy variation corresponding to the heat transfer converted at the source is considered as reference heat transfer entropy, Δ*S*, ΔSH = ΔS. becomes:

$$\mathcal{W} = Q\_{\rm HS} - |Q\_{\rm CS}| = (T\_{\rm HS} - T\_{\rm CS})\Delta S - T\_{\rm CS}\Delta S\_I. \tag{10}$$

The first term of the second equality represents the reversible work, and the second one, the mechanical dissipation (by fluid and solid friction mainly).

The expression of *W* in (10) marks the presence of the internal entropy production over a cycle Δ*SI* that is supposed as a parameter. Its relationship with the ratio method is introduced below, by emphasizing Δ*S* in (10):

$$\mathcal{W} = \Delta S \left[ (T\_{HS} - T\_{CS}) - T\_{CS} \frac{\Delta S\_I}{\Delta S} \right]. \tag{11}$$

Thus, the ratio Δ*SI*/Δ*S* appears in (11) and it corresponds to the irreversibility degree *dI* introduced by Novikov [32]. This parameter is also related to an entropic ratio according to Ibrahim's approach [4], which represents the absolute value of the ratio of the entropy change in the cold bath to the entropy change in the hot bath and is given as:

$$I = \frac{\Delta S\_S}{\Delta S}.\tag{12}$$

One notes that this ratio can be particularized (i.e., *IH* = Δ*SS*/Δ*SH*), since it represents a coefficient relative to an entropy variation corresponding to the heat exchanges at the hot and cold sides of the converter. Hence, other assignments could be given (*IC*, *IHS*, *ICS*). For the adiabatic exo-reversible Carnot engine, this ratio is *I* = *IH* = *IHS* and moreover, it is easy to show that:

$$I = 1 + d\_I = 1 + \frac{\Delta S\_I}{\Delta S}'\tag{13}$$

and

$$\mathcal{W} = \Delta S \left[ \left( T\_{\rm HS} - T\_{\rm CS} \right) - T\_{\rm CS} (I - 1) \right] = \Delta S \left[ T\_{\rm HS} - I \cdot T\_{\rm CS} \right]\_{\prime} \tag{14}$$

$$
\eta\_l = \frac{\mathcal{W}}{\mathcal{Q}\_{HS}} = 1 - I \frac{T\_{\text{CS}}}{T\_{HS}}.\tag{15}
$$

It results that the internal irreversibility diminishes the mechanical work and cycle efficiency.

It remains to analyze how *I* or Δ*SI* vary with the cycle quantities. It can be reasonably assumed that Δ*SI* and (or) *I* depend on Δ*S* and (or) Δ*TS* = *THS – TCS*, as the two temperatures are generally parameters of the problem for the Carnot endo-irreversible engine. Hence, two functions can be proposed, whose general forms (currently unknown in practice) are written as:

$$
\Delta S\_I = f\_{\rm SI}(\Delta T\_{\rm S}, \Delta S) \; ; \; I = f\_l(\Delta T\_{\rm S}, \Delta S) . \tag{16}
$$

If there is an optimum of *W*, it must satisfy the necessary condition imposed by one of the following equation sets:

$$\frac{\partial \mathcal{W}}{\partial \Delta T\_S} = \Delta \mathcal{S} - T\_{\text{CS}} \frac{\partial f\_{\text{SI}}}{\partial \Delta T\_S} = 0 \; ; \; \frac{\partial \mathcal{W}}{\partial \Delta T\_S} = \Delta \mathcal{S} \left( 1 - \frac{\partial f\_I}{\partial \Delta T\_S} \right) = 0 \; \tag{17}$$

$$\frac{\partial \mathcal{W}}{\partial \Delta \mathcal{S}} = \Delta T\_S - T\_{\mathbb{CS}} \frac{\partial f\_{\mathcal{S}I}}{\partial \Delta \mathcal{S}} = 0 \; ; \; \frac{\partial \mathcal{W}}{\partial \Delta \mathcal{S}} = \Delta T\_S - T\_{\mathbb{CS}} \frac{\partial f\_I}{\partial \Delta \mathcal{S}} = 0. \tag{18}$$

#### **3. The Chambadal Engine**

The representation of the Chambadal engine irreversible cycle in Figure 3 shows that in addition to the internal irreversibility of the cycle that was graphically detailed in Section 2.1, the external irreversibility corresponding to the heat transfer at temperature difference at the hot side appears. Since the same components of the internal irreversibility for the endo-irreversible Carnot engine are considered here as well, the cycle representation was simplified by only preserving its shape, and the new irreversibility completing the model was emphasized. Hence, in Figure 3 case (a) corresponds to a heat transfer from a source of constant temperature *THS*, while case (b) shows a finite heat capacity source with the inlet temperature *THSi*. The temperature difference of the source and sink level, Δ*TS*, compared to the cycled fluid one, Δ*TCF*, that remains the same, is also relevant for the heat input in the two cases.

Note that the external irreversibility at the sink is neglected in this approach by considering the heat rejection to sink occurring at ambient temperature (*TC* = *TCS* = *T0*).

**Figure 3.** Representation of the associated cycle to the Chambadal engine in T-S diagram: (**a**) source of constant temperature; (**b**) source of finite heat capacity.

The Chambadal engine model is concerned with steady-state operation of the engine and consequently, heat rates and power output are used. We propose here to convert this modeling with reference to a cycle and the related energies-heat and work, thus leading to a different model, the quasi-Chambadal engine.

It involves a thermostat or source of finite heat capacity rate . *CH* = . *mHcpH*, with an input temperature *THSi*.

Hence, when the source is a thermostat of constant temperature, *THS*, the heat transfer at the hot end is expressed as: .

$$Q\_H = \mathcal{U}\_H A\_H (T\_{HS} - T\_H)\_\prime \tag{19}$$

with *KH* = *UH* · *AH*, heat transfer conductance of the source corresponding to the steady state operation regime.

When the source has a finite heat capacity, it involves a temperature variation of the primary fluid in the corresponding heat exchanger. As the input temperature of the primary fluid *THSi* is generally known, by using the effectiveness ε – number of heat transfer units *NTU* method [27], one gets:

$$
\dot{Q}\_H = \varepsilon\_H \dot{\mathbb{C}}\_H (T\_{HSi} - T\_H). \tag{20}
$$

Note that the two expressions of . *QH* averaged on a time duration Δ*t*, allow to recover the caloric energy *QH*, or the mass specific energy (often used) that results by dividing . *QH* with the mass flow rate of the cycled fluid. Thus, a general expression of the heat transferred at the source is:

$$Q\_H = G\_H(T\_{HSi} - T\_H) = T\_H \cdot \Delta S\_\prime \tag{21}$$

where *GH* generally represents a finite physical dimension of the source (thus also of the system) with reference to energy here, its unit being J/K.

#### *3.1. Optimization Approach for the Entropic Ratio Model*

The previous equation is completed in this approach by the entropy balance expressed over a cycle as:

$$I\_H \frac{Q\_H}{T\_H} = \frac{Q\_C}{T\_0}.\tag{22}$$

This leads to the expression of the mechanical work output as:

$$\mathcal{W} = G\_H (T\_{HSi} - T\_H) \Big(1 - I\_H \frac{T\_0}{T\_H} \Big). \tag{23}$$

By taking into account that *IH* is a potential function of *TH*, the mechanical work maximum value *MaxW* search should satisfy the necessary condition:

$$\frac{\partial W}{\partial T\_H} = 0 = -1 + I\_H \frac{T\_0}{T\_H} - (T\_{H\text{Si}} - T\_H) \frac{I\_{H,H} \ T\_0 \ T\_H - I\_H T\_0}{T\_H^2},\tag{24}$$

where *IH*,*H* = ∂*IH* ∂*TH* .

The term rearrangement leads to an equation of second degree or more to be solved:

$$(T\_{H\text{Si}} - T\_H)T\_0 \ T\_H I\_{H,H}{}^1 = I\_H T\_0 T\_{H\text{Si}} - T\_H{}^2. \tag{25}$$

Possible cases are:

(i) *IH* is a constant parameter.

This implies ∂*IH*/∂*TH* = *IH*,*H* = 0.

Thereby, the optimum temperature at the hot-end, *MaxW* and the corresponding cycle efficiency respectively, result as:

$$T\_H{}^\* = \sqrt{I\_H T\_0 \ T\_{HSi}} \tag{26}$$

$$\text{MaxW} = G\_H \Big(\sqrt{T\_{HSi}} - \sqrt{I\_H T\_0} \Big)^2,\tag{27}$$

$$
\eta\_I(\text{MaxW}) = 1 - \sqrt{\frac{I\_H T\_0}{T\_{HSi}}} \tag{28}
$$

It is obvious that the rise of *IH* parameter results in an increase of the optimal temperature *TH*∗ and has the opposite effect (decrease) on *MaxW* and the associated cycle efficiency.

(ii) *IH* is a linear function of Δ*TT* = *TH* – *T0* (see Figure 3), with values ≥ 1.

One considers the following expression for *IH*:

$$I\_H = \mathbb{C}\_I (T\_H - T\_0) + 1,\quad \text{with}\quad \mathbb{C}\_I = I\_{H,H} \tag{29}$$

By combining (25) with (29), one gets:

$$\mathbf{C}\_{I} \left( T\_{HSi} - T\_{H} \right) T\_{0} \ T\_{H} = \left[ \mathbf{C}\_{I} \left( T\_{H} - T\_{0} \right) + 1 \right] T\_{0} T\_{HSi} - T\_{H} \, ^{2} \, . \tag{30}$$

The above equation leads to the expression of the optimum temperature of the cycled fluid at the hot side expressed by:

$$T\_H{}^\* = \sqrt{T\_0 \ T\_{HSi}} \ . \tag{31}$$

It results that irreversibility does not affect the temperature *TH*∗ , but it does affect the mechanical work and the cycle efficiency, whose expressions become:

$$\text{Max}W = \text{G}\_{H}(1 - \text{C}\_{I}T\_{0})\left(\sqrt{T\_{HSi}} - \sqrt{T\_{0}}\right)^{2},\tag{32}$$

$$\eta\_I(\text{Max}\mathcal{W}) = (1 - \mathbb{C}\_I T\_0) \left( 1 - \sqrt{\frac{T\_0}{T\_{HSi}}} \right) \tag{33}$$

The comparison of (27) and (32) clearly shows the maximum work decrease in case ii) and by a completely different expression. The same happens for the efficiency at maximum work, when comparing (28) and (33).

#### *3.2. Optimization Approach for the Entropic Production Model*

The entropy balance takes a similar form to that of Section 2.2, namely:

$$\frac{Q\_H}{T\_H} + \Delta S\_I = \frac{Q\_\mathbb{C}}{T\_\mathbb{C}}\,\tag{34}$$

with *TC* = *TCS* = *T*0.

One notes that the production of entropy on the cycle in (34) is not the same with (1) in the endo-irreversible Carnot engine case, since it also considers the production of entropy corresponding to the heat transfer at finite temperature difference (see Figure 3).

The mechanical work is expressed as:

$$\mathcal{W} = Q\_H \Big( 1 - \frac{T\_{\text{CS}}}{T\_H} \Big) - T\_{\text{CS}} \Delta S\_I. \tag{35}$$

By using (21) in (35), one gets:

$$\mathcal{W} = G\_H (T\_{HSi} - T\_H) \left( 1 - \frac{T\_{CS}}{T\_H} \right) - T\_{CS} \Delta S\_I. \tag{36}$$

The term Δ*SI* is a potential function of *TH* (also increasing one). Therefore, the *MaxW* search should satisfy the necessary condition:

$$\frac{\partial W}{\partial T\_H} = 0 = -\left(1 - \frac{T\_{CS}}{T\_H}\right) + (T\_{HSi} - T\_H)\frac{T\_{CS}}{T\_H^2} - \frac{T\_{CS}\Delta S\_{IH}}{G\_H} = 0. \tag{37}$$

This form is simpler than the previous one, providing an equation of the second degree or more to solve.

The possible cases are as follows:

(i) Δ*SI* is a constant parameter.

This implies ∂*SI*/∂*TH* = Δ*SI*,*H* = 0, which delivers:

$$T\_H{}^\* = \sqrt{T\_{H\text{Si}} \, T\_{\text{CS}}} \, . \tag{38}$$

The expressions of *MaxW* and η*I*(*MaxW*) are straightforward:

$$
\Delta \text{MaxW} = G\_H \left( \sqrt{T\_{HSi}} - \sqrt{T\_{CS}} \right)^2 - T\_{CS} \Delta S\_{I\prime} \tag{39}
$$

$$
\eta\_I(Max\mathcal{W}) = 1 - \sqrt{\frac{T\_{CS}}{T\_{HSi}}} \left( 1 + \frac{\Delta S\_I}{\Delta S} \right) . \tag{40}
$$

(ii) A linear dependence of Δ*SI* on the temperature difference Δ*TT* = *TH* – *TCS* is considered.

We assume that:

Δ*SI* = 0 if Δ*TT* = 0;

Δ*SI* = Δ*SIS* (new parameter) if Δ*TT* = Δ*TS* = *THSi* – *TCS* (see Figure 3b), where from:

$$
\Delta S\_{\rm I} = \Delta S\_{\rm IS} \frac{\Delta T\_{\rm T}}{\Delta T\_{\rm S}} = \Delta S\_{\rm IS} \frac{T\_H - T\_{\rm CS}}{T\_{\rm HSi} - T\_{\rm CS}} = \mathcal{C}\_{\rm IS} (T\_H - T\_{\rm CS}).\tag{41}
$$

The mechanical work optimization imposes:

$$\frac{\partial W}{\partial T\_H} = 0 = G\_H \left( \frac{T\_{HSi} \ T\_{CS}}{T\_H \tau^2} - 1 \right) - \frac{\Delta S\_{IS}}{\Delta T\_S} T\_{CS\prime} \tag{42}$$

which leads to:

$$T\_H{}^\* = \sqrt{\frac{T\_{HSi} T\_{CS}}{1 + \frac{T\_{CS}}{\Delta T\_S} \frac{\Delta S\_{IS}}{\bar{G}\_H}}}\,. \tag{43}$$

It is well known that internal irreversibility always decreases *W*. Hence, (41) is valuable by emphasizing in the denominator two factors that modify the optimal temperature *TH\**:

The last factor is not only related to the converter through Δ*SIS*, but also to the hot source by the finite physical dimension *GH* (coupling).

This shows the interest of an entropic description of the system. Thus, the corresponding maximum power output is given by:

$$\text{MaxW} = \text{G}\_{H} \left( \sqrt{T\_{HSi}} - \sqrt{I \cdot T\_{0}} \right)^{2},\tag{44}$$

with

$$I = \frac{T\_0}{\Delta T\_S} \cdot \frac{\Delta S\_{IS}}{G\_H}.\tag{45}$$

The associated first law efficiency is:

$$\eta\_I(\text{MaxW}) = \frac{\left(1 - \sqrt{\frac{I \cdot T\_0}{T\_{HSi}}}\right)^2}{1 - \sqrt{\frac{T\_0}{I \cdot T\_{HSi}}}},\tag{46}$$

#### *3.3. Quasi-Chambadal Model with Added Heat Transfer Entropy Constraint and Production of Entropy*

This optimization is based on (21) from which the temperature *TH* is expressed as:

$$T\_H = \frac{G\_H}{G\_H + \Delta S} T\_{HS} \,\, \, \, \, \, \tag{47}$$

with Δ*S*, reference heat transfer entropy associated to the heat input. This result is an important one, since it illustrates the coupling between the source (*GH*) and the converter (Δ*S*).

The expression of the mechanical work *W* can be easily derived as a function of the newly chosen variable Δ*S*:

$$\mathcal{W} = \begin{bmatrix} T\_{HSi} \ G\_H \\ \hline G\_H + \Delta S \end{bmatrix} - T\_0 \begin{bmatrix} \Delta S - T\_0 \ \Delta S\_I \end{bmatrix} \tag{48}$$

This optimum with respect to Δ*S* corresponds to a converter adapted to the hot source. It results that *W* becomes maximum when Δ*SI* is related to Δ*S* (to be specified) by the following function:

$$\frac{\partial W}{\partial \Delta S} = 0 = \left(\frac{G\_H}{G\_H + \Delta S}\right)^2 T\_{HSi} - T\_0 - T\_0 \left.\frac{\partial \Delta S\_I}{\partial \Delta S}\right. \tag{49}$$

Following different assumptions, one can consider:

(i) the presence of the Novikov's irreversibility degree [9], that is expressed by:

$$\frac{\partial \Delta S\_I}{\partial \Delta S} = d\_I. \tag{50}$$

In this case, one gets at the optimum:

$$
\Delta S^\* = G\_H \left[ \frac{\sqrt{T\_{HSi}}}{\sqrt{T\_0 \left(1 + d\_I\right)}} - 1 \right]. \tag{51}
$$

It results that the optimum heat transfer entropy Δ*S\** diminishes with increasing irreversibility *dI*, and the same goes for *MaxW* and the cycle efficiency:

$$\text{MaxW} = \text{G}\_{H} \left( \sqrt{T\_{HSi}} - \sqrt{T\_0 \left(1 + d\_I\right)} \right)^2,\tag{52}$$

$$
\eta\_I(\text{MaxW}) = 1 - \sqrt{\frac{T\_0 \left(1 + d\_I\right)}{T\_{HSi}}},\tag{53}
$$

where *dI* ≤ (*THSi* − *T*0 )/*T*0 .

#### (ii) when Δ*SI* is a constant parameter, one finds similarly:

$$
\Delta S^\* = G\_H \left[ \frac{\sqrt{T\_{HSi}}}{\sqrt{T\_0}} - 1 \right] \tag{54}
$$

and

$$
\Delta\text{MaxW} = G\_H \left(\sqrt{T\_{H\text{Si}}} - \sqrt{T\_0}\right)^2 - T\_0 \,\Delta S\_{I\prime} \tag{55}
$$

$$
\ln \eta \left( \text{MaxW} \right) = 1 - \sqrt{\frac{T\_0}{T\_{HSi}}} \left( 1 + \frac{\sqrt{T\_0}}{\sqrt{T\_{HSi}} - \sqrt{T\_0}} \frac{\Delta S\_I}{G\_H} \right). \tag{56}
$$

(iii) Δ*SI* may also depend of *TH* in a linear form, as in Section 3.2, case ii), namely:

$$
\Delta S\_I = d\_{IS} \frac{T\_H - T\_0}{T\_{HSi} - T\_0} \Delta S\_\prime \tag{57}
$$

from which one gets:

$$\mathcal{W} = (T\_H - T\_0)\Delta S \Big(1 - T\_0 \, \frac{d\_{IS}}{T\_{HSi} - T\_0} \Big),\tag{58}$$

where *dIS* ≤ (*THSi* − *T*0 )/*T*0 is the parameter of entropic proportionality corresponding to the irreversibility degree of Novikov [24], but relative to the system composed of a source and converter (the heat transfer from the converter to the sink being neglected in the model).

Knowing the expression of *TH* as a function of Δ*S*, one gets:

$$\mathcal{W} = \left( T\_{HSi} \frac{G\_H}{G\_H + \Delta S} - T\_0 \right) \Delta S \left( 1 - T\_0 \frac{d\_{IS}}{T\_{HSi} - T\_0} \right). \tag{59}$$

The optimum of the mechanical work with respect to Δ*S* is obtained after some calculations as:

$$\text{Max}W = G\_H \Big(\sqrt{T\_{HSi}} - \sqrt{T\_0}\Big)^2 \Big(1 - \frac{T\_0}{T\_{HSi} - T\_0} d\_{IS}\Big). \tag{60}$$

The corresponding first law efficiency is:

$$n\eta\_I(\text{Max}\,\mathcal{W}) = \left(1 - \sqrt{\frac{T\_0}{T\_{HSi}}}\right) \left(1 - \frac{T\_0 \, d\_{lS}}{T\_{HSi} - T\_0}\right). \tag{61}$$

These two quantities are decreasing with the parameter *dIS*. Thus, the mechanical work *W* is diminished by the term 1 − *T*0 *dI*,*S THSi* −*T*0 , as shown in (59). Also, (61) clearly proves that irreversibility decreases the efficiency corresponding to maximum work.

#### **4. Conclusions**

This work presents a short history of the Carnot cycle approaches developed in the frame of Equilibrium Thermodynamics, of the actual endo-irreversible Carnot engine in Irreversible Thermodynamics, and for the Chambadal model.

The analytical model developed in the frame of Equilibrium Thermodynamics integrates the irreversibility in the natural form of an entropy production, or in an entropic ratio form (with various justified and correlated definitions) and is mainly related to the irreversibility degree introduced by Novikov [32].

The mechanical work of the irreversible cycle remains linked to the form of the irreversible isotherms and adiabatics, as has been shown in Section 2.1. The irreversibilities distribution between isothermal and adiabatic processes leads to framing the actual work between zero and max *MaxW*, with the corresponding efficiencies pertaining to the interval between zero and the Carnot efficiency.

For the Chambadal model, the cycle approach or the one in the stationary dynamic regime come down to the same form, by introducing a characteristic property *GH*, which is representative of the finite physical dimensions connected to the reference heat transfer entropy Δ*S*, characterizing the converter.

It results in the existence of an optimum of the mechanical work either in terms of intensive variable *TH*, or in terms of extensive variable Δ*S*.

The two approaches leading to coherent results, but with different interpretations, provide a new perspective on the optimization of the Carnot engine, mainly by coupling of the hot source with the converter (*GH* and Δ*S*).

Extensions are in progress, which are based on more complete models, particularly on the Curzon-Ahlborn one, that considers the non-equilibrium at source and sink. Also, the stochastic thermodynamics approach [33,34] is intended to be used in future works to evaluate different sources of irreversibility in the corresponding heat engines exactly, without additional assumptions. It could offer an alternative to evaluate the analytical results provided by our phenomenological approach.

**Author Contributions:** M.F. contributed to the development of the model, M.C. contributed to the preparation of the manuscript, design of the study and final proof, and to the analysis and interpretation of the results. All authors have read and agreed to the published version of the manuscript.

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

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

#### **References**

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).


*3.4. CD8 Cellular Responses Were Robust in Outbred CD-1 Mice*

To further study these immunogens in a more relevant outbred animal model, we next vaccinated CD-1 mice and compared their responses to control-vaccinated animals. These mice were vaccinated three times at two-week intervals, and immune studies were performed a week after the final vaccination (Figure 3A). Cellular responses were once again more robust for EBNA1 and LMP2A than for LMP1, as was again observed in the inbred mouse models. However, stimulation with each of the latent protein peptide pools produced some responses, as measured by IFNγ ELISPOT (Figure 3B). CD8 responses were dominant when the splenocytes were analyzed by flow cytometry, and CD4 responses were lower (Figure 3C). The CD-1 response supports the CD8 potency of this vaccine approach.

**Figure 3.** Cellular responses produced by combination vaccine in outbred CD-1 mice. (**A**) Vaccination schedule in outbred CD-1 mice. Mice were vaccinated with a combination of EBNA1vax, LMP1vax, and LMP2Avax three times at biweekly intervals, followed by harvesting of their splenocytes a week after the final vaccination. (**B**) Cellular responses to respective peptide pools, shown by IFNγ ELISPOT. (**C**) Plots showing CD4 or CD8 responses of CD-1 mice immunized with the triple vaccine or empty vector (pVax), stimulated with pooled peptides derived from EBNA1, LMP2A and LMP1. Cellular responses are driven by CD8+ cells, as shown by flow cytometry following stimulation of splenocytes.


Meet the editor

Dr. Maryam Takht Ravanchi holds a Ph.D. in Chemical Engineering. She is a researcher for a petrochemical research and technology company. Her research interests are in the fields of natural gas conversion, C1 chemistry, heterogeneous catalyst synthesis, membrane separation technologies, and the environment. She has about twenty years of experience in the petrochemical industry as a process engineer and researcher. She

has published seventy journal papers, seventy conference papers, seven national patents, and fifteen books.


*2.5. Data Analysis*

First, a hierarchical regression analysis was conducted in order to examine the explained variance of alcohol consumption during pregnancy. In the first step, demographics (i.e., age, educational level, and employment status) were introduced in the regression equation, while obstetric history was added in the second (i.e., number of pregnancies and pregnancy planning). In the third and fourth steps, previous alcohol consumption and the partner's alcohol consumption were included. In the fifth and sixth steps of the regression analysis, advice received from health professionals (i.e., the number of health professionals who gave advice and the percentage of health professionals who provided the correct advice) and beliefs about risks (i.e., risk awareness of alcohol consumption during pregnancy, perceived duration of the damage caused by prenatal alcohol exposure, and the risk perception of drinking beer or wine during pregnancy) were included to explain alcohol consumption during pregnancy. R2 were calculated at each step including subsequent variables in the analysis, as well as the change in F. Additionally, t and β coefficients were examined for each indicator. These analyses were carried out with SPSS 21.0 (IBM Corp, New York, NY, USA, 2012).

Second, moderation analyses were conducted to explore how the previous indicators (i.e., demographics, obstetric history, the partner's alcohol consumption, advice received from health professionals, and beliefs about risks) moderate the relationship between previous alcohol consumption and consumption during pregnancy. These analyses were carried out following the recommendations described by Hayes [34], based on regression analyses. The effects described in this model represent causal assumptions, because there is no causation verification without variable manipulation. Thus, only associations among variables may be concluded. Standardized coefficients were calculated to estimate the effect of one variable (assumed to be the independent variable) on another variable (assumed to be the criterion variable), and the moderation was analyzed as the interaction between the independent variable and the moderator to explain the dependent variable. Process v3.3 macro for SPSS was used, by specifically applying the model number 1, which performs a total of 1000 bootstrap samples for bias-corrected bootstrap confidence intervals. Huber-White heteroscedasticity-consistent inference was carried out.

Third, structural equation modelling was performed to integrate the effects of demographics, obstetric history, self-reported previous alcohol consumption, the partner's alcohol consumption, advice received from health professionals, and beliefs about risks, on self-reported alcohol consumption during pregnancy, as well as the relationships between those indicators. χ2, Comparative Fit Index (CFI), and Root Mean Square Error of Approximation (RMSEA) were analyzed as overall data fit indexes. Lagrange multipliers and Wald tests were sequentially performed for model modifications to improve overall fit. R2 was calculated to analyze the explained variance, and standardized solutions were examined. This model was tested with EQS 6.3 (Multivariate Software Inc., Temple City, CA, USA, 2017), following the recommendations by Byrne [35].

#### **3. Results**

#### *3.1. Descriptive Characteristics of the Sample*

A total of 832 pregnant women randomly selected in accordance with the procedure described above were invited to participate. Of them, 426 (51.2%) accepted. The total number of pregnant women who attended the morphological ultrasound clinic during the period in which the study was performed (5 months in 2016) was 1664. Most of the participants were Spanish (92.2%). The average age was 31.9 years (SD = 5.3). Information concerning demographic and obstetric variables was described in a previous work [32].

Table 1 displays the primary information from the different variables on which data were collected.

**Table 1.** Descriptive statistics of study variables.

**Table 1.** *Cont*.

## *3.2. Regression Analysis to Explain Alcohol Consumption during Pregnancy*

Table 2 presents the results of the hierarchical regression analysis to explain self-reported alcohol consumption during pregnancy. In the first step, both educational level and employment status showed negative effects, such that lower alcohol consumption was detected in women with a higher educational level and among those self-labelled as "housewives". In the second step, obstetric history showed a significant effect, with more alcohol consumption in women who had more pregnancies. In the third step, previous alcohol consumption had a remarkable positive effect. Those women who reported higher previous alcohol consumption also indicated higher alcohol consumption during pregnancy. In the fourth step, the partner's alcohol consumption did not have a significant effect. In the fifth, a notable negative effect was observed for the percentage of professionals who provided correct advice. Thus, a lower percentage of professionals providing correct advice—not to consume any alcohol at all during pregnancy—is related to higher self-reported alcohol consumption. Lastly, in the sixth step, beliefs about risks were added, obtaining a final explained variance of 27%. Higher alcohol consumption during pregnancy was observed in those women who reported lower risk perception for wine.

**Table 2.** Hierarchical regression analysis of demographics, obstetric history, previous alcohol consumption, the partner's alcohol consumption, advice received from health professionals, and beliefs about risks, as correlates of alcohol consumption during pregnancy.

\*\*\* *p* < 0.001; \*\* *p* < 0.01.

#### *3.3. Moderation Analysis in the Relationship between Previous Alcohol Consumption and Consumption during Pregnancy*

Table 3 shows the results of the regression analyses to examine moderations in the relationships between previous and current alcohol consumption. Higher alcohol consumption during pregnancy was observed in women who reported higher previous consumption and had a low level of education. With regard to obstetric history, higher consumption during pregnancy was observed in women with greater previous consumption and more experience of pregnancies. Furthermore, higher consumption was also observed in women with higher previous consumption and those who reported a lower degree of correct advice received from health professionals. Lastly, risk perception regarding beer and wine also moderated that relationship. Higher alcohol consumption during pregnancy was observed in women with higher previous consumption and lower risk perception for the two types of alcoholic drinks studied.

**Table 3.** Regression analyses of the moderations by demographics, obstetric history, the partner's alcohol consumption, advice received from health professionals, and beliefs about risks, in the relationships between previous and current alcohol consumption.

Note. Dependent variable: Alcohol consumption during pregnancy. \*\*\* *p* < 0.001; \*\* *p* < 0.01; \* *p* < 0.05.

#### *3.4. Structural Equation Model*

Lastly, the relationships between the study variables were integrated in a structural equation model. After conducting Lagrange multipliers and Wald tests, the final model reached a good overall data fit, χ2(63, *N* = 426) = 118.17, *p* < 0.001, χ2/df = 1.88, CFI = 0.95, RMSEA = 0.05, 90% CI RMSEA = 0.03–0.06. Table 4 describes the effects and associations included in the model, which all reached statistical significance (*p* < 0.05).

First, regarding alcohol consumption during pregnancy, the model showed negative effects for risk awareness of alcohol consumption during pregnancy, the percentage of health professionals who provided correct advice, educational level and employment status, with higher consumption among those women with better employment status, and positive effects for risk perception of drinking wine during pregnancy, previous alcohol consumption, and number of pregnancies. This equation presented a R2 = 0.25 (MSE = 0.87), with the strongest effects for the percentage of health professionals who provided correct advice and previous alcohol consumption. Second, with regard to risk perception of drinking beer during pregnancy (R2 = 0.05, MSE = 0.97) and wine (R2 = 0.01, MSE = 0.99), previous alcohol consumption was positively related. Moreover, age and the number of health professionals who provided information were negatively related to risk perception of drinking beer during pregnancy.

Furthermore, some associations were also significant in the model. First, perceived risks of wine and beer were found to be positively interrelated. Moreover, beliefs about the duration of the damage and risk awareness of alcohol consumption during pregnancy were also positively associated. Second, the partner's alcohol consumption was positively associated with previous consumption and age, and negatively with beliefs about the duration of the damage. Third, the number of pregnancies was negatively related to previous alcohol consumption. Moreover, pregnancy planning was positively associated with age and educational level.

#### **4. Discussion**

The aim of this study was to analyze a wide range of potential predictors of alcohol consumption during pregnancy, with a view of identifying the specific weight of each of them, as well as the interactions between them. We thus intended to address the fragmented vision offered by studies conducted on this subject in general to date [8,24,31]. In order to examine the role of different factors as predictors of alcohol consumption during pregnancy, a random and representative sample of pregnant women receiving care in the outpatient clinics of a public hospital in a southern European city (Seville, Spain) was interviewed in the 20th week of pregnancy.

As in other previous studies [23–27], alcohol consumption prior to pregnancy was identified as the most powerful predictor of alcoholic beverage intake during pregnancy. This finding suggests, in short, that an expectant mother's previous lifestyle tends to continue during her pregnancy, particularly in terms of products that can lead to dependence and whose consumption is socially accepted in societies like Spain, such as alcoholic beverages. In this country, the average maternal age at delivery of the first child is particularly high (31.02 years of age in 2018, [36]), and the average age to start drinking alcoholic beverages is notably low (14.1 years of age among those female students who have ever drunk alcohol, [37]), and, as such, many women will have been drinking alcohol regularly for almost 20 years before their first pregnancy. It is not easy to drastically change behavior that is deeply rooted in lifestyles and has strong social support. It should not be forgotten, furthermore, that many pregnancies are unplanned (44% worldwide [38]; 25.4% in the sample used in this study) and that alcohol may be

having a teratogenic effect on the embryo before the woman is aware she is pregnant, precisely in the period of prenatal development that is most sensitive to the action of teratogens (organogenesis).

A review carried out by Stephenson et al. highlights that the state of health of the expectant mother, as well as her lifestyle during the perigestational period, has an influence on the perinatal results of the new-born baby. It therefore proves very important to promote healthy lifestyles among women of child-bearing age, and more specifically, among those who are trying to conceive, by providing preconception care [39]. According to another retrospective study, developed by Goossens et al., the adoption of these healthy lifestyles before pregnancy is more likely in nulliparous women and in those with a previous miscarriage. At the same time, women who have had previous pregnancies, as well as those who are of a lower socio-economic level are less likely to change their lifestyles and make them healthier [40]. It is therefore necessary to combine general strategies for promoting healthy lifestyles among women of child-bearing age with others aimed specifically at each sector of these women, in such a way that makes it easier for all of them to choose the healthiest options in their daily lives.

The structural equations model created also concludes that another important predictive factor, although with less weight than the previous one, is health advice received from health professionals and, more specifically, the percentage of health professionals who have provided pregnant women with the correct advice: To abstain completely from consuming alcoholic beverages during pregnancy. This is a new finding and one that had not been previously identified in the research in this field. This result suggests that the performance of health professionals who treat pregnant women (GPs, obstetricians, midwives) may have a significant influence on their lifestyle, and specifically, on their alcohol consumption. This is consistent with the results of previous studies which corroborated the thinking that adequate health advice from professionals who care for pregnant women first-hand tends to reduce or stop alcohol consumption during pregnancy [41,42].

However, several studies carried out in the United Kingdom [43], Australia [44], and Spain [10] conclude that health advice on alcohol consumption provided to pregnant women is often contradictory and inconsistent. What the result of our study suggests is that providing pregnant women with correct advice on the issue—clearly explaining the appropriateness of not consuming any alcohol during pregnancy—proves to be crucial, as well as consistency of information in this regard among the different health professionals who care for pregnant women or women of childbearing age.

Although the predictive factors described above are those that have greater specific weight in the model developed in our work, other factors that may be relevant are also identified. Thus, the model establishes that pregnant women with better employment status (in the sense of having a full-time job) are more likely to consume alcohol than those with a part-time job or those who are unemployed. It is possible that the explanation for this lies in the likely higher level of income of the former compared to the latter. The greater their purchasing power, the more alcoholic beverages become financially accessible. A number of studies on correlates of alcohol consumption during pregnancy carried out in Ireland and Australia have concluded that high socioeconomic status (or a high income level) is associated with greater alcohol consumption during pregnancy [29,45,46]. At the same time, a study carried out in the USA also concluded that estimated level of income is positively related to drinking alcohol during pregnancy [23]. In a review of predictors of alcohol consumption during pregnancy, it was found that higher income or higher social class was found to be a predictor of drinking during pregnancy in four out of five studies that assessed this factor [25]. It has also been established that certain social situations (business dinners, etiquette ... ) can encourage alcohol consumption, which is a pressure that might also affect pregnant women [47].

Educational level is identified as a predictor of relevant significance in this study, with a weight equivalent to that of the number of pregnancies. The model establishes that the higher the educational level, the lower the consumption of alcohol tends to be during pregnancy. This could be interpreted as meaning that women with a higher level of education are more easily able to seek and incorporate quality information in this field. However, this result is different from that found in a study carried out with pregnant women from 15 European countries, selected through websites, in which it was detected that pregnant women and new mothers of a higher educational level are those who state in a greater proportion that they consume or have consumed alcohol during pregnancy [48]. It is possible that the relationship between the level of education and alcohol consumption during pregnancy varies depending on the country, and also, depending on the way in which the sample of pregnant women is selected, or depending on the procedure used to estimate alcohol consumption.

The model shows that a higher number of previous pregnancies has a positive effect on alcohol consumption during pregnancy. This may have a plausible explanation, since the experience of a higher number of pregnancies in pregnant women who have presumably consumed alcohol without visible negative effects in the perinatal results, can result in consumption in later pregnancies, due to decreasing the perceived risk with respect to the harmful effect of alcohol. This interpretation was described in Testa's 1996 article [49], and later by Raymond [43], whose study suggests that pregnant women are influenced by experiences in their previous pregnancies with respect to alcohol consumption. If this consumption has not had a pernicious effect on her or on the fetus, this may make it easier for the pregnant woman to be more permissive in terms of intake.

The model identifies the perceived risk of drinking wine while pregnant as another predictor of alcohol consumption during pregnancy, in the sense that might be expected: The lower the perceived risk, the greater the consumption (estimated in grams of pure alcohol). Studies carried out in Australia [50], France [16], and Spain [32] found that low perception of the risks posed by consuming wine while pregnant dominates among expectant mothers. In Spain (and perhaps in other social contexts where low perception of the potential teratogenic effects of this alcoholic beverage dominates), it is precisely those expectant mothers who are most aware of the adverse effects on the fetus who present lower alcohol consumption during pregnancy.

Interactions between the predictors, laid out in the Results section, appear generally logical and may have clear implications for prevention. Thus, for example, it was found that the effect of alcohol consumption before pregnancy on consumption during the actual pregnancy is particularly intense when the expectant mother has a low level of education. Therefore, according to these results, those women with the lowest level of education would constitute a high-priority sector for interventions aimed at preventing FASD, probably requiring communication strategies (both within and outside the healthcare system) that are specially adapted to their socio-educational characteristics. It can also be observed that alcohol consumption by the partner and alcohol consumption before pregnancy are interrelated, which suggests that preventive interventions should not be aimed solely at expectant mothers and women before they become pregnant, but also at their partners.

As intervention suggestions resulting from the analysis of these predictive factors, we can highlight the need for health professionals to warn pregnant women of the deleterious effect of alcohol in pregnancy, conveying in clear and understandable terms the message that abstaining from alcohol consumption is the only safe practice. In turn, for health professionals to adequately assess the alcohol consumption habits of pregnant women (or women of a childbearing age in general) and develop with them culturally adapted and effective communication strategies, the implementation of suitable continued training is required, as well as the development of institutional programs in the health system that facilitate and promote the full exercising of their role in the prevention of FASD. In this field, the experience of countries that have made a greater effort in preventing FASD to date, such as Australia, Canada, the United States, and New Zealand, among others [51–53], should be taken into account in particular.

Finally, we should not forget that a pregnant woman is influenced by social perceptions about alcoholic beverages, as well as whatever interpretation she might have made of her own personal experiences of drinking alcoholic beverages, if she has had any. A popular perception of alcohol which has become more widespread over the last few decades is the idea that the regular consumption of moderate quantities of alcoholic beverages (wine in particular) can prove to be a cardiovascular protector. This belief serves to support another: Adults are recommended to drink low doses of alcohol regularly. Today, it is clear that both ideas are lacking in any solid foundation. According to Naimi et al. (2017), to date, there has been no randomized clinical trial of low-volume alcohol consumption that has assessed any mortality outcome. Everything we know about the impact on health of drinking low doses of alcohol is based on observational studies which, in general, suffer from serious selection biases, as detailed by these authors, which constitutes in their opinion a reason to suggest that the existing research may systematically overestimate the protective effects of "moderate" alcohol consumption [54]. At the same time, the Global Burden of Disease Study 2016, carried out using data from 195 countries and territories in the period 1990-2016, concluded that the level of alcohol consumption that minimized harm across health outcomes was zero standard drinks per week [55]. This could be expressed in other terms: No level of alcohol consumption improves health [56]. It proves easier to provide pregnant women and the people around them with correct information about the risks of drinking alcoholic beverages during pregnancy in a social context which is neutral to alcohol consumption than in one where ideas in favor of drinking are widespread. If it is explained to the population as a whole in appropriate terms by the healthcare system that there is no solid scientific basis to support the idea that moderate alcohol consumption is beneficial for health, this will contribute to reducing the enormous burden of health, social and education problems resulting from alcohol consumption, including FASD.

The study performed has both strengths and limitations. Among its strengths, it should be noted that the sample was randomly selected among all pregnant women who attended a programmed control clinic in the same week of pregnancy (week 20). Furthermore, the interviews were conducted in person (face to face) by health staff trained specifically in this area. Data analysis includes the use of a structural equations model and other confirmatory multivariate techniques. On the other hand, one limitation that can be highlighted is that, since the study is cross-sectional, it is not possible to establish inferences of causal relationships between variables. Furthermore, all immigrant pregnant women who could not take part in the interview because they had limited fluency in Spanish were excluded from the sample, due to the absence of auxiliary translation services. The participation rate was 51.2%, which does not exclude the likelihood of selection bias. Alcohol consumption was evaluated only through self-reported data, and not through biomarker analysis too. A validated scale was not used to assess the degree of planning of the pregnancy.

#### **5. Conclusions**

Among the conclusions derived from this study, we can establish that alcohol consumption prior to pregnancy is a predictor that has a powerful direct relationship with alcohol during pregnancy. Second, the percentage of health professionals who adequately inform pregnant women about the harmful effects of alcohol consumption in pregnancy has a powerful inverse relationship with alcohol intake during pregnancy. Furthermore, previous alcohol consumption during pregnancy is especially related to this consumption being maintained during pregnancy among expectant mothers with low educational levels.

**Author Contributions:** I.C.-G., F.L.-L., D.G.-B. and R.M. conceived and designed the study. I.C.-G., F.L.-L. and R.M. coordinated the data collection. D.G.-B. was responsible for the data analysis. All authors interpreted the results, drafted, reviewed and approved the final version of the article. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Research Group on Health Promotion and Development of Lifestyle across a LifeSpan (University of Huelva) with funding received from the Scientific Policy Strategy of the University of Huelva and the Andalusian Plan for Research, Development and Innovation(PAIDI).

**Acknowledgments:** The authors acknowledge E. Morales-Marente, M.S. Palacios and C. Rodriguez-Reinado (University of Huelva) O. García-Algar (Hospital Clinic, Barcelona), and Rocío Medero (Hospital N.S. Valme, Andalusian Health Service) for their contributions to the design and development of this study as research team members.

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


**2. Results**

#### *2.1. E*ff*ects of Juglone on Cell Viability*

To determine the juglone concentration range that is non-toxic to J774.1 cells, cells were treated with increasing concentrations of juglone (3.1–50 μM), followed by 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay. When juglone was used at 10 μM or less, no significant cytotoxic e ffects were observed (*p* > 0.05; Figure 1). Therefore, juglone was used at 2.5, 5, or 10 μM in subsequent experiments.

**Figure 1.** Assessment of the cytotoxic e ffects of juglone in J774.1 cells using the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay. (**a**) Chemical structure of juglone. (**b**) J774.1 cells were treated with increasing concentrations of juglone (3.1–50 μM) for 24 h, followed by quantification of cell viability using the MTT assay. Data are presented as mean ± standard deviation (SD) of three independent experiments. \* *p* < 0.05; \*\* *p* < 0.01; vs. control.

#### *2.2. E*ff*ects of Juglone on Reactive Oxygen Species (ROS) Production*

ROS have a strong oxidative capacity and are essential mediators of NLRP3 (NACHT, LRR and PYD domains-containing protein 3) inflammasome activation. To determine the ability of juglone to inhibit lipopolysaccharide (LPS)-induced ROS production in J774.1 cells, we used the cell-permeable ROS-sensitive dye DCFH-DA, which is non-fluorescent in a reduced state and emits fluorescence upon oxidation by ROS. We found that treatment with LPS enhanced ROS production in J774.1 cells. However, when cells were treated with 10 μM juglone, ROS production was significantly impaired (Figure 2a). The fluorescence intensity in LPS-treated cells was approximately 120%, while the fluorescence intensity in juglone-treated (10 μM) cells after LPS stimulation was only 84.5%. Thus, juglone may exert anti-inflammatory effects by suppressing ROS generation by macrophages during inflammation.

**Figure 2.** Effects of juglone on the production of inflammatory mediators. (**a**) reactive oxygen species (ROS) production in J774.1 cells treated with lipopolysaccharide (LPS). Cells were treated with different concentrations of juglone (2.5, 5, and 10 μM) for 2 h, followed by treatment with 1 μg/mL LPS for an additional 24 h. (**b**) NO production in J774.1 cells treated with LPS. Cells were treated with increasing concentrations of juglone (3.1–50 μM or 0 μM control) for 2 h, followed by treatment with 1 μg/mL LPS for an additional 24 h. The levels of NO in the cell culture media were measured using Griess reagent. (**c**,**d**) Effects of juglone on the LPS/ATP-induced secretion of interleukin-1β (IL-1β) and IL-18 in J774.1 cells. J774.1 macrophages were treated with different concentrations of juglone for 2 h, followed by treatment with 1 μg/mL LPS for 6 h and treatment with 5 mM ATP for 1 h. The levels of IL-1β and IL-18 secreted in the culture medium were analyzed by enzyme-linked immunosorbent assay (ELISA). Data are presented as mean ± SD of three independent experiments. \* *p* < 0.05; \*\* *p* < 0.01 vs. LPS or LPS + ATP cells, respectively.

#### *2.3. E*ff*ects of Juglone on Nitric Oxide (NO) Production*

Inflammatory mediators, such as reactive nitrogen species and ROS, are essential mediators of inflammatory responses, especially in the initial stages of inflammation. Therefore, we assessed the effects of juglone in LPS-induced NO production. We found that even though LPS treatment resulted in a significant increase in NO production in J774.1 cells, juglone treatment suppressed LPS-induced NO production in a dose-dependent manner (*p* < 0.05; Figure 2b).

#### *2.4. E*ff*ects of Juglone on the Secretion of the Pro-Inflammatory Cytokines IL-1*β *and IL-18*

Inflammatory cytokines are important mediators of immune responses and orchestrate the initial stages of inflammation. The pro-inflammatory cytokines IL-1β and IL-18 are known to mediate the first steps of an inflammatory immune response [22]. Therefore, targeting these upstream mediators of inflammation has emerged as a promising approach to treat inflammation-related diseases. Thus, we sought to investigate whether juglone could affect the levels of mRNA, protein, or extracellular secretion of IL-18 and IL-1β. We found that treatment with juglone suppressed the induction of IL-18 and IL-1β at the mRNA and protein level in response to LPS and ATP in J774.1 cells (Figure 3 and Figure S1). The secretory inhibition of pro-inflammatory cytokines (IL-1β and IL-18) of juglone on murine macrophage cells was studied and the results are shown Figure 2c,d. Treatment of macrophage cells with juglone caused a concentration-dependent reduction in their IL-1β (5 μM, \* *p* < 0.05) and IL-18 (10 μM, \*\* *p* < 0.01). Juglone-treated cell was reduced 25.9% of IL-1β secretion (5 μM, \* *p* < 0.05) and 22.6% of IL-18 secretion (10 μM, \*\* *p* < 0.01) compared to the LPS plus STP-primed control group. These results suggested that juglone could inhibit the initial steps of the inflammatory immune response by suppressing the expression and secretion of the pro-inflammatory cytokines IL-1β and IL-18 in macrophages.

**Figure 3.** Effects of juglone on IL-1β and IL-18 expression in LPS-treated J774.1 cells. J774.1 macrophages were treated with different concentrations of juglone (2.5, 5, and 10 μM) for 2 h, followed by treatment with 1 μg/mL LPS for 6 h and 5 mM ATP for 1 h. (**a**) The mRNA levels of IL-1β and IL-18 in J774.1 cells were determined with RT-qPCR. Glyceraldehyde 3-phosphate dehydrogenase gene (GAPDH) was used as a reference gene. (**b**) The protein levels of IL-1β and IL-18 in J774.1 cells were assessed by Western blotting and are presented as relative to β-actin intensity. Data are presented as mean ± SD. \* *p* < 0.05; \*\* *p* < 0.01 vs. LPS + ATP treated cells.

#### *2.5. E*ff*ects of Juglone on NLRP3 and Caspase-1 Expression*

We then assessed the e ffects of juglone treatment on the mRNA and protein levels of NLRP3 and caspase-1. We found that even though NLRP3 was induced in J774.1 cells following stimulation with LPS and ATP, treatment with juglone suppressed the LPS/ATP-mediated NLRP3 induction at the mRNA level in a dose-dependent manner. The mRNA levels of caspase-1 were not significantly a ffected by juglone treatment (Figure 4a). Importantly, juglone treatment suppressed the LPS/ATP-mediated NLRP3 ATPase upregulation at the protein level in J774.1 macrophages (Figure 4b and Figure S2). Juglone also reduced the levels of cleaved caspase-1 in a concentration-dependent manner (Figure 4b). These results suggested that juglone could inhibit the interaction of NLRP3 and apoptosis-associated speck-like protein containing a C-terminal caspase recruitment domain (ASC) and subsequent NLRP3 inflammasome formation by downregulating the expression of NLRP3. Moreover, the decreased NLRP3 expression might impair ASC speck formation, leading to reduced cleavage and subsequent activation of the downstream signaling mediator, caspase-1.

**Figure 4.** J774.1 cells were treated with various concentrations of juglone for 2 h and then treated with 1 μg/mL LPS for 24 h. (**a**) The mRNA levels of NACHT, LRR and PYD domains-containing protein 3 (NLRP3) and caspase-1 in J774.1 cells were determined by RT-qPCR. GAPDH was used as a reference gene. (**b**) The relative protein levels of NLRP3, procaspase-1, and cleaved caspase-1 were assessed by Western blotting and are presented as relative to β-actin intensity. Data are presented as the mean ± SD.\* *p* < 0.05; \*\* *p* < 0.01 vs. LPS + ATP treated cells.

#### *2.6. E*ff*ects of Juglone on the ATPase Activity of NLRP3*

The pyrin ATP-binding domain of NLRP3 exhibits ATPase activity, which is essential for NLRP3 inflammasome oligomerization. Therefore, we investigated the effects of juglone treatment on the ATPase activity of NLRP3 in J774.1 cells. Treatment with LPS and ATP in J774.1 macrophages increased the ATPase activity of NLRP3 (Figure 5). However, treatment with 10 μM of juglone significantly reduced the ATPase activity of NLRP3 (*p* < 0.05).

**Figure 5.** Effects of juglone on the ATPase activity of NLRP3 in LPS/ATP-treated J774.1 cells. J774.1 macrophages were treated with different concentrations of juglone for 2 h, followed by treatment with 1 μg/mL LPS for 6 h and 5 mM ATP for an additional hour. Analysis of the ATPase activity of NLRP3 was performed using a reaction mixture containing 40 mM Tris, 80 mM NaCl, 8 mM MgAc2, 1 mM EDTA, and 4 mM ATP, pH 7.5. Data are presented as mean ± SD of three independent experiments. \* *p* < 0.05 vs. LPS/ATP treated cells.


B. Appendix 2

Name of Child.

A. Appendix 1

176 Learning Disabilities - An International Perspective

Date of Birth Grade at School

Date commenced reading fluency programme.

Problems with reading accuracy and fluency prior to commencement of programme (tick each of the following if these apply)

Number of weeks so far on reading fluency programme.

Child's response so far to reading fluency programme (please comment)